Photochemical and Dynamics Studies of Oxygen Isotope Exchange Reactions of CO₂ Citation Yeung, Laurence Yip-Lun (2010) Photochemical and Dynamics Studies of Oxygen Isotope Exchange Reactions of CO₂. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/TQKB-3T76. https://resolver.caltech.edu/CaltechTHESIS:12222009-120450275 Abstract This dissertation describes laboratory studies of three oxygen isotope exchange reactions — O( 1 D) + CO 2 , O 2 + CO 2 , and O( 3 P) + CO 2 — and their importance to oxygen cycling in the upper atmosphere. First, we studied the isotope exchange reaction O( 1 D) + CO 2 , which is believed to govern the oxygen-isotope budget of CO 2 in the stratosphere. Our combined field, laboratory, and modeling study of the exceptionally rare 16 O 13 C 18 O isotopologue revealed that O( 1 D) + CO 2 explains only part of the stratospheric CO 2 isotopologue budget, not all of it as previously thought: O( 1 D) + CO 2 could not explain the large enrichments of 16 O 13 C 18 O (i.e., of the "Δ 47 " tracer) at high Northern latitudes. Mesospheric and heterogeneous chemistry of CO 2 were proposed as possible sources of this meridional variation in 16 O 13 C 18 O. Therefore, we performed crossed-molecular-beam experiments to investigate the chemistry of CO 2 at hyperthermal collision energies; this class of reaction could be important in the upper atmosphere, where low gas densities and high rates of photochemistry increase the relative probability of hyperthermal reactions. Our experimental and theoretical study of the O 2 + CO 2 isotope exchange reaction showed that the reaction can occur through a short-lived CO 4 reaction complex, which leads to O 2 + CO 2 products that are highly internally excited, but possibly still in their ground electronic state. Our study of O( 3 P) + CO 2 collisions at hyperthermal energies showed that O( 3 P) + CO 2 isotope exchange can occur in the upper atmosphere, proceeding through a short-lived CO 3 reaction complex. The O( 3 P) + CO 2 → O 2 + CO reaction was also observed, and our data suggest that it can proceed through a 'stripping' mechanism or a CO 3 complex. These reactions demonstrate new ways in which oxygen can be cycled through CO 2 in the atmosphere; their isotope effects, manifest in the isotopic composition of atmospheric CO 2 , may impose independent constraints on atmospheric transport and biosphere-atmosphere interactions. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: Stable isotopes, clumped isotopes, stratosphere, mesosphere, polar stratospheric cloud, carbon dioxide, crossed molecular beam, CO3, CO4, quasiclassical trajectory Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Okumura, Mitchio (co-advisor) Eiler, John M. (co-advisor) Thesis Committee: Beauchamp, Jesse L. (chair) Marcus, Rudolph A. Blake, Geoffrey A. Chen, Pin Okumura, Mitchio Eiler, John M. Defense Date: 10 December 2009 Funders: Funding Agency Grant Number Davidow Fund UNSPECIFIED NSF UNSPECIFIED Missile Defense Agency HQ0006-05-2-0001 Air Force Office of Scientific Research (AFOSR) FA955D-07-1-0095 NASA UNSPECIFIED Record Number: CaltechTHESIS:12222009-120450275 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:12222009-120450275 DOI: 10.7907/TQKB-3T76 ORCID: Author ORCID Yeung, Laurence Yip-Lun 0000-0001-9901-2607 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 5474 Collection: CaltechTHESIS Deposited By: Laurence Yeung Deposited On: 05 Feb 2010 17:15 Last Modified: 08 Nov 2019 18:07 Thesis Files Preview PDF (Complete thesis) - Final Version See Usage Policy. 26MB Preview PDF (Complete thesis for two-sided printing) - Final Version See Usage Policy. 26MB Preview PDF (Front matter: Acknowledgements, abstract, table of contents, lists of figures and tables) - Final Version See Usage Policy. 162kB Preview PDF (Chapter 1: Introduction) - Final Version See Usage Policy. 1MB Preview PDF (Chapter 2: Large and unexpected enrichment in stratospheric 16O13C18O) - Final Version See Usage Policy. 4MB Preview PDF (Chapter 3: A hyperthermal O-atom exchange reaction, O2 + CO2) - Final Version See Usage Policy. 11MB Preview PDF (Chapter 4: Dynamics of O(3P) + CO2 collisions at hyperthermal energies) - Final Version See Usage Policy. 10MB Preview PDF (Chapter 5: Summary and outlook) - Final Version See Usage Policy. 124kB Preview PDF (Bibliography) - Final Version See Usage Policy. 154kB Repository Staff Only: item control page

Photochemical and dynamics studies of oxygen isotope exchange reactions of CO2 Thesis by Laurence Yip-Lun Yeung In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2010 (Defended December 10, 2009) L. Y. Yeung Oxygen isotope exchange reactions of CO2 © 2010 Laurence Yip-Lun Yeung All Rights Reserved ii Copyright L. Y. Yeung Oxygen isotope exchange reactions of CO2 Inspiration Small quantities of different gases were added to separate portions of a non-inflammable mixture of dry carbonic oxide and oxygen, and the spark was then passed. In all cases where a gas containing hydrogen was introduced, the mixture exploded; in all cases where a gas containing no hydrogen was introduced, the mixture did not explode. — Harold Dixon, The Combustion of Carbonic Oxide and Hydrogen, 1886. iii L. Y. Yeung Oxygen isotope exchange reactions of CO2 Acknowledgements Acknowledgements This body of work would not have been possible without the intellectual, spiritual, and financial support from professor Mitchio Okumura, professor John Eiler, and Dr. William Davidow. Mitchio and John have taught me how to think critically and quantitatively about scientific problems; their unending creativity, enthusiasm, and wisdom continue to inspire me. Dr. Davidow’s generous endowment funded all of this research and much more not documented here. Only with his support was I able to pursue these risky projects. To my collaborators, professors Hagit Affek, Kristie Boering, Elliot Atlas, Tim Minton, Jon Camden, and George Schatz; Drs. Sue Schauffler, Jeff Paci, Weifu Guo, Kate Hoag, and Jianming Zhang; and Mr. Aaron Wiegel: This work was a collective effort, and I dare not take the credit for any more than my own modest contribution to it. Thank you for your time, patience, lab equipment, and fishing lessons. To the Okumura group, the Eiler group, and other mentors, professors Jack Beauchamp, Rudy Marcus, Geoff Blake, Yuk Yung, Zhengrong Wang, Julie Fry, Rose Came, Kate Huntington, Ben Passey, Naomi Levin, and Aradhna Tripathi; Drs. Pin Chen, Joe Hodges, Chip Miller, Linda Brown, Andrew Mollner, David Robichaud, Aaron Noell, Nathan Eddingsaas, and Mathieu Daëron; Mr. Bill Bing; fellow students Kana Takematsu, Matt Sprague, Kathleen Spencer, Dave Long, Sigrid Barklund, Aileen Hui, Thinh Bui, Nathan Honsowetz, and Heather Widgren: Most of my education here has been at your hands. Thank you for your time, wisdom, skepticism, and coffee. Finally, to my friends and family: You are the music of my life. You are the rhythm, the harmony, and melody. If music be the food of love, play on. Nothing I could say would ever be enough to express my gratitude. I am excited for whatever misadventures lie ahead. iv L. Y. Yeung Oxygen isotope exchange reactions of CO2 Abstract Abstract This dissertation describes laboratory studies of three oxygen isotope exchange reactions — O(1 D) + CO2 , O2 + CO2 , and O(3 P) + CO2 — and their importance to oxygen cycling in the upper atmosphere. First, we studied the isotope exchange reaction O(1 D) + CO2 , which is believed to govern the oxygen-isotope budget of CO2 in the stratosphere. Our combined field, laboratory, and modeling study of the exceptionally rare 16 O13 C18 O isotopologue revealed that O(1 D) + CO2 explains only part of the stratospheric CO2 isotopologue budget, not all of it as previously thought: O(1 D) + CO2 could not explain the large enrichments of 16 O13 C18 O (i.e., of the “∆47 ” tracer) at high Northern latitudes. Mesospheric and heterogeneous chemistry of CO2 were proposed as possible sources of this meridional variation in 16 O13 C18 O. Therefore, we performed crossed-molecular-beam experiments to investigate the chemistry of CO2 at hyperthermal collision energies; this class of reaction could be important in the upper atmosphere, where low gas densities and high rates of photochemistry increase the relative probability of hyperthermal reactions. Our experimental and theoretical study of the O2 + CO2 isotope exchange reaction showed that the reaction can occur through a short-lived CO4 reaction complex, which leads to O2 + CO2 products that are highly internally excited, but possibly still in their ground electronic state. Our study of O(3 P) + CO2 collisions at hyperthermal energies showed that O(3 P) + CO2 isotope exchange can occur in the upper atmosphere, proceeding through a short-lived CO3 reaction complex. The O(3 P) + CO2 → O2 + CO reaction was also observed, and our data suggest that it can proceed through a ‘stripping’ mechanism or a CO3 complex. These reactions demonstrate new ways in which oxygen can be cycled through CO2 in the atmosphere; their isotope effects, manifest in the isotopic composition of atmospheric CO2 , may impose independent constraints on atmospheric transport and biosphere-atmosphere interactions. v L. Y. Yeung Oxygen isotope exchange reactions of CO2 Table of contents Contents Acknowledgements iv Abstract v 1 Introduction 1.1 CO2 in the global carbon cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Stable isotopes, ‘clumped’ and otherwise . . . . . . . . . . . . . . . . . . . . 1.3 Anomalous isotopic enrichments in stratospheric CO2 . . . . . . . . . . . . . 1.4 Insights from the physical chemist’s toolbox . . . . . . . . . . . . . . . . . . 1.5 Executive summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 2 5 8 Appendices 1.A Isotopic notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.B Copyright declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 10 12 2 Large and unexpected enrichment in stratospheric 16 O13 C18 O 2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Field sample collection and analysis . . . . . . . . . . . . . . . . . . . . . . . 2.4 Field results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Laboratory photochemical experiments . . . . . . . . . . . . . . . . . . . . . 2.5.1 13 C/12 C kinetic isotope effect experiments . . . . . . . . . . . . . . . 2.5.2 Continuous-irradiation experiments . . . . . . . . . . . . . . . . . . . 2.5.3 Conclusions from laboratory measurements . . . . . . . . . . . . . . 2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 O(1 D)+CO2 only explains mid-latitude 16 O13 C18 O variations . . . . . 2.6.2 Effects of intra-stratospheric chemistry and mixing . . . . . . . . . . 2.6.3 Effects of mesospheric and heterogeneous chemistry . . . . . . . . . 2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 14 15 16 17 18 21 32 34 36 36 37 39 47 47 Appendices 2.A Mixing effects on isotopic composition . . . . . . . . . . . . . . . . . . . . . 2.B Practical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.B.1 IRMS long-term signal stability . . . . . . . . . . . . . . . . . . . . . 2.B.2 IRMS vs. optical methods . . . . . . . . . . . . . . . . . . . . . . . . 2.C Low-temperature cell for 13 C/12 C KIE experiments . . . . . . . . . . . . . . . 2.D MATLAB code for hard-sphere collision model . . . . . . . . . . . . . . . . . 49 50 52 52 53 58 67 vi L. Y. Yeung Oxygen isotope exchange reactions of CO2 Table of contents 2.D.1 montecarlo.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.D.2 scatter.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 69 3 A hyperthermal O-atom exchange reaction, O2 + CO2 3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Theoretical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Proposed mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 72 73 73 73 80 87 89 92 93 Appendices 3.A Non-reactive scattering of O2 and CO2 . . . . . . . . . . . . . . . . . . . . . 3.B MATLAB program for generating Newton diagrams . . . . . . . . . . . . . . 3.B.1 NewtonD.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.B.2 NewtonDcalc.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.B.3 NewtonDplot.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 96 101 101 103 104 4 Dynamics of O(3 P) + CO2 collisions at hyperthermal energies 4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Theoretical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Electronic structure calculations . . . . . . . . . . . . . . . . . . . . . 4.3.2 Reaction dynamics calculations . . . . . . . . . . . . . . . . . . . . . 4.4 Experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Theoretical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Non-reactive scattering of O(3 P) and CO2 . . . . . . . . . . . . . . . 4.5.3 Oxygen isotope exchange, O(3 P) + CO2 → O + CO2 . . . . . . . . . 4.5.4 Oxygen-atom abstraction, O(3 P) + CO2 → O2 + CO . . . . . . . . . 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 110 111 113 113 118 123 123 125 139 139 141 142 144 147 148 Appendices 149 4.A Differential scattering cross-sections from 1.0 – 6.5 eV . . . . . . . . . . . . 150 4.B Estimating uncertainty in the laboratory angular distributions . . . . . . . . 152 5 Summary and outlook 153 5.1 New signatures, new reactions . . . . . . . . . . . . . . . . . . . . . . . . . 153 5.2 Potential atmospheric importance of O(3 P) + CO2 . . . . . . . . . . . . . . . 154 Bibliography 157 vii L. Y. Yeung Oxygen isotope exchange reactions of CO2 Figures List of Figures 1.1 1.2 1.3 Schematic of atmospheric CO2 sources and sinks. . . . . . . . . . . . . . . . . Bulk oxygen isotope composition of stratospheric CO2 . . . . . . . . . . . . . . Potential energy surface for CO3 (3 A00 ) from Mebel et al. [2004]. . . . . . . . . 2.1 2.2 2.3 2.4 2.5 2.6 Meridional variation of ∆47 measured in stratospheric samples. . . . . . . . . 18 Correlation between ∆47 and stratospheric tracers. . . . . . . . . . . . . . . . 19 ∆17 O values vs. long-lived stratospheric tracer mixing ratios. . . . . . . . . . . 19 Schematic of O(1 D) + CO2 reaction-purification-analysis procedure. . . . . . 21 FT-IR spectrum of synthesized N2 18 O between 1100 cm−1 and 4000 cm−1 . . 24 Modeled O(1 D) + CO2 reaction collision energy distributions at different He bath gas pressure (T = 300 K). . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Changes in ∆47 vs. ∆δ 18 O after pulsed UV photolysis at 300 K and 229 K. . . . 30 Changes in ∆47 vs. ∆17 O of CO2 after continuous UV irradiation of O2 /O3 /CO2 mixtures with a Hg lamp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 How mixing two arbitrary reservoirs of CO2 can be nonlinear in ∆47 . . . . . . 51 Allan-variance plot of ∆47 over 40 IRMS acquisitions. . . . . . . . . . . . . . . 53 Schematic of conflat chamber used for low-temperature 13 C/12 C KIE experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Photograph of conflat chamber used for low-temperature 13 C/12 C KIE experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Cold cell assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Machining diagram for the OFHC copper tube. . . . . . . . . . . . . . . . . . 61 Machining diagram for the OFHC copper conduction block. . . . . . . . . . . 62 Machining diagram for the OFHC copper heat transfer block. . . . . . . . . . 63 Machining diagram for the brass heat transfer block. . . . . . . . . . . . . . . 63 Machining diagram for the OFHC copper connection to the liquid N2 feedthrough. 64 Cold cell assembly for O(1 D), OH + CH4 KIE experiments. . . . . . . . . . . . 65 Machining diagram illustrating the modifications made to the conduction block for O(1 D), OH + CH4 KIE experiments. . . . . . . . . . . . . . . . . . . . . . 65 Machining diagram for the OFHC copper heat transfer block designed for O(1 D), OH + CH4 KIE experiments. . . . . . . . . . . . . . . . . . . . . . . . 66 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 3.1 3.2 3.3 3.4 Crossed-molecular-beam apparatus with hyperthermal oxygen source. . . . . Canonical Newton diagram for hyperthermal 16 O2 + 12 C18 O2 collisions. . . . Velocity distribution of hyperthermal oxygen beam. . . . . . . . . . . . . . . . Laboratory TOF distribution of m/z = 46 (16 O12 C18 O+ ) at Θ = 6◦ , with the inelastic scattering signal removed. . . . . . . . . . . . . . . . . . . . . . . . . viii 3 5 6 74 75 77 80 L. Y. Yeung 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 Oxygen isotope exchange reactions of CO2 Figures TOF distributions for 16 O12 C18 O products at laboratory angles Θ = 6◦ and 8◦ with the inelastic scattering signal removed. . . . . . . . . . . . . . . . . . . . 82 TOF distributions for 16 O12 C18 O (m/z = 46) at various laboratory angles Θ with the inelastic scattering signal removed. . . . . . . . . . . . . . . . . . . . 83 Center-of-mass-frame (A) angular and (B) translational energy distributions from the 16 O2 + 12 C18 O2 oxygen isotope exchange reaction obtained from TOF fits of m/z = 46. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Velocity-flux contour diagram for 16 O12 C18 O products of 16 O2 + 12 C18 O2 collisions in the center-of-mass frame. . . . . . . . . . . . . . . . . . . . . . . . . 84 Energetically allowed neutral product channels from O2 + CO2 collisions. . . 86 Calculated energies and structures on the lowest triplet PES of O2 + CO2 . . . 87 Calculated stationary point geometries on the lowest triplet PES of CO4 . . . . 89 Calculated energies and structures on the lowest triplet PES of O2 + CO2 . . . 89 Singly-occupied molecular orbitals (SOMOs) in the CO4 (3 A00 ) and TS3 structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Molecular orbital diagrams for O2 and CO2 , adapted from DeKock and Gray [1980]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Electron-pushing diagram of an adiabatic CO4 (3 A00 ) isomerization through TS3. 92 Laboratory scattering data detected at m/z = 32. . . . . . . . . . . . . . . . . 98 Laboratory inelastic scattering data detected at m/z = 48. . . . . . . . . . . . 99 Velocity-flux contour diagram for inelastically scattered 12 C18 O2 from 16 O2 + 12 C18 O collisions in the center-of-mass frame. . . . . . . . . . . . . . . . . . . 100 2 Sample output of the NewtonD.m program. . . . . . . . . . . . . . . . . . . . 101 Stationary-point structures for O(3 P) + CO2 reactions below 100 kcal mol−1 calculated at the CCSD(T)/aug-cc-pVTZ level of theory on the 3 A00 surface. . . 114 Comparison of CO3 stationary point geometries relevant to the QCT calculations.116 Comparison of TS1 and TS3 geometries and energies at various levels of theory.116 Reactive scattering cross-sections for the O(3 P) + CO2 isotope exchange reaction obtained from the QCT calculations. . . . . . . . . . . . . . . . . . . . . 121 Opacity functions for the O(3 P) + CO2 isotope exchange reaction and for inelastic scattering of the two reagents obtained from QCT calculations at the B3LYP/6-311G(d) and BMK/6-311G(d) levels of theory. . . . . . . . . . . . . 122 Canonical Newton diagram for 16 O + 12 C18 O2 collisions at Ecoll = 98.8 kcal mol−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Laboratory inelastic scattering data detected at m/z = 16. . . . . . . . . . . . 126 Laboratory inelastic scattering data detected at m/z = 48. . . . . . . . . . . . 128 Velocity-flux contour diagram for inelastically scattered 12 C18 O2 from 16 O(3 P) + 12 C18 O2 collisions in the center-of-mass frame. . . . . . . . . . . . . . . . . 129 Comparison of laboratory and theoretical c.m. (A) angular and (B) translational energy distributions for inelastic scattering of O(3 P) and CO2 at hEcoll i ≈ 100 kcal mol−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Laboratory reactive scattering data detected at m/z = 46. . . . . . . . . . . . 132 Velocity-flux contour diagram for 16 O12 C18 O products of 16 O(3 P) + 12 C18 O2 collisions in the center-of-mass frame. . . . . . . . . . . . . . . . . . . . . . . 133 Comparison of laboratory and theoretical c.m. (A) angular and (B) translational energy distributions for the O(3 P) and CO2 isotope exchange reaction at hEcoll i ≈ 100 kcal mol−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 ix L. Y. Yeung 4.14 4.15 4.16 4.17 4.18 Oxygen isotope exchange reactions of CO2 Figures Laboratory reactive scattering data detected at m/z = 34. . . . . . . . . . . . 136 Snapshots of a quasiclassical trajectory for O(3 P) + CO2 isotope exchange through a short-lived CO3 ∗ complex at 1.5 eV (34.6 kcal mol−1 ) collision energy.142 Laboratory reactive scattering data detected at m/z = 46, fit assuming an ISC mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Snapshots of quasiclassical trajectories for the O(3 P) + CO2 → O2 + CO reaction.146 Center-of-mass angular and translational energy distributions for the O(3 P) + CO2 isotope exchange reaction derived from QCT calculations at the (A and B) B3LYP/6-311G(d) and (C and D) BMK/6-311G(d) levels of theory. . . . . . 151 x L. Y. Yeung Oxygen isotope exchange reactions of CO2 Tables List of Tables 2.1 2.2 2.3 2.4 2.5 2.6 Stratospheric air sample data . . . . . . . . . . . . . . . . . . . . . . . . . . . IR band assignments for the spectra in Figure 2.5 . . . . . . . . . . . . . . . . IRMS ion signals from the synthesized N2 18 O . . . . . . . . . . . . . . . . . . Results of pulsed photochemical experiments . . . . . . . . . . . . . . . . . . Results of continuous irradiation experiments . . . . . . . . . . . . . . . . . . Tropospheric-stratospheric-mesospheric mixing model results . . . . . . . . . 17 23 25 30 33 41 3.1 Energies of stationary points associated with the exchange reaction O2 + CO2 → O2 + CO2 on the lowest triplet potential energy surface . . . . . . . . . . . 88 4.1 4.2 4.3 Energies (kcal mol−1 ) for the stationary points on the lowest triplet CO3 potential energy surface for 16 O(3 P) + 12 C16 O2 → 16 O + 12 C16 O2 collisions . . . 115 Number of reactive QCTs observed at different collision energies. . . . . . . . 121 Comparison of experimental and theoretical yields for the products of O(3 P) + CO2 collisions near 100 kcal mol−1 . . . . . . . . . . . . . . . . . . . . . . 137 xi L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 Chapter 1 Introduction 1.1 CO2 in the global carbon cycle Carbon dioxide (CO2 ) is the most important anthropogenic greenhouse gas in the earth’s atmosphere. Over the past half-century, atmospheric CO2 concentrations have increased at a rate that correlates with the increase in anthropogenic fossil fuel burning and deforestation [Solomon et al., 2007]. Carbon budget inventories indicate, however, that not all of the CO2 released into the atmosphere from these activities persists in the atmosphere; approximately half of the anthropogenic CO2 flux is sequestered in the oceanic and land biospheres [Ciais et al., 1995]. Modeling the fate of anthropogenic CO2 becomes a considerable technical challenge because of myriad interactions between the atmosphere, the oceans, and the terrestrial biosphere. Our ability to predict future changes in the carbon cycle and their effects on global climate relies on our quantitative understanding of these interactions. The first step towards understanding these interactions is learning how to differentiate between atmospheric CO2 molecules derived from various sources and sinks, so we can eventually de-convolve atmospheric observations into their individual components and describe the workings of the global budget through those observations. This task is more complex than it might at first seem because the atmosphere mixes efficiently over the atmospheric lifetime of CO2 ; thus each parcel of air contains CO2 molecules with many different origins and fates (see Figure 1.1). We find some of the needed constraints for these interactions in the variations of naturally occurring stable isotopes. 1 L. Y. Yeung 1.2 Oxygen isotope exchange reactions of CO2 Chapter 1 Stable isotopes, ‘clumped’ and otherwise The stable isotope composition of CO2 (i.e., the relative abundances of those isotopes that do not decay radioactively: 12 C, 13 C, 16 O, 17 O and 18 O) varies according to its sources and subsequent atmospheric chemistry and transport. Physical, chemical kinetic, and equilibrium isotope effects act together to determine the stable isotope composition of CO2 in a given parcel of air. Differences in mass and symmetry of the twelve distinct CO2 isotopologues (isotopic variants, e.g., 12 C16 O2 , 13 C16 O2 , 16 O12 C18 O, 16 O13 C17 O, etc.) formed from the five stable isotopes lead to subtle, but measurable differences in the rate of chemical transformations such as photosynthesis, respiration, air-sea exchange, or photochemical reactions. In principle, measuring the stable isotope distribution in CO2 could lead to an exceptionally detailed analysis of the ‘history’ of CO2 in every sample of the atmosphere, as each natural process imparts its own unique isotopic signature; however, only four of these twelve isotopologues (12 C16 O2 , 13 C16 O2 , 16 O12 C17 O, and 16 O12 C18 O) have been used extensively as tracers in atmospheric chemistry. By themselves, they are insufficient to constrain the relative influences of all the sources and sinks that have acted on a single sample. The remaining eight species (all of which contain two or three heavy rare isotopes) are exceptionally rare and, until recently, were considered to be essentially un-analyzable in natural materials. Measuring these very rare ‘clumped’ isotopologues would add new and essential independent constraints on the origins of CO2 in samples of air. In the laboratory, an equally daunting challenge exists: What are the most important reactions governing the isotopic composition of atmospheric CO2 , and what are the fundamental isotope effects? We wish to know, in the end, if our knowledge of the pertinent atmospheric chemistry is sufficient to explain atmospheric observations. 1.3 Anomalous isotopic enrichments in stratospheric CO2 Shortly after the discovery of ‘mass-independent’ enrichments of 18 O and 17 O in stratospheric ozone [Mauersberger, 1981, 1987] and the demonstration of its chemical origin 2 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 hν O2 λ = 121.6 nm O(1D) hν hν CO CO2 hν in vortex Stratopause O3 + hν → O2 + O(1D) CH4 O(1D), OH Cl CO O(1D) hν OH CO2 CO2 O(3P) particles? H2O Tropopause OH VOCs CO etc. OH CO2 clouds leaves CA soils oceans emissions CA Carbonic anhydrase (CA)-assisted Figure 1.1: Schematic of atmospheric CO2 sources and sinks. Photochemical reactions (single-headed arrows), isotope exchange reactions (double-headed arrows), and atmospheric transport (dotted arrows) are shown. Isotopic exchange on stratospheric liquid water and/or acid particles is uncertain, so its double-headed arrow is dashed. 3 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 [Thiemens and Heidenreich, 1983], similar enrichments were observed in stratospheric CO2 (e.g., Figure 1.2) [Alexander et al., 2001; Boering et al., 2004; Gamo et al., 1989; Kawagucci et al., 2008; Lämmerzahl et al., 2002; Thiemens et al., 1991, 1995]. Yung et al. [1991] suggested that photochemical transfer of the heavy-isotope signature (∆17 O) from O3 to CO2 stratospheric CO2 was possible after photolysis of O3 : O3 + hν(λ < 305 nm) → O2 + O(1 D) (1.1) → O2 + O(3 P) (1.2) and then subsequent isotope exchange through reaction 1.3: O(1 D) + CO2 → OCO∗2 → O(3 P) + OCO (1.3) The authors cited the isotope exchange mechanism in Baulch and Breckenridge’s early study of the reaction in which the incident oxygen atom was incorporated into the product CO2 molecule 2/3 of the time [Baulch and Breckenridge, 1966]. While this ‘statistical’ mechanism could explain the stratospheric 18 O and 17 O measurements qualitatively, a quantitative discrepancy remained between the observed and modeled 17 O/16 O vs. 18 O/16 O relationships: 17 O in CO 2 was more enriched than reaction 1.3 and Yung’s model would have predicted. Unfortunately, the isotope effects in O3 formation and photolysis and in the O(1 D) + CO2 isotope exchange reaction (reaction 1.3) were not yet well understood. Tests of the ‘statistical’ isotope exchange hypothesis were first conducted by Wen and Thiemens [1993], who photolyzed a mixture of O3 and CO2 with a mercury lamp at 254 nm. They observed heavy-atom enrichments in CO2 that implied a non-statistical isotope exchange mechanism between O3 and CO2 (i.e., 17 O appeared to be preferentially incorporated into CO2 ), but their result was misleading; the isotopic composition of the incident O(1 D) changed significantly over the course of their experiment due to O(3 P) and O2 recombination. They did not account for these effects and thus were led to a spurious conclusion, as a later study showed [Johnston et al., 2000]. To date, only one of these bulk photochemical experiments has been able to reproduce the relative 17 O-to-18 O enrichments observed in 4 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 Figure 1.2: Bulk oxygen isotope composition of stratospheric CO2 . Departure from ‘mass-dependent’ compositions (∆17 O; see Appendix 1.A) are observed, owing to oxygen isotope exchange with stratospheric O3 through reaction 1.3. the stratosphere [Chakraborty and Bhattacharya, 2003], and those results have been controversial [Shaheen et al., 2007]. Mechanistic insights have been limited because bulk stable isotope analysis is not able to differentiate isotope effects in O3 photolysis and formation from isotope effects in reaction 1.3 unambiguously. Recent theoretical and modeling work on ozone has shed light on the effects of the former [Babikov et al., 2003; Cole and Boering, 2006; Gao and Marcus, 2001, 2002; Gao et al., 2002; Hathorn and Marcus, 1999, 2000; Schinke et al., 2006], but the understanding of the stratospheric CO2 isotopic distribution remains incomplete. The persistence of this field-laboratory disagreement was the primary inspiration for the ‘clumped’ isotope studies of reaction 1.3 described in this dissertation. 1.4 Insights from the physical chemist’s toolbox The techniques of physical chemistry have been invaluable for unraveling features in the complex mechanism of reaction 1.3. CO3 ∗ was believed to play a critical role in the isotope exchange reaction ever since the first experiments of Katakis and Taube [1962]. 5 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 Figure 1.3: Potential energy surface for CO3 (3 A00 ) from Mebel et al. [2004]. Geometries were optimized at the CASSCF(16,13)/6-311G(d) level of theory. Energies were calculated at the MRCI+Q(16,13)/6-311+G(3df) level of theory. Moll et al. [1966] first identified a CO3 molecule spectroscopically upon irradiating CO2 ice with vacuum-UV light. Although their data implied that stable CO3 had C2v symmetry, their experiments with 18 O-labeled CO2 ices indicated that a CO3 (D3h ) species might be important in a reaction between atomic oxygen and CO2 , as was implied by the statistical mechanism of Baulch and Breckenridge [1966]. The O(1 D) + CO2 potential energy surface (PES) calculated by Mebel et al. [2004] is shown in Figure 1.3. On the 1 A1 surface (1 A0 dynamically), the association reaction has an early barrier at 1 kcal mol−1 , which is consistent with its collision-limited reaction rate coefficient (1 × 10−10 cm3 molecule−1 s−1 ) [Sander et al., 2006]. The binding energy of CO3 (1 A1 ) is nearly 50 kcal mol−1 , and two structures (C2v and D3h ) were predicted as bound 6 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 species at the bottom of the potential well. CO3 (C2v ) was detected shortly thereafter in a low-temperature CO2 matrix [Bennett et al., 2004]; the presence of a true CO3 (D3h ) minimum on the PES had been debated (see Kaiser and Mebel [2008]; Kowalczyk and Krylov [2007]; Liu et al. [2009] and references therein), but it was recently detected experimentally in a 10 K CO2 ice bombarded with high-energy electrons [Jamieson et al., 2006]. Intersystem crossing (ISC) from the singlet to the triplet PESs is believed to occur through nonradiative transitions rather than through the minimum of the intersection seam (near the 3 A0 transition state); the product O(3 Pj ) spin-orbit state distribution is consistent with an adiabatic CO3 dissociation [Matsumi et al., 1994a]. The ISC rate was also calculated to be ten times faster through a radiationless transition than through the singlet-triplet crossing seam [Mebel et al., 2004]. Yang et al. [2005] later proposed that a direct quenching mechanism (i.e., not through a CO3 complex) might also be important. Gas-phase studies of reaction 1.3 show evidence for CO3 , though none have detected it directly. Perri et al. [2003, 2004] reported evidence for a long-lived CO3 ∗ reaction complex in their crossed-molecular-beam experiments. This long-lived (1 – 10 ps lifetime) intermediate had been suggested in previous temperature- and pressure-dependent studies [Clerc and Reiffsteck, 1968; DeMore and Dede, 1970; Weissberger et al., 1967], but never directly confirmed; its lifetime was later confirmed to be long enough for nearly statistical intramolecular vibrational redistribution [Chen et al., 2009]. The structure and dynamics of CO3 are not yet completely understood, however. For instance, O(1 D) + CO2 collision energy appears to be important dynamically; Perri et al. [2003, 2004] reported that O(1 D) + CO2 collisions yielded spin-conserving, isotopically exchanged products (1.4): O(1 D) + CO2 → OCO∗2 → O(1 D) + OCO (1.4) Their crossed-molecular-beam experiments were performed at elevated collision energies (4.2 and 7.7 kcal mol−1 ) so the importance of reaction 1.4 to the stratosphere is unknown. Mebel et al.’s companion computation study suggested that reaction 1.4 has a ∼5% branching fraction at stratospheric collision energies, but this prediction has not been tested. Still, Perri et al.’s experimental result casts significant doubt on the applicability of the previous 7 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 bulk photochemical experiments. All the recent studies of the O2 /O3 /CO2 photochemical system used O2 /O3 as a source of O(1 D) with a significant mixing fraction of CO2 , so the O(1 D) atoms reacting with CO2 probably had an elevated average kinetic energy as high as ∼9 kcal mol−1 [Thelen et al., 1995], six times the calculated average in the stratosphere [Kharchenko and Dalgarno, 2004; Takahashi et al., 2002]. 1.5 Executive summary This dissertation describes studies of three oxygen isotope exchange reactions involving CO2 — one well-studied and two we discovered — and their potential implications for oxygen cycling in the upper atmosphere. First, I will describe the meridional (latitudinal) variations of stratospheric 16 O13 C18 O relative to those of 12 C16 O2 , 13 C16 O2 , 16 O12 C18 O, and 16 O12 C17 O; we identified a meridional gradient, with 16 O13 C18 O most enriched at the Arctic polar vortex. Our experimental and modeling study revealed that the variations in 16 O13 C18 O proportions cannot be explained in full by the known stratospheric chemistry af- fecting CO2 . Instead, we propose — because of the localization of a 16 O13 C18 O anomaly in the wintertime pole — that the chemistry either in the mesosphere or on stratospheric particles leads to the newly discovered isotopic enrichments. Second, I will describe crossedmolecular-beam experiments that led to the discovery of the isotope exchange reaction O2 + CO2 . We show that the isotope exchange reaction occurs through a short-lived CO4 intermediate, and that an adiabatic reaction mechanism exists despite a variety of energetically accessible product channels. Third, I will discuss a computational and laboratory dynamics study of hyperthermal collisions between ground-state oxygen-atoms and CO2 . We identified two reactions: oxygen-atom isotope exchange and abstraction. The isotope exchange reaction proceeds through a short-lived CO3 ∗ reaction complex, and it may have implications for the oxygen-isotope budget in the upper atmosphere and/or the stratospheric polar vortex. The oxygen-atom abstraction reaction may proceed through either a ‘stripping’-type mechanism or a CO3 complex, although the data cannot distinguish between the two mechanisms definitively. In the final chapter, I will attempt to synthesize what we have learned from these three studies, and what questions have emerged as a result. 8 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Appendices 9 Chapter 1 L. Y. Yeung 1.A Oxygen isotope exchange reactions of CO2 Chapter 1 Isotopic notation The natural abundance of the rare isotopes that are the focus of this thesis are 1.1% (13 C), 0.02% (18 O), and 0.038% (17 O). Variations in these stable isotope abundances are typically ≤10−3 . Consequently, bulk stable isotope abundances are commonly reported in δ -notation, in units of per mil (‰): δ 13 C = δ 18 O = R13 sample ! − 1 R13 VPDB R18 sample × 1000 (1.5) × 1000 (1.6) ! R18 VSMOW − 1 where Rn is the abundance ratio of a rare isotope or isotopologue of mass n to its most abundant analogue, i.e., R13 = [13 C] [12 C] R18 = [18 O] [16 O] R17 = [17 O] [16 O] (1.7) δ 17 O is defined similarly to δ 18 O in Eq. 1.6. δ 13 C, δ 18 O, and δ 17 O are reported relative to the international standards VPDB (Vienna Pee Dee Belemnite; R13 = 0.0112372) and VSMOW (Vienna Standard Mean Ocean Water; R18 = 0.0020052 and R17 = 0.0003799). These standards were established under the International Atomic Energy Agency, but are otherwise arbitrary. They represent convenient reference points against which all isotopic measurements can be compared. Positive δ -values mean that the sample bulk isotope composition is enriched relative to the standard, and negative δ -values mean that the sample bulk isotope composition is depleted relative to the standard. Within bulk stable isotope geochemistry, a second family of notation has emerged since the discovery of ‘mass-independent’ oxygen isotope fractionation (MIF) in carbonaceous chondrites [Clayton et al., 1973] and during the formation of ozone (O3 ) [Thiemens and Heidenreich, 1983]. The magnitude of MIF in oxygen (∆17 O) is defined in Eq. 1.8: ∆17 O = δ 17 O − 0.516 × δ 18 O 10 (1.8) L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 This terminology is used to describe deviations from the canonical mass-dependent isotopic relationships derived by Urey [1947] and Bigeleisen [Bigeleisen and Mayer, 1947; Bigeleisen and Wolfsberg, 1958]. Most equilibrium and kinetic isotope effects are half as pronounced for 17 O/16 O ratios vs. 18 O/16 O ratios, so the slope of a δ 17 O vs. δ 18 O plot (similar to 17 O/16 O vs. 18 O/16 O) is nominally 0.5. Departures from mass-dependent fractionation in oxygen are calculated using Eq. 1.8: ∆17 O > 0 represents a ‘mass-independent’ enrichment in 17 O, whereas ∆17 O < 0 represents a “mass-independent” depletion in 17 O. Several excellent reviews of this topic have been published, e.g., Weston [1999] and Thiemens [2006]. The language of ‘clumped’ isotope geochemistry is potentially even more confusing because the reference isotopic ratio (e.g., the denominator in Eq. 1.6) is no longer a constant: R 47 [47 CO2 ] = 44 [ CO2 ] ∆47 = R47 sample R47 stochastic ! ) − 1 × 1000 (1.9) 13 18 + 2R17 R18 + R13 (R17 )2 , the distribution of stable carbon and In Eq. 1.9, R47 stochastic = 2R R oxygen isotopes if they were randomly distributed among all isotopologues of CO2 [Eiler, 2007]. It is important to recognize that the terms used in ‘clumped’ isotope geochemistry (Eq. 1.9) differ fundamentally from those in bulk-isotope measurements; the “reference” to which the measured R47 sample is compared is a varying internal standard (the bulk isotopic composition), rather than the fixed external standard used in Eqs. 1.5 and 1.6. This distinction also leads to quirky, yet ultimately useful changes in ∆47 when subject to various physical processes such as mixing and diffusion [Eiler and Schauble, 2004]. A common question has been: “What is the difference between an isotopomer and an isotopologue?” Two isotopomers, like chemical isomers, share the same isotopic composition, but the stable isotopes themselves are in positions that render the two molecules chemically distinct. A good example can be found in the comparison of isotopically substituted N2 O and CO2 molecules: 14 N–15 N–16 O and 15 N–14 N–16 O are isotopomers of one another because the N-atom substitutions are not symmetrically equivalent. The two isotopomers, consequently, have differing chemical properties, e.g., vibrational frequencies and rotational constants. In contrast, 16 O–12 C–18 O and 18 O–12 C–16 O are equivalent upon rotation, so they are equivalent structures of a single isotopologue. 11 L. Y. Yeung 1.B Oxygen isotope exchange reactions of CO2 Chapter 1 Copyright declaration This thesis contains excerpts from three publications in which the author was involved: • Huntington, K. W., J. M. Eiler, H. P. Affek, W. Guo, M. Bonafacie, L. Y. Yeung, N. Thiagarajan, B. Passey, A. Tripati, M. Daëron, R. Came (2009), Methods and limitations of ‘clumped’ CO2 isotope (∆47 ) analysis by gas source isotope ratio mass spectrometry, J. Mass Spectrom., 44(9), 1318–1329. ©2009 John Wiley & Sons. • Yeung, L. Y., H. P. Affek, K. J. Hoag, W. Guo, A. A. Wiegel, E. L. Atlas, S. M. Schauffler, M. Okumura, K. A. Boering, and J. M. Eiler (2009), Large and unexpected enrichment in stratospheric 16 O13 C18 O and its meridional variation, Proc. Natl. Acad. Sci. U. S. A., 106(28), 11,496–11,501. ©2009 National Academy of Sciences. • Yeung, L. Y., M. Okumura, J. T. Paci, G. C. Schatz, J. Zhang, and T. K. Minton (2009), Hyperthermal O-Atom Exchange Reaction O2 + CO2 through a CO4 Intermediate, J. Am. Chem. Soc., 131(39): 13,940–13,942. ©2009 American Chemical Society Publications. 12 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Chapter 2 Large and unexpected enrichment in stratospheric 16O13C18O Adapted from Yeung, L. Y., H. P. Affek, K. J. Hoag, W. Guo, A. A. Wiegel, E. L. Atlas, S. M. Schauffler, M. Okumura, K. A. Boering, and J. M. Eiler (2009), Large and unexpected enrichment in stratospheric 16 O13 C18 O and its meridional variation, Proc. Natl. Acad. Sci. U. S. A., 106(28), 11,496–11,501. ©2009 National Academy of Sciences. 13 L. Y. Yeung 2.1 Oxygen isotope exchange reactions of CO2 Chapter 2 Abstract The stratospheric CO2 oxygen isotope budget is thought to be governed primarily by the O(1 D) + CO2 isotope exchange reaction. However, there is increasing evidence that other important physical processes may be occurring that standard isotopic tools have been unable to identify. Measuring the distribution of the exceedingly rare CO2 isotopologue 16 O13 C18 O, in concert with 18 O and 17 O abundances, provides sensitivities to these additional processes, and thus is a valuable test of current models. We identify a large and unexpected meridional variation in stratospheric 16 O13 C18 O, observed as proportions in the polar vortex that are higher than in any naturally derived CO2 sample to date. We show, through photochemical experiments, that lower 16 O13 C18 O proportions observed in the mid-latitudes are determined primarily by the O(1 D) + CO2 isotope exchange reaction, which promotes a stochastic isotopologue distribution. In contrast, higher 16 O13 C18 O proportions in the polar vortex show correlations with long-lived stratospheric tracer and bulk isotope abundances opposite to those observed at mid-latitudes, and thus opposite to those easily explained by O(1 D) + CO2 . We believe the most plausible explanation for this meridional variation is either an unrecognized isotopic fractionation associated with the mesospheric photochemistry of CO2 or a temperature-dependent isotopic exchange on polar stratospheric clouds (PSCs). Unraveling the ultimate source of stratospheric 16 O13 C18 O enrichments may impose additional isotopic constraints on biosphere-atmosphere carbon exchange, biosphere productivity, and their respective responses to climate change. 14 L. Y. Yeung 2.2 Oxygen isotope exchange reactions of CO2 Chapter 2 Introduction Predicting future CO2 concentrations and carbon cycle-climate feedbacks depends on one’s ability to quantify the contributions from the sources and sinks governing the global carbon budget and how they may change over time. The bulk stable isotope composition of CO2 (i.e., its 13 C/12 C, 18 O/16 O, and 17 O/16 O ratios) plays an important role in constraining this budget (see Yakir [2003] and references therein). In the stratosphere, the oxygenisotope composition of CO2 is thought to be modified by oxygen isotope exchange reactions with O(1 D) generated by ozone photolysis [Yung et al., 1997], whereas in the troposphere it is controlled by isotope exchange reactions with liquid water in the oceans, soils, and plant leaves [Ciais and Meijer, 1998]. The interplay between stratospheric and tropospheric isotope exchange reactions, in principle, could allow the relative abundances of 12 C16 O2 , 16 O12 C18 O, and 16 O12 C17 O isotopologues to be used as tracers for gross biosphere produc- tivity [Hoag et al., 2005; Luz et al., 1999], but the stratospheric CO2 photochemical system is still under-constrained and our understanding of it is incomplete. Discrepancies between laboratory and stratospheric measurements [Lämmerzahl et al., 2002; Shaheen et al., 2007; Thiemens et al., 1995] have prompted questions about whether the O(1 D) + CO2 isotope exchange reaction acts alone on stratospheric CO2 or whether other photochemical [Bhattacharya et al., 2000] or dynamical [Boering et al., 2004] processes significantly affect the stable isotopologue distribution in CO2 . Stratospheric oxygen isotope covariations in CO2 [Kawagucci et al., 2008; Lämmerzahl et al., 2002; Liang et al., 2008] consistently differ from those found in laboratory experiments simulating stratospheric photochemistry [Baulch and Breckenridge, 1966; Chakraborty and Bhattacharya, 2003; Johnston et al., 2000; Shaheen et al., 2007; Wen and Thiemens, 1993], and the origin of this disagreement is still uncertain because bulk stable isotope measurements alone (i.e., of δ 13 C, δ 18 O, and δ 17 O values) cannot differentiate extrinsic effects [e.g., the O(1 D) isotope composition] from intrinsic (i.e., photolytic or kinetic isotope) effects on the isotope composition of stratospheric CO2 . Additional constraints arising from analysis of multiplysubstituted isotopologues of CO2 can provide sensitivities to these processes [Affek and Eiler, 2006; Affek et al., 2007; Eiler, 2007; Eiler and Schauble, 2004]. To investigate stratospheric 15 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 CO2 chemistry, we examine here the proportions of 16 O13 C18 O (reported as a ∆47 value) in stratospheric CO2 and in laboratory kinetics experiments. 2.3 Field sample collection and analysis Twelve stratospheric CO2 samples were analyzed for bulk stable isotope compositions and ∆47 values: Six samples of stratospheric CO2 were collected from the NASA ER-2 aircraft during the 1999/2000 Arctic winter Stratospheric Aerosol and Gas Experiment III (SAGE III) Ozone Loss and Validation Experiment (SOLVE) campaign [Newman et al., 2002], and six samples were collected from a balloon flight from Fort Sumner, New Mexico on 29 September 2004. SOLVE mission samples (January – March 2000, 29 – 79◦ N, 11 – 20 km) were collected as whole air samples [Flocke et al., 1999]. CO2 was then isolated from the ∼5 L STP of air by a combination of liquid N2 and ethanol-dry ice traps, then separated into aliquots of 12 – 18 µmol CO2 each and sealed into glass ampoules. Balloon samples were collected using a cryogenic whole air sampler (34.5◦ N, 103.6◦ W, 27 – 33 km) [Froidevaux et al., 2006; Lueb et al., 1975] and purified and stored as above. δ 13 C, δ 18 O, and δ 17 O of CO2 were measured on a Finnigan MAT 252 isotope ratio mass spectrometer (IRMS) at UC-Berkeley. ∆17 O was measured using the CeO2 technique with a precision of ± 0.5‰ [Assonov and Brenninkmeijer, 2001]. Aliquots of the same CO2 samples were analyzed for ∆47 using a Finnigan MAT 253 IRMS at Caltech configured to collect masses 44 – 49, inclusive, and standardized by comparison with CO2 gases of known bulk isotopic composition that had been heated for two hours at 1000◦ C to achieve a stochastic isotopic distribution [Eiler and Schauble, 2004]. Masses 48 and 49 were used to detect residual hydrocarbon contamination. For ∆47 analysis, the 12 – 18 µmol aliquots of SOLVE-mission and balloon CO2 samples were purified of potential contaminants, such as hydrocarbons, by a pentane-liquid N2 slush (–120◦ C) as well as by passing it through a gas chromatographic (GC) column (Supleco Qplot, 530 µm ID, 30 m length) at –20◦ C, with column baking at 150◦ C between samples [Affek and Eiler, 2006; Ghosh et al., 2006]. All data were corrected for the presence of N2 O using the method described previously [Affek and Eiler, 2006]. Each measurement consisted of 5 – 9 acquisitions (of 10 measurement 16 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Table 2.1: Stratospheric air sample data Air Sample Name Type∗ Altitude Latitude (km) (◦ N) θ (K) CH4 N2 O CFC-11 CFC-12 δ 13 C (ppbv) (ppbv) (pptv) (pptv) (‰) δ 18 O (‰) ∆17 O (‰) ∆47 (‰) ER-2 samples V V V VE M M 20000312(25)1120 20000131(30)1001 20000203(10)1173 20000127(5)1060 20000106(30)1169 20000111(25)2021 19.33 19.85 17.63 19.45 19.40 11.40 79.2 73.5 70.4 57.7 29.3 43.5 443.61 448.08 409.37 445.10 467.43 358.26 948 1066 1250 1385 1495 1726 111.5 142.1 192.8 227.6 256.4 307.9 33.34 32.22 30.78 29.26 28.73 27.27 34.5 34.6 34.6 34.6 34.6 34.6 931.14 896.15 861.84 778.08 757.89 709.67 835 843 913 957 1014 1176 54.0 56.7 77.8 92.1 107.9 155.9 19. 31. 72. 112. 157. 246. 147. 198. 293. 362. 421. 526. -8.11 -8.08 -8.06 -8.07 -8.08 -8.06 44.55 43.62 43.06 42.79 42.50 40.98 5.76 4.38 3.69 2.45 2.13 0.18 1.614 1.555 1.436 1.233 1.071 1.075 46.0 51.2 78.2 100.2 78.2 123.6 -8.07 -7.99 -8.03 -8.07 -8.04 -8.03 45.14 45.44 45.14 44.98 44.79 44.09 6.46 6.29 5.91 6.12 5.00 4.26 0.976 0.923 0.913 0.912 1.004 0.916 Balloon samples M M M M M M 1-A010-R (2035) 3-A01-R (1141) 5-A013-R (2079) 7-A026-R (1057) 8-A017-E (1113) 10-A022-E (1186) 0.13 0.23 0.15 0.63 1.10 5.90 ∗ Air type is abbreviated as V = vortex, VE = vortex edge, and M = mid-latitude based on N O:θ correlations, where θ is 2 potential temperature in Kelvin. Non-isotopic tracer measurement methodology can be found in Flocke et al. [1999] and Froidevaux et al. [2006]. cycles each), with typical standard deviations (acquisition-to-acquisition) of 0.06‰ in ∆47 . 2.4 Field results The stratospheric samples (see Table 2.1) display ∆47 values both higher and more variable than those exhibited by tropospheric air at the surface, which has an average ∆47 value of 0.92 ± 0.01‰ in remote regions (Cape Grim, Tasmania and Barrow, Alaska) [Affek et al., 2007]. The high-latitude (> 57◦ N) stratospheric samples, in particular, are significantly more enriched in ∆47 than any material analyzed before in nature (see Figure 2.1 and see Affek et al. [2007] and Eiler [2007]). At high latitudes, ∆47 varies strongly and increases monotonically with decreasing mixing ratios of long-lived trace gases that have tropospheric sources and stratospheric sinks, such as N2 O and CH4 . At mid-latitudes, ∆47 varies relatively little and shows correlations with trace gas mixing ratios having the opposite sign of those observed at high latitudes (see Figure 2.2 and Table 2.1). Using the correlation between simultaneously measured N2 O mixing ratios and potential temperature [Greenblatt et al., 2002], we found that the high-latitude samples were collected in inner polar vortex air (three samples) or vortex edge air (one sample). Thus, differences in the sign and magnitude of ∆47 variations with N2 O mixing ratio in the two subsets of 17 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.1: Meridional variation of ∆47 measured in stratospheric samples. Typical values in the troposphere are ∆47 ∼ 0.9‰. Error bars show 2σ standard errors. samples are presumably due to differences between vortex and non-vortex processes. In contrast to these ∆47 trends, covariations of ∆17 O with δ 18 O and mixing ratios of long-lived trace gases for our mid-latitude samples resemble those of our polar vortex samples (or show the expected differences for slightly shorter-lived tracers, e.g., CFC-11) and also those reported in earlier studies of high-latitude [Boering et al., 2004; Kawagucci et al., 2008] and polar vortex air (see Figure 2.3) [Alexander et al., 2001]. This suggests that ∆47 records a process to which ∆17 O is not sensitive. In order to rule out the possibility that the observed high ∆47 values result from sample contamination by organic compounds in the stratospheric samples, one of the samples [20000131(30)1001] was exposed to water at 25◦ C for 24 hours to reach CO2 –water isotopic equilibrium. The exchanged sample had a ∆47 value of 0.862 ± 0.078‰, identical to the cylinder CO2 working standard, whose ∆47 value reflects CO2 isotopic equilibrium at room temperature [Wang et al., 2004]. In contrast, the presence of contaminants would have resulted in a high ∆47 value even after isotopic equilibrium was reached. Hence, no evidence for contamination was observed in the high-latitude samples. 2.5 Laboratory photochemical experiments To gain further insight into the correlations we observed between ∆47 , ∆17 O, and δ 18 O, we conducted several laboratory photochemistry experiments. Enrichments of ∆17 O and δ 18 O 18 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.2: Correlation between ∆47 and stratospheric tracers. (A), best-fit lines are shown for mid-latitude (solid line) and high-latitude (dashed line) ∆47 vs. N2 O mixing ratio. Correlations between ∆47 and other tracers with tropospheric sources and stratospheric sinks are similar (see Figure 2.3). Also shown is the best-fit line of (B), ∆47 vs. ∆17 O, and (C), ∆47 vs. δ 18 O in mid-latitude air, which is used to estimate the integrated effective isotopic composition of stratospheric O(1 D) (see text). Error bars represent 2σ standard errors. Figure 2.3: ∆17 O values vs. long-lived stratospheric tracer mixing ratios. In both panels, measurements reported in this work (ER-2 and Balloon data) are compared with previous high-latitude (> 48◦ N; left panel) and polar vortex (right panel) measurements. The measured ∆17 O correlations with N2 O and CFC-12 do not reveal obvious distinctions among the mid- and high-latitude CO2 samples; ∆47 measurements, in contrast, reveal strong mesospheric or other polar vortex influence. 19 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 in stratospheric CO2 are generally understood to arise from isotope exchange with O(1 D), which is produced by photolysis of 18 O- and 17 O-enriched stratospheric ozone [Liang et al., 2007; Yung et al., 1997], but the kinetics of the isotope exchange reactions for multiplysubstituted isotopologues of CO2 , and their effects on ∆47 , have not yet been explored. Changes in ∆47 caused by these reactions should principally reflect relative changes in 16 O13 C18 O and 16 O12 C18 O abundances because the 13 C composition is not affected by iso- tope exchange with O(1 D); variations in 17 O12 C18 O and 13 C17 O2 abundances will change ∆47 more subtly. Thus, reactions 2.1 and 2.2 are most relevant. 18 O(1 D) + 12 C16 O2 → 18 O12 C16 O∗2 → 16 O + 16 O12 C18 O (2.1) 18 O(1 D) + 13 C16 O2 → 18 O13 C16 O∗2 → 16 O + 16 O13 C18 O (2.2) Statistical partitioning of isotope exchange products, through a process governed by random chance such that 18 O(1 D) has a 2/3 probability of being incorporated into the product CO2 , would drive the CO2 isotopologues towards a stochastic distribution (i.e., ∆47 = 0). If any one (or more) of the isotope exchange reactions does not partition products statistically, however, ∆47 can increase [e.g., if 18 O(1 D) exchanges isotopes with 13 C16 O2 more readily than with 12 C16 O2 ] or decrease accordingly. Two sets of laboratory experiments were conducted. First, the relative rates of reactions 2.1 and 2.2 were probed directly to obtain the 13 C/12 C kinetic isotope effect (KIE) for the 18 O(1 D) + CO 2 isotope exchange reaction at 300 K and 229 K. These experiments used pulsed photolysis of 97% N2 18 O at 193 nm as a source of 18 O(1 D), and the extent of isotope exchange was minimized. Second, we performed continuous-irradiation experiments, using a mercury lamp, on mixtures of isotopically unlabeled O2 , O3 , and CO2 as a function of different irradiation times to determine the aggregate effects of the O2 /O3 /CO2 photochemical system on ∆47 . 20 L. Y. Yeung Oxygen isotope exchange reactions of CO2 2.5.1 13 C/12 C kinetic isotope effect experiments 2.5.1.1 Methods overview Chapter 2 For experiments performed at 300 K, a 15 cm-long stainless steel conflat chamber with quartz windows was used as a reaction chamber. Low-temperature experiments were performed in a 25 cm-long, all-quartz chamber, cooled to 229 K under vacuum via direct conduction with a cold copper jacket (see Appendix 2.C). Experiments were initiated with pulsed excimer laser photolysis of N2 18 O (193 nm, 50 – 100 mJ pulse−1 , 1 Hz repetition rate, < 200 pulses), producing 18 O(1 D), in ∼1:100:3000 static mixtures of N2 18 O:CO2 :He (100 Torr total pressure). N2 18 O was synthesized from the acid-catalyzed reduction of 18 O-labeled aqueous NaNO [McIlvin and Altabet, 2005; Samuel and Wassermann, 1971]; a 2 detailed description of its synthesis and characterization can be found in Section 2.5.1.2. A schematic of the reaction scheme is shown in Figure 2.4. Starting samples of CO2 contained a stochastic distribution of isotopologues, generated in the manner described in Section 2.3. The initial CO2 isotopic composition was measured and CO2 was recollected cryogenically for use in the reaction chamber. Residence time in the reaction chamber had a negligible effect on ∆47 in the 300 K experiments, whereas the chamber cooling process alone was observed to enrich the starting material in δ 18 O and ∆47 , by 0.5‰ and 0.13‰, respectively. These offset values were subtracted from final δ 18 O Figure 2.4: Schematic of O(1 D) + CO2 reaction-purification-analysis procedure. 21 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 and ∆47 values in 229 K experiments. The reaction products were recollected cryogenically and purified in two GC steps. Separation of residual N2 18 O and reacted CO2 was achieved through a packed-column (PoraPak Q) GC separation at 25◦ C, after which the samples were purified with a capillary GC as described above. Due to the presence of N2 18 O isobars with CO2 at masses 46 – 49, mass 14 was also monitored to measure the extent of N2 18 O contamination. Differences in mass-14 signal between the starting and product material of greater than 5 mV (a variation typical of ‘clean’ laboratory standards) were deemed contaminated, and the data points were rejected. The difference between the initial and final δ 18 O (hereafter referred to as ∆δ 18 O) and ∆47 compositions was calculated assuming that δ 13 C was unchanged, since there was no external carbon reservoir in the reaction. GC separation of N2 18 O and CO2 yielded a small, yet reproducible ∆47 change of +0.13‰, which was present both when gases of stochastic isotope composition were analyzed as well as when aliquots of cylinder CO2 working standard (∆47 = 0.86‰) were analyzed. The source of this offset may be a small amount of diffusive or adsorptive fractionation on the GC column, but it was not investigated further. Because of the apparent insensitivity of the ∆47 change to initial isotopic composition, the sample purification step was treated as a small additive effect on the measured ∆47 , with no effect on the overall kinetics measured. The following sections, 2.5.1.2 and 2.5.1.3, provide a detailed description of the materials and methods utilized to obtain the results summarized in Section 2.5.1.4. 2.5.1.2 N2 18 O synthesis Precursor samples of N2 18 O were synthesized from the acid-catalyzed reduction of aqueous nitrite (NO2 − ) [McIlvin and Altabet, 2005; Samuel and Wassermann, 1971]. A description of a synthesis and characterization follows. First, a solution of 0.4 mmol sodium nitrite (NaNO2 ) in 800 µl >97% H2 18 O (Isonics) was placed in a three-neck round-bottom flask and flushed with He at 30 mL min−1 for 20 minutes to remove any dissolved gases. The flow was then stopped and the flask closed off and put in an ice bath. 350 µl glacial acetic acid was then added through a rubber septum with a syringe to acidify the water. For 3 minutes, 22 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 the nitrite was allowed to exchange oxygen atoms fully with H2 18 O in the acidic environment [Ott, 1981]. Then, the nitrite was reacted with 220 µl of a solution of 1.5 mmol sodium azide (NaN3 ), 100 µl glacial acetic acid, and 150 µl H2 18 O, also added through the septum, for 40 minutes with stirring. Due to the high concentration of acid, the dominant reaction was expected to be that between nitrous acid (HNO2 ) and hydrazoic acid (HN3 ) to produce N2 18 O: HNO2 + HN3 → N2 O + N2 + H2 O (2.3) After the 40-minute reaction time, 1 mL of a ∼17 M NaOH solution was added through the septum to stop the reaction and remove any residual CO2 . The gas-phase products were collected by flowing He through the flask at 5 mL min−1 for 1 h into a “U-trap” held at liquid nitrogen temperature (77 K). Synthesized N2 18 O was dried cryogenically using a pentane slush (–120 ◦ C), then a dry ice/ethanol slush (–76 ◦ C), and recollected in a trap at liquid nitrogen temperature. Chemical yield in the N2 18 O was determined by expanding the product gas into a calibrated volume on a vacuum line, and the total product yield was determined to be 53% (0.195 mmol). Table 2.2: IR band assignments for the spectra in Figure 2.5 Frequency (cm−1 ) Band Frequency (cm−1 ) Band 1155 1247 1840 2217 2295 2412 2491 2787 3345 3435 3663 3737 2ν2 ν1 ν1 + ν2 ∗ ν3 4ν2 ν1 + 2ν2 ∗ 2ν1 ν2 + ν3 2ν2 + ν3 ∗ ν1 + ν3 2ν1 + 2ν2 ∗ 3ν1 ∗ 1285 1595 2350 2563 3481 3657 3756 ν1 (14 N2 16 O) ν2 (H2 16 O) ν3 (CO2 ) 2ν1 (14 N2 16 O) ν1 + ν3 (14 N2 16 O) ν1 (H2 16 O) ν3 (H2 16 O) Assignments taken from Łapiński et al., and references therein. Literature values are ν1 = 1247 cm−1 , ν2 = 571 cm−1 , and ν1 = 2217 cm−1 for N2 18 O. ∗ Temporary assignment because band has yet not been reported in the literature. 23 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.5: FT-IR spectrum of synthesized N2 18 O between 1100 cm−1 and 4000 cm−1 . Inset shows the zoomed-in area between 2100–2400 cm−1 . Samples were then measured on a Fourier-transform infrared spectrometer (FT-IR) for chemical purity and a IRMS for isotopic purity. FT-IR analysis was conducted on a Nicolet FT-IR spectrometer with 3 Torr N2 18 O, 0.125 cm−1 resolution, and 2000 scans in an 18 cmpathlength cell with CaF2 windows. Table 2.2 contains the band assignments for the N2 18 O IR spectrum shown in Figure 2.5. The IR spectrum (see inset of Figure 2.5) contains a small amount of CO2 , but it is considered too small an amount to affect isotopic measurements. The absorption cross-section of the CO2 (ν3 ) band is three times that of the N2 O(ν3 ) band [Rothman et al., 2009], yet in the experimental spectrum, the N2 O band is stronger than the CO2 band by an order of magnitude; consequently, the concentration of CO2 in the N2 18 O sample is estimated to be 3%. Because N2 18 O was used as a 1% mixture in CO2 for the photolysis experiments, the estimated mixing ratio of contaminant CO2 is 3 × 10−4 in the sample CO2 . This mixing ratio amounts to a maximum absolute error less than 0.001‰ in the observed δ 18 O at natural abundance (0.2% 18 O), and it is therefore negligible. H2 O lines in the spectrum are believed to come from atmospheric water vapor, as they are consistent with H2 16 O instead of the H2 18 O used in the synthesis. Because all of the H2 18 O appears 24 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Table 2.3: IRMS ion signals from the synthesized N2 18 O m/z Signal (mV) 18 O content 44 46 1276 37870 96.7% 30 32 482 14773 96.8% to have been removed by the cryogenic drying steps, and the sample compartment was continuously purged with dry N2 , this water vapor is believed to arise from desorbing water from the FT-IR cell walls. Mass-spectrometric analysis was performed on a Finnigan MAT 253 using cup position 3 (3 × 1010 Ω resistor). Isotope ratios were determined at two different m/z ranges: 46/44 (mainly 14 N2 18 O/14 N2 16 O) and 32/30 (mainly 14 N18 O/14 N16 O). Table 2.3 contains the observed signals and calculated isotopic purity at 16.5 mbar in the sample bellows. Here we see that the synthesized N2 O is indeed 97% labeled with 18 O, and it was used in experiments without further purification. 2.5.1.3 Reaction models Two models for the 13 C/12 C KIE experiments were constructed. One was a chemical kinetic model designed to calculate the expected trends in ∆47 vs. ∆δ 18 O given specific KIEs. The second was a hard-sphere collision model designed to model the velocity relaxation of the nascent 18 O(1 D), from which a collision energy distribution for each experiment could be calculated. C HEMICAL KINETIC MODEL . A comprehensive, isotopologue-specific kinetics model of the O(1 D)-CO2 photochemical experiment (144 isotope exchange reactions) was constructed in the FACSIMILE kinetics modeling package. Stochastic isotope exchange branching fractions [Baulch and Breckenridge, 1966; Yung et al., 1997] were used: Incident O(1 D) atoms had a 2/3 probability of isotope exchange, regardless of the isotope exchange reaction. The isotopic composition of the initial O(1 D) was treated as a constant; for these 18 O-labeled 25 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 experiments, trace 17 O and 16 O abundances had negligible effects on the measured 13 C/12 C KIE. We expect to observe subtle isotope effects due to differences in the 18 O(1 D)–CO2 collision frequencies between different isotopologues in the helium-buffer-gas experiments because the collision-limited rate of reaction for O(1 D) + CO2 [Sander et al., 2006] implies that the reaction probability for any given O(1 D)–CO2 collision is near unity. For instance, more 18 O(1 D) + 12 C16 O2 collisions than 18 O(1 D) + 13 C16 O2 collisions occur because the average velocity for 12 C16 O2 is higher than that for 13 C16 O2 at a given temperature. This reduces the rate at which reaction 2.2 occurs relative to reaction 2.1 in the laboratory by about 5%. The O(1 D)-CO2 collision frequencies in these experiments scale directly with the collision pair’s relative velocity, which depends inversely on the pair’s reduced mass (µ) according to equation 2.4: s k2.2 = µ18 O + 44 CO 2 µ18 O + 45 CO × k2.1 = µe f f k2.1 (2.4) 2 k represents the rate coefficient for the subscripted reaction, and µ represents the reduced mass of the subscripted reactant pair. Analogous relationships can be computed for each unique reactant pair. ∆47 is expected to decrease with increasing ∆δ 18 O because the collision frequency for 18 O(1 D) + 44 CO2 is ∼5% larger than that for 18 O(1 D) + 45 CO2 . Such biases are expected to be small in the atmosphere due to competing electronic quenching reactions (e.g., O(1 D) + N2 → O(3 P) + N2 ) [Johnston et al., 2000]. These electronic quenching reactions were minimized in our pulsed photolysis experiments because He was used as the buffer gas [Heidner and Husain, 1974; Shi and Barker, 1990]. Thus a 13 C/12 C KIE = k2.2 /k2.1 = 1 in our laboratory experiment will appear as an anti-correlation in a plot of ∆47 vs. ∆δ 18 O. A 13 C/12 C KIE ≈ 1.01 and an O(1 D) source with δ 18 O = δ 17 O ≈ 100‰ would be required to generate the polar vortex ∆47 enrichment and also the polar vortex ∆47 vs. ∆17 O correlation. On the ∆47 vs. ∆δ 18 O plot, the slope would be +0.0055 using k2.2 /k2.1 = 1.01. O(1 D) + CO2 COLLISION ENERGY DISTRIBUTION . The 13 C/12 C experiment was also modeled on the collision-by-collision level because the O(1 D) + CO2 isotope exchange reaction occurs through two reaction channels whose branching ratio depends on collision energy 26 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 [Perri et al., 2003]: O(1 D) + CO2 → O(3 P) + CO2 (2.5) → O(1 D) + CO2 (2.6) The branching fraction of the non-quenching channel (2.6) increases significantly with reaction collision energy, Ecoll [Mebel et al., 2004; Perri et al., 2004]. Observed isotope effects, then, may also depend on the distribution of Ecoll . Nascent O(1 D) atoms from the N2 O photolysis scheme employed in this study had a high average translational energy, so He was chosen as buffer gas to lower the average collision energy, hEcoll i, to a stratospherically relevant value; He quenches the translational energy of O(1 D) atoms efficiently while quenching the electronic energy inefficiently [Heidner and Husain, 1974; Shi and Barker, 1990]. Furthermore, the translational energy transfer during O(1 D) + He collisions can be modeled well using a hard-sphere collision model [Matsumi et al., 1994b]. We constructed a Monte Carlo hard-sphere collision model in the MATLAB programming environment based on the solution to the general elastic hard-sphere problem; the mathematical derivation can be found in the literature [Nan and Houston, 1992], and the program code can be found in Appendix 2.D. The basic function of the program was to calculate the final velocity vectors for two colliding hard spheres of masses m1 (the O-atom) and m2 (the He-atom) with initial velocity vectors (v1i , θ1i , φ1i ) and (v2i , θ2i , φ2i ), respectively. The elastic hard-sphere calculation was performed for a distribution of initial O-atom velocities in a He bath gas at thermal equilibrium (e.g., at 298 K). First, O-atom velocity vectors, (vO,i , θO,i , φO,i ), were sampled according to a velocity distribution for O(1 D) ejected from the photolysis of 14 N2 16 O at 193 nm [Felder et al., 1991; Hanisco and Kummel, 1993; Springsteen et al., 1993] centered at ET = 18.2 kcal mol−1 . In the absence of experimental data for 14 N2 18 O photodissociation, the 18 O(1 D) velocity distribution was approximated by a gaussian distribution centered at ∼2900 m s−1 with a full-width at half-maximum (FWHM) of ∼1000 m s−1 (i.e., hET i ∼18 ± 7 kcal mol−1 ). Second, a He-atom velocity vector, (vHe,i , θHe,i , φHe,i ), was selected randomly from a Maxwell-Boltzmann velocity distribution. Using this pair of initial conditions and a random impact parameter b (sampled with a probability proportional to itself), the final velocity vector of the O-atom after one collision, (vO, f , θO, f , 27 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 φO, f ), was computed and stored. The final velocity was then re-used as an initial velocity for the next collision with a second He-atom, whose velocity was randomly sampled as above. This calculation was repeated for up to 200 total collisions and N = 50,000 initial O(1 D) velocities, a total of 106 – 107 calculations. After 200 collisions, > 96% of the O(1 D) would have reacted with CO2 under our experimental conditions. Using the O(1 D) velocity distribution after each O(1 D)–He collision, the distribution of O(1 D)–CO2 collision energies, Pj (Ecoll ), for the jth collision could then be calculated similarly. The relative CO2 concentration, i.e., ρCO2 ∼ 0.03, was then used to weight the Pj (Ecoll ) distribution at the jth collision to obtain a O(1 D)–CO2 collision energy distribution over the whole experiment. The results were summed according to equation 2.7: Ptotal (Ecoll ) = ρCO2 ∑ Pj (Ecoll ) (2.7) j The model was tested by confirming that the average kinetic energy approached (and remained at) the value expected at thermal equilibrium by the equipartition theorem, e.g., 3 −1 at 300 K. Calculated P total (Ecoll ) distributions for several different 2 RT = 0.89 kcal mol experimental conditions are shown in Figure 2.6. Our simulation of the initial O(1 D) collision cascade shows that 81% of all O(1 D) + CO2 collisions occur with Ecoll < 2 kcal mol−1 , with hEcoll i = 1.6 kcal mol−1 , similar to the Ecoll distribution expected in the stratosphere [Kharchenko and Dalgarno, 2004; Takahashi et al., 2002]. As we noted earlier, the nascent 18 O(1 D) translational energy distribution is somewhat uncertain because the existing pho- todissociaton dynamics studies focused on the 14 N2 16 O molecule, not the 14 N2 18 O used in these experiments. Changing the peak of the nascent 18 O(1 D) translational energy distribution by 1 – 2 kcal mol−1 changed the average O(1 D)-CO2 collision energy by < 0.1 kcal mol−1 . The shape of the laboratory Ptotal (Ecoll ) distribution appears different from that modeled in conditions resembling the stratosphere [Kharchenko and Dalgarno, 2004]; this difference is due to O(1 D) having a slower nascent O(1 D) velocity distribution (O3 vs. N2 O photolysis) [Thelen et al., 1995] and more efficient electronic quenchers (N2 /O2 vs. He bath gas) [Sander et al., 2006] in the stratosphere. In addition, minor O(1 D)-producing channels 28 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.6: Modeled O(1 D) + CO2 reaction collision energy distributions at different He bath gas pressure (T = 300 K). Also shown is the modeled P(Ecoll ) under conditions resembling the stratosphere, using O3 as a source of O(1 D). important to the stratosphere have not been included in this model (see Taniguchi et al. [2000]). Last, the velocity relaxation problem is only qualitatively represented by the hardsphere model; inelastic collisions are not necessarily described well by the hard-sphere cross-sections, especially when the collision partners are diatomic, and spin-orbit coupling is important [Kharchenko and Dalgarno, 2004]. Thus, the “stratospheric” O(1 D) collision model results are only intended for qualitative comparison with the laboratory O(1 D)–He results. 2.5.1.4 Pulsed-photolysis results The results of the pulsed laser experiments are plotted in Figure 2.7 and shown in Table 2.4. At both temperatures, ∆47 of CO2 decreases with increasing extent of photochemical isotope exchange (∆δ 18 O), indicating the O(1 D) + CO2 reaction does not selectively enrich 16 O13 C18 O relative to 16 O12 C18 O. Additionally, no significant temperature dependence was observed in ∆47 vs. ∆δ 18 O, as the 300 K and 229 K data are indistinguishable within our experimental uncertainty; consequently, the data were considered together in the subsequent determination of the 13 C/12 C KIE. The best-fit slope of the ∆47 vs. ∆δ 18 O relationship in the experimental data was calculated to be –0.0036 ± 0.0008 (2σ ), corresponding to a 29 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.7: Changes in ∆47 vs. ∆δ 18 O after pulsed UV photolysis at 300 K (circles) and 229 K (triangles). ∆δ 18 O = δ 18 Ofinal - δ 18 Oinitial . Also shown is the modeled ∆47 vs. ∆δ 18 O dependence for 13 C/12 C KIE = 13 k/12 k = 0.999 and 1.01 (offset by ∆47 = +0.13‰ for clarity; the significance of this and of the slopes is discussed in the text). Error bars represent 2σ standard errors. Table 2.4: Results of pulsed photochemical experiments δ 13 C (‰) Temperature δ 18 Oi (‰) δ 18 Of (‰) ∆δ 18 O† (‰) ∆47,f (‰) σ ∆47,f (‰) 29.84 29.95 15.50 15.48 30.08 29.63 15.28 14.46 66.41 54.03 58.44 55.89 48.79 41.17 58.33 59.86 36.57 24.08 42.94 40.41 18.71 11.54 43.05 45.40 -0.009 0.036 0.104 -0.018 0.038 0.057 -0.024 0.036 0.012 0.025 0.017 0.009 0.013 0.012 0.032 0.023 29.81 20.84 14.22 29.72 20.88 14.29 -0.09 0.04 0.07 0.150 0.127 0.165 0.011 0.012 0.028 Photolysis experiments 300 K 229 K -10.76 -10.56 -23.79 -24.24 -10.69 -10.55 -24.13 -25.15 Blank experiments 300 K 229 K -10.67 -19.22 -25.09 Blank experiments were run without photolysis step. † ∆δ 18 O = δ 18 Of - δ 18 Oi 30 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 13 C/12 C KIE of 0.999 ± 0.001 (2σ ). This KIE value was obtained by modeling the 13 C/12 C KIE value corresponding to the best-fit slope of the ∆47 vs. ∆δ 18 O data shown in Figure 2.7 (0.999, assuming a 13 C/12 C KIE of 1 in reaction 2.2). Its uncertainty was estimated by varying the 13 C/12 C KIE until the modeled slope varied ± 0.0008; the upper and lower limits of the 13 C/12 C KIE (1.000 and 0.998, respectively) were then taken as the 2σ uncertainty bounds. In contrast, a 13 C/12 C KIE of 1.01, the KIE required to explain the polar vortex ∆47 vs. ∆17 O correlation (see Section 2.5.1.3), would yield a slope of +0.0055 in Figure 2.7. The negative experimental slope, however, rules out this 13 C/12 C KIE > 1 and thus a selective enrichment in 16 O13 C18 O resulting from reaction 2.1. While this experiment was unable to isolate the 13 C/12 C KIEs in reactions 2.5 and 2.6, the laboratory data are consistent with the 13 C/12 C KIE in reaction 2.5 dominating the observed ∆47 vs. ∆δ 18 O relationship. Reactions 2.5 and 2.6 are both important in the stratosphere, with the branching ratio between them likely 9:1 (2.5:2.6) at the average stratospheric collision energy (see Mebel et al. [2004]) and thus also at the hEcoll i in our experiments. Using this branching ratio, we calculate that the experiment is approximately three times more sensitive to a 13 C/12 C KIE in reaction 2.5 than in reaction 2.6. A 13 C/12 C KIE ∼ 0.993 in reaction 2.6, then, is also consistent with the laboratory ∆47 vs. δ 18 O slope. If the observed slope were arising exclusively from a 13 C/12 C KIE in reaction 2.6, it would become increasingly negative with increasing initial hEcoll i because reaction 2.6 is favored at higher Ecoll [Mebel et al., 2004; Perri et al., 2004]. Several high-collision-energy (no buffer gas, initial hEcoll i ≈ 13.6 kcal mol−1 ) experiments were performed to test this hypothesis; they also showed depletions in ∆47 as the extent of photochemical isotope exchange increased, with no significant (i.e., factor-of-three) change in ∆47 vs. ∆δ 18 O. Other combinations of 13 C/12 C KIEs in reactions 2.5 and 2.6 could also yield the laboratory ∆47 vs. ∆δ 18 O slope, but the absence of significant temperature and collision-energy dependence in the laboratory data, along with negligible O(1 D)–CO2 association and dissociation barriers on the singlet electronic potential energy surface [Mebel et al., 2004], support our attribution of the measured isotope effects to reaction 2.5. As such, we report a 13 C/12 C KIE of 0.999 ± 0.001 (2σ ), which is within the uncertainty of a KIE of 1.000 expected for 31 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 stochastic isotope exchange. 2.5.2 Continuous-irradiation experiments 2.5.2.1 Methods Continuous-irradiation experiments on the O2 /O3 /CO2 photochemical system were performed at UC-Berkeley to examine whether the aggregate isotope effect from all O(1 D)–CO2 reaction pairs would still yield depletions in ∆47 with increasing extent of photochemical isotope exchange. A 2 L glass reaction bulb was filled with mixtures of O2 and CO2 of known isotopic composition between 100 – 150 Torr total pressure at 295 K, and the mixture was irradiated between 0 – 48 hours with a pen-ray mercury lamp through a MgF2 window. This scheme generates O(1 D) through narrow-band photolysis of O2 at 185 nm (6 × 1013 – 1.5 × 1014 photons cm−2 s−1 ) and subsequent photolysis of O3 at 254 nm (2 × 1015 photons cm−2 s−1 ). Residual O2 was separated cryogenically from the mixture, and O3 was catalytically decomposed on hot nickel foil at 333 K for 15 minutes before the CO2 was purified for isotopic analysis. A commercially available software program, KINTECUS (Windows version 3.95, 2008; [Ianni, 2003]), was used to simulate the kinetics of the photochemical oxygen isotope exchange between O2 and CO2 in the continuous-irradiation experiments. The species mod3 1 eled were O2 , O2 (1 ∆), O2 (1 Σ+ g ), O( P), O( D), O3 , and CO2 and included both singly- and doubly-substituted 17 O- and 18 O- isotopologues as well as 13 C isotopologues of CO2 , yielding more than 400 isotope-specific reactions. Rate coefficients for each reaction corresponding to all common isotopologues were from Sander et al. [2006], while photolysis rate coefficients (J-values) were calculated from the reported irradiance of the mercury pen-ray lamp at 254 nm [Reader et al., 1996], the geometry of the bulb, and the measured cross sections of O2 at 185 nm and O3 at 254 nm [Sander et al., 2006]. The only oxygen KIEs included in the model are in the ozone recombination reaction [Janssen et al., 2001] and in O + O2 isotope exchange [Kaye and Strobel, 1983; Wiegell et al., 1997]. Stochastic scrambling of oxygen was assumed to occur in the O(1 D) + CO2 isotope exchange reaction [Baulch and Breckenridge, 1966; Yung et al., 1997], and scenarios with hypothetical 13 C/12 C KIEs of 1, 32 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Table 2.5: Results of continuous irradiation experiments Sample name† Irradiation time (h) δ 18 O (‰) ∆17 O (‰) ∆47 (‰) Starting CO2 ANOM 1 ANOM 1 ANOM 2 ANOM 2 ANOM 4 0.0 48.0 48.0 4.5 4.5 10.0 6.4 67.4 67.4 13.1 13.2 19.0 0.0 24.8 24.8 2.3 2.3 4.8 1.10 0.72 0.85 0.96 1.04 0.75 † Samples with the same names are replicate analyses for ∆ , taken as separate aliquots of the 47 same experiment. 0.999, and 0.998 were considered a priori. The model was initialized with the experimental partial pressures, temperature, and starting isotopic compositions of O2 and CO2 . 2.5.2.2 Continuous-irradiation results The laboratory results from the continuous-irradiation experiments are shown in Table 2.5 and compared with the modeling results in Figure 2.8. We observed a depletion in ∆47 with increasing ∆17 O (a proxy for the extent of photochemical isotope exchange), in agreement with the results from our pulsed photolysis experiments. Within the uncertainty bounds reported for the 13 C/12 C KIE, the continuous irradiation experiments are also generally consistent quantitatively with our pulsed photolysis experiments. There is a noticeable disagreement, however, at the largest ∆17 O value (48-hour irradiation time). Some of this error could be attributed to our assumptions about the initial distribution of CO2 isotopologues in the model: The initial ∆47 > 0 was modeled as an excess of 16 O13 C18 O exclusively, although contributions from 17 O12 C18 O and 13 C17 O2 may be nontrivial. In addition, trace water in the reaction bulb (in the gas phase or adsorbed onto the glass) could catalyze CO2 – water isotope exchange reactions and drive the distribution of CO2 isotopologues towards equilibrium, i.e., ∆47 = 0.86‰ at 298K. Both of these uncertainties would be exacerbated as the irradiation time increases, leading to a marked deviation from the modeled result at longer irradiation times. Last, the effects of the O3 decomposition step on ∆47 have not been fully elucidated; previous reports have documented some oxygen isotope exchange 33 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.8: Changes in ∆47 vs. ∆17 O of CO2 after continuous UV irradiation of O2 /O3 /CO2 mixtures with a Hg lamp. Experimental results are compared with calculated results (13 C/12 C KIE = = 13 k/12 k = 1, 0.999, and 0.998 obtained a priori from a kinetics model of the photochemical experiment. Error bars represent 2σ standard errors. when O3 is decomposed on hot nickel [Johnston et al., 2000; Shaheen et al., 2007], perhaps with the nickel oxide layer or surface-adsorbed water, so the post-irradiation O3 decomposition step during CO2 purification may drive ∆47 towards its isotopic equilibrium value (∆47 ∼ 0.8‰ at 333 K; see Wang et al. [2004]) at the nickel’s temperature. We performed experiments to test this hypothesis by heating O3 /CO2 mixtures (with initial ∆47 = 0) in the presence of nickel foil and/or powder at 88, 125, and 155◦ C. The resulting ∆47 values of CO2 showed 1 – 2‰ changes in δ 18 O and 0.5 – 0.6‰ increases in ∆47 , consistent with isotopic equilibration occurring on the nickel surface. Still, the continuous irradiation experiments are consistent with the results of the pulsed photolysis experiments. They show that the O(1 D) + CO2 isotope exchange reaction drives the CO2 isotopologue distribution towards a stochastic distribution. 2.5.3 Conclusions from laboratory measurements In both sets of experiments, ∆47 of CO2 decreases with increasing extent of photochemical isotope exchange, as measured by the change in δ 18 O (∆δ 18 O; see Figure 2.7) or ∆17 O 34 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 of CO2 (see Figure 2.8), indicating the O(1 D) + CO2 reaction does not selectively enrich 16 O13 C18 O relative to 16 O12 C18 O. Furthermore, these results are consistent with a statistical oxygen isotope exchange mechanism; using the results from the 18 O-labeled experiments at 300 K and 229 K and the comprehensive kinetics model of the pulsed photolysis experiment, we calculated a 13 C/12 C KIE of 0.999 ± 0.001 (2σ est.), which is not significantly different from the KIE of 1.000 expected for statistical isotope exchange branching fractions and is quantitatively consistent with the results from the continuous irradiation experiments. Hence, our results are consistent with previous studies asserting that the O(1 D) + CO2 isotope exchange branching fractions are partitioned statistically [Baulch and Breckenridge, 1966; Johnston et al., 2000; Perri et al., 2004]. In contrast, a 13 C/12 C KIE of ∼1.01 would be required to explain the high-latitude isotopic correlations shown in Figure 2.2. A significant ∆47 change due to reactions other than 2.1 and 2.2 in the O(1 D)–CO2 photochemical system is unlikely. The KIEs for the other reactions (e.g., the 17 O12 C18 O-producing channel, which is absent in the pulsed photolysis experiments) would need to be at least 1.01 to be of comparable importance. In addition, the ∆47 – δ 18 O – ∆17 O covariation observed in the continuous-irradiation experiments (which included the 17 O12 C18 O-producing channel; see Figure 2.8) agreed well with our laboratory model, which assumes statistical partitioning of isotope exchange products in the O(1 D) + CO2 reaction. While not all of the relative rates for the O(1 D) + CO2 isotope exchange reaction were measured directly, the agreement between the pulsed-photolysis and continuous-irradiation experiments suggests that KIEs in the other O(1 D) + CO2 reactions [e.g., 18 O(1 D) + 16 O12 C17 O] are described well using statistical product partitioning in this case. Direct measurements of the other KIEs would be required to determine whether the statistical partitioning of isotope exchange products applies rigorously for all O(1 D)–CO2 reactant pairs. As such, we report a 13 C/12 C KIE of 0.999 ± 0.001 (2σ ), which is within the uncertainty of a KIE of 1.000 expected for stochastic isotope exchange. 35 L. Y. Yeung Oxygen isotope exchange reactions of CO2 2.6 Discussion 2.6.1 O(1 D)+CO2 only explains mid-latitude 16 O13 C18 O variations Chapter 2 We conclude that intrinsic isotope effects in O(1 D) + CO2 isotope exchange cannot produce the elevated values of ∆47 observed in stratospheric polar vortex air. Instead, the statistical partitioning of isotope exchange products in the O(1 D) + CO2 reaction drives the isotopic composition of CO2 towards a stochastic distribution, thus decreasing ∆47 . Indeed, the mid-latitude observations show evidence for decreasing ∆47 with increasing extent of photochemical isotope exchange (see Figure 2.2). As photochemical isotope exchange approaches completion (the unlikely, but instructive case in which all the oxygen atoms in CO2 have been exchanged), the ∆17 O and δ 18 O of CO2 will approach the ∆17 O and δ 18 O of O(1 D) because the size of the total oxygen reservoir (i.e., O2 , O3 , etc.) is >500x that of CO2 . Concurrently, the distribution of stable isotopes will become increasingly random, so the ∆47 value of CO2 will approach zero. The slope of this approach, then, reflects the integrated effective isotope composition of O(1 D) with which the CO2 molecules in the air samples have exchanged since entering the stratosphere; it is possible, however, that other terms in the stratospheric CO2 budget (e.g., CO oxidation) may, more subtly, change the isotopic composition of CO2 and thus the isotopic composition of O(1 D) one would infer from such a trend. We constructed a box model to calculate the effective integrated mid-latitude O(1 D) isotope composition to evaluate this hypothesis quantitatively. The results of our laboratory photochemistry model (13 C/12 C KIE experiments) were fit to the slope of weighted linear regressions of the mid-latitude ∆47 data (Figure 2.2). A quenching (reaction 2.5) and nonquenching (reaction 2.6) branching ratio of 9:1 in the isotope exchange reaction was used. Atmospheric ∆47 enrichments (e.g., ∆47 = 1.1‰) were treated as 16 O13 C18 O enrichments exclusively, since contributions to ∆47 from 17 O12 C18 O and 13 C17 O2 are ≤ 3%. Uncertainties in the fit ∆17 O and δ 18 O values were estimated by varying δ 17 O and δ 18 O to match the 2σ uncertainty in the slope of the weighted linear regressions. Using this box model and the mid-latitude observations, we estimate ∆17 O = 80.6+59.7 −24.1 ‰ 36 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 and δ 18 O = 98.0+43.7 −17.1 ‰ (2σ est.) as values for the integrated effective isotopic composition of O(1 D), which is consistent with ozone photolysis being the primary O(1 D) source in the stratosphere. While the δ 18 O of O(1 D) we calculate is similar to that found in low- and mid-latitude stratospheric ozone, ∆17 O is larger, on average, by 35‰ [Krankowsky et al., 2007]. This is expected because ∆17 O enrichments in ozone are concentrated at terminal atom positions [Michalski and Bhattacharya, 2009]; when ozone is photolyzed to O(1 D) and O2 , one of the terminal atoms is ejected [Dylewski et al., 2001], elevating the proportion of heavy oxygen isotopes in O(1 D). We note that the upper and lower uncertainty limits of the reported ∆17 O and δ 18 O values are correlated; they correspond to fits that simultaneously match the upper and lower uncertainty limits of the mid-latitude ∆47 vs. ∆17 O and ∆47 vs. δ 18 O weighted linear regressions. They reflect spatial and temporal variations in O(1 D) isotope composition expected to be caused by variations in ozone concentrations, temperature, pressure, actinic flux, and various mass-dependent kinetic and photolytic isotope effects that depend on these variables. 2.6.2 Effects of intra-stratospheric chemistry and mixing Having experimentally excluded intrinsic isotope effects in the O(1 D) + CO2 isotope exchange reaction as the source of high stratospheric ∆47 in polar vortex air, we consider the possible effects of other gas-phase stratospheric processes on the CO2 isotopologue budget. CO is produced in the stratosphere by CH4 oxidation and destroyed with an e-folding time of about two to three months by reaction with OH radicals to form CO2 . We estimate that up to 0.9 ppmv CO2 could be derived from CH4 oxidation in our samples based on the difference between the observed CH4 concentrations (Table 2.1) and the average CH4 concentration in air entering the stratosphere from the troposphere (1.7 ppmv). 12 C/13 C KIEs for CH4 + OH, CH4 + O(1 D), and CH4 + Cl of 1.004, 1.01, and 1.07, respectively [Brenninkmeijer et al., 2003], should yield 13 C-depleted CH3 radicals at all latitudes, particularly in the polar vortex, where Cl levels are elevated. CH3 radicals then undergo several rapid oxidation steps to form formaldehyde (CH2 O). Isotope effects in CH2 O photolysis to form CO also favor the light isotopologues [Feilberg et al., 2005a]. These isotope effects, com- 37 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 bined with expected 13 C compositions for stratospheric CH4 in these samples (δ 13 C = –47 to –35‰) should produce CO that is depleted in 13 C relative to background stratospheric CO2 . Small inverse 12 C/13 C, 16 O/18 O, and 16 C/17 O KIEs (i.e., < 1) in the reaction CO + OH to form CO2 at low pressures [Röckmann et al., 1998] imply that, in principle, CO + OH reactions could increase ∆47 values in the product CO2 , while at higher pressures, the CO + OH reaction yields 13 C-, 18 O-, and 17 O-depleted CO2 [Feilberg et al., 2005b]. Ultimately, however, the size of ∆47 values in the ≤ 0.9 ppmv CO2 derived from CH4 oxidation would likely be orders of magnitude too small to increase ∆47 values significantly in the other ∼365 ppmv of background stratospheric CO2 . A possibility remains that unusual timing in the competition between oxidation and photolysis of species in the polar vortex, combined with unexpectedly large carbon and oxygen KIEs in some Cl and Br reactions (e.g., Br + CH2 O; see Feilberg et al. [2004]) or other gas-phase processes might be responsible for the mid-latitude-polar vortex differences in ∆47 given the large differences in Cl and Br concentrations in polar vortex vs. mid-latitude air, but this seems unlikely in light of the known chemistry and KIEs. Expected changes in δ 18 O and δ 17 O due to intra-stratospheric mixing are also too small to yield highly enriched polar vortex ∆47 . Effects of CO2 sources on ∆47 can be calculated by solving the three-end-member mixing problem between (1) tropospheric CO2 , (2) stratospheric CO2 undergoing photochemical isotope exchange, and (3) stratospheric CO2 derived from a third source and accounting for the non-linearity in mixing (see Appendix 2.A). Therefore, we constructed a mixing model to simulate the effects of mixing isotopically distinct CO2 sources on stratospheric air. The tropospheric end-member was given an isotopic composition equal to measured ‘clean’ troposphere values (based on measurements of air sampled from Barrow, Alaska, and Cape Grim, Tasmania; see Affek et al. [2007]), namely, δ 13 Ctrop = –8‰, δ 18 Otrop = 41‰, δ 17 Otrop = 21‰, and ∆47trop = 0.92‰. Unfortunately, no measurements of ∆47 in the tropical troposphere exist, so ∆47trop of the air entering the stratosphere from the tropics is uncertain. The mid-latitude ∆47 vs. ∆17 O relationship implies that ∆47 may be as high as 1.09‰, but changes of ∆47trop on this order do not affect our qualitative understanding of mixing on stratospheric ∆47 . The stratospheric end- 38 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 member was δ 13 Cstrat = –8‰, ∆17 O = 80.6‰, and δ 18 O = 98.0‰; this was our integrated effective isotopic composition for O(1 D) calculated from the mid-latitude ∆47 variations. We find that two-component mixing between tropospheric and stratospheric air masses does not exhibit sufficient non-linearity to generate the observed ∆47 enrichments in highlatitude samples. Mixing non-linearities in ∆47 increase as the bulk isotope compositions of the two end-members become more dissimilar, but stratospheric O(1 D)–CO2 isotope exchange alone cannot produce a CO2 mixture of sufficiently high ∆47 . For instance, mixing effects generate ∆47 changes < 0.1‰ in the troposphere [Eiler and Schauble, 2004], where bulk isotope compositions of major constituents of the CO2 budget vary typically < 20‰ [Affek et al., 2007; Ciais and Meijer, 1998]. A mixture of tropospheric CO2 and midlatitude stratospheric CO2 would generate a similar enrichment because their bulk isotope compositions differ by a similar amount. Even in the extreme case of δ 18 Ostrat = 146‰, δ 17 Ostrat = 142‰ and ∆47strat = 0‰, the oxygen isotope composition of CO2 when it is at isotopic equilibrium with excess O3 (an unlikely case, but an ultimately useful one in illustrating this point; see Shaheen et al. [2007]), two-component mixing would yield a maximum ∆47 change more than an order of magnitude smaller than, and in the opposite direction of, that which is observed in polar vortex samples over the same range in ∆17 O. Bulk isotope compositions of the two CO2 reservoirs must differ in δ 18 O and/or δ 13 C by orders of magnitude not previously observed in the stratosphere to generate ∆47 enrichments of ∼0.7‰ observed in polar vortex samples. 2.6.3 Effects of mesospheric and heterogeneous chemistry Physical or chemical processes in the mesosphere may yield extreme isotopic enrichments in CO2 or CO such that subsidence of mesospheric air into the 1999/2000 stratospheric polar vortex [Plumb et al., 2003] could explain the observed meridional variation in ∆47 . Thus, we will next consider three mesospheric processes that have been previously studied in other contexts: Gravitational separation of upper atmospheric air, UV photolysis of O2 , and UV photolysis of CO2 . 39 L. Y. Yeung 2.6.3.1 Oxygen isotope exchange reactions of CO2 Chapter 2 Mixing of gravitationally separated air into the stratosphere Gravitational separation can concentrate heavy isotopologues of CO2 into the lower mesosphere [Ishidoya et al., 2008], which could elevate stratospheric ∆47 values after mesospheric subsidence and mixing. The expression in Craig [Craig et al., 1988] for the enrichment of a species Ni versus a second species N in per mil is based on the kinetic theory of gases [Gibbs, 1948]:  Ni ∆ N  = ∆M gZ × 103 RT (2.8) where ∆M is the difference in mass, g is the acceleration due to gravity (9.81 m s−2 ), Z is the column length, R is the gas constant, and T is the temperature. Using a reasonable column length of 50 km at a temperature of 220 K, gravitational separation of CO2 would increase δ 13 C, δ 18 O, and δ 17 O by 266‰, 6223‰, and 1113‰, respectively, but would lead to a decrease in ∆47 by 74‰ at the bottom of the column. In addition, polar vortex δ 13 C is not markedly more enriched from mid-latitude δ 13 C, implying that gravitational separation is generally negligible for the samples in this study. 2.6.3.2 Mixing of mesospheric air highly enriched in 17 O and 18 O Isotope effects in the photolysis of O2 by short-wavelength UV radiation in the upper mesosphere might lead to unusually enriched CO2 in the mesosphere. Liang et al. predicted recently that differences in photolysis cross-sections between light and heavy isotopologues of O2 in the narrow solar Lyman-α region (121.6 nm) may result in a population of mesospheric O(1 D) enormously enriched in 17 O and 18 O [Liang et al., 2007]. This extreme enrichment in O(1 D) could then be transferred to mesospheric CO2 through the O(1 D)+CO2 isotope exchange reaction. CO2 photolysis in the mesosphere to form CO, followed by oxidation of that same CO by OH in the polar vortex, might also significantly affect the ∆47 values of CO2 in the polar vortex. To evaluate the effects of 17 O- and 18 O-enriched mesospheric CO2 mixing into the stratospheric polar vortex, we constructed a three-component mixing model that included air 40 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Table 2.6: Tropospheric-stratospheric-mesospheric mixing model results Sample name f ∗trop f strat f meso 0.075 0.057 0.048 0.033 2.6 × 10−6 δ 18 Ostrat (‰) δ 18 Omeso (‰) 82.5 80.0 77.7 87.9 1.76 × 105 δ 18 O (‰) ∆17 O (‰) ∆47 (‰) Mixing model results 20000312(25)1120 20000131(30)1001 20000203(10)1173 20000127(5)1060 0.925 0.943 0.952 0.967 2.1 × 10−6 1.4 × 10−6 1.7 × 10−6 ∗ Mixing fraction of tropospheric air, calculated as 1 – f 1.86 × 105 2.07 × 105 1.47 × 105 44.55 43.62 43.06 42.79 5.76 4.38 3.69 2.45 1.614 1.555 1.436 1.233 strat – f meso . mass contributions from the troposphere, stratosphere, and mesosphere. Each polar vortex datum (i.e., with unique ∆17 O, δ 18 O, and ∆47 values) was fit individually because of the presence of mesospheric filaments in the polar vortex [Plumb et al., 2003] and consequent heterogeneity in the mixing fraction and end-member isotopic composition between samples. The multiply-substituted isotopologue distribution was fixed at ∆47meso = 0 for this simple mixing-only scenario because our kinetics experiments and the mid-latitude stratosphere ∆47 values indicate that isotope exchange drives the isotopologue distribution towards a stochastic one. No measurements of mesospheric δ 13 C exist, so δ 13 Cmeso = –8‰ was used; however, the calculated enrichment in mesospheric δ 18 O was insensitive to the choice of δ 13 C. We were unable to reproduce the polar vortex data in both bulk isotope compositions and ∆47 simultaneously when using the mesospheric 18 O and 17 O enrichments in CO2 mixing end-member suggested by Liang et al. [2007] (i.e., δ 18 O = 10,603‰, δ 17 O = 3,149‰, and ∆47 = 0). Only after δ 18 O and δ 17 O of the mesospheric CO2 end-member were increased an additional tenfold (i.e., δ 18 O ∼ 105 ‰ and δ 17 O ∼ 104 ‰) were the ∆47 – δ 18 O – ∆17 O systematics of the polar vortex samples reproduced. Modeled mixing fractions ( ftrop , fstrat , and fmeso ) and isotopic compositions for each of the high-latitude CO2 samples are given in Table 2.6. Due to the uncertainty in our calculated ∆17 Ostrat and δ 18 Ostrat values (see Section 2.6.1), δ 18 Ostrat was allowed to vary freely about our estimate above; the resulting δ 18 Ostrat values generally fell within the range we predicted. The combined uncertainties introduced by our calculated mid-latitude O(1 D) isotope composition and the other parameters used in these 41 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 fits suggest that these results are likely only meaningful to within an order of magnitude. No laboratory measurements of the isotopic fractionations in O2 due to Lyman-α photolysis are available to compare with our modeled isotopic compositions, however. Because 3 − the Lyman-α lines fall on the edge of the Ẽ 3 Σ− u ← X̃ Σg (1,0) absorption band of O2 , a small absolute absorption cross-section error for one O2 isotopologue can translate into a significant isotopic fractionation error. Relaxing the mesospheric δ 18 O vs. δ 17 O relationship predicted by Liang et al. [2007], i.e, δ 17 O = 0.3 × δ 18 O, increases the modeled δ 18 Ostrat values and lowers the predicted δ 18 Omeso values, but the mesospheric CO2 mixing end-member is still enriched overall to ∼100,000‰ in δ 18 O and δ 17 O. A simple calculation (assuming 365 ppm CO2 and an initial δ 18 O = 23.5‰ in O2 ) predicts that the mesospheric O2 end-member should have a δ 18 O value on the order of –100‰. Furthermore, we note that the O(1 D) + CO2 reaction may not necessarily partition products statistically (i.e., drive ∆47 → 0) in the mesosphere, as we assumed here, because the average collision energy there is higher than in the stratosphere. In principle, measurements of the isotopic composition of mesospheric CO should constrain the isotopic composition of mesospheric CO2 downwelling into the polar vortex. Large elevations in CO above background stratospheric levels, observed at high altitudes in the polar vortex [Plumb et al., 2003], are due to CO2 photolysis in the mesosphere and subsequent transport to the stratosphere, so the isotopic composition of CO in these cases should reflect that of the mesospheric CO2 population and any fractionations arising from CO2 photolysis there. The bulk isotope composition in mesospheric CO2 predicted by our three-component mixing model (e.g., tens of percent in 18 O-atom abundance, or 100x natural abundance) would result in isotopic enrichments in mesospheric CO that are detectable with remote-sensing spectrometers because CO2 photolysis isotope effects are expected to be much smaller in magnitude. For example, Bhattacharya et al. [2000] measured fractionations of ∼100‰ in 17 O and 18 O in their UV-photolysis experiments; CO2 -photolysis fractionation in the mesosphere could be larger, but the wavelength dependence of these across the actinic spectrum is difficult to estimate because the physical origin of the laboratory fractionations is not understood (see below). Remote-sensing measurements by the JPL 42 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 MkIV Fourier-transform spectrometer, however, does not show hundred-fold enrichments in 18 O of mesospheric CO observed downwelling to 30 km altitude in the polar vortex (G. C. Toon, personal communication, 2009). On the basis of this observation, mesospheric CO2 does not appear to possess oxygen isotopic enrichments of sufficient size to produce high ∆47 values in the polar vortex upon mixing with stratospheric air masses, although the long path-length and consequent averaging over mesospheric filaments and background stratospheric air of the MkIV instrument will dilute any mesospheric signal. Remote sensing of CO and/or CO2 isotopologue abundances in the mesosphere are thus needed to constrain this hypothesis. 2.6.3.3 Oxidation of mesospheric CO in the polar vortex Next, we examine the potential impacts of mesospheric CO2 photolysis to form CO, followed by mixing and re-oxidation into CO2 , on polar vortex ∆47 values. The photolysis of CO2 in the UV region may result in wavelength-dependent isotope effects, although this contention is based on a single laboratory measurement. Bhattacharya et al. [2000] performed laboratory experiments in which they photolyzed CO2 with either a Kr lamp (120 – 160 nm) or a Hg lamp (185 nm) and measured the 17 O and 18 O compositions of the product CO and O2 . The 120 – 160 nm results suggest that mass-dependent depletions of order 50‰ and 100‰ in 18 O and 17 O of CO, respectively, are possible, which would enrich the remaining CO2 reservoir in 18 O and 17 O. The 185-nm results were quite different: Photolysis of CO2 near natural isotopic abundance showed mass-independent enrichments in 17 O up to 150‰ with little change in 18 O in the CO and O2 products, while photolysis of 13 C-labeled CO2 showed mass-dependent enrichments in 18 O and 17 O in the 13 CO and O2 products of ∼50 and 100‰, respectively. Taken alone, these latter isotope dependences could result in mesospheric CO that is significantly enriched in 18 O, 17 O, and 13 C, and perhaps even 13 C18 O. The remaining mesospheric CO2 would be correspondingly depleted in heavy isotopologues. If similar isotopic fractionations occur in CO and CO2 when CO2 is photolyzed by UV radiation in the mesosphere, then the population of mesospheric CO downwelling into the 43 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 stratospheric polar vortex could have a large impact on the ∆47 values of CO2 in the polar vortex. Once in the stratosphere, mesospheric CO will be oxidized by OH to produce CO2 in the polar vortex. Oxidation of this CO could, in principle, contribute to the large polar vortex values of ∆47 in CO2 observed because: (1) CO mixing ratios as large as 10 ppmv have been observed in mesospheric filaments in the stratosphere (a thousand-fold higher than background stratospheric CO abundances in the polar vortex) [Plumb et al., 2003], (2) the known KIEs for the CO + OH reaction are expected to favor formation of 13 C18 Ocontaining CO2 molecules in the stratosphere [Feilberg et al., 2005b; Röckmann et al., 1998], and (3) the lifetime of CO with respect to oxidation is several months, and is therefore not immediately quantitative. These three phenomena could result in a sub-population of CO2 with elevated concentrations of 16 O12 C17 O, 16 C12 C18 O, and 16 C13 C18 O (or other mass-47 isotopologues of CO2 ), given the sign and magnitude of known KIEs for the CO + OH reaction [Feilberg et al., 2005b; Röckmann et al., 1998]. The slow oxidation of CO may only produce temporary increases of heavy-isotopologue abundances, as large fractionations due to KIEs will decrease in magnitude as CO oxidizes quantitatively to CO2 . Measurements of the 13 C18 O + OH vs. 12 C18 O + OH KIE by Feilberg et al. at 298K and 1 atm suggest that the oxidation of mesospheric CO alone could account for elevated ∆47 in the stratospheric polar vortex [Feilberg et al., 2005b]. Consequently, CO2 photolysis in the mesosphere, followed by oxidation of the product CO in the mesosphere and/or stratosphere, may allow the heavy oxygen and carbon isotopes in CO2 to ‘reorganize’ in a manner that could elevate ∆47 values of CO2 in the polar vortex. The mixing of the remaining (unphotolyzed) mesospheric CO2 with stratospheric CO2 in the polar vortex, however, may have the opposite effect on ∆47 values of CO2 . Measurements of all the relevant KIEs of CO + OH reaction at stratospheric temperatures and pressures and a model of the oxidation of mesospheric CO in the stratospheric polar vortex will be required to evaluate the impact of this mechanism quantitatively. The full impact of this mechanism is not well-constrained, however, because (1) the isotopic composition of mesospheric CO2 has not been measured, (2) not all the KIEs for the CO + OH reaction are known at the relevant temperatures and pressures, and (3) the 44 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 physical origin of the photolytic fractionations associated with CO2 photolysis are not understood. The first two points were discussed earlier, so they will not be discussed here. For the physical origin of the photolytic fractionations associated with CO2 photolysis, Bhattacharya et al. suggested that dissociation rates for certain CO2 isotopologues could be enhanced if their excited vibrational states (which get populated when the molecule absorbs UV light) overlap sufficiently with the vibrational states of another CO2 electronic state. This would facilitate conversion of the electronically excited species CO2 (1 B2 ), which is promoted from ground-state CO2 when it absorbs UV light and does not have enough energy to dissociate into O + CO under the experimental conditions, into the electronically excited species CO2 (3 B2 ), which does have enough energy to dissociate. If this mechanism is a general feature of the dynamics of CO2 photodissociation, it could lead to additional mass-independent fractionations at wavelengths other than at 185 nm. Unfortunately, this hypothesis has not been tested at other wavelengths yet, and without a firm theoretical understanding, or at least an empirical wavelength dependence, of the isotopic fractionations associated with CO2 photolysis, convolving the 120 – 160 nm results with the 185 nm results from Bhattacharya et al.’s experiments, and then convolving those with the actinic flux to make a prediction for ∆47 of mesospheric CO and CO2 is not possible. 2.6.3.4 Heterogeneous chemistry on stratospheric particles Finally, we consider the potential role stratospheric particles could play in the stratospheric CO2 isotopic budget. Oxygen isotope exchange on particle surfaces could drive the population of CO2 towards isotopic equilibrium by catalyzing CO2 –CO2 isotope exchange reactions (e.g., 16 O12 C18 O+13 C16 O2 * ) 12 C16 O2 + 16 O13 C18 O) that are too slow to occur in the gas phase under stratospheric conditions. Zero-point energy isotope effects dominate in these reactions at equilibrium, driving the ∆47 value towards its equilibrium value at a given temperature. We calculate that ∆47 adopts a value of 1.6‰ if 70% of the CO2 molecules achieve isotopic equilibrium at temperatures coincident with PSC formation in the polar vortex, ∼190 K [Wang et al., 2004] . Thus, in principle, particle-catalyzed equilibration of CO2 , perhaps via CO2 hydration reactions in quasi-liquid films at the surface of ice particles 45 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 [Dash et al., 2006], could produce the observed polar vortex ∆47 values. Bulk isotopic compositions would be little-affected by these isotope exchange reactions, consistent with the data presented in Table 2.1 and Figure 2.2, if the catalyst reservoir (e.g., liquid water layers on a surface) is much smaller than the CO2 reservoir; CO2 would impart its bulk isotopic composition on the catalyst while the multiply-substituted isotopologue distribution in CO2 , which is insensitive to the isotopic composition of the catalyst, approaches that at isotopic equilibrium. However, CO2 –liquid water isotope exchange may not occur quickly enough at low temperatures and low pH to be the relevant process. Last, we note that, in order for this PSC-catalyzed isotope-exchange mechanism to explain the polar vortex ∆47 measurements, the mechanism must result in a strong anti-correlation with N2 O mixing ratios (Figure 2.2a); this would imply that transport is fast compared to isotope exchange on the PSCs, whose distributions are highly variable in space and time in the polar vortex. Future 2-D modeling efforts will examine whether such a mechanism remains consistent with the observations or whether transport and mixing of a mesospheric isotope signal into the polar vortex better explains the observed anti-correlation of ∆47 with N2 O. We conducted preliminary experiments on the kinetics of isotope exchange on PSClike surfaces (e.g., H2 SO4 /HNO3 /H2 O mixtures; see Molina et al. [1993]) to test the PSCisotope-exchange hypothesis. PSCs made from HNO3 :H2 O mixtures, i.e. ‘Type Ia’ PSCs, were tested first because they were a major component of the PSCs formed during the 1999/2000 Arctic winter [Voigt et al., 2000] and their crystallization has been studied in the laboratory [Hanson and Mauersberger, 1988]. 50% HNO3 in H2 O was crystallized at 197 K using an ethanol/dry ice bath according to the protocol outlined by Hanson and Mauersberger [1988]; the crystal structure and stoichiometry of the ice was not measured. Pure CO2 of known isotopic composition was then exposed to the HNO3 ice for 3 hours in a glass reaction vessel held at 197 K. No change in the ∆47 values were observed (within statistical uncertainty). Based on the volume of the reaction vessel and the amount CO2 , the root-mean-square (RMS) displacement was 2.5 cm s−1 . This RMS displacement was significant compared to the 15-cm length of the reaction vessel; therefore, the reaction’s progress was probably not hindered by diffusion. The same experiment was performed also 46 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 with 1:1:1 H2 SO4 :HNO3 :H2 O mixtures (similar to ‘Type Ib’ PSCs) at 197 K, and no isotope exchange was observed in those experiments, either. These preliminary results imply that CO2 isotope exchange on PSCs is slow at stratospheric temperatures, although the chemical composition of the surfaces generated in the laboratory may have been different from those of real PSCs. Future studies should explore the isotope exchange reaction on all known PSC surfaces (e.g., types Ia, Ib, and II; see Zondlo et al. [2000] and Prenni and Tolbert [2001]) and assign upper limits to their rates. 2.7 Conclusions The signature of a new process preserved in stratospheric 16 O13 C18 O proportions reveals that a second mechanism, in addition to the O(1 D) + CO2 isotope exchange reaction, alters the isotopic composition of stratospheric CO2 and thus the interpretation of its chemical and transport ‘history.’ This second mechanism, which elevates ∆47 values in the polar vortex, is likely of either mesospheric photochemical or heterogeneous origin. To constrain further the role of each of these mechanisms, isotopic fractionations due to broadband UV photolysis of O2 and CO2 , the KIEs of the CO + OH reaction under stratospheric conditions, and the kinetics of CO2 isotope equilibration on the surfaces of PSCs and other stratospheric aerosols need to be studied experimentally. Additionally, kinetic and photolysis-induced isotope effects that may affect CO and CO2 should be incorporated into atmospheric models to quantify their contributions to both the bulk and multiply-substituted isotopologue budgets of stratospheric CO2 , whose influence on the isotopologue budgets of tropospheric CO2 may be significant. 2.8 Acknowledgements We thank R. Lueb for whole-air-sampler and cryogenic whole-air-sampler field support, Y. L. Yung, G. A. Blake, and P. O. Wennberg for manuscript comments, and financial support from the Davidow Fund, the National Science Foundation, the NASA Upper Atmosphere Research Program. K. A. B. was supported by the Camille Dreyfus Teacher-Scholar Award. 47 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Appendices 48 Chapter 2 L. Y. Yeung 2.A Oxygen isotope exchange reactions of CO2 Chapter 2 Mixing effects on isotopic composition The effects of CO2 air parcel mixing on isotopic composition have specific relevance for ∆47 in Chapter 2, so an example follows below. In general, mixing of two or more reservoirs of CO2 is linear in δ 13 C, δ 18 O, and δ 17 O (the mixture has δ -value in between that of the two mixing end-members) because the references against which they are compared are constant (see Eqs. 1.5 and 1.6) Mixing of two reservoirs with the same ∆47 and differing bulk isotope distributions, however, can yield ∆47 values in the mixture different from those in the endmember gases. This nonlinear dependence of ∆47 on mixing arises because both R47 sample and the reference against which it is measured (R47 stochastic ) change upon mixing; the reference is defined by, and therefore varies with, the bulk stable isotope ratios of that mixture. In contrast, the references used in bulk stable isotope measurements are external standards whose values are constant (e.g., VSMOW), so the bulk isotope ratios vary linearly with mixing. The degree of nonlinearity in ∆47 is a function of the differences in bulk isotopic composition between the mixing end-member reservoirs and their mixing fractions [Affek and Eiler, 2006; Eiler and Schauble, 2004]. Because ∆47 depends non-linearly on mixing fraction, even for two CO2 reservoirs with similar ∆47 [Affek and Eiler, 2006; Eiler and Schauble, 2004], mixing relationships are often counterintuitive. An illustrative example is shown in Figure 2.9: The two mixing endmembers (given as the bottom-left and bottom-right corners) have different initial δ 18 O and δ 17 O values, though both have δ 13 C = –8‰ and ∆47 = 0.92‰. The concentration of 47 CO2 (i.e., R47 mix ) varies linearly with mixing fraction, but the stochastic distribution for 47 CO2 molecules also changes, varying as ∼2R13 R18 . Consequently, mixing these two isotopically dissimilar CO2 reservoirs yields a ∆47mix > 0.92‰ despite each reservoir being initially at ∆47 = 0.92‰. This type of relationship is general, and so holds for all ∆47 ; the sign and magnitude of the resulting ∆47 change will depend on the end-member bulk and clumped isotope compositions. 49 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.9: How mixing two arbitrary reservoirs of CO2 can be nonlinear in ∆47 . The resulting mixture is more enriched in 47 CO2 relative to its stochastic distribution, as compared to either of the mixing end-members. The isotopic compositions used in this plot are for illustration purposes only; qualitatively similar effects will apply for all mixing relationships. 50 L. Y. Yeung Oxygen isotope exchange reactions of CO2 2.B Practical considerations 2.B.1 IRMS long-term signal stability Chapter 2 ∆47 measurements currently take ∼4 hours of instrument averaging time per sample analysis. We examined the stability and accuracy of our IRMS system over this time period by using a modified form of the Allan variance technique, originally developed to characterize ultrastable oscillators [Allan, 1987]. Instead of using time as the independent variable, here we use individual IRMS acquisitions x: 2 σAllan (x) = 1 [hxii+1 − hxii ]2 2(N − 1) ∑ i (2.9) Data are first binned into N bins (each consisting of one or more acquisitions), and the average of each bin, hxii , is taken. The difference between adjacent bins is squared and then summed before being normalized to compute the Allan variance. For example, a data set with six elements [x1 , x2 , x3 , x4 , x5 , x6 ] will produce three values of Allan variance corresponding to bins of one ([x1 ], [x2 ], [x3 ], [x4 ], [x5 ], [x6 ]), two ([x1 , x2 ], [x3 , x4 ], [x5 , x6 ]) and three ([x1 , x2 , x3 ] and [x4 , x5 , x6 ]) elements each. The maximum bin size is therefore half the total number of elements in a data set. Plotting Allan variance versus bin size, then, conveniently presents both noise- and driftrelated effects on single plot. An example of the ∆47 Allan variance for a relatively longduration analysis, consisting of 40 acquisitions of 80 s sample integration each (ten 8 s cycles), is shown in Figure 2.10. An ideal statistical-noise-limited measurement, for which long-term drifts are negligible, will display a power-law relationship σ 2 = Cxα in the Allan variance plot, where α = –0.5, reflecting the Poisson statistics governing the precision of the overall measurement. In contrast, a measurement dominated by long-term, correlated random-walk drifts will have α = 0.5. Consequently, the optimum number of measurements to average together in a given analysis (i.e., the optimum bin size) will occur near where the Allan variance reaches a minimum, i.e. where dα/dx = 0. For our instrument, measurements seem to be dominated by statistical noise for N < 10 acquisitions, with only a small contribution from long-term drift. The variability of σ 2 appears to increase for 51 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.10: Allan-variance plot of ∆47 over 40 IRMS acquisitions. A power-law regression is shown for bins up to nine acquisitions. α = –0.47 was obtained, indicating that Poisson statistics, not long-term drifts, dominate the uncertainties in the measured ∆47 value in this range. measurements made in excess of nine acquisitions (see Figure 2.10), although we attribute this to the smaller number of bins with greater than nine acquisitions contributing to the Allan variance calculation. More precise values of the Allan variance with these numbers of acquisitions would require a more sustained analytical run by several factors in time. Nevertheless, the ideal precision that should be attainable on a single gas run for measurements that are clearly dominated by statistical noise (nine acquisitions, or 720-s counting time) at the optimal voltage (16 V) is 0.013‰. 2.B.2 IRMS vs. optical methods The best high-precision isotope-ratio measurements have been made routinely on gassource mass spectrometers based on Nier’s original 1947 design [Nier, 1947]. These instruments are fundamentally sensitive to that which makes stable isotopes unique — their mass — so IRMS continues to be the technique-of-choice used for stable isotope abundance measurements. It achieves high precision over a large dynamic range by utilizing multiple Faraday cups with differing amplifier gains (over a factor of 3000 for ∆47 measurements) 52 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 and rapid sample-standard comparison. However, the relatively poor mass-resolving power (M/∆M ∼ 500) that comes as a consequence of using a magnetic sector and high-sensitivity, electrically stable Faraday-cup detectors leads to well known isobaric (same-nominal-mass) interferences, e.g., between 13 CO2 and 16 O12 C17 O at m/z = 45. In ‘clumped’ isotopologue measurements of CO2 , isobars and other impurities (e.g., N2 O, hydrocarbons) are especially important given the low absolute abundance of m/z = 47 isotopologues. A new concern also arises in the study of ‘clumped’ isotopologues: ion recombination after electron-impact ionization source can alter the measured distribution of stable isotopes vs. that present in the original sample. High-resolution and thermal-ionization mass-spectrometric techniques can potentially address these uncertainties, but none have yet demonstrated the precision and stability necessary for ∆47 measurements. Spectroscopic techniques, however, show great promise for measuring stable isotopologue abundances in natural samples because they are non-destructive, sensitive to both mass and molecular symmetry, and field-deployable. These characteristics are particularly desirable for studying the stable isotope distribution in atmospheric gases, and how they evolve over time. The author has had some experience with these techniques so the following discussion represents a synthesis of his experience. While most examples relate to CO2 , the general considerations presented here should be applicable to spectroscopic stable isotope measurements of other species. More general and thorough reviews of the literature have been published (e.g., Kerstel [2004]; Kerstel and Gianfrani [2008]), so the references herein are exemplary rather than comprehensive. Three main instrumental requirements for highly precise optical measurements of rare and/or ‘clumped’ isotopologues near natural isotopic abundance are apparent: absolute sensitivity, dynamic range, and long-term signal stability. A more subtle problem is the selection of spectral region; the spectral absorption scales not only with analyte concentration, but also the optical pathlength and the size of the transition dipole (i.e., the absorption line strength, S, for the transition). In addition, spectral overlap between isotopologues and also from contaminants will lead to systematic errors. The type of spectroscopic technique, then, will depend on the analyte identity and spectral region. For instance, Tuzson et al. 53 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 [2008] used the strong CO2 lines (S ∼ 10−18 cm molecule−1 ) near 2300 cm−1 and a multipass direct absorption cell [Herriott et al., 1964] to measure δ 13 C and δ 18 O with better than 0.1‰ precision (100-s averaging). The authors utilized that region because the transitions for 12 C16 O2 , 13 C16 O2 , and 16 O12 C18 O were of nearly equal strengths. Bergamaschi et al. [1994] made similar line choices for δ 13 C and δ D measurements in CH4 . McManus et al. [2002] surmounted the dynamic range problem for their CO2 isotopologue measurements by designing an optical cell with differential absorption pathlengths for each isotopologue, allowing CO2 lines differing in intensity by several orders of magnitude to be measured precisely. In both cases, long-term drifts (e.g., temperature, laser power, frequency jitter etc.) were accounted for by simultaneous measurement of a reference gas. Other important variables to consider are sample temperature stability and spectral line function. Bergamaschi et al. [1994] reported an approximate sensitivity of the measured δ -value and temperature (T ) in per-mil units: ∆δ ∆E × 1000 ≈ ∆T kT 2 (2.10) where k is Boltzmann’s constant and ∆E is the difference in lower-state energies of the corresponding transitions. It is derived from the Taylor series expansion of a normal (Gaussian) distribution [Schupp, 1992]. Empirically, this translates to ± 5‰ K−1 for bulk stable isotope measurements of H2 O and CO2 [Kerstel and Gianfrani, 2008], so a temperature stability between the reference gas and the sample of 50 mK would yield temperature-induced errors of 0.1‰. Kerstel and Gianfrani [2008] also make the argument that measurement of peak intensities is sufficient so long as the lineshape functions are the same between the sample and standard transitions. ‘Clumped’ isotope measurements present a new set of concerns due to the more stringent technical demands, e.g., measuring a signal 4.5 × 10−5 with 0.005‰ precision for ∆47 based carbonate thermometry [Huntington et al., 2009]. At present, high-precision IRMS measurements of ∆47 involve multiple comparisons between the sample CO2 gas, bulk stable isotope working standards, and ‘clumped’ stable isotope standards (CO2 with a stochastic distribution of isotopologues). Any spectroscopic technique will require similar calibrations 54 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 because the instrument response, in general, will not be sufficiently linear over such a large range in concentration. For instance, the required linear dynamic range for rovibrational transitions of 12 C16 O2 and 16 O13 C18 O with identical v and J (absolute sensitivity concerns notwithstanding) is ≥109 . Photoacoustic methods are capable of this dynamic range, in principle, but previous attempts to make high-precision isotopic measurements have been limited by fluctuations in pump laser power [Samura et al., 2002]. On the other hand, if a convenient spectral window is found such that line strengths of the dominant and minor isotopologues are similar, the temperature sensitivity will be large (e.g., due to large differences in the lower-state energies). From a practical perspective, the line strength of the minor isotopologue will dictate the choice of method; for instance, the strongest 16 O13 C18 O transition in the mid-IR has a line intensity S ∼ 10−23 cm molecule−1 , which is out of range for all but the most sensitive spectroscopic techniques. Of the high-sensitivity optical techniques, cavity ringdown spectroscopy (CRDS; O’Keefe and Deacon [1988]) with frequency-axis stabilization and single-mode operation (FS-CRDS; [Hodges et al., 2004]) shows the most promise, in this author’s opinion. A key feature in FS-CRDS is its ability to average spectra on the timescales of hours; the utility of other ultrasensitive methods, such as the shot-noiselimited NICE-OHMS technique (noise-immune, cavity-enhanced optical heterodyne molecular spectroscopy) [Ye et al., 1998], have been ultimately limited by technical pitfalls and long-term drifts [Foltynowicz et al., 2008]. In contrast, FS-CRDS can be averaged continuously for nearly 10 hours to achieve a signal-to-noise ratio (SNR) of 18,000 (i.e., 0.6‰ precision) on a single line of intensity S = 1 × 10−24 cm molecule−1 at 0.5 Torr [Long et al., 2009]. Higher SNRs may be possible with the implementation of single-mode optical feedback [Motto-Ros et al., 2008], optoelectronic laser-locking [Drever et al., 1983], or in combination with rapid (kHz) sample-background ringdown comparison [Ye and Hall, 2000]; increasing sample concentration will also improve the SNR, but the dynamic range of the instrument will place an upper limit on the maximum line strength. The choice of lineshape theory used to obtain the integrated intensity might also be important [Lisak et al., 2006, 2009], as the integrated intensity is a more robust measurement of isotopic abundance than 55 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 peak height, which increases nonlinearly with gas pressure. At present, IRMS is the only practical method for measuring ‘clumped’ isotopologue abundances in in CO2 with precisions better than 0.1‰. Spectroscopic measurements for CO2 will be best in the mid-IR region, where the rovibrational transitions are strongest (S16 O13 C18 O ∼ 10−23 cm molecule−1 ); single-mode quantum-cascade lasers with ≥ 5 mW power are becoming widely available in that region. Another possibility for CO2 is the 2-µm region, where the strongest 16 O13 C18 O line strength is S16 O13 C18 O ∼ 3 × 10−26 cm molecule−1 (4826.05 cm−1 ); analysis time will be increased accordingly. The NICE-OHMS method is capable of reducing analysis times significantly, in principle, because it has demonstrated a shot-noise-limited sensitivity for strong laser sources (e.g., SNR = 7700 in 1s for S = 1 × 10−23 cm molecule−1 using a 5 mW Nd:YAG) [Ye and Lynn, 2003; Ye et al., 1998]. However, technical challenges such as long-term temperature and frequency stability must be addressed. While examining the possibility for measuring ‘clumped’ CO2 isotopologues spectroscopically is useful for illustrating the general principles involved, this approach will ultimately be the most useful for other species of atmospheric and geochemical interest. For instance, isotopic abundances in SO2 are canonically difficult to measure due to its polarity [Gao and Thiemens, 1991, 1993]; high-precision IRMS systems rely on a viscous-flow injection into the ionization region, and high-polarity gases such as SO2 often display a pronounced ‘memory’ effect that limits measurement precision and reproducibility [Ono et al., 2006]. SO2 lines in the mid-IR (∼2500 cm−1 ) are of comparable strength to those of CO2 in the 2-µm region (see above), so ‘clumped’ isotopologue measurements of SO2 may be possible, with long averaging times, in the near future. These measurements have the potential to establish a link between the ancient atmosphere and the geologic record. For instance, Lyons [2009] has proposed that the unique sulfur and oxygen isotope composition of Archaean Fig-tree barites [Bao et al., 2007] may reflect gas-phase SO2 –H2 O isotope exchange reactions; ‘clumped’ isotope analysis would place additional constraints on the origins of these and other barites, which contain information about the sulfur and oxygen cycles, atmospheric composition, and climate of the ancient past. 56 L. Y. Yeung 2.C Oxygen isotope exchange reactions of CO2 Chapter 2 Low-temperature cell for 13 C/12 C KIE experiments For the low-temperature 13 C/12 C KIE experiments, the quartz reaction chamber (filled with N2 O, CO2 , and He) was placed inside a cooling assembly within a conflat vacuum chamber. The vacuum chamber was first pumped down to ∼20 – 50 mTorr, and then liquid N2 coolant (∆Hvap = 1.33 kcal mol−1 ) was added through a feedthrough at the top of the chamber. The liquid N2 cooled a series of metal (“conduction” and “transfer”) blocks, which, in turn, cooled the quartz reaction cell along its entire length. Temperature was monitored using a standard type-K thermocouple; active temperature control was possible, though it was not necessary to achieve temperatures near 230 ± 1 K when the liquid N2 was poured into the feedthrough. The cooling assembly was designed to fit inside a spare ∼27 × 27 × 21 cm (l × w × h, interior dimensions) conflat chamber with a 9.5-cm ID (see Figures 2.11, 2.12, and 2.13). Experimental and spatial constraints dictated the design parameters, and the resulting assembly had little flexibility. Use of 193-nm laser radiation to photolyze N2 O meant that quartz (UV-grade fused silica) windows were the most affordable and robust window material; MgF2 windows can provide ∼10% greater transmission at 193 nm, but quartz was chosen because it was cheaper and could be bonded with a quartz tube to make a monolithic, leak-tight reaction chamber without need for adhesives. During an experiment, the reaction chamber was inserted directly into the oxygen-free, high conductivity (OFHC) copper tube (2.14). This tube was fastened to the “conduction block” (Figure 2.15), which was itself attached to the OFHC copper “heat-transfer block” by a countersunk screw on the rounded underside of the conduction block. A second heat-transfer block (Figure 2.17) was sandwiched between the heat-transfer block and the connection to the liquid N2 feedthrough (Figure 2.18); this block had a relatively small surface area and was machined out of brass (120 W m−1 K−1 vs. 401 W m−1 K−1 for copper at 300 K) to retard heat transfer from the liquid N2 to the reaction cell. The second heat-transfer block also had a hole drilled through the center so a heating resistor could be inserted, if necessary, to control the temperature in future experiments. All components were mated with a thin layer of Apiezon “N” grease; this material was 57 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.11: Schematic of conflat chamber used for low-temperature 13 C/12 C KIE experiments. Figure 2.12: Photograph of conflat chamber used for low-temperature 13 C/12 C KIE experiments. 58 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 chosen over other compounds because of its ability to perform at low temperatures (down to liquid He), low coefficient of thermal expansion (≤ 10−4 K−1 ) and minimal thermal creep. However, it has a very low thermal conductivity (0.1 – 0.2 W m−1 K−1 ), which slowed the cooling process. Typically, the assembly took 40 – 60 min to cool from 300 K to 229 K. While higher-efficiency thermal compounds would have accelerated cooling of the reaction chamber, Apiezon “N” was sufficient to achieve stable temperatures above 200 K. Small modifications were made to the cooling assembly for planned O(1 D) + CH4 and OH + CH4 KIE experiments (see Figure 2.19). Because the target temperatures for those experiments are 140 K ≤ T ≤ 200 K, the two “heat-transfer” blocks were combined into a single OFHC copper heat-transfer block with a larger contact area with the existing “conduction block” (see Figures 2.20 and 2.21). The primary cooling block was smoothed (the shallow channel removed) to mate well with the new conduction block. Last, metal-tometal mating surfaces were cleaned and the Apiezon “N” grease replaced with a thermal paste containing silver particles (thermal conductivity ∼ 9 W m−1 K−1 ). With this new assembly and the pressurized delivery of liquid N2 from a free-standing dewar into the feedthrough, the quartz reaction cell was cooled to temperatures of ∼140 K within 10 min. Temperature control electronics are currently being designed. 59 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Figure 2.13: Cold cell assembly. Figure 2.14: Machining diagram for the OFHC copper tube. 60 Chapter 2 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.15: Machining diagram for the OFHC copper conduction block. 61 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.16: Machining diagram for the OFHC copper heat transfer block. Figure 2.17: Machining diagram for the brass heat transfer block. 62 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.18: Machining diagram for the OFHC copper connection to the liquid N2 feedthrough. 63 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.19: Cold cell assembly for O(1 D), OH + CH4 KIE experiments. Figure 2.20: Machining diagram illustrating the modifications made to the conduction block for O(1 D), OH + CH4 KIE experiments. 64 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.21: Machining diagram for the OFHC copper heat transfer block designed for O(1 D), OH + CH4 KIE experiments. 65 L. Y. Yeung Oxygen isotope exchange reactions of CO2 2.D MATLAB code for hard-sphere collision model 2.D.1 montecarlo.m Chapter 2 % Program for calculating 18O(1D)−CO2 collision energy in experiments clear x y z j v1i v2i r; points=50000; % number of points per collision T=300; % temperature in K m1=18; % mass of O(1D) m2=4; % mass of buffer gas (He: 4, N2: 28) mCO2=44; ET2lab=18.2; %8.6 for O3 photolysis at 248 nm % Etrans (kcal/mol) in the Lab frame Equil=(3/2)*8.314472/4.184/1000*T; % Equipartition energy vOpeak=sqrt((ET2lab*1000*4.184*2)/(m1/1000)); % O(1D) atom velocity vMreduced=vOpeak/sqrt((Equil*1000*4.184*2)/(m2/1000)); % buffer gas velocity in units of O(1D) velocity %vMreducedCO2=vOpeak/sqrt((Equil*1000*4.18*2)/(mCO2/1000)); ncolltot=200; % Number of collisions zz=zeros(points,ncolltot); % distribution of final O(1D) velocities zzz=zeros(points,1); % distribution of initial O(1D) velocities CO2=zeros(points,ncolltot); % distribution of collision energies with CO2 dist=zeros(points,ncolltot); % distribution of buffer gas velocities PM=97; %1−380e−6 for 'stratospheric' % pressure of buffer gas in Torr PCO2=3; %380e−6 for 'stratospheric' % pressure of CO2 in Torr Pcoll=PCO2/(PCO2+PM); % ratio of CO2 to buffer gas (reaction probability per collision) for l=1:ncolltot nPcoll(l)= Pcoll*(1−Pcoll)ˆ(l−1); % multiplied by (1−(3.1e−11/1e−10))ˆ(l−1) for 'stratospheric' % fraction of O(1D) that reacts at each collision end digits(10); nPcoll=vpa(nPcoll); for j=1:points ncoll=1; v1i=randn*exp(−1.5)+vMreduced; % pick a random v for O(1D) from a gaussian distribution about vMreduced zzz(j)=v1i; % record the velocity in a matrix 66 L. Y. Yeung Oxygen isotope exchange reactions of CO2 theta1i=rand*3.14159265359; % pick a random azimuthal angle between 0 and pi for O(1D) phi1i=rand*2*3.14159265359; % pick a random azimuthal angle between 0 and 2pi for O(1D) v2i=randn;%metropolis([v2i,5]); theta2i=rand*3.14159265359; % pick a random azimuthal angle between 0 and pi for M phi2i=rand*2*3.14159265359; % pick a random azimuthal angle between 0 and 2pi for M while (phi1i < phi2i) phi2i=rand*2*3.14159265359; % prevents imaginary results in scatter function end impact=randˆ2; % pick a random (b/bmax) with probability proportional to itself omega=rand*3.14159265359; % pick a random azimuthal angle for b between 0 and pi while (ncoll ≤ ncolltot) % calculate O(1D) trajectory for n collisions vrel=sqrt((v1i*sqrt(mCO2/m2))ˆ2+v2iˆ2−2*v1i*v2i*(sin(theta1i)* sin(theta2i)*cos(phi1i−phi2i)+cos(theta1i)*cos(theta2i))); % calculating initial relative velocity CO2(j,ncoll)=((1/2)*((mCO2*m1/(mCO2+m1))/1000)*(vrel* sqrt((Equil*1000*4.184*2)/(mCO2/1000)))ˆ2)/(4.184*1000); % calculate initial collision energy w/CO2 v1f=scatter(m1, m2, v1i, theta1i, phi1i, v2i, theta2i, phi2i, impact, omega); % calculate final velocity after one more collision zz(j,ncoll)=real(v1f); % record the final velocity dist(j,ncoll)=v2i; % record in initial velocity of M v1i=real(v1f); % reset initial velocity as the final velocity after a collision theta1i=rand*3.14159265359; % pick a new azimuthal angle for O(1D) phi1i=rand*2*3.14159265359; % pick a new polar angle for O(1D) v2i=randn; % pick a new velocity for M theta2i=rand*3.14159265359; % pick a new azimuthal angle for M phi2i=rand*2*3.14159265359; % pick a new polar angle for M while (phi1i < phi2i) % prevents imaginary results in scatter program phi2i=rand*2*3.14159265359; end impact=randˆ2; % pick a new impact parameter (b/bmax) omega=rand*3.14159265359; % pick a new scattering angle ncoll=ncoll+1; % rinse, repeat end end bins=250; % number of bins 67 Chapter 2 L. Y. Yeung Oxygen isotope exchange reactions of CO2 upperlimit=25; % range, 0 − upperlimit binsvector=zeros(1,upperlimit); % generating empty histogram bin vector to improve performance for c=1:bins binsvector(1,c)=(upperlimit/bins)*c; % generating histogram bins end [Ppercollision,bin]=histc(CO2,binsvector); % generating binned histogram matrix of CO2, Ppercollision for k=1:ncolltot % each column is reactive probability distribution at that collision Ppercollision(:,k)=Ppercollision(:,k)*double(nPcoll(k)); % each column is weighted by the fraction of remaining O(1D) atoms end Ecollavg=sum(CO2)/points; % average collision energy at each collision number dlmwrite('v1i.csv',zzz); % write matrix of initial O(1D) velocities to file, v1i.csv dlmwrite('v1f.csv',zz); % write matrix of final O(1D) velocities to file, v1f.csv dlmwrite('Ecollpercollision.csv',CO2); % write matrix of per−collision collision energies to file dlmwrite('Ppercollision.csv',Ppercollision); % write binned histogram matrix of CO2 to file, Ppercollision.csv 2.D.2 scatter.m % Function solving the two−particle scattering problem function v1f=scatter(m1, m2, v1i, theta1i, phi1i, v2i, theta2i, phi2i, impact, omega) vrel=sqrt(v1iˆ2+v2iˆ2−2*v1i*v2i*(sin(theta1i)*sin(theta2i)* cos(phi1i−phi2i)+cos(theta1i)*cos(theta2i))); % relative veocity calculation v1c=(m2*vrel)/(m1+m2); % v1 (O(1D)) in the COM frame v2c=(m1*vrel)/(m1+m2); % v2 (M) in the COM frame vcm=sqrt(m1ˆ2*v1iˆ2+m2ˆ2*v2iˆ2+2*m1*m2*v1i*v2i*(sin(theta1i)* sin(theta2i)*cos(phi1i−phi2i)+cos(theta1i)*cos(theta2i)))/(m1+m2); % velocity of the COM thetacm=acos((m1*v1i*cos(theta1i)+m2*v2i*cos(theta2i))/((m1+m2)*vcm)); % azimuthal angle in the COM frame phicm=acos((m1*v1i*sin(theta1i)*cos(phi1i)+m2*v2i*sin(theta2i)* cos(phi2i))/((m1+m2)*vcm*sin(thetacm))); % polar angle in the COM frame alpha=acos((v1iˆ2−(vcmˆ2+v1cˆ2))/(2*vcm*v1c)); % azimuthal scattering angle in the COM frame deflect=2*acos(impact); % polar scattering angle in the COM frame l=v1c*(cos(deflect)*cos(alpha)−sin(deflect)*sin(alpha)*cos(omega)); v1f=sqrt((vcm+l)ˆ2+v1cˆ2−lˆ2); 68 Chapter 2 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Chapter 3 A hyperthermal O-atom exchange reaction, O2 + CO2 Adapted from Yeung, L. Y., M. Okumura, J. T. Paci, G. C. Schatz, J. Zhang, and T. K. Minton (2009), Hyperthermal O-Atom Exchange Reaction O2 + CO2 through a CO4 Intermediate, J. Am. Chem. Soc., 131(39): 13,940–13,942. ©2009 American Chemical Society Publications. 69 L. Y. Yeung 3.1 Oxygen isotope exchange reactions of CO2 Chapter 3 Abstract O2 and CO2 do not react under ordinary conditions, owing to the thermodynamic stability of CO2 and the large activation energy required for multiple double-bond cleavage. We present evidence for a gas-phase O-atom exchange reaction between neutral O2 and CO2 at elevated collision energies (≈ 160 kcal mol−1 ) from crossedmolecular-beams experiments. Products were scattered mainly in the forward direction, i.e., in the initial direction of the hyperthermal oxygen beam in the centerof-mass (c.m.) frame, with 16% of the available energy in translation, on average. CCSD(T)/aug-cc-pVTZ calculations demonstrate that isotope exchange can occur on the ground triplet potential energy surface through a short-lived CO4 intermediate that isomerizes via a symmetric CO4 transition state containing a bridging oxygen atom. We propose a plausible adiabatic mechanism for this reaction supported by additional spin-density calculations. 70 L. Y. Yeung 3.2 Oxygen isotope exchange reactions of CO2 Chapter 3 Introduction O2 and CO2 do not react under ordinary conditions. This can be attributed to the large activation energy for multiple double-bond cleavage, as Dixon illustrated in his early experiments in which dry CO–O2 –CO2 mixtures “did not explode” when subjected to a spark discharge [Dixon, 1886]. Otomo et al. [2000] later reported a reaction of CO2 and electronically excited O2 ∗ when they observed O3 products after irradiating super- and subcritical O2 /CO2 mixtures with UV light. While investigating the isotope exchange reaction 16 O(3 P) +12 C18 O2 →18 O +16 O12 C18 O (3.1) at hyperthermal collision energies in a crossed-molecular-beams experiment, we found evidence for the gas-phase oxygen isotope exchange reaction 16 O2 +12 C18 O2 →18 O16 O +16 O12 C18 O (3.2) of ground-state reactants at high collision energies (∼160 kcal mol−1 ). Our observations on the dynamics of this reaction, taken together with ab initio calculations of stationary points on the lowest triplet potential energy surface (PES), suggest a plausible adiabatic mechanism for the reaction of O2 with CO2 through a CO4 transition complex. 3.3 Experimental studies 3.3.1 Methods Crossed-molecular-beam experiments were performed with a hyperthermal oxygen source containing ∼87% O(3 P) and ∼13% O2 (3 Σ− g ) [Brunsvold et al., 2007, 2008; Garton et al., 2006, 2009]. A diagram of the experimental setup, configured for 16 O(3 P) + 12 C18 O 2 collisions, is shown in Figure 3.1. A pulsed beam of 16 O(3 P) and 16 O2 (3 Σ+ g ; at an unknown vibrational temperature) was generated by laser-induced detonation of 16 O2 using a high-energy CO2 TEA laser (6 – 7 J pulse−1 ) operating at a pulse repetition rate of 2 Hz. Though initially broad in velocity distribution (6 – 9 km s−1 ), a portion of the overall 71 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 beam was velocity-selected for the scattering experiments using a synchronized chopper wheel operating at 300 Hz. This velocity-selected beam was crossed, at a nominal angle of 90◦ , with a pulsed supersonic expansion of 98% 12 C18 O2 gas (2% 16 O12 C18 O; Spectra Gas). The molecular beams and scattered products were detected with a rotatable quadrupole mass spectrometer with electron-bombardment ionization [Brink, 1966] at 160 eV and a Daly-type ion counter [Daly, 1960]. 12 C18 O2 and 16 O12 C18 O products were detected at m/z 16 12 18 + = 48 (12 C18 O+ 2 ) and 46 ( O C O ), respectively, with a rotatable mass spectrometer that collected number density distributions as a function of arrival time, N(t), at a given laboratory angle, Θ, using a multi-channel plate (MCP). Here, Θ is defined as the angle at which the 16 O12 C18 O scatters with respect to the direction of the reagent oxygen beam (i.e., Θ = 0◦ ). Time-of-flight (TOF) distributions for 16 O(3 P), 16 O2 , 12 C18 O2 , and 16 O12 C18 O were collected over a range of laboratory angles (6◦ – 54◦ ); at each angle, the TOF distribution for the 33.7-cm distance between the beam interaction region to the ionizer was integrated to give a laboratory angular distribution, N(Θ). A forward-convolution method was used to derive the center-of-mass (c.m.) translational energy P(ET ) and angular T(θ c.m. ) distributions from the laboratory N(t) and N(Θ) distributions [Lee, 1988], where θ c.m. is the angle at which 16 O12 C18 O scatters with respect to the reagent oxygen direction in the c.m. frame. The canonical Newton diagrams used in this analysis are shown in Figure 3.2. Figure 3.1: Crossed-molecular-beam apparatus with hyperthermal oxygen source. 72 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.2: Canonical Newton diagram for hyperthermal 16 O2 + 12 C18 O2 collisions. The Newton circles represent the maximum recoil velocities of the products. The hyperthermal oxygen beam was generated by laser detonation of a pulsed expansion of O2 gas with 500 psig stagnation pressure using a source based on the design of Caledonia et al. [1987]. 174 µs after the pulsed valve is triggered, the CO2 laser is fired; the laser pulse passed through an antireflection-coated ZnSe window in to the source chamber, whereupon it was reflected back towards the gold-plated, water-cooled copper nozzle with a 1 m radius concave gold mirror. The focused laser pulse initiates a breakdown of the O2 gas and heats the resulting plasma to > 20,000 K, which accelerates both the atomic and molecular oxygen fractions of the pulsed beam to 6 – 9 km s−1 . Use of a conical nozzle allowed for efficient ion-electron recombination and inefficient atom-atom and atom-molecule recombination as the plasma expanded and cooled. The resulting gas pulse was collimated by a 1 cm diameter aperture located 80 cm downstream of the inlet nozzle into a differentially pumped region (10−5 – 10−6 Torr), after which it passed through a 1.2-mm-diameter skimmer 16 cm further downstream. The beam interaction region was an additional 3 cm downstream in the main chamber (2 × 10−7 Torr), a total distance of 99 cm from the inlet nozzle. For velocity selection within the hyperthermal oxygen beam, a chopper wheel running at 300 Hz (synchronized with the 2-Hz laser pulses) was placed inside the main scattering 73 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 chamber, just downstream of the skimmer. Three equally-spaced slots (1.5 mm wide) of the chopper wheel pass over an LED/photodiode assembly a quarter-turn before each slot enters the beam axis, generating a 900 Hz (3 × 300 Hz) train of pulses. These chopper wheel pulses are sent to a digital delay generator and used as references for triggering the O2 gas pulses. The time delay between the chopper wheel pulse and the O2 pulse determined the portion of the overall hyperthermal oxygen beam allowed to pass through into the interaction region. We characterized the velocity distribution of the hyperthermal oxygen beam under two conditions: on axis (Θ = 0◦ ) with a small aperture (∼125 µm diameter) to obtain the peak of the distribution, and off axis (Θ = 3◦ ) with a large aperture (4 mm × 4 mm) to obtain the width of the distribution. For the on-axis configuration, a 2 mA emission current at the ionizer and a –18 kV potential at the secondary emitting electrode of the Daly ion counter was used. For the off-axis configuration, a 10 mA emission current at the ionizer and a –30 kV potential at the secondary emitting electrode was used. Laboratory TOF distributions under both conditions were measured, for both 16 O and 16 O2 , to determine the laboratory-frame velocities and translational energy distributions for the hyperthermal oxygen beam. In these experiments, the average velocity of the hyperthermal oxygen beam was thus determined to be 8262 ± 450 m s−1 (i.e., 900 m s−1 full width at half maximum; FWHM), which corresponds to average translational energies hET i = 130.5 ± 14 kcal mol−1 and 261.0 ± 28 kcal mol−1 FWHM for 16 O(3 P) and 16 O2 , respectively (see Figure 3.3). The relative amounts of atomic (∼87%) and molecular (∼13%) oxygen were determined by integrating the TOF distributions at m/z = 16 (16 O+ ) and 32 (16 O2 + ) at Θ = 0◦ and correcting for O2 fragmentation (11% of the m/z = 32 signal) in the electron-bombardment ionization region. A pulsed supersonic expansion of 12 C18 O2 was generated using a piezoelectric pulsed general valve with a 1300-Torr stagnation pressure. The expansion passed through a 2 mm diameter skimmer (9.2 cm from the nozzle) into a differential pumping region, and then through a 2.5 mm diameter (2.8 cm downstream of the skimmer) aperture into the main scattering chamber. The distance from this aperture to the interaction region was 1.5 cm. 74 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.3: Velocity distribution of hyperthermal oxygen beam. The velocity distribution of the 12 C18 O2 beam was not measured directly, and instead was determined iteratively by first estimating the terminal velocity of the supersonic expansion [Lee, 1988] and then fitting the 12 C18 O2 velocity to the value that yielded the best Newton circle for non-reactively scattered O-atoms while keeping the measured O-atom velocity distribution fixed at its measured values. This contributes some uncertainty to the measured TOF distributions because the 12 C18 O2 beam velocity is likely only accurate to ±10%. However, because the magnitude of the hyperthermal oxygen beam velocity at the interaction region was ten times that of the 12 C18 O2 beam, and its FWHM was also 4 – 5 times that of the 12 C18 O2 beam, uncertainties in the “time-zero” of the hyperthermal oxygen source dominated the overall uncertainty in the measured translational energy distributions. Laboratory TOF product distributions were measured every 2◦ between Θ = 6◦ – 54◦ . Scattered product TOF distributions were collected for 200 beam pulses for for m/z = 16 (16 O+ ) and 32 (16 O2 + ), for 1000 beam pulses for m/z = 46 (16 O12 C18 O+ ), and for 500 beam pulses for m/z = 48 (12 C18 O2 + ). Dwell time for each channel at the MCP was 1 µs. At a representative laboratory angle of 10◦ , integrated count rates were 1.1 × 107 s−1 for m/z = 16, 1.3 × 107 s−1 for m/z = 32, 1.8 × 105 s−1 for m/z = 46 , and 4.2 × 106 s−1 for m/z 75 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 = 48. Raw flight times were converted to flight times over the 33.7 cm distance between the interaction region and the electron-bombardment ionizer by subtracting the O2 triggerpulse-to-laser-fire delay time (174 µs), an electronic-latency delay time (3 µs), the oxygen flight time from the nozzle to the interaction region (120 µs, corresponding to the average velocity of the hyperthermal oxygen beam), and finally the ion flight time between the 1 ionizer and the Daly ion counter. The ion flight time is given by α(m/z) 2 , where α = 2.44 in these experiments, determined by comparing the relative arrival times of hyperthermal 16 O and 16 O at the detector [Garton et al., 2006]. Some uncertainty arises in the product 2 times-of-flight because the exact time- and point-of-origin of the hyperthermal oxygen beam are not well determined; we estimate this uncertainty to be ∼2 µs because the laser pulse width in the hyperthermal oxygen source could be as long as 1 µs (a 100 ns-wide peak with a slow tail). Two signal corrections were made before data analysis. First, we corrected for beam divergence at Θ = 6◦ – 16◦ . The divergent intensity with the 12 C18 O2 beam turned off was measured by obtaining TOF distributions at m/z = 16 and 32 from Θ = 6◦ – 16◦ . These TOF distributions were then scaled and subtracted from the corresponding experimental TOF distributions at m/z = 16 and 32 that had the 12 C18 O2 beam turned on. Uncertainties in the inelastic and reactive scattering signals due to collisions of the divergent hyperthermal oxygen could not quantified, however; they were instead considered in the analysis of the laboratory data, where collisions at crossing angles of 88◦ , 89◦ , 90◦ , 91◦ , and 92◦ were included during forward-convolution fitting. Adding more crossing angles did not affect the forward-convolution fits significantly. Second, we verified that the 12 C18 O2 beam contained 2% 16 O12 C18 O using the instrument’s mass spectrometer. Thus, 2% of the inelastic scattering signal (m/z = 48) at each laboratory angle (Θ = 6◦ – 54◦ ) was subtracted from raw m/z = 46 (16 O12 C18 O+ ) TOF distributions to obtain reactive-scattering-only distributions. A forward-convolution method was employed to perform the laboratory-to-c.m. frame coordinate transformation [Lee, 1988] of the data using the MSU XBEAM program (Version 6). Trial P(ET ) and T(θ c.m. ) distributions were used to simulate the laboratory-frame TOF distributions using the following relationship derived from the Jacobian transformation: 76 L. Y. Yeung Oxygen isotope exchange reactions of CO2 N(t, Θ) α l3 P(ET )T (θc.m. ) ut 3 Chapter 3 (3.3) where l and t are the distance and flight time, respectively, from the interaction region to the ionizer, and u is the product velocity in the c.m. frame. During the fitting process, 12 C18 O2 was assumed to have a single-valued velocity, 800 m s−1 , because the large magnitude and width of the hyperthermal oxygen beam velocity distribution is principally responsible (i.e., it contributed ≥ 98% of the uncertainty in the c.m. collision energy; see above) for the observed width of the laboratory TOF distributions and the c.m. translational energy distributions. The width of the hyperthermal beam velocity distribution was fit by a Gaussian function centered at 8262 m s−1 and a FWHM of 900 m s−1 , which was used during data analysis. Note that the data we report for flight times over a 33.7 cm distance were calculated by subtracting the average oxygen flight time from the nozzle to the interaction region; the reported product arrival times, then, reflect a convolution of the oxygen beam’s wide velocity distribution and the ‘true’ product translational energy distribution, so the best-fit P(ET ) distributions may not be unique. As such, we estimate the uncertainties in the reported P(ET ) distribution to be 10 – 20%. To allow for easy manipulation of the P(ET ) and T(θ c.m. ) distributions, parameterized functions were often used. The fitting process often relied on the RRK form of the P(ET ) distribution: P(ET ) = (ET − B) p (Eavail − ET )q (3.4) where Eavail is the available translational energy in the c.m. frame (i.e., the collision energy, Ecoll , minus the endothermicity, ∆E). The parameters B, p, and q were adjusted to vary the peak and width of the c.m. translational energy distribution when obtaining a best fit to the laboratory data. The T(θ c.m. ) distribution was described by a Legendre polynomial form: Tk (θc.m. ) = ak ck (cos2 θc.m. − 1)k 2k k! c(cos θc.m. ) (3.5) where ak is an adjustable parameter for each of the eleven polynomial terms used, which 77 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.4: Laboratory TOF distribution of m/z = 46 (16 O12 C18 O+ ; green circles) at Θ = 6◦ , with the inelastic scattering signal removed. The data are shown with the O(3 P) + CO2 (dot-dashed black line), O2 + CO2 (dashed blue line), and summed (solid red line) forward-convolution fits. Flight times less than 72 µs violate energy conservation for 16 O(3 P) + 12 C18 O2 . The inset compares the raw TOF distribution with the IS TOF distribution, which is subtracted. were denoted by the subscripted k = 0, 1, 2,...10. The functional forms for the P(ET ) and T(θ c.m. ) distributions (3.4 and 3.5, respectively), were iterated in XBEAM until they provided satisfactory fits to the laboratory data, though, in some cases, point forms of the P(ET ) and T(θ c.m. ) distributions were used. Finally, the “best-fit” P(ET ) and T(θ c.m. ) distributions were used to create a c.m. velocity-flux contour map or a differential scattering cross-section plot for the products. 3.3.2 Results The inset in Figure 3.4 shows a raw m/z = 46 TOF distribution of 16 O12 C18 O products recorded at Θ = 6◦ . A small fraction of the signal can be attributed to inelastic scattering (IS) of 16 O12 C18 O impurities in the CO2 beam by 16 O and 16 O2 , and it can be subtracted. The remaining signal, shown in Figure 3.4, represents 16 O12 C18 O products from O-atom exchange reactions of 12 C18 O2 (see Chapter 4). We initially expected the reactive m/z = 46 signal to arise from reactions of 12 C18 O2 with the 16 O atoms (reaction 3.1) with a broad distribution of c.m. collision energies (Ecoll ) 78 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 peaked at 98.8 kcal mol−1 and a full width at half maximum (FWHM) of 18 kcal mol−1 . However, at small laboratory angles, we observed products with velocities that would violate energy conservation for this O(3 P) + CO2 reaction (e.g., t < 72 µs in Figure 3.4). 12 C18 O −1 (see Lee [1988]). 2 was estimated to have a laboratory velocity of 800 ± 80 m s Given the broad velocity distribution in the O(3 P)/O2 beam (8262 m s−1 with 900 m s−1 FWHM), the velocity spread in the 12 C18 O2 beam was insignificant by comparison, so the hyperthermal oxygen beam largely determined the broad distribution of collision energies sampled in these experiments. To calculate the maximum available translational energy in the laboratory frame for 16 O(3 P) + 12 C18 O2 and 16 O2 + 12 C18 O2 isotope exchange reactions, an initial 16 O(3 P)/16 O2 beam velocity of 8862 m s−1 was used because < 5% of the O(3 P)/O2 beam had a greater velocity. A non-negligible population of 16 O12 C18 O was observed at translational energies above the maximum allowed for 16 O(3 P) + 12 C18 O2 collisions at small laboratory angles. Despite the uncertainties in the Ecoll distribution and product flight times (see Section 3.3.1), we observed 16 O12 C18 O products arrive 10 – 20 µs faster than the minimum times allowed by the distribution of available energies, Eavail (≈Ecoll ; the zero-point energy change is +0.1 kcal mol−1 ), for reaction 3.1. Forward-convolution best-fits to the TOF distributions that only treat the 16 O(3 P) + 12 C18 O2 isotope exchange reaction cannot explain the fastest laboratory data at small laboratory angles (e.g., Θ = 6◦ and 8◦ ; see Figure 3.5). Increasing hET i in the product P(ET ) shifts the fastest part of the fit towards shorter flight times at all laboratory angles. While this improves the TOF fits at small laboratory angles, it decreases the quality of the TOF fits at larger laboratory angles (see Θ = 36◦ in Figure 3.6). Introducing the 16 O2 + 12 C18 O2 isotope exchange reaction yields good fits at all laboratory angles. A sizeable fraction of the products assigned to the 16 O2 + 12 C18 O2 reaction are slow enough that they do not violate conservation of energy; however, assigning them to the 16 O(3 P) + 12 C18 O 2 reaction leads to poor fits. Collisions between CO2 and ions or electronically excited O atoms could also yield 16 O12 C18 O products with elevated velocities, previous experience with this hyperthermal source indicates that they are not present in the beam [Troya et al., 2004]. 79 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.5: TOF distributions (green dots) for 16 O12 C18 O products at laboratory angles Θ = 6◦ and 8◦ with the inelastic scattering signal removed. Also shown are forwardconvolution best fits (solid red line) that treat only one isotope exchange reaction, 16 O(3 P) + 12 C18 O2 → O + 12 C18 O2 . The forward-convolution fits cannot account for the fastest 16 O12 C18 O product signals at small laboratory angles. We therefore hypothesize that the fast 16 O12 C18 O products come from reaction of 12 C18 O2 with 16 O2 in the hyperthermal beam. Because the velocity-selected 16 O2 molecules have the same laboratory-frame velocity distribution as the 16 O atoms, the 16 O2 molecules collide with the 12 C18 O2 molecules at substantially higher c.m. energies (see Newton diagram in Figure 3.2). The resulting collision energy distribution peaked at Ecoll = 158 kcal mol−1 with FWHM = 28 kcal mol−1 . Thus, 16 O12 C18 O products from reaction 3.2 have sufficient Eavail to account for the fastest products detected. The m/z = 46 signal would then contain products of both reactions 3.1 and 3.2, the fastest products arising exclusively from reaction 3.2. P(ET ) and T(θ c.m. ) distributions for reactions 3.1 and 3.2 were simultaneously obtained from forward-convolution fits of the m/z = 46 TOF distributions. The results for the 16 O2 + 12 C18 O2 reaction are presented in Figure 3.7; a c.m. velocity-flux contour diagram of 16 O12 C18 O products is shown in Figure 3.8, in which the observed product flux is peaked in the forward direction. The presence of signal at flight times violating energy conservation for 16 O(3 P)–12 C18 O2 collisions was used to guide the fitting process because the TOF distributions do not resolve the products unambiguously. As such, we cannot rule out an additional dynamical channel in reaction 3.1 contributing to some of the signal we attribute to reaction 3.2 because energy conservation in reaction 3.1 is only violated at small lab angles. 80 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.6: TOF distributions for 16 O12 C18 O (m/z = 46) at various laboratory angles Θ with the inelastic scattering signal removed. The raw data are shown as circles. Forwardconvolution fits of the 16 O2 + 12 C18 O2 (blue dashed curve) and 16 O(3 P) + 12 C18 O2 (black dot-dashed dashed curve) channels, along with their sum (red solid curve), are also shown. 81 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.7: Center-of-mass-frame (A) angular and (B) translational energy distributions from the 16 O2 + 12 C18 O2 oxygen isotope exchange reaction obtained from TOF fits of m/z = 46. The peak of the distribution of available energies is Eavail = 158 kcal mol−1 . Only the experimentally accessible range of c.m. angles (θ c.m. < 100◦ ) is shown. Figure 3.8: Velocity-flux contour diagram for 16 O12 C18 O products of 16 O2 + 12 C18 O2 collisions in the center-of-mass frame. The white arrows are the initial 16 O2 and 12 C18 O2 velocity vectors, and dashed white line is the maximum recoil velocity for 16 O12 C18 O (vmax ). 16 O12 C18 O products are scattered opposite the initial direction of the 12 C18 O velocity vector. 2 82 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 The 16 O12 C18 O products scattered mainly in the forward direction (θ c.m. = 0◦ ), though there was significant sideways scattering. Experimental sensitivity in the backward direction was insufficient to detect backward-scattered 16 O12 C18 O products, so forward-backward symmetric scattering (i.e., evidence for a long-lived intermediate complex) could not be ruled out. At these collision energies, however, an intermediate is unlikely to survive for a rotational period. The average total translational energy distribution for the two products was 25 kcal mol−1 , or 16% of the available energy; the P(ET ) distribution was peaked at ET = 10 kcal mol−1 . We estimate the yield for reaction 3.2 to be ≤ 2% of all O2 –CO2 collisions. This estimate is an upper limit because the complete Newton circle for inelastically scattered 16 O 2 + 12 C18 O 2 products was not observed in these experiments. Vibrational excitation of the O2 may also be important in promoting reaction, but the vibrational temperature of O2 present in the expanded plasma is unknown. Our experimental results are consistent with a 16 O12 C18 O product that rebounds from the 12 C18 O2 reactant’s initial direction after it collides with O2 ; this mechanism is characteristic of reactions with substantial activation energies that require high collision energies. The highly peaked angular distribution is consistent with a direct mechanism or a very short-lived intermediate, but more surprising is the substantial internal energy of the products, which is much greater than that found for similar oxygen isotope exchange reactions between O(3 P) + CO, O(1 D) + CO2 , and O + O2 [Brunsvold et al., 2008; Perri et al., 2004; Van Wyngarden et al., 2007]. This large translational-to-internal energy conversion suggests that the reaction proceeds through an intermediate species that facilitates efficient translational-to-internal energy transfer or through a non-adiabatic transition to another electronic surface. On average, 134 kcal mol−1 of internal energy is available to both products. This excess energy could be distributed among the five vibrational and four rotational degrees of freedom in O2 and CO2 . Alternatively, this energy could be in the form of electronically 3 + 3 00 excited products, including the a1 ∆g , b1 Σ+ g , and A Σu states of O2 , and the a A state of CO2 , which lies 119 kcal mol−1 above that for CO2 (1 Σ+ g ) [Braunstein and Duff , 2000]. The mass-spectrometric detection, however, did not allow us to determine the electronic states 83 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.9: Energetically allowed neutral product channels from O2 + CO2 collisions. Energies are taken from the NIST Webbook [http://webbook.nist.gov], [Mebel et al., 2004], and [Braunstein and Duff , 2000]. of the products. Other reaction channels are possible (see Figure 3.9). We cannot rule out a CO2 + O + O product channel because we did not collect sufficient data on the counter-fragment 18 O16 O. However, the energetically allowed CO 3 3 2 + O( P) + O( P) channel (∆H = 118 kcal mol−1 ) is spin-forbidden, and spin conservation would instead favor O(1 D) + O(3 P) products, whose energetic threshold is 163 kcal mol−1 and above the average Eavail in the experiment. There is also sufficient energy to form O3 + CO or O + CO3 [Mebel et al., 2004], and to dissociate CO2 to form O2 + O + CO, but because we were not anticipating these reactions, we did not search for the relevant detectable products. 84 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.10: Calculated energies and structures on the lowest triplet PES of O2 + CO2 . TS3 connects isoenergetic isomers of the CO4 shelf. 3.4 Theoretical studies To investigate whether an adiabatic mechanism exists for the O2 –CO2 isotope exchange reaction, we performed ab initio calculations to find stationary points on the lowest triplet PES for O2 + CO2 reaction at the CCSD(T)/aug-cc-pVTZ level of theory using the MOLPRO electronic structure code [Werner et al., 2006]. We identified two transition states (TS1 and TS2) connecting O2 + CO2 reactants with a triplet shelf state [CO4 (3 A00 ); see Figure 3.10 and Table 3.1]. All three structures are planar. One atom of the oxygen molecule approaches the carbon atom of CO2 and surmounts an activation barrier of 77.9 kcal mol−1 over TS1 to form a weak C–O bond and a CO4 (3 A00 ) shelf (76.4 kcal mol−1 , just 1.5 kcal mol−1 below TS1) similar to a weakly bound CO4 complex found at the B3LYP level of theory [Cacace et al., 2003; Elliott and Boldyrev, 2005]. At 121.8 kcal mol−1 , we identified an effective transition state for CO4 (3 A00 ) isomerization, TS3, containing a four-membered ring between the carbon atom and three oxygen atoms. A grid-based search revealed that TS3 is bound by 0.02 kcal mol−1 when zero-point energy is not considered, and that TS3 85 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Table 3.1: Energies of stationary points associated with the exchange reaction O2 + CO2 → O2 + CO2 on the lowest triplet potential energy surface∗ † CHF ∆E [CCSD(T)/aug-cc-pVTZ] ‡ ∆EZPE [CCSD(T)/aug-cc-pVTZ] ∆E (CASPT2/cc-pVTZ) CO4 TS1 TS2 TS3 0.973 76.0 76.4 91.2 0.977 77.9 77.9 95.6 0.969 80.0 78.3 97.1 0.945 120.9 121.8 137.4 ∗ ∆E in kcal mol−1 . † Coefficient of the Hartree-Fock configuration in the (8,10)-CASSCF expansion of the wave- functions. ‡ ZPE-corrected. This calculation was not performed at the CASPT2 level of theory. is connected to CO4 ; a displacement in Od < 0.01 Å towards CO4 produced CO4 upon geometry optimization. Thus, it acts as an ‘effective’ transition state for CO4 isomerization; it resembles the bound CO4 (1 A1 ) structure lying 52.5 kcal mol−1 below it, although with a longer Oc –Od bond length; both structures have C2v symmetry [Cacace et al., 2003; Elliott and Boldyrev, 2005; Jamieson et al., 2007]. We observed some evidence for multi-reference character in CO4 . An additional bound state was found 0.8 kcal mol−1 above the energy of CO4 at the MP2/cc-pVTZ level of theory, although it does not exist at the CCSD(T)/aug-cc-pVTZ level; the species is believed to be a resonance structure of CO4 (3 A00 ). A spin contamination of hS2 − Sz2 − Sz i = 0.011 in the region of the PES near TS3 also suggests some multi-reference character. Thus, CASPT2/cc-pVTZ calculations, which represent resonance qualitatively correctly and do not suffer from spin contamination, were performed to validate the CCSD(T) structures and energies. CO4 (3 A00 ) was confirmed as a resonance hybrid of two bound-state structures, although the contribution from the single-reference structure to the resonance hybrid dominates the final geometry. The results of those calculations are summarized in Table 3.1 and Figure 3.11. The uncertainty in the CCSD(T)/aug-cc-pVTZ energies is unknown, although a similar study in which the stationary points of the closely related O(3 P) + CO2 system were characterized was recently completed (see Chapter 4). In addition to CCSD(T)/aug-cc-pVTZ simulations, W4 calculations (close to the full configuration-interaction and infinite-basis-set 86 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.11: Calculated stationary point geometries on the lowest triplet PES of CO4 . CCSD(T)/aug-cc-pVTZ values (upper) and CASPT2/cc-pVTZ (lower) values are shown. limits; see [Karton et al., 2006]) were also performed, as they were found to be affordable, albeit marginally. The differences between the CCSD(T) and W4 results for the transition and bound states indicated a mean-unsigned error of 2.2 kcal mol−1 . We expect the errors in the analogous O2 + CO2 energies to be approximately the same. 3.5 Proposed mechanism A possible pathway for oxygen isotope exchange occurs through the forward and reverse directions of the following three steps: O2 + CO2 → [CO4 ]‡ (TS1/TS2) → CO4 (3 A00 ) → [CO4 ]‡ (TS3); see Figure 3.12. Spin-density maps (Figure 3.13) depicting the singlyoccupied molecular orbitals (SOMOs) for CO4 and TS3 are consistent with this mechanism. CO4 (3 A00 ) is a diradical with unpaired electron density concentrated in p-type orbitals of the Figure 3.12: Calculated energies and structures on the lowest triplet PES of O2 + CO2 . TS3 connects isoenergetic isomers of the CO4 shelf. 87 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.13: Singly-occupied molecular orbitals (SOMOs) in the CO4 (3 A00 ) and TS3 structures. Surfaces containing 70% of the electron density are shown. Note that the highest SOMO of CO4 (3 A00 ) and the lowest SOMO of TS3 have electron density primarily on Od , suggesting the SOMO is a spectator during isomerization. single-bonded oxygens, Ob and Od . This spin density is consistent with the radical character expected for an association of the O2 diradical with the carbon atom of CO2 , because the unpaired electrons in O2 are in orthogonal π ∗g orbitals: As one C–O bond is formed between the in-plane π ∗g orbital of O2 and the in-plane π bu orbital of CO2 (the higher-energy ∗ π nb g orbital does not interact due to symmetry; see Figure 3.14), the out-of-plane π g orbital on O2 is a relative spectator to the O2 radical addition. This interaction, along with the bending of the CO2 , produces the SOMOs for CO4 (3 A00 ) shown in Figure 3.13. In TS3, the lowest SOMO contains localized electron density on Od in an out-of-plane p-type orbital, suggesting that the unpaired electron on Od continues to be a spectator during CO4 (3 A00 ) isomerization. The highest SOMO, however, contains delocalized electron density, of antibonding (σ ∗ ) character, in the plane of the molecule. This σ ∗ character may be interpreted as electron density taken from the lowest SOMO in CO4 (3 A00 ) while being localized onto Oc during isomerization. These theoretical results imply that an adiabatic mechanism exists for the oxygen isotope exchange reaction between O2 and CO2 . During the isomerization of CO4 (3 A00 ), the Oc –Od σ -bond is cleaved homolytically (Figure 3.15): One electron moves to a p-type orbital on 88 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.14: Molecular orbital diagrams for O2 and CO2 , adapted from DeKock and Gray [1980]. Sketches of the highlighted orbitals are shown. As O2 collides with CO2 , it becomes stretched. In addition, CO2 bends, increasing the energy of its doubly occupied, ∗ in-plane π-orbitals, π bu and π nb g . A weak interaction between the π g orbital on O2 and the π bu orbital on CO2 is likely responsible for the small (1.5 kcal mol−1 ) binding energy of CO4 . The π nb g orbital does not interact, to first approximation, due to symmetry. Oc , while the other electron forms a bond with the unpaired electron on Ob . This pathway can account for the σ ∗ character of the highest-energy SOMO in TS3 (the Ob –Od bond takes an electron from the Oc –Od bond), and it preserves radical character on Od . Thus, the 3 A00 symmetry is preserved throughout the association, isomerization, and dissociation steps. This mechanism is qualitatively consistent with the small reaction cross-section and a preference for rebounding reactive collisions inferred from the dynamics observed in the experiment. The O2 must approach the CO2 at very low impact parameters with high energies to overcome the initial barrier (TS1/TS2) and reach the ‘shelf’ of the bound CO4 (3 A00 ). Momentum along the reaction coordinate beyond CO4 (3 A00 ) with ∼80 kcal mol−1 excess energy should further compress the C–Oc bond with synchronous bending of the C–Oc –Od 89 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.15: Electron-pushing diagram of an adiabatic CO4 (3 A00 ) isomerization through TS3. angle, stretching of Oc –Od , and ring formation to form TS3, followed by rapid repulsion from the final TS1/TS2 state. Finally, the large change in geometry from reactants to TS3 should facilitate the transfer of some translational energy into internal degrees of freedom of the products. Reactive scattering should become less ‘rebound’-like (forward-scattered) as Ecoll is increased above the reactive threshold; at 37 kcal mol−1 above the reactive barrier, the tight transition state, repulsive exit channel leading out of TS1/TS2, and low angular momentum must limit the extent of sideways scattering. While some sideways scattering is indeed observed in the experiment, the Ecoll dependence of T(θ c.m. ) is not known. A non-adiabatic transition to another potential surface cannot be excluded, especially given the high internal energies observed in the products. At these high energies [80 kcal mol−1 above even the CO4 (3 A00 ) shelf state], many excited-state surfaces must exist, and radiationless transitions via conical intersections may occur. While intersystem crossing (ISC) in the exit or entrance channels is unlikely at the high relative velocities of the experiment [Landau, 1932], spin transitions could readily occur if a complex is formed. For instance, the bridging oxygen atom in TS3, Od , must be equivalently bound to Ob and Oc , and chemical intuition suggests that an intersection with a singlet surface may occur by spin-paired CO4 (1 A1 ) [Cacace et al., 2003; Elliott and Boldyrev, 2005; Jamieson et al., 2007]. 3.6 Conclusion An O2 –CO2 isotope exchange reaction on the ground triplet electronic surface is possible and is consistent with our laboratory observations. Nevertheless, additional work would 90 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 be valuable in the confirmation of this hypothesis. Collision-energy-dependence studies of the product angular distribution may elucidate the mechanistic origins of the low average translational energy of products. Experimental detection of O2 counter-fragments and a search for products from other channels (e.g., spectroscopic identification of electronically excited states) would also be revealing. Last, a more complete surface, reactive trajectories, and locations of possible surface intersection seams leading to ISC would be vital to a full explanation of the reaction dynamics. 3.7 Acknowledgements We thank G. B. Ellison, S. L. Mielke, and J. E. Wulff for insightful discussions. This work was supported by the Missile Defense Agency under cooperative agreement HQ0006-05-20001. L. Y. Y. was supported by the Davidow Fund, and G. C. S. was supported by AFOSR grant FA955D-07-1-0095. 91 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Appendices 92 Chapter 3 L. Y. Yeung 3.A Oxygen isotope exchange reactions of CO2 Chapter 3 Non-reactive scattering of O2 and CO2 The experiment mainly observed signals due to 16 O2 scattered with little deflection from its initial direction (see Newton diagram in Figure 3.2); these signals corresponded to the sum of elastic and inelastic scattering collisions of 16 O2 , which we could not resolve, so they will be referenced collectively as “scattered 16 O2 .” Five representative laboratory-frame TOF distributions (m/z = 32), the c.m. angular and translational energy distributions, and the laboratory-frame angular distribution obtained from 16 O2 product detection are shown in Figure 3.16. Scattered 16 O2 had 126.3 kcal mol−1 total translational energy, or 80% of the available energy, on average. The experimental translational energy distribution was peaked at ∼148 kcal mol−1 . The c.m. angular distribution for 16 O was highly peaked in the forward direction with little scattered intensity for θc.m. > 30◦ ; however, the velocity and angular range for 16 O2 product detection in the experiment prevented the detection of backward-scattered 16 O2 (see Figure 3.2). Some dependence of the c.m. translational energy distribution on the c.m. angular distribution was observed in the 16 O TOF data; the forward-convolution simulations became increasingly faster than the data at larger laboratory and c.m. angles (e.g, Θ = 18◦ , 28◦ , and 42◦ in Figure 3.16). We also note that, like for 16 O (see Sections 4.4.2.1 and 4.5.2), the c.m. angular distribution for inelastically scattered 16 O 2 at θc.m. ∼ 0 ◦ is an extrapolation because of high background from the hyperthermal source at the small laboratory angles corresponding to small c.m. angles for 16 O2 . Most of the 16 O2 probably scatters forward through high-impact-parameter collisions, but the limited constraints on the θc.m. ∼ 0◦ angular distribution (e.g., the laboratory-frame angular distribution, which only probes Θ = 6◦ ) increase the uncertainty in that part of the c.m. angular distribution. The experiment mainly observed 12 C18 O2 scattered opposite its initial direction in the c.m. frame (see Newton diagram in Figure 3.2). Detected 12 C18 O2 products (m/z = 48) showed best-fit c.m. translational energy distributions that were both broader and lower in energy, on average, than that obtained for forward-scattered 16 O2 . A single pair of P(ET ) and T(θc.m. ) distributions was not sufficient to describe the m/z = 48 TOF distributions (see Sections 4.4.2.1 and 4.5.2), and a second pair of P(ET ) and T(θc.m. ) distributions was 93 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 included in the fit; five representative laboratory-frame TOF distributions, the c.m. angular and translational energy distributions, and the laboratory-frame angular distribution obtained from 12 C18 O2 product detection are shown in Figure 3.17, along with the c.m. velocity-flux diagram in Figure 3.18. The first P(ET ) and T(θc.m. ) pair for inelastically scattered 12 C18 O2 described the scattering at θc.m. < 125◦ . In this region, the angular distribution was peaked near θc.m. = 60◦ , though the probability of scattered products was roughly constant for 0◦ < θc.m. < 40◦ . The probability of finding these products decayed steadily at θc.m. > 60◦ . The corresponding translational energy distribution was peaked at 60 kcal mol−1 with an average hET i = 62.8 kcal mol−1 , or 40% the available energy. The second P(ET ) and T(θc.m. ) pair for inelastically scattered 12 C18 O2 described the scattering at 60◦ < θc.m. < 125◦ (corresponding to the maximum θc.m. observed in the experiment), although there was a small component 0◦ < θc.m. < 60◦ . This angular distribution overlapped, in the sideways-scattering region, with the first pair. For θc.m. > 60◦ the distribution increased rapidly until it peaked near θc.m. = 120◦ and decayed quickly at θc.m. > 120◦ . This part of the distribution, however, is uncertain because our experiment did not probe it directly. The translational energy distribution was peaked at 103 kcal mol−1 with an average hET i = 100.8 kcal mol−1 , or 64% the available energy. The similarity in product c.m. angular and translational energy distributions in the O2 + CO2 system and the O(3 P) + CO2 system (see Sections 4.4.2.1 and 4.5.2) suggests that the collisional energy transfer mechanism is similar in both cases. Ryali et al. [1982] found that CO2 collisions with N2 , O2 , and Ar near at high collision energies all had similar translational-to-vibrational energy transfer cross-sections for the excitation of CO2 (ν3 ), so they suggested that energy transfer sampled the repulsive part of the intermolecular potential in all cases. Transfer of vibrational energy from O2 to CO2 cannot be ruled out in our experiments because we did not characterize the vibrational temperature of the hyperthermal O2 . Consequently, the similarity in inelastic scattering dynamics of O(3 P) and O2 collisions with CO2 could also be coincidental. 94 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.16: Laboratory scattering data detected at m/z = 32. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for scattered 16 O2 products from 16 O2 + 12 C18 O2 collisions at hEcoll i = 158.1 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines (orange and brown) are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). These data indicate that 16 O2 is scattered mainly in the forward direction with little change in its initial direction or velocity. 95 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.17: Laboratory inelastic scattering data detected at m/z = 48. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for inelastically scattered 12 C18 O2 products from 16 O2 + 12 C18 O2 collisions at hEcoll i = 158.1 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). The dark blue and cyan lines correspond to products of 16 O(3 P) + 12 C18 O2 collisions, and they are discussed in Section 4.4.2.1. A single c.m. translational energy and angular distribution for each collision partner was insufficient to describe the TOF distributions of inelastically scattered 12 C18 O2 , suggesting a scattering dependence on impact parameter. 96 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.18: Velocity-flux contour diagram for inelastically scattered 12 C18 O2 from 16 O2 + 12 C18 O2 collisions in the center-of-mass frame. The white arrows are the initial 16 O2 and 12 C18 O2 velocity vectors and dashed white line is the maximum recoil velocity for 12 C18 O (v 2 max ). Only the c.m. angles for which the experiment were sensitive are shown; inelastically scattered 12 C18 O2 from high-impact-parameter collisions are not shown, as their flux would be off-scale. Strong coupling of the P(ET ) and T(θ c.m. ) distributions was observed. 97 L. Y. Yeung 3.B Oxygen isotope exchange reactions of CO2 Chapter 3 MATLAB program for generating Newton diagrams A series of programs (linked as functions) was written in MATLAB so meaningful Newton diagrams could be generated with little effort. This proved to be quite useful during data analysis because the program could display expected product times-of-flight, speeding up the forward-convolution fitting process considerably. The programs included here (NewtonD.m, NewtonDcalc.m, and NewtonDplot.m) use parameters specific to the MSU crossedbeam apparatus, but the code is general and the parameters adjustable for use with any crossed-beam apparatus with arbitrary crossing angle. Figure 3.19 shows a sample input and output. Figure 3.19: Sample output of the NewtonD.m program. Predicted c.m. angles are defined relative to the slow product’s c.m. velocity vector. 3.B.1 NewtonD.m % Program for generating Newton diagrams for molecular scattering. % Command line input is NewtonD(observed,labangle) function NewtonD(observed, labangle) clear m1 m2 v1 v2 theta e DEint observed=observed; labangle=labangle; % observed product (1 or 2) as inputted below % lab angle of observation relative to initial v1 % vector, in degrees 98 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 % Begin input section m1=16; v1=8262; % mass of particle 1 in g/mol % initial velocity of particle 1 in m/s m2=48; v2=800; % mass of particle 2 in g/mol % initial velocity of particle 2 in m/s theta=0.5; % angle between v1 and v2 in pi radians, e.g. 0.5 −−> 0.5*pi % = 90 degrees e=0.5; DEint=0; % elastic scattering efficiency 0 < e ≤ 1) % gain of internal energy upon reaction in kcal/mol mp1=16; mp2=48; % mass of product 1 in g/mol % mass of product 2 in g/mol minangle=6; maxangle=54; % minimum lab angle relative to v1 vector, in degrees % maximum lab angle relative to v1 vector, in degrees length=33.66; % distance between interaction region and ionizer in cm if observed == 1 IFT=0;2.44*sqrt(mp1); % ion flight time (delay) in microseconds else if observed == 2 IFT=0;2.44*sqrt(mp2); end end delec=0;3; % electronics delay in microseconds dlaser=0;174; % laser firing delay in microseconds otravel=0;(0.99/v1)*10ˆ6; % O−atom travel time from nozzle to % interaction region in microseconds % End input section % Input error check if observed 6= 1 && observed 6= 2 disp('Invalid input, "observed" must equal 1 or 2'); return; end % Begin calculations hold off format short g disp('Observed m/z'); % Display observed mass if observed == 1 disp(mp1); else if observed == 2 disp(mp2); end end disp('Lab angle (degrees)'); disp(labangle); 99 L. 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Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 disp('Predicted center−of−mass angles (degrees)'); disp(' Fast channel | Slow channel'); % Iterate; first round includes specified change in internal energy, % second round sets the internal energy change to zero, i.e. % elastic scattering. for i = 1:2 [vc, thetavc, vrel, u1, u2, vrelp, up1, up2, Ecoll, phi, vd, chi]= NewtonDcalc(m1, m2, v1, v2, theta, e, DEint, mp1, mp2, labangle, observed); NewtonDplot(v1, v2, vc, thetavc, up1, up2, e, minangle, maxangle, labangle, vd, length, IFT, delec, dlaser, otravel, chi); if DEint == 0 return; else DEint=0; end end disp('Collision Energy (kcal/mol)'); disp(Ecoll); 3.B.2 NewtonDcalc.m % Function for calculating center−of−mass quantities function [vc, thetavc, vrel, u1, u2, vrelp, up1, up2, Ecoll, phi, vd, chi]=NewtonDcalc(m1, m2, v1, v2, theta, e, DEint, mp1, mp2, labangle, observed) % reactant parameters mu=m1*m2/(m1+m2); vc=sqrt((m1/(m1+m2)*v1)ˆ2+(m2/(m1+m2)*v2)ˆ2); vrel=sqrt(v1ˆ2+v2ˆ2−2*v1*v2*cos(theta*pi)); u1=m2/(m1+m2)*vrel; u2=m1/(m1+m2)*vrel; thetavc=asin((u2/vc)*(v1/vrel)*sin(theta*pi)); Ecoll=(1/2)*mu/1000*vrelˆ2/4.184/1000; % reduced mass % CM velocity % relative velocity % velocity of particle 1 % in CM frame % velocity of particle 2 % in CM frame % angle between CM % velocity and v2 % CM collision energy % reactive product parameters mup=mp1*mp2/(mp1+mp2); % reduced mass vrelp=sqrt(((mu/1000)*vrelˆ2−2*(DEint*1000*4.184))/(mup/1000)); %relative velocity up1=mp2/(mp1+mp2)*vrelp; % velocity of product 1 % in CM frame up2=mp1/(mp1+mp2)*vrelp; % velocity of product 2 % in CM frame phi=labangle*pi/180−(theta*pi−(thetavc)); % case structure determining output parameters if observed == 1 100 % angle between lab % detection vector and % CM velocity L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 up=up1; u=u1; v=v1; else if observed == 2 up=up2; u=u2; v=v2; end end % product velocity in lab frame with case structure for removal of % imaginary roots. if imag(roots([1 −2*vc*cos(phi) vcˆ2−(up*sqrt(e))ˆ2])) == 0 vd=roots([1 −2*vc*cos(phi) vcˆ2−(up*sqrt(e))ˆ2]); % Solve for product velocity observed at detector if vd(1) ≤ 0 && vd(2) ≤ 0 vd(1)=0; vd(2)=0; else if vd(1) > 0 && vd(2) ≤ 0 vd(2)=0; else if vd(1) < 0 && vd(2) > 0 vd(1)=0; end end end % Product scattering angle relative to CM velocity vector of reactant 2 if phi > 0 chi=(acos((diag(vd*vd')−vcˆ2−diag(up*up')*e)/(−2*vc*up*sqrt(e)))− asin(v2/u2*sin(thetavc)))*180/pi; else chi=360−(acos((diag(vd*vd')−vcˆ2−diag(up*up')*e)/(−2*vc*up*sqrt(e)))+ asin(v2/u2*sin(thetavc)))*180/pi; end if imag(chi(1)) 6= 0 chi(1) = 0; end if imag(chi(2)) 6= 0 chi(2) = 0; end if chi(1) > 180 chi(1)= chi(1)−360; end if chi(2) > 180 chi(2)= chi(2)−360; end % In case of imaginary roots else vd(1,1)=10000; vd(2,1)=10000; chi=1; disp(' N/A end N/A') %((1/2)*(mp1/1000)*(up1)ˆ2*e)/4184 %((1/2)*(mp2/1000)*(up2)ˆ2*e)/4184 3.B.3 % Display lack of solutions % CM Translational energy of % product 1 % CM Translational energy of % product 2 NewtonDplot.m 101 L. 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Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 function NewtonDplot(v1, v2, vc, thetavc, up1, up2, e, minangle, maxangle, labangle, vd, length, IFT, delec, dlaser, otravel, chi) % Messy plotting code for pretty pictures x1 = vc*cos(thetavc); y1 = vc*sin(thetavc); N=256; t=(0:N)*2*pi/N; plot(sqrt(e)*up2*cos(t)+x1, sqrt(e)*up2*sin(t)+y1, '−.r'); % Newton circle for product 2 hold on grid on plot(sqrt(e)*up1*cos(t)+x1, sqrt(e)*up1*sin(t)+y1, '−.b'); % Newton circle for product 1 legend('Particle 2', 'Particle 1') % text(1,1,'Collision energy = \Ecoll kcal/mol') x0 = 0; y0 = 0; x1 = 0; y1 = v1; plot([x0;x1],[y0;y1]) alpha = 0.05; % Particle 1 % Size of arrow head relative to the length of % the vector beta = 0.2; % Width of the base of the arrow head relative to % the length hu = [x1−alpha*((x1−x0)+beta*((y1−y0)+eps)); x1; x1−alpha* ((x1−x0)−beta*((y1−y0)+eps))]; hv = [y1−alpha*((y1−y0)−beta*((x1−x0)+eps)); y1; y1−alpha* ((y1−y0)+beta*((x1−x0)+eps))]; plot(hu(:),hv(:)) % Plot arrow head x0 = 0; y0 = 0; x1 = v2; y1 = 0; plot([x0;x1],[y0;y1],'r') % Particle 2 alpha = 0.4; % Size of arrow head relative to the length of % the vector beta = 0.5; % Width of the base of the arrow head relative to % the length hu = [x1−alpha*((x1−x0)+beta*((y1−y0)+eps)); x1; x1−alpha* ((x1−x0)−beta*((y1−y0)+eps))]; hv = [y1−alpha*((y1−y0)−beta*((x1−x0)+eps)); y1; y1−alpha* ((y1−y0)+beta*((x1−x0)+eps))]; plot(hu(:),hv(:),'r') % Plot arrow head x0 = v2; y0 = 0; x1 = 0; y1 = v1; plot([x0;x1],[y0;y1],'m') % vrel alpha = 0.05; % Size of arrow head relative to the length of % the vector beta = 0.2; % Width of the base of the arrow head relative to 102 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 % the length hu = [x1−alpha*((x1−x0)+beta*((y1−y0)+eps)); x1; x1−alpha* ((x1−x0)−beta*((y1−y0)+eps))]; hv = [y1−alpha*((y1−y0)−beta*((x1−x0)+eps)); y1; y1−alpha* ((y1−y0)+beta*((x1−x0)+eps))]; plot(hu(:),hv(:),'m') % Plot arrow head x0 = 0; y0 = 0; x1 = vc*cos(thetavc); y1 = vc*sin(thetavc); plot([x0;x1],[y0;y1],'g') % vc alpha = 0.1; % Size of arrow head relative to the length of % the vector beta = 0.25; % Width of the base of the arrow head relative to % the length hu = [x1−alpha*((x1−x0)+beta*((y1−y0)+eps)); x1; x1−alpha* ((x1−x0)−beta*((y1−y0)+eps))]; hv = [y1−alpha*((y1−y0)−beta*((x1−x0)+eps)); y1; y1−alpha* ((y1−y0)+beta*((x1−x0)+eps))]; plot(hu(:),hv(:),'g') % Plot arrow head x1=10000*sin(minangle*pi/180); y1=10000*cos(minangle*pi/180); plot([0;x1],[0;y1],'k') % minimum lab angle x1=10000*sin(maxangle*pi/180); y1=10000*cos(maxangle*pi/180); plot([0;x1],[0;y1],'k') % maximum lab angle if chi == 1 return else if chi 6= 1 x1=vd*sin(labangle*pi/180); y1=vd*cos(labangle*pi/180); plot([0;x1],[0;y1],'k') % observed lab angle x0=vc*cos(thetavc); y0=vc*sin(thetavc); x1=vd*sin(labangle*pi/180); y1=vd*cos(labangle*pi/180); plot([x0;x1],[y0;y1],'k') % center−of−mass scattering end end xlabel('Velocity of Particle B (m/s)') ylabel('Velocity of Particle A (m/s)') axis([−9000 11000 −5500 9500]) % Relevant quantities disp(chi'); if vd(1) == 0 && vd (2) == 0 TOF=[0 0]; else if vd(1) == 0 TOF=[((length/100)/vd(1))*10ˆ6 0]; 103 % Predicted TOF times in % microseconds L. Y. Yeung Oxygen isotope exchange reactions of CO2 else if vd(2) == 0 TOF=[((length/100)/vd(1))*10ˆ6 0]; % Predicted TOF times in % microseconds else if vd(1) == 10000 && vd(2) == 10000 TOF=[0 0]; else if vd(1) > 0 && vd(2) > 0 % Predicted TOF times in microseconds TOFfast=((length/100)/vd(1))*10ˆ6; TOFslow=((length/100)/vd(2))*10ˆ6; TOF=[TOFfast TOFslow]; end end end end end % Display TOF on graph next to Newton circle text(x1(1),y1(1),[' \leftarrow ',num2str(round(TOF(1)+IFT+delec+dlaser+ otravel)), ' \mus'],'FontSize',14) % Only display second TOF value if there is a product to display if TOF(2) 6= 0 text(x1(2),y1(2),[' \leftarrow ',num2str(round(TOF(2)+IFT+delec+ dlaser+otravel)), ' \mus'],'FontSize',14) else return end 104 Chapter 3 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Chapter 4 Dynamics of O(3P) + CO2 collisions at hyperthermal energies In collaboration with Mitchio Okumura, Jianming Zhang, Timothy K. Minton, Jeffrey T. Paci, Jan M. L. Martin, Jon M. Camden, and George C. Schatz; parts of this will be submitted to Journal of Physical Chemistry A for publication. 105 L. Y. Yeung 4.1 Oxygen isotope exchange reactions of CO2 Chapter 4 Abstract The dynamics of O(3 P) + CO2 collisions at hyperthermal collision energies near 100 kcal mol−1 were investigated experimentally and theoretically. Crossed-molecularbeam experiments at hEcoll i = 98.8 kcal mol−1 were performed with isotopically labeled 12 C18 O 16 3 12 C18 O ] from 2 to distinguish products of non-reactive scattering [ O( P) + 2 products of reactive scattering (18 O + 16 O12 C18 O and 18 O16 O + 12 C18 O). 16 O products were detected mainly in the forward direction, i.e., in the initial direction of the hyperthermal oxygen beam in the center-of-mass (c.m.) frame, and they contained ∼87% of the collision energy in translation, on average; the amount of energy transfer during non-reactive scattering depended on impact parameter. 16 O12 C18 O products from the oxygen isotope exchange reaction were scattered mainly in the backward direction with 35% of the available energy in translation, on average. 18 O16 O products from the oxygen-atom abstraction reaction were detected in the forward direction, with 56% of the available energy in translation, on average. Stationary points on the lowest triplet potential energy surface of the O(3 P) + CO2 system were characterized at the CCSD(T)/aug-cc-pVTZ level of theory. Quasi-classical trajectory (QCT) calculations of O(3 P) + CO2 collisions at energies between 1.0 – 6.5 eV (23 – 150 kcal mol−1 ) were performed at the B3LYP/6-311G(d) and BMK/6-311G(d) levels of theory, and both reactive channels observed in the experiment were also predicted by the theory. In addition, trajectories leading to the formation of 18 O2 + 12 C16 O products were predicted. The c.m. translational energy and angular distributions derived from the QCT calculations show qualitative, but not quantitative agreement with experimental results. The theoretical relative product yield for the oxygen isotope exchange reaction also agreed well with the experiment. The isotope exchange reaction demonstrates a new pathway through which oxygen isotopes may be cycled in the upper atmosphere, where O(3 P) atoms with hyperthermal translational energy distributions can be generated through the photolysis of ozone and molecular oxygen. 106 L. Y. Yeung 4.2 Oxygen isotope exchange reactions of CO2 Chapter 4 Introduction Atomic oxygen radicals in the atmosphere play an important role in regulating Earth’s oxidative and radiative balance. Photodissociation of molecular oxygen and ozone by solar ultraviolet radiation produces not only electronically excited O(1 D) and O(1 S), but also ground-state O(3 P) with velocities as high as 6 km s−1 [Matsumi and Kawasaki, 2003; Stranges et al., 1995]. O(3 P) has received less attention than O(1 D) and O(1 S), however, because it is less reactive at low collision energies. Yet, its important role in the terrestrial mesosphere and thermosphere is widely recognized; for instance, its collisions with CO2 significantly influence the population of CO2 (010), whose emission at 15 µm cools the atmosphere and regulates the height of the mesopause [Sharma and Roble, 2002]. O(3 P) can also interact with CO2 from space vehicle exhaust streams at relative velocities near 8 km s−1 and collision energies near 100 kcal mol−1 , well above those expected at local thermodynamic equilibrium. These high collision energies exceed barriers to (1) CO3 formation, leading to oxygen isotope exchange, and (2) oxygen-atom abstraction on the triplet potential energy surface (PES) [Averyanov et al., 1999; Bennett et al., 2004; Froese and Goddard, 1993; Mebel et al., 2004; Yang et al., 2005]. The enthalpies associated with these reactions are: 3 1 + O(3 P) + CO2 (1 Σ+ g ) → O( P) + CO2 ( Σg ) 1 + → O2 (3 Σ− g ) + CO( Σ ) ∆H ∼ 0 (4.1) ∆H = 8 kcal mol−1 (4.2) A reaction analogous to reaction 4.1, between O(1 D) and CO2 in the stratosphere [Baulch and Breckenridge, 1966; Chakraborty and Bhattacharya, 2003; DeMore and Dede, 1970; Johnston et al., 2000; Mebel et al., 2004; Perri et al., 2003, 2004; Shaheen et al., 2007; Wen and Thiemens, 1993; Yeung et al., 2009a], alters the stable isotope composition of stratospheric CO2 , allowing the isotopic composition of stratospheric CO2 to be used as a tracer of O(1 D) [Thiemens et al., 1995; Yung et al., 1991, 1997] and atmospheric transport [Boering et al., 2004]. The isotopic composition of CO2 has also been proposed as a tracer of biogeochemical cycles on annual and decadal timescales [Hoag et al., 2005]. Consequently, the dynamics of reactive channels that could alter the isotopic composition of 107 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 upper atmospheric CO2 are also of interest [Perri et al., 2003, 2004]. Early studies on the O(3 P) + CO2 system were primarily theoretical and focused on the vibrational-state-specific energy transfer [Bass, 1974; Garrett, 1983; Harvey, 1982; Schatz and Redmon, 1981]. The mechanism was found to be primarily impulsive at high collision energies, like that of collisions between CO2 and noble gases [Billing and Clary, 1983; Harvey, 1982; Schatz and Redmon, 1981]. More recent quantum calculations on the O(3 PJ ) + CO2 (010) system indicate that vibrational-to-translational energy transfer is sensitive to the total angular momentum J at thermal collision energies, although the importance of spin-orbit coupling decreases with increasing collision energy [de Lara-Castells et al., 2006, 2007]. Two experimental studies also focused on state-specific excitation in O(3 P) + CO2 collisions, specifically to CO2 (001); both studies also reported evidence that reaction 4.2, which is important in combustion chemistry [Tsang and Hampson, 1986] yielded vibrationally excited CO products [Oakes et al., 1994; Upschulte and Caledonia, 1992]; no mechanism was proposed, however. We recently confirmed the presence of reaction 4.1 at hyperthermal collision energies [Yeung et al., 2009b], and we intend now to investigate its dynamics. Mebel et al. [2004] suggested that the dynamics of CO3 formation on the triplet (3 A0 ) PES with hyperthermal O(3 P) atoms might be complicated by a nearby 3 A0 –1 A0 intersection seam, which could lead to non-adiabatic effects along reactive trajectories. Indeed, many low-lying electronic states of CO3 (e.g., 3 A00 ) lie within several eV of CO3 (3 A0 ), so vibronic [Kowalczyk and Krylov, 2007] and/or spin-orbit [Mebel et al., 2004] coupling could result in unexpected curvature and dynamics on the triplet PES. Here, the results of theoretical and crossed-molecular-beam studies of O(3 P) + CO2 collisions at hyperthermal collision energies will be presented. Theoretical direct dynamics calculations using the QCT method on an adiabatic PES were compared with the results from an experimental dynamics study obtained for an average collision energy hEcoll i = 98.8 kcal mol−1 . The oxygen isotope exchange and oxygen-atom abstraction reactions were observed in both the QCT calculations and the laboratory experiment, and center-of-mass (c.m.) angular and translational energy distributions for the oxygen isotope exchange reaction were 108 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 obtained. Their implications for atomic oxygen cycling through CO2 in the atmosphere will be discussed. 4.3 Theoretical studies 4.3.1 Electronic structure calculations Geometry-optimization, single-point, and vibrational-frequency calculations were performed on stationary points of the lowest triplet PES of CO3 , 3 A00 ; a discussion of the relative energetics of the 3 A0 and 3 A00 surfaces can be found in Section 4.5. Stationary points for reactions 4.1 and 4.2 were characterized using electronic structure calculations at the B3LYP/6-311G(d) [Becke, 1993; Frisch et al., 1984; Lee et al., 1988], BMK/6-311G(d) [Boese and Martin, 2004], and CCSD(T)/aug-cc-pVTZ [Kendall et al., 1992; Raghavachari et al., 1989] levels of theory/basis using the MOLPRO electronic structure code [Werner et al., 2006]. Confirmation of transition-state character was achieved by inspection of the associated vibrational frequencies. Other reactive channels were not characterized because reactant energies in excess of 250 kcal mol−1 are required to open them, according to our B3LYP/6-311G(d) calculations. Here, we report three transition-state structures and one bound-state structure on the CO3 (3 A00 ) PES; the results are shown in Figures 4.1 and 4.2 and Table 4.1 [Mebel et al., 2004]. All structures are planar. One transition state (TS1) and the bound state (CO3 ) were associated with the O(3 P) + CO2 isotope exchange reaction. Two transition states (TS2 and TS3) were associated with the oxygen-atom abstraction reaction producing O2 and CO. Two additional bound states and two associated transition states were also found; they resemble the Cs minima reported in previous work [Bennett et al., 2004; Froese and Goddard, 1993; Mebel et al., 2004], but they will not be discussed here because neither of the bound states were bound when zero-point energy (ZPE) was considered. For this reason, we are also not reporting minima in the van der Waals region of the PES, e.g., the quadrupole-induced minimum (∆E ∼ 335 cm−1 ) at the RCCSD(T)/aug-cc-pVTZ level of theory [de Lara-Castells et al., 2006, 2007], because the binding energies were below the ZPE of the system. Further 109 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.1: Stationary-point structures for O(3 P) + CO2 reactions below 100 kcal mol−1 calculated at the CCSD(T)/aug-cc-pVTZ level of theory on the 3 A00 . The relative energies have been corrected for zero-point energy. comparisons of the structures with previous work on the lowest triplet PES will be presented in Section 4.5. Of the levels of theory and basis examined in this study, CCSD(T)/aug-cc-pVTZ is probably the most accurate combination; however, multi-reference character in the stationary points may be important because several electronic surfaces are within several eV of the PES that is the subject of this study [Bennett et al., 2004; Kowalczyk and Krylov, 2007; Mebel et al., 2004]. Multi-reference CCSD(T) calculations, unfortunately, were not computationally affordable. Still, our CCSD(T)/aug-cc-pVTZ geometries are nearly identical to those obtained in recent calculations using the W4 method [Karton et al., 2006] near the full-configuration-interaction and complete-basis-set limits, with transition-state energies within 2 kcal mol−1 and the bound-state energy within 4 kcal mol−1 (J. M. L. Martin, per- 110 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Table 4.1: Energies (kcal mol−1 ) for the stationary points on the lowest triplet CO3 potential energy surface for 16 O(3 P) + 12 C16 O2 → 16 O + 12 C16 O2 collisions B3LYP 6-311G(d) BMK 6-311G(d) w/ZPEC† O(3 P) + CO2 TS1 CO3 TS2 TS3 O2 + CO 0.0 18.0 11.8 56.2 70.3 9.7 0.0 17.7 11.3 55.2 69.2 7.9 CCSD(T) aug-cc-pVTZ w/ZPEC† 0.0 25.2 20.2 65.3 80.0 14.3 0.0 25.0 19.0 64.5 78.9 12.6 CCSD(T) 6-311+G(3df)∗ w/ZPEC† 0.0 25.2 21.8 63.0 76.5 10.2 0.0 25.0 20.2 62.1 75.3 8.3 0.0 35.2 22.0 ∗ From Mebel et al. [2004] using a 3 A0 geometry optimized at the CASSCF(16,13)/6-311G(d) level of theory. The authors noted that the more ideal MRCI+Q/6-311+G(3df) energy calculation was not affordable. † Zero-point-energy correction (ZPEC). sonal communication). Thus, we used the CCSD(T)/aug-cc-pVTZ geometries and energies as benchmarks for comparison with those calculated by the density-functional methods, which are more affordable for QCT calculations. In addition to using the B3LYP and BMK levels of theory, we characterized the transitionstate structures at the MP2 [Møller and Plesset, 1934], M06-2X [Zhao and Truhlar, 2008], and CCSD [Purvis and Bartlett, 1982] levels using the 6-31G(d,p), 6-311G(d), and cc-pVTZ [Dunning, 1989] basis sets during our search for an appropriate level of theory for QCT calculations (optimizing computational cost and accuracy). The density-functional methods B3LYP/6-311G(d) and BMK/6-311G(d), however, were found to have the best balance between computational cost and accuracy, so we will only report the results of those calculations here along with the results of CCSD(T)/aug-cc-pVTZ calculations (see Figure 4.2). The results of the lower-level B3LYP and BMK calculations, along with the MP2, M06-2X, and CCSD calculations, are shown in Figure 4.3. TS1 had Cs symmetry in all cases. Mild compression of one C–O bond and stretching of the other C–O bond in the parent CO2 , along with moderate bending (∼30◦ ) of the O– C–O bond angle, was found at all levels of theory. The geometries were similar to that calculated at the CCSD(T) level of theory, which had C–O bond lengths of 1.24 Å, 1.18 Å, and 1.60 Å and bond angles of 87◦ , 123◦ , and 150◦ (see Figure 4.2). The B3LYP geometry 111 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.2: Comparison of CO3 stationary point geometries relevant to the QCT calculations. Our geometry optimizations at the CCSD(T)/aug-cc-pVTZ, B3LYP/6-311G(d), and BMK/6-311G(d) levels of theory (bold) are shown with Mebel et al.’s CASSCF(16,13)/6311G(d) geometries for CO3 and TS1. Figure 4.3: Comparison of TS1 and TS3 geometries and energies at various levels of theory. ZPE-corrected transition-state (∆E ‡ ) and reaction (∆E) energies are shown. 112 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 generally agrees well with that at CCSD(T), deviating by < 0.02 Å in the two shorter C–O bond lengths and by < 3◦ in all the bond angles. The longest bond length, however, is 0.06 Å longer at B3LYP than at CCSD(T). Its ZPE-corrected energy is also 7.3 kcal mol−1 lower. At the BMK level of theory, the TS1 geometry agrees with the CCSD(T) geometry within 0.02 Å in all the bond lengths and within 3◦ in all the bond angles, and with the CCSD(T) energy within 0.1 kcal mol−1 . The CO3 bound state had C2v symmetry at the B3LYP and CCSD(T) levels of theory and Cs symmetry at the BMK level of theory. C–O bond lengths were larger than typical CO2 bond lengths (1.21 Å), consistent with an overall decrease in C–O bond order upon CO3 formation. The B3LYP geometry agreed within 0.04 Å and 1◦ with the CCSD(T) geometry, which had C–O bond lengths of 1.27 Å, 1.27 Å, and 1.30 Å and bond angles of 118◦ , 118◦ , and 123◦ (see Figure 4.2). The ZPE-corrected B3LYP energy, however, is 8.9 kcal mol−1 lower than that at CCSD(T). At the BMK level of theory, moderate agreement in the CCSD(T) geometry was observed; in addition to displaying lower symmetry, the C–O bond lengths calculated at BMK were different from CCSD(T) bond lengths by up to 0.07 Å, while the bond angles were different by up to 8◦ . The lower symmetry for CO3 using the BMK functional may be a consequence of the large amount of Hartree-Fock exchange mixed into the functional [Boese and Martin, 2004], which can result in orbital symmetry-breaking [Sherrill et al., 1999]. The ZPE corrected CO3 energy at BMK is in better agreement, however, at 1.2 kcal mol−1 below the energy at CCSD(T). Both B3LYP and BMK theories do show a CO3 potential well of 6.4 and 6.0 kcal mol−1 , respectively, in reasonable agreement with the CCSD(T) well depth of 4.8 kcal mol−1 . TS2 and TS3 were associated with an oxygen-atom abstraction reaction producing O2 + CO. They had Cs symmetry at all levels of theory. In both transition states, one C–O bond on the parent CO2 was compressed, while the other C–O bond, which is eventually broken, was stretched (see Figure 4.2). The O–C–O bond angle was bent ∼40◦ , and the only qualitative difference between the structures was the C–O–O bond angle: The C–O–O angle bent inwards to form a ‘C’-shape in TS2, whereas it bent outwards to form a ‘S’-shape in TS3. Both B3LYP and BMK geometries agreed with the CCSD(T) geometry with a maximum dis- 113 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 crepancy of 0.04 Å in the O–O bond length at the BMK level. The two bond angles agreed to within 2◦ . Resulting ZPE-corrected barrier heights showed larger discrepancies: B3LYP and BMK energies for TS2 differed from CCSD(T) values by –6.9 and +2.4 kcal mol−1 , respectively, while they differed from CCSD(T) values by +6.1 and –3.6 kcal mol−1 , respectively, in TS3. We note that BMK overpredicted the endothermicity of the O(3 P) + CO2 → O2 + CO reaction by ∼4.5 kcal mol−1 ; this disagreement is again probably a consequence of the large amount of Hartree-Fock exchange mixed into the BMK functional, which was included to improve the performance of the functional when predicting transition state properties. 4.3.2 Reaction dynamics calculations QCT calculations were run on the 3 A00 PES with both B3LYP/6-311G(d) and BMK/6311G(d) methods. Both methods showed reasonable agreement with the geometries and energies of the stationary points calculated at CCSD(T)/aug-cc-pVTZ and were computationally affordable for direct dynamics calculations. Four hundred trajectories were run at collision energies of 1.0, 1.5, 2.5, 3.5, 4.5, 5.5, and 6.5 eV (23.0, 34.6, 57.6, 80.7, 103.7, 126.7, and 149.8 kcal mol−1 , respectively) using the B3LYP level of theory for a total of 2800 trajectories. This range of energies was selected because the ZPE-corrected barriers for TS1, TS2, and TS3 according to this level of theory were 17.7, 55.2, and 69.2 kcal mol−1 (0.77, 2.4, and 3.0 eV, respectively). In addition, four hundred BMK trajectories were run at collision energies of 1.5, 2.5, 3.5, 4.5, 5.5, and 6.5 eV for a total of 2400 trajectories. At this level of theory, the ZPE-corrected reaction thresholds were 25.0, 64.5, and 78.9 kcal mol−1 (1.1, 2.8, and 3.4 eV, respectively) for TS1, TS2, and TS3, respectively. The collision energy of 1.0 eV (23 kcal mol−1 ) was not considered because it is below the threshold for both reactions 4.1 and 4.2, according to the BMK level of theory. Trajectories were integrated using a standard fifth-order predicator, sixth-order corrector integration algorithm [Bunker, 1970; Press et al., 1992] with an integration time-step of 10.0 a.u. (0.24 fs). The energy and gradient were calculated at each point using the Q-Chem software package [Shao et al., 2006], and the initial orientation and impact parameter was sampled randomly. To simulate the ZPE, an intermolecular trajectory starting from CO2 in its equilibrium configuration was run 114 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 with kinetic energy corresponding to the ZPE in each normal mode, and the atomic coordinates along this trajectory were used to sample the initial CO2 vibrational phase randomly in subsequent trajectories. An estimate of a reasonable value for the maximum impact parameter for reactive scattering, bmax , was calculated using the expression [Levine, 2005]: 1  E0 2 bmax = d 1 − ET (4.3) where d is the distance in the transition-state structure between the center of mass of the reactant CO2 and the colliding oxygen atom, E0 is the transition-state energy, and ET is the collision energy. Because large collision energies were of principal interest, we chose to consider the largest value for bmax suitable for trajectories with unlimited collision energy by setting ET = ∞ in Eq. 4.3. Reaction 4.2 had the larger of the two d values, with a value of d ∼ 4.3 a0 (2.3 Å). This d value, combined with a ∼15% safety margin, suggested a bmax = 5.0 a0 (2.6 Å); thus, the trajectories were sampled with impact parameters 0 < b < 5.0 a0 . Trajectories were stopped when the distance between any two atoms exceeded 12 a0 (6.3 Å). Energy conservation and spin contamination were checked at each time-step. Trajectories in which energy was not conserved to within 3 kcal mol−1 or spin contamination rose above hS2 i = 2.5 were flagged. Less than 1.3% and 10% of the B3LYP and BMK trajectories, respectively, failed to meet these acceptance criteria. Most problems were related to energy conservation, and were attributed to self-consistent field convergence to an excited electronic state. Trajectories that initially did not meet the criteria were run again using a different set of self-consistent field convergence tools, which improved the energyconservation or spin-contamination problem in many cases. Results of the re-run trajectories were compared to their initial-run analogues, and the one that met or came closest to meeting the acceptance criteria was included in the analysis. To do otherwise would have resulted in an underestimate of the reaction cross-sections, as most of the problematic trajectories were reactive ones. Reactive cross-sections (σR ) were calculated from the QCT data using the expression: 115 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 N σR = π R (2li + 1)lmax ∑ Ntotal p2 i=1 (4.4) 1 where p = (2µET ) 2 is the momentum of the reactant system, li = bi p is the angular momentum of the ith trajectory, and lmax = bmax p. NR is the number of reactive trajectories in the set of Ntotal trajectories run. The total collision cross-section, σtotal , was estimated using the Lennard-Jones parameters for O and CO2 according to the expression for the total cross-section: σtotal = πb2total (4.5) where btotal is the radius beyond which no elastic, inelastic, or reactive scattering occurs. This radius can be estimated using the Lennard-Jones potential [Hirschfelder et al., 1964]: V (r) = 4ε   r 12 e r −  r 6  e r (4.6) where ε and re correspond to the well depth and the separation distance, respectively, at the potential minimum for an interaction between a pair of like atoms or molecules. The separation distance, re , is a measure of the atomic or molecular size. The values for the O-atom and for CO2 have been estimated to be re (O) = 2.78 Å and re (CO2 ) = 3.897 Å, respectively [Hirschfelder et al., 1964; Némethy et al., 1983]. Combining these radii with the usual method [Hirschfelder and Meath, 1967], i.e., re (O + CO2 ) = 1 [re (O) + re (CO2 )] 2 (4.7) we calculated an intermolecular interaction distance re (O + CO2 ) = btotal of 3.34 Å and a total collision cross-section of 125.2 a20 , which we used to calculate the relative product yields in Section 4.4.2.4. The theoretical reactive cross-section was divided by three for the comparison with experiment because the O(3 P) + CO2 surface is triply degenerate at large O(3 P)–CO2 separation distances (see Section 4.4.2.4). Trajectories corresponding to oxygen isotope exchange were observed at all collision 116 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.4: Reactive scattering cross-sections for the O(3 P) + CO2 isotope exchange reaction obtained from the QCT calculations. energies (see Table 4.2), and the resulting excitation functions were calculated from the QCT data (see Figure 4.4). These excitation functions had the same shape at the B3LYP/6311G(d) and BMK/6-311G(d) levels of theory. The BMK excitation function was shifted to slightly higher energies compared to the B3LYP prediction, consistent with the 7.3 kcal mol−1 (0.32 eV) higher ZPE-corrected transition-state barrier for isotope exchange. Opacity functions for the isotope exchange reaction showed a slight decrease in reaction probability at smaller impact parameters as the collision energy increased (see Figure 4.5). P(b) also appeared to reach a maximum near b ∼ 1.5 – 2 a0 (1 Å). The O2 + CO channel appears to open at higher energies than the exchange channel (see Table 4.2), consistent with the higher ZPE-corrected transition-state barriers for the oxygen-atom abstraction reaction of 37.5 kcal mol−1 (1.63 eV) and 39.5 kcal mol−1 (1.71 Table 4.2: Number of reactive QCTs observed at different collision energies. Theory/Basis Products 1.0 B3LYP/6-311G(d) BMK/6-311G(d) O + CO2 O2 + CO O + CO2 O2 + CO 1 0 117 Collision energy (eV) 1.5 2.5 3.5 4.5 5.5 6.5 16 0 2 0 78 11 80 8 54 0 37 0 66 0 66 0 68 1 80 0 80 4 76 5 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.5: Opacity functions for the O(3 P) + CO2 isotope exchange reaction and for inelastic scattering of the two reagents obtained from QCT calculations at the B3LYP/6311G(d) and BMK/6-311G(d) levels of theory. eV) higher than the exchange channel barrier according to the B3LYP and BMK predictions, respectively. The B3LYP threshold is slightly higher than that calculated using BMK, which is consistent with a ZPE-corrected barrier 9.3 kcal mol−1 (0.40 eV) larger at BMK than at B3LYP. Because only a small number of oxygen-atom abstraction reactions were observed, even at collision energies significantly in excess of the calculated reaction barrier, the amount of mechanistic insight available from the O(3 P) + CO2 → O2 + CO reaction is limited. A full discussion of the trajectory calculations, including the resulting product angular and translational energy distributions, can be found in Sections 4.4.2 and 4.5; they will be analyzed with the experimental data to elucidate the possible reaction mechanisms for each channel. 118 L. Y. Yeung Oxygen isotope exchange reactions of CO2 4.4 Experimental studies 4.4.1 Methods Chapter 4 Crossed-molecular-beam experiments were performed with an apparatus equipped with a hyperthermal atomic oxygen beam source at Montana State University, which was described in the preceding chapter. Briefly, a pulsed, hyperthermal beam of ∼87% 16 O(3 P) and ∼13% 16 O 3 − 16 O using a high-energy CO 2 ( Σg ) was generated by laser-induced detonation of 2 2 TEA laser (6 – 7 J pulse−1 ). Though initially broad in velocity distribution (6 – 9 km s−1 ), a portion of the overall beam was velocity-selected with a chopper wheel (see Figure 3.1) at an average velocity hvi = 8262 m s−1 . The resulting beam was crossed at a right angle with a pulsed supersonic expansion of 98% 12 C18 O2 . The scattered products were detected with a rotatable quadrupole mass spectrometer that collected number-density distributions for each product as a function of arrival time at the ionizer, N(t), at a given laboratory angle, Θ, the angle at which the product scatters with respect to the direction of the reagent oxygen beam. Time-of-flight (TOF) distributions for 16 O, 18 O16 O, 16 O12 C18 O, and 12 C18 O2 were collected over a range of laboratory angles; at each angle, the TOF distribution was integrated to give a laboratory angular distribution, N(Θ). A forward-convolution method was then used to derive c.m. translational energy P(ET ) and angular T(θc.m. ) distributions from the laboratory N(t) and N(Θ) distributions [Lee, 1988], where θc.m. is the angle at which a product scatters with respect to the reagent oxygen direction in the c.m. frame. The canonical Newton diagrams used in this analysis are shown in Figure 4.6. Laboratory TOF product distributions were measured every 2◦ between Θ = 6◦ – 54◦ . Scattered product TOF distributions were collected for 200 beam pulses for m/z = 16 (16 O+ ) and 32 (16 O2 + ), for 1000 beam pulses for m/z = 46 (16 O12 C18 O+ ), and for 500 beam pulses for m/z = 48 (12 C18 O2 + ). Scattered products at m/z = 34 (18 O16 O+ ) were collected for 12000 beam pulses at Θ = 6◦ and 10◦ and 6000 beam pulses at Θ = 14◦ . Dwell time for each channel at the MCP was 1 µs. At a representative laboratory angle of 10◦ , integrated count rates were 1.1 × 107 s−1 for m/z = 16, 1.3 × 107 s−1 for m/z = 32, 1.4 × 104 s−1 for m/z = 34 (18 O16 O+ ), 1.8 × 105 s−1 for m/z = 46 , and 4.2 × 106 s−1 for 119 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.6: Canonical Newton diagram for 16 O + 12 C18 O2 collisions at Ecoll = 98.8 kcal mol−1 The 16 O-atom beam velocity is 8262 m s−1 and the 12 C18 O2 beam velocity is 800 m s−1 . The shaded region indicates the range of laboratory angles probed. The radii of each circle represent the maximum recoil velocities of the following products of 16 O(3 P) + 12 C18 O collisions: 12 C18 O (blue solid) + 16 O (blue dashed), 16 O12 C18 O (red solid) + 18 O 2 2 (red dashed), and 18 O16 O (green solid) + 12 C18 O (green dashed). m/z = 48. Three signal corrections were made before data analysis. First, we corrected for beam divergence at Θ = 6◦ – 16◦ . The divergent intensity with the 12 C18 O2 beam turned off was measured by obtaining TOF distributions at m/z = 16 and 32 from Θ = 6◦ – 16◦ . These TOF distributions were then scaled and subtracted from the corresponding experimental TOF distributions at m/z = 16 and 32 that had the 12 C18 O2 beam turned on. Uncertainties in the non-reactive and reactive scattering signals due to collisions of the divergent hyperthermal oxygen could not be quantified, however; they were instead considered in the analysis of the laboratory data, where collisions at crossing angles of 88◦ , 89◦ , 90◦ , 91◦ , and 92◦ were included during forward-convolution fitting. Adding more crossing angles did not affect the forward-convolution fits significantly. Second, we measured that the 12 C18 O2 beam contained 2% 16 O12 C18 O using the instrument’s mass spectrometer. Thus, 2% of the inelastic scattering signal (m/z = 48) at each laboratory angle (Θ = 6◦ – 54◦ ) was subtracted from 120 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 raw m/z = 46 (16 O12 C18 O+ ) TOF distributions to obtain reactive-scattering-only distributions. Last, the hyperthermal O2 beam contained 0.4% 18 O16 O (at natural isotopic abundances), so 0.4% of the non-reactive scattering signal (m/z = 32) was subtracted from the raw m/z = 34 (18 O16 O+ ) TOF distributions to obtain reactive-scattering-only distributions. 4.4.2 Results 4.4.2.1 Non-reactive scattering of 16 O(3 P) and 12 C18 O2 The experiment mainly observed signals due to 16 O scattered with little deflection from its initial direction; these signals corresponded to the sum of elastic and inelastic scattering collisions of 16 O, which we could not resolve, so they will be referenced collectively as “scattered 16 O.” Five representative laboratory-frame TOF distributions (m/z = 16), the c.m. angular and translational energy distributions and the laboratory-frame angular distribution are shown in Figure 4.7. Scattered 16 O had 85.6 kcal mol−1 total translational energy, or 87% of the available energy (see Figure 4.7B), on average. The experimental translational energy distribution was peaked at ∼97 kcal mol−1 . The c.m. angular distribution for 16 O was highly peaked in the forward direction with little scattered intensity for θc.m. > 20◦ ; however, the velocity and angular range for 16 O product detection in the experiment prevented the detection of backward-scattered 16 O (see Newton diagram in Figure 4.6). Some dependence of the c.m. translational energy distribution on the c.m. angular distribution was observed in the 16 O TOF data; the forward-convolution simulations became increasingly faster than the data at larger laboratory and c.m. angles (e.g, Θ = 20◦ , 30◦ , and 40◦ in Figure 4.7A). We also note that the c.m. angular distribution for scattered 16 O at θ c.m. ∼ 0 ◦ is an extrapolation because of high background from the hyperthermal oxygen source at the small laboratory angles corresponding to small c.m. angles for 16 O. Most of the 16 O probably scatters forward through high-impact-parameter collisions, but the limited constraints on the θc.m. ∼ 0◦ angular distribution (e.g., the laboratory-frame angular distribution, which only probes Θ = 6◦ ) increase the uncertainty in that part of the c.m. angular distribution. This extrapolation had a small effect on the relative product yield measurements (see Section 4.4.2.4), but did not alter the results qualitatively. 121 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.7: Laboratory inelastic scattering data detected at m/z = 16. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for inelastically scattered 16 O products from 16 O + 12 C18 O2 collisions at hEcoll i = 98.8 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). These data indicate that 16 O is scattered mainly in the forward direction with little change in its initial direction or velocity. 122 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 The experiment mainly observed 12 C18 O2 scattered opposite its initial direction in the c.m. frame (see Newton diagram in Figure 4.6). Detected 12 C18 O2 products (m/z = 48) showed best-fit c.m. translational energy distributions that were both broader and lower in energy, on average, than that obtained for forward-scattered 16 O. Furthermore, a single pair of P(ET ) and T(θc.m. ) distributions was not sufficient to describe the m/z = 48 TOF distributions. Consequently, a second pair of P(ET ) and T(θc.m. ) distributions was included in the fit of inelastically scattered 12 C18 O2 ; five representative laboratory-frame TOF distributions, the c.m. angular and translational energy distributions, and the laboratory-frame angular distribution obtained from 12 C18 O2 product detection are shown in Figure 4.8, along with the c.m. velocity-flux diagram in Figure 4.9. The first P(ET ) and T(θc.m. ) pair for inelastically scattered 12 C18 O2 described the scattering at θc.m. < 120◦ . In this region, the angular distribution was peaked near θc.m. = 60◦ , though the probability of scattered products was roughly constant for all θc.m. < 60◦ before decaying steadily at θc.m. > 60◦ . The corresponding translational energy distribution was peaked at ∼39 kcal mol−1 with an average hET i = 40.1 kcal mol−1 , or 41% the available energy. The second P(ET ) and T(θc.m. ) pair for inelastically scattered 12 C18 O2 described the scattering at 60◦ < θc.m. < 125◦ (corresponding to the maximum θc.m. observed in the experiment); this range overlapped, in the sidewaysscattering region, with the first pair. The second T(θc.m. ) distribution increased rapidly from θc.m. = 60◦ peaked near θc.m. = 120◦ . It decayed quickly at θc.m. > 120◦ , although this part of the distribution is uncertain because our experiment did not probe it directly. The translational energy distribution was peaked at 65 kcal mol−1 with an average hET i = 63.8 kcal mol−1 , or 65% the available energy. Mechanistic implications of the additional P(ET ) and T(θc.m. ) distributions will be addressed in Section 4.5. While the forward-convolution laboratory fitting method produced c.m. angular and translational energy distributions that yielded good fits to the data in Figures 4.7 and 4.8, they may not be unique fits to the data because of the temporal and angular width of the incident O(3 P) source beam and the low resolution and SNR in the resulting TOF distributions. Small changes to the c.m. angular and translational energy distributions still produced good fits to the data that were within the uncertainty bounds of the laboratory-frame 123 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.8: Laboratory inelastic scattering data detected at m/z = 48. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for inelastically scattered 12 C18 O2 products from 16 O + 12 C18 O2 collisions at hEcoll i = 98.8 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines (dark blue and cyan) are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). The orange and brown lines correspond to products of 16 O + 12 C18 O collisions, and they are discussed in Appendix 3.A. A single c.m. transla2 2 tional energy and angular distribution for each collision partner was insufficient to describe the TOF distributions of inelastically scattered 12 C18 O2 , suggesting a scattering dependence on impact parameter. 124 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.9: Velocity-flux contour diagram for inelastically scattered 12 C18 O2 from 16 O(3 P) + 12 C18 O collisions in the center-of-mass frame. The white arrows are the 2 initial 16 O(3 P) and 12 C18 O2 velocity vectors, and the dashed white line is the maximum recoil velocity for 12 C18 O2 (vmax ). Only the c.m. angles for which the experiment were sensitive are shown; inelastically scattered 12 C18 O2 from high-impact-parameter collisions are not shown, as their flux would be off-scale. Strong coupling of the P(ET ) and T(θ c.m. ) distributions was observed. angular distribution (see Figures 4.7D and 4.8D), but larger, qualitative changes to the c.m. angular and translational energy distributions did not. Consequently, general statements regarding the scattering direction and degree of energy transfer in the c.m. frame can be made with some certainty. The c.m. angular and translational energy distributions derived from the QCT calculations at Ecoll = 4.5 eV (103.7 kcal mol−1 ) are shown in Figure 4.10 for comparison with the experimental results for scattered 16 O. Center-of-mass angular and translational energy distributions for inelastic scattering obtained from the QCT calculations were in qualitative agreement with the laboratory data, although there are noticeable quantitative disagreements. The theoretical c.m. angular distribution showed fewer scattered products at θc.m. < 20◦ and more scattered products at 40◦ < θc.m. < 90◦ . In addition, the theoretical c.m. translational energy distribution had a sharper peak at high energies and a broader tail at low energies, although the average translational energies were similar (hET i = 85 and 86 kcal mol−1 for B3LYP and BMK, respectively). However, forward convolution of these dis- 125 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.10: Comparison of laboratory and theoretical c.m. (A) angular and (B) translational energy distributions for inelastic scattering of O(3 P) and CO2 at hEcoll i ≈ 100 kcal mol−1 . Distributions obtained from the inelastic scattering of 16 O and from the QCTs are shown here. They were binned (midpoints are shown, connected by spline curves) to provide better statistics for comparison. Both B3LYP and BMK theories show fewer forwardscattered products than were observed in the experiment. Also, the theories predict a translational energy distribution that is more highly peaked at high energies and that has a longer tail at low energies. 126 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 tributions resulted in simulations of the laboratory data that underestimated the proportion of products scattered to low laboratory angles (i.e., Θ = 6◦ , 8◦ , and 10◦ ) and overestimated the low-energy tail in the TOF distributions. Some of this disagreement may be attributable to the ∼14 kcal mol−1 width of the initial collision energy distribution, the inability of the experiment to resolve elastic- from inelastic-scattering contributions to the 16 O signal, and the observed coupling between the c.m. angular and translational energy distributions (see Section 4.5). Still, these laboratory results are consistent with previous studies of hyperthermal O(3 P) scattering from small molecules; a forward-scattering preference and minimal energy transfer was also observed in our earlier studies of D2 , CO, and C2 H6 collisions [Brunsvold et al., 2008; Garton et al., 2006, 2009]. 4.4.2.2 16 O(3 P) + 12 C18 O 2 → 18 O + 16 O12 C18 O As we reported in the preceding chapter, some of the fastest reactively scattered 16 O12 C18 O was attributed to an O-atom exchange reaction between fast-moving 16 O2 and 12 C18 O2 at Ecoll ∼ 160 kcal mol−1 . We describe here the results for the remaining product signal at m/z = 46, which we attribute to the O(3 P) + CO2 isotope exchange reaction. Products of the isotope exchange reaction near 100 kcal mol−1 scattered mainly in the backward direction (θc.m. = 180◦ ), as implied by the five representative laboratory-frame TOF distributions, the c.m. angular and translational energy distributions, and the laboratory-frame angular distribution shown in Figure 4.11. The product c.m. velocity-flux diagram is shown in Figure 4.12. Significant forward and sideways scattering of products was also observed in addition to backward scattering; the T(θc.m. ) distribution indicates that products scattered to 0◦ < θc.m. < 90◦ do so with nearly equal probability, and that scattered products become increasingly more probable as θc.m. approaches 180◦ . On average, the two products had 34.8 kcal mol−1 of total translational energy, or 35% of the available energy (see Figure 4.11B). The peak of the experimental translational energy distribution, P(ET ), was ∼30 kcal mol−1 . These results indicate a significant transfer of translational energy to internal degrees of freedom of the products, which is characteristic of reactions with significant barriers (e.g., ∼25 kcal mol−1 ). 127 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.11: Laboratory reactive scattering data detected at m/z = 46. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for 16 O12 C18 O products of the 16 O(3 P) + 12 C18 O2 → 18 O + 16 O12 C18 O reaction at hEcoll i = 98.8 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. In (A), the best-fit forward-convolution simulations of 16 O12 C18 O products from 16 O(3 P) + 12 C18 O2 collisions (black dot-dashed lines) are shown with those from 16 O2 + 12 C18 O2 collisions at hEcoll i = 158.1 kcal mol−1 (blue dashed lines). The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). 128 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.12: Velocity-flux contour diagram for 16 O12 C18 O products of 16 O(3 P) + 12 C18 O2 collisions in the center-of-mass frame. The white arrows are the initial 16 O(3 P) and 12 C18 O velocity vectors, and the dashed white line is the maximum recoil velocity for 2 16 O12 C18 O (v 16 O12 C18 O products are scattered mainly in the same direction as the max ). initial 12 C18 O2 velocity vector. The theoretical c.m. angular and translational energy distributions derived from the QCT calculations at Ecoll = 4.5 eV (103.7 kcal mol−1 ) are plotted with the experimental data for comparison in Figure 4.13. In general, good agreement between experiments and the theoretical predictions was observed. The experimental best-fit c.m. angular distribution agreed nearly quantitatively for products scattered in the forward direction (small θc.m. ), while only qualitative agreement was found for products scattered in the backward direction (large θc.m. ). The preference for backward-scattered 16 O12 C18 O products suggested by the QCT calculations is also observed in the experimental data. hET i for the experimental P(ET ) is in good agreement, within uncertainty, with those obtained from the B3LYP (hET i = 43 ± 15%) and BMK (hET i = 47 ± 16%) trajectories. Qualitative aspects of the energy transfer during reactive scattering collisions appear to be reproduced in the QCT results, namely, that the product 16 O12 C18 O has a significant amount (≥ 50 kcal mol−1 ) of internal energy, on average. The experimental peak ET , however, is slightly less than the most probable translational energies predicted by the QCT calculations, ∼40 kcal mol−1 . This mild disagreement in the shape of the P(ET ) distribution may arise from uncer- 129 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.13: Comparison of laboratory and theoretical c.m. (A) angular and (B) translational energy distributions for the O(3 P) and CO2 isotope exchange reaction at hEcoll i ≈ 100 kcal mol−1 . Distributions obtained from the inelastic scattering of 16 O and from the QCTs are shown here. They were binned (midpoints are shown, connected by spline curves) to provide better statistics for comparison. Both B3LYP and BMK theories predict fewer backward-scattered products than were observed in the experiment. Also, the theories predict a translational energy distribution that is peaked at slightly higher energies. 130 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 tainties in the experiment and in the forward-convolution analysis. First, the broad O(3 P) velocity distribution in the experiment, and the resulting broad collision energy distribution, could mask any underlying structure in the P(ET ) distribution if the location of the peak in the P(ET ) distribution depends on collision energy. Indeed, the theoretical excitation functions indicate that the reaction cross-section is sensitive to collision energy in near Ecoll = 100 kcal mol−1 (see Figure 4.4). Second, the presence of the O2 + CO2 isotope exchange channel, which was not resolved from the forward-scattered 16 O12 C18 O peak in the laboratory TOF, renders the higher-ET portion of the P(ET ) less certain. Constraints from the backward-scattered component of the laboratory TOF distributions were also limited due to the t −3 dependence of the scattered product intensity in the laboratory-to-c.m.frame Jacobian transformation (see Eq. 3.3), which reduces the instrument’s sensitivity to backward-scattered products. Consequently, the angular distribution of products near θc.m. = 180◦ is less certain, and the observed disagreement between experimental and theoretical c.m. angular and translational distributions could be refined with additional measurements. Last, some uncertainty in the average and peak of the product translational energy distribution in the QCT data arises from the binning process used to obtain better statistics in the distribution; the width of each ET bin was ∼11.5 kcal mol−1 , so disagreements in the P(ET ) peak locations between theory and experiment on the order of 10 kcal mol−1 are not unreasonable. 4.4.2.3 16 O(3 P) + 12 C18 O 2 → 18 O16 O + 12 C18 O Reactively scattered products at m/z = 34 were clearly resolved at Θ = 6◦ , barely detectable at Θ = 10◦ , and not detectable at Θ = 14◦ (see Figure 4.14). While this laboratoryframe angular dependence may imply that 18 O16 O products are mainly forward-scattered, we cannot rule out backward scattering because the experiment was not sensitive to it (see Newton diagram in Figure 4.6); the signal corresponding to the counterproducts at m/z = 30 (12 C18 O+ ) could not be resolved because of high background signal from 12 C18 O2 fragmentation at the ionizer. We obtained a c.m. translational distribution peaked at 56 kcal mol−1 from the laboratory data, which indicated that 18 O16 O + 12 C18 O products had 55.0 131 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.14: Laboratory reactive scattering data detected at m/z = 34. (A) Laboratory TOF, (B) c.m. translational energy, and (C) laboratory angular distributions for 18 O16 O products of the 16 O(3 P) + 12 C18 O2 → 18 O16 O + 12 C18 O reaction at hEcoll i = 98.8 kcal mol−1 . The circles in (A) and (C) are experimental data, while the lines are the best-fit forwardconvolution simulations of the experimental data derived from the c.m. translational energy distribution shown in (B). Experimental sensitivity was not sufficient to obtain a full c.m. angular distribution, so a T(θc.m. ) distribution is not shown. The error bars in (C) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). kcal mol−1 translational energy, or 61% of the available energy, on average. No products were detected at m/z = 36 (18 O2 + ), which would have corresponded to an oxygen-atom abstraction mechanism more complex than simple stripping. Qualitatively, these results are consistent with the QCT results, which predicted a lower reactive cross-section for the oxygen abstraction channel than for the isotope exchange channel. 4.4.2.4 Relative product yields Experimental relative product yields for 16 O(3 P) + 12 C18 O2 collisions at hEcoll i = 98.8 kcal mol−1 were calculated from the integrated cross-sections for each channel, which were obtained from the forward-convolution simulations of the TOF data. Because the signal at m/z = 46 contained contributions from both 16 O(3 P) + 12 C18 O2 and 16 O2 + 12 C18 O2 collisions, 132 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Table 4.3: Comparison of experimental and theoretical yields for the products of O(3 P) + CO2 collisions near 100 kcal mol−1∗ Experiment B3LYP/6-311G(d) BMK/6-311G(d) Non-reactive scattering Oxygen isotope exchange 98.4% 98.2% 98.1% 1.6% 1.8% 1.9% ∗ Uncertainty bounds in the experimental estimates are probably less than ± 0.25%, based on the uncertainties in the integrated count rates at m/z = 46. Uncertainties in the QCT-derived relative yields are less than ± 0.1%. the forward-convolution fits for 16 O2 + 12 C18 O2 isotope exchange were subtracted from the laboratory TOF data before the 16 O(3 P) + 12 C18 O2 cross-section was calculated. Resulting integrated cross-sections were scaled by their electron-impact ionization cross-sections and fragmentation patterns for the comparison; the transmission through the quadrupole mass filter was assumed to be similar for all the small molecules examined here. Using this method, we calculated branching fractions for non-reactive scattering (98.5%), oxygenatom abstraction (0.0004%), and oxygen isotope exchange (1.6%) based on the integrated cross-sections obtained at m/z = 16, 34, and 46, respectively. The oxygen-atom abstraction yield is a lower limit because only a portion of the Newton sphere was observed. The oxygen isotope exchange yield is an upper limit because we compared the integrated cross-section of 16 O12 C18 O products to the yield of scattered 16 O only; the strongly coupled P(ET ) and T(θc.m. ) distributions for inelastic scattering make momentum-matching of 16 O and 12 C18 O2 products difficult. Our experimental branching fractions for the isotope exchange reaction at hEcoll i = 98.8 kcal mol−1 and those calculated from the QCT calculations at Ecoll = 4.5 eV (103.7 kcal mol−1 ) agree within 0.3%, despite a difference of 5 kcal mol−1 in the collision energy (see Table 4.3). This agreement could be coincidental because both the theoretical and laboratory data have significant uncertainties when defining the total cross-section, but our analysis suggests that the agreement persists in spite of these uncertainties. First, Eq. 4.4 shows that the theoretical calculation for the total cross-section depends on the square of maximum impact parameter sampled for reactive scattering (bmax ), but examination of the theoretical opacity function for the oxygen isotope exchange reaction (Figure 4.5) indicates 133 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 that no reactions occur beyond b = 3.5 a0 , so the reactive cross-section should be sufficiently converged with a bmax = 5.0 a0 . Second, the accuracy of the laboratory integrated cross-sections depends on the accuracy of the best-fit c.m. angular and translational energy distributions, but our sensitivity study on the θc.m. → 0◦ extrapolation we used for scattered 16 O resulted in the non-reactive scattering and oxygen isotope-exchange branching fractions fluctuating ∼0.5% when the scattered intensity at θc.m. < 4◦ was varied between twice the best-fit value and zero. Third, the oxygen-atom abstraction reaction contributes to the overall reactive cross-section, but this channel had a negligible contribution to the overall product yield based on the small number of reactive trajectories observed in the QCT calculations and the small amount of 18 O16 O detected in the experiment. Consequently, the agreement between the theoretically derived and experimental relative product yields for the oxygen isotope exchange reaction should be robust. The theoretical reactive cross-sections (Eq. 4.4) were divided by three for the comparison with experiment because the O(3 P) + CO2 surface is triply degenerate at large O(3 P)–CO2 separation distances;. All three electronic states were probed by the experiment, but only one (3 A00 ) was probed in the QCT calculations. Whether the two additional states (e.g., 3 A0 ) lead to reaction under our experimental conditions is unknown, but the good agreement between theory and experiment is consistent with the other two electronic surfaces being either repulsive or unimportant for producing 16 O12 C18 O at these collision energies. If the barrier to isotope exchange on the 3 A0 surface is close to the one the 3 A00 surface, isotope exchange on the 3 A0 surface could also contribute to the experimental product yield; the current theoretical product yield, therefore, should be treated as a lower limit when compared to the experimental value. Degenerate triplet states were also a concern in our study of O(3 P) + C2 H6 collisions, but the laboratory relative product yields there also agreed, within uncertainty, with those derived from QCT calculations [Garton et al., 2009]. 134 L. Y. Yeung Oxygen isotope exchange reactions of CO2 4.5 Discussion 4.5.1 Theoretical studies Chapter 4 Our electronic structure calculations yielded some disagreements with previous work [Bennett et al., 2004; Froese and Goddard, 1993; Mebel et al., 2004; Yang et al., 2005]. First, we reported a geometry and energy for TS1 structure that was significantly different from that predicted by Mebel and coworkers calculated at the CASSCF(16,13)/6-311G(d) level of theory (see Figure 4.2) [Bennett et al., 2004; Mebel et al., 2004]. For example, in Mebel et al.’s 3 A0 TS1 structure, the longest C–O bond was 0.08 Å shorter, the shortest C–O bond was ∼0.02 Å longer, and the most acute bond angle was 17◦ smaller than in our CCSD(T)/aug-cc-pVTZ structure. Interestingly, our 3 A00 TS1 structure shows smaller disagreements with the 3 A0 TS1 structures calculated by Froese and Goddard at the HF/6-31G* and MP2/6-31G* levels of theory. These differences in geometries and the difference in symmetry yielded a TS1 energy 11 kcal mol−1 higher in Mebel et al.’s CCSD(T)/6-311+G(3df) calculation than in our calculation. Mebel et al. did note that their truncated (16,13) active space was a clear shortcoming of their study; it was chosen over the full-valence (22,16) active space due to computational limitations. Second, our calculations indicated that the lowest-energy triplet PES near TS1 had 3 A00 symmetry, not 3 A0 symmetry, as others had reported [Bennett et al., 2004; Froese and Goddard, 1993; Mebel et al., 2004]. We examined this discrepancy first by calculating the single-point CCSD(T)/aug-cc-pVTZ energy of Froese and Goddard’s “T9” structure at both orbital symmetries. In this case, the 3 A0 energy was ∼10 kcal mol−1 above the 3 A00 energy. We also attempted to optimize a TS1-like 3 A0 structure at the CCSD(T)/aug-cc-pVTZ and W4 levels of theory, but we found self-consistent field convergence problems similar to those reported by Froese and Goddard and thus could not locate any stationary points. The 3 A00 state of CO3 near TS1, then, appears to be lower in energy than the 3 A0 state. We argue that these discrepancies were caused by the differing treatment of dynamical correlation in this study and others. The electronic structure of ground singlet CO3 displays vibronic coupling with an array of Jahn-Teller states [Kowalczyk and Krylov, 2007; Liu et al., 135 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 2009], and the resulting energy minima required a high level of dynamical correlation to represent correctly; because of the large number of electronic states within several eV of the lowest triplet PES, vibronic coupling (and therefore dynamical correlation) is likely important here as well. Multiconfigurational self-consistent field methods like CASSCF (used by Mebel et al. for geometry optimizations) do not treat dynamical correlation, and this shortcoming has been implicated in the poor representation of the singlet-CO3 , NO3 , and parabenzyne radicals with these methods [Crawford et al., 2001; Eisfeld and Morokuma, 2000; Kowalczyk and Krylov, 2007]. High-level dynamical correlation is included in coupledcluster methods, which generally yield more accurate thermochemical properties for this class of problems. Furthermore, the agreement between our TS1, TS2, and CO3 energies and those calculated using the W4 method (J. M. L. Martin, private communication) suggest that single-reference calculations with high-level treatment of dynamical correlation can describe the triplet stationary points appropriately. Multi-reference character on other regions of the PES could still be important, however, and is not ruled out by the correspondence between the CCSD(T) and W4 calculations at the stationary points. If strong vibronic coupling on the low-lying electronic states of CO3 is important during reactive trajectories, it could lead to a misrepresentation of the PES curvature by the B3LYP and BMK methods during the QCT calculations. Russ et al. [2004] noted that B3LYP underestimated the magnitude of vibronic interactions in the B–N–B and C3 + model systems, and attributed this tendency to the behavior of the Kohm-Sham molecular orbital Hessian near conical intersections. Because the Kohm-Sham Hessian is common to both B3LYP and BMK theories, both functionals are subject to the same tendency. Large fractions of Hartree-Fock exchange mixed into the BMK functional for improved barrier height prediction may also result in unintended symmetry-breaking on the CO3 PES [Sherrill et al., 1999], as was the case for the CO3 minimum (see Figure 4.2). The results of these calculations are compared with the experimental results below. 136 L. Y. Yeung 4.5.2 Oxygen isotope exchange reactions of CO2 Chapter 4 Non-reactive scattering of O(3 P) and CO2 Non-reactive 16 O(3 P) + 12 C18 O2 collisions mainly scattered products with little change in the initial direction or speed, although some products scattered in directions sideways and opposite their initial direction; these products had lower average velocities. Products showing little deflection from their initial trajectories probably arise from high-impactparameter collisions, while products that are highly deflected probably arise from lowimpact-parameter collisions. These two molecular regimes were supported qualitatively by the theoretical opacity functions (see Figure 4.5), which display separate peaks at low (1.75 a0 ) and high (3.25 a0 ) impact parameters. While large impulsive energy transfer was observed for hyperthermal collisions of Ar and O(3 P) with C2 H6 at low impact parameters [Brunsvold et al., 2004; Garton et al., 2009; Tasic et al., 2007], large energy transfer was also observed for “failed” reactive collisions of hyperthermal O(3 P) and CO; the CO2 * complex resulting from these collisions can dissociate to yield products corresponding to isotope exchange or inelastic scattering, depending on the identity of the dissociating oxygen atom. This mechanism resulted in a low-energy tail in the translational energy distribution for inelastic scattering of O(3 P) + CO [Brunsvold et al., 2008]. Our analysis of inelastically scattered 12 C18 O2 molecules indicated that one pair of P(ET ) and T(θc.m. ) distributions was insufficient to simulate the laboratory data accurately. This observation corresponds to a breakdown of the assumption that the c.m. angular and translational energy distributions are separable. Our use of two pairs of P(ET ) and T(θc.m. ) distributions to fit the laboratory data is similar to previous studies where inelastic scattering of Cl + C3 H8 and hyperthermal O(3 P) + C2 H6 were investigated [Blank et al., 1998; Garton et al., 2009]. In both the previous cases and in the present case, the polyatomic species had a large number of degrees of freedom into which translational energy can be transferred upon collision. Consequently, a dependence of energy transfer on the impact parameter is not unexpected; different impact parameters may preferentially excite different degrees of freedom. In the system studied here, the product translational energy decreases as 12 C18 O2 becomes more forward-scattered (small Θ, corresponding to low-impact-parameter collisions), implying that 12 C18 O2 becomes increasingly internally excited as O–CO2 collisions 137 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 become more rebound-like. The type and mechanism of internal excitation are uncertain, however, because the “failed” reaction might also contribute to the observed c.m. angular and translational energy distributions of forward-scattered 12 C18 O2 . We note that our experimental data did not display a slow tail in the 16 O TOF distributions characteristic of the “failed” reaction in the O(3 P) + CO system. 4.5.3 Oxygen isotope exchange, O(3 P) + CO2 → O + CO2 Laboratory data for the isotope exchange reaction at hEcoll i = 98.8 kcal mol−1 shows a backward-scattering preference, and thus is evidence for a direct reaction mechanism. The isotopically exchanged products also had relatively low translational energy (hET i = 35% Eavail ). These two observations suggest that the reaction involves a short-lived CO3 ∗ intermediate and/or occurs at low impact parameters where the transfer of energy to internal degrees of freedom of the products is efficient. With 74 kcal mol−1 excess energy, the O(3 P)–CO2 collision need not be head-on to have enough energy to surmount the TS1 activation barrier. The long C–O bond length (1.6 Å) and mild O–C–O bending angle (150◦ vs. 180◦ for CO2 ) in TS1 also suggests that the entrance and exit barriers are neither particularly early nor late. Hence, the CO3 ∗ complex could exist for several vibrational periods. Efficient transfer of energy into vibrational modes of the CO3 ∗ intermediate would be required for an isotope exchange event to occur because inefficient coupling of that energy would increase the probability of redissociating the incident oxygen atom, resulting in an inelastic collision. A direct isotope exchange mechanism through a short-lived CO3 complex is qualitatively in agreement with our QCT calculations (see Figure 4.15). For O(3 P) + CO2 collisions Figure 4.15: Snapshots of a quasiclassical trajectory for O(3 P) + CO2 isotope exchange through a short-lived CO3 ∗ complex at 1.5 eV (34.6 kcal mol−1 ) collision energy. The incident oxygen atom is highlighted for clarity. 138 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 resulting in oxygen isotope exchange, a CO3 ∗ complex forms when the incoming oxygen atom interacts with the carbon atom on CO2 (see also the opacity functions in Figure 4.5). In some cases, the CO3 ∗ complex existed for less than one vibrational period (the reaction is nearly direct) while in others it existed for many vibrational periods. After some time (typically leq 200 fs), one of the oxygen atoms initially part of the CO2 detaches to leave behind a new CO2 molecule. Head-on collisions at higher collision energies tended to form complexes existing for shorter times than those formed similarly at lower energies. Higher energies also tended to form CO3 ∗ complexes that tumbled ≥ 360◦ in the plane of the reaction. In all cases, however, the CO3 ∗ complex lasted less than a picosecond. These data support an isotope exchange reaction mechanism that begins with an interaction between O(3 P) and the carbon atom of CO2 to form a short-lived CO3 ∗ reaction complex. The identity of the dissociating oxygen atom determines the reaction’s classification. If the dissociating oxygen atom is one originally on CO2 , then the trajectory is reactive; if it is the incident oxygen atom, then the trajectory is inelastic. The lifetime of the CO3 reaction complex determines the c.m. angular and translational energy distributions of product CO2 . Longer-lived CO3 complexes should yield smaller average translational energies because they will have more time to redistribute the initial translational energy to internal degrees of freedom. This mechanism for the O(3 P) + CO2 isotope exchange reaction is different from that observed by Perri et al. for the O(1 D) + CO2 → O(3 P) + CO2 isotope exchange reaction at Ecoll = 4.2 and 7.7 kcal mol−1 , which samples part of the same PES [Perri et al., 2003, 2004]. In those molecular-beam experiments, the reactively scattered CO2 products had an isotropic (forward-backward symmetric) angular distribution and ∼50% of the available energy in translation; these results were evidence for a CO3 ∗ intermediate complex that lasted for at least several rotational periods (> 1 ps). These dynamics are not inconsistent with our O(3 P) + CO2 results, however, because the two studies may sample different parts of the 3 A00 and/or 3 A0 PESs. O(3 P) + CO2 collisions on the 3 A0 surface could, in principle, cross onto the 1 A0 surface to yield reactively scattered O(1 D) + CO2 products. One possible triplet-singlet crossing mech- 139 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 anism could be through spin-orbit coupled radiationless transitions, i.e., the reverse of what Mebel et al. had suggested for the O(1 D) + CO2 reaction, because the spin-orbit coupling terms and Franck-Condon factors are favorable [Mebel et al., 2004]. Thus, we evaluated the general possibility of intersystem crossing (ISC) during our experiments by performing forward-convolution fits of the laboratory data that included the ∼45 kcal mol−1 endothermicity of O(1 D) vs. O(3 P). Satisfactory fits of the laboratory TOF and angular distributions were obtained (see Figure 4.16); the peak and average of the P(ET ) distribution were 34 and 30.7 kcal mol−1 (63% and 58% Eavail ), respectively. Consequently, ISC cannot be explicitly ruled out by the experimental data. The diabatic radiationless transition probability, however, decreases exponentially as a function of velocity [Landau, 1932], and no evidence for ISC has been observed during our previous dynamics studies at hyperthermal velocities [Brunsvold et al., 2007]. The qualitative agreement between the experimental and QCTderived dynamics on the lowest triplet PES is consistent with the oxygen isotope exchange reaction exiting on a triplet surface, although more dynamics studies will be necessary to test this hypothesis. 4.5.4 Oxygen-atom abstraction, O(3 P) + CO2 → O2 + CO Our laboratory observation of the oxygen abstraction reaction in the forward direction with a moderate amount of energy transfer (∼50%) could arise from early-barrier strippingtype mechanisms through TS2 or TS3. Hammond’s postulate states that for endothermic reactions, the transition state should be late and product-like. However, the small endothermicity relative to the barrier height (see Figure 4.1 and Table 4.1) for oxygen-atom abstraction suggests that TS2 and TS3 should be more reactant-like. Indeed, the bond lengths of CO and O2 are significantly longer in TS2 and TS3 than at equilibrium for the isolated molecules, which are 1.14 and 1.21 Å, respectively, at CCSD(T)/aug-cc-pVTZ. Theoretical trajectories yielding O2 + CO products occurred generally in one of two ways: through a stripping-type mechanism and through a CO3 ∗ complex. In the strippingtype mechanism (see Figure 4.17A), the incoming oxygen atom interacts principally with one of the oxygen atoms on CO2 to form TS3 directly. The C–O bond then breaks, releas- 140 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.16: Laboratory reactive scattering data detected at m/z = 46, fit assuming an ISC mechanism. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for 16 O12 C18 O products of the 16 O(3 P) + 12 C18 O2 → 18 O16 O(1 D) + 12 C18 O reaction at hE −1 coll i = 98.8 kcal mol . The circles in (A) and (D) are experimental data, while the lines are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. In (A), the best-fit forward-convolution simulations of 16 O12 C18 O products from 16 O(3 P) + 12 C18 O collisions (black dot-dashed lines) are shown 2 with those from 16 O2 + 12 C18 O2 collisions at hEcoll i = 158.1 kcal mol−1 (blue dashed lines). The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). 141 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.17: Snapshots of quasiclassical trajectories for the O(3 P) + CO2 → O2 + CO reaction. (A) A stripping-type mechanism through TS3 at 6.5 eV (149.8 kcal mol−1 ) collision energy calculated at the B3LYP/6-311G(d) level of theory. (B) A CO3 reaction-complex mechanism through TS2 at 5.5 eV (126.7 kcal mol−1 ) collision energy calculated at the BMK/6-311G(d) level of theory. The incident oxygen atoms are highlighted for clarity. ing O2 + CO products. Of all the QCTs run, only two of these stripping-type trajectories were observed, and they occurred at Ecoll = 6.5 eV (149.8 kcal mol−1 ) using B3LYP/6311G(d). The remaining 27 O2 + CO-producing trajectories proceeded through a CO3 ∗ complex mechanism (see Figure 4.17B). In that mechanism, the incoming oxygen atom interacts first with the carbon atom of CO2 to form a short-lived CO3 ∗ complex, similar to that observed in the isotope-exchange trajectories. This complex rarely survived more than one vibrational period. An oxygen atom is then released and then interacts with a CO2 bound oxygen atom as the CO2 rotates. Last, an O–O bond forms as the adjacent C–O bond breaks to form O2 + CO products. A key difference between the two O2 + CO-producing mechanisms is that the CO3 ∗ complex mechanism requires a slow recoil of the oxygen atom that dissociated initially. Following complex formation in a high-energy collision, the nascent CO2 will have sufficient internal energy (∼70 kcal mol−1 ) to form the O2 + CO products only if the O atom dissociates with low translational energy. When the O atom escapes the CO3 ∗ complex with high translational energy, the nascent CO2 rotates too slowly for any further reaction to take place (in these cases, the trajectory results in either inelastic scattering or isotope 142 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 exchange). With so much excess energy, however, the reaction need not take the lowest energy path [Zhang et al., 2008]; the slow recoiling oxygen atom in the CO3 ∗ -complex mechanism resembles the “roaming’ H-atom and methyl group in formaldehyde [Townsend et al., 2004] and acetaldehyde [Houston and Kable, 2006] photodissociation, respectively. We note that the stripping-type mechanism would have produced 18 O16 O molecules in the experiment exclusively, whereas the CO3 ∗ -complex mechanism can produce 18 O2 in addition to 18 O16 O. Our laboratory observation of m/z = 34 products is consistent with both oxygen abstraction mechanisms, but the lack of signal due to m/z = 36 products in the forward direction (where there was negligible background) is evidence against the CO3 ∗ complex mechanism. The CO3 ∗ -complex mechanism, however, comprised 27 of the 29 oxygen-atom abstraction trajectories obtained from the QCT calculations, and only one of those trajectories would have produced m/z = 34 products. The two remaining trajectories proceeded through the stripping mechanism. This preference for the CO3 ∗ -complex mechanism observed in the QCT calculations may be a consequence of the ∼50 kcal mol−1 lower barrier for CO3 formation and the ∼13 kcal mol−1 lower energy of TS2, both relative to the energy of TS3. Additional experimental and theoretical studies with a higher SNR, perhaps at higher collision energies, will be required to elucidate the mechanisms of this reaction. 4.6 Conclusions We have investigated the dynamics of O(3 P) + CO2 collisions at hyperthermal collision energies. Non-reactive scattering was dominated by high-impact-parameter collisions, which did not perturb the initial velocity of the reactants significantly. Lower impact parameters resulted in increased translational-to-internal energy transfer. Both the oxygen isotope-exchange and the atom-abstraction reaction channels were observed directly by our crossed-molecular-beam apparatus. The oxygen isotope exchange reaction displayed an anisotropic angular distribution with a large amount of translational-to-internal energy transfer, suggesting that the reaction occurs at low impact parameters through a short-lived intermediate CO3 ∗ complex. The mechanisms for both non-reactive scattering and oxygen isotope exchange were supported qualitatively, but not quantitatively, by the QCT calcula143 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 tions on the 3 A00 surface. Nonadiabaticity during inelastic and reactive trajectories cannot be ruled out and its effects should be investigated; both inelastic and reactive trajectories may be sensitive to the coupling between the lowest triplet (3 A00 ) PES and nearby (e.g., 3 A0 ) electronic surfaces. With ∼100 kcal mol−1 collision energy, the experiment may probe regions of the PES far from the TS1, TS2, TS3, and CO3 structures; the presence of several other surfaces (both triplet and singlet) within this energy range [Kowalczyk and Krylov, 2007; Liu et al., 2009], the possibility of vibronic effects due to Jahn-Teller-like distortion, and the failure of densityfunctional methods to capture the dynamics quantitatively all suggest that a higher-level treatment of the PES would be desirable. While the transition states and stationary points on the lowest triplet PES may be described well with density-functional calculations, this may not be the case in other regions of the PES where vibronic interactions can affect its curvature. A more complete, high-level description of the PES, along with more dynamics experiments, will be required to describe the dynamics of isotope exchange on the lowest triplet PES quantitatively. 4.7 Acknowledgements We thank Ned F. Lindholm for experimental assistance. This work was supported by the Missile Defense Agency under cooperative agreement HQ0006-05-2-0001. L. Y. Y. was supported by the Davidow Fund, and G. C. S. was supported by the Air Force Office of Scientific Research grant FA955D-07-1-0095. 144 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Appendices 145 Chapter 4 L. Y. Yeung 4.A Oxygen isotope exchange reactions of CO2 Chapter 4 Differential scattering cross-sections from 1.0 – 6.5 eV Theoretical center-of-mass differential scattering cross-sections for the oxygen isotope exchange reaction (Figure 4.18) showed a preference for backward scattering at all collision energies. The incident oxygen atom, attached to the product CO2 molecule, appeared to prefer scattering in a direction opposite its initial direction. As the collision energy increased, however, the angular distribution of products showed little qualitative change: Reactively scattered products showed a slight preference for backward scattering up to Ecoll = 6.5 eV (149.8 kcal mol−1 ), the highest collision energy considered in this study. The theoretical c.m. product translational energy distributions showed significant (≥ 50%) transfer of the available energy into internal degrees of freedom of the products at all collision energies = 2.5 eV (57.6 kcal mol−1 ). The QCT data below Ecoll ≥ 2.5 eV did not contain statistically significant number of reactive trajectories, i.e., > 30, so they were not included in this analysis. P(ET ) distributions became broader as the collision energy increased, though the proportion of energy remaining translation was similar at all collision energies. A bimodal distribution of translational energies may exist in the products of BMK trajectories run at 2.5, 3.5, and 4.5 eV collision energy (57.6, 80.7, and 103.7 kcal mol−1 , respectively); for instance, separate peaks were observed at ∼50% and ∼80% of the available energy for the 2.5-eV trajectories, although there is considerable uncertainty in the theoretical translational energy distribution (see Figure 4.18). Additional QCT calculations will be required before structure in the product translational energy distributions can be determined conclusively. 146 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.18: Center-of-mass angular and translational energy distributions for the O(3 P) + CO2 isotope exchange reaction derived from QCT calculations at the (A and B) B3LYP/6-311G(d) and (C and D) BMK/6-311G(d) levels of theory. Distributions with more than 30 reactive trajectories are shown. At both levels of theory and all collision energies shown, reactive scattering shows a preference for backward scattering (θc.m. > 90◦ ) with a moderate (≥ 50%) transfer of translational energy to internal degrees of freedom of the products. 147 L. Y. Yeung 4.B Oxygen isotope exchange reactions of CO2 Chapter 4 Estimating uncertainty in the laboratory angular distributions For this analysis we treat the TOF distribution at a given laboratory angle Θ as a type of Monte Carlo integration of the ‘true’ TOF distribution, and we estimate the variance in the integrated area accordingly. Under this approximation, the integrated area, I(Θ), is equivalent to the area of a rectangle with a width equal to the total time range, ttotal , and height equal to the average number density over that time range, hN(t)itotal . More formally, this relation can be written as a discrete sum over the channels on the MCP, each of which corresponded to a 1 µs dwell time: ttotal I(Θ) = 1 ttotal ∑ N(ti ) = ttotal [ ttotal ∑ N(ti )] = ttotal hN(t)itotal i=1 (4.8) i=1 The variance of I(Θ), however, must be evaluated as a function of time because the number density at a given arrival time at the detector, N(t), varied with flight time in each TOF distribution. Consequently, the TOF distribution was further divided into a set of bins for which the variance was calculated and summed over the total TOF distribution using the following relation: 2 σN(t) bin = 1 f [tbin N(ti )]2 − [tbin hN(t)ibin ]2 tbin ∑ i 2 σI(Θ) = 2 ∑ σN(t) bin (4.9) (4.10) bins where i and f represent the first and last members of each data bin. The standard deviation, σI(Θ) , was calculated by taking the square root of the variance. We note some degree of sensitivity in the calculated σI(Θ) values on tbin because the N(t) distributions show significant structure; consequently, we have reported conservative estimates of σI(Θ) using the 2 minimum bin size of tbin = 3 µs, or 3 data points per σN(t) bin 148 calculation. L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 5 Chapter 5 Summary and outlook 5.1 New signatures, new reactions Presently, the large enrichment in 16 O13 C18 O we found in the stratospheric polar vortex is still unexplained. The laboratory photochemical experiments we reported in Chapter 2 seem to rule out O(1 D) + CO2 isotope exchange; stratospheric 16 O13 C18 O should get more depleted with increasing extent of isotope exchange, not enriched, and we observed this trend as a decrease in ∆47 in field samples from the mid-latitude stratosphere. What, then, could enrich 16 O13 C18 O in the polar vortex, and what might we be able to learn from future studies? We suggested in Chapter 2 that fast low-temperature isotopic equilibration of CO2 on stratospheric particles (e.g., PSCs) could be responsible for the high ∆47 values in the polar vortex. Our initial tests of the PSC-isotope-equilibration hypothesis suggested that isotopic equilibration on certain HNO3 ices and H2 SO4 :HNO3 :H2 O mixtures is slow, and is therefore unlikely to produce 16 O13 C18 O enrichments on timescales that would be consistent with our polar vortex data. The CO2 isotopic equilibration rate, however, could be sensitive to particle structure and composition. PSCs and cirrus clouds form under similar conditions, but they can differ in bulk and surface composition [Zondlo et al., 2000]; the structure, physics, and chemistry of these particles are still not understood [Dash et al., 2006; Lowe and MacKenzie, 2008], so the role of CO2 isotopic equilibration on ice particle surfaces remains uncertain. Future laboratory work on CO2 –ice surface interactions may shed light on the structure and composition of these and other atmospherically important particles. 149 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 5 We also identified three new reactions, O2 + CO2 and O(3 P) + CO2 isotope exchange and O(3 P) + CO2 → O2 + CO, in our crossed-molecular-beam experiments. Because of the ≈160 kcal mol−1 reaction barrier for O2 + CO2 isotope exchange, and the ≈75 kcal mol−1 barrier for O(3 P) + CO2 → O2 + CO, they are unlikely to be important in the stratosphere. O(3 P) + CO2 , in contrast, has a reaction barrier (≈ 25 kcal mol−1 ) that is atmospherically accessible, in principle. 5.2 Potential atmospheric importance of O(3 P) + CO2 The laboratory observation of O(3 P) + CO2 isotope exchange at hyperthermal energies may have implications for modeling the oxygen isotope cycling in the middle and upper atmosphere because current models do not include O(3 P) + CO2 reactions explicitly [Liang et al., 2007, 2008; Thiemens et al., 1995; Yung et al., 1991, 1997]. Here, I suggest that O(3 P) + CO2 reactions in the upper atmosphere could affect the oxygen isotope distribution in CO2 . The O(3 P) + CO2 isotope exchange reaction could yield isotope effects qualitatively different from those in the O(1 D) + CO2 reaction because its mechanism is direct, unlike the mechanism involving a long-lived CO3 ∗ intermediate for the O(1 D) + CO2 reaction [Chen et al., 2009; Perri et al., 2003, 2004]. Instead, like the O3 ∗ complex in the O(3 P) + O2 isotope exchange reaction [Van Wyngarden et al., 2007], the CO3 ∗ reaction complex formed from O(3 P) + CO2 does not live long enough for its energy to randomize; thus, dynamical isotope effects are likely to be important to its isotope-specific branching fractions. These types of non-statistical isotope effects are believed to be partly responsible for “anomalous” formation rates of stable O3 from the O3 ∗ complex for different isotopologues [Babikov et al., 2003; Gao and Marcus, 2001; Schinke et al., 2006]. Due to limitations in our apparatus, however, we were unable to investigate the O(3 P) + CO2 isotope exchange dynamics near the predicted reaction threshold, which is more relevant to the atmosphere. Our reactive trajectories at Ecoll = 1.0 and 1.5 eV (23.0 and 34.6 kcal mol−1 , respectively), however, suggest that isotope exchange is still direct near the calculated reaction barrier. The overall importance of the O(3 P) + CO2 isotope exchange reaction to reactive oxygen cycling in the atmosphere, however, depends on (1) the reaction’s excitation function 150 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 5 and (2) the proportion of O(3 P) in the atmosphere with sufficient translational energy to surmount the reaction barrier. In the absence of experimental data, high-level variational quantum calculations can assign an upper limit to the TS1 barrier. The CCSD(T)/aug-ccpVTZ energy for TS1 (25 kcal mol−1 ) reported in this work implies that relative velocities of ≥ 3 km s−1 in the ground-state reactants will be required to open the isotope exchange channel; ozone photolysis in the Hartley band (220 – 310 nm) and at shorter wavelengths yields O(3 P) + O2 (3 Σ− g ) photofragments having a total translational energy in excess of 25 kcal mol−1 and as high as 100 kcal mol−1 [Fairchild et al., 1978; Kinugawa et al., 1990; Shamsuddin et al., 1994; Stranges et al., 1995; Syage, 1995; Takahashi et al., 1998]. Our preliminary hard-sphere collision modeling (see Appendix 2.D) using cross-sections for the velocity relaxation of O(1 D) by N2 [Matsumi and Chowdhury, 1996; Matsumi et al., 1994b] suggests that the size of the reactive O(3 P) reservoir could be as high as several percent that of O(1 D). Future theoretical and experimental studies can elucidate the shape of the reaction’s excitation function, which is needed before an appropriate simulation can be constructed. Finally, we note that during our laboratory study of the O2 /O3 /CO2 photochemical system using a mercury lamp as an actinic light source (185 and 254 nm), we observed deviations from modeled results at long irradiation times (t ∼ days; see Figure 2.8); a minor O(3 P) + CO2 channel could address part of this discrepancy, as well as some of the disagreements between earlier studies [Chakraborty and Bhattacharya, 2003; Johnston et al., 2000; Shaheen et al., 2007; Wen and Thiemens, 1993]. The yield of hyperthermal O(3 P) during O3 photolysis depends on wavelength [Stranges et al., 1995; Takahashi et al., 1998], however, so this hypothesis awaits further testing with systematic studies of the O2 /O3 /CO2 photochemical system. Claims of hyperthermal O(3 P) + CO2 chemistry in the atmosphere based on laboratory data must be met with some skepticism, however. Both N2 and O2 are efficient energy quenchers for even the most reactive atmospheric species, and the steady-state population of fast-moving O(3 P) will be determined largely by its translational relaxation rate in air. In addition, thermal averaging collapses most reaction rates towards the chemical kinetic limit, so any atmospheric signature of the O(3 P) + CO2 reaction will be difficult to identify 151 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 5 unless the associated isotope effect is large and unique. Previously published reports of hyperthermal chemistry in the atmosphere based only on laboratory evidence have been controversial due to the lack of an unequivocal signature in the field data [Li et al., 2008; Miller et al., 1994]. 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Yeung Oxygen isotope exchange reactions of CO2 © 2010 Laurence Yip-Lun Yeung All Rights Reserved ii Copyright L. Y. Yeung Oxygen isotope exchange reactions of CO2 Inspiration Small quantities of different gases were added to separate portions of a non-inflammable mixture of dry carbonic oxide and oxygen, and the spark was then passed. In all cases where a gas containing hydrogen was introduced, the mixture exploded; in all cases where a gas containing no hydrogen was introduced, the mixture did not explode. — Harold Dixon, The Combustion of Carbonic Oxide and Hydrogen, 1886. iii L. Y. Yeung Oxygen isotope exchange reactions of CO2 Acknowledgements Acknowledgements This body of work would not have been possible without the intellectual, spiritual, and financial support from professor Mitchio Okumura, professor John Eiler, and Dr. William Davidow. Mitchio and John have taught me how to think critically and quantitatively about scientific problems; their unending creativity, enthusiasm, and wisdom continue to inspire me. Dr. Davidow’s generous endowment funded all of this research and much more not documented here. Only with his support was I able to pursue these risky projects. To my collaborators, professors Hagit Affek, Kristie Boering, Elliot Atlas, Tim Minton, Jon Camden, and George Schatz; Drs. Sue Schauffler, Jeff Paci, Weifu Guo, Kate Hoag, and Jianming Zhang; and Mr. Aaron Wiegel: This work was a collective effort, and I dare not take the credit for any more than my own modest contribution to it. Thank you for your time, patience, lab equipment, and fishing lessons. To the Okumura group, the Eiler group, and other mentors, professors Jack Beauchamp, Rudy Marcus, Geoff Blake, Yuk Yung, Zhengrong Wang, Julie Fry, Rose Came, Kate Huntington, Ben Passey, Naomi Levin, and Aradhna Tripathi; Drs. Pin Chen, Joe Hodges, Chip Miller, Linda Brown, Andrew Mollner, David Robichaud, Aaron Noell, Nathan Eddingsaas, and Mathieu Daëron; Mr. Bill Bing; fellow students Kana Takematsu, Matt Sprague, Kathleen Spencer, Dave Long, Sigrid Barklund, Aileen Hui, Thinh Bui, Nathan Honsowetz, and Heather Widgren: Most of my education here has been at your hands. Thank you for your time, wisdom, skepticism, and coffee. Finally, to my friends and family: You are the music of my life. You are the rhythm, the harmony, and melody. If music be the food of love, play on. Nothing I could say would ever be enough to express my gratitude. I am excited for whatever misadventures lie ahead. iv L. Y. Yeung Oxygen isotope exchange reactions of CO2 Abstract Abstract This dissertation describes laboratory studies of three oxygen isotope exchange reactions — O(1 D) + CO2 , O2 + CO2 , and O(3 P) + CO2 — and their importance to oxygen cycling in the upper atmosphere. First, we studied the isotope exchange reaction O(1 D) + CO2 , which is believed to govern the oxygen-isotope budget of CO2 in the stratosphere. Our combined field, laboratory, and modeling study of the exceptionally rare 16 O13 C18 O isotopologue revealed that O(1 D) + CO2 explains only part of the stratospheric CO2 isotopologue budget, not all of it as previously thought: O(1 D) + CO2 could not explain the large enrichments of 16 O13 C18 O (i.e., of the “∆47 ” tracer) at high Northern latitudes. Mesospheric and heterogeneous chemistry of CO2 were proposed as possible sources of this meridional variation in 16 O13 C18 O. Therefore, we performed crossed-molecular-beam experiments to investigate the chemistry of CO2 at hyperthermal collision energies; this class of reaction could be important in the upper atmosphere, where low gas densities and high rates of photochemistry increase the relative probability of hyperthermal reactions. Our experimental and theoretical study of the O2 + CO2 isotope exchange reaction showed that the reaction can occur through a short-lived CO4 reaction complex, which leads to O2 + CO2 products that are highly internally excited, but possibly still in their ground electronic state. Our study of O(3 P) + CO2 collisions at hyperthermal energies showed that O(3 P) + CO2 isotope exchange can occur in the upper atmosphere, proceeding through a short-lived CO3 reaction complex. The O(3 P) + CO2 → O2 + CO reaction was also observed, and our data suggest that it can proceed through a ‘stripping’ mechanism or a CO3 complex. These reactions demonstrate new ways in which oxygen can be cycled through CO2 in the atmosphere; their isotope effects, manifest in the isotopic composition of atmospheric CO2 , may impose independent constraints on atmospheric transport and biosphere-atmosphere interactions. v L. Y. Yeung Oxygen isotope exchange reactions of CO2 Table of contents Contents Acknowledgements iv Abstract v 1 Introduction 1.1 CO2 in the global carbon cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Stable isotopes, ‘clumped’ and otherwise . . . . . . . . . . . . . . . . . . . . 1.3 Anomalous isotopic enrichments in stratospheric CO2 . . . . . . . . . . . . . 1.4 Insights from the physical chemist’s toolbox . . . . . . . . . . . . . . . . . . 1.5 Executive summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 2 5 8 Appendices 1.A Isotopic notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.B Copyright declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 10 12 2 Large and unexpected enrichment in stratospheric 16 O13 C18 O 2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Field sample collection and analysis . . . . . . . . . . . . . . . . . . . . . . . 2.4 Field results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Laboratory photochemical experiments . . . . . . . . . . . . . . . . . . . . . 2.5.1 13 C/12 C kinetic isotope effect experiments . . . . . . . . . . . . . . . 2.5.2 Continuous-irradiation experiments . . . . . . . . . . . . . . . . . . . 2.5.3 Conclusions from laboratory measurements . . . . . . . . . . . . . . 2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 O(1 D)+CO2 only explains mid-latitude 16 O13 C18 O variations . . . . . 2.6.2 Effects of intra-stratospheric chemistry and mixing . . . . . . . . . . 2.6.3 Effects of mesospheric and heterogeneous chemistry . . . . . . . . . 2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 14 15 16 17 18 21 32 34 36 36 37 39 47 47 Appendices 2.A Mixing effects on isotopic composition . . . . . . . . . . . . . . . . . . . . . 2.B Practical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.B.1 IRMS long-term signal stability . . . . . . . . . . . . . . . . . . . . . 2.B.2 IRMS vs. optical methods . . . . . . . . . . . . . . . . . . . . . . . . 2.C Low-temperature cell for 13 C/12 C KIE experiments . . . . . . . . . . . . . . . 2.D MATLAB code for hard-sphere collision model . . . . . . . . . . . . . . . . . 49 50 52 52 53 58 67 vi L. Y. Yeung Oxygen isotope exchange reactions of CO2 Table of contents 2.D.1 montecarlo.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.D.2 scatter.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 69 3 A hyperthermal O-atom exchange reaction, O2 + CO2 3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Theoretical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Proposed mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 72 73 73 73 80 87 89 92 93 Appendices 3.A Non-reactive scattering of O2 and CO2 . . . . . . . . . . . . . . . . . . . . . 3.B MATLAB program for generating Newton diagrams . . . . . . . . . . . . . . 3.B.1 NewtonD.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.B.2 NewtonDcalc.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.B.3 NewtonDplot.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 96 101 101 103 104 4 Dynamics of O(3 P) + CO2 collisions at hyperthermal energies 4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Theoretical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Electronic structure calculations . . . . . . . . . . . . . . . . . . . . . 4.3.2 Reaction dynamics calculations . . . . . . . . . . . . . . . . . . . . . 4.4 Experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Theoretical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Non-reactive scattering of O(3 P) and CO2 . . . . . . . . . . . . . . . 4.5.3 Oxygen isotope exchange, O(3 P) + CO2 → O + CO2 . . . . . . . . . 4.5.4 Oxygen-atom abstraction, O(3 P) + CO2 → O2 + CO . . . . . . . . . 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 110 111 113 113 118 123 123 125 139 139 141 142 144 147 148 Appendices 149 4.A Differential scattering cross-sections from 1.0 – 6.5 eV . . . . . . . . . . . . 150 4.B Estimating uncertainty in the laboratory angular distributions . . . . . . . . 152 5 Summary and outlook 153 5.1 New signatures, new reactions . . . . . . . . . . . . . . . . . . . . . . . . . 153 5.2 Potential atmospheric importance of O(3 P) + CO2 . . . . . . . . . . . . . . . 154 Bibliography 157 vii L. Y. Yeung Oxygen isotope exchange reactions of CO2 Figures List of Figures 1.1 1.2 1.3 Schematic of atmospheric CO2 sources and sinks. . . . . . . . . . . . . . . . . Bulk oxygen isotope composition of stratospheric CO2 . . . . . . . . . . . . . . Potential energy surface for CO3 (3 A00 ) from Mebel et al. [2004]. . . . . . . . . 2.1 2.2 2.3 2.4 2.5 2.6 Meridional variation of ∆47 measured in stratospheric samples. . . . . . . . . 18 Correlation between ∆47 and stratospheric tracers. . . . . . . . . . . . . . . . 19 ∆17 O values vs. long-lived stratospheric tracer mixing ratios. . . . . . . . . . . 19 Schematic of O(1 D) + CO2 reaction-purification-analysis procedure. . . . . . 21 FT-IR spectrum of synthesized N2 18 O between 1100 cm−1 and 4000 cm−1 . . 24 Modeled O(1 D) + CO2 reaction collision energy distributions at different He bath gas pressure (T = 300 K). . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Changes in ∆47 vs. ∆δ 18 O after pulsed UV photolysis at 300 K and 229 K. . . . 30 Changes in ∆47 vs. ∆17 O of CO2 after continuous UV irradiation of O2 /O3 /CO2 mixtures with a Hg lamp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 How mixing two arbitrary reservoirs of CO2 can be nonlinear in ∆47 . . . . . . 51 Allan-variance plot of ∆47 over 40 IRMS acquisitions. . . . . . . . . . . . . . . 53 Schematic of conflat chamber used for low-temperature 13 C/12 C KIE experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Photograph of conflat chamber used for low-temperature 13 C/12 C KIE experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Cold cell assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Machining diagram for the OFHC copper tube. . . . . . . . . . . . . . . . . . 61 Machining diagram for the OFHC copper conduction block. . . . . . . . . . . 62 Machining diagram for the OFHC copper heat transfer block. . . . . . . . . . 63 Machining diagram for the brass heat transfer block. . . . . . . . . . . . . . . 63 Machining diagram for the OFHC copper connection to the liquid N2 feedthrough. 64 Cold cell assembly for O(1 D), OH + CH4 KIE experiments. . . . . . . . . . . . 65 Machining diagram illustrating the modifications made to the conduction block for O(1 D), OH + CH4 KIE experiments. . . . . . . . . . . . . . . . . . . . . . 65 Machining diagram for the OFHC copper heat transfer block designed for O(1 D), OH + CH4 KIE experiments. . . . . . . . . . . . . . . . . . . . . . . . 66 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 3.1 3.2 3.3 3.4 Crossed-molecular-beam apparatus with hyperthermal oxygen source. . . . . Canonical Newton diagram for hyperthermal 16 O2 + 12 C18 O2 collisions. . . . Velocity distribution of hyperthermal oxygen beam. . . . . . . . . . . . . . . . Laboratory TOF distribution of m/z = 46 (16 O12 C18 O+ ) at Θ = 6◦ , with the inelastic scattering signal removed. . . . . . . . . . . . . . . . . . . . . . . . . viii 3 5 6 74 75 77 80 L. Y. Yeung 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 Oxygen isotope exchange reactions of CO2 Figures TOF distributions for 16 O12 C18 O products at laboratory angles Θ = 6◦ and 8◦ with the inelastic scattering signal removed. . . . . . . . . . . . . . . . . . . . 82 TOF distributions for 16 O12 C18 O (m/z = 46) at various laboratory angles Θ with the inelastic scattering signal removed. . . . . . . . . . . . . . . . . . . . 83 Center-of-mass-frame (A) angular and (B) translational energy distributions from the 16 O2 + 12 C18 O2 oxygen isotope exchange reaction obtained from TOF fits of m/z = 46. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Velocity-flux contour diagram for 16 O12 C18 O products of 16 O2 + 12 C18 O2 collisions in the center-of-mass frame. . . . . . . . . . . . . . . . . . . . . . . . . 84 Energetically allowed neutral product channels from O2 + CO2 collisions. . . 86 Calculated energies and structures on the lowest triplet PES of O2 + CO2 . . . 87 Calculated stationary point geometries on the lowest triplet PES of CO4 . . . . 89 Calculated energies and structures on the lowest triplet PES of O2 + CO2 . . . 89 Singly-occupied molecular orbitals (SOMOs) in the CO4 (3 A00 ) and TS3 structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Molecular orbital diagrams for O2 and CO2 , adapted from DeKock and Gray [1980]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Electron-pushing diagram of an adiabatic CO4 (3 A00 ) isomerization through TS3. 92 Laboratory scattering data detected at m/z = 32. . . . . . . . . . . . . . . . . 98 Laboratory inelastic scattering data detected at m/z = 48. . . . . . . . . . . . 99 Velocity-flux contour diagram for inelastically scattered 12 C18 O2 from 16 O2 + 12 C18 O collisions in the center-of-mass frame. . . . . . . . . . . . . . . . . . . 100 2 Sample output of the NewtonD.m program. . . . . . . . . . . . . . . . . . . . 101 Stationary-point structures for O(3 P) + CO2 reactions below 100 kcal mol−1 calculated at the CCSD(T)/aug-cc-pVTZ level of theory on the 3 A00 surface. . . 114 Comparison of CO3 stationary point geometries relevant to the QCT calculations.116 Comparison of TS1 and TS3 geometries and energies at various levels of theory.116 Reactive scattering cross-sections for the O(3 P) + CO2 isotope exchange reaction obtained from the QCT calculations. . . . . . . . . . . . . . . . . . . . . 121 Opacity functions for the O(3 P) + CO2 isotope exchange reaction and for inelastic scattering of the two reagents obtained from QCT calculations at the B3LYP/6-311G(d) and BMK/6-311G(d) levels of theory. . . . . . . . . . . . . 122 Canonical Newton diagram for 16 O + 12 C18 O2 collisions at Ecoll = 98.8 kcal mol−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Laboratory inelastic scattering data detected at m/z = 16. . . . . . . . . . . . 126 Laboratory inelastic scattering data detected at m/z = 48. . . . . . . . . . . . 128 Velocity-flux contour diagram for inelastically scattered 12 C18 O2 from 16 O(3 P) + 12 C18 O2 collisions in the center-of-mass frame. . . . . . . . . . . . . . . . . 129 Comparison of laboratory and theoretical c.m. (A) angular and (B) translational energy distributions for inelastic scattering of O(3 P) and CO2 at hEcoll i ≈ 100 kcal mol−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Laboratory reactive scattering data detected at m/z = 46. . . . . . . . . . . . 132 Velocity-flux contour diagram for 16 O12 C18 O products of 16 O(3 P) + 12 C18 O2 collisions in the center-of-mass frame. . . . . . . . . . . . . . . . . . . . . . . 133 Comparison of laboratory and theoretical c.m. (A) angular and (B) translational energy distributions for the O(3 P) and CO2 isotope exchange reaction at hEcoll i ≈ 100 kcal mol−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 ix L. Y. Yeung 4.14 4.15 4.16 4.17 4.18 Oxygen isotope exchange reactions of CO2 Figures Laboratory reactive scattering data detected at m/z = 34. . . . . . . . . . . . 136 Snapshots of a quasiclassical trajectory for O(3 P) + CO2 isotope exchange through a short-lived CO3 ∗ complex at 1.5 eV (34.6 kcal mol−1 ) collision energy.142 Laboratory reactive scattering data detected at m/z = 46, fit assuming an ISC mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Snapshots of quasiclassical trajectories for the O(3 P) + CO2 → O2 + CO reaction.146 Center-of-mass angular and translational energy distributions for the O(3 P) + CO2 isotope exchange reaction derived from QCT calculations at the (A and B) B3LYP/6-311G(d) and (C and D) BMK/6-311G(d) levels of theory. . . . . . 151 x L. Y. Yeung Oxygen isotope exchange reactions of CO2 Tables List of Tables 2.1 2.2 2.3 2.4 2.5 2.6 Stratospheric air sample data . . . . . . . . . . . . . . . . . . . . . . . . . . . IR band assignments for the spectra in Figure 2.5 . . . . . . . . . . . . . . . . IRMS ion signals from the synthesized N2 18 O . . . . . . . . . . . . . . . . . . Results of pulsed photochemical experiments . . . . . . . . . . . . . . . . . . Results of continuous irradiation experiments . . . . . . . . . . . . . . . . . . Tropospheric-stratospheric-mesospheric mixing model results . . . . . . . . . 17 23 25 30 33 41 3.1 Energies of stationary points associated with the exchange reaction O2 + CO2 → O2 + CO2 on the lowest triplet potential energy surface . . . . . . . . . . . 88 4.1 4.2 4.3 Energies (kcal mol−1 ) for the stationary points on the lowest triplet CO3 potential energy surface for 16 O(3 P) + 12 C16 O2 → 16 O + 12 C16 O2 collisions . . . 115 Number of reactive QCTs observed at different collision energies. . . . . . . . 121 Comparison of experimental and theoretical yields for the products of O(3 P) + CO2 collisions near 100 kcal mol−1 . . . . . . . . . . . . . . . . . . . . . . 137 xi L. Y. Yeung Oxygen isotope exchange reactions of CO2 This page intentionally left blank. xii Blank L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 Chapter 1 Introduction 1.1 CO2 in the global carbon cycle Carbon dioxide (CO2 ) is the most important anthropogenic greenhouse gas in the earth’s atmosphere. Over the past half-century, atmospheric CO2 concentrations have increased at a rate that correlates with the increase in anthropogenic fossil fuel burning and deforestation [Solomon et al., 2007]. Carbon budget inventories indicate, however, that not all of the CO2 released into the atmosphere from these activities persists in the atmosphere; approximately half of the anthropogenic CO2 flux is sequestered in the oceanic and land biospheres [Ciais et al., 1995]. Modeling the fate of anthropogenic CO2 becomes a considerable technical challenge because of myriad interactions between the atmosphere, the oceans, and the terrestrial biosphere. Our ability to predict future changes in the carbon cycle and their effects on global climate relies on our quantitative understanding of these interactions. The first step towards understanding these interactions is learning how to differentiate between atmospheric CO2 molecules derived from various sources and sinks, so we can eventually de-convolve atmospheric observations into their individual components and describe the workings of the global budget through those observations. This task is more complex than it might at first seem because the atmosphere mixes efficiently over the atmospheric lifetime of CO2 ; thus each parcel of air contains CO2 molecules with many different origins and fates (see Figure 1.1). We find some of the needed constraints for these interactions in the variations of naturally occurring stable isotopes. 1 L. Y. Yeung 1.2 Oxygen isotope exchange reactions of CO2 Chapter 1 Stable isotopes, ‘clumped’ and otherwise The stable isotope composition of CO2 (i.e., the relative abundances of those isotopes that do not decay radioactively: 12 C, 13 C, 16 O, 17 O and 18 O) varies according to its sources and subsequent atmospheric chemistry and transport. Physical, chemical kinetic, and equilibrium isotope effects act together to determine the stable isotope composition of CO2 in a given parcel of air. Differences in mass and symmetry of the twelve distinct CO2 isotopologues (isotopic variants, e.g., 12 C16 O2 , 13 C16 O2 , 16 O12 C18 O, 16 O13 C17 O, etc.) formed from the five stable isotopes lead to subtle, but measurable differences in the rate of chemical transformations such as photosynthesis, respiration, air-sea exchange, or photochemical reactions. In principle, measuring the stable isotope distribution in CO2 could lead to an exceptionally detailed analysis of the ‘history’ of CO2 in every sample of the atmosphere, as each natural process imparts its own unique isotopic signature; however, only four of these twelve isotopologues (12 C16 O2 , 13 C16 O2 , 16 O12 C17 O, and 16 O12 C18 O) have been used extensively as tracers in atmospheric chemistry. By themselves, they are insufficient to constrain the relative influences of all the sources and sinks that have acted on a single sample. The remaining eight species (all of which contain two or three heavy rare isotopes) are exceptionally rare and, until recently, were considered to be essentially un-analyzable in natural materials. Measuring these very rare ‘clumped’ isotopologues would add new and essential independent constraints on the origins of CO2 in samples of air. In the laboratory, an equally daunting challenge exists: What are the most important reactions governing the isotopic composition of atmospheric CO2 , and what are the fundamental isotope effects? We wish to know, in the end, if our knowledge of the pertinent atmospheric chemistry is sufficient to explain atmospheric observations. 1.3 Anomalous isotopic enrichments in stratospheric CO2 Shortly after the discovery of ‘mass-independent’ enrichments of 18 O and 17 O in stratospheric ozone [Mauersberger, 1981, 1987] and the demonstration of its chemical origin 2 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 hν O2 λ = 121.6 nm O(1D) hν hν CO CO2 hν in vortex Stratopause O3 + hν → O2 + O(1D) CH4 O(1D), OH Cl CO O(1D) hν OH CO2 CO2 O(3P) particles? H2O Tropopause OH VOCs CO etc. OH CO2 clouds leaves CA soils oceans emissions CA Carbonic anhydrase (CA)-assisted Figure 1.1: Schematic of atmospheric CO2 sources and sinks. Photochemical reactions (single-headed arrows), isotope exchange reactions (double-headed arrows), and atmospheric transport (dotted arrows) are shown. Isotopic exchange on stratospheric liquid water and/or acid particles is uncertain, so its double-headed arrow is dashed. 3 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 [Thiemens and Heidenreich, 1983], similar enrichments were observed in stratospheric CO2 (e.g., Figure 1.2) [Alexander et al., 2001; Boering et al., 2004; Gamo et al., 1989; Kawagucci et al., 2008; Lämmerzahl et al., 2002; Thiemens et al., 1991, 1995]. Yung et al. [1991] suggested that photochemical transfer of the heavy-isotope signature (∆17 O) from O3 to CO2 stratospheric CO2 was possible after photolysis of O3 : O3 + hν(λ < 305 nm) → O2 + O(1 D) (1.1) → O2 + O(3 P) (1.2) and then subsequent isotope exchange through reaction 1.3: O(1 D) + CO2 → OCO∗2 → O(3 P) + OCO (1.3) The authors cited the isotope exchange mechanism in Baulch and Breckenridge’s early study of the reaction in which the incident oxygen atom was incorporated into the product CO2 molecule 2/3 of the time [Baulch and Breckenridge, 1966]. While this ‘statistical’ mechanism could explain the stratospheric 18 O and 17 O measurements qualitatively, a quantitative discrepancy remained between the observed and modeled 17 O/16 O vs. 18 O/16 O relationships: 17 O in CO 2 was more enriched than reaction 1.3 and Yung’s model would have predicted. Unfortunately, the isotope effects in O3 formation and photolysis and in the O(1 D) + CO2 isotope exchange reaction (reaction 1.3) were not yet well understood. Tests of the ‘statistical’ isotope exchange hypothesis were first conducted by Wen and Thiemens [1993], who photolyzed a mixture of O3 and CO2 with a mercury lamp at 254 nm. They observed heavy-atom enrichments in CO2 that implied a non-statistical isotope exchange mechanism between O3 and CO2 (i.e., 17 O appeared to be preferentially incorporated into CO2 ), but their result was misleading; the isotopic composition of the incident O(1 D) changed significantly over the course of their experiment due to O(3 P) and O2 recombination. They did not account for these effects and thus were led to a spurious conclusion, as a later study showed [Johnston et al., 2000]. To date, only one of these bulk photochemical experiments has been able to reproduce the relative 17 O-to-18 O enrichments observed in 4 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 Figure 1.2: Bulk oxygen isotope composition of stratospheric CO2 . Departure from ‘mass-dependent’ compositions (∆17 O; see Appendix 1.A) are observed, owing to oxygen isotope exchange with stratospheric O3 through reaction 1.3. the stratosphere [Chakraborty and Bhattacharya, 2003], and those results have been controversial [Shaheen et al., 2007]. Mechanistic insights have been limited because bulk stable isotope analysis is not able to differentiate isotope effects in O3 photolysis and formation from isotope effects in reaction 1.3 unambiguously. Recent theoretical and modeling work on ozone has shed light on the effects of the former [Babikov et al., 2003; Cole and Boering, 2006; Gao and Marcus, 2001, 2002; Gao et al., 2002; Hathorn and Marcus, 1999, 2000; Schinke et al., 2006], but the understanding of the stratospheric CO2 isotopic distribution remains incomplete. The persistence of this field-laboratory disagreement was the primary inspiration for the ‘clumped’ isotope studies of reaction 1.3 described in this dissertation. 1.4 Insights from the physical chemist’s toolbox The techniques of physical chemistry have been invaluable for unraveling features in the complex mechanism of reaction 1.3. CO3 ∗ was believed to play a critical role in the isotope exchange reaction ever since the first experiments of Katakis and Taube [1962]. 5 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 Figure 1.3: Potential energy surface for CO3 (3 A00 ) from Mebel et al. [2004]. Geometries were optimized at the CASSCF(16,13)/6-311G(d) level of theory. Energies were calculated at the MRCI+Q(16,13)/6-311+G(3df) level of theory. Moll et al. [1966] first identified a CO3 molecule spectroscopically upon irradiating CO2 ice with vacuum-UV light. Although their data implied that stable CO3 had C2v symmetry, their experiments with 18 O-labeled CO2 ices indicated that a CO3 (D3h ) species might be important in a reaction between atomic oxygen and CO2 , as was implied by the statistical mechanism of Baulch and Breckenridge [1966]. The O(1 D) + CO2 potential energy surface (PES) calculated by Mebel et al. [2004] is shown in Figure 1.3. On the 1 A1 surface (1 A0 dynamically), the association reaction has an early barrier at 1 kcal mol−1 , which is consistent with its collision-limited reaction rate coefficient (1 × 10−10 cm3 molecule−1 s−1 ) [Sander et al., 2006]. The binding energy of CO3 (1 A1 ) is nearly 50 kcal mol−1 , and two structures (C2v and D3h ) were predicted as bound 6 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 species at the bottom of the potential well. CO3 (C2v ) was detected shortly thereafter in a low-temperature CO2 matrix [Bennett et al., 2004]; the presence of a true CO3 (D3h ) minimum on the PES had been debated (see Kaiser and Mebel [2008]; Kowalczyk and Krylov [2007]; Liu et al. [2009] and references therein), but it was recently detected experimentally in a 10 K CO2 ice bombarded with high-energy electrons [Jamieson et al., 2006]. Intersystem crossing (ISC) from the singlet to the triplet PESs is believed to occur through nonradiative transitions rather than through the minimum of the intersection seam (near the 3 A0 transition state); the product O(3 Pj ) spin-orbit state distribution is consistent with an adiabatic CO3 dissociation [Matsumi et al., 1994a]. The ISC rate was also calculated to be ten times faster through a radiationless transition than through the singlet-triplet crossing seam [Mebel et al., 2004]. Yang et al. [2005] later proposed that a direct quenching mechanism (i.e., not through a CO3 complex) might also be important. Gas-phase studies of reaction 1.3 show evidence for CO3 , though none have detected it directly. Perri et al. [2003, 2004] reported evidence for a long-lived CO3 ∗ reaction complex in their crossed-molecular-beam experiments. This long-lived (1 – 10 ps lifetime) intermediate had been suggested in previous temperature- and pressure-dependent studies [Clerc and Reiffsteck, 1968; DeMore and Dede, 1970; Weissberger et al., 1967], but never directly confirmed; its lifetime was later confirmed to be long enough for nearly statistical intramolecular vibrational redistribution [Chen et al., 2009]. The structure and dynamics of CO3 are not yet completely understood, however. For instance, O(1 D) + CO2 collision energy appears to be important dynamically; Perri et al. [2003, 2004] reported that O(1 D) + CO2 collisions yielded spin-conserving, isotopically exchanged products (1.4): O(1 D) + CO2 → OCO∗2 → O(1 D) + OCO (1.4) Their crossed-molecular-beam experiments were performed at elevated collision energies (4.2 and 7.7 kcal mol−1 ) so the importance of reaction 1.4 to the stratosphere is unknown. Mebel et al.’s companion computation study suggested that reaction 1.4 has a ∼5% branching fraction at stratospheric collision energies, but this prediction has not been tested. Still, Perri et al.’s experimental result casts significant doubt on the applicability of the previous 7 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 bulk photochemical experiments. All the recent studies of the O2 /O3 /CO2 photochemical system used O2 /O3 as a source of O(1 D) with a significant mixing fraction of CO2 , so the O(1 D) atoms reacting with CO2 probably had an elevated average kinetic energy as high as ∼9 kcal mol−1 [Thelen et al., 1995], six times the calculated average in the stratosphere [Kharchenko and Dalgarno, 2004; Takahashi et al., 2002]. 1.5 Executive summary This dissertation describes studies of three oxygen isotope exchange reactions involving CO2 — one well-studied and two we discovered — and their potential implications for oxygen cycling in the upper atmosphere. First, I will describe the meridional (latitudinal) variations of stratospheric 16 O13 C18 O relative to those of 12 C16 O2 , 13 C16 O2 , 16 O12 C18 O, and 16 O12 C17 O; we identified a meridional gradient, with 16 O13 C18 O most enriched at the Arctic polar vortex. Our experimental and modeling study revealed that the variations in 16 O13 C18 O proportions cannot be explained in full by the known stratospheric chemistry af- fecting CO2 . Instead, we propose — because of the localization of a 16 O13 C18 O anomaly in the wintertime pole — that the chemistry either in the mesosphere or on stratospheric particles leads to the newly discovered isotopic enrichments. Second, I will describe crossedmolecular-beam experiments that led to the discovery of the isotope exchange reaction O2 + CO2 . We show that the isotope exchange reaction occurs through a short-lived CO4 intermediate, and that an adiabatic reaction mechanism exists despite a variety of energetically accessible product channels. Third, I will discuss a computational and laboratory dynamics study of hyperthermal collisions between ground-state oxygen-atoms and CO2 . We identified two reactions: oxygen-atom isotope exchange and abstraction. The isotope exchange reaction proceeds through a short-lived CO3 ∗ reaction complex, and it may have implications for the oxygen-isotope budget in the upper atmosphere and/or the stratospheric polar vortex. The oxygen-atom abstraction reaction may proceed through either a ‘stripping’-type mechanism or a CO3 complex, although the data cannot distinguish between the two mechanisms definitively. In the final chapter, I will attempt to synthesize what we have learned from these three studies, and what questions have emerged as a result. 8 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Appendices 9 Chapter 1 L. Y. Yeung 1.A Oxygen isotope exchange reactions of CO2 Chapter 1 Isotopic notation The natural abundance of the rare isotopes that are the focus of this thesis are 1.1% (13 C), 0.02% (18 O), and 0.038% (17 O). Variations in these stable isotope abundances are typically ≤10−3 . Consequently, bulk stable isotope abundances are commonly reported in δ -notation, in units of per mil (‰): δ 13 C = δ 18 O = R13 sample ! − 1 R13 VPDB R18 sample × 1000 (1.5) × 1000 (1.6) ! R18 VSMOW − 1 where Rn is the abundance ratio of a rare isotope or isotopologue of mass n to its most abundant analogue, i.e., R13 = [13 C] [12 C] R18 = [18 O] [16 O] R17 = [17 O] [16 O] (1.7) δ 17 O is defined similarly to δ 18 O in Eq. 1.6. δ 13 C, δ 18 O, and δ 17 O are reported relative to the international standards VPDB (Vienna Pee Dee Belemnite; R13 = 0.0112372) and VSMOW (Vienna Standard Mean Ocean Water; R18 = 0.0020052 and R17 = 0.0003799). These standards were established under the International Atomic Energy Agency, but are otherwise arbitrary. They represent convenient reference points against which all isotopic measurements can be compared. Positive δ -values mean that the sample bulk isotope composition is enriched relative to the standard, and negative δ -values mean that the sample bulk isotope composition is depleted relative to the standard. Within bulk stable isotope geochemistry, a second family of notation has emerged since the discovery of ‘mass-independent’ oxygen isotope fractionation (MIF) in carbonaceous chondrites [Clayton et al., 1973] and during the formation of ozone (O3 ) [Thiemens and Heidenreich, 1983]. The magnitude of MIF in oxygen (∆17 O) is defined in Eq. 1.8: ∆17 O = δ 17 O − 0.516 × δ 18 O 10 (1.8) L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 This terminology is used to describe deviations from the canonical mass-dependent isotopic relationships derived by Urey [1947] and Bigeleisen [Bigeleisen and Mayer, 1947; Bigeleisen and Wolfsberg, 1958]. Most equilibrium and kinetic isotope effects are half as pronounced for 17 O/16 O ratios vs. 18 O/16 O ratios, so the slope of a δ 17 O vs. δ 18 O plot (similar to 17 O/16 O vs. 18 O/16 O) is nominally 0.5. Departures from mass-dependent fractionation in oxygen are calculated using Eq. 1.8: ∆17 O > 0 represents a ‘mass-independent’ enrichment in 17 O, whereas ∆17 O < 0 represents a “mass-independent” depletion in 17 O. Several excellent reviews of this topic have been published, e.g., Weston [1999] and Thiemens [2006]. The language of ‘clumped’ isotope geochemistry is potentially even more confusing because the reference isotopic ratio (e.g., the denominator in Eq. 1.6) is no longer a constant: R 47 [47 CO2 ] = 44 [ CO2 ] ∆47 = R47 sample R47 stochastic ! ) − 1 × 1000 (1.9) 13 18 + 2R17 R18 + R13 (R17 )2 , the distribution of stable carbon and In Eq. 1.9, R47 stochastic = 2R R oxygen isotopes if they were randomly distributed among all isotopologues of CO2 [Eiler, 2007]. It is important to recognize that the terms used in ‘clumped’ isotope geochemistry (Eq. 1.9) differ fundamentally from those in bulk-isotope measurements; the “reference” to which the measured R47 sample is compared is a varying internal standard (the bulk isotopic composition), rather than the fixed external standard used in Eqs. 1.5 and 1.6. This distinction also leads to quirky, yet ultimately useful changes in ∆47 when subject to various physical processes such as mixing and diffusion [Eiler and Schauble, 2004]. A common question has been: “What is the difference between an isotopomer and an isotopologue?” Two isotopomers, like chemical isomers, share the same isotopic composition, but the stable isotopes themselves are in positions that render the two molecules chemically distinct. A good example can be found in the comparison of isotopically substituted N2 O and CO2 molecules: 14 N–15 N–16 O and 15 N–14 N–16 O are isotopomers of one another because the N-atom substitutions are not symmetrically equivalent. The two isotopomers, consequently, have differing chemical properties, e.g., vibrational frequencies and rotational constants. In contrast, 16 O–12 C–18 O and 18 O–12 C–16 O are equivalent upon rotation, so they are equivalent structures of a single isotopologue. 11 L. Y. Yeung 1.B Oxygen isotope exchange reactions of CO2 Chapter 1 Copyright declaration This thesis contains excerpts from three publications in which the author was involved: • Huntington, K. W., J. M. Eiler, H. P. Affek, W. Guo, M. Bonafacie, L. Y. Yeung, N. Thiagarajan, B. Passey, A. Tripati, M. Daëron, R. Came (2009), Methods and limitations of ‘clumped’ CO2 isotope (∆47 ) analysis by gas source isotope ratio mass spectrometry, J. Mass Spectrom., 44(9), 1318–1329. ©2009 John Wiley & Sons. • Yeung, L. Y., H. P. Affek, K. J. Hoag, W. Guo, A. A. Wiegel, E. L. Atlas, S. M. Schauffler, M. Okumura, K. A. Boering, and J. M. Eiler (2009), Large and unexpected enrichment in stratospheric 16 O13 C18 O and its meridional variation, Proc. Natl. Acad. Sci. U. S. A., 106(28), 11,496–11,501. ©2009 National Academy of Sciences. • Yeung, L. Y., M. Okumura, J. T. Paci, G. C. Schatz, J. Zhang, and T. K. Minton (2009), Hyperthermal O-Atom Exchange Reaction O2 + CO2 through a CO4 Intermediate, J. Am. Chem. Soc., 131(39): 13,940–13,942. ©2009 American Chemical Society Publications. 12 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Chapter 2 Large and unexpected enrichment in stratospheric 16O13C18O Adapted from Yeung, L. Y., H. P. Affek, K. J. Hoag, W. Guo, A. A. Wiegel, E. L. Atlas, S. M. Schauffler, M. Okumura, K. A. Boering, and J. M. Eiler (2009), Large and unexpected enrichment in stratospheric 16 O13 C18 O and its meridional variation, Proc. Natl. Acad. Sci. U. S. A., 106(28), 11,496–11,501. ©2009 National Academy of Sciences. 13 L. Y. Yeung 2.1 Oxygen isotope exchange reactions of CO2 Chapter 2 Abstract The stratospheric CO2 oxygen isotope budget is thought to be governed primarily by the O(1 D) + CO2 isotope exchange reaction. However, there is increasing evidence that other important physical processes may be occurring that standard isotopic tools have been unable to identify. Measuring the distribution of the exceedingly rare CO2 isotopologue 16 O13 C18 O, in concert with 18 O and 17 O abundances, provides sensitivities to these additional processes, and thus is a valuable test of current models. We identify a large and unexpected meridional variation in stratospheric 16 O13 C18 O, observed as proportions in the polar vortex that are higher than in any naturally derived CO2 sample to date. We show, through photochemical experiments, that lower 16 O13 C18 O proportions observed in the mid-latitudes are determined primarily by the O(1 D) + CO2 isotope exchange reaction, which promotes a stochastic isotopologue distribution. In contrast, higher 16 O13 C18 O proportions in the polar vortex show correlations with long-lived stratospheric tracer and bulk isotope abundances opposite to those observed at mid-latitudes, and thus opposite to those easily explained by O(1 D) + CO2 . We believe the most plausible explanation for this meridional variation is either an unrecognized isotopic fractionation associated with the mesospheric photochemistry of CO2 or a temperature-dependent isotopic exchange on polar stratospheric clouds (PSCs). Unraveling the ultimate source of stratospheric 16 O13 C18 O enrichments may impose additional isotopic constraints on biosphere-atmosphere carbon exchange, biosphere productivity, and their respective responses to climate change. 14 L. Y. Yeung 2.2 Oxygen isotope exchange reactions of CO2 Chapter 2 Introduction Predicting future CO2 concentrations and carbon cycle-climate feedbacks depends on one’s ability to quantify the contributions from the sources and sinks governing the global carbon budget and how they may change over time. The bulk stable isotope composition of CO2 (i.e., its 13 C/12 C, 18 O/16 O, and 17 O/16 O ratios) plays an important role in constraining this budget (see Yakir [2003] and references therein). In the stratosphere, the oxygenisotope composition of CO2 is thought to be modified by oxygen isotope exchange reactions with O(1 D) generated by ozone photolysis [Yung et al., 1997], whereas in the troposphere it is controlled by isotope exchange reactions with liquid water in the oceans, soils, and plant leaves [Ciais and Meijer, 1998]. The interplay between stratospheric and tropospheric isotope exchange reactions, in principle, could allow the relative abundances of 12 C16 O2 , 16 O12 C18 O, and 16 O12 C17 O isotopologues to be used as tracers for gross biosphere produc- tivity [Hoag et al., 2005; Luz et al., 1999], but the stratospheric CO2 photochemical system is still under-constrained and our understanding of it is incomplete. Discrepancies between laboratory and stratospheric measurements [Lämmerzahl et al., 2002; Shaheen et al., 2007; Thiemens et al., 1995] have prompted questions about whether the O(1 D) + CO2 isotope exchange reaction acts alone on stratospheric CO2 or whether other photochemical [Bhattacharya et al., 2000] or dynamical [Boering et al., 2004] processes significantly affect the stable isotopologue distribution in CO2 . Stratospheric oxygen isotope covariations in CO2 [Kawagucci et al., 2008; Lämmerzahl et al., 2002; Liang et al., 2008] consistently differ from those found in laboratory experiments simulating stratospheric photochemistry [Baulch and Breckenridge, 1966; Chakraborty and Bhattacharya, 2003; Johnston et al., 2000; Shaheen et al., 2007; Wen and Thiemens, 1993], and the origin of this disagreement is still uncertain because bulk stable isotope measurements alone (i.e., of δ 13 C, δ 18 O, and δ 17 O values) cannot differentiate extrinsic effects [e.g., the O(1 D) isotope composition] from intrinsic (i.e., photolytic or kinetic isotope) effects on the isotope composition of stratospheric CO2 . Additional constraints arising from analysis of multiplysubstituted isotopologues of CO2 can provide sensitivities to these processes [Affek and Eiler, 2006; Affek et al., 2007; Eiler, 2007; Eiler and Schauble, 2004]. To investigate stratospheric 15 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 CO2 chemistry, we examine here the proportions of 16 O13 C18 O (reported as a ∆47 value) in stratospheric CO2 and in laboratory kinetics experiments. 2.3 Field sample collection and analysis Twelve stratospheric CO2 samples were analyzed for bulk stable isotope compositions and ∆47 values: Six samples of stratospheric CO2 were collected from the NASA ER-2 aircraft during the 1999/2000 Arctic winter Stratospheric Aerosol and Gas Experiment III (SAGE III) Ozone Loss and Validation Experiment (SOLVE) campaign [Newman et al., 2002], and six samples were collected from a balloon flight from Fort Sumner, New Mexico on 29 September 2004. SOLVE mission samples (January – March 2000, 29 – 79◦ N, 11 – 20 km) were collected as whole air samples [Flocke et al., 1999]. CO2 was then isolated from the ∼5 L STP of air by a combination of liquid N2 and ethanol-dry ice traps, then separated into aliquots of 12 – 18 µmol CO2 each and sealed into glass ampoules. Balloon samples were collected using a cryogenic whole air sampler (34.5◦ N, 103.6◦ W, 27 – 33 km) [Froidevaux et al., 2006; Lueb et al., 1975] and purified and stored as above. δ 13 C, δ 18 O, and δ 17 O of CO2 were measured on a Finnigan MAT 252 isotope ratio mass spectrometer (IRMS) at UC-Berkeley. ∆17 O was measured using the CeO2 technique with a precision of ± 0.5‰ [Assonov and Brenninkmeijer, 2001]. Aliquots of the same CO2 samples were analyzed for ∆47 using a Finnigan MAT 253 IRMS at Caltech configured to collect masses 44 – 49, inclusive, and standardized by comparison with CO2 gases of known bulk isotopic composition that had been heated for two hours at 1000◦ C to achieve a stochastic isotopic distribution [Eiler and Schauble, 2004]. Masses 48 and 49 were used to detect residual hydrocarbon contamination. For ∆47 analysis, the 12 – 18 µmol aliquots of SOLVE-mission and balloon CO2 samples were purified of potential contaminants, such as hydrocarbons, by a pentane-liquid N2 slush (–120◦ C) as well as by passing it through a gas chromatographic (GC) column (Supleco Qplot, 530 µm ID, 30 m length) at –20◦ C, with column baking at 150◦ C between samples [Affek and Eiler, 2006; Ghosh et al., 2006]. All data were corrected for the presence of N2 O using the method described previously [Affek and Eiler, 2006]. Each measurement consisted of 5 – 9 acquisitions (of 10 measurement 16 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Table 2.1: Stratospheric air sample data Air Sample Name Type∗ Altitude Latitude (km) (◦ N) θ (K) CH4 N2 O CFC-11 CFC-12 δ 13 C (ppbv) (ppbv) (pptv) (pptv) (‰) δ 18 O (‰) ∆17 O (‰) ∆47 (‰) ER-2 samples V V V VE M M 20000312(25)1120 20000131(30)1001 20000203(10)1173 20000127(5)1060 20000106(30)1169 20000111(25)2021 19.33 19.85 17.63 19.45 19.40 11.40 79.2 73.5 70.4 57.7 29.3 43.5 443.61 448.08 409.37 445.10 467.43 358.26 948 1066 1250 1385 1495 1726 111.5 142.1 192.8 227.6 256.4 307.9 33.34 32.22 30.78 29.26 28.73 27.27 34.5 34.6 34.6 34.6 34.6 34.6 931.14 896.15 861.84 778.08 757.89 709.67 835 843 913 957 1014 1176 54.0 56.7 77.8 92.1 107.9 155.9 19. 31. 72. 112. 157. 246. 147. 198. 293. 362. 421. 526. -8.11 -8.08 -8.06 -8.07 -8.08 -8.06 44.55 43.62 43.06 42.79 42.50 40.98 5.76 4.38 3.69 2.45 2.13 0.18 1.614 1.555 1.436 1.233 1.071 1.075 46.0 51.2 78.2 100.2 78.2 123.6 -8.07 -7.99 -8.03 -8.07 -8.04 -8.03 45.14 45.44 45.14 44.98 44.79 44.09 6.46 6.29 5.91 6.12 5.00 4.26 0.976 0.923 0.913 0.912 1.004 0.916 Balloon samples M M M M M M 1-A010-R (2035) 3-A01-R (1141) 5-A013-R (2079) 7-A026-R (1057) 8-A017-E (1113) 10-A022-E (1186) 0.13 0.23 0.15 0.63 1.10 5.90 ∗ Air type is abbreviated as V = vortex, VE = vortex edge, and M = mid-latitude based on N O:θ correlations, where θ is 2 potential temperature in Kelvin. Non-isotopic tracer measurement methodology can be found in Flocke et al. [1999] and Froidevaux et al. [2006]. cycles each), with typical standard deviations (acquisition-to-acquisition) of 0.06‰ in ∆47 . 2.4 Field results The stratospheric samples (see Table 2.1) display ∆47 values both higher and more variable than those exhibited by tropospheric air at the surface, which has an average ∆47 value of 0.92 ± 0.01‰ in remote regions (Cape Grim, Tasmania and Barrow, Alaska) [Affek et al., 2007]. The high-latitude (> 57◦ N) stratospheric samples, in particular, are significantly more enriched in ∆47 than any material analyzed before in nature (see Figure 2.1 and see Affek et al. [2007] and Eiler [2007]). At high latitudes, ∆47 varies strongly and increases monotonically with decreasing mixing ratios of long-lived trace gases that have tropospheric sources and stratospheric sinks, such as N2 O and CH4 . At mid-latitudes, ∆47 varies relatively little and shows correlations with trace gas mixing ratios having the opposite sign of those observed at high latitudes (see Figure 2.2 and Table 2.1). Using the correlation between simultaneously measured N2 O mixing ratios and potential temperature [Greenblatt et al., 2002], we found that the high-latitude samples were collected in inner polar vortex air (three samples) or vortex edge air (one sample). Thus, differences in the sign and magnitude of ∆47 variations with N2 O mixing ratio in the two subsets of 17 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.1: Meridional variation of ∆47 measured in stratospheric samples. Typical values in the troposphere are ∆47 ∼ 0.9‰. Error bars show 2σ standard errors. samples are presumably due to differences between vortex and non-vortex processes. In contrast to these ∆47 trends, covariations of ∆17 O with δ 18 O and mixing ratios of long-lived trace gases for our mid-latitude samples resemble those of our polar vortex samples (or show the expected differences for slightly shorter-lived tracers, e.g., CFC-11) and also those reported in earlier studies of high-latitude [Boering et al., 2004; Kawagucci et al., 2008] and polar vortex air (see Figure 2.3) [Alexander et al., 2001]. This suggests that ∆47 records a process to which ∆17 O is not sensitive. In order to rule out the possibility that the observed high ∆47 values result from sample contamination by organic compounds in the stratospheric samples, one of the samples [20000131(30)1001] was exposed to water at 25◦ C for 24 hours to reach CO2 –water isotopic equilibrium. The exchanged sample had a ∆47 value of 0.862 ± 0.078‰, identical to the cylinder CO2 working standard, whose ∆47 value reflects CO2 isotopic equilibrium at room temperature [Wang et al., 2004]. In contrast, the presence of contaminants would have resulted in a high ∆47 value even after isotopic equilibrium was reached. Hence, no evidence for contamination was observed in the high-latitude samples. 2.5 Laboratory photochemical experiments To gain further insight into the correlations we observed between ∆47 , ∆17 O, and δ 18 O, we conducted several laboratory photochemistry experiments. Enrichments of ∆17 O and δ 18 O 18 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.2: Correlation between ∆47 and stratospheric tracers. (A), best-fit lines are shown for mid-latitude (solid line) and high-latitude (dashed line) ∆47 vs. N2 O mixing ratio. Correlations between ∆47 and other tracers with tropospheric sources and stratospheric sinks are similar (see Figure 2.3). Also shown is the best-fit line of (B), ∆47 vs. ∆17 O, and (C), ∆47 vs. δ 18 O in mid-latitude air, which is used to estimate the integrated effective isotopic composition of stratospheric O(1 D) (see text). Error bars represent 2σ standard errors. Figure 2.3: ∆17 O values vs. long-lived stratospheric tracer mixing ratios. In both panels, measurements reported in this work (ER-2 and Balloon data) are compared with previous high-latitude (> 48◦ N; left panel) and polar vortex (right panel) measurements. The measured ∆17 O correlations with N2 O and CFC-12 do not reveal obvious distinctions among the mid- and high-latitude CO2 samples; ∆47 measurements, in contrast, reveal strong mesospheric or other polar vortex influence. 19 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 in stratospheric CO2 are generally understood to arise from isotope exchange with O(1 D), which is produced by photolysis of 18 O- and 17 O-enriched stratospheric ozone [Liang et al., 2007; Yung et al., 1997], but the kinetics of the isotope exchange reactions for multiplysubstituted isotopologues of CO2 , and their effects on ∆47 , have not yet been explored. Changes in ∆47 caused by these reactions should principally reflect relative changes in 16 O13 C18 O and 16 O12 C18 O abundances because the 13 C composition is not affected by iso- tope exchange with O(1 D); variations in 17 O12 C18 O and 13 C17 O2 abundances will change ∆47 more subtly. Thus, reactions 2.1 and 2.2 are most relevant. 18 O(1 D) + 12 C16 O2 → 18 O12 C16 O∗2 → 16 O + 16 O12 C18 O (2.1) 18 O(1 D) + 13 C16 O2 → 18 O13 C16 O∗2 → 16 O + 16 O13 C18 O (2.2) Statistical partitioning of isotope exchange products, through a process governed by random chance such that 18 O(1 D) has a 2/3 probability of being incorporated into the product CO2 , would drive the CO2 isotopologues towards a stochastic distribution (i.e., ∆47 = 0). If any one (or more) of the isotope exchange reactions does not partition products statistically, however, ∆47 can increase [e.g., if 18 O(1 D) exchanges isotopes with 13 C16 O2 more readily than with 12 C16 O2 ] or decrease accordingly. Two sets of laboratory experiments were conducted. First, the relative rates of reactions 2.1 and 2.2 were probed directly to obtain the 13 C/12 C kinetic isotope effect (KIE) for the 18 O(1 D) + CO 2 isotope exchange reaction at 300 K and 229 K. These experiments used pulsed photolysis of 97% N2 18 O at 193 nm as a source of 18 O(1 D), and the extent of isotope exchange was minimized. Second, we performed continuous-irradiation experiments, using a mercury lamp, on mixtures of isotopically unlabeled O2 , O3 , and CO2 as a function of different irradiation times to determine the aggregate effects of the O2 /O3 /CO2 photochemical system on ∆47 . 20 L. Y. Yeung Oxygen isotope exchange reactions of CO2 2.5.1 13 C/12 C kinetic isotope effect experiments 2.5.1.1 Methods overview Chapter 2 For experiments performed at 300 K, a 15 cm-long stainless steel conflat chamber with quartz windows was used as a reaction chamber. Low-temperature experiments were performed in a 25 cm-long, all-quartz chamber, cooled to 229 K under vacuum via direct conduction with a cold copper jacket (see Appendix 2.C). Experiments were initiated with pulsed excimer laser photolysis of N2 18 O (193 nm, 50 – 100 mJ pulse−1 , 1 Hz repetition rate, < 200 pulses), producing 18 O(1 D), in ∼1:100:3000 static mixtures of N2 18 O:CO2 :He (100 Torr total pressure). N2 18 O was synthesized from the acid-catalyzed reduction of 18 O-labeled aqueous NaNO [McIlvin and Altabet, 2005; Samuel and Wassermann, 1971]; a 2 detailed description of its synthesis and characterization can be found in Section 2.5.1.2. A schematic of the reaction scheme is shown in Figure 2.4. Starting samples of CO2 contained a stochastic distribution of isotopologues, generated in the manner described in Section 2.3. The initial CO2 isotopic composition was measured and CO2 was recollected cryogenically for use in the reaction chamber. Residence time in the reaction chamber had a negligible effect on ∆47 in the 300 K experiments, whereas the chamber cooling process alone was observed to enrich the starting material in δ 18 O and ∆47 , by 0.5‰ and 0.13‰, respectively. These offset values were subtracted from final δ 18 O Figure 2.4: Schematic of O(1 D) + CO2 reaction-purification-analysis procedure. 21 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 and ∆47 values in 229 K experiments. The reaction products were recollected cryogenically and purified in two GC steps. Separation of residual N2 18 O and reacted CO2 was achieved through a packed-column (PoraPak Q) GC separation at 25◦ C, after which the samples were purified with a capillary GC as described above. Due to the presence of N2 18 O isobars with CO2 at masses 46 – 49, mass 14 was also monitored to measure the extent of N2 18 O contamination. Differences in mass-14 signal between the starting and product material of greater than 5 mV (a variation typical of ‘clean’ laboratory standards) were deemed contaminated, and the data points were rejected. The difference between the initial and final δ 18 O (hereafter referred to as ∆δ 18 O) and ∆47 compositions was calculated assuming that δ 13 C was unchanged, since there was no external carbon reservoir in the reaction. GC separation of N2 18 O and CO2 yielded a small, yet reproducible ∆47 change of +0.13‰, which was present both when gases of stochastic isotope composition were analyzed as well as when aliquots of cylinder CO2 working standard (∆47 = 0.86‰) were analyzed. The source of this offset may be a small amount of diffusive or adsorptive fractionation on the GC column, but it was not investigated further. Because of the apparent insensitivity of the ∆47 change to initial isotopic composition, the sample purification step was treated as a small additive effect on the measured ∆47 , with no effect on the overall kinetics measured. The following sections, 2.5.1.2 and 2.5.1.3, provide a detailed description of the materials and methods utilized to obtain the results summarized in Section 2.5.1.4. 2.5.1.2 N2 18 O synthesis Precursor samples of N2 18 O were synthesized from the acid-catalyzed reduction of aqueous nitrite (NO2 − ) [McIlvin and Altabet, 2005; Samuel and Wassermann, 1971]. A description of a synthesis and characterization follows. First, a solution of 0.4 mmol sodium nitrite (NaNO2 ) in 800 µl >97% H2 18 O (Isonics) was placed in a three-neck round-bottom flask and flushed with He at 30 mL min−1 for 20 minutes to remove any dissolved gases. The flow was then stopped and the flask closed off and put in an ice bath. 350 µl glacial acetic acid was then added through a rubber septum with a syringe to acidify the water. For 3 minutes, 22 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 the nitrite was allowed to exchange oxygen atoms fully with H2 18 O in the acidic environment [Ott, 1981]. Then, the nitrite was reacted with 220 µl of a solution of 1.5 mmol sodium azide (NaN3 ), 100 µl glacial acetic acid, and 150 µl H2 18 O, also added through the septum, for 40 minutes with stirring. Due to the high concentration of acid, the dominant reaction was expected to be that between nitrous acid (HNO2 ) and hydrazoic acid (HN3 ) to produce N2 18 O: HNO2 + HN3 → N2 O + N2 + H2 O (2.3) After the 40-minute reaction time, 1 mL of a ∼17 M NaOH solution was added through the septum to stop the reaction and remove any residual CO2 . The gas-phase products were collected by flowing He through the flask at 5 mL min−1 for 1 h into a “U-trap” held at liquid nitrogen temperature (77 K). Synthesized N2 18 O was dried cryogenically using a pentane slush (–120 ◦ C), then a dry ice/ethanol slush (–76 ◦ C), and recollected in a trap at liquid nitrogen temperature. Chemical yield in the N2 18 O was determined by expanding the product gas into a calibrated volume on a vacuum line, and the total product yield was determined to be 53% (0.195 mmol). Table 2.2: IR band assignments for the spectra in Figure 2.5 Frequency (cm−1 ) Band Frequency (cm−1 ) Band 1155 1247 1840 2217 2295 2412 2491 2787 3345 3435 3663 3737 2ν2 ν1 ν1 + ν2 ∗ ν3 4ν2 ν1 + 2ν2 ∗ 2ν1 ν2 + ν3 2ν2 + ν3 ∗ ν1 + ν3 2ν1 + 2ν2 ∗ 3ν1 ∗ 1285 1595 2350 2563 3481 3657 3756 ν1 (14 N2 16 O) ν2 (H2 16 O) ν3 (CO2 ) 2ν1 (14 N2 16 O) ν1 + ν3 (14 N2 16 O) ν1 (H2 16 O) ν3 (H2 16 O) Assignments taken from Łapiński et al., and references therein. Literature values are ν1 = 1247 cm−1 , ν2 = 571 cm−1 , and ν1 = 2217 cm−1 for N2 18 O. ∗ Temporary assignment because band has yet not been reported in the literature. 23 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.5: FT-IR spectrum of synthesized N2 18 O between 1100 cm−1 and 4000 cm−1 . Inset shows the zoomed-in area between 2100–2400 cm−1 . Samples were then measured on a Fourier-transform infrared spectrometer (FT-IR) for chemical purity and a IRMS for isotopic purity. FT-IR analysis was conducted on a Nicolet FT-IR spectrometer with 3 Torr N2 18 O, 0.125 cm−1 resolution, and 2000 scans in an 18 cmpathlength cell with CaF2 windows. Table 2.2 contains the band assignments for the N2 18 O IR spectrum shown in Figure 2.5. The IR spectrum (see inset of Figure 2.5) contains a small amount of CO2 , but it is considered too small an amount to affect isotopic measurements. The absorption cross-section of the CO2 (ν3 ) band is three times that of the N2 O(ν3 ) band [Rothman et al., 2009], yet in the experimental spectrum, the N2 O band is stronger than the CO2 band by an order of magnitude; consequently, the concentration of CO2 in the N2 18 O sample is estimated to be 3%. Because N2 18 O was used as a 1% mixture in CO2 for the photolysis experiments, the estimated mixing ratio of contaminant CO2 is 3 × 10−4 in the sample CO2 . This mixing ratio amounts to a maximum absolute error less than 0.001‰ in the observed δ 18 O at natural abundance (0.2% 18 O), and it is therefore negligible. H2 O lines in the spectrum are believed to come from atmospheric water vapor, as they are consistent with H2 16 O instead of the H2 18 O used in the synthesis. Because all of the H2 18 O appears 24 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Table 2.3: IRMS ion signals from the synthesized N2 18 O m/z Signal (mV) 18 O content 44 46 1276 37870 96.7% 30 32 482 14773 96.8% to have been removed by the cryogenic drying steps, and the sample compartment was continuously purged with dry N2 , this water vapor is believed to arise from desorbing water from the FT-IR cell walls. Mass-spectrometric analysis was performed on a Finnigan MAT 253 using cup position 3 (3 × 1010 Ω resistor). Isotope ratios were determined at two different m/z ranges: 46/44 (mainly 14 N2 18 O/14 N2 16 O) and 32/30 (mainly 14 N18 O/14 N16 O). Table 2.3 contains the observed signals and calculated isotopic purity at 16.5 mbar in the sample bellows. Here we see that the synthesized N2 O is indeed 97% labeled with 18 O, and it was used in experiments without further purification. 2.5.1.3 Reaction models Two models for the 13 C/12 C KIE experiments were constructed. One was a chemical kinetic model designed to calculate the expected trends in ∆47 vs. ∆δ 18 O given specific KIEs. The second was a hard-sphere collision model designed to model the velocity relaxation of the nascent 18 O(1 D), from which a collision energy distribution for each experiment could be calculated. C HEMICAL KINETIC MODEL . A comprehensive, isotopologue-specific kinetics model of the O(1 D)-CO2 photochemical experiment (144 isotope exchange reactions) was constructed in the FACSIMILE kinetics modeling package. Stochastic isotope exchange branching fractions [Baulch and Breckenridge, 1966; Yung et al., 1997] were used: Incident O(1 D) atoms had a 2/3 probability of isotope exchange, regardless of the isotope exchange reaction. The isotopic composition of the initial O(1 D) was treated as a constant; for these 18 O-labeled 25 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 experiments, trace 17 O and 16 O abundances had negligible effects on the measured 13 C/12 C KIE. We expect to observe subtle isotope effects due to differences in the 18 O(1 D)–CO2 collision frequencies between different isotopologues in the helium-buffer-gas experiments because the collision-limited rate of reaction for O(1 D) + CO2 [Sander et al., 2006] implies that the reaction probability for any given O(1 D)–CO2 collision is near unity. For instance, more 18 O(1 D) + 12 C16 O2 collisions than 18 O(1 D) + 13 C16 O2 collisions occur because the average velocity for 12 C16 O2 is higher than that for 13 C16 O2 at a given temperature. This reduces the rate at which reaction 2.2 occurs relative to reaction 2.1 in the laboratory by about 5%. The O(1 D)-CO2 collision frequencies in these experiments scale directly with the collision pair’s relative velocity, which depends inversely on the pair’s reduced mass (µ) according to equation 2.4: s k2.2 = µ18 O + 44 CO 2 µ18 O + 45 CO × k2.1 = µe f f k2.1 (2.4) 2 k represents the rate coefficient for the subscripted reaction, and µ represents the reduced mass of the subscripted reactant pair. Analogous relationships can be computed for each unique reactant pair. ∆47 is expected to decrease with increasing ∆δ 18 O because the collision frequency for 18 O(1 D) + 44 CO2 is ∼5% larger than that for 18 O(1 D) + 45 CO2 . Such biases are expected to be small in the atmosphere due to competing electronic quenching reactions (e.g., O(1 D) + N2 → O(3 P) + N2 ) [Johnston et al., 2000]. These electronic quenching reactions were minimized in our pulsed photolysis experiments because He was used as the buffer gas [Heidner and Husain, 1974; Shi and Barker, 1990]. Thus a 13 C/12 C KIE = k2.2 /k2.1 = 1 in our laboratory experiment will appear as an anti-correlation in a plot of ∆47 vs. ∆δ 18 O. A 13 C/12 C KIE ≈ 1.01 and an O(1 D) source with δ 18 O = δ 17 O ≈ 100‰ would be required to generate the polar vortex ∆47 enrichment and also the polar vortex ∆47 vs. ∆17 O correlation. On the ∆47 vs. ∆δ 18 O plot, the slope would be +0.0055 using k2.2 /k2.1 = 1.01. O(1 D) + CO2 COLLISION ENERGY DISTRIBUTION . The 13 C/12 C experiment was also modeled on the collision-by-collision level because the O(1 D) + CO2 isotope exchange reaction occurs through two reaction channels whose branching ratio depends on collision energy 26 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 [Perri et al., 2003]: O(1 D) + CO2 → O(3 P) + CO2 (2.5) → O(1 D) + CO2 (2.6) The branching fraction of the non-quenching channel (2.6) increases significantly with reaction collision energy, Ecoll [Mebel et al., 2004; Perri et al., 2004]. Observed isotope effects, then, may also depend on the distribution of Ecoll . Nascent O(1 D) atoms from the N2 O photolysis scheme employed in this study had a high average translational energy, so He was chosen as buffer gas to lower the average collision energy, hEcoll i, to a stratospherically relevant value; He quenches the translational energy of O(1 D) atoms efficiently while quenching the electronic energy inefficiently [Heidner and Husain, 1974; Shi and Barker, 1990]. Furthermore, the translational energy transfer during O(1 D) + He collisions can be modeled well using a hard-sphere collision model [Matsumi et al., 1994b]. We constructed a Monte Carlo hard-sphere collision model in the MATLAB programming environment based on the solution to the general elastic hard-sphere problem; the mathematical derivation can be found in the literature [Nan and Houston, 1992], and the program code can be found in Appendix 2.D. The basic function of the program was to calculate the final velocity vectors for two colliding hard spheres of masses m1 (the O-atom) and m2 (the He-atom) with initial velocity vectors (v1i , θ1i , φ1i ) and (v2i , θ2i , φ2i ), respectively. The elastic hard-sphere calculation was performed for a distribution of initial O-atom velocities in a He bath gas at thermal equilibrium (e.g., at 298 K). First, O-atom velocity vectors, (vO,i , θO,i , φO,i ), were sampled according to a velocity distribution for O(1 D) ejected from the photolysis of 14 N2 16 O at 193 nm [Felder et al., 1991; Hanisco and Kummel, 1993; Springsteen et al., 1993] centered at ET = 18.2 kcal mol−1 . In the absence of experimental data for 14 N2 18 O photodissociation, the 18 O(1 D) velocity distribution was approximated by a gaussian distribution centered at ∼2900 m s−1 with a full-width at half-maximum (FWHM) of ∼1000 m s−1 (i.e., hET i ∼18 ± 7 kcal mol−1 ). Second, a He-atom velocity vector, (vHe,i , θHe,i , φHe,i ), was selected randomly from a Maxwell-Boltzmann velocity distribution. Using this pair of initial conditions and a random impact parameter b (sampled with a probability proportional to itself), the final velocity vector of the O-atom after one collision, (vO, f , θO, f , 27 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 φO, f ), was computed and stored. The final velocity was then re-used as an initial velocity for the next collision with a second He-atom, whose velocity was randomly sampled as above. This calculation was repeated for up to 200 total collisions and N = 50,000 initial O(1 D) velocities, a total of 106 – 107 calculations. After 200 collisions, > 96% of the O(1 D) would have reacted with CO2 under our experimental conditions. Using the O(1 D) velocity distribution after each O(1 D)–He collision, the distribution of O(1 D)–CO2 collision energies, Pj (Ecoll ), for the jth collision could then be calculated similarly. The relative CO2 concentration, i.e., ρCO2 ∼ 0.03, was then used to weight the Pj (Ecoll ) distribution at the jth collision to obtain a O(1 D)–CO2 collision energy distribution over the whole experiment. The results were summed according to equation 2.7: Ptotal (Ecoll ) = ρCO2 ∑ Pj (Ecoll ) (2.7) j The model was tested by confirming that the average kinetic energy approached (and remained at) the value expected at thermal equilibrium by the equipartition theorem, e.g., 3 −1 at 300 K. Calculated P total (Ecoll ) distributions for several different 2 RT = 0.89 kcal mol experimental conditions are shown in Figure 2.6. Our simulation of the initial O(1 D) collision cascade shows that 81% of all O(1 D) + CO2 collisions occur with Ecoll < 2 kcal mol−1 , with hEcoll i = 1.6 kcal mol−1 , similar to the Ecoll distribution expected in the stratosphere [Kharchenko and Dalgarno, 2004; Takahashi et al., 2002]. As we noted earlier, the nascent 18 O(1 D) translational energy distribution is somewhat uncertain because the existing pho- todissociaton dynamics studies focused on the 14 N2 16 O molecule, not the 14 N2 18 O used in these experiments. Changing the peak of the nascent 18 O(1 D) translational energy distribution by 1 – 2 kcal mol−1 changed the average O(1 D)-CO2 collision energy by < 0.1 kcal mol−1 . The shape of the laboratory Ptotal (Ecoll ) distribution appears different from that modeled in conditions resembling the stratosphere [Kharchenko and Dalgarno, 2004]; this difference is due to O(1 D) having a slower nascent O(1 D) velocity distribution (O3 vs. N2 O photolysis) [Thelen et al., 1995] and more efficient electronic quenchers (N2 /O2 vs. He bath gas) [Sander et al., 2006] in the stratosphere. In addition, minor O(1 D)-producing channels 28 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.6: Modeled O(1 D) + CO2 reaction collision energy distributions at different He bath gas pressure (T = 300 K). Also shown is the modeled P(Ecoll ) under conditions resembling the stratosphere, using O3 as a source of O(1 D). important to the stratosphere have not been included in this model (see Taniguchi et al. [2000]). Last, the velocity relaxation problem is only qualitatively represented by the hardsphere model; inelastic collisions are not necessarily described well by the hard-sphere cross-sections, especially when the collision partners are diatomic, and spin-orbit coupling is important [Kharchenko and Dalgarno, 2004]. Thus, the “stratospheric” O(1 D) collision model results are only intended for qualitative comparison with the laboratory O(1 D)–He results. 2.5.1.4 Pulsed-photolysis results The results of the pulsed laser experiments are plotted in Figure 2.7 and shown in Table 2.4. At both temperatures, ∆47 of CO2 decreases with increasing extent of photochemical isotope exchange (∆δ 18 O), indicating the O(1 D) + CO2 reaction does not selectively enrich 16 O13 C18 O relative to 16 O12 C18 O. Additionally, no significant temperature dependence was observed in ∆47 vs. ∆δ 18 O, as the 300 K and 229 K data are indistinguishable within our experimental uncertainty; consequently, the data were considered together in the subsequent determination of the 13 C/12 C KIE. The best-fit slope of the ∆47 vs. ∆δ 18 O relationship in the experimental data was calculated to be –0.0036 ± 0.0008 (2σ ), corresponding to a 29 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.7: Changes in ∆47 vs. ∆δ 18 O after pulsed UV photolysis at 300 K (circles) and 229 K (triangles). ∆δ 18 O = δ 18 Ofinal - δ 18 Oinitial . Also shown is the modeled ∆47 vs. ∆δ 18 O dependence for 13 C/12 C KIE = 13 k/12 k = 0.999 and 1.01 (offset by ∆47 = +0.13‰ for clarity; the significance of this and of the slopes is discussed in the text). Error bars represent 2σ standard errors. Table 2.4: Results of pulsed photochemical experiments δ 13 C (‰) Temperature δ 18 Oi (‰) δ 18 Of (‰) ∆δ 18 O† (‰) ∆47,f (‰) σ ∆47,f (‰) 29.84 29.95 15.50 15.48 30.08 29.63 15.28 14.46 66.41 54.03 58.44 55.89 48.79 41.17 58.33 59.86 36.57 24.08 42.94 40.41 18.71 11.54 43.05 45.40 -0.009 0.036 0.104 -0.018 0.038 0.057 -0.024 0.036 0.012 0.025 0.017 0.009 0.013 0.012 0.032 0.023 29.81 20.84 14.22 29.72 20.88 14.29 -0.09 0.04 0.07 0.150 0.127 0.165 0.011 0.012 0.028 Photolysis experiments 300 K 229 K -10.76 -10.56 -23.79 -24.24 -10.69 -10.55 -24.13 -25.15 Blank experiments 300 K 229 K -10.67 -19.22 -25.09 Blank experiments were run without photolysis step. † ∆δ 18 O = δ 18 Of - δ 18 Oi 30 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 13 C/12 C KIE of 0.999 ± 0.001 (2σ ). This KIE value was obtained by modeling the 13 C/12 C KIE value corresponding to the best-fit slope of the ∆47 vs. ∆δ 18 O data shown in Figure 2.7 (0.999, assuming a 13 C/12 C KIE of 1 in reaction 2.2). Its uncertainty was estimated by varying the 13 C/12 C KIE until the modeled slope varied ± 0.0008; the upper and lower limits of the 13 C/12 C KIE (1.000 and 0.998, respectively) were then taken as the 2σ uncertainty bounds. In contrast, a 13 C/12 C KIE of 1.01, the KIE required to explain the polar vortex ∆47 vs. ∆17 O correlation (see Section 2.5.1.3), would yield a slope of +0.0055 in Figure 2.7. The negative experimental slope, however, rules out this 13 C/12 C KIE > 1 and thus a selective enrichment in 16 O13 C18 O resulting from reaction 2.1. While this experiment was unable to isolate the 13 C/12 C KIEs in reactions 2.5 and 2.6, the laboratory data are consistent with the 13 C/12 C KIE in reaction 2.5 dominating the observed ∆47 vs. ∆δ 18 O relationship. Reactions 2.5 and 2.6 are both important in the stratosphere, with the branching ratio between them likely 9:1 (2.5:2.6) at the average stratospheric collision energy (see Mebel et al. [2004]) and thus also at the hEcoll i in our experiments. Using this branching ratio, we calculate that the experiment is approximately three times more sensitive to a 13 C/12 C KIE in reaction 2.5 than in reaction 2.6. A 13 C/12 C KIE ∼ 0.993 in reaction 2.6, then, is also consistent with the laboratory ∆47 vs. δ 18 O slope. If the observed slope were arising exclusively from a 13 C/12 C KIE in reaction 2.6, it would become increasingly negative with increasing initial hEcoll i because reaction 2.6 is favored at higher Ecoll [Mebel et al., 2004; Perri et al., 2004]. Several high-collision-energy (no buffer gas, initial hEcoll i ≈ 13.6 kcal mol−1 ) experiments were performed to test this hypothesis; they also showed depletions in ∆47 as the extent of photochemical isotope exchange increased, with no significant (i.e., factor-of-three) change in ∆47 vs. ∆δ 18 O. Other combinations of 13 C/12 C KIEs in reactions 2.5 and 2.6 could also yield the laboratory ∆47 vs. ∆δ 18 O slope, but the absence of significant temperature and collision-energy dependence in the laboratory data, along with negligible O(1 D)–CO2 association and dissociation barriers on the singlet electronic potential energy surface [Mebel et al., 2004], support our attribution of the measured isotope effects to reaction 2.5. As such, we report a 13 C/12 C KIE of 0.999 ± 0.001 (2σ ), which is within the uncertainty of a KIE of 1.000 expected for 31 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 stochastic isotope exchange. 2.5.2 Continuous-irradiation experiments 2.5.2.1 Methods Continuous-irradiation experiments on the O2 /O3 /CO2 photochemical system were performed at UC-Berkeley to examine whether the aggregate isotope effect from all O(1 D)–CO2 reaction pairs would still yield depletions in ∆47 with increasing extent of photochemical isotope exchange. A 2 L glass reaction bulb was filled with mixtures of O2 and CO2 of known isotopic composition between 100 – 150 Torr total pressure at 295 K, and the mixture was irradiated between 0 – 48 hours with a pen-ray mercury lamp through a MgF2 window. This scheme generates O(1 D) through narrow-band photolysis of O2 at 185 nm (6 × 1013 – 1.5 × 1014 photons cm−2 s−1 ) and subsequent photolysis of O3 at 254 nm (2 × 1015 photons cm−2 s−1 ). Residual O2 was separated cryogenically from the mixture, and O3 was catalytically decomposed on hot nickel foil at 333 K for 15 minutes before the CO2 was purified for isotopic analysis. A commercially available software program, KINTECUS (Windows version 3.95, 2008; [Ianni, 2003]), was used to simulate the kinetics of the photochemical oxygen isotope exchange between O2 and CO2 in the continuous-irradiation experiments. The species mod3 1 eled were O2 , O2 (1 ∆), O2 (1 Σ+ g ), O( P), O( D), O3 , and CO2 and included both singly- and doubly-substituted 17 O- and 18 O- isotopologues as well as 13 C isotopologues of CO2 , yielding more than 400 isotope-specific reactions. Rate coefficients for each reaction corresponding to all common isotopologues were from Sander et al. [2006], while photolysis rate coefficients (J-values) were calculated from the reported irradiance of the mercury pen-ray lamp at 254 nm [Reader et al., 1996], the geometry of the bulb, and the measured cross sections of O2 at 185 nm and O3 at 254 nm [Sander et al., 2006]. The only oxygen KIEs included in the model are in the ozone recombination reaction [Janssen et al., 2001] and in O + O2 isotope exchange [Kaye and Strobel, 1983; Wiegell et al., 1997]. Stochastic scrambling of oxygen was assumed to occur in the O(1 D) + CO2 isotope exchange reaction [Baulch and Breckenridge, 1966; Yung et al., 1997], and scenarios with hypothetical 13 C/12 C KIEs of 1, 32 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Table 2.5: Results of continuous irradiation experiments Sample name† Irradiation time (h) δ 18 O (‰) ∆17 O (‰) ∆47 (‰) Starting CO2 ANOM 1 ANOM 1 ANOM 2 ANOM 2 ANOM 4 0.0 48.0 48.0 4.5 4.5 10.0 6.4 67.4 67.4 13.1 13.2 19.0 0.0 24.8 24.8 2.3 2.3 4.8 1.10 0.72 0.85 0.96 1.04 0.75 † Samples with the same names are replicate analyses for ∆ , taken as separate aliquots of the 47 same experiment. 0.999, and 0.998 were considered a priori. The model was initialized with the experimental partial pressures, temperature, and starting isotopic compositions of O2 and CO2 . 2.5.2.2 Continuous-irradiation results The laboratory results from the continuous-irradiation experiments are shown in Table 2.5 and compared with the modeling results in Figure 2.8. We observed a depletion in ∆47 with increasing ∆17 O (a proxy for the extent of photochemical isotope exchange), in agreement with the results from our pulsed photolysis experiments. Within the uncertainty bounds reported for the 13 C/12 C KIE, the continuous irradiation experiments are also generally consistent quantitatively with our pulsed photolysis experiments. There is a noticeable disagreement, however, at the largest ∆17 O value (48-hour irradiation time). Some of this error could be attributed to our assumptions about the initial distribution of CO2 isotopologues in the model: The initial ∆47 > 0 was modeled as an excess of 16 O13 C18 O exclusively, although contributions from 17 O12 C18 O and 13 C17 O2 may be nontrivial. In addition, trace water in the reaction bulb (in the gas phase or adsorbed onto the glass) could catalyze CO2 – water isotope exchange reactions and drive the distribution of CO2 isotopologues towards equilibrium, i.e., ∆47 = 0.86‰ at 298K. Both of these uncertainties would be exacerbated as the irradiation time increases, leading to a marked deviation from the modeled result at longer irradiation times. Last, the effects of the O3 decomposition step on ∆47 have not been fully elucidated; previous reports have documented some oxygen isotope exchange 33 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.8: Changes in ∆47 vs. ∆17 O of CO2 after continuous UV irradiation of O2 /O3 /CO2 mixtures with a Hg lamp. Experimental results are compared with calculated results (13 C/12 C KIE = = 13 k/12 k = 1, 0.999, and 0.998 obtained a priori from a kinetics model of the photochemical experiment. Error bars represent 2σ standard errors. when O3 is decomposed on hot nickel [Johnston et al., 2000; Shaheen et al., 2007], perhaps with the nickel oxide layer or surface-adsorbed water, so the post-irradiation O3 decomposition step during CO2 purification may drive ∆47 towards its isotopic equilibrium value (∆47 ∼ 0.8‰ at 333 K; see Wang et al. [2004]) at the nickel’s temperature. We performed experiments to test this hypothesis by heating O3 /CO2 mixtures (with initial ∆47 = 0) in the presence of nickel foil and/or powder at 88, 125, and 155◦ C. The resulting ∆47 values of CO2 showed 1 – 2‰ changes in δ 18 O and 0.5 – 0.6‰ increases in ∆47 , consistent with isotopic equilibration occurring on the nickel surface. Still, the continuous irradiation experiments are consistent with the results of the pulsed photolysis experiments. They show that the O(1 D) + CO2 isotope exchange reaction drives the CO2 isotopologue distribution towards a stochastic distribution. 2.5.3 Conclusions from laboratory measurements In both sets of experiments, ∆47 of CO2 decreases with increasing extent of photochemical isotope exchange, as measured by the change in δ 18 O (∆δ 18 O; see Figure 2.7) or ∆17 O 34 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 of CO2 (see Figure 2.8), indicating the O(1 D) + CO2 reaction does not selectively enrich 16 O13 C18 O relative to 16 O12 C18 O. Furthermore, these results are consistent with a statistical oxygen isotope exchange mechanism; using the results from the 18 O-labeled experiments at 300 K and 229 K and the comprehensive kinetics model of the pulsed photolysis experiment, we calculated a 13 C/12 C KIE of 0.999 ± 0.001 (2σ est.), which is not significantly different from the KIE of 1.000 expected for statistical isotope exchange branching fractions and is quantitatively consistent with the results from the continuous irradiation experiments. Hence, our results are consistent with previous studies asserting that the O(1 D) + CO2 isotope exchange branching fractions are partitioned statistically [Baulch and Breckenridge, 1966; Johnston et al., 2000; Perri et al., 2004]. In contrast, a 13 C/12 C KIE of ∼1.01 would be required to explain the high-latitude isotopic correlations shown in Figure 2.2. A significant ∆47 change due to reactions other than 2.1 and 2.2 in the O(1 D)–CO2 photochemical system is unlikely. The KIEs for the other reactions (e.g., the 17 O12 C18 O-producing channel, which is absent in the pulsed photolysis experiments) would need to be at least 1.01 to be of comparable importance. In addition, the ∆47 – δ 18 O – ∆17 O covariation observed in the continuous-irradiation experiments (which included the 17 O12 C18 O-producing channel; see Figure 2.8) agreed well with our laboratory model, which assumes statistical partitioning of isotope exchange products in the O(1 D) + CO2 reaction. While not all of the relative rates for the O(1 D) + CO2 isotope exchange reaction were measured directly, the agreement between the pulsed-photolysis and continuous-irradiation experiments suggests that KIEs in the other O(1 D) + CO2 reactions [e.g., 18 O(1 D) + 16 O12 C17 O] are described well using statistical product partitioning in this case. Direct measurements of the other KIEs would be required to determine whether the statistical partitioning of isotope exchange products applies rigorously for all O(1 D)–CO2 reactant pairs. As such, we report a 13 C/12 C KIE of 0.999 ± 0.001 (2σ ), which is within the uncertainty of a KIE of 1.000 expected for stochastic isotope exchange. 35 L. Y. Yeung Oxygen isotope exchange reactions of CO2 2.6 Discussion 2.6.1 O(1 D)+CO2 only explains mid-latitude 16 O13 C18 O variations Chapter 2 We conclude that intrinsic isotope effects in O(1 D) + CO2 isotope exchange cannot produce the elevated values of ∆47 observed in stratospheric polar vortex air. Instead, the statistical partitioning of isotope exchange products in the O(1 D) + CO2 reaction drives the isotopic composition of CO2 towards a stochastic distribution, thus decreasing ∆47 . Indeed, the mid-latitude observations show evidence for decreasing ∆47 with increasing extent of photochemical isotope exchange (see Figure 2.2). As photochemical isotope exchange approaches completion (the unlikely, but instructive case in which all the oxygen atoms in CO2 have been exchanged), the ∆17 O and δ 18 O of CO2 will approach the ∆17 O and δ 18 O of O(1 D) because the size of the total oxygen reservoir (i.e., O2 , O3 , etc.) is >500x that of CO2 . Concurrently, the distribution of stable isotopes will become increasingly random, so the ∆47 value of CO2 will approach zero. The slope of this approach, then, reflects the integrated effective isotope composition of O(1 D) with which the CO2 molecules in the air samples have exchanged since entering the stratosphere; it is possible, however, that other terms in the stratospheric CO2 budget (e.g., CO oxidation) may, more subtly, change the isotopic composition of CO2 and thus the isotopic composition of O(1 D) one would infer from such a trend. We constructed a box model to calculate the effective integrated mid-latitude O(1 D) isotope composition to evaluate this hypothesis quantitatively. The results of our laboratory photochemistry model (13 C/12 C KIE experiments) were fit to the slope of weighted linear regressions of the mid-latitude ∆47 data (Figure 2.2). A quenching (reaction 2.5) and nonquenching (reaction 2.6) branching ratio of 9:1 in the isotope exchange reaction was used. Atmospheric ∆47 enrichments (e.g., ∆47 = 1.1‰) were treated as 16 O13 C18 O enrichments exclusively, since contributions to ∆47 from 17 O12 C18 O and 13 C17 O2 are ≤ 3%. Uncertainties in the fit ∆17 O and δ 18 O values were estimated by varying δ 17 O and δ 18 O to match the 2σ uncertainty in the slope of the weighted linear regressions. Using this box model and the mid-latitude observations, we estimate ∆17 O = 80.6+59.7 −24.1 ‰ 36 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 and δ 18 O = 98.0+43.7 −17.1 ‰ (2σ est.) as values for the integrated effective isotopic composition of O(1 D), which is consistent with ozone photolysis being the primary O(1 D) source in the stratosphere. While the δ 18 O of O(1 D) we calculate is similar to that found in low- and mid-latitude stratospheric ozone, ∆17 O is larger, on average, by 35‰ [Krankowsky et al., 2007]. This is expected because ∆17 O enrichments in ozone are concentrated at terminal atom positions [Michalski and Bhattacharya, 2009]; when ozone is photolyzed to O(1 D) and O2 , one of the terminal atoms is ejected [Dylewski et al., 2001], elevating the proportion of heavy oxygen isotopes in O(1 D). We note that the upper and lower uncertainty limits of the reported ∆17 O and δ 18 O values are correlated; they correspond to fits that simultaneously match the upper and lower uncertainty limits of the mid-latitude ∆47 vs. ∆17 O and ∆47 vs. δ 18 O weighted linear regressions. They reflect spatial and temporal variations in O(1 D) isotope composition expected to be caused by variations in ozone concentrations, temperature, pressure, actinic flux, and various mass-dependent kinetic and photolytic isotope effects that depend on these variables. 2.6.2 Effects of intra-stratospheric chemistry and mixing Having experimentally excluded intrinsic isotope effects in the O(1 D) + CO2 isotope exchange reaction as the source of high stratospheric ∆47 in polar vortex air, we consider the possible effects of other gas-phase stratospheric processes on the CO2 isotopologue budget. CO is produced in the stratosphere by CH4 oxidation and destroyed with an e-folding time of about two to three months by reaction with OH radicals to form CO2 . We estimate that up to 0.9 ppmv CO2 could be derived from CH4 oxidation in our samples based on the difference between the observed CH4 concentrations (Table 2.1) and the average CH4 concentration in air entering the stratosphere from the troposphere (1.7 ppmv). 12 C/13 C KIEs for CH4 + OH, CH4 + O(1 D), and CH4 + Cl of 1.004, 1.01, and 1.07, respectively [Brenninkmeijer et al., 2003], should yield 13 C-depleted CH3 radicals at all latitudes, particularly in the polar vortex, where Cl levels are elevated. CH3 radicals then undergo several rapid oxidation steps to form formaldehyde (CH2 O). Isotope effects in CH2 O photolysis to form CO also favor the light isotopologues [Feilberg et al., 2005a]. These isotope effects, com- 37 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 bined with expected 13 C compositions for stratospheric CH4 in these samples (δ 13 C = –47 to –35‰) should produce CO that is depleted in 13 C relative to background stratospheric CO2 . Small inverse 12 C/13 C, 16 O/18 O, and 16 C/17 O KIEs (i.e., < 1) in the reaction CO + OH to form CO2 at low pressures [Röckmann et al., 1998] imply that, in principle, CO + OH reactions could increase ∆47 values in the product CO2 , while at higher pressures, the CO + OH reaction yields 13 C-, 18 O-, and 17 O-depleted CO2 [Feilberg et al., 2005b]. Ultimately, however, the size of ∆47 values in the ≤ 0.9 ppmv CO2 derived from CH4 oxidation would likely be orders of magnitude too small to increase ∆47 values significantly in the other ∼365 ppmv of background stratospheric CO2 . A possibility remains that unusual timing in the competition between oxidation and photolysis of species in the polar vortex, combined with unexpectedly large carbon and oxygen KIEs in some Cl and Br reactions (e.g., Br + CH2 O; see Feilberg et al. [2004]) or other gas-phase processes might be responsible for the mid-latitude-polar vortex differences in ∆47 given the large differences in Cl and Br concentrations in polar vortex vs. mid-latitude air, but this seems unlikely in light of the known chemistry and KIEs. Expected changes in δ 18 O and δ 17 O due to intra-stratospheric mixing are also too small to yield highly enriched polar vortex ∆47 . Effects of CO2 sources on ∆47 can be calculated by solving the three-end-member mixing problem between (1) tropospheric CO2 , (2) stratospheric CO2 undergoing photochemical isotope exchange, and (3) stratospheric CO2 derived from a third source and accounting for the non-linearity in mixing (see Appendix 2.A). Therefore, we constructed a mixing model to simulate the effects of mixing isotopically distinct CO2 sources on stratospheric air. The tropospheric end-member was given an isotopic composition equal to measured ‘clean’ troposphere values (based on measurements of air sampled from Barrow, Alaska, and Cape Grim, Tasmania; see Affek et al. [2007]), namely, δ 13 Ctrop = –8‰, δ 18 Otrop = 41‰, δ 17 Otrop = 21‰, and ∆47trop = 0.92‰. Unfortunately, no measurements of ∆47 in the tropical troposphere exist, so ∆47trop of the air entering the stratosphere from the tropics is uncertain. The mid-latitude ∆47 vs. ∆17 O relationship implies that ∆47 may be as high as 1.09‰, but changes of ∆47trop on this order do not affect our qualitative understanding of mixing on stratospheric ∆47 . The stratospheric end- 38 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 member was δ 13 Cstrat = –8‰, ∆17 O = 80.6‰, and δ 18 O = 98.0‰; this was our integrated effective isotopic composition for O(1 D) calculated from the mid-latitude ∆47 variations. We find that two-component mixing between tropospheric and stratospheric air masses does not exhibit sufficient non-linearity to generate the observed ∆47 enrichments in highlatitude samples. Mixing non-linearities in ∆47 increase as the bulk isotope compositions of the two end-members become more dissimilar, but stratospheric O(1 D)–CO2 isotope exchange alone cannot produce a CO2 mixture of sufficiently high ∆47 . For instance, mixing effects generate ∆47 changes < 0.1‰ in the troposphere [Eiler and Schauble, 2004], where bulk isotope compositions of major constituents of the CO2 budget vary typically < 20‰ [Affek et al., 2007; Ciais and Meijer, 1998]. A mixture of tropospheric CO2 and midlatitude stratospheric CO2 would generate a similar enrichment because their bulk isotope compositions differ by a similar amount. Even in the extreme case of δ 18 Ostrat = 146‰, δ 17 Ostrat = 142‰ and ∆47strat = 0‰, the oxygen isotope composition of CO2 when it is at isotopic equilibrium with excess O3 (an unlikely case, but an ultimately useful one in illustrating this point; see Shaheen et al. [2007]), two-component mixing would yield a maximum ∆47 change more than an order of magnitude smaller than, and in the opposite direction of, that which is observed in polar vortex samples over the same range in ∆17 O. Bulk isotope compositions of the two CO2 reservoirs must differ in δ 18 O and/or δ 13 C by orders of magnitude not previously observed in the stratosphere to generate ∆47 enrichments of ∼0.7‰ observed in polar vortex samples. 2.6.3 Effects of mesospheric and heterogeneous chemistry Physical or chemical processes in the mesosphere may yield extreme isotopic enrichments in CO2 or CO such that subsidence of mesospheric air into the 1999/2000 stratospheric polar vortex [Plumb et al., 2003] could explain the observed meridional variation in ∆47 . Thus, we will next consider three mesospheric processes that have been previously studied in other contexts: Gravitational separation of upper atmospheric air, UV photolysis of O2 , and UV photolysis of CO2 . 39 L. Y. Yeung 2.6.3.1 Oxygen isotope exchange reactions of CO2 Chapter 2 Mixing of gravitationally separated air into the stratosphere Gravitational separation can concentrate heavy isotopologues of CO2 into the lower mesosphere [Ishidoya et al., 2008], which could elevate stratospheric ∆47 values after mesospheric subsidence and mixing. The expression in Craig [Craig et al., 1988] for the enrichment of a species Ni versus a second species N in per mil is based on the kinetic theory of gases [Gibbs, 1948]:  Ni ∆ N  = ∆M gZ × 103 RT (2.8) where ∆M is the difference in mass, g is the acceleration due to gravity (9.81 m s−2 ), Z is the column length, R is the gas constant, and T is the temperature. Using a reasonable column length of 50 km at a temperature of 220 K, gravitational separation of CO2 would increase δ 13 C, δ 18 O, and δ 17 O by 266‰, 6223‰, and 1113‰, respectively, but would lead to a decrease in ∆47 by 74‰ at the bottom of the column. In addition, polar vortex δ 13 C is not markedly more enriched from mid-latitude δ 13 C, implying that gravitational separation is generally negligible for the samples in this study. 2.6.3.2 Mixing of mesospheric air highly enriched in 17 O and 18 O Isotope effects in the photolysis of O2 by short-wavelength UV radiation in the upper mesosphere might lead to unusually enriched CO2 in the mesosphere. Liang et al. predicted recently that differences in photolysis cross-sections between light and heavy isotopologues of O2 in the narrow solar Lyman-α region (121.6 nm) may result in a population of mesospheric O(1 D) enormously enriched in 17 O and 18 O [Liang et al., 2007]. This extreme enrichment in O(1 D) could then be transferred to mesospheric CO2 through the O(1 D)+CO2 isotope exchange reaction. CO2 photolysis in the mesosphere to form CO, followed by oxidation of that same CO by OH in the polar vortex, might also significantly affect the ∆47 values of CO2 in the polar vortex. To evaluate the effects of 17 O- and 18 O-enriched mesospheric CO2 mixing into the stratospheric polar vortex, we constructed a three-component mixing model that included air 40 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Table 2.6: Tropospheric-stratospheric-mesospheric mixing model results Sample name f ∗trop f strat f meso 0.075 0.057 0.048 0.033 2.6 × 10−6 δ 18 Ostrat (‰) δ 18 Omeso (‰) 82.5 80.0 77.7 87.9 1.76 × 105 δ 18 O (‰) ∆17 O (‰) ∆47 (‰) Mixing model results 20000312(25)1120 20000131(30)1001 20000203(10)1173 20000127(5)1060 0.925 0.943 0.952 0.967 2.1 × 10−6 1.4 × 10−6 1.7 × 10−6 ∗ Mixing fraction of tropospheric air, calculated as 1 – f 1.86 × 105 2.07 × 105 1.47 × 105 44.55 43.62 43.06 42.79 5.76 4.38 3.69 2.45 1.614 1.555 1.436 1.233 strat – f meso . mass contributions from the troposphere, stratosphere, and mesosphere. Each polar vortex datum (i.e., with unique ∆17 O, δ 18 O, and ∆47 values) was fit individually because of the presence of mesospheric filaments in the polar vortex [Plumb et al., 2003] and consequent heterogeneity in the mixing fraction and end-member isotopic composition between samples. The multiply-substituted isotopologue distribution was fixed at ∆47meso = 0 for this simple mixing-only scenario because our kinetics experiments and the mid-latitude stratosphere ∆47 values indicate that isotope exchange drives the isotopologue distribution towards a stochastic one. No measurements of mesospheric δ 13 C exist, so δ 13 Cmeso = –8‰ was used; however, the calculated enrichment in mesospheric δ 18 O was insensitive to the choice of δ 13 C. We were unable to reproduce the polar vortex data in both bulk isotope compositions and ∆47 simultaneously when using the mesospheric 18 O and 17 O enrichments in CO2 mixing end-member suggested by Liang et al. [2007] (i.e., δ 18 O = 10,603‰, δ 17 O = 3,149‰, and ∆47 = 0). Only after δ 18 O and δ 17 O of the mesospheric CO2 end-member were increased an additional tenfold (i.e., δ 18 O ∼ 105 ‰ and δ 17 O ∼ 104 ‰) were the ∆47 – δ 18 O – ∆17 O systematics of the polar vortex samples reproduced. Modeled mixing fractions ( ftrop , fstrat , and fmeso ) and isotopic compositions for each of the high-latitude CO2 samples are given in Table 2.6. Due to the uncertainty in our calculated ∆17 Ostrat and δ 18 Ostrat values (see Section 2.6.1), δ 18 Ostrat was allowed to vary freely about our estimate above; the resulting δ 18 Ostrat values generally fell within the range we predicted. The combined uncertainties introduced by our calculated mid-latitude O(1 D) isotope composition and the other parameters used in these 41 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 fits suggest that these results are likely only meaningful to within an order of magnitude. No laboratory measurements of the isotopic fractionations in O2 due to Lyman-α photolysis are available to compare with our modeled isotopic compositions, however. Because 3 − the Lyman-α lines fall on the edge of the Ẽ 3 Σ− u ← X̃ Σg (1,0) absorption band of O2 , a small absolute absorption cross-section error for one O2 isotopologue can translate into a significant isotopic fractionation error. Relaxing the mesospheric δ 18 O vs. δ 17 O relationship predicted by Liang et al. [2007], i.e, δ 17 O = 0.3 × δ 18 O, increases the modeled δ 18 Ostrat values and lowers the predicted δ 18 Omeso values, but the mesospheric CO2 mixing end-member is still enriched overall to ∼100,000‰ in δ 18 O and δ 17 O. A simple calculation (assuming 365 ppm CO2 and an initial δ 18 O = 23.5‰ in O2 ) predicts that the mesospheric O2 end-member should have a δ 18 O value on the order of –100‰. Furthermore, we note that the O(1 D) + CO2 reaction may not necessarily partition products statistically (i.e., drive ∆47 → 0) in the mesosphere, as we assumed here, because the average collision energy there is higher than in the stratosphere. In principle, measurements of the isotopic composition of mesospheric CO should constrain the isotopic composition of mesospheric CO2 downwelling into the polar vortex. Large elevations in CO above background stratospheric levels, observed at high altitudes in the polar vortex [Plumb et al., 2003], are due to CO2 photolysis in the mesosphere and subsequent transport to the stratosphere, so the isotopic composition of CO in these cases should reflect that of the mesospheric CO2 population and any fractionations arising from CO2 photolysis there. The bulk isotope composition in mesospheric CO2 predicted by our three-component mixing model (e.g., tens of percent in 18 O-atom abundance, or 100x natural abundance) would result in isotopic enrichments in mesospheric CO that are detectable with remote-sensing spectrometers because CO2 photolysis isotope effects are expected to be much smaller in magnitude. For example, Bhattacharya et al. [2000] measured fractionations of ∼100‰ in 17 O and 18 O in their UV-photolysis experiments; CO2 -photolysis fractionation in the mesosphere could be larger, but the wavelength dependence of these across the actinic spectrum is difficult to estimate because the physical origin of the laboratory fractionations is not understood (see below). Remote-sensing measurements by the JPL 42 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 MkIV Fourier-transform spectrometer, however, does not show hundred-fold enrichments in 18 O of mesospheric CO observed downwelling to 30 km altitude in the polar vortex (G. C. Toon, personal communication, 2009). On the basis of this observation, mesospheric CO2 does not appear to possess oxygen isotopic enrichments of sufficient size to produce high ∆47 values in the polar vortex upon mixing with stratospheric air masses, although the long path-length and consequent averaging over mesospheric filaments and background stratospheric air of the MkIV instrument will dilute any mesospheric signal. Remote sensing of CO and/or CO2 isotopologue abundances in the mesosphere are thus needed to constrain this hypothesis. 2.6.3.3 Oxidation of mesospheric CO in the polar vortex Next, we examine the potential impacts of mesospheric CO2 photolysis to form CO, followed by mixing and re-oxidation into CO2 , on polar vortex ∆47 values. The photolysis of CO2 in the UV region may result in wavelength-dependent isotope effects, although this contention is based on a single laboratory measurement. Bhattacharya et al. [2000] performed laboratory experiments in which they photolyzed CO2 with either a Kr lamp (120 – 160 nm) or a Hg lamp (185 nm) and measured the 17 O and 18 O compositions of the product CO and O2 . The 120 – 160 nm results suggest that mass-dependent depletions of order 50‰ and 100‰ in 18 O and 17 O of CO, respectively, are possible, which would enrich the remaining CO2 reservoir in 18 O and 17 O. The 185-nm results were quite different: Photolysis of CO2 near natural isotopic abundance showed mass-independent enrichments in 17 O up to 150‰ with little change in 18 O in the CO and O2 products, while photolysis of 13 C-labeled CO2 showed mass-dependent enrichments in 18 O and 17 O in the 13 CO and O2 products of ∼50 and 100‰, respectively. Taken alone, these latter isotope dependences could result in mesospheric CO that is significantly enriched in 18 O, 17 O, and 13 C, and perhaps even 13 C18 O. The remaining mesospheric CO2 would be correspondingly depleted in heavy isotopologues. If similar isotopic fractionations occur in CO and CO2 when CO2 is photolyzed by UV radiation in the mesosphere, then the population of mesospheric CO downwelling into the 43 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 stratospheric polar vortex could have a large impact on the ∆47 values of CO2 in the polar vortex. Once in the stratosphere, mesospheric CO will be oxidized by OH to produce CO2 in the polar vortex. Oxidation of this CO could, in principle, contribute to the large polar vortex values of ∆47 in CO2 observed because: (1) CO mixing ratios as large as 10 ppmv have been observed in mesospheric filaments in the stratosphere (a thousand-fold higher than background stratospheric CO abundances in the polar vortex) [Plumb et al., 2003], (2) the known KIEs for the CO + OH reaction are expected to favor formation of 13 C18 Ocontaining CO2 molecules in the stratosphere [Feilberg et al., 2005b; Röckmann et al., 1998], and (3) the lifetime of CO with respect to oxidation is several months, and is therefore not immediately quantitative. These three phenomena could result in a sub-population of CO2 with elevated concentrations of 16 O12 C17 O, 16 C12 C18 O, and 16 C13 C18 O (or other mass-47 isotopologues of CO2 ), given the sign and magnitude of known KIEs for the CO + OH reaction [Feilberg et al., 2005b; Röckmann et al., 1998]. The slow oxidation of CO may only produce temporary increases of heavy-isotopologue abundances, as large fractionations due to KIEs will decrease in magnitude as CO oxidizes quantitatively to CO2 . Measurements of the 13 C18 O + OH vs. 12 C18 O + OH KIE by Feilberg et al. at 298K and 1 atm suggest that the oxidation of mesospheric CO alone could account for elevated ∆47 in the stratospheric polar vortex [Feilberg et al., 2005b]. Consequently, CO2 photolysis in the mesosphere, followed by oxidation of the product CO in the mesosphere and/or stratosphere, may allow the heavy oxygen and carbon isotopes in CO2 to ‘reorganize’ in a manner that could elevate ∆47 values of CO2 in the polar vortex. The mixing of the remaining (unphotolyzed) mesospheric CO2 with stratospheric CO2 in the polar vortex, however, may have the opposite effect on ∆47 values of CO2 . Measurements of all the relevant KIEs of CO + OH reaction at stratospheric temperatures and pressures and a model of the oxidation of mesospheric CO in the stratospheric polar vortex will be required to evaluate the impact of this mechanism quantitatively. The full impact of this mechanism is not well-constrained, however, because (1) the isotopic composition of mesospheric CO2 has not been measured, (2) not all the KIEs for the CO + OH reaction are known at the relevant temperatures and pressures, and (3) the 44 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 physical origin of the photolytic fractionations associated with CO2 photolysis are not understood. The first two points were discussed earlier, so they will not be discussed here. For the physical origin of the photolytic fractionations associated with CO2 photolysis, Bhattacharya et al. suggested that dissociation rates for certain CO2 isotopologues could be enhanced if their excited vibrational states (which get populated when the molecule absorbs UV light) overlap sufficiently with the vibrational states of another CO2 electronic state. This would facilitate conversion of the electronically excited species CO2 (1 B2 ), which is promoted from ground-state CO2 when it absorbs UV light and does not have enough energy to dissociate into O + CO under the experimental conditions, into the electronically excited species CO2 (3 B2 ), which does have enough energy to dissociate. If this mechanism is a general feature of the dynamics of CO2 photodissociation, it could lead to additional mass-independent fractionations at wavelengths other than at 185 nm. Unfortunately, this hypothesis has not been tested at other wavelengths yet, and without a firm theoretical understanding, or at least an empirical wavelength dependence, of the isotopic fractionations associated with CO2 photolysis, convolving the 120 – 160 nm results with the 185 nm results from Bhattacharya et al.’s experiments, and then convolving those with the actinic flux to make a prediction for ∆47 of mesospheric CO and CO2 is not possible. 2.6.3.4 Heterogeneous chemistry on stratospheric particles Finally, we consider the potential role stratospheric particles could play in the stratospheric CO2 isotopic budget. Oxygen isotope exchange on particle surfaces could drive the population of CO2 towards isotopic equilibrium by catalyzing CO2 –CO2 isotope exchange reactions (e.g., 16 O12 C18 O+13 C16 O2 * ) 12 C16 O2 + 16 O13 C18 O) that are too slow to occur in the gas phase under stratospheric conditions. Zero-point energy isotope effects dominate in these reactions at equilibrium, driving the ∆47 value towards its equilibrium value at a given temperature. We calculate that ∆47 adopts a value of 1.6‰ if 70% of the CO2 molecules achieve isotopic equilibrium at temperatures coincident with PSC formation in the polar vortex, ∼190 K [Wang et al., 2004] . Thus, in principle, particle-catalyzed equilibration of CO2 , perhaps via CO2 hydration reactions in quasi-liquid films at the surface of ice particles 45 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 [Dash et al., 2006], could produce the observed polar vortex ∆47 values. Bulk isotopic compositions would be little-affected by these isotope exchange reactions, consistent with the data presented in Table 2.1 and Figure 2.2, if the catalyst reservoir (e.g., liquid water layers on a surface) is much smaller than the CO2 reservoir; CO2 would impart its bulk isotopic composition on the catalyst while the multiply-substituted isotopologue distribution in CO2 , which is insensitive to the isotopic composition of the catalyst, approaches that at isotopic equilibrium. However, CO2 –liquid water isotope exchange may not occur quickly enough at low temperatures and low pH to be the relevant process. Last, we note that, in order for this PSC-catalyzed isotope-exchange mechanism to explain the polar vortex ∆47 measurements, the mechanism must result in a strong anti-correlation with N2 O mixing ratios (Figure 2.2a); this would imply that transport is fast compared to isotope exchange on the PSCs, whose distributions are highly variable in space and time in the polar vortex. Future 2-D modeling efforts will examine whether such a mechanism remains consistent with the observations or whether transport and mixing of a mesospheric isotope signal into the polar vortex better explains the observed anti-correlation of ∆47 with N2 O. We conducted preliminary experiments on the kinetics of isotope exchange on PSClike surfaces (e.g., H2 SO4 /HNO3 /H2 O mixtures; see Molina et al. [1993]) to test the PSCisotope-exchange hypothesis. PSCs made from HNO3 :H2 O mixtures, i.e. ‘Type Ia’ PSCs, were tested first because they were a major component of the PSCs formed during the 1999/2000 Arctic winter [Voigt et al., 2000] and their crystallization has been studied in the laboratory [Hanson and Mauersberger, 1988]. 50% HNO3 in H2 O was crystallized at 197 K using an ethanol/dry ice bath according to the protocol outlined by Hanson and Mauersberger [1988]; the crystal structure and stoichiometry of the ice was not measured. Pure CO2 of known isotopic composition was then exposed to the HNO3 ice for 3 hours in a glass reaction vessel held at 197 K. No change in the ∆47 values were observed (within statistical uncertainty). Based on the volume of the reaction vessel and the amount CO2 , the root-mean-square (RMS) displacement was 2.5 cm s−1 . This RMS displacement was significant compared to the 15-cm length of the reaction vessel; therefore, the reaction’s progress was probably not hindered by diffusion. The same experiment was performed also 46 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 with 1:1:1 H2 SO4 :HNO3 :H2 O mixtures (similar to ‘Type Ib’ PSCs) at 197 K, and no isotope exchange was observed in those experiments, either. These preliminary results imply that CO2 isotope exchange on PSCs is slow at stratospheric temperatures, although the chemical composition of the surfaces generated in the laboratory may have been different from those of real PSCs. Future studies should explore the isotope exchange reaction on all known PSC surfaces (e.g., types Ia, Ib, and II; see Zondlo et al. [2000] and Prenni and Tolbert [2001]) and assign upper limits to their rates. 2.7 Conclusions The signature of a new process preserved in stratospheric 16 O13 C18 O proportions reveals that a second mechanism, in addition to the O(1 D) + CO2 isotope exchange reaction, alters the isotopic composition of stratospheric CO2 and thus the interpretation of its chemical and transport ‘history.’ This second mechanism, which elevates ∆47 values in the polar vortex, is likely of either mesospheric photochemical or heterogeneous origin. To constrain further the role of each of these mechanisms, isotopic fractionations due to broadband UV photolysis of O2 and CO2 , the KIEs of the CO + OH reaction under stratospheric conditions, and the kinetics of CO2 isotope equilibration on the surfaces of PSCs and other stratospheric aerosols need to be studied experimentally. Additionally, kinetic and photolysis-induced isotope effects that may affect CO and CO2 should be incorporated into atmospheric models to quantify their contributions to both the bulk and multiply-substituted isotopologue budgets of stratospheric CO2 , whose influence on the isotopologue budgets of tropospheric CO2 may be significant. 2.8 Acknowledgements We thank R. Lueb for whole-air-sampler and cryogenic whole-air-sampler field support, Y. L. Yung, G. A. Blake, and P. O. Wennberg for manuscript comments, and financial support from the Davidow Fund, the National Science Foundation, the NASA Upper Atmosphere Research Program. K. A. B. was supported by the Camille Dreyfus Teacher-Scholar Award. 47 L. Y. Yeung Oxygen isotope exchange reactions of CO2 This page intentionally left blank. 48 Chapter 2 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Appendices 49 Chapter 2 L. Y. Yeung 2.A Oxygen isotope exchange reactions of CO2 Chapter 2 Mixing effects on isotopic composition The effects of CO2 air parcel mixing on isotopic composition have specific relevance for ∆47 in Chapter 2, so an example follows below. In general, mixing of two or more reservoirs of CO2 is linear in δ 13 C, δ 18 O, and δ 17 O (the mixture has δ -value in between that of the two mixing end-members) because the references against which they are compared are constant (see Eqs. 1.5 and 1.6) Mixing of two reservoirs with the same ∆47 and differing bulk isotope distributions, however, can yield ∆47 values in the mixture different from those in the endmember gases. This nonlinear dependence of ∆47 on mixing arises because both R47 sample and the reference against which it is measured (R47 stochastic ) change upon mixing; the reference is defined by, and therefore varies with, the bulk stable isotope ratios of that mixture. In contrast, the references used in bulk stable isotope measurements are external standards whose values are constant (e.g., VSMOW), so the bulk isotope ratios vary linearly with mixing. The degree of nonlinearity in ∆47 is a function of the differences in bulk isotopic composition between the mixing end-member reservoirs and their mixing fractions [Affek and Eiler, 2006; Eiler and Schauble, 2004]. Because ∆47 depends non-linearly on mixing fraction, even for two CO2 reservoirs with similar ∆47 [Affek and Eiler, 2006; Eiler and Schauble, 2004], mixing relationships are often counterintuitive. An illustrative example is shown in Figure 2.9: The two mixing endmembers (given as the bottom-left and bottom-right corners) have different initial δ 18 O and δ 17 O values, though both have δ 13 C = –8‰ and ∆47 = 0.92‰. The concentration of 47 CO2 (i.e., R47 mix ) varies linearly with mixing fraction, but the stochastic distribution for 47 CO2 molecules also changes, varying as ∼2R13 R18 . Consequently, mixing these two isotopically dissimilar CO2 reservoirs yields a ∆47mix > 0.92‰ despite each reservoir being initially at ∆47 = 0.92‰. This type of relationship is general, and so holds for all ∆47 ; the sign and magnitude of the resulting ∆47 change will depend on the end-member bulk and clumped isotope compositions. 50 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.9: How mixing two arbitrary reservoirs of CO2 can be nonlinear in ∆47 . The resulting mixture is more enriched in 47 CO2 relative to its stochastic distribution, as compared to either of the mixing end-members. The isotopic compositions used in this plot are for illustration purposes only; qualitatively similar effects will apply for all mixing relationships. 51 L. Y. Yeung Oxygen isotope exchange reactions of CO2 2.B Practical considerations 2.B.1 IRMS long-term signal stability Chapter 2 ∆47 measurements currently take ∼4 hours of instrument averaging time per sample analysis. We examined the stability and accuracy of our IRMS system over this time period by using a modified form of the Allan variance technique, originally developed to characterize ultrastable oscillators [Allan, 1987]. Instead of using time as the independent variable, here we use individual IRMS acquisitions x: 2 σAllan (x) = 1 [hxii+1 − hxii ]2 2(N − 1) ∑ i (2.9) Data are first binned into N bins (each consisting of one or more acquisitions), and the average of each bin, hxii , is taken. The difference between adjacent bins is squared and then summed before being normalized to compute the Allan variance. For example, a data set with six elements [x1 , x2 , x3 , x4 , x5 , x6 ] will produce three values of Allan variance corresponding to bins of one ([x1 ], [x2 ], [x3 ], [x4 ], [x5 ], [x6 ]), two ([x1 , x2 ], [x3 , x4 ], [x5 , x6 ]) and three ([x1 , x2 , x3 ] and [x4 , x5 , x6 ]) elements each. The maximum bin size is therefore half the total number of elements in a data set. Plotting Allan variance versus bin size, then, conveniently presents both noise- and driftrelated effects on single plot. An example of the ∆47 Allan variance for a relatively longduration analysis, consisting of 40 acquisitions of 80 s sample integration each (ten 8 s cycles), is shown in Figure 2.10. An ideal statistical-noise-limited measurement, for which long-term drifts are negligible, will display a power-law relationship σ 2 = Cxα in the Allan variance plot, where α = –0.5, reflecting the Poisson statistics governing the precision of the overall measurement. In contrast, a measurement dominated by long-term, correlated random-walk drifts will have α = 0.5. Consequently, the optimum number of measurements to average together in a given analysis (i.e., the optimum bin size) will occur near where the Allan variance reaches a minimum, i.e. where dα/dx = 0. For our instrument, measurements seem to be dominated by statistical noise for N < 10 acquisitions, with only a small contribution from long-term drift. The variability of σ 2 appears to increase for 52 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.10: Allan-variance plot of ∆47 over 40 IRMS acquisitions. A power-law regression is shown for bins up to nine acquisitions. α = –0.47 was obtained, indicating that Poisson statistics, not long-term drifts, dominate the uncertainties in the measured ∆47 value in this range. measurements made in excess of nine acquisitions (see Figure 2.10), although we attribute this to the smaller number of bins with greater than nine acquisitions contributing to the Allan variance calculation. More precise values of the Allan variance with these numbers of acquisitions would require a more sustained analytical run by several factors in time. Nevertheless, the ideal precision that should be attainable on a single gas run for measurements that are clearly dominated by statistical noise (nine acquisitions, or 720-s counting time) at the optimal voltage (16 V) is 0.013‰. 2.B.2 IRMS vs. optical methods The best high-precision isotope-ratio measurements have been made routinely on gassource mass spectrometers based on Nier’s original 1947 design [Nier, 1947]. These instruments are fundamentally sensitive to that which makes stable isotopes unique — their mass — so IRMS continues to be the technique-of-choice used for stable isotope abundance measurements. It achieves high precision over a large dynamic range by utilizing multiple Faraday cups with differing amplifier gains (over a factor of 3000 for ∆47 measurements) 53 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 and rapid sample-standard comparison. However, the relatively poor mass-resolving power (M/∆M ∼ 500) that comes as a consequence of using a magnetic sector and high-sensitivity, electrically stable Faraday-cup detectors leads to well known isobaric (same-nominal-mass) interferences, e.g., between 13 CO2 and 16 O12 C17 O at m/z = 45. In ‘clumped’ isotopologue measurements of CO2 , isobars and other impurities (e.g., N2 O, hydrocarbons) are especially important given the low absolute abundance of m/z = 47 isotopologues. A new concern also arises in the study of ‘clumped’ isotopologues: ion recombination after electron-impact ionization source can alter the measured distribution of stable isotopes vs. that present in the original sample. High-resolution and thermal-ionization mass-spectrometric techniques can potentially address these uncertainties, but none have yet demonstrated the precision and stability necessary for ∆47 measurements. Spectroscopic techniques, however, show great promise for measuring stable isotopologue abundances in natural samples because they are non-destructive, sensitive to both mass and molecular symmetry, and field-deployable. These characteristics are particularly desirable for studying the stable isotope distribution in atmospheric gases, and how they evolve over time. The author has had some experience with these techniques so the following discussion represents a synthesis of his experience. While most examples relate to CO2 , the general considerations presented here should be applicable to spectroscopic stable isotope measurements of other species. More general and thorough reviews of the literature have been published (e.g., Kerstel [2004]; Kerstel and Gianfrani [2008]), so the references herein are exemplary rather than comprehensive. Three main instrumental requirements for highly precise optical measurements of rare and/or ‘clumped’ isotopologues near natural isotopic abundance are apparent: absolute sensitivity, dynamic range, and long-term signal stability. A more subtle problem is the selection of spectral region; the spectral absorption scales not only with analyte concentration, but also the optical pathlength and the size of the transition dipole (i.e., the absorption line strength, S, for the transition). In addition, spectral overlap between isotopologues and also from contaminants will lead to systematic errors. The type of spectroscopic technique, then, will depend on the analyte identity and spectral region. For instance, Tuzson et al. 54 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 [2008] used the strong CO2 lines (S ∼ 10−18 cm molecule−1 ) near 2300 cm−1 and a multipass direct absorption cell [Herriott et al., 1964] to measure δ 13 C and δ 18 O with better than 0.1‰ precision (100-s averaging). The authors utilized that region because the transitions for 12 C16 O2 , 13 C16 O2 , and 16 O12 C18 O were of nearly equal strengths. Bergamaschi et al. [1994] made similar line choices for δ 13 C and δ D measurements in CH4 . McManus et al. [2002] surmounted the dynamic range problem for their CO2 isotopologue measurements by designing an optical cell with differential absorption pathlengths for each isotopologue, allowing CO2 lines differing in intensity by several orders of magnitude to be measured precisely. In both cases, long-term drifts (e.g., temperature, laser power, frequency jitter etc.) were accounted for by simultaneous measurement of a reference gas. Other important variables to consider are sample temperature stability and spectral line function. Bergamaschi et al. [1994] reported an approximate sensitivity of the measured δ -value and temperature (T ) in per-mil units: ∆δ ∆E × 1000 ≈ ∆T kT 2 (2.10) where k is Boltzmann’s constant and ∆E is the difference in lower-state energies of the corresponding transitions. It is derived from the Taylor series expansion of a normal (Gaussian) distribution [Schupp, 1992]. Empirically, this translates to ± 5‰ K−1 for bulk stable isotope measurements of H2 O and CO2 [Kerstel and Gianfrani, 2008], so a temperature stability between the reference gas and the sample of 50 mK would yield temperature-induced errors of 0.1‰. Kerstel and Gianfrani [2008] also make the argument that measurement of peak intensities is sufficient so long as the lineshape functions are the same between the sample and standard transitions. ‘Clumped’ isotope measurements present a new set of concerns due to the more stringent technical demands, e.g., measuring a signal 4.5 × 10−5 with 0.005‰ precision for ∆47 based carbonate thermometry [Huntington et al., 2009]. At present, high-precision IRMS measurements of ∆47 involve multiple comparisons between the sample CO2 gas, bulk stable isotope working standards, and ‘clumped’ stable isotope standards (CO2 with a stochastic distribution of isotopologues). Any spectroscopic technique will require similar calibrations 55 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 because the instrument response, in general, will not be sufficiently linear over such a large range in concentration. For instance, the required linear dynamic range for rovibrational transitions of 12 C16 O2 and 16 O13 C18 O with identical v and J (absolute sensitivity concerns notwithstanding) is ≥109 . Photoacoustic methods are capable of this dynamic range, in principle, but previous attempts to make high-precision isotopic measurements have been limited by fluctuations in pump laser power [Samura et al., 2002]. On the other hand, if a convenient spectral window is found such that line strengths of the dominant and minor isotopologues are similar, the temperature sensitivity will be large (e.g., due to large differences in the lower-state energies). From a practical perspective, the line strength of the minor isotopologue will dictate the choice of method; for instance, the strongest 16 O13 C18 O transition in the mid-IR has a line intensity S ∼ 10−23 cm molecule−1 , which is out of range for all but the most sensitive spectroscopic techniques. Of the high-sensitivity optical techniques, cavity ringdown spectroscopy (CRDS; O’Keefe and Deacon [1988]) with frequency-axis stabilization and single-mode operation (FS-CRDS; [Hodges et al., 2004]) shows the most promise, in this author’s opinion. A key feature in FS-CRDS is its ability to average spectra on the timescales of hours; the utility of other ultrasensitive methods, such as the shot-noiselimited NICE-OHMS technique (noise-immune, cavity-enhanced optical heterodyne molecular spectroscopy) [Ye et al., 1998], have been ultimately limited by technical pitfalls and long-term drifts [Foltynowicz et al., 2008]. In contrast, FS-CRDS can be averaged continuously for nearly 10 hours to achieve a signal-to-noise ratio (SNR) of 18,000 (i.e., 0.6‰ precision) on a single line of intensity S = 1 × 10−24 cm molecule−1 at 0.5 Torr [Long et al., 2009]. Higher SNRs may be possible with the implementation of single-mode optical feedback [Motto-Ros et al., 2008], optoelectronic laser-locking [Drever et al., 1983], or in combination with rapid (kHz) sample-background ringdown comparison [Ye and Hall, 2000]; increasing sample concentration will also improve the SNR, but the dynamic range of the instrument will place an upper limit on the maximum line strength. The choice of lineshape theory used to obtain the integrated intensity might also be important [Lisak et al., 2006, 2009], as the integrated intensity is a more robust measurement of isotopic abundance than 56 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 peak height, which increases nonlinearly with gas pressure. At present, IRMS is the only practical method for measuring ‘clumped’ isotopologue abundances in in CO2 with precisions better than 0.1‰. Spectroscopic measurements for CO2 will be best in the mid-IR region, where the rovibrational transitions are strongest (S16 O13 C18 O ∼ 10−23 cm molecule−1 ); single-mode quantum-cascade lasers with ≥ 5 mW power are becoming widely available in that region. Another possibility for CO2 is the 2-µm region, where the strongest 16 O13 C18 O line strength is S16 O13 C18 O ∼ 3 × 10−26 cm molecule−1 (4826.05 cm−1 ); analysis time will be increased accordingly. The NICE-OHMS method is capable of reducing analysis times significantly, in principle, because it has demonstrated a shot-noise-limited sensitivity for strong laser sources (e.g., SNR = 7700 in 1s for S = 1 × 10−23 cm molecule−1 using a 5 mW Nd:YAG) [Ye and Lynn, 2003; Ye et al., 1998]. However, technical challenges such as long-term temperature and frequency stability must be addressed. While examining the possibility for measuring ‘clumped’ CO2 isotopologues spectroscopically is useful for illustrating the general principles involved, this approach will ultimately be the most useful for other species of atmospheric and geochemical interest. For instance, isotopic abundances in SO2 are canonically difficult to measure due to its polarity [Gao and Thiemens, 1991, 1993]; high-precision IRMS systems rely on a viscous-flow injection into the ionization region, and high-polarity gases such as SO2 often display a pronounced ‘memory’ effect that limits measurement precision and reproducibility [Ono et al., 2006]. SO2 lines in the mid-IR (∼2500 cm−1 ) are of comparable strength to those of CO2 in the 2-µm region (see above), so ‘clumped’ isotopologue measurements of SO2 may be possible, with long averaging times, in the near future. These measurements have the potential to establish a link between the ancient atmosphere and the geologic record. For instance, Lyons [2009] has proposed that the unique sulfur and oxygen isotope composition of Archaean Fig-tree barites [Bao et al., 2007] may reflect gas-phase SO2 –H2 O isotope exchange reactions; ‘clumped’ isotope analysis would place additional constraints on the origins of these and other barites, which contain information about the sulfur and oxygen cycles, atmospheric composition, and climate of the ancient past. 57 L. Y. Yeung 2.C Oxygen isotope exchange reactions of CO2 Chapter 2 Low-temperature cell for 13 C/12 C KIE experiments For the low-temperature 13 C/12 C KIE experiments, the quartz reaction chamber (filled with N2 O, CO2 , and He) was placed inside a cooling assembly within a conflat vacuum chamber. The vacuum chamber was first pumped down to ∼20 – 50 mTorr, and then liquid N2 coolant (∆Hvap = 1.33 kcal mol−1 ) was added through a feedthrough at the top of the chamber. The liquid N2 cooled a series of metal (“conduction” and “transfer”) blocks, which, in turn, cooled the quartz reaction cell along its entire length. Temperature was monitored using a standard type-K thermocouple; active temperature control was possible, though it was not necessary to achieve temperatures near 230 ± 1 K when the liquid N2 was poured into the feedthrough. The cooling assembly was designed to fit inside a spare ∼27 × 27 × 21 cm (l × w × h, interior dimensions) conflat chamber with a 9.5-cm ID (see Figures 2.11, 2.12, and 2.13). Experimental and spatial constraints dictated the design parameters, and the resulting assembly had little flexibility. Use of 193-nm laser radiation to photolyze N2 O meant that quartz (UV-grade fused silica) windows were the most affordable and robust window material; MgF2 windows can provide ∼10% greater transmission at 193 nm, but quartz was chosen because it was cheaper and could be bonded with a quartz tube to make a monolithic, leak-tight reaction chamber without need for adhesives. During an experiment, the reaction chamber was inserted directly into the oxygen-free, high conductivity (OFHC) copper tube (2.14). This tube was fastened to the “conduction block” (Figure 2.15), which was itself attached to the OFHC copper “heat-transfer block” by a countersunk screw on the rounded underside of the conduction block. A second heat-transfer block (Figure 2.17) was sandwiched between the heat-transfer block and the connection to the liquid N2 feedthrough (Figure 2.18); this block had a relatively small surface area and was machined out of brass (120 W m−1 K−1 vs. 401 W m−1 K−1 for copper at 300 K) to retard heat transfer from the liquid N2 to the reaction cell. The second heat-transfer block also had a hole drilled through the center so a heating resistor could be inserted, if necessary, to control the temperature in future experiments. All components were mated with a thin layer of Apiezon “N” grease; this material was 58 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.11: Schematic of conflat chamber used for low-temperature 13 C/12 C KIE experiments. Figure 2.12: Photograph of conflat chamber used for low-temperature 13 C/12 C KIE experiments. 59 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 chosen over other compounds because of its ability to perform at low temperatures (down to liquid He), low coefficient of thermal expansion (≤ 10−4 K−1 ) and minimal thermal creep. However, it has a very low thermal conductivity (0.1 – 0.2 W m−1 K−1 ), which slowed the cooling process. Typically, the assembly took 40 – 60 min to cool from 300 K to 229 K. While higher-efficiency thermal compounds would have accelerated cooling of the reaction chamber, Apiezon “N” was sufficient to achieve stable temperatures above 200 K. Small modifications were made to the cooling assembly for planned O(1 D) + CH4 and OH + CH4 KIE experiments (see Figure 2.19). Because the target temperatures for those experiments are 140 K ≤ T ≤ 200 K, the two “heat-transfer” blocks were combined into a single OFHC copper heat-transfer block with a larger contact area with the existing “conduction block” (see Figures 2.20 and 2.21). The primary cooling block was smoothed (the shallow channel removed) to mate well with the new conduction block. Last, metal-tometal mating surfaces were cleaned and the Apiezon “N” grease replaced with a thermal paste containing silver particles (thermal conductivity ∼ 9 W m−1 K−1 ). With this new assembly and the pressurized delivery of liquid N2 from a free-standing dewar into the feedthrough, the quartz reaction cell was cooled to temperatures of ∼140 K within 10 min. Temperature control electronics are currently being designed. 60 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Figure 2.13: Cold cell assembly. Figure 2.14: Machining diagram for the OFHC copper tube. 61 Chapter 2 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.15: Machining diagram for the OFHC copper conduction block. 62 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.16: Machining diagram for the OFHC copper heat transfer block. Figure 2.17: Machining diagram for the brass heat transfer block. 63 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.18: Machining diagram for the OFHC copper connection to the liquid N2 feedthrough. 64 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.19: Cold cell assembly for O(1 D), OH + CH4 KIE experiments. Figure 2.20: Machining diagram illustrating the modifications made to the conduction block for O(1 D), OH + CH4 KIE experiments. 65 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.21: Machining diagram for the OFHC copper heat transfer block designed for O(1 D), OH + CH4 KIE experiments. 66 L. Y. Yeung Oxygen isotope exchange reactions of CO2 2.D MATLAB code for hard-sphere collision model 2.D.1 montecarlo.m Chapter 2 % Program for calculating 18O(1D)−CO2 collision energy in experiments clear x y z j v1i v2i r; points=50000; % number of points per collision T=300; % temperature in K m1=18; % mass of O(1D) m2=4; % mass of buffer gas (He: 4, N2: 28) mCO2=44; ET2lab=18.2; %8.6 for O3 photolysis at 248 nm % Etrans (kcal/mol) in the Lab frame Equil=(3/2)*8.314472/4.184/1000*T; % Equipartition energy vOpeak=sqrt((ET2lab*1000*4.184*2)/(m1/1000)); % O(1D) atom velocity vMreduced=vOpeak/sqrt((Equil*1000*4.184*2)/(m2/1000)); % buffer gas velocity in units of O(1D) velocity %vMreducedCO2=vOpeak/sqrt((Equil*1000*4.18*2)/(mCO2/1000)); ncolltot=200; % Number of collisions zz=zeros(points,ncolltot); % distribution of final O(1D) velocities zzz=zeros(points,1); % distribution of initial O(1D) velocities CO2=zeros(points,ncolltot); % distribution of collision energies with CO2 dist=zeros(points,ncolltot); % distribution of buffer gas velocities PM=97; %1−380e−6 for 'stratospheric' % pressure of buffer gas in Torr PCO2=3; %380e−6 for 'stratospheric' % pressure of CO2 in Torr Pcoll=PCO2/(PCO2+PM); % ratio of CO2 to buffer gas (reaction probability per collision) for l=1:ncolltot nPcoll(l)= Pcoll*(1−Pcoll)ˆ(l−1); % multiplied by (1−(3.1e−11/1e−10))ˆ(l−1) for 'stratospheric' % fraction of O(1D) that reacts at each collision end digits(10); nPcoll=vpa(nPcoll); for j=1:points ncoll=1; v1i=randn*exp(−1.5)+vMreduced; % pick a random v for O(1D) from a gaussian distribution about vMreduced zzz(j)=v1i; % record the velocity in a matrix 67 L. Y. Yeung Oxygen isotope exchange reactions of CO2 theta1i=rand*3.14159265359; % pick a random azimuthal angle between 0 and pi for O(1D) phi1i=rand*2*3.14159265359; % pick a random azimuthal angle between 0 and 2pi for O(1D) v2i=randn;%metropolis([v2i,5]); theta2i=rand*3.14159265359; % pick a random azimuthal angle between 0 and pi for M phi2i=rand*2*3.14159265359; % pick a random azimuthal angle between 0 and 2pi for M while (phi1i < phi2i) phi2i=rand*2*3.14159265359; % prevents imaginary results in scatter function end impact=randˆ2; % pick a random (b/bmax) with probability proportional to itself omega=rand*3.14159265359; % pick a random azimuthal angle for b between 0 and pi while (ncoll ≤ ncolltot) % calculate O(1D) trajectory for n collisions vrel=sqrt((v1i*sqrt(mCO2/m2))ˆ2+v2iˆ2−2*v1i*v2i*(sin(theta1i)* sin(theta2i)*cos(phi1i−phi2i)+cos(theta1i)*cos(theta2i))); % calculating initial relative velocity CO2(j,ncoll)=((1/2)*((mCO2*m1/(mCO2+m1))/1000)*(vrel* sqrt((Equil*1000*4.184*2)/(mCO2/1000)))ˆ2)/(4.184*1000); % calculate initial collision energy w/CO2 v1f=scatter(m1, m2, v1i, theta1i, phi1i, v2i, theta2i, phi2i, impact, omega); % calculate final velocity after one more collision zz(j,ncoll)=real(v1f); % record the final velocity dist(j,ncoll)=v2i; % record in initial velocity of M v1i=real(v1f); % reset initial velocity as the final velocity after a collision theta1i=rand*3.14159265359; % pick a new azimuthal angle for O(1D) phi1i=rand*2*3.14159265359; % pick a new polar angle for O(1D) v2i=randn; % pick a new velocity for M theta2i=rand*3.14159265359; % pick a new azimuthal angle for M phi2i=rand*2*3.14159265359; % pick a new polar angle for M while (phi1i < phi2i) % prevents imaginary results in scatter program phi2i=rand*2*3.14159265359; end impact=randˆ2; % pick a new impact parameter (b/bmax) omega=rand*3.14159265359; % pick a new scattering angle ncoll=ncoll+1; % rinse, repeat end end bins=250; % number of bins 68 Chapter 2 L. Y. Yeung Oxygen isotope exchange reactions of CO2 upperlimit=25; % range, 0 − upperlimit binsvector=zeros(1,upperlimit); % generating empty histogram bin vector to improve performance for c=1:bins binsvector(1,c)=(upperlimit/bins)*c; % generating histogram bins end [Ppercollision,bin]=histc(CO2,binsvector); % generating binned histogram matrix of CO2, Ppercollision for k=1:ncolltot % each column is reactive probability distribution at that collision Ppercollision(:,k)=Ppercollision(:,k)*double(nPcoll(k)); % each column is weighted by the fraction of remaining O(1D) atoms end Ecollavg=sum(CO2)/points; % average collision energy at each collision number dlmwrite('v1i.csv',zzz); % write matrix of initial O(1D) velocities to file, v1i.csv dlmwrite('v1f.csv',zz); % write matrix of final O(1D) velocities to file, v1f.csv dlmwrite('Ecollpercollision.csv',CO2); % write matrix of per−collision collision energies to file dlmwrite('Ppercollision.csv',Ppercollision); % write binned histogram matrix of CO2 to file, Ppercollision.csv 2.D.2 scatter.m % Function solving the two−particle scattering problem function v1f=scatter(m1, m2, v1i, theta1i, phi1i, v2i, theta2i, phi2i, impact, omega) vrel=sqrt(v1iˆ2+v2iˆ2−2*v1i*v2i*(sin(theta1i)*sin(theta2i)* cos(phi1i−phi2i)+cos(theta1i)*cos(theta2i))); % relative veocity calculation v1c=(m2*vrel)/(m1+m2); % v1 (O(1D)) in the COM frame v2c=(m1*vrel)/(m1+m2); % v2 (M) in the COM frame vcm=sqrt(m1ˆ2*v1iˆ2+m2ˆ2*v2iˆ2+2*m1*m2*v1i*v2i*(sin(theta1i)* sin(theta2i)*cos(phi1i−phi2i)+cos(theta1i)*cos(theta2i)))/(m1+m2); % velocity of the COM thetacm=acos((m1*v1i*cos(theta1i)+m2*v2i*cos(theta2i))/((m1+m2)*vcm)); % azimuthal angle in the COM frame phicm=acos((m1*v1i*sin(theta1i)*cos(phi1i)+m2*v2i*sin(theta2i)* cos(phi2i))/((m1+m2)*vcm*sin(thetacm))); % polar angle in the COM frame alpha=acos((v1iˆ2−(vcmˆ2+v1cˆ2))/(2*vcm*v1c)); % azimuthal scattering angle in the COM frame deflect=2*acos(impact); % polar scattering angle in the COM frame l=v1c*(cos(deflect)*cos(alpha)−sin(deflect)*sin(alpha)*cos(omega)); v1f=sqrt((vcm+l)ˆ2+v1cˆ2−lˆ2); 69 Chapter 2 L. Y. Yeung Oxygen isotope exchange reactions of CO2 This page intentionally left blank. 70 Chapter 2 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Chapter 3 A hyperthermal O-atom exchange reaction, O2 + CO2 Adapted from Yeung, L. Y., M. Okumura, J. T. Paci, G. C. Schatz, J. Zhang, and T. K. Minton (2009), Hyperthermal O-Atom Exchange Reaction O2 + CO2 through a CO4 Intermediate, J. Am. Chem. Soc., 131(39): 13,940–13,942. ©2009 American Chemical Society Publications. 71 L. Y. Yeung 3.1 Oxygen isotope exchange reactions of CO2 Chapter 3 Abstract O2 and CO2 do not react under ordinary conditions, owing to the thermodynamic stability of CO2 and the large activation energy required for multiple double-bond cleavage. We present evidence for a gas-phase O-atom exchange reaction between neutral O2 and CO2 at elevated collision energies (≈ 160 kcal mol−1 ) from crossedmolecular-beams experiments. Products were scattered mainly in the forward direction, i.e., in the initial direction of the hyperthermal oxygen beam in the centerof-mass (c.m.) frame, with 16% of the available energy in translation, on average. CCSD(T)/aug-cc-pVTZ calculations demonstrate that isotope exchange can occur on the ground triplet potential energy surface through a short-lived CO4 intermediate that isomerizes via a symmetric CO4 transition state containing a bridging oxygen atom. We propose a plausible adiabatic mechanism for this reaction supported by additional spin-density calculations. 72 L. Y. Yeung 3.2 Oxygen isotope exchange reactions of CO2 Chapter 3 Introduction O2 and CO2 do not react under ordinary conditions. This can be attributed to the large activation energy for multiple double-bond cleavage, as Dixon illustrated in his early experiments in which dry CO–O2 –CO2 mixtures “did not explode” when subjected to a spark discharge [Dixon, 1886]. Otomo et al. [2000] later reported a reaction of CO2 and electronically excited O2 ∗ when they observed O3 products after irradiating super- and subcritical O2 /CO2 mixtures with UV light. While investigating the isotope exchange reaction 16 O(3 P) +12 C18 O2 →18 O +16 O12 C18 O (3.1) at hyperthermal collision energies in a crossed-molecular-beams experiment, we found evidence for the gas-phase oxygen isotope exchange reaction 16 O2 +12 C18 O2 →18 O16 O +16 O12 C18 O (3.2) of ground-state reactants at high collision energies (∼160 kcal mol−1 ). Our observations on the dynamics of this reaction, taken together with ab initio calculations of stationary points on the lowest triplet potential energy surface (PES), suggest a plausible adiabatic mechanism for the reaction of O2 with CO2 through a CO4 transition complex. 3.3 Experimental studies 3.3.1 Methods Crossed-molecular-beam experiments were performed with a hyperthermal oxygen source containing ∼87% O(3 P) and ∼13% O2 (3 Σ− g ) [Brunsvold et al., 2007, 2008; Garton et al., 2006, 2009]. A diagram of the experimental setup, configured for 16 O(3 P) + 12 C18 O 2 collisions, is shown in Figure 3.1. A pulsed beam of 16 O(3 P) and 16 O2 (3 Σ+ g ; at an unknown vibrational temperature) was generated by laser-induced detonation of 16 O2 using a high-energy CO2 TEA laser (6 – 7 J pulse−1 ) operating at a pulse repetition rate of 2 Hz. Though initially broad in velocity distribution (6 – 9 km s−1 ), a portion of the overall 73 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 beam was velocity-selected for the scattering experiments using a synchronized chopper wheel operating at 300 Hz. This velocity-selected beam was crossed, at a nominal angle of 90◦ , with a pulsed supersonic expansion of 98% 12 C18 O2 gas (2% 16 O12 C18 O; Spectra Gas). The molecular beams and scattered products were detected with a rotatable quadrupole mass spectrometer with electron-bombardment ionization [Brink, 1966] at 160 eV and a Daly-type ion counter [Daly, 1960]. 12 C18 O2 and 16 O12 C18 O products were detected at m/z 16 12 18 + = 48 (12 C18 O+ 2 ) and 46 ( O C O ), respectively, with a rotatable mass spectrometer that collected number density distributions as a function of arrival time, N(t), at a given laboratory angle, Θ, using a multi-channel plate (MCP). Here, Θ is defined as the angle at which the 16 O12 C18 O scatters with respect to the direction of the reagent oxygen beam (i.e., Θ = 0◦ ). Time-of-flight (TOF) distributions for 16 O(3 P), 16 O2 , 12 C18 O2 , and 16 O12 C18 O were collected over a range of laboratory angles (6◦ – 54◦ ); at each angle, the TOF distribution for the 33.7-cm distance between the beam interaction region to the ionizer was integrated to give a laboratory angular distribution, N(Θ). A forward-convolution method was used to derive the center-of-mass (c.m.) translational energy P(ET ) and angular T(θ c.m. ) distributions from the laboratory N(t) and N(Θ) distributions [Lee, 1988], where θ c.m. is the angle at which 16 O12 C18 O scatters with respect to the reagent oxygen direction in the c.m. frame. The canonical Newton diagrams used in this analysis are shown in Figure 3.2. Figure 3.1: Crossed-molecular-beam apparatus with hyperthermal oxygen source. 74 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.2: Canonical Newton diagram for hyperthermal 16 O2 + 12 C18 O2 collisions. The Newton circles represent the maximum recoil velocities of the products. The hyperthermal oxygen beam was generated by laser detonation of a pulsed expansion of O2 gas with 500 psig stagnation pressure using a source based on the design of Caledonia et al. [1987]. 174 µs after the pulsed valve is triggered, the CO2 laser is fired; the laser pulse passed through an antireflection-coated ZnSe window in to the source chamber, whereupon it was reflected back towards the gold-plated, water-cooled copper nozzle with a 1 m radius concave gold mirror. The focused laser pulse initiates a breakdown of the O2 gas and heats the resulting plasma to > 20,000 K, which accelerates both the atomic and molecular oxygen fractions of the pulsed beam to 6 – 9 km s−1 . Use of a conical nozzle allowed for efficient ion-electron recombination and inefficient atom-atom and atom-molecule recombination as the plasma expanded and cooled. The resulting gas pulse was collimated by a 1 cm diameter aperture located 80 cm downstream of the inlet nozzle into a differentially pumped region (10−5 – 10−6 Torr), after which it passed through a 1.2-mm-diameter skimmer 16 cm further downstream. The beam interaction region was an additional 3 cm downstream in the main chamber (2 × 10−7 Torr), a total distance of 99 cm from the inlet nozzle. For velocity selection within the hyperthermal oxygen beam, a chopper wheel running at 300 Hz (synchronized with the 2-Hz laser pulses) was placed inside the main scattering 75 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 chamber, just downstream of the skimmer. Three equally-spaced slots (1.5 mm wide) of the chopper wheel pass over an LED/photodiode assembly a quarter-turn before each slot enters the beam axis, generating a 900 Hz (3 × 300 Hz) train of pulses. These chopper wheel pulses are sent to a digital delay generator and used as references for triggering the O2 gas pulses. The time delay between the chopper wheel pulse and the O2 pulse determined the portion of the overall hyperthermal oxygen beam allowed to pass through into the interaction region. We characterized the velocity distribution of the hyperthermal oxygen beam under two conditions: on axis (Θ = 0◦ ) with a small aperture (∼125 µm diameter) to obtain the peak of the distribution, and off axis (Θ = 3◦ ) with a large aperture (4 mm × 4 mm) to obtain the width of the distribution. For the on-axis configuration, a 2 mA emission current at the ionizer and a –18 kV potential at the secondary emitting electrode of the Daly ion counter was used. For the off-axis configuration, a 10 mA emission current at the ionizer and a –30 kV potential at the secondary emitting electrode was used. Laboratory TOF distributions under both conditions were measured, for both 16 O and 16 O2 , to determine the laboratory-frame velocities and translational energy distributions for the hyperthermal oxygen beam. In these experiments, the average velocity of the hyperthermal oxygen beam was thus determined to be 8262 ± 450 m s−1 (i.e., 900 m s−1 full width at half maximum; FWHM), which corresponds to average translational energies hET i = 130.5 ± 14 kcal mol−1 and 261.0 ± 28 kcal mol−1 FWHM for 16 O(3 P) and 16 O2 , respectively (see Figure 3.3). The relative amounts of atomic (∼87%) and molecular (∼13%) oxygen were determined by integrating the TOF distributions at m/z = 16 (16 O+ ) and 32 (16 O2 + ) at Θ = 0◦ and correcting for O2 fragmentation (11% of the m/z = 32 signal) in the electron-bombardment ionization region. A pulsed supersonic expansion of 12 C18 O2 was generated using a piezoelectric pulsed general valve with a 1300-Torr stagnation pressure. The expansion passed through a 2 mm diameter skimmer (9.2 cm from the nozzle) into a differential pumping region, and then through a 2.5 mm diameter (2.8 cm downstream of the skimmer) aperture into the main scattering chamber. The distance from this aperture to the interaction region was 1.5 cm. 76 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.3: Velocity distribution of hyperthermal oxygen beam. The velocity distribution of the 12 C18 O2 beam was not measured directly, and instead was determined iteratively by first estimating the terminal velocity of the supersonic expansion [Lee, 1988] and then fitting the 12 C18 O2 velocity to the value that yielded the best Newton circle for non-reactively scattered O-atoms while keeping the measured O-atom velocity distribution fixed at its measured values. This contributes some uncertainty to the measured TOF distributions because the 12 C18 O2 beam velocity is likely only accurate to ±10%. However, because the magnitude of the hyperthermal oxygen beam velocity at the interaction region was ten times that of the 12 C18 O2 beam, and its FWHM was also 4 – 5 times that of the 12 C18 O2 beam, uncertainties in the “time-zero” of the hyperthermal oxygen source dominated the overall uncertainty in the measured translational energy distributions. Laboratory TOF product distributions were measured every 2◦ between Θ = 6◦ – 54◦ . Scattered product TOF distributions were collected for 200 beam pulses for for m/z = 16 (16 O+ ) and 32 (16 O2 + ), for 1000 beam pulses for m/z = 46 (16 O12 C18 O+ ), and for 500 beam pulses for m/z = 48 (12 C18 O2 + ). Dwell time for each channel at the MCP was 1 µs. At a representative laboratory angle of 10◦ , integrated count rates were 1.1 × 107 s−1 for m/z = 16, 1.3 × 107 s−1 for m/z = 32, 1.8 × 105 s−1 for m/z = 46 , and 4.2 × 106 s−1 for m/z 77 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 = 48. Raw flight times were converted to flight times over the 33.7 cm distance between the interaction region and the electron-bombardment ionizer by subtracting the O2 triggerpulse-to-laser-fire delay time (174 µs), an electronic-latency delay time (3 µs), the oxygen flight time from the nozzle to the interaction region (120 µs, corresponding to the average velocity of the hyperthermal oxygen beam), and finally the ion flight time between the 1 ionizer and the Daly ion counter. The ion flight time is given by α(m/z) 2 , where α = 2.44 in these experiments, determined by comparing the relative arrival times of hyperthermal 16 O and 16 O at the detector [Garton et al., 2006]. Some uncertainty arises in the product 2 times-of-flight because the exact time- and point-of-origin of the hyperthermal oxygen beam are not well determined; we estimate this uncertainty to be ∼2 µs because the laser pulse width in the hyperthermal oxygen source could be as long as 1 µs (a 100 ns-wide peak with a slow tail). Two signal corrections were made before data analysis. First, we corrected for beam divergence at Θ = 6◦ – 16◦ . The divergent intensity with the 12 C18 O2 beam turned off was measured by obtaining TOF distributions at m/z = 16 and 32 from Θ = 6◦ – 16◦ . These TOF distributions were then scaled and subtracted from the corresponding experimental TOF distributions at m/z = 16 and 32 that had the 12 C18 O2 beam turned on. Uncertainties in the inelastic and reactive scattering signals due to collisions of the divergent hyperthermal oxygen could not quantified, however; they were instead considered in the analysis of the laboratory data, where collisions at crossing angles of 88◦ , 89◦ , 90◦ , 91◦ , and 92◦ were included during forward-convolution fitting. Adding more crossing angles did not affect the forward-convolution fits significantly. Second, we verified that the 12 C18 O2 beam contained 2% 16 O12 C18 O using the instrument’s mass spectrometer. Thus, 2% of the inelastic scattering signal (m/z = 48) at each laboratory angle (Θ = 6◦ – 54◦ ) was subtracted from raw m/z = 46 (16 O12 C18 O+ ) TOF distributions to obtain reactive-scattering-only distributions. A forward-convolution method was employed to perform the laboratory-to-c.m. frame coordinate transformation [Lee, 1988] of the data using the MSU XBEAM program (Version 6). Trial P(ET ) and T(θ c.m. ) distributions were used to simulate the laboratory-frame TOF distributions using the following relationship derived from the Jacobian transformation: 78 L. Y. Yeung Oxygen isotope exchange reactions of CO2 N(t, Θ) α l3 P(ET )T (θc.m. ) ut 3 Chapter 3 (3.3) where l and t are the distance and flight time, respectively, from the interaction region to the ionizer, and u is the product velocity in the c.m. frame. During the fitting process, 12 C18 O2 was assumed to have a single-valued velocity, 800 m s−1 , because the large magnitude and width of the hyperthermal oxygen beam velocity distribution is principally responsible (i.e., it contributed ≥ 98% of the uncertainty in the c.m. collision energy; see above) for the observed width of the laboratory TOF distributions and the c.m. translational energy distributions. The width of the hyperthermal beam velocity distribution was fit by a Gaussian function centered at 8262 m s−1 and a FWHM of 900 m s−1 , which was used during data analysis. Note that the data we report for flight times over a 33.7 cm distance were calculated by subtracting the average oxygen flight time from the nozzle to the interaction region; the reported product arrival times, then, reflect a convolution of the oxygen beam’s wide velocity distribution and the ‘true’ product translational energy distribution, so the best-fit P(ET ) distributions may not be unique. As such, we estimate the uncertainties in the reported P(ET ) distribution to be 10 – 20%. To allow for easy manipulation of the P(ET ) and T(θ c.m. ) distributions, parameterized functions were often used. The fitting process often relied on the RRK form of the P(ET ) distribution: P(ET ) = (ET − B) p (Eavail − ET )q (3.4) where Eavail is the available translational energy in the c.m. frame (i.e., the collision energy, Ecoll , minus the endothermicity, ∆E). The parameters B, p, and q were adjusted to vary the peak and width of the c.m. translational energy distribution when obtaining a best fit to the laboratory data. The T(θ c.m. ) distribution was described by a Legendre polynomial form: Tk (θc.m. ) = ak ck (cos2 θc.m. − 1)k 2k k! c(cos θc.m. ) (3.5) where ak is an adjustable parameter for each of the eleven polynomial terms used, which 79 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.4: Laboratory TOF distribution of m/z = 46 (16 O12 C18 O+ ; green circles) at Θ = 6◦ , with the inelastic scattering signal removed. The data are shown with the O(3 P) + CO2 (dot-dashed black line), O2 + CO2 (dashed blue line), and summed (solid red line) forward-convolution fits. Flight times less than 72 µs violate energy conservation for 16 O(3 P) + 12 C18 O2 . The inset compares the raw TOF distribution with the IS TOF distribution, which is subtracted. were denoted by the subscripted k = 0, 1, 2,...10. The functional forms for the P(ET ) and T(θ c.m. ) distributions (3.4 and 3.5, respectively), were iterated in XBEAM until they provided satisfactory fits to the laboratory data, though, in some cases, point forms of the P(ET ) and T(θ c.m. ) distributions were used. Finally, the “best-fit” P(ET ) and T(θ c.m. ) distributions were used to create a c.m. velocity-flux contour map or a differential scattering cross-section plot for the products. 3.3.2 Results The inset in Figure 3.4 shows a raw m/z = 46 TOF distribution of 16 O12 C18 O products recorded at Θ = 6◦ . A small fraction of the signal can be attributed to inelastic scattering (IS) of 16 O12 C18 O impurities in the CO2 beam by 16 O and 16 O2 , and it can be subtracted. The remaining signal, shown in Figure 3.4, represents 16 O12 C18 O products from O-atom exchange reactions of 12 C18 O2 (see Chapter 4). We initially expected the reactive m/z = 46 signal to arise from reactions of 12 C18 O2 with the 16 O atoms (reaction 3.1) with a broad distribution of c.m. collision energies (Ecoll ) 80 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 peaked at 98.8 kcal mol−1 and a full width at half maximum (FWHM) of 18 kcal mol−1 . However, at small laboratory angles, we observed products with velocities that would violate energy conservation for this O(3 P) + CO2 reaction (e.g., t < 72 µs in Figure 3.4). 12 C18 O −1 (see Lee [1988]). 2 was estimated to have a laboratory velocity of 800 ± 80 m s Given the broad velocity distribution in the O(3 P)/O2 beam (8262 m s−1 with 900 m s−1 FWHM), the velocity spread in the 12 C18 O2 beam was insignificant by comparison, so the hyperthermal oxygen beam largely determined the broad distribution of collision energies sampled in these experiments. To calculate the maximum available translational energy in the laboratory frame for 16 O(3 P) + 12 C18 O2 and 16 O2 + 12 C18 O2 isotope exchange reactions, an initial 16 O(3 P)/16 O2 beam velocity of 8862 m s−1 was used because < 5% of the O(3 P)/O2 beam had a greater velocity. A non-negligible population of 16 O12 C18 O was observed at translational energies above the maximum allowed for 16 O(3 P) + 12 C18 O2 collisions at small laboratory angles. Despite the uncertainties in the Ecoll distribution and product flight times (see Section 3.3.1), we observed 16 O12 C18 O products arrive 10 – 20 µs faster than the minimum times allowed by the distribution of available energies, Eavail (≈Ecoll ; the zero-point energy change is +0.1 kcal mol−1 ), for reaction 3.1. Forward-convolution best-fits to the TOF distributions that only treat the 16 O(3 P) + 12 C18 O2 isotope exchange reaction cannot explain the fastest laboratory data at small laboratory angles (e.g., Θ = 6◦ and 8◦ ; see Figure 3.5). Increasing hET i in the product P(ET ) shifts the fastest part of the fit towards shorter flight times at all laboratory angles. While this improves the TOF fits at small laboratory angles, it decreases the quality of the TOF fits at larger laboratory angles (see Θ = 36◦ in Figure 3.6). Introducing the 16 O2 + 12 C18 O2 isotope exchange reaction yields good fits at all laboratory angles. A sizeable fraction of the products assigned to the 16 O2 + 12 C18 O2 reaction are slow enough that they do not violate conservation of energy; however, assigning them to the 16 O(3 P) + 12 C18 O 2 reaction leads to poor fits. Collisions between CO2 and ions or electronically excited O atoms could also yield 16 O12 C18 O products with elevated velocities, previous experience with this hyperthermal source indicates that they are not present in the beam [Troya et al., 2004]. 81 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.5: TOF distributions (green dots) for 16 O12 C18 O products at laboratory angles Θ = 6◦ and 8◦ with the inelastic scattering signal removed. Also shown are forwardconvolution best fits (solid red line) that treat only one isotope exchange reaction, 16 O(3 P) + 12 C18 O2 → O + 12 C18 O2 . The forward-convolution fits cannot account for the fastest 16 O12 C18 O product signals at small laboratory angles. We therefore hypothesize that the fast 16 O12 C18 O products come from reaction of 12 C18 O2 with 16 O2 in the hyperthermal beam. Because the velocity-selected 16 O2 molecules have the same laboratory-frame velocity distribution as the 16 O atoms, the 16 O2 molecules collide with the 12 C18 O2 molecules at substantially higher c.m. energies (see Newton diagram in Figure 3.2). The resulting collision energy distribution peaked at Ecoll = 158 kcal mol−1 with FWHM = 28 kcal mol−1 . Thus, 16 O12 C18 O products from reaction 3.2 have sufficient Eavail to account for the fastest products detected. The m/z = 46 signal would then contain products of both reactions 3.1 and 3.2, the fastest products arising exclusively from reaction 3.2. P(ET ) and T(θ c.m. ) distributions for reactions 3.1 and 3.2 were simultaneously obtained from forward-convolution fits of the m/z = 46 TOF distributions. The results for the 16 O2 + 12 C18 O2 reaction are presented in Figure 3.7; a c.m. velocity-flux contour diagram of 16 O12 C18 O products is shown in Figure 3.8, in which the observed product flux is peaked in the forward direction. The presence of signal at flight times violating energy conservation for 16 O(3 P)–12 C18 O2 collisions was used to guide the fitting process because the TOF distributions do not resolve the products unambiguously. As such, we cannot rule out an additional dynamical channel in reaction 3.1 contributing to some of the signal we attribute to reaction 3.2 because energy conservation in reaction 3.1 is only violated at small lab angles. 82 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.6: TOF distributions for 16 O12 C18 O (m/z = 46) at various laboratory angles Θ with the inelastic scattering signal removed. The raw data are shown as circles. Forwardconvolution fits of the 16 O2 + 12 C18 O2 (blue dashed curve) and 16 O(3 P) + 12 C18 O2 (black dot-dashed dashed curve) channels, along with their sum (red solid curve), are also shown. 83 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.7: Center-of-mass-frame (A) angular and (B) translational energy distributions from the 16 O2 + 12 C18 O2 oxygen isotope exchange reaction obtained from TOF fits of m/z = 46. The peak of the distribution of available energies is Eavail = 158 kcal mol−1 . Only the experimentally accessible range of c.m. angles (θ c.m. < 100◦ ) is shown. Figure 3.8: Velocity-flux contour diagram for 16 O12 C18 O products of 16 O2 + 12 C18 O2 collisions in the center-of-mass frame. The white arrows are the initial 16 O2 and 12 C18 O2 velocity vectors, and dashed white line is the maximum recoil velocity for 16 O12 C18 O (vmax ). 16 O12 C18 O products are scattered opposite the initial direction of the 12 C18 O velocity vector. 2 84 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 The 16 O12 C18 O products scattered mainly in the forward direction (θ c.m. = 0◦ ), though there was significant sideways scattering. Experimental sensitivity in the backward direction was insufficient to detect backward-scattered 16 O12 C18 O products, so forward-backward symmetric scattering (i.e., evidence for a long-lived intermediate complex) could not be ruled out. At these collision energies, however, an intermediate is unlikely to survive for a rotational period. The average total translational energy distribution for the two products was 25 kcal mol−1 , or 16% of the available energy; the P(ET ) distribution was peaked at ET = 10 kcal mol−1 . We estimate the yield for reaction 3.2 to be ≤ 2% of all O2 –CO2 collisions. This estimate is an upper limit because the complete Newton circle for inelastically scattered 16 O 2 + 12 C18 O 2 products was not observed in these experiments. Vibrational excitation of the O2 may also be important in promoting reaction, but the vibrational temperature of O2 present in the expanded plasma is unknown. Our experimental results are consistent with a 16 O12 C18 O product that rebounds from the 12 C18 O2 reactant’s initial direction after it collides with O2 ; this mechanism is characteristic of reactions with substantial activation energies that require high collision energies. The highly peaked angular distribution is consistent with a direct mechanism or a very short-lived intermediate, but more surprising is the substantial internal energy of the products, which is much greater than that found for similar oxygen isotope exchange reactions between O(3 P) + CO, O(1 D) + CO2 , and O + O2 [Brunsvold et al., 2008; Perri et al., 2004; Van Wyngarden et al., 2007]. This large translational-to-internal energy conversion suggests that the reaction proceeds through an intermediate species that facilitates efficient translational-to-internal energy transfer or through a non-adiabatic transition to another electronic surface. On average, 134 kcal mol−1 of internal energy is available to both products. This excess energy could be distributed among the five vibrational and four rotational degrees of freedom in O2 and CO2 . Alternatively, this energy could be in the form of electronically 3 + 3 00 excited products, including the a1 ∆g , b1 Σ+ g , and A Σu states of O2 , and the a A state of CO2 , which lies 119 kcal mol−1 above that for CO2 (1 Σ+ g ) [Braunstein and Duff , 2000]. The mass-spectrometric detection, however, did not allow us to determine the electronic states 85 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.9: Energetically allowed neutral product channels from O2 + CO2 collisions. Energies are taken from the NIST Webbook [http://webbook.nist.gov], [Mebel et al., 2004], and [Braunstein and Duff , 2000]. of the products. Other reaction channels are possible (see Figure 3.9). We cannot rule out a CO2 + O + O product channel because we did not collect sufficient data on the counter-fragment 18 O16 O. However, the energetically allowed CO 3 3 2 + O( P) + O( P) channel (∆H = 118 kcal mol−1 ) is spin-forbidden, and spin conservation would instead favor O(1 D) + O(3 P) products, whose energetic threshold is 163 kcal mol−1 and above the average Eavail in the experiment. There is also sufficient energy to form O3 + CO or O + CO3 [Mebel et al., 2004], and to dissociate CO2 to form O2 + O + CO, but because we were not anticipating these reactions, we did not search for the relevant detectable products. 86 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.10: Calculated energies and structures on the lowest triplet PES of O2 + CO2 . TS3 connects isoenergetic isomers of the CO4 shelf. 3.4 Theoretical studies To investigate whether an adiabatic mechanism exists for the O2 –CO2 isotope exchange reaction, we performed ab initio calculations to find stationary points on the lowest triplet PES for O2 + CO2 reaction at the CCSD(T)/aug-cc-pVTZ level of theory using the MOLPRO electronic structure code [Werner et al., 2006]. We identified two transition states (TS1 and TS2) connecting O2 + CO2 reactants with a triplet shelf state [CO4 (3 A00 ); see Figure 3.10 and Table 3.1]. All three structures are planar. One atom of the oxygen molecule approaches the carbon atom of CO2 and surmounts an activation barrier of 77.9 kcal mol−1 over TS1 to form a weak C–O bond and a CO4 (3 A00 ) shelf (76.4 kcal mol−1 , just 1.5 kcal mol−1 below TS1) similar to a weakly bound CO4 complex found at the B3LYP level of theory [Cacace et al., 2003; Elliott and Boldyrev, 2005]. At 121.8 kcal mol−1 , we identified an effective transition state for CO4 (3 A00 ) isomerization, TS3, containing a four-membered ring between the carbon atom and three oxygen atoms. A grid-based search revealed that TS3 is bound by 0.02 kcal mol−1 when zero-point energy is not considered, and that TS3 87 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Table 3.1: Energies of stationary points associated with the exchange reaction O2 + CO2 → O2 + CO2 on the lowest triplet potential energy surface∗ † CHF ∆E [CCSD(T)/aug-cc-pVTZ] ‡ ∆EZPE [CCSD(T)/aug-cc-pVTZ] ∆E (CASPT2/cc-pVTZ) CO4 TS1 TS2 TS3 0.973 76.0 76.4 91.2 0.977 77.9 77.9 95.6 0.969 80.0 78.3 97.1 0.945 120.9 121.8 137.4 ∗ ∆E in kcal mol−1 . † Coefficient of the Hartree-Fock configuration in the (8,10)-CASSCF expansion of the wave- functions. ‡ ZPE-corrected. This calculation was not performed at the CASPT2 level of theory. is connected to CO4 ; a displacement in Od < 0.01 Å towards CO4 produced CO4 upon geometry optimization. Thus, it acts as an ‘effective’ transition state for CO4 isomerization; it resembles the bound CO4 (1 A1 ) structure lying 52.5 kcal mol−1 below it, although with a longer Oc –Od bond length; both structures have C2v symmetry [Cacace et al., 2003; Elliott and Boldyrev, 2005; Jamieson et al., 2007]. We observed some evidence for multi-reference character in CO4 . An additional bound state was found 0.8 kcal mol−1 above the energy of CO4 at the MP2/cc-pVTZ level of theory, although it does not exist at the CCSD(T)/aug-cc-pVTZ level; the species is believed to be a resonance structure of CO4 (3 A00 ). A spin contamination of hS2 − Sz2 − Sz i = 0.011 in the region of the PES near TS3 also suggests some multi-reference character. Thus, CASPT2/cc-pVTZ calculations, which represent resonance qualitatively correctly and do not suffer from spin contamination, were performed to validate the CCSD(T) structures and energies. CO4 (3 A00 ) was confirmed as a resonance hybrid of two bound-state structures, although the contribution from the single-reference structure to the resonance hybrid dominates the final geometry. The results of those calculations are summarized in Table 3.1 and Figure 3.11. The uncertainty in the CCSD(T)/aug-cc-pVTZ energies is unknown, although a similar study in which the stationary points of the closely related O(3 P) + CO2 system were characterized was recently completed (see Chapter 4). In addition to CCSD(T)/aug-cc-pVTZ simulations, W4 calculations (close to the full configuration-interaction and infinite-basis-set 88 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.11: Calculated stationary point geometries on the lowest triplet PES of CO4 . CCSD(T)/aug-cc-pVTZ values (upper) and CASPT2/cc-pVTZ (lower) values are shown. limits; see [Karton et al., 2006]) were also performed, as they were found to be affordable, albeit marginally. The differences between the CCSD(T) and W4 results for the transition and bound states indicated a mean-unsigned error of 2.2 kcal mol−1 . We expect the errors in the analogous O2 + CO2 energies to be approximately the same. 3.5 Proposed mechanism A possible pathway for oxygen isotope exchange occurs through the forward and reverse directions of the following three steps: O2 + CO2 → [CO4 ]‡ (TS1/TS2) → CO4 (3 A00 ) → [CO4 ]‡ (TS3); see Figure 3.12. Spin-density maps (Figure 3.13) depicting the singlyoccupied molecular orbitals (SOMOs) for CO4 and TS3 are consistent with this mechanism. CO4 (3 A00 ) is a diradical with unpaired electron density concentrated in p-type orbitals of the Figure 3.12: Calculated energies and structures on the lowest triplet PES of O2 + CO2 . TS3 connects isoenergetic isomers of the CO4 shelf. 89 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.13: Singly-occupied molecular orbitals (SOMOs) in the CO4 (3 A00 ) and TS3 structures. Surfaces containing 70% of the electron density are shown. Note that the highest SOMO of CO4 (3 A00 ) and the lowest SOMO of TS3 have electron density primarily on Od , suggesting the SOMO is a spectator during isomerization. single-bonded oxygens, Ob and Od . This spin density is consistent with the radical character expected for an association of the O2 diradical with the carbon atom of CO2 , because the unpaired electrons in O2 are in orthogonal π ∗g orbitals: As one C–O bond is formed between the in-plane π ∗g orbital of O2 and the in-plane π bu orbital of CO2 (the higher-energy ∗ π nb g orbital does not interact due to symmetry; see Figure 3.14), the out-of-plane π g orbital on O2 is a relative spectator to the O2 radical addition. This interaction, along with the bending of the CO2 , produces the SOMOs for CO4 (3 A00 ) shown in Figure 3.13. In TS3, the lowest SOMO contains localized electron density on Od in an out-of-plane p-type orbital, suggesting that the unpaired electron on Od continues to be a spectator during CO4 (3 A00 ) isomerization. The highest SOMO, however, contains delocalized electron density, of antibonding (σ ∗ ) character, in the plane of the molecule. This σ ∗ character may be interpreted as electron density taken from the lowest SOMO in CO4 (3 A00 ) while being localized onto Oc during isomerization. These theoretical results imply that an adiabatic mechanism exists for the oxygen isotope exchange reaction between O2 and CO2 . During the isomerization of CO4 (3 A00 ), the Oc –Od σ -bond is cleaved homolytically (Figure 3.15): One electron moves to a p-type orbital on 90 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.14: Molecular orbital diagrams for O2 and CO2 , adapted from DeKock and Gray [1980]. Sketches of the highlighted orbitals are shown. As O2 collides with CO2 , it becomes stretched. In addition, CO2 bends, increasing the energy of its doubly occupied, ∗ in-plane π-orbitals, π bu and π nb g . A weak interaction between the π g orbital on O2 and the π bu orbital on CO2 is likely responsible for the small (1.5 kcal mol−1 ) binding energy of CO4 . The π nb g orbital does not interact, to first approximation, due to symmetry. Oc , while the other electron forms a bond with the unpaired electron on Ob . This pathway can account for the σ ∗ character of the highest-energy SOMO in TS3 (the Ob –Od bond takes an electron from the Oc –Od bond), and it preserves radical character on Od . Thus, the 3 A00 symmetry is preserved throughout the association, isomerization, and dissociation steps. This mechanism is qualitatively consistent with the small reaction cross-section and a preference for rebounding reactive collisions inferred from the dynamics observed in the experiment. The O2 must approach the CO2 at very low impact parameters with high energies to overcome the initial barrier (TS1/TS2) and reach the ‘shelf’ of the bound CO4 (3 A00 ). Momentum along the reaction coordinate beyond CO4 (3 A00 ) with ∼80 kcal mol−1 excess energy should further compress the C–Oc bond with synchronous bending of the C–Oc –Od 91 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.15: Electron-pushing diagram of an adiabatic CO4 (3 A00 ) isomerization through TS3. angle, stretching of Oc –Od , and ring formation to form TS3, followed by rapid repulsion from the final TS1/TS2 state. Finally, the large change in geometry from reactants to TS3 should facilitate the transfer of some translational energy into internal degrees of freedom of the products. Reactive scattering should become less ‘rebound’-like (forward-scattered) as Ecoll is increased above the reactive threshold; at 37 kcal mol−1 above the reactive barrier, the tight transition state, repulsive exit channel leading out of TS1/TS2, and low angular momentum must limit the extent of sideways scattering. While some sideways scattering is indeed observed in the experiment, the Ecoll dependence of T(θ c.m. ) is not known. A non-adiabatic transition to another potential surface cannot be excluded, especially given the high internal energies observed in the products. At these high energies [80 kcal mol−1 above even the CO4 (3 A00 ) shelf state], many excited-state surfaces must exist, and radiationless transitions via conical intersections may occur. While intersystem crossing (ISC) in the exit or entrance channels is unlikely at the high relative velocities of the experiment [Landau, 1932], spin transitions could readily occur if a complex is formed. For instance, the bridging oxygen atom in TS3, Od , must be equivalently bound to Ob and Oc , and chemical intuition suggests that an intersection with a singlet surface may occur by spin-paired CO4 (1 A1 ) [Cacace et al., 2003; Elliott and Boldyrev, 2005; Jamieson et al., 2007]. 3.6 Conclusion An O2 –CO2 isotope exchange reaction on the ground triplet electronic surface is possible and is consistent with our laboratory observations. Nevertheless, additional work would 92 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 be valuable in the confirmation of this hypothesis. Collision-energy-dependence studies of the product angular distribution may elucidate the mechanistic origins of the low average translational energy of products. Experimental detection of O2 counter-fragments and a search for products from other channels (e.g., spectroscopic identification of electronically excited states) would also be revealing. Last, a more complete surface, reactive trajectories, and locations of possible surface intersection seams leading to ISC would be vital to a full explanation of the reaction dynamics. 3.7 Acknowledgements We thank G. B. Ellison, S. L. Mielke, and J. E. Wulff for insightful discussions. This work was supported by the Missile Defense Agency under cooperative agreement HQ0006-05-20001. L. Y. Y. was supported by the Davidow Fund, and G. C. S. was supported by AFOSR grant FA955D-07-1-0095. 93 L. Y. Yeung Oxygen isotope exchange reactions of CO2 This page intentionally left blank. 94 Chapter 3 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Appendices 95 Chapter 3 L. Y. Yeung 3.A Oxygen isotope exchange reactions of CO2 Chapter 3 Non-reactive scattering of O2 and CO2 The experiment mainly observed signals due to 16 O2 scattered with little deflection from its initial direction (see Newton diagram in Figure 3.2); these signals corresponded to the sum of elastic and inelastic scattering collisions of 16 O2 , which we could not resolve, so they will be referenced collectively as “scattered 16 O2 .” Five representative laboratory-frame TOF distributions (m/z = 32), the c.m. angular and translational energy distributions, and the laboratory-frame angular distribution obtained from 16 O2 product detection are shown in Figure 3.16. Scattered 16 O2 had 126.3 kcal mol−1 total translational energy, or 80% of the available energy, on average. The experimental translational energy distribution was peaked at ∼148 kcal mol−1 . The c.m. angular distribution for 16 O was highly peaked in the forward direction with little scattered intensity for θc.m. > 30◦ ; however, the velocity and angular range for 16 O2 product detection in the experiment prevented the detection of backward-scattered 16 O2 (see Figure 3.2). Some dependence of the c.m. translational energy distribution on the c.m. angular distribution was observed in the 16 O TOF data; the forward-convolution simulations became increasingly faster than the data at larger laboratory and c.m. angles (e.g, Θ = 18◦ , 28◦ , and 42◦ in Figure 3.16). We also note that, like for 16 O (see Sections 4.4.2.1 and 4.5.2), the c.m. angular distribution for inelastically scattered 16 O 2 at θc.m. ∼ 0 ◦ is an extrapolation because of high background from the hyperthermal source at the small laboratory angles corresponding to small c.m. angles for 16 O2 . Most of the 16 O2 probably scatters forward through high-impact-parameter collisions, but the limited constraints on the θc.m. ∼ 0◦ angular distribution (e.g., the laboratory-frame angular distribution, which only probes Θ = 6◦ ) increase the uncertainty in that part of the c.m. angular distribution. The experiment mainly observed 12 C18 O2 scattered opposite its initial direction in the c.m. frame (see Newton diagram in Figure 3.2). Detected 12 C18 O2 products (m/z = 48) showed best-fit c.m. translational energy distributions that were both broader and lower in energy, on average, than that obtained for forward-scattered 16 O2 . A single pair of P(ET ) and T(θc.m. ) distributions was not sufficient to describe the m/z = 48 TOF distributions (see Sections 4.4.2.1 and 4.5.2), and a second pair of P(ET ) and T(θc.m. ) distributions was 96 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 included in the fit; five representative laboratory-frame TOF distributions, the c.m. angular and translational energy distributions, and the laboratory-frame angular distribution obtained from 12 C18 O2 product detection are shown in Figure 3.17, along with the c.m. velocity-flux diagram in Figure 3.18. The first P(ET ) and T(θc.m. ) pair for inelastically scattered 12 C18 O2 described the scattering at θc.m. < 125◦ . In this region, the angular distribution was peaked near θc.m. = 60◦ , though the probability of scattered products was roughly constant for 0◦ < θc.m. < 40◦ . The probability of finding these products decayed steadily at θc.m. > 60◦ . The corresponding translational energy distribution was peaked at 60 kcal mol−1 with an average hET i = 62.8 kcal mol−1 , or 40% the available energy. The second P(ET ) and T(θc.m. ) pair for inelastically scattered 12 C18 O2 described the scattering at 60◦ < θc.m. < 125◦ (corresponding to the maximum θc.m. observed in the experiment), although there was a small component 0◦ < θc.m. < 60◦ . This angular distribution overlapped, in the sideways-scattering region, with the first pair. For θc.m. > 60◦ the distribution increased rapidly until it peaked near θc.m. = 120◦ and decayed quickly at θc.m. > 120◦ . This part of the distribution, however, is uncertain because our experiment did not probe it directly. The translational energy distribution was peaked at 103 kcal mol−1 with an average hET i = 100.8 kcal mol−1 , or 64% the available energy. The similarity in product c.m. angular and translational energy distributions in the O2 + CO2 system and the O(3 P) + CO2 system (see Sections 4.4.2.1 and 4.5.2) suggests that the collisional energy transfer mechanism is similar in both cases. Ryali et al. [1982] found that CO2 collisions with N2 , O2 , and Ar near at high collision energies all had similar translational-to-vibrational energy transfer cross-sections for the excitation of CO2 (ν3 ), so they suggested that energy transfer sampled the repulsive part of the intermolecular potential in all cases. Transfer of vibrational energy from O2 to CO2 cannot be ruled out in our experiments because we did not characterize the vibrational temperature of the hyperthermal O2 . Consequently, the similarity in inelastic scattering dynamics of O(3 P) and O2 collisions with CO2 could also be coincidental. 97 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.16: Laboratory scattering data detected at m/z = 32. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for scattered 16 O2 products from 16 O2 + 12 C18 O2 collisions at hEcoll i = 158.1 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines (orange and brown) are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). These data indicate that 16 O2 is scattered mainly in the forward direction with little change in its initial direction or velocity. 98 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.17: Laboratory inelastic scattering data detected at m/z = 48. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for inelastically scattered 12 C18 O2 products from 16 O2 + 12 C18 O2 collisions at hEcoll i = 158.1 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). The dark blue and cyan lines correspond to products of 16 O(3 P) + 12 C18 O2 collisions, and they are discussed in Section 4.4.2.1. A single c.m. translational energy and angular distribution for each collision partner was insufficient to describe the TOF distributions of inelastically scattered 12 C18 O2 , suggesting a scattering dependence on impact parameter. 99 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.18: Velocity-flux contour diagram for inelastically scattered 12 C18 O2 from 16 O2 + 12 C18 O2 collisions in the center-of-mass frame. The white arrows are the initial 16 O2 and 12 C18 O2 velocity vectors and dashed white line is the maximum recoil velocity for 12 C18 O (v 2 max ). Only the c.m. angles for which the experiment were sensitive are shown; inelastically scattered 12 C18 O2 from high-impact-parameter collisions are not shown, as their flux would be off-scale. Strong coupling of the P(ET ) and T(θ c.m. ) distributions was observed. 100 L. Y. Yeung 3.B Oxygen isotope exchange reactions of CO2 Chapter 3 MATLAB program for generating Newton diagrams A series of programs (linked as functions) was written in MATLAB so meaningful Newton diagrams could be generated with little effort. This proved to be quite useful during data analysis because the program could display expected product times-of-flight, speeding up the forward-convolution fitting process considerably. The programs included here (NewtonD.m, NewtonDcalc.m, and NewtonDplot.m) use parameters specific to the MSU crossedbeam apparatus, but the code is general and the parameters adjustable for use with any crossed-beam apparatus with arbitrary crossing angle. Figure 3.19 shows a sample input and output. Figure 3.19: Sample output of the NewtonD.m program. Predicted c.m. angles are defined relative to the slow product’s c.m. velocity vector. 3.B.1 NewtonD.m % Program for generating Newton diagrams for molecular scattering. % Command line input is NewtonD(observed,labangle) function NewtonD(observed, labangle) clear m1 m2 v1 v2 theta e DEint observed=observed; labangle=labangle; % observed product (1 or 2) as inputted below % lab angle of observation relative to initial v1 % vector, in degrees 101 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 % Begin input section m1=16; v1=8262; % mass of particle 1 in g/mol % initial velocity of particle 1 in m/s m2=48; v2=800; % mass of particle 2 in g/mol % initial velocity of particle 2 in m/s theta=0.5; % angle between v1 and v2 in pi radians, e.g. 0.5 −−> 0.5*pi % = 90 degrees e=0.5; DEint=0; % elastic scattering efficiency 0 < e ≤ 1) % gain of internal energy upon reaction in kcal/mol mp1=16; mp2=48; % mass of product 1 in g/mol % mass of product 2 in g/mol minangle=6; maxangle=54; % minimum lab angle relative to v1 vector, in degrees % maximum lab angle relative to v1 vector, in degrees length=33.66; % distance between interaction region and ionizer in cm if observed == 1 IFT=0;2.44*sqrt(mp1); % ion flight time (delay) in microseconds else if observed == 2 IFT=0;2.44*sqrt(mp2); end end delec=0;3; % electronics delay in microseconds dlaser=0;174; % laser firing delay in microseconds otravel=0;(0.99/v1)*10ˆ6; % O−atom travel time from nozzle to % interaction region in microseconds % End input section % Input error check if observed 6= 1 && observed 6= 2 disp('Invalid input, "observed" must equal 1 or 2'); return; end % Begin calculations hold off format short g disp('Observed m/z'); % Display observed mass if observed == 1 disp(mp1); else if observed == 2 disp(mp2); end end disp('Lab angle (degrees)'); disp(labangle); 102 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 disp('Predicted center−of−mass angles (degrees)'); disp(' Fast channel | Slow channel'); % Iterate; first round includes specified change in internal energy, % second round sets the internal energy change to zero, i.e. % elastic scattering. for i = 1:2 [vc, thetavc, vrel, u1, u2, vrelp, up1, up2, Ecoll, phi, vd, chi]= NewtonDcalc(m1, m2, v1, v2, theta, e, DEint, mp1, mp2, labangle, observed); NewtonDplot(v1, v2, vc, thetavc, up1, up2, e, minangle, maxangle, labangle, vd, length, IFT, delec, dlaser, otravel, chi); if DEint == 0 return; else DEint=0; end end disp('Collision Energy (kcal/mol)'); disp(Ecoll); 3.B.2 NewtonDcalc.m % Function for calculating center−of−mass quantities function [vc, thetavc, vrel, u1, u2, vrelp, up1, up2, Ecoll, phi, vd, chi]=NewtonDcalc(m1, m2, v1, v2, theta, e, DEint, mp1, mp2, labangle, observed) % reactant parameters mu=m1*m2/(m1+m2); vc=sqrt((m1/(m1+m2)*v1)ˆ2+(m2/(m1+m2)*v2)ˆ2); vrel=sqrt(v1ˆ2+v2ˆ2−2*v1*v2*cos(theta*pi)); u1=m2/(m1+m2)*vrel; u2=m1/(m1+m2)*vrel; thetavc=asin((u2/vc)*(v1/vrel)*sin(theta*pi)); Ecoll=(1/2)*mu/1000*vrelˆ2/4.184/1000; % reduced mass % CM velocity % relative velocity % velocity of particle 1 % in CM frame % velocity of particle 2 % in CM frame % angle between CM % velocity and v2 % CM collision energy % reactive product parameters mup=mp1*mp2/(mp1+mp2); % reduced mass vrelp=sqrt(((mu/1000)*vrelˆ2−2*(DEint*1000*4.184))/(mup/1000)); %relative velocity up1=mp2/(mp1+mp2)*vrelp; % velocity of product 1 % in CM frame up2=mp1/(mp1+mp2)*vrelp; % velocity of product 2 % in CM frame phi=labangle*pi/180−(theta*pi−(thetavc)); % case structure determining output parameters if observed == 1 103 % angle between lab % detection vector and % CM velocity L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 up=up1; u=u1; v=v1; else if observed == 2 up=up2; u=u2; v=v2; end end % product velocity in lab frame with case structure for removal of % imaginary roots. if imag(roots([1 −2*vc*cos(phi) vcˆ2−(up*sqrt(e))ˆ2])) == 0 vd=roots([1 −2*vc*cos(phi) vcˆ2−(up*sqrt(e))ˆ2]); % Solve for product velocity observed at detector if vd(1) ≤ 0 && vd(2) ≤ 0 vd(1)=0; vd(2)=0; else if vd(1) > 0 && vd(2) ≤ 0 vd(2)=0; else if vd(1) < 0 && vd(2) > 0 vd(1)=0; end end end % Product scattering angle relative to CM velocity vector of reactant 2 if phi > 0 chi=(acos((diag(vd*vd')−vcˆ2−diag(up*up')*e)/(−2*vc*up*sqrt(e)))− asin(v2/u2*sin(thetavc)))*180/pi; else chi=360−(acos((diag(vd*vd')−vcˆ2−diag(up*up')*e)/(−2*vc*up*sqrt(e)))+ asin(v2/u2*sin(thetavc)))*180/pi; end if imag(chi(1)) 6= 0 chi(1) = 0; end if imag(chi(2)) 6= 0 chi(2) = 0; end if chi(1) > 180 chi(1)= chi(1)−360; end if chi(2) > 180 chi(2)= chi(2)−360; end % In case of imaginary roots else vd(1,1)=10000; vd(2,1)=10000; chi=1; disp(' N/A end N/A') %((1/2)*(mp1/1000)*(up1)ˆ2*e)/4184 %((1/2)*(mp2/1000)*(up2)ˆ2*e)/4184 3.B.3 % Display lack of solutions % CM Translational energy of % product 1 % CM Translational energy of % product 2 NewtonDplot.m 104 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 function NewtonDplot(v1, v2, vc, thetavc, up1, up2, e, minangle, maxangle, labangle, vd, length, IFT, delec, dlaser, otravel, chi) % Messy plotting code for pretty pictures x1 = vc*cos(thetavc); y1 = vc*sin(thetavc); N=256; t=(0:N)*2*pi/N; plot(sqrt(e)*up2*cos(t)+x1, sqrt(e)*up2*sin(t)+y1, '−.r'); % Newton circle for product 2 hold on grid on plot(sqrt(e)*up1*cos(t)+x1, sqrt(e)*up1*sin(t)+y1, '−.b'); % Newton circle for product 1 legend('Particle 2', 'Particle 1') % text(1,1,'Collision energy = \Ecoll kcal/mol') x0 = 0; y0 = 0; x1 = 0; y1 = v1; plot([x0;x1],[y0;y1]) alpha = 0.05; % Particle 1 % Size of arrow head relative to the length of % the vector beta = 0.2; % Width of the base of the arrow head relative to % the length hu = [x1−alpha*((x1−x0)+beta*((y1−y0)+eps)); x1; x1−alpha* ((x1−x0)−beta*((y1−y0)+eps))]; hv = [y1−alpha*((y1−y0)−beta*((x1−x0)+eps)); y1; y1−alpha* ((y1−y0)+beta*((x1−x0)+eps))]; plot(hu(:),hv(:)) % Plot arrow head x0 = 0; y0 = 0; x1 = v2; y1 = 0; plot([x0;x1],[y0;y1],'r') % Particle 2 alpha = 0.4; % Size of arrow head relative to the length of % the vector beta = 0.5; % Width of the base of the arrow head relative to % the length hu = [x1−alpha*((x1−x0)+beta*((y1−y0)+eps)); x1; x1−alpha* ((x1−x0)−beta*((y1−y0)+eps))]; hv = [y1−alpha*((y1−y0)−beta*((x1−x0)+eps)); y1; y1−alpha* ((y1−y0)+beta*((x1−x0)+eps))]; plot(hu(:),hv(:),'r') % Plot arrow head x0 = v2; y0 = 0; x1 = 0; y1 = v1; plot([x0;x1],[y0;y1],'m') % vrel alpha = 0.05; % Size of arrow head relative to the length of % the vector beta = 0.2; % Width of the base of the arrow head relative to 105 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 % the length hu = [x1−alpha*((x1−x0)+beta*((y1−y0)+eps)); x1; x1−alpha* ((x1−x0)−beta*((y1−y0)+eps))]; hv = [y1−alpha*((y1−y0)−beta*((x1−x0)+eps)); y1; y1−alpha* ((y1−y0)+beta*((x1−x0)+eps))]; plot(hu(:),hv(:),'m') % Plot arrow head x0 = 0; y0 = 0; x1 = vc*cos(thetavc); y1 = vc*sin(thetavc); plot([x0;x1],[y0;y1],'g') % vc alpha = 0.1; % Size of arrow head relative to the length of % the vector beta = 0.25; % Width of the base of the arrow head relative to % the length hu = [x1−alpha*((x1−x0)+beta*((y1−y0)+eps)); x1; x1−alpha* ((x1−x0)−beta*((y1−y0)+eps))]; hv = [y1−alpha*((y1−y0)−beta*((x1−x0)+eps)); y1; y1−alpha* ((y1−y0)+beta*((x1−x0)+eps))]; plot(hu(:),hv(:),'g') % Plot arrow head x1=10000*sin(minangle*pi/180); y1=10000*cos(minangle*pi/180); plot([0;x1],[0;y1],'k') % minimum lab angle x1=10000*sin(maxangle*pi/180); y1=10000*cos(maxangle*pi/180); plot([0;x1],[0;y1],'k') % maximum lab angle if chi == 1 return else if chi 6= 1 x1=vd*sin(labangle*pi/180); y1=vd*cos(labangle*pi/180); plot([0;x1],[0;y1],'k') % observed lab angle x0=vc*cos(thetavc); y0=vc*sin(thetavc); x1=vd*sin(labangle*pi/180); y1=vd*cos(labangle*pi/180); plot([x0;x1],[y0;y1],'k') % center−of−mass scattering end end xlabel('Velocity of Particle B (m/s)') ylabel('Velocity of Particle A (m/s)') axis([−9000 11000 −5500 9500]) % Relevant quantities disp(chi'); if vd(1) == 0 && vd (2) == 0 TOF=[0 0]; else if vd(1) == 0 TOF=[((length/100)/vd(1))*10ˆ6 0]; 106 % Predicted TOF times in % microseconds L. Y. Yeung Oxygen isotope exchange reactions of CO2 else if vd(2) == 0 TOF=[((length/100)/vd(1))*10ˆ6 0]; % Predicted TOF times in % microseconds else if vd(1) == 10000 && vd(2) == 10000 TOF=[0 0]; else if vd(1) > 0 && vd(2) > 0 % Predicted TOF times in microseconds TOFfast=((length/100)/vd(1))*10ˆ6; TOFslow=((length/100)/vd(2))*10ˆ6; TOF=[TOFfast TOFslow]; end end end end end % Display TOF on graph next to Newton circle text(x1(1),y1(1),[' \leftarrow ',num2str(round(TOF(1)+IFT+delec+dlaser+ otravel)), ' \mus'],'FontSize',14) % Only display second TOF value if there is a product to display if TOF(2) 6= 0 text(x1(2),y1(2),[' \leftarrow ',num2str(round(TOF(2)+IFT+delec+ dlaser+otravel)), ' \mus'],'FontSize',14) else return end 107 Chapter 3 L. Y. Yeung Oxygen isotope exchange reactions of CO2 This page intentionally left blank. 108 Chapter 3 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Chapter 4 Dynamics of O(3P) + CO2 collisions at hyperthermal energies In collaboration with Mitchio Okumura, Jianming Zhang, Timothy K. Minton, Jeffrey T. Paci, Jan M. L. Martin, Jon M. Camden, and George C. Schatz; parts of this will be submitted to Journal of Physical Chemistry A for publication. 109 L. Y. Yeung 4.1 Oxygen isotope exchange reactions of CO2 Chapter 4 Abstract The dynamics of O(3 P) + CO2 collisions at hyperthermal collision energies near 100 kcal mol−1 were investigated experimentally and theoretically. Crossed-molecularbeam experiments at hEcoll i = 98.8 kcal mol−1 were performed with isotopically labeled 12 C18 O 16 3 12 C18 O ] from 2 to distinguish products of non-reactive scattering [ O( P) + 2 products of reactive scattering (18 O + 16 O12 C18 O and 18 O16 O + 12 C18 O). 16 O products were detected mainly in the forward direction, i.e., in the initial direction of the hyperthermal oxygen beam in the center-of-mass (c.m.) frame, and they contained ∼87% of the collision energy in translation, on average; the amount of energy transfer during non-reactive scattering depended on impact parameter. 16 O12 C18 O products from the oxygen isotope exchange reaction were scattered mainly in the backward direction with 35% of the available energy in translation, on average. 18 O16 O products from the oxygen-atom abstraction reaction were detected in the forward direction, with 56% of the available energy in translation, on average. Stationary points on the lowest triplet potential energy surface of the O(3 P) + CO2 system were characterized at the CCSD(T)/aug-cc-pVTZ level of theory. Quasi-classical trajectory (QCT) calculations of O(3 P) + CO2 collisions at energies between 1.0 – 6.5 eV (23 – 150 kcal mol−1 ) were performed at the B3LYP/6-311G(d) and BMK/6-311G(d) levels of theory, and both reactive channels observed in the experiment were also predicted by the theory. In addition, trajectories leading to the formation of 18 O2 + 12 C16 O products were predicted. The c.m. translational energy and angular distributions derived from the QCT calculations show qualitative, but not quantitative agreement with experimental results. The theoretical relative product yield for the oxygen isotope exchange reaction also agreed well with the experiment. The isotope exchange reaction demonstrates a new pathway through which oxygen isotopes may be cycled in the upper atmosphere, where O(3 P) atoms with hyperthermal translational energy distributions can be generated through the photolysis of ozone and molecular oxygen. 110 L. Y. Yeung 4.2 Oxygen isotope exchange reactions of CO2 Chapter 4 Introduction Atomic oxygen radicals in the atmosphere play an important role in regulating Earth’s oxidative and radiative balance. Photodissociation of molecular oxygen and ozone by solar ultraviolet radiation produces not only electronically excited O(1 D) and O(1 S), but also ground-state O(3 P) with velocities as high as 6 km s−1 [Matsumi and Kawasaki, 2003; Stranges et al., 1995]. O(3 P) has received less attention than O(1 D) and O(1 S), however, because it is less reactive at low collision energies. Yet, its important role in the terrestrial mesosphere and thermosphere is widely recognized; for instance, its collisions with CO2 significantly influence the population of CO2 (010), whose emission at 15 µm cools the atmosphere and regulates the height of the mesopause [Sharma and Roble, 2002]. O(3 P) can also interact with CO2 from space vehicle exhaust streams at relative velocities near 8 km s−1 and collision energies near 100 kcal mol−1 , well above those expected at local thermodynamic equilibrium. These high collision energies exceed barriers to (1) CO3 formation, leading to oxygen isotope exchange, and (2) oxygen-atom abstraction on the triplet potential energy surface (PES) [Averyanov et al., 1999; Bennett et al., 2004; Froese and Goddard, 1993; Mebel et al., 2004; Yang et al., 2005]. The enthalpies associated with these reactions are: 3 1 + O(3 P) + CO2 (1 Σ+ g ) → O( P) + CO2 ( Σg ) 1 + → O2 (3 Σ− g ) + CO( Σ ) ∆H ∼ 0 (4.1) ∆H = 8 kcal mol−1 (4.2) A reaction analogous to reaction 4.1, between O(1 D) and CO2 in the stratosphere [Baulch and Breckenridge, 1966; Chakraborty and Bhattacharya, 2003; DeMore and Dede, 1970; Johnston et al., 2000; Mebel et al., 2004; Perri et al., 2003, 2004; Shaheen et al., 2007; Wen and Thiemens, 1993; Yeung et al., 2009a], alters the stable isotope composition of stratospheric CO2 , allowing the isotopic composition of stratospheric CO2 to be used as a tracer of O(1 D) [Thiemens et al., 1995; Yung et al., 1991, 1997] and atmospheric transport [Boering et al., 2004]. The isotopic composition of CO2 has also been proposed as a tracer of biogeochemical cycles on annual and decadal timescales [Hoag et al., 2005]. Consequently, the dynamics of reactive channels that could alter the isotopic composition of 111 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 upper atmospheric CO2 are also of interest [Perri et al., 2003, 2004]. Early studies on the O(3 P) + CO2 system were primarily theoretical and focused on the vibrational-state-specific energy transfer [Bass, 1974; Garrett, 1983; Harvey, 1982; Schatz and Redmon, 1981]. The mechanism was found to be primarily impulsive at high collision energies, like that of collisions between CO2 and noble gases [Billing and Clary, 1983; Harvey, 1982; Schatz and Redmon, 1981]. More recent quantum calculations on the O(3 PJ ) + CO2 (010) system indicate that vibrational-to-translational energy transfer is sensitive to the total angular momentum J at thermal collision energies, although the importance of spin-orbit coupling decreases with increasing collision energy [de Lara-Castells et al., 2006, 2007]. Two experimental studies also focused on state-specific excitation in O(3 P) + CO2 collisions, specifically to CO2 (001); both studies also reported evidence that reaction 4.2, which is important in combustion chemistry [Tsang and Hampson, 1986] yielded vibrationally excited CO products [Oakes et al., 1994; Upschulte and Caledonia, 1992]; no mechanism was proposed, however. We recently confirmed the presence of reaction 4.1 at hyperthermal collision energies [Yeung et al., 2009b], and we intend now to investigate its dynamics. Mebel et al. [2004] suggested that the dynamics of CO3 formation on the triplet (3 A0 ) PES with hyperthermal O(3 P) atoms might be complicated by a nearby 3 A0 –1 A0 intersection seam, which could lead to non-adiabatic effects along reactive trajectories. Indeed, many low-lying electronic states of CO3 (e.g., 3 A00 ) lie within several eV of CO3 (3 A0 ), so vibronic [Kowalczyk and Krylov, 2007] and/or spin-orbit [Mebel et al., 2004] coupling could result in unexpected curvature and dynamics on the triplet PES. Here, the results of theoretical and crossed-molecular-beam studies of O(3 P) + CO2 collisions at hyperthermal collision energies will be presented. Theoretical direct dynamics calculations using the QCT method on an adiabatic PES were compared with the results from an experimental dynamics study obtained for an average collision energy hEcoll i = 98.8 kcal mol−1 . The oxygen isotope exchange and oxygen-atom abstraction reactions were observed in both the QCT calculations and the laboratory experiment, and center-of-mass (c.m.) angular and translational energy distributions for the oxygen isotope exchange reaction were 112 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 obtained. Their implications for atomic oxygen cycling through CO2 in the atmosphere will be discussed. 4.3 Theoretical studies 4.3.1 Electronic structure calculations Geometry-optimization, single-point, and vibrational-frequency calculations were performed on stationary points of the lowest triplet PES of CO3 , 3 A00 ; a discussion of the relative energetics of the 3 A0 and 3 A00 surfaces can be found in Section 4.5. Stationary points for reactions 4.1 and 4.2 were characterized using electronic structure calculations at the B3LYP/6-311G(d) [Becke, 1993; Frisch et al., 1984; Lee et al., 1988], BMK/6-311G(d) [Boese and Martin, 2004], and CCSD(T)/aug-cc-pVTZ [Kendall et al., 1992; Raghavachari et al., 1989] levels of theory/basis using the MOLPRO electronic structure code [Werner et al., 2006]. Confirmation of transition-state character was achieved by inspection of the associated vibrational frequencies. Other reactive channels were not characterized because reactant energies in excess of 250 kcal mol−1 are required to open them, according to our B3LYP/6-311G(d) calculations. Here, we report three transition-state structures and one bound-state structure on the CO3 (3 A00 ) PES; the results are shown in Figures 4.1 and 4.2 and Table 4.1 [Mebel et al., 2004]. All structures are planar. One transition state (TS1) and the bound state (CO3 ) were associated with the O(3 P) + CO2 isotope exchange reaction. Two transition states (TS2 and TS3) were associated with the oxygen-atom abstraction reaction producing O2 and CO. Two additional bound states and two associated transition states were also found; they resemble the Cs minima reported in previous work [Bennett et al., 2004; Froese and Goddard, 1993; Mebel et al., 2004], but they will not be discussed here because neither of the bound states were bound when zero-point energy (ZPE) was considered. For this reason, we are also not reporting minima in the van der Waals region of the PES, e.g., the quadrupole-induced minimum (∆E ∼ 335 cm−1 ) at the RCCSD(T)/aug-cc-pVTZ level of theory [de Lara-Castells et al., 2006, 2007], because the binding energies were below the ZPE of the system. Further 113 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.1: Stationary-point structures for O(3 P) + CO2 reactions below 100 kcal mol−1 calculated at the CCSD(T)/aug-cc-pVTZ level of theory on the 3 A00 . The relative energies have been corrected for zero-point energy. comparisons of the structures with previous work on the lowest triplet PES will be presented in Section 4.5. Of the levels of theory and basis examined in this study, CCSD(T)/aug-cc-pVTZ is probably the most accurate combination; however, multi-reference character in the stationary points may be important because several electronic surfaces are within several eV of the PES that is the subject of this study [Bennett et al., 2004; Kowalczyk and Krylov, 2007; Mebel et al., 2004]. Multi-reference CCSD(T) calculations, unfortunately, were not computationally affordable. Still, our CCSD(T)/aug-cc-pVTZ geometries are nearly identical to those obtained in recent calculations using the W4 method [Karton et al., 2006] near the full-configuration-interaction and complete-basis-set limits, with transition-state energies within 2 kcal mol−1 and the bound-state energy within 4 kcal mol−1 (J. M. L. Martin, per- 114 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Table 4.1: Energies (kcal mol−1 ) for the stationary points on the lowest triplet CO3 potential energy surface for 16 O(3 P) + 12 C16 O2 → 16 O + 12 C16 O2 collisions B3LYP 6-311G(d) BMK 6-311G(d) w/ZPEC† O(3 P) + CO2 TS1 CO3 TS2 TS3 O2 + CO 0.0 18.0 11.8 56.2 70.3 9.7 0.0 17.7 11.3 55.2 69.2 7.9 CCSD(T) aug-cc-pVTZ w/ZPEC† 0.0 25.2 20.2 65.3 80.0 14.3 0.0 25.0 19.0 64.5 78.9 12.6 CCSD(T) 6-311+G(3df)∗ w/ZPEC† 0.0 25.2 21.8 63.0 76.5 10.2 0.0 25.0 20.2 62.1 75.3 8.3 0.0 35.2 22.0 ∗ From Mebel et al. [2004] using a 3 A0 geometry optimized at the CASSCF(16,13)/6-311G(d) level of theory. The authors noted that the more ideal MRCI+Q/6-311+G(3df) energy calculation was not affordable. † Zero-point-energy correction (ZPEC). sonal communication). Thus, we used the CCSD(T)/aug-cc-pVTZ geometries and energies as benchmarks for comparison with those calculated by the density-functional methods, which are more affordable for QCT calculations. In addition to using the B3LYP and BMK levels of theory, we characterized the transitionstate structures at the MP2 [Møller and Plesset, 1934], M06-2X [Zhao and Truhlar, 2008], and CCSD [Purvis and Bartlett, 1982] levels using the 6-31G(d,p), 6-311G(d), and cc-pVTZ [Dunning, 1989] basis sets during our search for an appropriate level of theory for QCT calculations (optimizing computational cost and accuracy). The density-functional methods B3LYP/6-311G(d) and BMK/6-311G(d), however, were found to have the best balance between computational cost and accuracy, so we will only report the results of those calculations here along with the results of CCSD(T)/aug-cc-pVTZ calculations (see Figure 4.2). The results of the lower-level B3LYP and BMK calculations, along with the MP2, M06-2X, and CCSD calculations, are shown in Figure 4.3. TS1 had Cs symmetry in all cases. Mild compression of one C–O bond and stretching of the other C–O bond in the parent CO2 , along with moderate bending (∼30◦ ) of the O– C–O bond angle, was found at all levels of theory. The geometries were similar to that calculated at the CCSD(T) level of theory, which had C–O bond lengths of 1.24 Å, 1.18 Å, and 1.60 Å and bond angles of 87◦ , 123◦ , and 150◦ (see Figure 4.2). The B3LYP geometry 115 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.2: Comparison of CO3 stationary point geometries relevant to the QCT calculations. Our geometry optimizations at the CCSD(T)/aug-cc-pVTZ, B3LYP/6-311G(d), and BMK/6-311G(d) levels of theory (bold) are shown with Mebel et al.’s CASSCF(16,13)/6311G(d) geometries for CO3 and TS1. Figure 4.3: Comparison of TS1 and TS3 geometries and energies at various levels of theory. ZPE-corrected transition-state (∆E ‡ ) and reaction (∆E) energies are shown. 116 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 generally agrees well with that at CCSD(T), deviating by < 0.02 Å in the two shorter C–O bond lengths and by < 3◦ in all the bond angles. The longest bond length, however, is 0.06 Å longer at B3LYP than at CCSD(T). Its ZPE-corrected energy is also 7.3 kcal mol−1 lower. At the BMK level of theory, the TS1 geometry agrees with the CCSD(T) geometry within 0.02 Å in all the bond lengths and within 3◦ in all the bond angles, and with the CCSD(T) energy within 0.1 kcal mol−1 . The CO3 bound state had C2v symmetry at the B3LYP and CCSD(T) levels of theory and Cs symmetry at the BMK level of theory. C–O bond lengths were larger than typical CO2 bond lengths (1.21 Å), consistent with an overall decrease in C–O bond order upon CO3 formation. The B3LYP geometry agreed within 0.04 Å and 1◦ with the CCSD(T) geometry, which had C–O bond lengths of 1.27 Å, 1.27 Å, and 1.30 Å and bond angles of 118◦ , 118◦ , and 123◦ (see Figure 4.2). The ZPE-corrected B3LYP energy, however, is 8.9 kcal mol−1 lower than that at CCSD(T). At the BMK level of theory, moderate agreement in the CCSD(T) geometry was observed; in addition to displaying lower symmetry, the C–O bond lengths calculated at BMK were different from CCSD(T) bond lengths by up to 0.07 Å, while the bond angles were different by up to 8◦ . The lower symmetry for CO3 using the BMK functional may be a consequence of the large amount of Hartree-Fock exchange mixed into the functional [Boese and Martin, 2004], which can result in orbital symmetry-breaking [Sherrill et al., 1999]. The ZPE corrected CO3 energy at BMK is in better agreement, however, at 1.2 kcal mol−1 below the energy at CCSD(T). Both B3LYP and BMK theories do show a CO3 potential well of 6.4 and 6.0 kcal mol−1 , respectively, in reasonable agreement with the CCSD(T) well depth of 4.8 kcal mol−1 . TS2 and TS3 were associated with an oxygen-atom abstraction reaction producing O2 + CO. They had Cs symmetry at all levels of theory. In both transition states, one C–O bond on the parent CO2 was compressed, while the other C–O bond, which is eventually broken, was stretched (see Figure 4.2). The O–C–O bond angle was bent ∼40◦ , and the only qualitative difference between the structures was the C–O–O bond angle: The C–O–O angle bent inwards to form a ‘C’-shape in TS2, whereas it bent outwards to form a ‘S’-shape in TS3. Both B3LYP and BMK geometries agreed with the CCSD(T) geometry with a maximum dis- 117 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 crepancy of 0.04 Å in the O–O bond length at the BMK level. The two bond angles agreed to within 2◦ . Resulting ZPE-corrected barrier heights showed larger discrepancies: B3LYP and BMK energies for TS2 differed from CCSD(T) values by –6.9 and +2.4 kcal mol−1 , respectively, while they differed from CCSD(T) values by +6.1 and –3.6 kcal mol−1 , respectively, in TS3. We note that BMK overpredicted the endothermicity of the O(3 P) + CO2 → O2 + CO reaction by ∼4.5 kcal mol−1 ; this disagreement is again probably a consequence of the large amount of Hartree-Fock exchange mixed into the BMK functional, which was included to improve the performance of the functional when predicting transition state properties. 4.3.2 Reaction dynamics calculations QCT calculations were run on the 3 A00 PES with both B3LYP/6-311G(d) and BMK/6311G(d) methods. Both methods showed reasonable agreement with the geometries and energies of the stationary points calculated at CCSD(T)/aug-cc-pVTZ and were computationally affordable for direct dynamics calculations. Four hundred trajectories were run at collision energies of 1.0, 1.5, 2.5, 3.5, 4.5, 5.5, and 6.5 eV (23.0, 34.6, 57.6, 80.7, 103.7, 126.7, and 149.8 kcal mol−1 , respectively) using the B3LYP level of theory for a total of 2800 trajectories. This range of energies was selected because the ZPE-corrected barriers for TS1, TS2, and TS3 according to this level of theory were 17.7, 55.2, and 69.2 kcal mol−1 (0.77, 2.4, and 3.0 eV, respectively). In addition, four hundred BMK trajectories were run at collision energies of 1.5, 2.5, 3.5, 4.5, 5.5, and 6.5 eV for a total of 2400 trajectories. At this level of theory, the ZPE-corrected reaction thresholds were 25.0, 64.5, and 78.9 kcal mol−1 (1.1, 2.8, and 3.4 eV, respectively) for TS1, TS2, and TS3, respectively. The collision energy of 1.0 eV (23 kcal mol−1 ) was not considered because it is below the threshold for both reactions 4.1 and 4.2, according to the BMK level of theory. Trajectories were integrated using a standard fifth-order predicator, sixth-order corrector integration algorithm [Bunker, 1970; Press et al., 1992] with an integration time-step of 10.0 a.u. (0.24 fs). The energy and gradient were calculated at each point using the Q-Chem software package [Shao et al., 2006], and the initial orientation and impact parameter was sampled randomly. To simulate the ZPE, an intermolecular trajectory starting from CO2 in its equilibrium configuration was run 118 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 with kinetic energy corresponding to the ZPE in each normal mode, and the atomic coordinates along this trajectory were used to sample the initial CO2 vibrational phase randomly in subsequent trajectories. An estimate of a reasonable value for the maximum impact parameter for reactive scattering, bmax , was calculated using the expression [Levine, 2005]: 1  E0 2 bmax = d 1 − ET (4.3) where d is the distance in the transition-state structure between the center of mass of the reactant CO2 and the colliding oxygen atom, E0 is the transition-state energy, and ET is the collision energy. Because large collision energies were of principal interest, we chose to consider the largest value for bmax suitable for trajectories with unlimited collision energy by setting ET = ∞ in Eq. 4.3. Reaction 4.2 had the larger of the two d values, with a value of d ∼ 4.3 a0 (2.3 Å). This d value, combined with a ∼15% safety margin, suggested a bmax = 5.0 a0 (2.6 Å); thus, the trajectories were sampled with impact parameters 0 < b < 5.0 a0 . Trajectories were stopped when the distance between any two atoms exceeded 12 a0 (6.3 Å). Energy conservation and spin contamination were checked at each time-step. Trajectories in which energy was not conserved to within 3 kcal mol−1 or spin contamination rose above hS2 i = 2.5 were flagged. Less than 1.3% and 10% of the B3LYP and BMK trajectories, respectively, failed to meet these acceptance criteria. Most problems were related to energy conservation, and were attributed to self-consistent field convergence to an excited electronic state. Trajectories that initially did not meet the criteria were run again using a different set of self-consistent field convergence tools, which improved the energyconservation or spin-contamination problem in many cases. Results of the re-run trajectories were compared to their initial-run analogues, and the one that met or came closest to meeting the acceptance criteria was included in the analysis. To do otherwise would have resulted in an underestimate of the reaction cross-sections, as most of the problematic trajectories were reactive ones. Reactive cross-sections (σR ) were calculated from the QCT data using the expression: 119 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 N σR = π R (2li + 1)lmax ∑ Ntotal p2 i=1 (4.4) 1 where p = (2µET ) 2 is the momentum of the reactant system, li = bi p is the angular momentum of the ith trajectory, and lmax = bmax p. NR is the number of reactive trajectories in the set of Ntotal trajectories run. The total collision cross-section, σtotal , was estimated using the Lennard-Jones parameters for O and CO2 according to the expression for the total cross-section: σtotal = πb2total (4.5) where btotal is the radius beyond which no elastic, inelastic, or reactive scattering occurs. This radius can be estimated using the Lennard-Jones potential [Hirschfelder et al., 1964]: V (r) = 4ε   r 12 e r −  r 6  e r (4.6) where ε and re correspond to the well depth and the separation distance, respectively, at the potential minimum for an interaction between a pair of like atoms or molecules. The separation distance, re , is a measure of the atomic or molecular size. The values for the O-atom and for CO2 have been estimated to be re (O) = 2.78 Å and re (CO2 ) = 3.897 Å, respectively [Hirschfelder et al., 1964; Némethy et al., 1983]. Combining these radii with the usual method [Hirschfelder and Meath, 1967], i.e., re (O + CO2 ) = 1 [re (O) + re (CO2 )] 2 (4.7) we calculated an intermolecular interaction distance re (O + CO2 ) = btotal of 3.34 Å and a total collision cross-section of 125.2 a20 , which we used to calculate the relative product yields in Section 4.4.2.4. The theoretical reactive cross-section was divided by three for the comparison with experiment because the O(3 P) + CO2 surface is triply degenerate at large O(3 P)–CO2 separation distances (see Section 4.4.2.4). Trajectories corresponding to oxygen isotope exchange were observed at all collision 120 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.4: Reactive scattering cross-sections for the O(3 P) + CO2 isotope exchange reaction obtained from the QCT calculations. energies (see Table 4.2), and the resulting excitation functions were calculated from the QCT data (see Figure 4.4). These excitation functions had the same shape at the B3LYP/6311G(d) and BMK/6-311G(d) levels of theory. The BMK excitation function was shifted to slightly higher energies compared to the B3LYP prediction, consistent with the 7.3 kcal mol−1 (0.32 eV) higher ZPE-corrected transition-state barrier for isotope exchange. Opacity functions for the isotope exchange reaction showed a slight decrease in reaction probability at smaller impact parameters as the collision energy increased (see Figure 4.5). P(b) also appeared to reach a maximum near b ∼ 1.5 – 2 a0 (1 Å). The O2 + CO channel appears to open at higher energies than the exchange channel (see Table 4.2), consistent with the higher ZPE-corrected transition-state barriers for the oxygen-atom abstraction reaction of 37.5 kcal mol−1 (1.63 eV) and 39.5 kcal mol−1 (1.71 Table 4.2: Number of reactive QCTs observed at different collision energies. Theory/Basis Products 1.0 B3LYP/6-311G(d) BMK/6-311G(d) O + CO2 O2 + CO O + CO2 O2 + CO 1 0 121 Collision energy (eV) 1.5 2.5 3.5 4.5 5.5 6.5 16 0 2 0 78 11 80 8 54 0 37 0 66 0 66 0 68 1 80 0 80 4 76 5 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.5: Opacity functions for the O(3 P) + CO2 isotope exchange reaction and for inelastic scattering of the two reagents obtained from QCT calculations at the B3LYP/6311G(d) and BMK/6-311G(d) levels of theory. eV) higher than the exchange channel barrier according to the B3LYP and BMK predictions, respectively. The B3LYP threshold is slightly higher than that calculated using BMK, which is consistent with a ZPE-corrected barrier 9.3 kcal mol−1 (0.40 eV) larger at BMK than at B3LYP. Because only a small number of oxygen-atom abstraction reactions were observed, even at collision energies significantly in excess of the calculated reaction barrier, the amount of mechanistic insight available from the O(3 P) + CO2 → O2 + CO reaction is limited. A full discussion of the trajectory calculations, including the resulting product angular and translational energy distributions, can be found in Sections 4.4.2 and 4.5; they will be analyzed with the experimental data to elucidate the possible reaction mechanisms for each channel. 122 L. Y. Yeung Oxygen isotope exchange reactions of CO2 4.4 Experimental studies 4.4.1 Methods Chapter 4 Crossed-molecular-beam experiments were performed with an apparatus equipped with a hyperthermal atomic oxygen beam source at Montana State University, which was described in the preceding chapter. Briefly, a pulsed, hyperthermal beam of ∼87% 16 O(3 P) and ∼13% 16 O 3 − 16 O using a high-energy CO 2 ( Σg ) was generated by laser-induced detonation of 2 2 TEA laser (6 – 7 J pulse−1 ). Though initially broad in velocity distribution (6 – 9 km s−1 ), a portion of the overall beam was velocity-selected with a chopper wheel (see Figure 3.1) at an average velocity hvi = 8262 m s−1 . The resulting beam was crossed at a right angle with a pulsed supersonic expansion of 98% 12 C18 O2 . The scattered products were detected with a rotatable quadrupole mass spectrometer that collected number-density distributions for each product as a function of arrival time at the ionizer, N(t), at a given laboratory angle, Θ, the angle at which the product scatters with respect to the direction of the reagent oxygen beam. Time-of-flight (TOF) distributions for 16 O, 18 O16 O, 16 O12 C18 O, and 12 C18 O2 were collected over a range of laboratory angles; at each angle, the TOF distribution was integrated to give a laboratory angular distribution, N(Θ). A forward-convolution method was then used to derive c.m. translational energy P(ET ) and angular T(θc.m. ) distributions from the laboratory N(t) and N(Θ) distributions [Lee, 1988], where θc.m. is the angle at which a product scatters with respect to the reagent oxygen direction in the c.m. frame. The canonical Newton diagrams used in this analysis are shown in Figure 4.6. Laboratory TOF product distributions were measured every 2◦ between Θ = 6◦ – 54◦ . Scattered product TOF distributions were collected for 200 beam pulses for m/z = 16 (16 O+ ) and 32 (16 O2 + ), for 1000 beam pulses for m/z = 46 (16 O12 C18 O+ ), and for 500 beam pulses for m/z = 48 (12 C18 O2 + ). Scattered products at m/z = 34 (18 O16 O+ ) were collected for 12000 beam pulses at Θ = 6◦ and 10◦ and 6000 beam pulses at Θ = 14◦ . Dwell time for each channel at the MCP was 1 µs. At a representative laboratory angle of 10◦ , integrated count rates were 1.1 × 107 s−1 for m/z = 16, 1.3 × 107 s−1 for m/z = 32, 1.4 × 104 s−1 for m/z = 34 (18 O16 O+ ), 1.8 × 105 s−1 for m/z = 46 , and 4.2 × 106 s−1 for 123 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.6: Canonical Newton diagram for 16 O + 12 C18 O2 collisions at Ecoll = 98.8 kcal mol−1 The 16 O-atom beam velocity is 8262 m s−1 and the 12 C18 O2 beam velocity is 800 m s−1 . The shaded region indicates the range of laboratory angles probed. The radii of each circle represent the maximum recoil velocities of the following products of 16 O(3 P) + 12 C18 O collisions: 12 C18 O (blue solid) + 16 O (blue dashed), 16 O12 C18 O (red solid) + 18 O 2 2 (red dashed), and 18 O16 O (green solid) + 12 C18 O (green dashed). m/z = 48. Three signal corrections were made before data analysis. First, we corrected for beam divergence at Θ = 6◦ – 16◦ . The divergent intensity with the 12 C18 O2 beam turned off was measured by obtaining TOF distributions at m/z = 16 and 32 from Θ = 6◦ – 16◦ . These TOF distributions were then scaled and subtracted from the corresponding experimental TOF distributions at m/z = 16 and 32 that had the 12 C18 O2 beam turned on. Uncertainties in the non-reactive and reactive scattering signals due to collisions of the divergent hyperthermal oxygen could not be quantified, however; they were instead considered in the analysis of the laboratory data, where collisions at crossing angles of 88◦ , 89◦ , 90◦ , 91◦ , and 92◦ were included during forward-convolution fitting. Adding more crossing angles did not affect the forward-convolution fits significantly. Second, we measured that the 12 C18 O2 beam contained 2% 16 O12 C18 O using the instrument’s mass spectrometer. Thus, 2% of the inelastic scattering signal (m/z = 48) at each laboratory angle (Θ = 6◦ – 54◦ ) was subtracted from 124 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 raw m/z = 46 (16 O12 C18 O+ ) TOF distributions to obtain reactive-scattering-only distributions. Last, the hyperthermal O2 beam contained 0.4% 18 O16 O (at natural isotopic abundances), so 0.4% of the non-reactive scattering signal (m/z = 32) was subtracted from the raw m/z = 34 (18 O16 O+ ) TOF distributions to obtain reactive-scattering-only distributions. 4.4.2 Results 4.4.2.1 Non-reactive scattering of 16 O(3 P) and 12 C18 O2 The experiment mainly observed signals due to 16 O scattered with little deflection from its initial direction; these signals corresponded to the sum of elastic and inelastic scattering collisions of 16 O, which we could not resolve, so they will be referenced collectively as “scattered 16 O.” Five representative laboratory-frame TOF distributions (m/z = 16), the c.m. angular and translational energy distributions and the laboratory-frame angular distribution are shown in Figure 4.7. Scattered 16 O had 85.6 kcal mol−1 total translational energy, or 87% of the available energy (see Figure 4.7B), on average. The experimental translational energy distribution was peaked at ∼97 kcal mol−1 . The c.m. angular distribution for 16 O was highly peaked in the forward direction with little scattered intensity for θc.m. > 20◦ ; however, the velocity and angular range for 16 O product detection in the experiment prevented the detection of backward-scattered 16 O (see Newton diagram in Figure 4.6). Some dependence of the c.m. translational energy distribution on the c.m. angular distribution was observed in the 16 O TOF data; the forward-convolution simulations became increasingly faster than the data at larger laboratory and c.m. angles (e.g, Θ = 20◦ , 30◦ , and 40◦ in Figure 4.7A). We also note that the c.m. angular distribution for scattered 16 O at θ c.m. ∼ 0 ◦ is an extrapolation because of high background from the hyperthermal oxygen source at the small laboratory angles corresponding to small c.m. angles for 16 O. Most of the 16 O probably scatters forward through high-impact-parameter collisions, but the limited constraints on the θc.m. ∼ 0◦ angular distribution (e.g., the laboratory-frame angular distribution, which only probes Θ = 6◦ ) increase the uncertainty in that part of the c.m. angular distribution. This extrapolation had a small effect on the relative product yield measurements (see Section 4.4.2.4), but did not alter the results qualitatively. 125 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.7: Laboratory inelastic scattering data detected at m/z = 16. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for inelastically scattered 16 O products from 16 O + 12 C18 O2 collisions at hEcoll i = 98.8 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). These data indicate that 16 O is scattered mainly in the forward direction with little change in its initial direction or velocity. 126 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 The experiment mainly observed 12 C18 O2 scattered opposite its initial direction in the c.m. frame (see Newton diagram in Figure 4.6). Detected 12 C18 O2 products (m/z = 48) showed best-fit c.m. translational energy distributions that were both broader and lower in energy, on average, than that obtained for forward-scattered 16 O. Furthermore, a single pair of P(ET ) and T(θc.m. ) distributions was not sufficient to describe the m/z = 48 TOF distributions. Consequently, a second pair of P(ET ) and T(θc.m. ) distributions was included in the fit of inelastically scattered 12 C18 O2 ; five representative laboratory-frame TOF distributions, the c.m. angular and translational energy distributions, and the laboratory-frame angular distribution obtained from 12 C18 O2 product detection are shown in Figure 4.8, along with the c.m. velocity-flux diagram in Figure 4.9. The first P(ET ) and T(θc.m. ) pair for inelastically scattered 12 C18 O2 described the scattering at θc.m. < 120◦ . In this region, the angular distribution was peaked near θc.m. = 60◦ , though the probability of scattered products was roughly constant for all θc.m. < 60◦ before decaying steadily at θc.m. > 60◦ . The corresponding translational energy distribution was peaked at ∼39 kcal mol−1 with an average hET i = 40.1 kcal mol−1 , or 41% the available energy. The second P(ET ) and T(θc.m. ) pair for inelastically scattered 12 C18 O2 described the scattering at 60◦ < θc.m. < 125◦ (corresponding to the maximum θc.m. observed in the experiment); this range overlapped, in the sidewaysscattering region, with the first pair. The second T(θc.m. ) distribution increased rapidly from θc.m. = 60◦ peaked near θc.m. = 120◦ . It decayed quickly at θc.m. > 120◦ , although this part of the distribution is uncertain because our experiment did not probe it directly. The translational energy distribution was peaked at 65 kcal mol−1 with an average hET i = 63.8 kcal mol−1 , or 65% the available energy. Mechanistic implications of the additional P(ET ) and T(θc.m. ) distributions will be addressed in Section 4.5. While the forward-convolution laboratory fitting method produced c.m. angular and translational energy distributions that yielded good fits to the data in Figures 4.7 and 4.8, they may not be unique fits to the data because of the temporal and angular width of the incident O(3 P) source beam and the low resolution and SNR in the resulting TOF distributions. Small changes to the c.m. angular and translational energy distributions still produced good fits to the data that were within the uncertainty bounds of the laboratory-frame 127 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.8: Laboratory inelastic scattering data detected at m/z = 48. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for inelastically scattered 12 C18 O2 products from 16 O + 12 C18 O2 collisions at hEcoll i = 98.8 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines (dark blue and cyan) are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). The orange and brown lines correspond to products of 16 O + 12 C18 O collisions, and they are discussed in Appendix 3.A. A single c.m. transla2 2 tional energy and angular distribution for each collision partner was insufficient to describe the TOF distributions of inelastically scattered 12 C18 O2 , suggesting a scattering dependence on impact parameter. 128 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.9: Velocity-flux contour diagram for inelastically scattered 12 C18 O2 from 16 O(3 P) + 12 C18 O collisions in the center-of-mass frame. The white arrows are the 2 initial 16 O(3 P) and 12 C18 O2 velocity vectors, and the dashed white line is the maximum recoil velocity for 12 C18 O2 (vmax ). Only the c.m. angles for which the experiment were sensitive are shown; inelastically scattered 12 C18 O2 from high-impact-parameter collisions are not shown, as their flux would be off-scale. Strong coupling of the P(ET ) and T(θ c.m. ) distributions was observed. angular distribution (see Figures 4.7D and 4.8D), but larger, qualitative changes to the c.m. angular and translational energy distributions did not. Consequently, general statements regarding the scattering direction and degree of energy transfer in the c.m. frame can be made with some certainty. The c.m. angular and translational energy distributions derived from the QCT calculations at Ecoll = 4.5 eV (103.7 kcal mol−1 ) are shown in Figure 4.10 for comparison with the experimental results for scattered 16 O. Center-of-mass angular and translational energy distributions for inelastic scattering obtained from the QCT calculations were in qualitative agreement with the laboratory data, although there are noticeable quantitative disagreements. The theoretical c.m. angular distribution showed fewer scattered products at θc.m. < 20◦ and more scattered products at 40◦ < θc.m. < 90◦ . In addition, the theoretical c.m. translational energy distribution had a sharper peak at high energies and a broader tail at low energies, although the average translational energies were similar (hET i = 85 and 86 kcal mol−1 for B3LYP and BMK, respectively). However, forward convolution of these dis- 129 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.10: Comparison of laboratory and theoretical c.m. (A) angular and (B) translational energy distributions for inelastic scattering of O(3 P) and CO2 at hEcoll i ≈ 100 kcal mol−1 . Distributions obtained from the inelastic scattering of 16 O and from the QCTs are shown here. They were binned (midpoints are shown, connected by spline curves) to provide better statistics for comparison. Both B3LYP and BMK theories show fewer forwardscattered products than were observed in the experiment. Also, the theories predict a translational energy distribution that is more highly peaked at high energies and that has a longer tail at low energies. 130 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 tributions resulted in simulations of the laboratory data that underestimated the proportion of products scattered to low laboratory angles (i.e., Θ = 6◦ , 8◦ , and 10◦ ) and overestimated the low-energy tail in the TOF distributions. Some of this disagreement may be attributable to the ∼14 kcal mol−1 width of the initial collision energy distribution, the inability of the experiment to resolve elastic- from inelastic-scattering contributions to the 16 O signal, and the observed coupling between the c.m. angular and translational energy distributions (see Section 4.5). Still, these laboratory results are consistent with previous studies of hyperthermal O(3 P) scattering from small molecules; a forward-scattering preference and minimal energy transfer was also observed in our earlier studies of D2 , CO, and C2 H6 collisions [Brunsvold et al., 2008; Garton et al., 2006, 2009]. 4.4.2.2 16 O(3 P) + 12 C18 O 2 → 18 O + 16 O12 C18 O As we reported in the preceding chapter, some of the fastest reactively scattered 16 O12 C18 O was attributed to an O-atom exchange reaction between fast-moving 16 O2 and 12 C18 O2 at Ecoll ∼ 160 kcal mol−1 . We describe here the results for the remaining product signal at m/z = 46, which we attribute to the O(3 P) + CO2 isotope exchange reaction. Products of the isotope exchange reaction near 100 kcal mol−1 scattered mainly in the backward direction (θc.m. = 180◦ ), as implied by the five representative laboratory-frame TOF distributions, the c.m. angular and translational energy distributions, and the laboratory-frame angular distribution shown in Figure 4.11. The product c.m. velocity-flux diagram is shown in Figure 4.12. Significant forward and sideways scattering of products was also observed in addition to backward scattering; the T(θc.m. ) distribution indicates that products scattered to 0◦ < θc.m. < 90◦ do so with nearly equal probability, and that scattered products become increasingly more probable as θc.m. approaches 180◦ . On average, the two products had 34.8 kcal mol−1 of total translational energy, or 35% of the available energy (see Figure 4.11B). The peak of the experimental translational energy distribution, P(ET ), was ∼30 kcal mol−1 . These results indicate a significant transfer of translational energy to internal degrees of freedom of the products, which is characteristic of reactions with significant barriers (e.g., ∼25 kcal mol−1 ). 131 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.11: Laboratory reactive scattering data detected at m/z = 46. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for 16 O12 C18 O products of the 16 O(3 P) + 12 C18 O2 → 18 O + 16 O12 C18 O reaction at hEcoll i = 98.8 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. In (A), the best-fit forward-convolution simulations of 16 O12 C18 O products from 16 O(3 P) + 12 C18 O2 collisions (black dot-dashed lines) are shown with those from 16 O2 + 12 C18 O2 collisions at hEcoll i = 158.1 kcal mol−1 (blue dashed lines). The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). 132 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.12: Velocity-flux contour diagram for 16 O12 C18 O products of 16 O(3 P) + 12 C18 O2 collisions in the center-of-mass frame. The white arrows are the initial 16 O(3 P) and 12 C18 O velocity vectors, and the dashed white line is the maximum recoil velocity for 2 16 O12 C18 O (v 16 O12 C18 O products are scattered mainly in the same direction as the max ). initial 12 C18 O2 velocity vector. The theoretical c.m. angular and translational energy distributions derived from the QCT calculations at Ecoll = 4.5 eV (103.7 kcal mol−1 ) are plotted with the experimental data for comparison in Figure 4.13. In general, good agreement between experiments and the theoretical predictions was observed. The experimental best-fit c.m. angular distribution agreed nearly quantitatively for products scattered in the forward direction (small θc.m. ), while only qualitative agreement was found for products scattered in the backward direction (large θc.m. ). The preference for backward-scattered 16 O12 C18 O products suggested by the QCT calculations is also observed in the experimental data. hET i for the experimental P(ET ) is in good agreement, within uncertainty, with those obtained from the B3LYP (hET i = 43 ± 15%) and BMK (hET i = 47 ± 16%) trajectories. Qualitative aspects of the energy transfer during reactive scattering collisions appear to be reproduced in the QCT results, namely, that the product 16 O12 C18 O has a significant amount (≥ 50 kcal mol−1 ) of internal energy, on average. The experimental peak ET , however, is slightly less than the most probable translational energies predicted by the QCT calculations, ∼40 kcal mol−1 . This mild disagreement in the shape of the P(ET ) distribution may arise from uncer- 133 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.13: Comparison of laboratory and theoretical c.m. (A) angular and (B) translational energy distributions for the O(3 P) and CO2 isotope exchange reaction at hEcoll i ≈ 100 kcal mol−1 . Distributions obtained from the inelastic scattering of 16 O and from the QCTs are shown here. They were binned (midpoints are shown, connected by spline curves) to provide better statistics for comparison. Both B3LYP and BMK theories predict fewer backward-scattered products than were observed in the experiment. Also, the theories predict a translational energy distribution that is peaked at slightly higher energies. 134 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 tainties in the experiment and in the forward-convolution analysis. First, the broad O(3 P) velocity distribution in the experiment, and the resulting broad collision energy distribution, could mask any underlying structure in the P(ET ) distribution if the location of the peak in the P(ET ) distribution depends on collision energy. Indeed, the theoretical excitation functions indicate that the reaction cross-section is sensitive to collision energy in near Ecoll = 100 kcal mol−1 (see Figure 4.4). Second, the presence of the O2 + CO2 isotope exchange channel, which was not resolved from the forward-scattered 16 O12 C18 O peak in the laboratory TOF, renders the higher-ET portion of the P(ET ) less certain. Constraints from the backward-scattered component of the laboratory TOF distributions were also limited due to the t −3 dependence of the scattered product intensity in the laboratory-to-c.m.frame Jacobian transformation (see Eq. 3.3), which reduces the instrument’s sensitivity to backward-scattered products. Consequently, the angular distribution of products near θc.m. = 180◦ is less certain, and the observed disagreement between experimental and theoretical c.m. angular and translational distributions could be refined with additional measurements. Last, some uncertainty in the average and peak of the product translational energy distribution in the QCT data arises from the binning process used to obtain better statistics in the distribution; the width of each ET bin was ∼11.5 kcal mol−1 , so disagreements in the P(ET ) peak locations between theory and experiment on the order of 10 kcal mol−1 are not unreasonable. 4.4.2.3 16 O(3 P) + 12 C18 O 2 → 18 O16 O + 12 C18 O Reactively scattered products at m/z = 34 were clearly resolved at Θ = 6◦ , barely detectable at Θ = 10◦ , and not detectable at Θ = 14◦ (see Figure 4.14). While this laboratoryframe angular dependence may imply that 18 O16 O products are mainly forward-scattered, we cannot rule out backward scattering because the experiment was not sensitive to it (see Newton diagram in Figure 4.6); the signal corresponding to the counterproducts at m/z = 30 (12 C18 O+ ) could not be resolved because of high background signal from 12 C18 O2 fragmentation at the ionizer. We obtained a c.m. translational distribution peaked at 56 kcal mol−1 from the laboratory data, which indicated that 18 O16 O + 12 C18 O products had 55.0 135 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.14: Laboratory reactive scattering data detected at m/z = 34. (A) Laboratory TOF, (B) c.m. translational energy, and (C) laboratory angular distributions for 18 O16 O products of the 16 O(3 P) + 12 C18 O2 → 18 O16 O + 12 C18 O reaction at hEcoll i = 98.8 kcal mol−1 . The circles in (A) and (C) are experimental data, while the lines are the best-fit forwardconvolution simulations of the experimental data derived from the c.m. translational energy distribution shown in (B). Experimental sensitivity was not sufficient to obtain a full c.m. angular distribution, so a T(θc.m. ) distribution is not shown. The error bars in (C) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). kcal mol−1 translational energy, or 61% of the available energy, on average. No products were detected at m/z = 36 (18 O2 + ), which would have corresponded to an oxygen-atom abstraction mechanism more complex than simple stripping. Qualitatively, these results are consistent with the QCT results, which predicted a lower reactive cross-section for the oxygen abstraction channel than for the isotope exchange channel. 4.4.2.4 Relative product yields Experimental relative product yields for 16 O(3 P) + 12 C18 O2 collisions at hEcoll i = 98.8 kcal mol−1 were calculated from the integrated cross-sections for each channel, which were obtained from the forward-convolution simulations of the TOF data. Because the signal at m/z = 46 contained contributions from both 16 O(3 P) + 12 C18 O2 and 16 O2 + 12 C18 O2 collisions, 136 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Table 4.3: Comparison of experimental and theoretical yields for the products of O(3 P) + CO2 collisions near 100 kcal mol−1∗ Experiment B3LYP/6-311G(d) BMK/6-311G(d) Non-reactive scattering Oxygen isotope exchange 98.4% 98.2% 98.1% 1.6% 1.8% 1.9% ∗ Uncertainty bounds in the experimental estimates are probably less than ± 0.25%, based on the uncertainties in the integrated count rates at m/z = 46. Uncertainties in the QCT-derived relative yields are less than ± 0.1%. the forward-convolution fits for 16 O2 + 12 C18 O2 isotope exchange were subtracted from the laboratory TOF data before the 16 O(3 P) + 12 C18 O2 cross-section was calculated. Resulting integrated cross-sections were scaled by their electron-impact ionization cross-sections and fragmentation patterns for the comparison; the transmission through the quadrupole mass filter was assumed to be similar for all the small molecules examined here. Using this method, we calculated branching fractions for non-reactive scattering (98.5%), oxygenatom abstraction (0.0004%), and oxygen isotope exchange (1.6%) based on the integrated cross-sections obtained at m/z = 16, 34, and 46, respectively. The oxygen-atom abstraction yield is a lower limit because only a portion of the Newton sphere was observed. The oxygen isotope exchange yield is an upper limit because we compared the integrated cross-section of 16 O12 C18 O products to the yield of scattered 16 O only; the strongly coupled P(ET ) and T(θc.m. ) distributions for inelastic scattering make momentum-matching of 16 O and 12 C18 O2 products difficult. Our experimental branching fractions for the isotope exchange reaction at hEcoll i = 98.8 kcal mol−1 and those calculated from the QCT calculations at Ecoll = 4.5 eV (103.7 kcal mol−1 ) agree within 0.3%, despite a difference of 5 kcal mol−1 in the collision energy (see Table 4.3). This agreement could be coincidental because both the theoretical and laboratory data have significant uncertainties when defining the total cross-section, but our analysis suggests that the agreement persists in spite of these uncertainties. First, Eq. 4.4 shows that the theoretical calculation for the total cross-section depends on the square of maximum impact parameter sampled for reactive scattering (bmax ), but examination of the theoretical opacity function for the oxygen isotope exchange reaction (Figure 4.5) indicates 137 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 that no reactions occur beyond b = 3.5 a0 , so the reactive cross-section should be sufficiently converged with a bmax = 5.0 a0 . Second, the accuracy of the laboratory integrated cross-sections depends on the accuracy of the best-fit c.m. angular and translational energy distributions, but our sensitivity study on the θc.m. → 0◦ extrapolation we used for scattered 16 O resulted in the non-reactive scattering and oxygen isotope-exchange branching fractions fluctuating ∼0.5% when the scattered intensity at θc.m. < 4◦ was varied between twice the best-fit value and zero. Third, the oxygen-atom abstraction reaction contributes to the overall reactive cross-section, but this channel had a negligible contribution to the overall product yield based on the small number of reactive trajectories observed in the QCT calculations and the small amount of 18 O16 O detected in the experiment. Consequently, the agreement between the theoretically derived and experimental relative product yields for the oxygen isotope exchange reaction should be robust. The theoretical reactive cross-sections (Eq. 4.4) were divided by three for the comparison with experiment because the O(3 P) + CO2 surface is triply degenerate at large O(3 P)–CO2 separation distances;. All three electronic states were probed by the experiment, but only one (3 A00 ) was probed in the QCT calculations. Whether the two additional states (e.g., 3 A0 ) lead to reaction under our experimental conditions is unknown, but the good agreement between theory and experiment is consistent with the other two electronic surfaces being either repulsive or unimportant for producing 16 O12 C18 O at these collision energies. If the barrier to isotope exchange on the 3 A0 surface is close to the one the 3 A00 surface, isotope exchange on the 3 A0 surface could also contribute to the experimental product yield; the current theoretical product yield, therefore, should be treated as a lower limit when compared to the experimental value. Degenerate triplet states were also a concern in our study of O(3 P) + C2 H6 collisions, but the laboratory relative product yields there also agreed, within uncertainty, with those derived from QCT calculations [Garton et al., 2009]. 138 L. Y. Yeung Oxygen isotope exchange reactions of CO2 4.5 Discussion 4.5.1 Theoretical studies Chapter 4 Our electronic structure calculations yielded some disagreements with previous work [Bennett et al., 2004; Froese and Goddard, 1993; Mebel et al., 2004; Yang et al., 2005]. First, we reported a geometry and energy for TS1 structure that was significantly different from that predicted by Mebel and coworkers calculated at the CASSCF(16,13)/6-311G(d) level of theory (see Figure 4.2) [Bennett et al., 2004; Mebel et al., 2004]. For example, in Mebel et al.’s 3 A0 TS1 structure, the longest C–O bond was 0.08 Å shorter, the shortest C–O bond was ∼0.02 Å longer, and the most acute bond angle was 17◦ smaller than in our CCSD(T)/aug-cc-pVTZ structure. Interestingly, our 3 A00 TS1 structure shows smaller disagreements with the 3 A0 TS1 structures calculated by Froese and Goddard at the HF/6-31G* and MP2/6-31G* levels of theory. These differences in geometries and the difference in symmetry yielded a TS1 energy 11 kcal mol−1 higher in Mebel et al.’s CCSD(T)/6-311+G(3df) calculation than in our calculation. Mebel et al. did note that their truncated (16,13) active space was a clear shortcoming of their study; it was chosen over the full-valence (22,16) active space due to computational limitations. Second, our calculations indicated that the lowest-energy triplet PES near TS1 had 3 A00 symmetry, not 3 A0 symmetry, as others had reported [Bennett et al., 2004; Froese and Goddard, 1993; Mebel et al., 2004]. We examined this discrepancy first by calculating the single-point CCSD(T)/aug-cc-pVTZ energy of Froese and Goddard’s “T9” structure at both orbital symmetries. In this case, the 3 A0 energy was ∼10 kcal mol−1 above the 3 A00 energy. We also attempted to optimize a TS1-like 3 A0 structure at the CCSD(T)/aug-cc-pVTZ and W4 levels of theory, but we found self-consistent field convergence problems similar to those reported by Froese and Goddard and thus could not locate any stationary points. The 3 A00 state of CO3 near TS1, then, appears to be lower in energy than the 3 A0 state. We argue that these discrepancies were caused by the differing treatment of dynamical correlation in this study and others. The electronic structure of ground singlet CO3 displays vibronic coupling with an array of Jahn-Teller states [Kowalczyk and Krylov, 2007; Liu et al., 139 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 2009], and the resulting energy minima required a high level of dynamical correlation to represent correctly; because of the large number of electronic states within several eV of the lowest triplet PES, vibronic coupling (and therefore dynamical correlation) is likely important here as well. Multiconfigurational self-consistent field methods like CASSCF (used by Mebel et al. for geometry optimizations) do not treat dynamical correlation, and this shortcoming has been implicated in the poor representation of the singlet-CO3 , NO3 , and parabenzyne radicals with these methods [Crawford et al., 2001; Eisfeld and Morokuma, 2000; Kowalczyk and Krylov, 2007]. High-level dynamical correlation is included in coupledcluster methods, which generally yield more accurate thermochemical properties for this class of problems. Furthermore, the agreement between our TS1, TS2, and CO3 energies and those calculated using the W4 method (J. M. L. Martin, private communication) suggest that single-reference calculations with high-level treatment of dynamical correlation can describe the triplet stationary points appropriately. Multi-reference character on other regions of the PES could still be important, however, and is not ruled out by the correspondence between the CCSD(T) and W4 calculations at the stationary points. If strong vibronic coupling on the low-lying electronic states of CO3 is important during reactive trajectories, it could lead to a misrepresentation of the PES curvature by the B3LYP and BMK methods during the QCT calculations. Russ et al. [2004] noted that B3LYP underestimated the magnitude of vibronic interactions in the B–N–B and C3 + model systems, and attributed this tendency to the behavior of the Kohm-Sham molecular orbital Hessian near conical intersections. Because the Kohm-Sham Hessian is common to both B3LYP and BMK theories, both functionals are subject to the same tendency. Large fractions of Hartree-Fock exchange mixed into the BMK functional for improved barrier height prediction may also result in unintended symmetry-breaking on the CO3 PES [Sherrill et al., 1999], as was the case for the CO3 minimum (see Figure 4.2). The results of these calculations are compared with the experimental results below. 140 L. Y. Yeung 4.5.2 Oxygen isotope exchange reactions of CO2 Chapter 4 Non-reactive scattering of O(3 P) and CO2 Non-reactive 16 O(3 P) + 12 C18 O2 collisions mainly scattered products with little change in the initial direction or speed, although some products scattered in directions sideways and opposite their initial direction; these products had lower average velocities. Products showing little deflection from their initial trajectories probably arise from high-impactparameter collisions, while products that are highly deflected probably arise from lowimpact-parameter collisions. These two molecular regimes were supported qualitatively by the theoretical opacity functions (see Figure 4.5), which display separate peaks at low (1.75 a0 ) and high (3.25 a0 ) impact parameters. While large impulsive energy transfer was observed for hyperthermal collisions of Ar and O(3 P) with C2 H6 at low impact parameters [Brunsvold et al., 2004; Garton et al., 2009; Tasic et al., 2007], large energy transfer was also observed for “failed” reactive collisions of hyperthermal O(3 P) and CO; the CO2 * complex resulting from these collisions can dissociate to yield products corresponding to isotope exchange or inelastic scattering, depending on the identity of the dissociating oxygen atom. This mechanism resulted in a low-energy tail in the translational energy distribution for inelastic scattering of O(3 P) + CO [Brunsvold et al., 2008]. Our analysis of inelastically scattered 12 C18 O2 molecules indicated that one pair of P(ET ) and T(θc.m. ) distributions was insufficient to simulate the laboratory data accurately. This observation corresponds to a breakdown of the assumption that the c.m. angular and translational energy distributions are separable. Our use of two pairs of P(ET ) and T(θc.m. ) distributions to fit the laboratory data is similar to previous studies where inelastic scattering of Cl + C3 H8 and hyperthermal O(3 P) + C2 H6 were investigated [Blank et al., 1998; Garton et al., 2009]. In both the previous cases and in the present case, the polyatomic species had a large number of degrees of freedom into which translational energy can be transferred upon collision. Consequently, a dependence of energy transfer on the impact parameter is not unexpected; different impact parameters may preferentially excite different degrees of freedom. In the system studied here, the product translational energy decreases as 12 C18 O2 becomes more forward-scattered (small Θ, corresponding to low-impact-parameter collisions), implying that 12 C18 O2 becomes increasingly internally excited as O–CO2 collisions 141 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 become more rebound-like. The type and mechanism of internal excitation are uncertain, however, because the “failed” reaction might also contribute to the observed c.m. angular and translational energy distributions of forward-scattered 12 C18 O2 . We note that our experimental data did not display a slow tail in the 16 O TOF distributions characteristic of the “failed” reaction in the O(3 P) + CO system. 4.5.3 Oxygen isotope exchange, O(3 P) + CO2 → O + CO2 Laboratory data for the isotope exchange reaction at hEcoll i = 98.8 kcal mol−1 shows a backward-scattering preference, and thus is evidence for a direct reaction mechanism. The isotopically exchanged products also had relatively low translational energy (hET i = 35% Eavail ). These two observations suggest that the reaction involves a short-lived CO3 ∗ intermediate and/or occurs at low impact parameters where the transfer of energy to internal degrees of freedom of the products is efficient. With 74 kcal mol−1 excess energy, the O(3 P)–CO2 collision need not be head-on to have enough energy to surmount the TS1 activation barrier. The long C–O bond length (1.6 Å) and mild O–C–O bending angle (150◦ vs. 180◦ for CO2 ) in TS1 also suggests that the entrance and exit barriers are neither particularly early nor late. Hence, the CO3 ∗ complex could exist for several vibrational periods. Efficient transfer of energy into vibrational modes of the CO3 ∗ intermediate would be required for an isotope exchange event to occur because inefficient coupling of that energy would increase the probability of redissociating the incident oxygen atom, resulting in an inelastic collision. A direct isotope exchange mechanism through a short-lived CO3 complex is qualitatively in agreement with our QCT calculations (see Figure 4.15). For O(3 P) + CO2 collisions Figure 4.15: Snapshots of a quasiclassical trajectory for O(3 P) + CO2 isotope exchange through a short-lived CO3 ∗ complex at 1.5 eV (34.6 kcal mol−1 ) collision energy. The incident oxygen atom is highlighted for clarity. 142 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 resulting in oxygen isotope exchange, a CO3 ∗ complex forms when the incoming oxygen atom interacts with the carbon atom on CO2 (see also the opacity functions in Figure 4.5). In some cases, the CO3 ∗ complex existed for less than one vibrational period (the reaction is nearly direct) while in others it existed for many vibrational periods. After some time (typically leq 200 fs), one of the oxygen atoms initially part of the CO2 detaches to leave behind a new CO2 molecule. Head-on collisions at higher collision energies tended to form complexes existing for shorter times than those formed similarly at lower energies. Higher energies also tended to form CO3 ∗ complexes that tumbled ≥ 360◦ in the plane of the reaction. In all cases, however, the CO3 ∗ complex lasted less than a picosecond. These data support an isotope exchange reaction mechanism that begins with an interaction between O(3 P) and the carbon atom of CO2 to form a short-lived CO3 ∗ reaction complex. The identity of the dissociating oxygen atom determines the reaction’s classification. If the dissociating oxygen atom is one originally on CO2 , then the trajectory is reactive; if it is the incident oxygen atom, then the trajectory is inelastic. The lifetime of the CO3 reaction complex determines the c.m. angular and translational energy distributions of product CO2 . Longer-lived CO3 complexes should yield smaller average translational energies because they will have more time to redistribute the initial translational energy to internal degrees of freedom. This mechanism for the O(3 P) + CO2 isotope exchange reaction is different from that observed by Perri et al. for the O(1 D) + CO2 → O(3 P) + CO2 isotope exchange reaction at Ecoll = 4.2 and 7.7 kcal mol−1 , which samples part of the same PES [Perri et al., 2003, 2004]. In those molecular-beam experiments, the reactively scattered CO2 products had an isotropic (forward-backward symmetric) angular distribution and ∼50% of the available energy in translation; these results were evidence for a CO3 ∗ intermediate complex that lasted for at least several rotational periods (> 1 ps). These dynamics are not inconsistent with our O(3 P) + CO2 results, however, because the two studies may sample different parts of the 3 A00 and/or 3 A0 PESs. O(3 P) + CO2 collisions on the 3 A0 surface could, in principle, cross onto the 1 A0 surface to yield reactively scattered O(1 D) + CO2 products. One possible triplet-singlet crossing mech- 143 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 anism could be through spin-orbit coupled radiationless transitions, i.e., the reverse of what Mebel et al. had suggested for the O(1 D) + CO2 reaction, because the spin-orbit coupling terms and Franck-Condon factors are favorable [Mebel et al., 2004]. Thus, we evaluated the general possibility of intersystem crossing (ISC) during our experiments by performing forward-convolution fits of the laboratory data that included the ∼45 kcal mol−1 endothermicity of O(1 D) vs. O(3 P). Satisfactory fits of the laboratory TOF and angular distributions were obtained (see Figure 4.16); the peak and average of the P(ET ) distribution were 34 and 30.7 kcal mol−1 (63% and 58% Eavail ), respectively. Consequently, ISC cannot be explicitly ruled out by the experimental data. The diabatic radiationless transition probability, however, decreases exponentially as a function of velocity [Landau, 1932], and no evidence for ISC has been observed during our previous dynamics studies at hyperthermal velocities [Brunsvold et al., 2007]. The qualitative agreement between the experimental and QCTderived dynamics on the lowest triplet PES is consistent with the oxygen isotope exchange reaction exiting on a triplet surface, although more dynamics studies will be necessary to test this hypothesis. 4.5.4 Oxygen-atom abstraction, O(3 P) + CO2 → O2 + CO Our laboratory observation of the oxygen abstraction reaction in the forward direction with a moderate amount of energy transfer (∼50%) could arise from early-barrier strippingtype mechanisms through TS2 or TS3. Hammond’s postulate states that for endothermic reactions, the transition state should be late and product-like. However, the small endothermicity relative to the barrier height (see Figure 4.1 and Table 4.1) for oxygen-atom abstraction suggests that TS2 and TS3 should be more reactant-like. Indeed, the bond lengths of CO and O2 are significantly longer in TS2 and TS3 than at equilibrium for the isolated molecules, which are 1.14 and 1.21 Å, respectively, at CCSD(T)/aug-cc-pVTZ. Theoretical trajectories yielding O2 + CO products occurred generally in one of two ways: through a stripping-type mechanism and through a CO3 ∗ complex. In the strippingtype mechanism (see Figure 4.17A), the incoming oxygen atom interacts principally with one of the oxygen atoms on CO2 to form TS3 directly. The C–O bond then breaks, releas- 144 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.16: Laboratory reactive scattering data detected at m/z = 46, fit assuming an ISC mechanism. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for 16 O12 C18 O products of the 16 O(3 P) + 12 C18 O2 → 18 O16 O(1 D) + 12 C18 O reaction at hE −1 coll i = 98.8 kcal mol . The circles in (A) and (D) are experimental data, while the lines are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. In (A), the best-fit forward-convolution simulations of 16 O12 C18 O products from 16 O(3 P) + 12 C18 O collisions (black dot-dashed lines) are shown 2 with those from 16 O2 + 12 C18 O2 collisions at hEcoll i = 158.1 kcal mol−1 (blue dashed lines). The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). 145 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.17: Snapshots of quasiclassical trajectories for the O(3 P) + CO2 → O2 + CO reaction. (A) A stripping-type mechanism through TS3 at 6.5 eV (149.8 kcal mol−1 ) collision energy calculated at the B3LYP/6-311G(d) level of theory. (B) A CO3 reaction-complex mechanism through TS2 at 5.5 eV (126.7 kcal mol−1 ) collision energy calculated at the BMK/6-311G(d) level of theory. The incident oxygen atoms are highlighted for clarity. ing O2 + CO products. Of all the QCTs run, only two of these stripping-type trajectories were observed, and they occurred at Ecoll = 6.5 eV (149.8 kcal mol−1 ) using B3LYP/6311G(d). The remaining 27 O2 + CO-producing trajectories proceeded through a CO3 ∗ complex mechanism (see Figure 4.17B). In that mechanism, the incoming oxygen atom interacts first with the carbon atom of CO2 to form a short-lived CO3 ∗ complex, similar to that observed in the isotope-exchange trajectories. This complex rarely survived more than one vibrational period. An oxygen atom is then released and then interacts with a CO2 bound oxygen atom as the CO2 rotates. Last, an O–O bond forms as the adjacent C–O bond breaks to form O2 + CO products. A key difference between the two O2 + CO-producing mechanisms is that the CO3 ∗ complex mechanism requires a slow recoil of the oxygen atom that dissociated initially. Following complex formation in a high-energy collision, the nascent CO2 will have sufficient internal energy (∼70 kcal mol−1 ) to form the O2 + CO products only if the O atom dissociates with low translational energy. When the O atom escapes the CO3 ∗ complex with high translational energy, the nascent CO2 rotates too slowly for any further reaction to take place (in these cases, the trajectory results in either inelastic scattering or isotope 146 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 exchange). With so much excess energy, however, the reaction need not take the lowest energy path [Zhang et al., 2008]; the slow recoiling oxygen atom in the CO3 ∗ -complex mechanism resembles the “roaming’ H-atom and methyl group in formaldehyde [Townsend et al., 2004] and acetaldehyde [Houston and Kable, 2006] photodissociation, respectively. We note that the stripping-type mechanism would have produced 18 O16 O molecules in the experiment exclusively, whereas the CO3 ∗ -complex mechanism can produce 18 O2 in addition to 18 O16 O. Our laboratory observation of m/z = 34 products is consistent with both oxygen abstraction mechanisms, but the lack of signal due to m/z = 36 products in the forward direction (where there was negligible background) is evidence against the CO3 ∗ complex mechanism. The CO3 ∗ -complex mechanism, however, comprised 27 of the 29 oxygen-atom abstraction trajectories obtained from the QCT calculations, and only one of those trajectories would have produced m/z = 34 products. The two remaining trajectories proceeded through the stripping mechanism. This preference for the CO3 ∗ -complex mechanism observed in the QCT calculations may be a consequence of the ∼50 kcal mol−1 lower barrier for CO3 formation and the ∼13 kcal mol−1 lower energy of TS2, both relative to the energy of TS3. Additional experimental and theoretical studies with a higher SNR, perhaps at higher collision energies, will be required to elucidate the mechanisms of this reaction. 4.6 Conclusions We have investigated the dynamics of O(3 P) + CO2 collisions at hyperthermal collision energies. Non-reactive scattering was dominated by high-impact-parameter collisions, which did not perturb the initial velocity of the reactants significantly. Lower impact parameters resulted in increased translational-to-internal energy transfer. Both the oxygen isotope-exchange and the atom-abstraction reaction channels were observed directly by our crossed-molecular-beam apparatus. The oxygen isotope exchange reaction displayed an anisotropic angular distribution with a large amount of translational-to-internal energy transfer, suggesting that the reaction occurs at low impact parameters through a short-lived intermediate CO3 ∗ complex. The mechanisms for both non-reactive scattering and oxygen isotope exchange were supported qualitatively, but not quantitatively, by the QCT calcula147 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 tions on the 3 A00 surface. Nonadiabaticity during inelastic and reactive trajectories cannot be ruled out and its effects should be investigated; both inelastic and reactive trajectories may be sensitive to the coupling between the lowest triplet (3 A00 ) PES and nearby (e.g., 3 A0 ) electronic surfaces. With ∼100 kcal mol−1 collision energy, the experiment may probe regions of the PES far from the TS1, TS2, TS3, and CO3 structures; the presence of several other surfaces (both triplet and singlet) within this energy range [Kowalczyk and Krylov, 2007; Liu et al., 2009], the possibility of vibronic effects due to Jahn-Teller-like distortion, and the failure of densityfunctional methods to capture the dynamics quantitatively all suggest that a higher-level treatment of the PES would be desirable. While the transition states and stationary points on the lowest triplet PES may be described well with density-functional calculations, this may not be the case in other regions of the PES where vibronic interactions can affect its curvature. A more complete, high-level description of the PES, along with more dynamics experiments, will be required to describe the dynamics of isotope exchange on the lowest triplet PES quantitatively. 4.7 Acknowledgements We thank Ned F. Lindholm for experimental assistance. This work was supported by the Missile Defense Agency under cooperative agreement HQ0006-05-2-0001. L. Y. Y. was supported by the Davidow Fund, and G. C. S. was supported by the Air Force Office of Scientific Research grant FA955D-07-1-0095. 148 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Appendices 149 Chapter 4 L. Y. Yeung 4.A Oxygen isotope exchange reactions of CO2 Chapter 4 Differential scattering cross-sections from 1.0 – 6.5 eV Theoretical center-of-mass differential scattering cross-sections for the oxygen isotope exchange reaction (Figure 4.18) showed a preference for backward scattering at all collision energies. The incident oxygen atom, attached to the product CO2 molecule, appeared to prefer scattering in a direction opposite its initial direction. As the collision energy increased, however, the angular distribution of products showed little qualitative change: Reactively scattered products showed a slight preference for backward scattering up to Ecoll = 6.5 eV (149.8 kcal mol−1 ), the highest collision energy considered in this study. The theoretical c.m. product translational energy distributions showed significant (≥ 50%) transfer of the available energy into internal degrees of freedom of the products at all collision energies = 2.5 eV (57.6 kcal mol−1 ). The QCT data below Ecoll ≥ 2.5 eV did not contain statistically significant number of reactive trajectories, i.e., > 30, so they were not included in this analysis. P(ET ) distributions became broader as the collision energy increased, though the proportion of energy remaining translation was similar at all collision energies. A bimodal distribution of translational energies may exist in the products of BMK trajectories run at 2.5, 3.5, and 4.5 eV collision energy (57.6, 80.7, and 103.7 kcal mol−1 , respectively); for instance, separate peaks were observed at ∼50% and ∼80% of the available energy for the 2.5-eV trajectories, although there is considerable uncertainty in the theoretical translational energy distribution (see Figure 4.18). Additional QCT calculations will be required before structure in the product translational energy distributions can be determined conclusively. 150 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.18: Center-of-mass angular and translational energy distributions for the O(3 P) + CO2 isotope exchange reaction derived from QCT calculations at the (A and B) B3LYP/6-311G(d) and (C and D) BMK/6-311G(d) levels of theory. Distributions with more than 30 reactive trajectories are shown. At both levels of theory and all collision energies shown, reactive scattering shows a preference for backward scattering (θc.m. > 90◦ ) with a moderate (≥ 50%) transfer of translational energy to internal degrees of freedom of the products. 151 L. Y. Yeung 4.B Oxygen isotope exchange reactions of CO2 Chapter 4 Estimating uncertainty in the laboratory angular distributions For this analysis we treat the TOF distribution at a given laboratory angle Θ as a type of Monte Carlo integration of the ‘true’ TOF distribution, and we estimate the variance in the integrated area accordingly. Under this approximation, the integrated area, I(Θ), is equivalent to the area of a rectangle with a width equal to the total time range, ttotal , and height equal to the average number density over that time range, hN(t)itotal . More formally, this relation can be written as a discrete sum over the channels on the MCP, each of which corresponded to a 1 µs dwell time: ttotal I(Θ) = 1 ttotal ∑ N(ti ) = ttotal [ ttotal ∑ N(ti )] = ttotal hN(t)itotal i=1 (4.8) i=1 The variance of I(Θ), however, must be evaluated as a function of time because the number density at a given arrival time at the detector, N(t), varied with flight time in each TOF distribution. Consequently, the TOF distribution was further divided into a set of bins for which the variance was calculated and summed over the total TOF distribution using the following relation: 2 σN(t) bin = 1 f [tbin N(ti )]2 − [tbin hN(t)ibin ]2 tbin ∑ i 2 σI(Θ) = 2 ∑ σN(t) bin (4.9) (4.10) bins where i and f represent the first and last members of each data bin. The standard deviation, σI(Θ) , was calculated by taking the square root of the variance. We note some degree of sensitivity in the calculated σI(Θ) values on tbin because the N(t) distributions show significant structure; consequently, we have reported conservative estimates of σI(Θ) using the 2 minimum bin size of tbin = 3 µs, or 3 data points per σN(t) bin 152 calculation. L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 5 Chapter 5 Summary and outlook 5.1 New signatures, new reactions Presently, the large enrichment in 16 O13 C18 O we found in the stratospheric polar vortex is still unexplained. The laboratory photochemical experiments we reported in Chapter 2 seem to rule out O(1 D) + CO2 isotope exchange; stratospheric 16 O13 C18 O should get more depleted with increasing extent of isotope exchange, not enriched, and we observed this trend as a decrease in ∆47 in field samples from the mid-latitude stratosphere. What, then, could enrich 16 O13 C18 O in the polar vortex, and what might we be able to learn from future studies? We suggested in Chapter 2 that fast low-temperature isotopic equilibration of CO2 on stratospheric particles (e.g., PSCs) could be responsible for the high ∆47 values in the polar vortex. Our initial tests of the PSC-isotope-equilibration hypothesis suggested that isotopic equilibration on certain HNO3 ices and H2 SO4 :HNO3 :H2 O mixtures is slow, and is therefore unlikely to produce 16 O13 C18 O enrichments on timescales that would be consistent with our polar vortex data. The CO2 isotopic equilibration rate, however, could be sensitive to particle structure and composition. PSCs and cirrus clouds form under similar conditions, but they can differ in bulk and surface composition [Zondlo et al., 2000]; the structure, physics, and chemistry of these particles are still not understood [Dash et al., 2006; Lowe and MacKenzie, 2008], so the role of CO2 isotopic equilibration on ice particle surfaces remains uncertain. Future laboratory work on CO2 –ice surface interactions may shed light on the structure and composition of these and other atmospherically important particles. 153 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 5 We also identified three new reactions, O2 + CO2 and O(3 P) + CO2 isotope exchange and O(3 P) + CO2 → O2 + CO, in our crossed-molecular-beam experiments. Because of the ≈160 kcal mol−1 reaction barrier for O2 + CO2 isotope exchange, and the ≈75 kcal mol−1 barrier for O(3 P) + CO2 → O2 + CO, they are unlikely to be important in the stratosphere. O(3 P) + CO2 , in contrast, has a reaction barrier (≈ 25 kcal mol−1 ) that is atmospherically accessible, in principle. 5.2 Potential atmospheric importance of O(3 P) + CO2 The laboratory observation of O(3 P) + CO2 isotope exchange at hyperthermal energies may have implications for modeling the oxygen isotope cycling in the middle and upper atmosphere because current models do not include O(3 P) + CO2 reactions explicitly [Liang et al., 2007, 2008; Thiemens et al., 1995; Yung et al., 1991, 1997]. Here, I suggest that O(3 P) + CO2 reactions in the upper atmosphere could affect the oxygen isotope distribution in CO2 . The O(3 P) + CO2 isotope exchange reaction could yield isotope effects qualitatively different from those in the O(1 D) + CO2 reaction because its mechanism is direct, unlike the mechanism involving a long-lived CO3 ∗ intermediate for the O(1 D) + CO2 reaction [Chen et al., 2009; Perri et al., 2003, 2004]. Instead, like the O3 ∗ complex in the O(3 P) + O2 isotope exchange reaction [Van Wyngarden et al., 2007], the CO3 ∗ reaction complex formed from O(3 P) + CO2 does not live long enough for its energy to randomize; thus, dynamical isotope effects are likely to be important to its isotope-specific branching fractions. These types of non-statistical isotope effects are believed to be partly responsible for “anomalous” formation rates of stable O3 from the O3 ∗ complex for different isotopologues [Babikov et al., 2003; Gao and Marcus, 2001; Schinke et al., 2006]. Due to limitations in our apparatus, however, we were unable to investigate the O(3 P) + CO2 isotope exchange dynamics near the predicted reaction threshold, which is more relevant to the atmosphere. Our reactive trajectories at Ecoll = 1.0 and 1.5 eV (23.0 and 34.6 kcal mol−1 , respectively), however, suggest that isotope exchange is still direct near the calculated reaction barrier. The overall importance of the O(3 P) + CO2 isotope exchange reaction to reactive oxygen cycling in the atmosphere, however, depends on (1) the reaction’s excitation function 154 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 5 and (2) the proportion of O(3 P) in the atmosphere with sufficient translational energy to surmount the reaction barrier. In the absence of experimental data, high-level variational quantum calculations can assign an upper limit to the TS1 barrier. The CCSD(T)/aug-ccpVTZ energy for TS1 (25 kcal mol−1 ) reported in this work implies that relative velocities of ≥ 3 km s−1 in the ground-state reactants will be required to open the isotope exchange channel; ozone photolysis in the Hartley band (220 – 310 nm) and at shorter wavelengths yields O(3 P) + O2 (3 Σ− g ) photofragments having a total translational energy in excess of 25 kcal mol−1 and as high as 100 kcal mol−1 [Fairchild et al., 1978; Kinugawa et al., 1990; Shamsuddin et al., 1994; Stranges et al., 1995; Syage, 1995; Takahashi et al., 1998]. Our preliminary hard-sphere collision modeling (see Appendix 2.D) using cross-sections for the velocity relaxation of O(1 D) by N2 [Matsumi and Chowdhury, 1996; Matsumi et al., 1994b] suggests that the size of the reactive O(3 P) reservoir could be as high as several percent that of O(1 D). Future theoretical and experimental studies can elucidate the shape of the reaction’s excitation function, which is needed before an appropriate simulation can be constructed. Finally, we note that during our laboratory study of the O2 /O3 /CO2 photochemical system using a mercury lamp as an actinic light source (185 and 254 nm), we observed deviations from modeled results at long irradiation times (t ∼ days; see Figure 2.8); a minor O(3 P) + CO2 channel could address part of this discrepancy, as well as some of the disagreements between earlier studies [Chakraborty and Bhattacharya, 2003; Johnston et al., 2000; Shaheen et al., 2007; Wen and Thiemens, 1993]. The yield of hyperthermal O(3 P) during O3 photolysis depends on wavelength [Stranges et al., 1995; Takahashi et al., 1998], however, so this hypothesis awaits further testing with systematic studies of the O2 /O3 /CO2 photochemical system. Claims of hyperthermal O(3 P) + CO2 chemistry in the atmosphere based on laboratory data must be met with some skepticism, however. Both N2 and O2 are efficient energy quenchers for even the most reactive atmospheric species, and the steady-state population of fast-moving O(3 P) will be determined largely by its translational relaxation rate in air. In addition, thermal averaging collapses most reaction rates towards the chemical kinetic limit, so any atmospheric signature of the O(3 P) + CO2 reaction will be difficult to identify 155 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 5 unless the associated isotope effect is large and unique. Previously published reports of hyperthermal chemistry in the atmosphere based only on laboratory evidence have been controversial due to the lack of an unequivocal signature in the field data [Li et al., 2008; Miller et al., 1994]. 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Over the past half-century, atmospheric CO2 concentrations have increased at a rate that correlates with the increase in anthropogenic fossil fuel burning and deforestation [Solomon et al., 2007]. Carbon budget inventories indicate, however, that not all of the CO2 released into the atmosphere from these activities persists in the atmosphere; approximately half of the anthropogenic CO2 flux is sequestered in the oceanic and land biospheres [Ciais et al., 1995]. Modeling the fate of anthropogenic CO2 becomes a considerable technical challenge because of myriad interactions between the atmosphere, the oceans, and the terrestrial biosphere. Our ability to predict future changes in the carbon cycle and their effects on global climate relies on our quantitative understanding of these interactions. The first step towards understanding these interactions is learning how to differentiate between atmospheric CO2 molecules derived from various sources and sinks, so we can eventually de-convolve atmospheric observations into their individual components and describe the workings of the global budget through those observations. This task is more complex than it might at first seem because the atmosphere mixes efficiently over the atmospheric lifetime of CO2 ; thus each parcel of air contains CO2 molecules with many different origins and fates (see Figure 1.1). We find some of the needed constraints for these interactions in the variations of naturally occurring stable isotopes. 1 L. Y. Yeung 1.2 Oxygen isotope exchange reactions of CO2 Chapter 1 Stable isotopes, ‘clumped’ and otherwise The stable isotope composition of CO2 (i.e., the relative abundances of those isotopes that do not decay radioactively: 12 C, 13 C, 16 O, 17 O and 18 O) varies according to its sources and subsequent atmospheric chemistry and transport. Physical, chemical kinetic, and equilibrium isotope effects act together to determine the stable isotope composition of CO2 in a given parcel of air. Differences in mass and symmetry of the twelve distinct CO2 isotopologues (isotopic variants, e.g., 12 C16 O2 , 13 C16 O2 , 16 O12 C18 O, 16 O13 C17 O, etc.) formed from the five stable isotopes lead to subtle, but measurable differences in the rate of chemical transformations such as photosynthesis, respiration, air-sea exchange, or photochemical reactions. In principle, measuring the stable isotope distribution in CO2 could lead to an exceptionally detailed analysis of the ‘history’ of CO2 in every sample of the atmosphere, as each natural process imparts its own unique isotopic signature; however, only four of these twelve isotopologues (12 C16 O2 , 13 C16 O2 , 16 O12 C17 O, and 16 O12 C18 O) have been used extensively as tracers in atmospheric chemistry. By themselves, they are insufficient to constrain the relative influences of all the sources and sinks that have acted on a single sample. The remaining eight species (all of which contain two or three heavy rare isotopes) are exceptionally rare and, until recently, were considered to be essentially un-analyzable in natural materials. Measuring these very rare ‘clumped’ isotopologues would add new and essential independent constraints on the origins of CO2 in samples of air. In the laboratory, an equally daunting challenge exists: What are the most important reactions governing the isotopic composition of atmospheric CO2 , and what are the fundamental isotope effects? We wish to know, in the end, if our knowledge of the pertinent atmospheric chemistry is sufficient to explain atmospheric observations. 1.3 Anomalous isotopic enrichments in stratospheric CO2 Shortly after the discovery of ‘mass-independent’ enrichments of 18 O and 17 O in stratospheric ozone [Mauersberger, 1981, 1987] and the demonstration of its chemical origin 2 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 hν O2 λ = 121.6 nm O(1D) hν hν CO CO2 hν in vortex Stratopause O3 + hν → O2 + O(1D) CH4 O(1D), OH Cl CO O(1D) hν OH CO2 CO2 O(3P) particles? H2O Tropopause OH VOCs CO etc. OH CO2 clouds leaves CA soils oceans emissions CA Carbonic anhydrase (CA)-assisted Figure 1.1: Schematic of atmospheric CO2 sources and sinks. Photochemical reactions (single-headed arrows), isotope exchange reactions (double-headed arrows), and atmospheric transport (dotted arrows) are shown. Isotopic exchange on stratospheric liquid water and/or acid particles is uncertain, so its double-headed arrow is dashed. 3 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 [Thiemens and Heidenreich, 1983], similar enrichments were observed in stratospheric CO2 (e.g., Figure 1.2) [Alexander et al., 2001; Boering et al., 2004; Gamo et al., 1989; Kawagucci et al., 2008; Lämmerzahl et al., 2002; Thiemens et al., 1991, 1995]. Yung et al. [1991] suggested that photochemical transfer of the heavy-isotope signature (∆17 O) from O3 to CO2 stratospheric CO2 was possible after photolysis of O3 : O3 + hν(λ < 305 nm) → O2 + O(1 D) (1.1) → O2 + O(3 P) (1.2) and then subsequent isotope exchange through reaction 1.3: O(1 D) + CO2 → OCO∗2 → O(3 P) + OCO (1.3) The authors cited the isotope exchange mechanism in Baulch and Breckenridge’s early study of the reaction in which the incident oxygen atom was incorporated into the product CO2 molecule 2/3 of the time [Baulch and Breckenridge, 1966]. While this ‘statistical’ mechanism could explain the stratospheric 18 O and 17 O measurements qualitatively, a quantitative discrepancy remained between the observed and modeled 17 O/16 O vs. 18 O/16 O relationships: 17 O in CO 2 was more enriched than reaction 1.3 and Yung’s model would have predicted. Unfortunately, the isotope effects in O3 formation and photolysis and in the O(1 D) + CO2 isotope exchange reaction (reaction 1.3) were not yet well understood. Tests of the ‘statistical’ isotope exchange hypothesis were first conducted by Wen and Thiemens [1993], who photolyzed a mixture of O3 and CO2 with a mercury lamp at 254 nm. They observed heavy-atom enrichments in CO2 that implied a non-statistical isotope exchange mechanism between O3 and CO2 (i.e., 17 O appeared to be preferentially incorporated into CO2 ), but their result was misleading; the isotopic composition of the incident O(1 D) changed significantly over the course of their experiment due to O(3 P) and O2 recombination. They did not account for these effects and thus were led to a spurious conclusion, as a later study showed [Johnston et al., 2000]. To date, only one of these bulk photochemical experiments has been able to reproduce the relative 17 O-to-18 O enrichments observed in 4 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 Figure 1.2: Bulk oxygen isotope composition of stratospheric CO2 . Departure from ‘mass-dependent’ compositions (∆17 O; see Appendix 1.A) are observed, owing to oxygen isotope exchange with stratospheric O3 through reaction 1.3. the stratosphere [Chakraborty and Bhattacharya, 2003], and those results have been controversial [Shaheen et al., 2007]. Mechanistic insights have been limited because bulk stable isotope analysis is not able to differentiate isotope effects in O3 photolysis and formation from isotope effects in reaction 1.3 unambiguously. Recent theoretical and modeling work on ozone has shed light on the effects of the former [Babikov et al., 2003; Cole and Boering, 2006; Gao and Marcus, 2001, 2002; Gao et al., 2002; Hathorn and Marcus, 1999, 2000; Schinke et al., 2006], but the understanding of the stratospheric CO2 isotopic distribution remains incomplete. The persistence of this field-laboratory disagreement was the primary inspiration for the ‘clumped’ isotope studies of reaction 1.3 described in this dissertation. 1.4 Insights from the physical chemist’s toolbox The techniques of physical chemistry have been invaluable for unraveling features in the complex mechanism of reaction 1.3. CO3 ∗ was believed to play a critical role in the isotope exchange reaction ever since the first experiments of Katakis and Taube [1962]. 5 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 Figure 1.3: Potential energy surface for CO3 (3 A00 ) from Mebel et al. [2004]. Geometries were optimized at the CASSCF(16,13)/6-311G(d) level of theory. Energies were calculated at the MRCI+Q(16,13)/6-311+G(3df) level of theory. Moll et al. [1966] first identified a CO3 molecule spectroscopically upon irradiating CO2 ice with vacuum-UV light. Although their data implied that stable CO3 had C2v symmetry, their experiments with 18 O-labeled CO2 ices indicated that a CO3 (D3h ) species might be important in a reaction between atomic oxygen and CO2 , as was implied by the statistical mechanism of Baulch and Breckenridge [1966]. The O(1 D) + CO2 potential energy surface (PES) calculated by Mebel et al. [2004] is shown in Figure 1.3. On the 1 A1 surface (1 A0 dynamically), the association reaction has an early barrier at 1 kcal mol−1 , which is consistent with its collision-limited reaction rate coefficient (1 × 10−10 cm3 molecule−1 s−1 ) [Sander et al., 2006]. The binding energy of CO3 (1 A1 ) is nearly 50 kcal mol−1 , and two structures (C2v and D3h ) were predicted as bound 6 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 species at the bottom of the potential well. CO3 (C2v ) was detected shortly thereafter in a low-temperature CO2 matrix [Bennett et al., 2004]; the presence of a true CO3 (D3h ) minimum on the PES had been debated (see Kaiser and Mebel [2008]; Kowalczyk and Krylov [2007]; Liu et al. [2009] and references therein), but it was recently detected experimentally in a 10 K CO2 ice bombarded with high-energy electrons [Jamieson et al., 2006]. Intersystem crossing (ISC) from the singlet to the triplet PESs is believed to occur through nonradiative transitions rather than through the minimum of the intersection seam (near the 3 A0 transition state); the product O(3 Pj ) spin-orbit state distribution is consistent with an adiabatic CO3 dissociation [Matsumi et al., 1994a]. The ISC rate was also calculated to be ten times faster through a radiationless transition than through the singlet-triplet crossing seam [Mebel et al., 2004]. Yang et al. [2005] later proposed that a direct quenching mechanism (i.e., not through a CO3 complex) might also be important. Gas-phase studies of reaction 1.3 show evidence for CO3 , though none have detected it directly. Perri et al. [2003, 2004] reported evidence for a long-lived CO3 ∗ reaction complex in their crossed-molecular-beam experiments. This long-lived (1 – 10 ps lifetime) intermediate had been suggested in previous temperature- and pressure-dependent studies [Clerc and Reiffsteck, 1968; DeMore and Dede, 1970; Weissberger et al., 1967], but never directly confirmed; its lifetime was later confirmed to be long enough for nearly statistical intramolecular vibrational redistribution [Chen et al., 2009]. The structure and dynamics of CO3 are not yet completely understood, however. For instance, O(1 D) + CO2 collision energy appears to be important dynamically; Perri et al. [2003, 2004] reported that O(1 D) + CO2 collisions yielded spin-conserving, isotopically exchanged products (1.4): O(1 D) + CO2 → OCO∗2 → O(1 D) + OCO (1.4) Their crossed-molecular-beam experiments were performed at elevated collision energies (4.2 and 7.7 kcal mol−1 ) so the importance of reaction 1.4 to the stratosphere is unknown. Mebel et al.’s companion computation study suggested that reaction 1.4 has a ∼5% branching fraction at stratospheric collision energies, but this prediction has not been tested. Still, Perri et al.’s experimental result casts significant doubt on the applicability of the previous 7 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 bulk photochemical experiments. All the recent studies of the O2 /O3 /CO2 photochemical system used O2 /O3 as a source of O(1 D) with a significant mixing fraction of CO2 , so the O(1 D) atoms reacting with CO2 probably had an elevated average kinetic energy as high as ∼9 kcal mol−1 [Thelen et al., 1995], six times the calculated average in the stratosphere [Kharchenko and Dalgarno, 2004; Takahashi et al., 2002]. 1.5 Executive summary This dissertation describes studies of three oxygen isotope exchange reactions involving CO2 — one well-studied and two we discovered — and their potential implications for oxygen cycling in the upper atmosphere. First, I will describe the meridional (latitudinal) variations of stratospheric 16 O13 C18 O relative to those of 12 C16 O2 , 13 C16 O2 , 16 O12 C18 O, and 16 O12 C17 O; we identified a meridional gradient, with 16 O13 C18 O most enriched at the Arctic polar vortex. Our experimental and modeling study revealed that the variations in 16 O13 C18 O proportions cannot be explained in full by the known stratospheric chemistry af- fecting CO2 . Instead, we propose — because of the localization of a 16 O13 C18 O anomaly in the wintertime pole — that the chemistry either in the mesosphere or on stratospheric particles leads to the newly discovered isotopic enrichments. Second, I will describe crossedmolecular-beam experiments that led to the discovery of the isotope exchange reaction O2 + CO2 . We show that the isotope exchange reaction occurs through a short-lived CO4 intermediate, and that an adiabatic reaction mechanism exists despite a variety of energetically accessible product channels. Third, I will discuss a computational and laboratory dynamics study of hyperthermal collisions between ground-state oxygen-atoms and CO2 . We identified two reactions: oxygen-atom isotope exchange and abstraction. The isotope exchange reaction proceeds through a short-lived CO3 ∗ reaction complex, and it may have implications for the oxygen-isotope budget in the upper atmosphere and/or the stratospheric polar vortex. The oxygen-atom abstraction reaction may proceed through either a ‘stripping’-type mechanism or a CO3 complex, although the data cannot distinguish between the two mechanisms definitively. In the final chapter, I will attempt to synthesize what we have learned from these three studies, and what questions have emerged as a result. 8 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Appendices 9 Chapter 1 L. Y. Yeung 1.A Oxygen isotope exchange reactions of CO2 Chapter 1 Isotopic notation The natural abundance of the rare isotopes that are the focus of this thesis are 1.1% (13 C), 0.02% (18 O), and 0.038% (17 O). Variations in these stable isotope abundances are typically ≤10−3 . Consequently, bulk stable isotope abundances are commonly reported in δ -notation, in units of per mil (‰): δ 13 C = δ 18 O = R13 sample ! − 1 R13 VPDB R18 sample × 1000 (1.5) × 1000 (1.6) ! R18 VSMOW − 1 where Rn is the abundance ratio of a rare isotope or isotopologue of mass n to its most abundant analogue, i.e., R13 = [13 C] [12 C] R18 = [18 O] [16 O] R17 = [17 O] [16 O] (1.7) δ 17 O is defined similarly to δ 18 O in Eq. 1.6. δ 13 C, δ 18 O, and δ 17 O are reported relative to the international standards VPDB (Vienna Pee Dee Belemnite; R13 = 0.0112372) and VSMOW (Vienna Standard Mean Ocean Water; R18 = 0.0020052 and R17 = 0.0003799). These standards were established under the International Atomic Energy Agency, but are otherwise arbitrary. They represent convenient reference points against which all isotopic measurements can be compared. Positive δ -values mean that the sample bulk isotope composition is enriched relative to the standard, and negative δ -values mean that the sample bulk isotope composition is depleted relative to the standard. Within bulk stable isotope geochemistry, a second family of notation has emerged since the discovery of ‘mass-independent’ oxygen isotope fractionation (MIF) in carbonaceous chondrites [Clayton et al., 1973] and during the formation of ozone (O3 ) [Thiemens and Heidenreich, 1983]. The magnitude of MIF in oxygen (∆17 O) is defined in Eq. 1.8: ∆17 O = δ 17 O − 0.516 × δ 18 O 10 (1.8) L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 1 This terminology is used to describe deviations from the canonical mass-dependent isotopic relationships derived by Urey [1947] and Bigeleisen [Bigeleisen and Mayer, 1947; Bigeleisen and Wolfsberg, 1958]. Most equilibrium and kinetic isotope effects are half as pronounced for 17 O/16 O ratios vs. 18 O/16 O ratios, so the slope of a δ 17 O vs. δ 18 O plot (similar to 17 O/16 O vs. 18 O/16 O) is nominally 0.5. Departures from mass-dependent fractionation in oxygen are calculated using Eq. 1.8: ∆17 O > 0 represents a ‘mass-independent’ enrichment in 17 O, whereas ∆17 O < 0 represents a “mass-independent” depletion in 17 O. Several excellent reviews of this topic have been published, e.g., Weston [1999] and Thiemens [2006]. The language of ‘clumped’ isotope geochemistry is potentially even more confusing because the reference isotopic ratio (e.g., the denominator in Eq. 1.6) is no longer a constant: R 47 [47 CO2 ] = 44 [ CO2 ] ∆47 = R47 sample R47 stochastic ! ) − 1 × 1000 (1.9) 13 18 + 2R17 R18 + R13 (R17 )2 , the distribution of stable carbon and In Eq. 1.9, R47 stochastic = 2R R oxygen isotopes if they were randomly distributed among all isotopologues of CO2 [Eiler, 2007]. It is important to recognize that the terms used in ‘clumped’ isotope geochemistry (Eq. 1.9) differ fundamentally from those in bulk-isotope measurements; the “reference” to which the measured R47 sample is compared is a varying internal standard (the bulk isotopic composition), rather than the fixed external standard used in Eqs. 1.5 and 1.6. This distinction also leads to quirky, yet ultimately useful changes in ∆47 when subject to various physical processes such as mixing and diffusion [Eiler and Schauble, 2004]. A common question has been: “What is the difference between an isotopomer and an isotopologue?” Two isotopomers, like chemical isomers, share the same isotopic composition, but the stable isotopes themselves are in positions that render the two molecules chemically distinct. A good example can be found in the comparison of isotopically substituted N2 O and CO2 molecules: 14 N–15 N–16 O and 15 N–14 N–16 O are isotopomers of one another because the N-atom substitutions are not symmetrically equivalent. The two isotopomers, consequently, have differing chemical properties, e.g., vibrational frequencies and rotational constants. In contrast, 16 O–12 C–18 O and 18 O–12 C–16 O are equivalent upon rotation, so they are equivalent structures of a single isotopologue. 11 L. Y. Yeung 1.B Oxygen isotope exchange reactions of CO2 Chapter 1 Copyright declaration This thesis contains excerpts from three publications in which the author was involved: • Huntington, K. W., J. M. Eiler, H. P. Affek, W. Guo, M. Bonafacie, L. Y. Yeung, N. Thiagarajan, B. Passey, A. Tripati, M. Daëron, R. Came (2009), Methods and limitations of ‘clumped’ CO2 isotope (∆47 ) analysis by gas source isotope ratio mass spectrometry, J. Mass Spectrom., 44(9), 1318–1329. ©2009 John Wiley & Sons. • Yeung, L. Y., H. P. Affek, K. J. Hoag, W. Guo, A. A. Wiegel, E. L. Atlas, S. M. Schauffler, M. Okumura, K. A. Boering, and J. M. Eiler (2009), Large and unexpected enrichment in stratospheric 16 O13 C18 O and its meridional variation, Proc. Natl. Acad. Sci. U. S. A., 106(28), 11,496–11,501. ©2009 National Academy of Sciences. • Yeung, L. Y., M. Okumura, J. T. Paci, G. C. Schatz, J. Zhang, and T. K. Minton (2009), Hyperthermal O-Atom Exchange Reaction O2 + CO2 through a CO4 Intermediate, J. Am. Chem. Soc., 131(39): 13,940–13,942. ©2009 American Chemical Society Publications. 12  L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Chapter 2 Large and unexpected enrichment in stratospheric 16O13C18O Adapted from Yeung, L. Y., H. P. Affek, K. J. Hoag, W. Guo, A. A. Wiegel, E. L. Atlas, S. M. Schauffler, M. Okumura, K. A. Boering, and J. M. Eiler (2009), Large and unexpected enrichment in stratospheric 16 O13 C18 O and its meridional variation, Proc. Natl. Acad. Sci. U. S. A., 106(28), 11,496–11,501. ©2009 National Academy of Sciences. 13 L. Y. Yeung 2.1 Oxygen isotope exchange reactions of CO2 Chapter 2 Abstract The stratospheric CO2 oxygen isotope budget is thought to be governed primarily by the O(1 D) + CO2 isotope exchange reaction. However, there is increasing evidence that other important physical processes may be occurring that standard isotopic tools have been unable to identify. Measuring the distribution of the exceedingly rare CO2 isotopologue 16 O13 C18 O, in concert with 18 O and 17 O abundances, provides sensitivities to these additional processes, and thus is a valuable test of current models. We identify a large and unexpected meridional variation in stratospheric 16 O13 C18 O, observed as proportions in the polar vortex that are higher than in any naturally derived CO2 sample to date. We show, through photochemical experiments, that lower 16 O13 C18 O proportions observed in the mid-latitudes are determined primarily by the O(1 D) + CO2 isotope exchange reaction, which promotes a stochastic isotopologue distribution. In contrast, higher 16 O13 C18 O proportions in the polar vortex show correlations with long-lived stratospheric tracer and bulk isotope abundances opposite to those observed at mid-latitudes, and thus opposite to those easily explained by O(1 D) + CO2 . We believe the most plausible explanation for this meridional variation is either an unrecognized isotopic fractionation associated with the mesospheric photochemistry of CO2 or a temperature-dependent isotopic exchange on polar stratospheric clouds (PSCs). Unraveling the ultimate source of stratospheric 16 O13 C18 O enrichments may impose additional isotopic constraints on biosphere-atmosphere carbon exchange, biosphere productivity, and their respective responses to climate change. 14 L. Y. Yeung 2.2 Oxygen isotope exchange reactions of CO2 Chapter 2 Introduction Predicting future CO2 concentrations and carbon cycle-climate feedbacks depends on one’s ability to quantify the contributions from the sources and sinks governing the global carbon budget and how they may change over time. The bulk stable isotope composition of CO2 (i.e., its 13 C/12 C, 18 O/16 O, and 17 O/16 O ratios) plays an important role in constraining this budget (see Yakir [2003] and references therein). In the stratosphere, the oxygenisotope composition of CO2 is thought to be modified by oxygen isotope exchange reactions with O(1 D) generated by ozone photolysis [Yung et al., 1997], whereas in the troposphere it is controlled by isotope exchange reactions with liquid water in the oceans, soils, and plant leaves [Ciais and Meijer, 1998]. The interplay between stratospheric and tropospheric isotope exchange reactions, in principle, could allow the relative abundances of 12 C16 O2 , 16 O12 C18 O, and 16 O12 C17 O isotopologues to be used as tracers for gross biosphere produc- tivity [Hoag et al., 2005; Luz et al., 1999], but the stratospheric CO2 photochemical system is still under-constrained and our understanding of it is incomplete. Discrepancies between laboratory and stratospheric measurements [Lämmerzahl et al., 2002; Shaheen et al., 2007; Thiemens et al., 1995] have prompted questions about whether the O(1 D) + CO2 isotope exchange reaction acts alone on stratospheric CO2 or whether other photochemical [Bhattacharya et al., 2000] or dynamical [Boering et al., 2004] processes significantly affect the stable isotopologue distribution in CO2 . Stratospheric oxygen isotope covariations in CO2 [Kawagucci et al., 2008; Lämmerzahl et al., 2002; Liang et al., 2008] consistently differ from those found in laboratory experiments simulating stratospheric photochemistry [Baulch and Breckenridge, 1966; Chakraborty and Bhattacharya, 2003; Johnston et al., 2000; Shaheen et al., 2007; Wen and Thiemens, 1993], and the origin of this disagreement is still uncertain because bulk stable isotope measurements alone (i.e., of δ 13 C, δ 18 O, and δ 17 O values) cannot differentiate extrinsic effects [e.g., the O(1 D) isotope composition] from intrinsic (i.e., photolytic or kinetic isotope) effects on the isotope composition of stratospheric CO2 . Additional constraints arising from analysis of multiplysubstituted isotopologues of CO2 can provide sensitivities to these processes [Affek and Eiler, 2006; Affek et al., 2007; Eiler, 2007; Eiler and Schauble, 2004]. To investigate stratospheric 15 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 CO2 chemistry, we examine here the proportions of 16 O13 C18 O (reported as a ∆47 value) in stratospheric CO2 and in laboratory kinetics experiments. 2.3 Field sample collection and analysis Twelve stratospheric CO2 samples were analyzed for bulk stable isotope compositions and ∆47 values: Six samples of stratospheric CO2 were collected from the NASA ER-2 aircraft during the 1999/2000 Arctic winter Stratospheric Aerosol and Gas Experiment III (SAGE III) Ozone Loss and Validation Experiment (SOLVE) campaign [Newman et al., 2002], and six samples were collected from a balloon flight from Fort Sumner, New Mexico on 29 September 2004. SOLVE mission samples (January – March 2000, 29 – 79◦ N, 11 – 20 km) were collected as whole air samples [Flocke et al., 1999]. CO2 was then isolated from the ∼5 L STP of air by a combination of liquid N2 and ethanol-dry ice traps, then separated into aliquots of 12 – 18 µmol CO2 each and sealed into glass ampoules. Balloon samples were collected using a cryogenic whole air sampler (34.5◦ N, 103.6◦ W, 27 – 33 km) [Froidevaux et al., 2006; Lueb et al., 1975] and purified and stored as above. δ 13 C, δ 18 O, and δ 17 O of CO2 were measured on a Finnigan MAT 252 isotope ratio mass spectrometer (IRMS) at UC-Berkeley. ∆17 O was measured using the CeO2 technique with a precision of ± 0.5‰ [Assonov and Brenninkmeijer, 2001]. Aliquots of the same CO2 samples were analyzed for ∆47 using a Finnigan MAT 253 IRMS at Caltech configured to collect masses 44 – 49, inclusive, and standardized by comparison with CO2 gases of known bulk isotopic composition that had been heated for two hours at 1000◦ C to achieve a stochastic isotopic distribution [Eiler and Schauble, 2004]. Masses 48 and 49 were used to detect residual hydrocarbon contamination. For ∆47 analysis, the 12 – 18 µmol aliquots of SOLVE-mission and balloon CO2 samples were purified of potential contaminants, such as hydrocarbons, by a pentane-liquid N2 slush (–120◦ C) as well as by passing it through a gas chromatographic (GC) column (Supleco Qplot, 530 µm ID, 30 m length) at –20◦ C, with column baking at 150◦ C between samples [Affek and Eiler, 2006; Ghosh et al., 2006]. All data were corrected for the presence of N2 O using the method described previously [Affek and Eiler, 2006]. Each measurement consisted of 5 – 9 acquisitions (of 10 measurement 16 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Table 2.1: Stratospheric air sample data Air Sample Name Type∗ Altitude Latitude (km) (◦ N) θ (K) CH4 N2 O CFC-11 CFC-12 δ 13 C (ppbv) (ppbv) (pptv) (pptv) (‰) δ 18 O (‰) ∆17 O (‰) ∆47 (‰) ER-2 samples V V V VE M M 20000312(25)1120 20000131(30)1001 20000203(10)1173 20000127(5)1060 20000106(30)1169 20000111(25)2021 19.33 19.85 17.63 19.45 19.40 11.40 79.2 73.5 70.4 57.7 29.3 43.5 443.61 448.08 409.37 445.10 467.43 358.26 948 1066 1250 1385 1495 1726 111.5 142.1 192.8 227.6 256.4 307.9 33.34 32.22 30.78 29.26 28.73 27.27 34.5 34.6 34.6 34.6 34.6 34.6 931.14 896.15 861.84 778.08 757.89 709.67 835 843 913 957 1014 1176 54.0 56.7 77.8 92.1 107.9 155.9 19. 31. 72. 112. 157. 246. 147. 198. 293. 362. 421. 526. -8.11 -8.08 -8.06 -8.07 -8.08 -8.06 44.55 43.62 43.06 42.79 42.50 40.98 5.76 4.38 3.69 2.45 2.13 0.18 1.614 1.555 1.436 1.233 1.071 1.075 46.0 51.2 78.2 100.2 78.2 123.6 -8.07 -7.99 -8.03 -8.07 -8.04 -8.03 45.14 45.44 45.14 44.98 44.79 44.09 6.46 6.29 5.91 6.12 5.00 4.26 0.976 0.923 0.913 0.912 1.004 0.916 Balloon samples M M M M M M 1-A010-R (2035) 3-A01-R (1141) 5-A013-R (2079) 7-A026-R (1057) 8-A017-E (1113) 10-A022-E (1186) 0.13 0.23 0.15 0.63 1.10 5.90 ∗ Air type is abbreviated as V = vortex, VE = vortex edge, and M = mid-latitude based on N O:θ correlations, where θ is 2 potential temperature in Kelvin. Non-isotopic tracer measurement methodology can be found in Flocke et al. [1999] and Froidevaux et al. [2006]. cycles each), with typical standard deviations (acquisition-to-acquisition) of 0.06‰ in ∆47 . 2.4 Field results The stratospheric samples (see Table 2.1) display ∆47 values both higher and more variable than those exhibited by tropospheric air at the surface, which has an average ∆47 value of 0.92 ± 0.01‰ in remote regions (Cape Grim, Tasmania and Barrow, Alaska) [Affek et al., 2007]. The high-latitude (> 57◦ N) stratospheric samples, in particular, are significantly more enriched in ∆47 than any material analyzed before in nature (see Figure 2.1 and see Affek et al. [2007] and Eiler [2007]). At high latitudes, ∆47 varies strongly and increases monotonically with decreasing mixing ratios of long-lived trace gases that have tropospheric sources and stratospheric sinks, such as N2 O and CH4 . At mid-latitudes, ∆47 varies relatively little and shows correlations with trace gas mixing ratios having the opposite sign of those observed at high latitudes (see Figure 2.2 and Table 2.1). Using the correlation between simultaneously measured N2 O mixing ratios and potential temperature [Greenblatt et al., 2002], we found that the high-latitude samples were collected in inner polar vortex air (three samples) or vortex edge air (one sample). Thus, differences in the sign and magnitude of ∆47 variations with N2 O mixing ratio in the two subsets of 17 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.1: Meridional variation of ∆47 measured in stratospheric samples. Typical values in the troposphere are ∆47 ∼ 0.9‰. Error bars show 2σ standard errors. samples are presumably due to differences between vortex and non-vortex processes. In contrast to these ∆47 trends, covariations of ∆17 O with δ 18 O and mixing ratios of long-lived trace gases for our mid-latitude samples resemble those of our polar vortex samples (or show the expected differences for slightly shorter-lived tracers, e.g., CFC-11) and also those reported in earlier studies of high-latitude [Boering et al., 2004; Kawagucci et al., 2008] and polar vortex air (see Figure 2.3) [Alexander et al., 2001]. This suggests that ∆47 records a process to which ∆17 O is not sensitive. In order to rule out the possibility that the observed high ∆47 values result from sample contamination by organic compounds in the stratospheric samples, one of the samples [20000131(30)1001] was exposed to water at 25◦ C for 24 hours to reach CO2 –water isotopic equilibrium. The exchanged sample had a ∆47 value of 0.862 ± 0.078‰, identical to the cylinder CO2 working standard, whose ∆47 value reflects CO2 isotopic equilibrium at room temperature [Wang et al., 2004]. In contrast, the presence of contaminants would have resulted in a high ∆47 value even after isotopic equilibrium was reached. Hence, no evidence for contamination was observed in the high-latitude samples. 2.5 Laboratory photochemical experiments To gain further insight into the correlations we observed between ∆47 , ∆17 O, and δ 18 O, we conducted several laboratory photochemistry experiments. Enrichments of ∆17 O and δ 18 O 18 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.2: Correlation between ∆47 and stratospheric tracers. (A), best-fit lines are shown for mid-latitude (solid line) and high-latitude (dashed line) ∆47 vs. N2 O mixing ratio. Correlations between ∆47 and other tracers with tropospheric sources and stratospheric sinks are similar (see Figure 2.3). Also shown is the best-fit line of (B), ∆47 vs. ∆17 O, and (C), ∆47 vs. δ 18 O in mid-latitude air, which is used to estimate the integrated effective isotopic composition of stratospheric O(1 D) (see text). Error bars represent 2σ standard errors. Figure 2.3: ∆17 O values vs. long-lived stratospheric tracer mixing ratios. In both panels, measurements reported in this work (ER-2 and Balloon data) are compared with previous high-latitude (> 48◦ N; left panel) and polar vortex (right panel) measurements. The measured ∆17 O correlations with N2 O and CFC-12 do not reveal obvious distinctions among the mid- and high-latitude CO2 samples; ∆47 measurements, in contrast, reveal strong mesospheric or other polar vortex influence. 19 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 in stratospheric CO2 are generally understood to arise from isotope exchange with O(1 D), which is produced by photolysis of 18 O- and 17 O-enriched stratospheric ozone [Liang et al., 2007; Yung et al., 1997], but the kinetics of the isotope exchange reactions for multiplysubstituted isotopologues of CO2 , and their effects on ∆47 , have not yet been explored. Changes in ∆47 caused by these reactions should principally reflect relative changes in 16 O13 C18 O and 16 O12 C18 O abundances because the 13 C composition is not affected by iso- tope exchange with O(1 D); variations in 17 O12 C18 O and 13 C17 O2 abundances will change ∆47 more subtly. Thus, reactions 2.1 and 2.2 are most relevant. 18 O(1 D) + 12 C16 O2 → 18 O12 C16 O∗2 → 16 O + 16 O12 C18 O (2.1) 18 O(1 D) + 13 C16 O2 → 18 O13 C16 O∗2 → 16 O + 16 O13 C18 O (2.2) Statistical partitioning of isotope exchange products, through a process governed by random chance such that 18 O(1 D) has a 2/3 probability of being incorporated into the product CO2 , would drive the CO2 isotopologues towards a stochastic distribution (i.e., ∆47 = 0). If any one (or more) of the isotope exchange reactions does not partition products statistically, however, ∆47 can increase [e.g., if 18 O(1 D) exchanges isotopes with 13 C16 O2 more readily than with 12 C16 O2 ] or decrease accordingly. Two sets of laboratory experiments were conducted. First, the relative rates of reactions 2.1 and 2.2 were probed directly to obtain the 13 C/12 C kinetic isotope effect (KIE) for the 18 O(1 D) + CO 2 isotope exchange reaction at 300 K and 229 K. These experiments used pulsed photolysis of 97% N2 18 O at 193 nm as a source of 18 O(1 D), and the extent of isotope exchange was minimized. Second, we performed continuous-irradiation experiments, using a mercury lamp, on mixtures of isotopically unlabeled O2 , O3 , and CO2 as a function of different irradiation times to determine the aggregate effects of the O2 /O3 /CO2 photochemical system on ∆47 . 20 L. Y. Yeung Oxygen isotope exchange reactions of CO2 2.5.1 13 C/12 C kinetic isotope effect experiments 2.5.1.1 Methods overview Chapter 2 For experiments performed at 300 K, a 15 cm-long stainless steel conflat chamber with quartz windows was used as a reaction chamber. Low-temperature experiments were performed in a 25 cm-long, all-quartz chamber, cooled to 229 K under vacuum via direct conduction with a cold copper jacket (see Appendix 2.C). Experiments were initiated with pulsed excimer laser photolysis of N2 18 O (193 nm, 50 – 100 mJ pulse−1 , 1 Hz repetition rate, < 200 pulses), producing 18 O(1 D), in ∼1:100:3000 static mixtures of N2 18 O:CO2 :He (100 Torr total pressure). N2 18 O was synthesized from the acid-catalyzed reduction of 18 O-labeled aqueous NaNO [McIlvin and Altabet, 2005; Samuel and Wassermann, 1971]; a 2 detailed description of its synthesis and characterization can be found in Section 2.5.1.2. A schematic of the reaction scheme is shown in Figure 2.4. Starting samples of CO2 contained a stochastic distribution of isotopologues, generated in the manner described in Section 2.3. The initial CO2 isotopic composition was measured and CO2 was recollected cryogenically for use in the reaction chamber. Residence time in the reaction chamber had a negligible effect on ∆47 in the 300 K experiments, whereas the chamber cooling process alone was observed to enrich the starting material in δ 18 O and ∆47 , by 0.5‰ and 0.13‰, respectively. These offset values were subtracted from final δ 18 O Figure 2.4: Schematic of O(1 D) + CO2 reaction-purification-analysis procedure. 21 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 and ∆47 values in 229 K experiments. The reaction products were recollected cryogenically and purified in two GC steps. Separation of residual N2 18 O and reacted CO2 was achieved through a packed-column (PoraPak Q) GC separation at 25◦ C, after which the samples were purified with a capillary GC as described above. Due to the presence of N2 18 O isobars with CO2 at masses 46 – 49, mass 14 was also monitored to measure the extent of N2 18 O contamination. Differences in mass-14 signal between the starting and product material of greater than 5 mV (a variation typical of ‘clean’ laboratory standards) were deemed contaminated, and the data points were rejected. The difference between the initial and final δ 18 O (hereafter referred to as ∆δ 18 O) and ∆47 compositions was calculated assuming that δ 13 C was unchanged, since there was no external carbon reservoir in the reaction. GC separation of N2 18 O and CO2 yielded a small, yet reproducible ∆47 change of +0.13‰, which was present both when gases of stochastic isotope composition were analyzed as well as when aliquots of cylinder CO2 working standard (∆47 = 0.86‰) were analyzed. The source of this offset may be a small amount of diffusive or adsorptive fractionation on the GC column, but it was not investigated further. Because of the apparent insensitivity of the ∆47 change to initial isotopic composition, the sample purification step was treated as a small additive effect on the measured ∆47 , with no effect on the overall kinetics measured. The following sections, 2.5.1.2 and 2.5.1.3, provide a detailed description of the materials and methods utilized to obtain the results summarized in Section 2.5.1.4. 2.5.1.2 N2 18 O synthesis Precursor samples of N2 18 O were synthesized from the acid-catalyzed reduction of aqueous nitrite (NO2 − ) [McIlvin and Altabet, 2005; Samuel and Wassermann, 1971]. A description of a synthesis and characterization follows. First, a solution of 0.4 mmol sodium nitrite (NaNO2 ) in 800 µl >97% H2 18 O (Isonics) was placed in a three-neck round-bottom flask and flushed with He at 30 mL min−1 for 20 minutes to remove any dissolved gases. The flow was then stopped and the flask closed off and put in an ice bath. 350 µl glacial acetic acid was then added through a rubber septum with a syringe to acidify the water. For 3 minutes, 22 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 the nitrite was allowed to exchange oxygen atoms fully with H2 18 O in the acidic environment [Ott, 1981]. Then, the nitrite was reacted with 220 µl of a solution of 1.5 mmol sodium azide (NaN3 ), 100 µl glacial acetic acid, and 150 µl H2 18 O, also added through the septum, for 40 minutes with stirring. Due to the high concentration of acid, the dominant reaction was expected to be that between nitrous acid (HNO2 ) and hydrazoic acid (HN3 ) to produce N2 18 O: HNO2 + HN3 → N2 O + N2 + H2 O (2.3) After the 40-minute reaction time, 1 mL of a ∼17 M NaOH solution was added through the septum to stop the reaction and remove any residual CO2 . The gas-phase products were collected by flowing He through the flask at 5 mL min−1 for 1 h into a “U-trap” held at liquid nitrogen temperature (77 K). Synthesized N2 18 O was dried cryogenically using a pentane slush (–120 ◦ C), then a dry ice/ethanol slush (–76 ◦ C), and recollected in a trap at liquid nitrogen temperature. Chemical yield in the N2 18 O was determined by expanding the product gas into a calibrated volume on a vacuum line, and the total product yield was determined to be 53% (0.195 mmol). Table 2.2: IR band assignments for the spectra in Figure 2.5 Frequency (cm−1 ) Band Frequency (cm−1 ) Band 1155 1247 1840 2217 2295 2412 2491 2787 3345 3435 3663 3737 2ν2 ν1 ν1 + ν2 ∗ ν3 4ν2 ν1 + 2ν2 ∗ 2ν1 ν2 + ν3 2ν2 + ν3 ∗ ν1 + ν3 2ν1 + 2ν2 ∗ 3ν1 ∗ 1285 1595 2350 2563 3481 3657 3756 ν1 (14 N2 16 O) ν2 (H2 16 O) ν3 (CO2 ) 2ν1 (14 N2 16 O) ν1 + ν3 (14 N2 16 O) ν1 (H2 16 O) ν3 (H2 16 O) Assignments taken from Łapiński et al., and references therein. Literature values are ν1 = 1247 cm−1 , ν2 = 571 cm−1 , and ν1 = 2217 cm−1 for N2 18 O. ∗ Temporary assignment because band has yet not been reported in the literature. 23 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.5: FT-IR spectrum of synthesized N2 18 O between 1100 cm−1 and 4000 cm−1 . Inset shows the zoomed-in area between 2100–2400 cm−1 . Samples were then measured on a Fourier-transform infrared spectrometer (FT-IR) for chemical purity and a IRMS for isotopic purity. FT-IR analysis was conducted on a Nicolet FT-IR spectrometer with 3 Torr N2 18 O, 0.125 cm−1 resolution, and 2000 scans in an 18 cmpathlength cell with CaF2 windows. Table 2.2 contains the band assignments for the N2 18 O IR spectrum shown in Figure 2.5. The IR spectrum (see inset of Figure 2.5) contains a small amount of CO2 , but it is considered too small an amount to affect isotopic measurements. The absorption cross-section of the CO2 (ν3 ) band is three times that of the N2 O(ν3 ) band [Rothman et al., 2009], yet in the experimental spectrum, the N2 O band is stronger than the CO2 band by an order of magnitude; consequently, the concentration of CO2 in the N2 18 O sample is estimated to be 3%. Because N2 18 O was used as a 1% mixture in CO2 for the photolysis experiments, the estimated mixing ratio of contaminant CO2 is 3 × 10−4 in the sample CO2 . This mixing ratio amounts to a maximum absolute error less than 0.001‰ in the observed δ 18 O at natural abundance (0.2% 18 O), and it is therefore negligible. H2 O lines in the spectrum are believed to come from atmospheric water vapor, as they are consistent with H2 16 O instead of the H2 18 O used in the synthesis. Because all of the H2 18 O appears 24 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Table 2.3: IRMS ion signals from the synthesized N2 18 O m/z Signal (mV) 18 O content 44 46 1276 37870 96.7% 30 32 482 14773 96.8% to have been removed by the cryogenic drying steps, and the sample compartment was continuously purged with dry N2 , this water vapor is believed to arise from desorbing water from the FT-IR cell walls. Mass-spectrometric analysis was performed on a Finnigan MAT 253 using cup position 3 (3 × 1010 Ω resistor). Isotope ratios were determined at two different m/z ranges: 46/44 (mainly 14 N2 18 O/14 N2 16 O) and 32/30 (mainly 14 N18 O/14 N16 O). Table 2.3 contains the observed signals and calculated isotopic purity at 16.5 mbar in the sample bellows. Here we see that the synthesized N2 O is indeed 97% labeled with 18 O, and it was used in experiments without further purification. 2.5.1.3 Reaction models Two models for the 13 C/12 C KIE experiments were constructed. One was a chemical kinetic model designed to calculate the expected trends in ∆47 vs. ∆δ 18 O given specific KIEs. The second was a hard-sphere collision model designed to model the velocity relaxation of the nascent 18 O(1 D), from which a collision energy distribution for each experiment could be calculated. C HEMICAL KINETIC MODEL . A comprehensive, isotopologue-specific kinetics model of the O(1 D)-CO2 photochemical experiment (144 isotope exchange reactions) was constructed in the FACSIMILE kinetics modeling package. Stochastic isotope exchange branching fractions [Baulch and Breckenridge, 1966; Yung et al., 1997] were used: Incident O(1 D) atoms had a 2/3 probability of isotope exchange, regardless of the isotope exchange reaction. The isotopic composition of the initial O(1 D) was treated as a constant; for these 18 O-labeled 25 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 experiments, trace 17 O and 16 O abundances had negligible effects on the measured 13 C/12 C KIE. We expect to observe subtle isotope effects due to differences in the 18 O(1 D)–CO2 collision frequencies between different isotopologues in the helium-buffer-gas experiments because the collision-limited rate of reaction for O(1 D) + CO2 [Sander et al., 2006] implies that the reaction probability for any given O(1 D)–CO2 collision is near unity. For instance, more 18 O(1 D) + 12 C16 O2 collisions than 18 O(1 D) + 13 C16 O2 collisions occur because the average velocity for 12 C16 O2 is higher than that for 13 C16 O2 at a given temperature. This reduces the rate at which reaction 2.2 occurs relative to reaction 2.1 in the laboratory by about 5%. The O(1 D)-CO2 collision frequencies in these experiments scale directly with the collision pair’s relative velocity, which depends inversely on the pair’s reduced mass (µ) according to equation 2.4: s k2.2 = µ18 O + 44 CO 2 µ18 O + 45 CO × k2.1 = µe f f k2.1 (2.4) 2 k represents the rate coefficient for the subscripted reaction, and µ represents the reduced mass of the subscripted reactant pair. Analogous relationships can be computed for each unique reactant pair. ∆47 is expected to decrease with increasing ∆δ 18 O because the collision frequency for 18 O(1 D) + 44 CO2 is ∼5% larger than that for 18 O(1 D) + 45 CO2 . Such biases are expected to be small in the atmosphere due to competing electronic quenching reactions (e.g., O(1 D) + N2 → O(3 P) + N2 ) [Johnston et al., 2000]. These electronic quenching reactions were minimized in our pulsed photolysis experiments because He was used as the buffer gas [Heidner and Husain, 1974; Shi and Barker, 1990]. Thus a 13 C/12 C KIE = k2.2 /k2.1 = 1 in our laboratory experiment will appear as an anti-correlation in a plot of ∆47 vs. ∆δ 18 O. A 13 C/12 C KIE ≈ 1.01 and an O(1 D) source with δ 18 O = δ 17 O ≈ 100‰ would be required to generate the polar vortex ∆47 enrichment and also the polar vortex ∆47 vs. ∆17 O correlation. On the ∆47 vs. ∆δ 18 O plot, the slope would be +0.0055 using k2.2 /k2.1 = 1.01. O(1 D) + CO2 COLLISION ENERGY DISTRIBUTION . The 13 C/12 C experiment was also modeled on the collision-by-collision level because the O(1 D) + CO2 isotope exchange reaction occurs through two reaction channels whose branching ratio depends on collision energy 26 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 [Perri et al., 2003]: O(1 D) + CO2 → O(3 P) + CO2 (2.5) → O(1 D) + CO2 (2.6) The branching fraction of the non-quenching channel (2.6) increases significantly with reaction collision energy, Ecoll [Mebel et al., 2004; Perri et al., 2004]. Observed isotope effects, then, may also depend on the distribution of Ecoll . Nascent O(1 D) atoms from the N2 O photolysis scheme employed in this study had a high average translational energy, so He was chosen as buffer gas to lower the average collision energy, hEcoll i, to a stratospherically relevant value; He quenches the translational energy of O(1 D) atoms efficiently while quenching the electronic energy inefficiently [Heidner and Husain, 1974; Shi and Barker, 1990]. Furthermore, the translational energy transfer during O(1 D) + He collisions can be modeled well using a hard-sphere collision model [Matsumi et al., 1994b]. We constructed a Monte Carlo hard-sphere collision model in the MATLAB programming environment based on the solution to the general elastic hard-sphere problem; the mathematical derivation can be found in the literature [Nan and Houston, 1992], and the program code can be found in Appendix 2.D. The basic function of the program was to calculate the final velocity vectors for two colliding hard spheres of masses m1 (the O-atom) and m2 (the He-atom) with initial velocity vectors (v1i , θ1i , φ1i ) and (v2i , θ2i , φ2i ), respectively. The elastic hard-sphere calculation was performed for a distribution of initial O-atom velocities in a He bath gas at thermal equilibrium (e.g., at 298 K). First, O-atom velocity vectors, (vO,i , θO,i , φO,i ), were sampled according to a velocity distribution for O(1 D) ejected from the photolysis of 14 N2 16 O at 193 nm [Felder et al., 1991; Hanisco and Kummel, 1993; Springsteen et al., 1993] centered at ET = 18.2 kcal mol−1 . In the absence of experimental data for 14 N2 18 O photodissociation, the 18 O(1 D) velocity distribution was approximated by a gaussian distribution centered at ∼2900 m s−1 with a full-width at half-maximum (FWHM) of ∼1000 m s−1 (i.e., hET i ∼18 ± 7 kcal mol−1 ). Second, a He-atom velocity vector, (vHe,i , θHe,i , φHe,i ), was selected randomly from a Maxwell-Boltzmann velocity distribution. Using this pair of initial conditions and a random impact parameter b (sampled with a probability proportional to itself), the final velocity vector of the O-atom after one collision, (vO, f , θO, f , 27 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 φO, f ), was computed and stored. The final velocity was then re-used as an initial velocity for the next collision with a second He-atom, whose velocity was randomly sampled as above. This calculation was repeated for up to 200 total collisions and N = 50,000 initial O(1 D) velocities, a total of 106 – 107 calculations. After 200 collisions, > 96% of the O(1 D) would have reacted with CO2 under our experimental conditions. Using the O(1 D) velocity distribution after each O(1 D)–He collision, the distribution of O(1 D)–CO2 collision energies, Pj (Ecoll ), for the jth collision could then be calculated similarly. The relative CO2 concentration, i.e., ρCO2 ∼ 0.03, was then used to weight the Pj (Ecoll ) distribution at the jth collision to obtain a O(1 D)–CO2 collision energy distribution over the whole experiment. The results were summed according to equation 2.7: Ptotal (Ecoll ) = ρCO2 ∑ Pj (Ecoll ) (2.7) j The model was tested by confirming that the average kinetic energy approached (and remained at) the value expected at thermal equilibrium by the equipartition theorem, e.g., 3 −1 at 300 K. Calculated P total (Ecoll ) distributions for several different 2 RT = 0.89 kcal mol experimental conditions are shown in Figure 2.6. Our simulation of the initial O(1 D) collision cascade shows that 81% of all O(1 D) + CO2 collisions occur with Ecoll < 2 kcal mol−1 , with hEcoll i = 1.6 kcal mol−1 , similar to the Ecoll distribution expected in the stratosphere [Kharchenko and Dalgarno, 2004; Takahashi et al., 2002]. As we noted earlier, the nascent 18 O(1 D) translational energy distribution is somewhat uncertain because the existing pho- todissociaton dynamics studies focused on the 14 N2 16 O molecule, not the 14 N2 18 O used in these experiments. Changing the peak of the nascent 18 O(1 D) translational energy distribution by 1 – 2 kcal mol−1 changed the average O(1 D)-CO2 collision energy by < 0.1 kcal mol−1 . The shape of the laboratory Ptotal (Ecoll ) distribution appears different from that modeled in conditions resembling the stratosphere [Kharchenko and Dalgarno, 2004]; this difference is due to O(1 D) having a slower nascent O(1 D) velocity distribution (O3 vs. N2 O photolysis) [Thelen et al., 1995] and more efficient electronic quenchers (N2 /O2 vs. He bath gas) [Sander et al., 2006] in the stratosphere. In addition, minor O(1 D)-producing channels 28 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.6: Modeled O(1 D) + CO2 reaction collision energy distributions at different He bath gas pressure (T = 300 K). Also shown is the modeled P(Ecoll ) under conditions resembling the stratosphere, using O3 as a source of O(1 D). important to the stratosphere have not been included in this model (see Taniguchi et al. [2000]). Last, the velocity relaxation problem is only qualitatively represented by the hardsphere model; inelastic collisions are not necessarily described well by the hard-sphere cross-sections, especially when the collision partners are diatomic, and spin-orbit coupling is important [Kharchenko and Dalgarno, 2004]. Thus, the “stratospheric” O(1 D) collision model results are only intended for qualitative comparison with the laboratory O(1 D)–He results. 2.5.1.4 Pulsed-photolysis results The results of the pulsed laser experiments are plotted in Figure 2.7 and shown in Table 2.4. At both temperatures, ∆47 of CO2 decreases with increasing extent of photochemical isotope exchange (∆δ 18 O), indicating the O(1 D) + CO2 reaction does not selectively enrich 16 O13 C18 O relative to 16 O12 C18 O. Additionally, no significant temperature dependence was observed in ∆47 vs. ∆δ 18 O, as the 300 K and 229 K data are indistinguishable within our experimental uncertainty; consequently, the data were considered together in the subsequent determination of the 13 C/12 C KIE. The best-fit slope of the ∆47 vs. ∆δ 18 O relationship in the experimental data was calculated to be –0.0036 ± 0.0008 (2σ ), corresponding to a 29 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.7: Changes in ∆47 vs. ∆δ 18 O after pulsed UV photolysis at 300 K (circles) and 229 K (triangles). ∆δ 18 O = δ 18 Ofinal - δ 18 Oinitial . Also shown is the modeled ∆47 vs. ∆δ 18 O dependence for 13 C/12 C KIE = 13 k/12 k = 0.999 and 1.01 (offset by ∆47 = +0.13‰ for clarity; the significance of this and of the slopes is discussed in the text). Error bars represent 2σ standard errors. Table 2.4: Results of pulsed photochemical experiments δ 13 C (‰) Temperature δ 18 Oi (‰) δ 18 Of (‰) ∆δ 18 O† (‰) ∆47,f (‰) σ ∆47,f (‰) 29.84 29.95 15.50 15.48 30.08 29.63 15.28 14.46 66.41 54.03 58.44 55.89 48.79 41.17 58.33 59.86 36.57 24.08 42.94 40.41 18.71 11.54 43.05 45.40 -0.009 0.036 0.104 -0.018 0.038 0.057 -0.024 0.036 0.012 0.025 0.017 0.009 0.013 0.012 0.032 0.023 29.81 20.84 14.22 29.72 20.88 14.29 -0.09 0.04 0.07 0.150 0.127 0.165 0.011 0.012 0.028 Photolysis experiments 300 K 229 K -10.76 -10.56 -23.79 -24.24 -10.69 -10.55 -24.13 -25.15 Blank experiments 300 K 229 K -10.67 -19.22 -25.09 Blank experiments were run without photolysis step. † ∆δ 18 O = δ 18 Of - δ 18 Oi 30 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 13 C/12 C KIE of 0.999 ± 0.001 (2σ ). This KIE value was obtained by modeling the 13 C/12 C KIE value corresponding to the best-fit slope of the ∆47 vs. ∆δ 18 O data shown in Figure 2.7 (0.999, assuming a 13 C/12 C KIE of 1 in reaction 2.2). Its uncertainty was estimated by varying the 13 C/12 C KIE until the modeled slope varied ± 0.0008; the upper and lower limits of the 13 C/12 C KIE (1.000 and 0.998, respectively) were then taken as the 2σ uncertainty bounds. In contrast, a 13 C/12 C KIE of 1.01, the KIE required to explain the polar vortex ∆47 vs. ∆17 O correlation (see Section 2.5.1.3), would yield a slope of +0.0055 in Figure 2.7. The negative experimental slope, however, rules out this 13 C/12 C KIE > 1 and thus a selective enrichment in 16 O13 C18 O resulting from reaction 2.1. While this experiment was unable to isolate the 13 C/12 C KIEs in reactions 2.5 and 2.6, the laboratory data are consistent with the 13 C/12 C KIE in reaction 2.5 dominating the observed ∆47 vs. ∆δ 18 O relationship. Reactions 2.5 and 2.6 are both important in the stratosphere, with the branching ratio between them likely 9:1 (2.5:2.6) at the average stratospheric collision energy (see Mebel et al. [2004]) and thus also at the hEcoll i in our experiments. Using this branching ratio, we calculate that the experiment is approximately three times more sensitive to a 13 C/12 C KIE in reaction 2.5 than in reaction 2.6. A 13 C/12 C KIE ∼ 0.993 in reaction 2.6, then, is also consistent with the laboratory ∆47 vs. δ 18 O slope. If the observed slope were arising exclusively from a 13 C/12 C KIE in reaction 2.6, it would become increasingly negative with increasing initial hEcoll i because reaction 2.6 is favored at higher Ecoll [Mebel et al., 2004; Perri et al., 2004]. Several high-collision-energy (no buffer gas, initial hEcoll i ≈ 13.6 kcal mol−1 ) experiments were performed to test this hypothesis; they also showed depletions in ∆47 as the extent of photochemical isotope exchange increased, with no significant (i.e., factor-of-three) change in ∆47 vs. ∆δ 18 O. Other combinations of 13 C/12 C KIEs in reactions 2.5 and 2.6 could also yield the laboratory ∆47 vs. ∆δ 18 O slope, but the absence of significant temperature and collision-energy dependence in the laboratory data, along with negligible O(1 D)–CO2 association and dissociation barriers on the singlet electronic potential energy surface [Mebel et al., 2004], support our attribution of the measured isotope effects to reaction 2.5. As such, we report a 13 C/12 C KIE of 0.999 ± 0.001 (2σ ), which is within the uncertainty of a KIE of 1.000 expected for 31 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 stochastic isotope exchange. 2.5.2 Continuous-irradiation experiments 2.5.2.1 Methods Continuous-irradiation experiments on the O2 /O3 /CO2 photochemical system were performed at UC-Berkeley to examine whether the aggregate isotope effect from all O(1 D)–CO2 reaction pairs would still yield depletions in ∆47 with increasing extent of photochemical isotope exchange. A 2 L glass reaction bulb was filled with mixtures of O2 and CO2 of known isotopic composition between 100 – 150 Torr total pressure at 295 K, and the mixture was irradiated between 0 – 48 hours with a pen-ray mercury lamp through a MgF2 window. This scheme generates O(1 D) through narrow-band photolysis of O2 at 185 nm (6 × 1013 – 1.5 × 1014 photons cm−2 s−1 ) and subsequent photolysis of O3 at 254 nm (2 × 1015 photons cm−2 s−1 ). Residual O2 was separated cryogenically from the mixture, and O3 was catalytically decomposed on hot nickel foil at 333 K for 15 minutes before the CO2 was purified for isotopic analysis. A commercially available software program, KINTECUS (Windows version 3.95, 2008; [Ianni, 2003]), was used to simulate the kinetics of the photochemical oxygen isotope exchange between O2 and CO2 in the continuous-irradiation experiments. The species mod3 1 eled were O2 , O2 (1 ∆), O2 (1 Σ+ g ), O( P), O( D), O3 , and CO2 and included both singly- and doubly-substituted 17 O- and 18 O- isotopologues as well as 13 C isotopologues of CO2 , yielding more than 400 isotope-specific reactions. Rate coefficients for each reaction corresponding to all common isotopologues were from Sander et al. [2006], while photolysis rate coefficients (J-values) were calculated from the reported irradiance of the mercury pen-ray lamp at 254 nm [Reader et al., 1996], the geometry of the bulb, and the measured cross sections of O2 at 185 nm and O3 at 254 nm [Sander et al., 2006]. The only oxygen KIEs included in the model are in the ozone recombination reaction [Janssen et al., 2001] and in O + O2 isotope exchange [Kaye and Strobel, 1983; Wiegell et al., 1997]. Stochastic scrambling of oxygen was assumed to occur in the O(1 D) + CO2 isotope exchange reaction [Baulch and Breckenridge, 1966; Yung et al., 1997], and scenarios with hypothetical 13 C/12 C KIEs of 1, 32 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Table 2.5: Results of continuous irradiation experiments Sample name† Irradiation time (h) δ 18 O (‰) ∆17 O (‰) ∆47 (‰) Starting CO2 ANOM 1 ANOM 1 ANOM 2 ANOM 2 ANOM 4 0.0 48.0 48.0 4.5 4.5 10.0 6.4 67.4 67.4 13.1 13.2 19.0 0.0 24.8 24.8 2.3 2.3 4.8 1.10 0.72 0.85 0.96 1.04 0.75 † Samples with the same names are replicate analyses for ∆ , taken as separate aliquots of the 47 same experiment. 0.999, and 0.998 were considered a priori. The model was initialized with the experimental partial pressures, temperature, and starting isotopic compositions of O2 and CO2 . 2.5.2.2 Continuous-irradiation results The laboratory results from the continuous-irradiation experiments are shown in Table 2.5 and compared with the modeling results in Figure 2.8. We observed a depletion in ∆47 with increasing ∆17 O (a proxy for the extent of photochemical isotope exchange), in agreement with the results from our pulsed photolysis experiments. Within the uncertainty bounds reported for the 13 C/12 C KIE, the continuous irradiation experiments are also generally consistent quantitatively with our pulsed photolysis experiments. There is a noticeable disagreement, however, at the largest ∆17 O value (48-hour irradiation time). Some of this error could be attributed to our assumptions about the initial distribution of CO2 isotopologues in the model: The initial ∆47 > 0 was modeled as an excess of 16 O13 C18 O exclusively, although contributions from 17 O12 C18 O and 13 C17 O2 may be nontrivial. In addition, trace water in the reaction bulb (in the gas phase or adsorbed onto the glass) could catalyze CO2 – water isotope exchange reactions and drive the distribution of CO2 isotopologues towards equilibrium, i.e., ∆47 = 0.86‰ at 298K. Both of these uncertainties would be exacerbated as the irradiation time increases, leading to a marked deviation from the modeled result at longer irradiation times. Last, the effects of the O3 decomposition step on ∆47 have not been fully elucidated; previous reports have documented some oxygen isotope exchange 33 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.8: Changes in ∆47 vs. ∆17 O of CO2 after continuous UV irradiation of O2 /O3 /CO2 mixtures with a Hg lamp. Experimental results are compared with calculated results (13 C/12 C KIE = = 13 k/12 k = 1, 0.999, and 0.998 obtained a priori from a kinetics model of the photochemical experiment. Error bars represent 2σ standard errors. when O3 is decomposed on hot nickel [Johnston et al., 2000; Shaheen et al., 2007], perhaps with the nickel oxide layer or surface-adsorbed water, so the post-irradiation O3 decomposition step during CO2 purification may drive ∆47 towards its isotopic equilibrium value (∆47 ∼ 0.8‰ at 333 K; see Wang et al. [2004]) at the nickel’s temperature. We performed experiments to test this hypothesis by heating O3 /CO2 mixtures (with initial ∆47 = 0) in the presence of nickel foil and/or powder at 88, 125, and 155◦ C. The resulting ∆47 values of CO2 showed 1 – 2‰ changes in δ 18 O and 0.5 – 0.6‰ increases in ∆47 , consistent with isotopic equilibration occurring on the nickel surface. Still, the continuous irradiation experiments are consistent with the results of the pulsed photolysis experiments. They show that the O(1 D) + CO2 isotope exchange reaction drives the CO2 isotopologue distribution towards a stochastic distribution. 2.5.3 Conclusions from laboratory measurements In both sets of experiments, ∆47 of CO2 decreases with increasing extent of photochemical isotope exchange, as measured by the change in δ 18 O (∆δ 18 O; see Figure 2.7) or ∆17 O 34 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 of CO2 (see Figure 2.8), indicating the O(1 D) + CO2 reaction does not selectively enrich 16 O13 C18 O relative to 16 O12 C18 O. Furthermore, these results are consistent with a statistical oxygen isotope exchange mechanism; using the results from the 18 O-labeled experiments at 300 K and 229 K and the comprehensive kinetics model of the pulsed photolysis experiment, we calculated a 13 C/12 C KIE of 0.999 ± 0.001 (2σ est.), which is not significantly different from the KIE of 1.000 expected for statistical isotope exchange branching fractions and is quantitatively consistent with the results from the continuous irradiation experiments. Hence, our results are consistent with previous studies asserting that the O(1 D) + CO2 isotope exchange branching fractions are partitioned statistically [Baulch and Breckenridge, 1966; Johnston et al., 2000; Perri et al., 2004]. In contrast, a 13 C/12 C KIE of ∼1.01 would be required to explain the high-latitude isotopic correlations shown in Figure 2.2. A significant ∆47 change due to reactions other than 2.1 and 2.2 in the O(1 D)–CO2 photochemical system is unlikely. The KIEs for the other reactions (e.g., the 17 O12 C18 O-producing channel, which is absent in the pulsed photolysis experiments) would need to be at least 1.01 to be of comparable importance. In addition, the ∆47 – δ 18 O – ∆17 O covariation observed in the continuous-irradiation experiments (which included the 17 O12 C18 O-producing channel; see Figure 2.8) agreed well with our laboratory model, which assumes statistical partitioning of isotope exchange products in the O(1 D) + CO2 reaction. While not all of the relative rates for the O(1 D) + CO2 isotope exchange reaction were measured directly, the agreement between the pulsed-photolysis and continuous-irradiation experiments suggests that KIEs in the other O(1 D) + CO2 reactions [e.g., 18 O(1 D) + 16 O12 C17 O] are described well using statistical product partitioning in this case. Direct measurements of the other KIEs would be required to determine whether the statistical partitioning of isotope exchange products applies rigorously for all O(1 D)–CO2 reactant pairs. As such, we report a 13 C/12 C KIE of 0.999 ± 0.001 (2σ ), which is within the uncertainty of a KIE of 1.000 expected for stochastic isotope exchange. 35 L. Y. Yeung Oxygen isotope exchange reactions of CO2 2.6 Discussion 2.6.1 O(1 D)+CO2 only explains mid-latitude 16 O13 C18 O variations Chapter 2 We conclude that intrinsic isotope effects in O(1 D) + CO2 isotope exchange cannot produce the elevated values of ∆47 observed in stratospheric polar vortex air. Instead, the statistical partitioning of isotope exchange products in the O(1 D) + CO2 reaction drives the isotopic composition of CO2 towards a stochastic distribution, thus decreasing ∆47 . Indeed, the mid-latitude observations show evidence for decreasing ∆47 with increasing extent of photochemical isotope exchange (see Figure 2.2). As photochemical isotope exchange approaches completion (the unlikely, but instructive case in which all the oxygen atoms in CO2 have been exchanged), the ∆17 O and δ 18 O of CO2 will approach the ∆17 O and δ 18 O of O(1 D) because the size of the total oxygen reservoir (i.e., O2 , O3 , etc.) is >500x that of CO2 . Concurrently, the distribution of stable isotopes will become increasingly random, so the ∆47 value of CO2 will approach zero. The slope of this approach, then, reflects the integrated effective isotope composition of O(1 D) with which the CO2 molecules in the air samples have exchanged since entering the stratosphere; it is possible, however, that other terms in the stratospheric CO2 budget (e.g., CO oxidation) may, more subtly, change the isotopic composition of CO2 and thus the isotopic composition of O(1 D) one would infer from such a trend. We constructed a box model to calculate the effective integrated mid-latitude O(1 D) isotope composition to evaluate this hypothesis quantitatively. The results of our laboratory photochemistry model (13 C/12 C KIE experiments) were fit to the slope of weighted linear regressions of the mid-latitude ∆47 data (Figure 2.2). A quenching (reaction 2.5) and nonquenching (reaction 2.6) branching ratio of 9:1 in the isotope exchange reaction was used. Atmospheric ∆47 enrichments (e.g., ∆47 = 1.1‰) were treated as 16 O13 C18 O enrichments exclusively, since contributions to ∆47 from 17 O12 C18 O and 13 C17 O2 are ≤ 3%. Uncertainties in the fit ∆17 O and δ 18 O values were estimated by varying δ 17 O and δ 18 O to match the 2σ uncertainty in the slope of the weighted linear regressions. Using this box model and the mid-latitude observations, we estimate ∆17 O = 80.6+59.7 −24.1 ‰ 36 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 and δ 18 O = 98.0+43.7 −17.1 ‰ (2σ est.) as values for the integrated effective isotopic composition of O(1 D), which is consistent with ozone photolysis being the primary O(1 D) source in the stratosphere. While the δ 18 O of O(1 D) we calculate is similar to that found in low- and mid-latitude stratospheric ozone, ∆17 O is larger, on average, by 35‰ [Krankowsky et al., 2007]. This is expected because ∆17 O enrichments in ozone are concentrated at terminal atom positions [Michalski and Bhattacharya, 2009]; when ozone is photolyzed to O(1 D) and O2 , one of the terminal atoms is ejected [Dylewski et al., 2001], elevating the proportion of heavy oxygen isotopes in O(1 D). We note that the upper and lower uncertainty limits of the reported ∆17 O and δ 18 O values are correlated; they correspond to fits that simultaneously match the upper and lower uncertainty limits of the mid-latitude ∆47 vs. ∆17 O and ∆47 vs. δ 18 O weighted linear regressions. They reflect spatial and temporal variations in O(1 D) isotope composition expected to be caused by variations in ozone concentrations, temperature, pressure, actinic flux, and various mass-dependent kinetic and photolytic isotope effects that depend on these variables. 2.6.2 Effects of intra-stratospheric chemistry and mixing Having experimentally excluded intrinsic isotope effects in the O(1 D) + CO2 isotope exchange reaction as the source of high stratospheric ∆47 in polar vortex air, we consider the possible effects of other gas-phase stratospheric processes on the CO2 isotopologue budget. CO is produced in the stratosphere by CH4 oxidation and destroyed with an e-folding time of about two to three months by reaction with OH radicals to form CO2 . We estimate that up to 0.9 ppmv CO2 could be derived from CH4 oxidation in our samples based on the difference between the observed CH4 concentrations (Table 2.1) and the average CH4 concentration in air entering the stratosphere from the troposphere (1.7 ppmv). 12 C/13 C KIEs for CH4 + OH, CH4 + O(1 D), and CH4 + Cl of 1.004, 1.01, and 1.07, respectively [Brenninkmeijer et al., 2003], should yield 13 C-depleted CH3 radicals at all latitudes, particularly in the polar vortex, where Cl levels are elevated. CH3 radicals then undergo several rapid oxidation steps to form formaldehyde (CH2 O). Isotope effects in CH2 O photolysis to form CO also favor the light isotopologues [Feilberg et al., 2005a]. These isotope effects, com- 37 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 bined with expected 13 C compositions for stratospheric CH4 in these samples (δ 13 C = –47 to –35‰) should produce CO that is depleted in 13 C relative to background stratospheric CO2 . Small inverse 12 C/13 C, 16 O/18 O, and 16 C/17 O KIEs (i.e., < 1) in the reaction CO + OH to form CO2 at low pressures [Röckmann et al., 1998] imply that, in principle, CO + OH reactions could increase ∆47 values in the product CO2 , while at higher pressures, the CO + OH reaction yields 13 C-, 18 O-, and 17 O-depleted CO2 [Feilberg et al., 2005b]. Ultimately, however, the size of ∆47 values in the ≤ 0.9 ppmv CO2 derived from CH4 oxidation would likely be orders of magnitude too small to increase ∆47 values significantly in the other ∼365 ppmv of background stratospheric CO2 . A possibility remains that unusual timing in the competition between oxidation and photolysis of species in the polar vortex, combined with unexpectedly large carbon and oxygen KIEs in some Cl and Br reactions (e.g., Br + CH2 O; see Feilberg et al. [2004]) or other gas-phase processes might be responsible for the mid-latitude-polar vortex differences in ∆47 given the large differences in Cl and Br concentrations in polar vortex vs. mid-latitude air, but this seems unlikely in light of the known chemistry and KIEs. Expected changes in δ 18 O and δ 17 O due to intra-stratospheric mixing are also too small to yield highly enriched polar vortex ∆47 . Effects of CO2 sources on ∆47 can be calculated by solving the three-end-member mixing problem between (1) tropospheric CO2 , (2) stratospheric CO2 undergoing photochemical isotope exchange, and (3) stratospheric CO2 derived from a third source and accounting for the non-linearity in mixing (see Appendix 2.A). Therefore, we constructed a mixing model to simulate the effects of mixing isotopically distinct CO2 sources on stratospheric air. The tropospheric end-member was given an isotopic composition equal to measured ‘clean’ troposphere values (based on measurements of air sampled from Barrow, Alaska, and Cape Grim, Tasmania; see Affek et al. [2007]), namely, δ 13 Ctrop = –8‰, δ 18 Otrop = 41‰, δ 17 Otrop = 21‰, and ∆47trop = 0.92‰. Unfortunately, no measurements of ∆47 in the tropical troposphere exist, so ∆47trop of the air entering the stratosphere from the tropics is uncertain. The mid-latitude ∆47 vs. ∆17 O relationship implies that ∆47 may be as high as 1.09‰, but changes of ∆47trop on this order do not affect our qualitative understanding of mixing on stratospheric ∆47 . The stratospheric end- 38 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 member was δ 13 Cstrat = –8‰, ∆17 O = 80.6‰, and δ 18 O = 98.0‰; this was our integrated effective isotopic composition for O(1 D) calculated from the mid-latitude ∆47 variations. We find that two-component mixing between tropospheric and stratospheric air masses does not exhibit sufficient non-linearity to generate the observed ∆47 enrichments in highlatitude samples. Mixing non-linearities in ∆47 increase as the bulk isotope compositions of the two end-members become more dissimilar, but stratospheric O(1 D)–CO2 isotope exchange alone cannot produce a CO2 mixture of sufficiently high ∆47 . For instance, mixing effects generate ∆47 changes < 0.1‰ in the troposphere [Eiler and Schauble, 2004], where bulk isotope compositions of major constituents of the CO2 budget vary typically < 20‰ [Affek et al., 2007; Ciais and Meijer, 1998]. A mixture of tropospheric CO2 and midlatitude stratospheric CO2 would generate a similar enrichment because their bulk isotope compositions differ by a similar amount. Even in the extreme case of δ 18 Ostrat = 146‰, δ 17 Ostrat = 142‰ and ∆47strat = 0‰, the oxygen isotope composition of CO2 when it is at isotopic equilibrium with excess O3 (an unlikely case, but an ultimately useful one in illustrating this point; see Shaheen et al. [2007]), two-component mixing would yield a maximum ∆47 change more than an order of magnitude smaller than, and in the opposite direction of, that which is observed in polar vortex samples over the same range in ∆17 O. Bulk isotope compositions of the two CO2 reservoirs must differ in δ 18 O and/or δ 13 C by orders of magnitude not previously observed in the stratosphere to generate ∆47 enrichments of ∼0.7‰ observed in polar vortex samples. 2.6.3 Effects of mesospheric and heterogeneous chemistry Physical or chemical processes in the mesosphere may yield extreme isotopic enrichments in CO2 or CO such that subsidence of mesospheric air into the 1999/2000 stratospheric polar vortex [Plumb et al., 2003] could explain the observed meridional variation in ∆47 . Thus, we will next consider three mesospheric processes that have been previously studied in other contexts: Gravitational separation of upper atmospheric air, UV photolysis of O2 , and UV photolysis of CO2 . 39 L. Y. Yeung 2.6.3.1 Oxygen isotope exchange reactions of CO2 Chapter 2 Mixing of gravitationally separated air into the stratosphere Gravitational separation can concentrate heavy isotopologues of CO2 into the lower mesosphere [Ishidoya et al., 2008], which could elevate stratospheric ∆47 values after mesospheric subsidence and mixing. The expression in Craig [Craig et al., 1988] for the enrichment of a species Ni versus a second species N in per mil is based on the kinetic theory of gases [Gibbs, 1948]:  Ni ∆ N  = ∆M gZ × 103 RT (2.8) where ∆M is the difference in mass, g is the acceleration due to gravity (9.81 m s−2 ), Z is the column length, R is the gas constant, and T is the temperature. Using a reasonable column length of 50 km at a temperature of 220 K, gravitational separation of CO2 would increase δ 13 C, δ 18 O, and δ 17 O by 266‰, 6223‰, and 1113‰, respectively, but would lead to a decrease in ∆47 by 74‰ at the bottom of the column. In addition, polar vortex δ 13 C is not markedly more enriched from mid-latitude δ 13 C, implying that gravitational separation is generally negligible for the samples in this study. 2.6.3.2 Mixing of mesospheric air highly enriched in 17 O and 18 O Isotope effects in the photolysis of O2 by short-wavelength UV radiation in the upper mesosphere might lead to unusually enriched CO2 in the mesosphere. Liang et al. predicted recently that differences in photolysis cross-sections between light and heavy isotopologues of O2 in the narrow solar Lyman-α region (121.6 nm) may result in a population of mesospheric O(1 D) enormously enriched in 17 O and 18 O [Liang et al., 2007]. This extreme enrichment in O(1 D) could then be transferred to mesospheric CO2 through the O(1 D)+CO2 isotope exchange reaction. CO2 photolysis in the mesosphere to form CO, followed by oxidation of that same CO by OH in the polar vortex, might also significantly affect the ∆47 values of CO2 in the polar vortex. To evaluate the effects of 17 O- and 18 O-enriched mesospheric CO2 mixing into the stratospheric polar vortex, we constructed a three-component mixing model that included air 40 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Table 2.6: Tropospheric-stratospheric-mesospheric mixing model results Sample name f ∗trop f strat f meso 0.075 0.057 0.048 0.033 2.6 × 10−6 δ 18 Ostrat (‰) δ 18 Omeso (‰) 82.5 80.0 77.7 87.9 1.76 × 105 δ 18 O (‰) ∆17 O (‰) ∆47 (‰) Mixing model results 20000312(25)1120 20000131(30)1001 20000203(10)1173 20000127(5)1060 0.925 0.943 0.952 0.967 2.1 × 10−6 1.4 × 10−6 1.7 × 10−6 ∗ Mixing fraction of tropospheric air, calculated as 1 – f 1.86 × 105 2.07 × 105 1.47 × 105 44.55 43.62 43.06 42.79 5.76 4.38 3.69 2.45 1.614 1.555 1.436 1.233 strat – f meso . mass contributions from the troposphere, stratosphere, and mesosphere. Each polar vortex datum (i.e., with unique ∆17 O, δ 18 O, and ∆47 values) was fit individually because of the presence of mesospheric filaments in the polar vortex [Plumb et al., 2003] and consequent heterogeneity in the mixing fraction and end-member isotopic composition between samples. The multiply-substituted isotopologue distribution was fixed at ∆47meso = 0 for this simple mixing-only scenario because our kinetics experiments and the mid-latitude stratosphere ∆47 values indicate that isotope exchange drives the isotopologue distribution towards a stochastic one. No measurements of mesospheric δ 13 C exist, so δ 13 Cmeso = –8‰ was used; however, the calculated enrichment in mesospheric δ 18 O was insensitive to the choice of δ 13 C. We were unable to reproduce the polar vortex data in both bulk isotope compositions and ∆47 simultaneously when using the mesospheric 18 O and 17 O enrichments in CO2 mixing end-member suggested by Liang et al. [2007] (i.e., δ 18 O = 10,603‰, δ 17 O = 3,149‰, and ∆47 = 0). Only after δ 18 O and δ 17 O of the mesospheric CO2 end-member were increased an additional tenfold (i.e., δ 18 O ∼ 105 ‰ and δ 17 O ∼ 104 ‰) were the ∆47 – δ 18 O – ∆17 O systematics of the polar vortex samples reproduced. Modeled mixing fractions ( ftrop , fstrat , and fmeso ) and isotopic compositions for each of the high-latitude CO2 samples are given in Table 2.6. Due to the uncertainty in our calculated ∆17 Ostrat and δ 18 Ostrat values (see Section 2.6.1), δ 18 Ostrat was allowed to vary freely about our estimate above; the resulting δ 18 Ostrat values generally fell within the range we predicted. The combined uncertainties introduced by our calculated mid-latitude O(1 D) isotope composition and the other parameters used in these 41 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 fits suggest that these results are likely only meaningful to within an order of magnitude. No laboratory measurements of the isotopic fractionations in O2 due to Lyman-α photolysis are available to compare with our modeled isotopic compositions, however. Because 3 − the Lyman-α lines fall on the edge of the Ẽ 3 Σ− u ← X̃ Σg (1,0) absorption band of O2 , a small absolute absorption cross-section error for one O2 isotopologue can translate into a significant isotopic fractionation error. Relaxing the mesospheric δ 18 O vs. δ 17 O relationship predicted by Liang et al. [2007], i.e, δ 17 O = 0.3 × δ 18 O, increases the modeled δ 18 Ostrat values and lowers the predicted δ 18 Omeso values, but the mesospheric CO2 mixing end-member is still enriched overall to ∼100,000‰ in δ 18 O and δ 17 O. A simple calculation (assuming 365 ppm CO2 and an initial δ 18 O = 23.5‰ in O2 ) predicts that the mesospheric O2 end-member should have a δ 18 O value on the order of –100‰. Furthermore, we note that the O(1 D) + CO2 reaction may not necessarily partition products statistically (i.e., drive ∆47 → 0) in the mesosphere, as we assumed here, because the average collision energy there is higher than in the stratosphere. In principle, measurements of the isotopic composition of mesospheric CO should constrain the isotopic composition of mesospheric CO2 downwelling into the polar vortex. Large elevations in CO above background stratospheric levels, observed at high altitudes in the polar vortex [Plumb et al., 2003], are due to CO2 photolysis in the mesosphere and subsequent transport to the stratosphere, so the isotopic composition of CO in these cases should reflect that of the mesospheric CO2 population and any fractionations arising from CO2 photolysis there. The bulk isotope composition in mesospheric CO2 predicted by our three-component mixing model (e.g., tens of percent in 18 O-atom abundance, or 100x natural abundance) would result in isotopic enrichments in mesospheric CO that are detectable with remote-sensing spectrometers because CO2 photolysis isotope effects are expected to be much smaller in magnitude. For example, Bhattacharya et al. [2000] measured fractionations of ∼100‰ in 17 O and 18 O in their UV-photolysis experiments; CO2 -photolysis fractionation in the mesosphere could be larger, but the wavelength dependence of these across the actinic spectrum is difficult to estimate because the physical origin of the laboratory fractionations is not understood (see below). Remote-sensing measurements by the JPL 42 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 MkIV Fourier-transform spectrometer, however, does not show hundred-fold enrichments in 18 O of mesospheric CO observed downwelling to 30 km altitude in the polar vortex (G. C. Toon, personal communication, 2009). On the basis of this observation, mesospheric CO2 does not appear to possess oxygen isotopic enrichments of sufficient size to produce high ∆47 values in the polar vortex upon mixing with stratospheric air masses, although the long path-length and consequent averaging over mesospheric filaments and background stratospheric air of the MkIV instrument will dilute any mesospheric signal. Remote sensing of CO and/or CO2 isotopologue abundances in the mesosphere are thus needed to constrain this hypothesis. 2.6.3.3 Oxidation of mesospheric CO in the polar vortex Next, we examine the potential impacts of mesospheric CO2 photolysis to form CO, followed by mixing and re-oxidation into CO2 , on polar vortex ∆47 values. The photolysis of CO2 in the UV region may result in wavelength-dependent isotope effects, although this contention is based on a single laboratory measurement. Bhattacharya et al. [2000] performed laboratory experiments in which they photolyzed CO2 with either a Kr lamp (120 – 160 nm) or a Hg lamp (185 nm) and measured the 17 O and 18 O compositions of the product CO and O2 . The 120 – 160 nm results suggest that mass-dependent depletions of order 50‰ and 100‰ in 18 O and 17 O of CO, respectively, are possible, which would enrich the remaining CO2 reservoir in 18 O and 17 O. The 185-nm results were quite different: Photolysis of CO2 near natural isotopic abundance showed mass-independent enrichments in 17 O up to 150‰ with little change in 18 O in the CO and O2 products, while photolysis of 13 C-labeled CO2 showed mass-dependent enrichments in 18 O and 17 O in the 13 CO and O2 products of ∼50 and 100‰, respectively. Taken alone, these latter isotope dependences could result in mesospheric CO that is significantly enriched in 18 O, 17 O, and 13 C, and perhaps even 13 C18 O. The remaining mesospheric CO2 would be correspondingly depleted in heavy isotopologues. If similar isotopic fractionations occur in CO and CO2 when CO2 is photolyzed by UV radiation in the mesosphere, then the population of mesospheric CO downwelling into the 43 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 stratospheric polar vortex could have a large impact on the ∆47 values of CO2 in the polar vortex. Once in the stratosphere, mesospheric CO will be oxidized by OH to produce CO2 in the polar vortex. Oxidation of this CO could, in principle, contribute to the large polar vortex values of ∆47 in CO2 observed because: (1) CO mixing ratios as large as 10 ppmv have been observed in mesospheric filaments in the stratosphere (a thousand-fold higher than background stratospheric CO abundances in the polar vortex) [Plumb et al., 2003], (2) the known KIEs for the CO + OH reaction are expected to favor formation of 13 C18 Ocontaining CO2 molecules in the stratosphere [Feilberg et al., 2005b; Röckmann et al., 1998], and (3) the lifetime of CO with respect to oxidation is several months, and is therefore not immediately quantitative. These three phenomena could result in a sub-population of CO2 with elevated concentrations of 16 O12 C17 O, 16 C12 C18 O, and 16 C13 C18 O (or other mass-47 isotopologues of CO2 ), given the sign and magnitude of known KIEs for the CO + OH reaction [Feilberg et al., 2005b; Röckmann et al., 1998]. The slow oxidation of CO may only produce temporary increases of heavy-isotopologue abundances, as large fractionations due to KIEs will decrease in magnitude as CO oxidizes quantitatively to CO2 . Measurements of the 13 C18 O + OH vs. 12 C18 O + OH KIE by Feilberg et al. at 298K and 1 atm suggest that the oxidation of mesospheric CO alone could account for elevated ∆47 in the stratospheric polar vortex [Feilberg et al., 2005b]. Consequently, CO2 photolysis in the mesosphere, followed by oxidation of the product CO in the mesosphere and/or stratosphere, may allow the heavy oxygen and carbon isotopes in CO2 to ‘reorganize’ in a manner that could elevate ∆47 values of CO2 in the polar vortex. The mixing of the remaining (unphotolyzed) mesospheric CO2 with stratospheric CO2 in the polar vortex, however, may have the opposite effect on ∆47 values of CO2 . Measurements of all the relevant KIEs of CO + OH reaction at stratospheric temperatures and pressures and a model of the oxidation of mesospheric CO in the stratospheric polar vortex will be required to evaluate the impact of this mechanism quantitatively. The full impact of this mechanism is not well-constrained, however, because (1) the isotopic composition of mesospheric CO2 has not been measured, (2) not all the KIEs for the CO + OH reaction are known at the relevant temperatures and pressures, and (3) the 44 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 physical origin of the photolytic fractionations associated with CO2 photolysis are not understood. The first two points were discussed earlier, so they will not be discussed here. For the physical origin of the photolytic fractionations associated with CO2 photolysis, Bhattacharya et al. suggested that dissociation rates for certain CO2 isotopologues could be enhanced if their excited vibrational states (which get populated when the molecule absorbs UV light) overlap sufficiently with the vibrational states of another CO2 electronic state. This would facilitate conversion of the electronically excited species CO2 (1 B2 ), which is promoted from ground-state CO2 when it absorbs UV light and does not have enough energy to dissociate into O + CO under the experimental conditions, into the electronically excited species CO2 (3 B2 ), which does have enough energy to dissociate. If this mechanism is a general feature of the dynamics of CO2 photodissociation, it could lead to additional mass-independent fractionations at wavelengths other than at 185 nm. Unfortunately, this hypothesis has not been tested at other wavelengths yet, and without a firm theoretical understanding, or at least an empirical wavelength dependence, of the isotopic fractionations associated with CO2 photolysis, convolving the 120 – 160 nm results with the 185 nm results from Bhattacharya et al.’s experiments, and then convolving those with the actinic flux to make a prediction for ∆47 of mesospheric CO and CO2 is not possible. 2.6.3.4 Heterogeneous chemistry on stratospheric particles Finally, we consider the potential role stratospheric particles could play in the stratospheric CO2 isotopic budget. Oxygen isotope exchange on particle surfaces could drive the population of CO2 towards isotopic equilibrium by catalyzing CO2 –CO2 isotope exchange reactions (e.g., 16 O12 C18 O+13 C16 O2 * ) 12 C16 O2 + 16 O13 C18 O) that are too slow to occur in the gas phase under stratospheric conditions. Zero-point energy isotope effects dominate in these reactions at equilibrium, driving the ∆47 value towards its equilibrium value at a given temperature. We calculate that ∆47 adopts a value of 1.6‰ if 70% of the CO2 molecules achieve isotopic equilibrium at temperatures coincident with PSC formation in the polar vortex, ∼190 K [Wang et al., 2004] . Thus, in principle, particle-catalyzed equilibration of CO2 , perhaps via CO2 hydration reactions in quasi-liquid films at the surface of ice particles 45 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 [Dash et al., 2006], could produce the observed polar vortex ∆47 values. Bulk isotopic compositions would be little-affected by these isotope exchange reactions, consistent with the data presented in Table 2.1 and Figure 2.2, if the catalyst reservoir (e.g., liquid water layers on a surface) is much smaller than the CO2 reservoir; CO2 would impart its bulk isotopic composition on the catalyst while the multiply-substituted isotopologue distribution in CO2 , which is insensitive to the isotopic composition of the catalyst, approaches that at isotopic equilibrium. However, CO2 –liquid water isotope exchange may not occur quickly enough at low temperatures and low pH to be the relevant process. Last, we note that, in order for this PSC-catalyzed isotope-exchange mechanism to explain the polar vortex ∆47 measurements, the mechanism must result in a strong anti-correlation with N2 O mixing ratios (Figure 2.2a); this would imply that transport is fast compared to isotope exchange on the PSCs, whose distributions are highly variable in space and time in the polar vortex. Future 2-D modeling efforts will examine whether such a mechanism remains consistent with the observations or whether transport and mixing of a mesospheric isotope signal into the polar vortex better explains the observed anti-correlation of ∆47 with N2 O. We conducted preliminary experiments on the kinetics of isotope exchange on PSClike surfaces (e.g., H2 SO4 /HNO3 /H2 O mixtures; see Molina et al. [1993]) to test the PSCisotope-exchange hypothesis. PSCs made from HNO3 :H2 O mixtures, i.e. ‘Type Ia’ PSCs, were tested first because they were a major component of the PSCs formed during the 1999/2000 Arctic winter [Voigt et al., 2000] and their crystallization has been studied in the laboratory [Hanson and Mauersberger, 1988]. 50% HNO3 in H2 O was crystallized at 197 K using an ethanol/dry ice bath according to the protocol outlined by Hanson and Mauersberger [1988]; the crystal structure and stoichiometry of the ice was not measured. Pure CO2 of known isotopic composition was then exposed to the HNO3 ice for 3 hours in a glass reaction vessel held at 197 K. No change in the ∆47 values were observed (within statistical uncertainty). Based on the volume of the reaction vessel and the amount CO2 , the root-mean-square (RMS) displacement was 2.5 cm s−1 . This RMS displacement was significant compared to the 15-cm length of the reaction vessel; therefore, the reaction’s progress was probably not hindered by diffusion. The same experiment was performed also 46 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 with 1:1:1 H2 SO4 :HNO3 :H2 O mixtures (similar to ‘Type Ib’ PSCs) at 197 K, and no isotope exchange was observed in those experiments, either. These preliminary results imply that CO2 isotope exchange on PSCs is slow at stratospheric temperatures, although the chemical composition of the surfaces generated in the laboratory may have been different from those of real PSCs. Future studies should explore the isotope exchange reaction on all known PSC surfaces (e.g., types Ia, Ib, and II; see Zondlo et al. [2000] and Prenni and Tolbert [2001]) and assign upper limits to their rates. 2.7 Conclusions The signature of a new process preserved in stratospheric 16 O13 C18 O proportions reveals that a second mechanism, in addition to the O(1 D) + CO2 isotope exchange reaction, alters the isotopic composition of stratospheric CO2 and thus the interpretation of its chemical and transport ‘history.’ This second mechanism, which elevates ∆47 values in the polar vortex, is likely of either mesospheric photochemical or heterogeneous origin. To constrain further the role of each of these mechanisms, isotopic fractionations due to broadband UV photolysis of O2 and CO2 , the KIEs of the CO + OH reaction under stratospheric conditions, and the kinetics of CO2 isotope equilibration on the surfaces of PSCs and other stratospheric aerosols need to be studied experimentally. Additionally, kinetic and photolysis-induced isotope effects that may affect CO and CO2 should be incorporated into atmospheric models to quantify their contributions to both the bulk and multiply-substituted isotopologue budgets of stratospheric CO2 , whose influence on the isotopologue budgets of tropospheric CO2 may be significant. 2.8 Acknowledgements We thank R. Lueb for whole-air-sampler and cryogenic whole-air-sampler field support, Y. L. Yung, G. A. Blake, and P. O. Wennberg for manuscript comments, and financial support from the Davidow Fund, the National Science Foundation, the NASA Upper Atmosphere Research Program. K. A. B. was supported by the Camille Dreyfus Teacher-Scholar Award. 47 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Appendices 48 Chapter 2 L. Y. Yeung 2.A Oxygen isotope exchange reactions of CO2 Chapter 2 Mixing effects on isotopic composition The effects of CO2 air parcel mixing on isotopic composition have specific relevance for ∆47 in Chapter 2, so an example follows below. In general, mixing of two or more reservoirs of CO2 is linear in δ 13 C, δ 18 O, and δ 17 O (the mixture has δ -value in between that of the two mixing end-members) because the references against which they are compared are constant (see Eqs. 1.5 and 1.6) Mixing of two reservoirs with the same ∆47 and differing bulk isotope distributions, however, can yield ∆47 values in the mixture different from those in the endmember gases. This nonlinear dependence of ∆47 on mixing arises because both R47 sample and the reference against which it is measured (R47 stochastic ) change upon mixing; the reference is defined by, and therefore varies with, the bulk stable isotope ratios of that mixture. In contrast, the references used in bulk stable isotope measurements are external standards whose values are constant (e.g., VSMOW), so the bulk isotope ratios vary linearly with mixing. The degree of nonlinearity in ∆47 is a function of the differences in bulk isotopic composition between the mixing end-member reservoirs and their mixing fractions [Affek and Eiler, 2006; Eiler and Schauble, 2004]. Because ∆47 depends non-linearly on mixing fraction, even for two CO2 reservoirs with similar ∆47 [Affek and Eiler, 2006; Eiler and Schauble, 2004], mixing relationships are often counterintuitive. An illustrative example is shown in Figure 2.9: The two mixing endmembers (given as the bottom-left and bottom-right corners) have different initial δ 18 O and δ 17 O values, though both have δ 13 C = –8‰ and ∆47 = 0.92‰. The concentration of 47 CO2 (i.e., R47 mix ) varies linearly with mixing fraction, but the stochastic distribution for 47 CO2 molecules also changes, varying as ∼2R13 R18 . Consequently, mixing these two isotopically dissimilar CO2 reservoirs yields a ∆47mix > 0.92‰ despite each reservoir being initially at ∆47 = 0.92‰. This type of relationship is general, and so holds for all ∆47 ; the sign and magnitude of the resulting ∆47 change will depend on the end-member bulk and clumped isotope compositions. 49 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.9: How mixing two arbitrary reservoirs of CO2 can be nonlinear in ∆47 . The resulting mixture is more enriched in 47 CO2 relative to its stochastic distribution, as compared to either of the mixing end-members. The isotopic compositions used in this plot are for illustration purposes only; qualitatively similar effects will apply for all mixing relationships. 50 L. Y. Yeung Oxygen isotope exchange reactions of CO2 2.B Practical considerations 2.B.1 IRMS long-term signal stability Chapter 2 ∆47 measurements currently take ∼4 hours of instrument averaging time per sample analysis. We examined the stability and accuracy of our IRMS system over this time period by using a modified form of the Allan variance technique, originally developed to characterize ultrastable oscillators [Allan, 1987]. Instead of using time as the independent variable, here we use individual IRMS acquisitions x: 2 σAllan (x) = 1 [hxii+1 − hxii ]2 2(N − 1) ∑ i (2.9) Data are first binned into N bins (each consisting of one or more acquisitions), and the average of each bin, hxii , is taken. The difference between adjacent bins is squared and then summed before being normalized to compute the Allan variance. For example, a data set with six elements [x1 , x2 , x3 , x4 , x5 , x6 ] will produce three values of Allan variance corresponding to bins of one ([x1 ], [x2 ], [x3 ], [x4 ], [x5 ], [x6 ]), two ([x1 , x2 ], [x3 , x4 ], [x5 , x6 ]) and three ([x1 , x2 , x3 ] and [x4 , x5 , x6 ]) elements each. The maximum bin size is therefore half the total number of elements in a data set. Plotting Allan variance versus bin size, then, conveniently presents both noise- and driftrelated effects on single plot. An example of the ∆47 Allan variance for a relatively longduration analysis, consisting of 40 acquisitions of 80 s sample integration each (ten 8 s cycles), is shown in Figure 2.10. An ideal statistical-noise-limited measurement, for which long-term drifts are negligible, will display a power-law relationship σ 2 = Cxα in the Allan variance plot, where α = –0.5, reflecting the Poisson statistics governing the precision of the overall measurement. In contrast, a measurement dominated by long-term, correlated random-walk drifts will have α = 0.5. Consequently, the optimum number of measurements to average together in a given analysis (i.e., the optimum bin size) will occur near where the Allan variance reaches a minimum, i.e. where dα/dx = 0. For our instrument, measurements seem to be dominated by statistical noise for N < 10 acquisitions, with only a small contribution from long-term drift. The variability of σ 2 appears to increase for 51 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.10: Allan-variance plot of ∆47 over 40 IRMS acquisitions. A power-law regression is shown for bins up to nine acquisitions. α = –0.47 was obtained, indicating that Poisson statistics, not long-term drifts, dominate the uncertainties in the measured ∆47 value in this range. measurements made in excess of nine acquisitions (see Figure 2.10), although we attribute this to the smaller number of bins with greater than nine acquisitions contributing to the Allan variance calculation. More precise values of the Allan variance with these numbers of acquisitions would require a more sustained analytical run by several factors in time. Nevertheless, the ideal precision that should be attainable on a single gas run for measurements that are clearly dominated by statistical noise (nine acquisitions, or 720-s counting time) at the optimal voltage (16 V) is 0.013‰. 2.B.2 IRMS vs. optical methods The best high-precision isotope-ratio measurements have been made routinely on gassource mass spectrometers based on Nier’s original 1947 design [Nier, 1947]. These instruments are fundamentally sensitive to that which makes stable isotopes unique — their mass — so IRMS continues to be the technique-of-choice used for stable isotope abundance measurements. It achieves high precision over a large dynamic range by utilizing multiple Faraday cups with differing amplifier gains (over a factor of 3000 for ∆47 measurements) 52 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 and rapid sample-standard comparison. However, the relatively poor mass-resolving power (M/∆M ∼ 500) that comes as a consequence of using a magnetic sector and high-sensitivity, electrically stable Faraday-cup detectors leads to well known isobaric (same-nominal-mass) interferences, e.g., between 13 CO2 and 16 O12 C17 O at m/z = 45. In ‘clumped’ isotopologue measurements of CO2 , isobars and other impurities (e.g., N2 O, hydrocarbons) are especially important given the low absolute abundance of m/z = 47 isotopologues. A new concern also arises in the study of ‘clumped’ isotopologues: ion recombination after electron-impact ionization source can alter the measured distribution of stable isotopes vs. that present in the original sample. High-resolution and thermal-ionization mass-spectrometric techniques can potentially address these uncertainties, but none have yet demonstrated the precision and stability necessary for ∆47 measurements. Spectroscopic techniques, however, show great promise for measuring stable isotopologue abundances in natural samples because they are non-destructive, sensitive to both mass and molecular symmetry, and field-deployable. These characteristics are particularly desirable for studying the stable isotope distribution in atmospheric gases, and how they evolve over time. The author has had some experience with these techniques so the following discussion represents a synthesis of his experience. While most examples relate to CO2 , the general considerations presented here should be applicable to spectroscopic stable isotope measurements of other species. More general and thorough reviews of the literature have been published (e.g., Kerstel [2004]; Kerstel and Gianfrani [2008]), so the references herein are exemplary rather than comprehensive. Three main instrumental requirements for highly precise optical measurements of rare and/or ‘clumped’ isotopologues near natural isotopic abundance are apparent: absolute sensitivity, dynamic range, and long-term signal stability. A more subtle problem is the selection of spectral region; the spectral absorption scales not only with analyte concentration, but also the optical pathlength and the size of the transition dipole (i.e., the absorption line strength, S, for the transition). In addition, spectral overlap between isotopologues and also from contaminants will lead to systematic errors. The type of spectroscopic technique, then, will depend on the analyte identity and spectral region. For instance, Tuzson et al. 53 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 [2008] used the strong CO2 lines (S ∼ 10−18 cm molecule−1 ) near 2300 cm−1 and a multipass direct absorption cell [Herriott et al., 1964] to measure δ 13 C and δ 18 O with better than 0.1‰ precision (100-s averaging). The authors utilized that region because the transitions for 12 C16 O2 , 13 C16 O2 , and 16 O12 C18 O were of nearly equal strengths. Bergamaschi et al. [1994] made similar line choices for δ 13 C and δ D measurements in CH4 . McManus et al. [2002] surmounted the dynamic range problem for their CO2 isotopologue measurements by designing an optical cell with differential absorption pathlengths for each isotopologue, allowing CO2 lines differing in intensity by several orders of magnitude to be measured precisely. In both cases, long-term drifts (e.g., temperature, laser power, frequency jitter etc.) were accounted for by simultaneous measurement of a reference gas. Other important variables to consider are sample temperature stability and spectral line function. Bergamaschi et al. [1994] reported an approximate sensitivity of the measured δ -value and temperature (T ) in per-mil units: ∆δ ∆E × 1000 ≈ ∆T kT 2 (2.10) where k is Boltzmann’s constant and ∆E is the difference in lower-state energies of the corresponding transitions. It is derived from the Taylor series expansion of a normal (Gaussian) distribution [Schupp, 1992]. Empirically, this translates to ± 5‰ K−1 for bulk stable isotope measurements of H2 O and CO2 [Kerstel and Gianfrani, 2008], so a temperature stability between the reference gas and the sample of 50 mK would yield temperature-induced errors of 0.1‰. Kerstel and Gianfrani [2008] also make the argument that measurement of peak intensities is sufficient so long as the lineshape functions are the same between the sample and standard transitions. ‘Clumped’ isotope measurements present a new set of concerns due to the more stringent technical demands, e.g., measuring a signal 4.5 × 10−5 with 0.005‰ precision for ∆47 based carbonate thermometry [Huntington et al., 2009]. At present, high-precision IRMS measurements of ∆47 involve multiple comparisons between the sample CO2 gas, bulk stable isotope working standards, and ‘clumped’ stable isotope standards (CO2 with a stochastic distribution of isotopologues). Any spectroscopic technique will require similar calibrations 54 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 because the instrument response, in general, will not be sufficiently linear over such a large range in concentration. For instance, the required linear dynamic range for rovibrational transitions of 12 C16 O2 and 16 O13 C18 O with identical v and J (absolute sensitivity concerns notwithstanding) is ≥109 . Photoacoustic methods are capable of this dynamic range, in principle, but previous attempts to make high-precision isotopic measurements have been limited by fluctuations in pump laser power [Samura et al., 2002]. On the other hand, if a convenient spectral window is found such that line strengths of the dominant and minor isotopologues are similar, the temperature sensitivity will be large (e.g., due to large differences in the lower-state energies). From a practical perspective, the line strength of the minor isotopologue will dictate the choice of method; for instance, the strongest 16 O13 C18 O transition in the mid-IR has a line intensity S ∼ 10−23 cm molecule−1 , which is out of range for all but the most sensitive spectroscopic techniques. Of the high-sensitivity optical techniques, cavity ringdown spectroscopy (CRDS; O’Keefe and Deacon [1988]) with frequency-axis stabilization and single-mode operation (FS-CRDS; [Hodges et al., 2004]) shows the most promise, in this author’s opinion. A key feature in FS-CRDS is its ability to average spectra on the timescales of hours; the utility of other ultrasensitive methods, such as the shot-noiselimited NICE-OHMS technique (noise-immune, cavity-enhanced optical heterodyne molecular spectroscopy) [Ye et al., 1998], have been ultimately limited by technical pitfalls and long-term drifts [Foltynowicz et al., 2008]. In contrast, FS-CRDS can be averaged continuously for nearly 10 hours to achieve a signal-to-noise ratio (SNR) of 18,000 (i.e., 0.6‰ precision) on a single line of intensity S = 1 × 10−24 cm molecule−1 at 0.5 Torr [Long et al., 2009]. Higher SNRs may be possible with the implementation of single-mode optical feedback [Motto-Ros et al., 2008], optoelectronic laser-locking [Drever et al., 1983], or in combination with rapid (kHz) sample-background ringdown comparison [Ye and Hall, 2000]; increasing sample concentration will also improve the SNR, but the dynamic range of the instrument will place an upper limit on the maximum line strength. The choice of lineshape theory used to obtain the integrated intensity might also be important [Lisak et al., 2006, 2009], as the integrated intensity is a more robust measurement of isotopic abundance than 55 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 peak height, which increases nonlinearly with gas pressure. At present, IRMS is the only practical method for measuring ‘clumped’ isotopologue abundances in in CO2 with precisions better than 0.1‰. Spectroscopic measurements for CO2 will be best in the mid-IR region, where the rovibrational transitions are strongest (S16 O13 C18 O ∼ 10−23 cm molecule−1 ); single-mode quantum-cascade lasers with ≥ 5 mW power are becoming widely available in that region. Another possibility for CO2 is the 2-µm region, where the strongest 16 O13 C18 O line strength is S16 O13 C18 O ∼ 3 × 10−26 cm molecule−1 (4826.05 cm−1 ); analysis time will be increased accordingly. The NICE-OHMS method is capable of reducing analysis times significantly, in principle, because it has demonstrated a shot-noise-limited sensitivity for strong laser sources (e.g., SNR = 7700 in 1s for S = 1 × 10−23 cm molecule−1 using a 5 mW Nd:YAG) [Ye and Lynn, 2003; Ye et al., 1998]. However, technical challenges such as long-term temperature and frequency stability must be addressed. While examining the possibility for measuring ‘clumped’ CO2 isotopologues spectroscopically is useful for illustrating the general principles involved, this approach will ultimately be the most useful for other species of atmospheric and geochemical interest. For instance, isotopic abundances in SO2 are canonically difficult to measure due to its polarity [Gao and Thiemens, 1991, 1993]; high-precision IRMS systems rely on a viscous-flow injection into the ionization region, and high-polarity gases such as SO2 often display a pronounced ‘memory’ effect that limits measurement precision and reproducibility [Ono et al., 2006]. SO2 lines in the mid-IR (∼2500 cm−1 ) are of comparable strength to those of CO2 in the 2-µm region (see above), so ‘clumped’ isotopologue measurements of SO2 may be possible, with long averaging times, in the near future. These measurements have the potential to establish a link between the ancient atmosphere and the geologic record. For instance, Lyons [2009] has proposed that the unique sulfur and oxygen isotope composition of Archaean Fig-tree barites [Bao et al., 2007] may reflect gas-phase SO2 –H2 O isotope exchange reactions; ‘clumped’ isotope analysis would place additional constraints on the origins of these and other barites, which contain information about the sulfur and oxygen cycles, atmospheric composition, and climate of the ancient past. 56 L. Y. Yeung 2.C Oxygen isotope exchange reactions of CO2 Chapter 2 Low-temperature cell for 13 C/12 C KIE experiments For the low-temperature 13 C/12 C KIE experiments, the quartz reaction chamber (filled with N2 O, CO2 , and He) was placed inside a cooling assembly within a conflat vacuum chamber. The vacuum chamber was first pumped down to ∼20 – 50 mTorr, and then liquid N2 coolant (∆Hvap = 1.33 kcal mol−1 ) was added through a feedthrough at the top of the chamber. The liquid N2 cooled a series of metal (“conduction” and “transfer”) blocks, which, in turn, cooled the quartz reaction cell along its entire length. Temperature was monitored using a standard type-K thermocouple; active temperature control was possible, though it was not necessary to achieve temperatures near 230 ± 1 K when the liquid N2 was poured into the feedthrough. The cooling assembly was designed to fit inside a spare ∼27 × 27 × 21 cm (l × w × h, interior dimensions) conflat chamber with a 9.5-cm ID (see Figures 2.11, 2.12, and 2.13). Experimental and spatial constraints dictated the design parameters, and the resulting assembly had little flexibility. Use of 193-nm laser radiation to photolyze N2 O meant that quartz (UV-grade fused silica) windows were the most affordable and robust window material; MgF2 windows can provide ∼10% greater transmission at 193 nm, but quartz was chosen because it was cheaper and could be bonded with a quartz tube to make a monolithic, leak-tight reaction chamber without need for adhesives. During an experiment, the reaction chamber was inserted directly into the oxygen-free, high conductivity (OFHC) copper tube (2.14). This tube was fastened to the “conduction block” (Figure 2.15), which was itself attached to the OFHC copper “heat-transfer block” by a countersunk screw on the rounded underside of the conduction block. A second heat-transfer block (Figure 2.17) was sandwiched between the heat-transfer block and the connection to the liquid N2 feedthrough (Figure 2.18); this block had a relatively small surface area and was machined out of brass (120 W m−1 K−1 vs. 401 W m−1 K−1 for copper at 300 K) to retard heat transfer from the liquid N2 to the reaction cell. The second heat-transfer block also had a hole drilled through the center so a heating resistor could be inserted, if necessary, to control the temperature in future experiments. All components were mated with a thin layer of Apiezon “N” grease; this material was 57 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.11: Schematic of conflat chamber used for low-temperature 13 C/12 C KIE experiments. Figure 2.12: Photograph of conflat chamber used for low-temperature 13 C/12 C KIE experiments. 58 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 chosen over other compounds because of its ability to perform at low temperatures (down to liquid He), low coefficient of thermal expansion (≤ 10−4 K−1 ) and minimal thermal creep. However, it has a very low thermal conductivity (0.1 – 0.2 W m−1 K−1 ), which slowed the cooling process. Typically, the assembly took 40 – 60 min to cool from 300 K to 229 K. While higher-efficiency thermal compounds would have accelerated cooling of the reaction chamber, Apiezon “N” was sufficient to achieve stable temperatures above 200 K. Small modifications were made to the cooling assembly for planned O(1 D) + CH4 and OH + CH4 KIE experiments (see Figure 2.19). Because the target temperatures for those experiments are 140 K ≤ T ≤ 200 K, the two “heat-transfer” blocks were combined into a single OFHC copper heat-transfer block with a larger contact area with the existing “conduction block” (see Figures 2.20 and 2.21). The primary cooling block was smoothed (the shallow channel removed) to mate well with the new conduction block. Last, metal-tometal mating surfaces were cleaned and the Apiezon “N” grease replaced with a thermal paste containing silver particles (thermal conductivity ∼ 9 W m−1 K−1 ). With this new assembly and the pressurized delivery of liquid N2 from a free-standing dewar into the feedthrough, the quartz reaction cell was cooled to temperatures of ∼140 K within 10 min. Temperature control electronics are currently being designed. 59 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Figure 2.13: Cold cell assembly. Figure 2.14: Machining diagram for the OFHC copper tube. 60 Chapter 2 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.15: Machining diagram for the OFHC copper conduction block. 61 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.16: Machining diagram for the OFHC copper heat transfer block. Figure 2.17: Machining diagram for the brass heat transfer block. 62 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.18: Machining diagram for the OFHC copper connection to the liquid N2 feedthrough. 63 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.19: Cold cell assembly for O(1 D), OH + CH4 KIE experiments. Figure 2.20: Machining diagram illustrating the modifications made to the conduction block for O(1 D), OH + CH4 KIE experiments. 64 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 2 Figure 2.21: Machining diagram for the OFHC copper heat transfer block designed for O(1 D), OH + CH4 KIE experiments. 65 L. Y. Yeung Oxygen isotope exchange reactions of CO2 2.D MATLAB code for hard-sphere collision model 2.D.1 montecarlo.m Chapter 2 % Program for calculating 18O(1D)−CO2 collision energy in experiments clear x y z j v1i v2i r; points=50000; % number of points per collision T=300; % temperature in K m1=18; % mass of O(1D) m2=4; % mass of buffer gas (He: 4, N2: 28) mCO2=44; ET2lab=18.2; %8.6 for O3 photolysis at 248 nm % Etrans (kcal/mol) in the Lab frame Equil=(3/2)*8.314472/4.184/1000*T; % Equipartition energy vOpeak=sqrt((ET2lab*1000*4.184*2)/(m1/1000)); % O(1D) atom velocity vMreduced=vOpeak/sqrt((Equil*1000*4.184*2)/(m2/1000)); % buffer gas velocity in units of O(1D) velocity %vMreducedCO2=vOpeak/sqrt((Equil*1000*4.18*2)/(mCO2/1000)); ncolltot=200; % Number of collisions zz=zeros(points,ncolltot); % distribution of final O(1D) velocities zzz=zeros(points,1); % distribution of initial O(1D) velocities CO2=zeros(points,ncolltot); % distribution of collision energies with CO2 dist=zeros(points,ncolltot); % distribution of buffer gas velocities PM=97; %1−380e−6 for 'stratospheric' % pressure of buffer gas in Torr PCO2=3; %380e−6 for 'stratospheric' % pressure of CO2 in Torr Pcoll=PCO2/(PCO2+PM); % ratio of CO2 to buffer gas (reaction probability per collision) for l=1:ncolltot nPcoll(l)= Pcoll*(1−Pcoll)ˆ(l−1); % multiplied by (1−(3.1e−11/1e−10))ˆ(l−1) for 'stratospheric' % fraction of O(1D) that reacts at each collision end digits(10); nPcoll=vpa(nPcoll); for j=1:points ncoll=1; v1i=randn*exp(−1.5)+vMreduced; % pick a random v for O(1D) from a gaussian distribution about vMreduced zzz(j)=v1i; % record the velocity in a matrix 66 L. Y. Yeung Oxygen isotope exchange reactions of CO2 theta1i=rand*3.14159265359; % pick a random azimuthal angle between 0 and pi for O(1D) phi1i=rand*2*3.14159265359; % pick a random azimuthal angle between 0 and 2pi for O(1D) v2i=randn;%metropolis([v2i,5]); theta2i=rand*3.14159265359; % pick a random azimuthal angle between 0 and pi for M phi2i=rand*2*3.14159265359; % pick a random azimuthal angle between 0 and 2pi for M while (phi1i < phi2i) phi2i=rand*2*3.14159265359; % prevents imaginary results in scatter function end impact=randˆ2; % pick a random (b/bmax) with probability proportional to itself omega=rand*3.14159265359; % pick a random azimuthal angle for b between 0 and pi while (ncoll ≤ ncolltot) % calculate O(1D) trajectory for n collisions vrel=sqrt((v1i*sqrt(mCO2/m2))ˆ2+v2iˆ2−2*v1i*v2i*(sin(theta1i)* sin(theta2i)*cos(phi1i−phi2i)+cos(theta1i)*cos(theta2i))); % calculating initial relative velocity CO2(j,ncoll)=((1/2)*((mCO2*m1/(mCO2+m1))/1000)*(vrel* sqrt((Equil*1000*4.184*2)/(mCO2/1000)))ˆ2)/(4.184*1000); % calculate initial collision energy w/CO2 v1f=scatter(m1, m2, v1i, theta1i, phi1i, v2i, theta2i, phi2i, impact, omega); % calculate final velocity after one more collision zz(j,ncoll)=real(v1f); % record the final velocity dist(j,ncoll)=v2i; % record in initial velocity of M v1i=real(v1f); % reset initial velocity as the final velocity after a collision theta1i=rand*3.14159265359; % pick a new azimuthal angle for O(1D) phi1i=rand*2*3.14159265359; % pick a new polar angle for O(1D) v2i=randn; % pick a new velocity for M theta2i=rand*3.14159265359; % pick a new azimuthal angle for M phi2i=rand*2*3.14159265359; % pick a new polar angle for M while (phi1i < phi2i) % prevents imaginary results in scatter program phi2i=rand*2*3.14159265359; end impact=randˆ2; % pick a new impact parameter (b/bmax) omega=rand*3.14159265359; % pick a new scattering angle ncoll=ncoll+1; % rinse, repeat end end bins=250; % number of bins 67 Chapter 2 L. Y. Yeung Oxygen isotope exchange reactions of CO2 upperlimit=25; % range, 0 − upperlimit binsvector=zeros(1,upperlimit); % generating empty histogram bin vector to improve performance for c=1:bins binsvector(1,c)=(upperlimit/bins)*c; % generating histogram bins end [Ppercollision,bin]=histc(CO2,binsvector); % generating binned histogram matrix of CO2, Ppercollision for k=1:ncolltot % each column is reactive probability distribution at that collision Ppercollision(:,k)=Ppercollision(:,k)*double(nPcoll(k)); % each column is weighted by the fraction of remaining O(1D) atoms end Ecollavg=sum(CO2)/points; % average collision energy at each collision number dlmwrite('v1i.csv',zzz); % write matrix of initial O(1D) velocities to file, v1i.csv dlmwrite('v1f.csv',zz); % write matrix of final O(1D) velocities to file, v1f.csv dlmwrite('Ecollpercollision.csv',CO2); % write matrix of per−collision collision energies to file dlmwrite('Ppercollision.csv',Ppercollision); % write binned histogram matrix of CO2 to file, Ppercollision.csv 2.D.2 scatter.m % Function solving the two−particle scattering problem function v1f=scatter(m1, m2, v1i, theta1i, phi1i, v2i, theta2i, phi2i, impact, omega) vrel=sqrt(v1iˆ2+v2iˆ2−2*v1i*v2i*(sin(theta1i)*sin(theta2i)* cos(phi1i−phi2i)+cos(theta1i)*cos(theta2i))); % relative veocity calculation v1c=(m2*vrel)/(m1+m2); % v1 (O(1D)) in the COM frame v2c=(m1*vrel)/(m1+m2); % v2 (M) in the COM frame vcm=sqrt(m1ˆ2*v1iˆ2+m2ˆ2*v2iˆ2+2*m1*m2*v1i*v2i*(sin(theta1i)* sin(theta2i)*cos(phi1i−phi2i)+cos(theta1i)*cos(theta2i)))/(m1+m2); % velocity of the COM thetacm=acos((m1*v1i*cos(theta1i)+m2*v2i*cos(theta2i))/((m1+m2)*vcm)); % azimuthal angle in the COM frame phicm=acos((m1*v1i*sin(theta1i)*cos(phi1i)+m2*v2i*sin(theta2i)* cos(phi2i))/((m1+m2)*vcm*sin(thetacm))); % polar angle in the COM frame alpha=acos((v1iˆ2−(vcmˆ2+v1cˆ2))/(2*vcm*v1c)); % azimuthal scattering angle in the COM frame deflect=2*acos(impact); % polar scattering angle in the COM frame l=v1c*(cos(deflect)*cos(alpha)−sin(deflect)*sin(alpha)*cos(omega)); v1f=sqrt((vcm+l)ˆ2+v1cˆ2−lˆ2); 68 Chapter 2  L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Chapter 3 A hyperthermal O-atom exchange reaction, O2 + CO2 Adapted from Yeung, L. Y., M. Okumura, J. T. Paci, G. C. Schatz, J. Zhang, and T. K. Minton (2009), Hyperthermal O-Atom Exchange Reaction O2 + CO2 through a CO4 Intermediate, J. Am. Chem. Soc., 131(39): 13,940–13,942. ©2009 American Chemical Society Publications. 69 L. Y. Yeung 3.1 Oxygen isotope exchange reactions of CO2 Chapter 3 Abstract O2 and CO2 do not react under ordinary conditions, owing to the thermodynamic stability of CO2 and the large activation energy required for multiple double-bond cleavage. We present evidence for a gas-phase O-atom exchange reaction between neutral O2 and CO2 at elevated collision energies (≈ 160 kcal mol−1 ) from crossedmolecular-beams experiments. Products were scattered mainly in the forward direction, i.e., in the initial direction of the hyperthermal oxygen beam in the centerof-mass (c.m.) frame, with 16% of the available energy in translation, on average. CCSD(T)/aug-cc-pVTZ calculations demonstrate that isotope exchange can occur on the ground triplet potential energy surface through a short-lived CO4 intermediate that isomerizes via a symmetric CO4 transition state containing a bridging oxygen atom. We propose a plausible adiabatic mechanism for this reaction supported by additional spin-density calculations. 70 L. Y. Yeung 3.2 Oxygen isotope exchange reactions of CO2 Chapter 3 Introduction O2 and CO2 do not react under ordinary conditions. This can be attributed to the large activation energy for multiple double-bond cleavage, as Dixon illustrated in his early experiments in which dry CO–O2 –CO2 mixtures “did not explode” when subjected to a spark discharge [Dixon, 1886]. Otomo et al. [2000] later reported a reaction of CO2 and electronically excited O2 ∗ when they observed O3 products after irradiating super- and subcritical O2 /CO2 mixtures with UV light. While investigating the isotope exchange reaction 16 O(3 P) +12 C18 O2 →18 O +16 O12 C18 O (3.1) at hyperthermal collision energies in a crossed-molecular-beams experiment, we found evidence for the gas-phase oxygen isotope exchange reaction 16 O2 +12 C18 O2 →18 O16 O +16 O12 C18 O (3.2) of ground-state reactants at high collision energies (∼160 kcal mol−1 ). Our observations on the dynamics of this reaction, taken together with ab initio calculations of stationary points on the lowest triplet potential energy surface (PES), suggest a plausible adiabatic mechanism for the reaction of O2 with CO2 through a CO4 transition complex. 3.3 Experimental studies 3.3.1 Methods Crossed-molecular-beam experiments were performed with a hyperthermal oxygen source containing ∼87% O(3 P) and ∼13% O2 (3 Σ− g ) [Brunsvold et al., 2007, 2008; Garton et al., 2006, 2009]. A diagram of the experimental setup, configured for 16 O(3 P) + 12 C18 O 2 collisions, is shown in Figure 3.1. A pulsed beam of 16 O(3 P) and 16 O2 (3 Σ+ g ; at an unknown vibrational temperature) was generated by laser-induced detonation of 16 O2 using a high-energy CO2 TEA laser (6 – 7 J pulse−1 ) operating at a pulse repetition rate of 2 Hz. Though initially broad in velocity distribution (6 – 9 km s−1 ), a portion of the overall 71 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 beam was velocity-selected for the scattering experiments using a synchronized chopper wheel operating at 300 Hz. This velocity-selected beam was crossed, at a nominal angle of 90◦ , with a pulsed supersonic expansion of 98% 12 C18 O2 gas (2% 16 O12 C18 O; Spectra Gas). The molecular beams and scattered products were detected with a rotatable quadrupole mass spectrometer with electron-bombardment ionization [Brink, 1966] at 160 eV and a Daly-type ion counter [Daly, 1960]. 12 C18 O2 and 16 O12 C18 O products were detected at m/z 16 12 18 + = 48 (12 C18 O+ 2 ) and 46 ( O C O ), respectively, with a rotatable mass spectrometer that collected number density distributions as a function of arrival time, N(t), at a given laboratory angle, Θ, using a multi-channel plate (MCP). Here, Θ is defined as the angle at which the 16 O12 C18 O scatters with respect to the direction of the reagent oxygen beam (i.e., Θ = 0◦ ). Time-of-flight (TOF) distributions for 16 O(3 P), 16 O2 , 12 C18 O2 , and 16 O12 C18 O were collected over a range of laboratory angles (6◦ – 54◦ ); at each angle, the TOF distribution for the 33.7-cm distance between the beam interaction region to the ionizer was integrated to give a laboratory angular distribution, N(Θ). A forward-convolution method was used to derive the center-of-mass (c.m.) translational energy P(ET ) and angular T(θ c.m. ) distributions from the laboratory N(t) and N(Θ) distributions [Lee, 1988], where θ c.m. is the angle at which 16 O12 C18 O scatters with respect to the reagent oxygen direction in the c.m. frame. The canonical Newton diagrams used in this analysis are shown in Figure 3.2. Figure 3.1: Crossed-molecular-beam apparatus with hyperthermal oxygen source. 72 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.2: Canonical Newton diagram for hyperthermal 16 O2 + 12 C18 O2 collisions. The Newton circles represent the maximum recoil velocities of the products. The hyperthermal oxygen beam was generated by laser detonation of a pulsed expansion of O2 gas with 500 psig stagnation pressure using a source based on the design of Caledonia et al. [1987]. 174 µs after the pulsed valve is triggered, the CO2 laser is fired; the laser pulse passed through an antireflection-coated ZnSe window in to the source chamber, whereupon it was reflected back towards the gold-plated, water-cooled copper nozzle with a 1 m radius concave gold mirror. The focused laser pulse initiates a breakdown of the O2 gas and heats the resulting plasma to > 20,000 K, which accelerates both the atomic and molecular oxygen fractions of the pulsed beam to 6 – 9 km s−1 . Use of a conical nozzle allowed for efficient ion-electron recombination and inefficient atom-atom and atom-molecule recombination as the plasma expanded and cooled. The resulting gas pulse was collimated by a 1 cm diameter aperture located 80 cm downstream of the inlet nozzle into a differentially pumped region (10−5 – 10−6 Torr), after which it passed through a 1.2-mm-diameter skimmer 16 cm further downstream. The beam interaction region was an additional 3 cm downstream in the main chamber (2 × 10−7 Torr), a total distance of 99 cm from the inlet nozzle. For velocity selection within the hyperthermal oxygen beam, a chopper wheel running at 300 Hz (synchronized with the 2-Hz laser pulses) was placed inside the main scattering 73 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 chamber, just downstream of the skimmer. Three equally-spaced slots (1.5 mm wide) of the chopper wheel pass over an LED/photodiode assembly a quarter-turn before each slot enters the beam axis, generating a 900 Hz (3 × 300 Hz) train of pulses. These chopper wheel pulses are sent to a digital delay generator and used as references for triggering the O2 gas pulses. The time delay between the chopper wheel pulse and the O2 pulse determined the portion of the overall hyperthermal oxygen beam allowed to pass through into the interaction region. We characterized the velocity distribution of the hyperthermal oxygen beam under two conditions: on axis (Θ = 0◦ ) with a small aperture (∼125 µm diameter) to obtain the peak of the distribution, and off axis (Θ = 3◦ ) with a large aperture (4 mm × 4 mm) to obtain the width of the distribution. For the on-axis configuration, a 2 mA emission current at the ionizer and a –18 kV potential at the secondary emitting electrode of the Daly ion counter was used. For the off-axis configuration, a 10 mA emission current at the ionizer and a –30 kV potential at the secondary emitting electrode was used. Laboratory TOF distributions under both conditions were measured, for both 16 O and 16 O2 , to determine the laboratory-frame velocities and translational energy distributions for the hyperthermal oxygen beam. In these experiments, the average velocity of the hyperthermal oxygen beam was thus determined to be 8262 ± 450 m s−1 (i.e., 900 m s−1 full width at half maximum; FWHM), which corresponds to average translational energies hET i = 130.5 ± 14 kcal mol−1 and 261.0 ± 28 kcal mol−1 FWHM for 16 O(3 P) and 16 O2 , respectively (see Figure 3.3). The relative amounts of atomic (∼87%) and molecular (∼13%) oxygen were determined by integrating the TOF distributions at m/z = 16 (16 O+ ) and 32 (16 O2 + ) at Θ = 0◦ and correcting for O2 fragmentation (11% of the m/z = 32 signal) in the electron-bombardment ionization region. A pulsed supersonic expansion of 12 C18 O2 was generated using a piezoelectric pulsed general valve with a 1300-Torr stagnation pressure. The expansion passed through a 2 mm diameter skimmer (9.2 cm from the nozzle) into a differential pumping region, and then through a 2.5 mm diameter (2.8 cm downstream of the skimmer) aperture into the main scattering chamber. The distance from this aperture to the interaction region was 1.5 cm. 74 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.3: Velocity distribution of hyperthermal oxygen beam. The velocity distribution of the 12 C18 O2 beam was not measured directly, and instead was determined iteratively by first estimating the terminal velocity of the supersonic expansion [Lee, 1988] and then fitting the 12 C18 O2 velocity to the value that yielded the best Newton circle for non-reactively scattered O-atoms while keeping the measured O-atom velocity distribution fixed at its measured values. This contributes some uncertainty to the measured TOF distributions because the 12 C18 O2 beam velocity is likely only accurate to ±10%. However, because the magnitude of the hyperthermal oxygen beam velocity at the interaction region was ten times that of the 12 C18 O2 beam, and its FWHM was also 4 – 5 times that of the 12 C18 O2 beam, uncertainties in the “time-zero” of the hyperthermal oxygen source dominated the overall uncertainty in the measured translational energy distributions. Laboratory TOF product distributions were measured every 2◦ between Θ = 6◦ – 54◦ . Scattered product TOF distributions were collected for 200 beam pulses for for m/z = 16 (16 O+ ) and 32 (16 O2 + ), for 1000 beam pulses for m/z = 46 (16 O12 C18 O+ ), and for 500 beam pulses for m/z = 48 (12 C18 O2 + ). Dwell time for each channel at the MCP was 1 µs. At a representative laboratory angle of 10◦ , integrated count rates were 1.1 × 107 s−1 for m/z = 16, 1.3 × 107 s−1 for m/z = 32, 1.8 × 105 s−1 for m/z = 46 , and 4.2 × 106 s−1 for m/z 75 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 = 48. Raw flight times were converted to flight times over the 33.7 cm distance between the interaction region and the electron-bombardment ionizer by subtracting the O2 triggerpulse-to-laser-fire delay time (174 µs), an electronic-latency delay time (3 µs), the oxygen flight time from the nozzle to the interaction region (120 µs, corresponding to the average velocity of the hyperthermal oxygen beam), and finally the ion flight time between the 1 ionizer and the Daly ion counter. The ion flight time is given by α(m/z) 2 , where α = 2.44 in these experiments, determined by comparing the relative arrival times of hyperthermal 16 O and 16 O at the detector [Garton et al., 2006]. Some uncertainty arises in the product 2 times-of-flight because the exact time- and point-of-origin of the hyperthermal oxygen beam are not well determined; we estimate this uncertainty to be ∼2 µs because the laser pulse width in the hyperthermal oxygen source could be as long as 1 µs (a 100 ns-wide peak with a slow tail). Two signal corrections were made before data analysis. First, we corrected for beam divergence at Θ = 6◦ – 16◦ . The divergent intensity with the 12 C18 O2 beam turned off was measured by obtaining TOF distributions at m/z = 16 and 32 from Θ = 6◦ – 16◦ . These TOF distributions were then scaled and subtracted from the corresponding experimental TOF distributions at m/z = 16 and 32 that had the 12 C18 O2 beam turned on. Uncertainties in the inelastic and reactive scattering signals due to collisions of the divergent hyperthermal oxygen could not quantified, however; they were instead considered in the analysis of the laboratory data, where collisions at crossing angles of 88◦ , 89◦ , 90◦ , 91◦ , and 92◦ were included during forward-convolution fitting. Adding more crossing angles did not affect the forward-convolution fits significantly. Second, we verified that the 12 C18 O2 beam contained 2% 16 O12 C18 O using the instrument’s mass spectrometer. Thus, 2% of the inelastic scattering signal (m/z = 48) at each laboratory angle (Θ = 6◦ – 54◦ ) was subtracted from raw m/z = 46 (16 O12 C18 O+ ) TOF distributions to obtain reactive-scattering-only distributions. A forward-convolution method was employed to perform the laboratory-to-c.m. frame coordinate transformation [Lee, 1988] of the data using the MSU XBEAM program (Version 6). Trial P(ET ) and T(θ c.m. ) distributions were used to simulate the laboratory-frame TOF distributions using the following relationship derived from the Jacobian transformation: 76 L. Y. Yeung Oxygen isotope exchange reactions of CO2 N(t, Θ) α l3 P(ET )T (θc.m. ) ut 3 Chapter 3 (3.3) where l and t are the distance and flight time, respectively, from the interaction region to the ionizer, and u is the product velocity in the c.m. frame. During the fitting process, 12 C18 O2 was assumed to have a single-valued velocity, 800 m s−1 , because the large magnitude and width of the hyperthermal oxygen beam velocity distribution is principally responsible (i.e., it contributed ≥ 98% of the uncertainty in the c.m. collision energy; see above) for the observed width of the laboratory TOF distributions and the c.m. translational energy distributions. The width of the hyperthermal beam velocity distribution was fit by a Gaussian function centered at 8262 m s−1 and a FWHM of 900 m s−1 , which was used during data analysis. Note that the data we report for flight times over a 33.7 cm distance were calculated by subtracting the average oxygen flight time from the nozzle to the interaction region; the reported product arrival times, then, reflect a convolution of the oxygen beam’s wide velocity distribution and the ‘true’ product translational energy distribution, so the best-fit P(ET ) distributions may not be unique. As such, we estimate the uncertainties in the reported P(ET ) distribution to be 10 – 20%. To allow for easy manipulation of the P(ET ) and T(θ c.m. ) distributions, parameterized functions were often used. The fitting process often relied on the RRK form of the P(ET ) distribution: P(ET ) = (ET − B) p (Eavail − ET )q (3.4) where Eavail is the available translational energy in the c.m. frame (i.e., the collision energy, Ecoll , minus the endothermicity, ∆E). The parameters B, p, and q were adjusted to vary the peak and width of the c.m. translational energy distribution when obtaining a best fit to the laboratory data. The T(θ c.m. ) distribution was described by a Legendre polynomial form: Tk (θc.m. ) = ak ck (cos2 θc.m. − 1)k 2k k! c(cos θc.m. ) (3.5) where ak is an adjustable parameter for each of the eleven polynomial terms used, which 77 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.4: Laboratory TOF distribution of m/z = 46 (16 O12 C18 O+ ; green circles) at Θ = 6◦ , with the inelastic scattering signal removed. The data are shown with the O(3 P) + CO2 (dot-dashed black line), O2 + CO2 (dashed blue line), and summed (solid red line) forward-convolution fits. Flight times less than 72 µs violate energy conservation for 16 O(3 P) + 12 C18 O2 . The inset compares the raw TOF distribution with the IS TOF distribution, which is subtracted. were denoted by the subscripted k = 0, 1, 2,...10. The functional forms for the P(ET ) and T(θ c.m. ) distributions (3.4 and 3.5, respectively), were iterated in XBEAM until they provided satisfactory fits to the laboratory data, though, in some cases, point forms of the P(ET ) and T(θ c.m. ) distributions were used. Finally, the “best-fit” P(ET ) and T(θ c.m. ) distributions were used to create a c.m. velocity-flux contour map or a differential scattering cross-section plot for the products. 3.3.2 Results The inset in Figure 3.4 shows a raw m/z = 46 TOF distribution of 16 O12 C18 O products recorded at Θ = 6◦ . A small fraction of the signal can be attributed to inelastic scattering (IS) of 16 O12 C18 O impurities in the CO2 beam by 16 O and 16 O2 , and it can be subtracted. The remaining signal, shown in Figure 3.4, represents 16 O12 C18 O products from O-atom exchange reactions of 12 C18 O2 (see Chapter 4). We initially expected the reactive m/z = 46 signal to arise from reactions of 12 C18 O2 with the 16 O atoms (reaction 3.1) with a broad distribution of c.m. collision energies (Ecoll ) 78 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 peaked at 98.8 kcal mol−1 and a full width at half maximum (FWHM) of 18 kcal mol−1 . However, at small laboratory angles, we observed products with velocities that would violate energy conservation for this O(3 P) + CO2 reaction (e.g., t < 72 µs in Figure 3.4). 12 C18 O −1 (see Lee [1988]). 2 was estimated to have a laboratory velocity of 800 ± 80 m s Given the broad velocity distribution in the O(3 P)/O2 beam (8262 m s−1 with 900 m s−1 FWHM), the velocity spread in the 12 C18 O2 beam was insignificant by comparison, so the hyperthermal oxygen beam largely determined the broad distribution of collision energies sampled in these experiments. To calculate the maximum available translational energy in the laboratory frame for 16 O(3 P) + 12 C18 O2 and 16 O2 + 12 C18 O2 isotope exchange reactions, an initial 16 O(3 P)/16 O2 beam velocity of 8862 m s−1 was used because < 5% of the O(3 P)/O2 beam had a greater velocity. A non-negligible population of 16 O12 C18 O was observed at translational energies above the maximum allowed for 16 O(3 P) + 12 C18 O2 collisions at small laboratory angles. Despite the uncertainties in the Ecoll distribution and product flight times (see Section 3.3.1), we observed 16 O12 C18 O products arrive 10 – 20 µs faster than the minimum times allowed by the distribution of available energies, Eavail (≈Ecoll ; the zero-point energy change is +0.1 kcal mol−1 ), for reaction 3.1. Forward-convolution best-fits to the TOF distributions that only treat the 16 O(3 P) + 12 C18 O2 isotope exchange reaction cannot explain the fastest laboratory data at small laboratory angles (e.g., Θ = 6◦ and 8◦ ; see Figure 3.5). Increasing hET i in the product P(ET ) shifts the fastest part of the fit towards shorter flight times at all laboratory angles. While this improves the TOF fits at small laboratory angles, it decreases the quality of the TOF fits at larger laboratory angles (see Θ = 36◦ in Figure 3.6). Introducing the 16 O2 + 12 C18 O2 isotope exchange reaction yields good fits at all laboratory angles. A sizeable fraction of the products assigned to the 16 O2 + 12 C18 O2 reaction are slow enough that they do not violate conservation of energy; however, assigning them to the 16 O(3 P) + 12 C18 O 2 reaction leads to poor fits. Collisions between CO2 and ions or electronically excited O atoms could also yield 16 O12 C18 O products with elevated velocities, previous experience with this hyperthermal source indicates that they are not present in the beam [Troya et al., 2004]. 79 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.5: TOF distributions (green dots) for 16 O12 C18 O products at laboratory angles Θ = 6◦ and 8◦ with the inelastic scattering signal removed. Also shown are forwardconvolution best fits (solid red line) that treat only one isotope exchange reaction, 16 O(3 P) + 12 C18 O2 → O + 12 C18 O2 . The forward-convolution fits cannot account for the fastest 16 O12 C18 O product signals at small laboratory angles. We therefore hypothesize that the fast 16 O12 C18 O products come from reaction of 12 C18 O2 with 16 O2 in the hyperthermal beam. Because the velocity-selected 16 O2 molecules have the same laboratory-frame velocity distribution as the 16 O atoms, the 16 O2 molecules collide with the 12 C18 O2 molecules at substantially higher c.m. energies (see Newton diagram in Figure 3.2). The resulting collision energy distribution peaked at Ecoll = 158 kcal mol−1 with FWHM = 28 kcal mol−1 . Thus, 16 O12 C18 O products from reaction 3.2 have sufficient Eavail to account for the fastest products detected. The m/z = 46 signal would then contain products of both reactions 3.1 and 3.2, the fastest products arising exclusively from reaction 3.2. P(ET ) and T(θ c.m. ) distributions for reactions 3.1 and 3.2 were simultaneously obtained from forward-convolution fits of the m/z = 46 TOF distributions. The results for the 16 O2 + 12 C18 O2 reaction are presented in Figure 3.7; a c.m. velocity-flux contour diagram of 16 O12 C18 O products is shown in Figure 3.8, in which the observed product flux is peaked in the forward direction. The presence of signal at flight times violating energy conservation for 16 O(3 P)–12 C18 O2 collisions was used to guide the fitting process because the TOF distributions do not resolve the products unambiguously. As such, we cannot rule out an additional dynamical channel in reaction 3.1 contributing to some of the signal we attribute to reaction 3.2 because energy conservation in reaction 3.1 is only violated at small lab angles. 80 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.6: TOF distributions for 16 O12 C18 O (m/z = 46) at various laboratory angles Θ with the inelastic scattering signal removed. The raw data are shown as circles. Forwardconvolution fits of the 16 O2 + 12 C18 O2 (blue dashed curve) and 16 O(3 P) + 12 C18 O2 (black dot-dashed dashed curve) channels, along with their sum (red solid curve), are also shown. 81 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.7: Center-of-mass-frame (A) angular and (B) translational energy distributions from the 16 O2 + 12 C18 O2 oxygen isotope exchange reaction obtained from TOF fits of m/z = 46. The peak of the distribution of available energies is Eavail = 158 kcal mol−1 . Only the experimentally accessible range of c.m. angles (θ c.m. < 100◦ ) is shown. Figure 3.8: Velocity-flux contour diagram for 16 O12 C18 O products of 16 O2 + 12 C18 O2 collisions in the center-of-mass frame. The white arrows are the initial 16 O2 and 12 C18 O2 velocity vectors, and dashed white line is the maximum recoil velocity for 16 O12 C18 O (vmax ). 16 O12 C18 O products are scattered opposite the initial direction of the 12 C18 O velocity vector. 2 82 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 The 16 O12 C18 O products scattered mainly in the forward direction (θ c.m. = 0◦ ), though there was significant sideways scattering. Experimental sensitivity in the backward direction was insufficient to detect backward-scattered 16 O12 C18 O products, so forward-backward symmetric scattering (i.e., evidence for a long-lived intermediate complex) could not be ruled out. At these collision energies, however, an intermediate is unlikely to survive for a rotational period. The average total translational energy distribution for the two products was 25 kcal mol−1 , or 16% of the available energy; the P(ET ) distribution was peaked at ET = 10 kcal mol−1 . We estimate the yield for reaction 3.2 to be ≤ 2% of all O2 –CO2 collisions. This estimate is an upper limit because the complete Newton circle for inelastically scattered 16 O 2 + 12 C18 O 2 products was not observed in these experiments. Vibrational excitation of the O2 may also be important in promoting reaction, but the vibrational temperature of O2 present in the expanded plasma is unknown. Our experimental results are consistent with a 16 O12 C18 O product that rebounds from the 12 C18 O2 reactant’s initial direction after it collides with O2 ; this mechanism is characteristic of reactions with substantial activation energies that require high collision energies. The highly peaked angular distribution is consistent with a direct mechanism or a very short-lived intermediate, but more surprising is the substantial internal energy of the products, which is much greater than that found for similar oxygen isotope exchange reactions between O(3 P) + CO, O(1 D) + CO2 , and O + O2 [Brunsvold et al., 2008; Perri et al., 2004; Van Wyngarden et al., 2007]. This large translational-to-internal energy conversion suggests that the reaction proceeds through an intermediate species that facilitates efficient translational-to-internal energy transfer or through a non-adiabatic transition to another electronic surface. On average, 134 kcal mol−1 of internal energy is available to both products. This excess energy could be distributed among the five vibrational and four rotational degrees of freedom in O2 and CO2 . Alternatively, this energy could be in the form of electronically 3 + 3 00 excited products, including the a1 ∆g , b1 Σ+ g , and A Σu states of O2 , and the a A state of CO2 , which lies 119 kcal mol−1 above that for CO2 (1 Σ+ g ) [Braunstein and Duff , 2000]. The mass-spectrometric detection, however, did not allow us to determine the electronic states 83 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.9: Energetically allowed neutral product channels from O2 + CO2 collisions. Energies are taken from the NIST Webbook [http://webbook.nist.gov], [Mebel et al., 2004], and [Braunstein and Duff , 2000]. of the products. Other reaction channels are possible (see Figure 3.9). We cannot rule out a CO2 + O + O product channel because we did not collect sufficient data on the counter-fragment 18 O16 O. However, the energetically allowed CO 3 3 2 + O( P) + O( P) channel (∆H = 118 kcal mol−1 ) is spin-forbidden, and spin conservation would instead favor O(1 D) + O(3 P) products, whose energetic threshold is 163 kcal mol−1 and above the average Eavail in the experiment. There is also sufficient energy to form O3 + CO or O + CO3 [Mebel et al., 2004], and to dissociate CO2 to form O2 + O + CO, but because we were not anticipating these reactions, we did not search for the relevant detectable products. 84 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.10: Calculated energies and structures on the lowest triplet PES of O2 + CO2 . TS3 connects isoenergetic isomers of the CO4 shelf. 3.4 Theoretical studies To investigate whether an adiabatic mechanism exists for the O2 –CO2 isotope exchange reaction, we performed ab initio calculations to find stationary points on the lowest triplet PES for O2 + CO2 reaction at the CCSD(T)/aug-cc-pVTZ level of theory using the MOLPRO electronic structure code [Werner et al., 2006]. We identified two transition states (TS1 and TS2) connecting O2 + CO2 reactants with a triplet shelf state [CO4 (3 A00 ); see Figure 3.10 and Table 3.1]. All three structures are planar. One atom of the oxygen molecule approaches the carbon atom of CO2 and surmounts an activation barrier of 77.9 kcal mol−1 over TS1 to form a weak C–O bond and a CO4 (3 A00 ) shelf (76.4 kcal mol−1 , just 1.5 kcal mol−1 below TS1) similar to a weakly bound CO4 complex found at the B3LYP level of theory [Cacace et al., 2003; Elliott and Boldyrev, 2005]. At 121.8 kcal mol−1 , we identified an effective transition state for CO4 (3 A00 ) isomerization, TS3, containing a four-membered ring between the carbon atom and three oxygen atoms. A grid-based search revealed that TS3 is bound by 0.02 kcal mol−1 when zero-point energy is not considered, and that TS3 85 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Table 3.1: Energies of stationary points associated with the exchange reaction O2 + CO2 → O2 + CO2 on the lowest triplet potential energy surface∗ † CHF ∆E [CCSD(T)/aug-cc-pVTZ] ‡ ∆EZPE [CCSD(T)/aug-cc-pVTZ] ∆E (CASPT2/cc-pVTZ) CO4 TS1 TS2 TS3 0.973 76.0 76.4 91.2 0.977 77.9 77.9 95.6 0.969 80.0 78.3 97.1 0.945 120.9 121.8 137.4 ∗ ∆E in kcal mol−1 . † Coefficient of the Hartree-Fock configuration in the (8,10)-CASSCF expansion of the wave- functions. ‡ ZPE-corrected. This calculation was not performed at the CASPT2 level of theory. is connected to CO4 ; a displacement in Od < 0.01 Å towards CO4 produced CO4 upon geometry optimization. Thus, it acts as an ‘effective’ transition state for CO4 isomerization; it resembles the bound CO4 (1 A1 ) structure lying 52.5 kcal mol−1 below it, although with a longer Oc –Od bond length; both structures have C2v symmetry [Cacace et al., 2003; Elliott and Boldyrev, 2005; Jamieson et al., 2007]. We observed some evidence for multi-reference character in CO4 . An additional bound state was found 0.8 kcal mol−1 above the energy of CO4 at the MP2/cc-pVTZ level of theory, although it does not exist at the CCSD(T)/aug-cc-pVTZ level; the species is believed to be a resonance structure of CO4 (3 A00 ). A spin contamination of hS2 − Sz2 − Sz i = 0.011 in the region of the PES near TS3 also suggests some multi-reference character. Thus, CASPT2/cc-pVTZ calculations, which represent resonance qualitatively correctly and do not suffer from spin contamination, were performed to validate the CCSD(T) structures and energies. CO4 (3 A00 ) was confirmed as a resonance hybrid of two bound-state structures, although the contribution from the single-reference structure to the resonance hybrid dominates the final geometry. The results of those calculations are summarized in Table 3.1 and Figure 3.11. The uncertainty in the CCSD(T)/aug-cc-pVTZ energies is unknown, although a similar study in which the stationary points of the closely related O(3 P) + CO2 system were characterized was recently completed (see Chapter 4). In addition to CCSD(T)/aug-cc-pVTZ simulations, W4 calculations (close to the full configuration-interaction and infinite-basis-set 86 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.11: Calculated stationary point geometries on the lowest triplet PES of CO4 . CCSD(T)/aug-cc-pVTZ values (upper) and CASPT2/cc-pVTZ (lower) values are shown. limits; see [Karton et al., 2006]) were also performed, as they were found to be affordable, albeit marginally. The differences between the CCSD(T) and W4 results for the transition and bound states indicated a mean-unsigned error of 2.2 kcal mol−1 . We expect the errors in the analogous O2 + CO2 energies to be approximately the same. 3.5 Proposed mechanism A possible pathway for oxygen isotope exchange occurs through the forward and reverse directions of the following three steps: O2 + CO2 → [CO4 ]‡ (TS1/TS2) → CO4 (3 A00 ) → [CO4 ]‡ (TS3); see Figure 3.12. Spin-density maps (Figure 3.13) depicting the singlyoccupied molecular orbitals (SOMOs) for CO4 and TS3 are consistent with this mechanism. CO4 (3 A00 ) is a diradical with unpaired electron density concentrated in p-type orbitals of the Figure 3.12: Calculated energies and structures on the lowest triplet PES of O2 + CO2 . TS3 connects isoenergetic isomers of the CO4 shelf. 87 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.13: Singly-occupied molecular orbitals (SOMOs) in the CO4 (3 A00 ) and TS3 structures. Surfaces containing 70% of the electron density are shown. Note that the highest SOMO of CO4 (3 A00 ) and the lowest SOMO of TS3 have electron density primarily on Od , suggesting the SOMO is a spectator during isomerization. single-bonded oxygens, Ob and Od . This spin density is consistent with the radical character expected for an association of the O2 diradical with the carbon atom of CO2 , because the unpaired electrons in O2 are in orthogonal π ∗g orbitals: As one C–O bond is formed between the in-plane π ∗g orbital of O2 and the in-plane π bu orbital of CO2 (the higher-energy ∗ π nb g orbital does not interact due to symmetry; see Figure 3.14), the out-of-plane π g orbital on O2 is a relative spectator to the O2 radical addition. This interaction, along with the bending of the CO2 , produces the SOMOs for CO4 (3 A00 ) shown in Figure 3.13. In TS3, the lowest SOMO contains localized electron density on Od in an out-of-plane p-type orbital, suggesting that the unpaired electron on Od continues to be a spectator during CO4 (3 A00 ) isomerization. The highest SOMO, however, contains delocalized electron density, of antibonding (σ ∗ ) character, in the plane of the molecule. This σ ∗ character may be interpreted as electron density taken from the lowest SOMO in CO4 (3 A00 ) while being localized onto Oc during isomerization. These theoretical results imply that an adiabatic mechanism exists for the oxygen isotope exchange reaction between O2 and CO2 . During the isomerization of CO4 (3 A00 ), the Oc –Od σ -bond is cleaved homolytically (Figure 3.15): One electron moves to a p-type orbital on 88 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.14: Molecular orbital diagrams for O2 and CO2 , adapted from DeKock and Gray [1980]. Sketches of the highlighted orbitals are shown. As O2 collides with CO2 , it becomes stretched. In addition, CO2 bends, increasing the energy of its doubly occupied, ∗ in-plane π-orbitals, π bu and π nb g . A weak interaction between the π g orbital on O2 and the π bu orbital on CO2 is likely responsible for the small (1.5 kcal mol−1 ) binding energy of CO4 . The π nb g orbital does not interact, to first approximation, due to symmetry. Oc , while the other electron forms a bond with the unpaired electron on Ob . This pathway can account for the σ ∗ character of the highest-energy SOMO in TS3 (the Ob –Od bond takes an electron from the Oc –Od bond), and it preserves radical character on Od . Thus, the 3 A00 symmetry is preserved throughout the association, isomerization, and dissociation steps. This mechanism is qualitatively consistent with the small reaction cross-section and a preference for rebounding reactive collisions inferred from the dynamics observed in the experiment. The O2 must approach the CO2 at very low impact parameters with high energies to overcome the initial barrier (TS1/TS2) and reach the ‘shelf’ of the bound CO4 (3 A00 ). Momentum along the reaction coordinate beyond CO4 (3 A00 ) with ∼80 kcal mol−1 excess energy should further compress the C–Oc bond with synchronous bending of the C–Oc –Od 89 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.15: Electron-pushing diagram of an adiabatic CO4 (3 A00 ) isomerization through TS3. angle, stretching of Oc –Od , and ring formation to form TS3, followed by rapid repulsion from the final TS1/TS2 state. Finally, the large change in geometry from reactants to TS3 should facilitate the transfer of some translational energy into internal degrees of freedom of the products. Reactive scattering should become less ‘rebound’-like (forward-scattered) as Ecoll is increased above the reactive threshold; at 37 kcal mol−1 above the reactive barrier, the tight transition state, repulsive exit channel leading out of TS1/TS2, and low angular momentum must limit the extent of sideways scattering. While some sideways scattering is indeed observed in the experiment, the Ecoll dependence of T(θ c.m. ) is not known. A non-adiabatic transition to another potential surface cannot be excluded, especially given the high internal energies observed in the products. At these high energies [80 kcal mol−1 above even the CO4 (3 A00 ) shelf state], many excited-state surfaces must exist, and radiationless transitions via conical intersections may occur. While intersystem crossing (ISC) in the exit or entrance channels is unlikely at the high relative velocities of the experiment [Landau, 1932], spin transitions could readily occur if a complex is formed. For instance, the bridging oxygen atom in TS3, Od , must be equivalently bound to Ob and Oc , and chemical intuition suggests that an intersection with a singlet surface may occur by spin-paired CO4 (1 A1 ) [Cacace et al., 2003; Elliott and Boldyrev, 2005; Jamieson et al., 2007]. 3.6 Conclusion An O2 –CO2 isotope exchange reaction on the ground triplet electronic surface is possible and is consistent with our laboratory observations. Nevertheless, additional work would 90 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 be valuable in the confirmation of this hypothesis. Collision-energy-dependence studies of the product angular distribution may elucidate the mechanistic origins of the low average translational energy of products. Experimental detection of O2 counter-fragments and a search for products from other channels (e.g., spectroscopic identification of electronically excited states) would also be revealing. Last, a more complete surface, reactive trajectories, and locations of possible surface intersection seams leading to ISC would be vital to a full explanation of the reaction dynamics. 3.7 Acknowledgements We thank G. B. Ellison, S. L. Mielke, and J. E. Wulff for insightful discussions. This work was supported by the Missile Defense Agency under cooperative agreement HQ0006-05-20001. L. Y. Y. was supported by the Davidow Fund, and G. C. S. was supported by AFOSR grant FA955D-07-1-0095. 91 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Appendices 92 Chapter 3 L. Y. Yeung 3.A Oxygen isotope exchange reactions of CO2 Chapter 3 Non-reactive scattering of O2 and CO2 The experiment mainly observed signals due to 16 O2 scattered with little deflection from its initial direction (see Newton diagram in Figure 3.2); these signals corresponded to the sum of elastic and inelastic scattering collisions of 16 O2 , which we could not resolve, so they will be referenced collectively as “scattered 16 O2 .” Five representative laboratory-frame TOF distributions (m/z = 32), the c.m. angular and translational energy distributions, and the laboratory-frame angular distribution obtained from 16 O2 product detection are shown in Figure 3.16. Scattered 16 O2 had 126.3 kcal mol−1 total translational energy, or 80% of the available energy, on average. The experimental translational energy distribution was peaked at ∼148 kcal mol−1 . The c.m. angular distribution for 16 O was highly peaked in the forward direction with little scattered intensity for θc.m. > 30◦ ; however, the velocity and angular range for 16 O2 product detection in the experiment prevented the detection of backward-scattered 16 O2 (see Figure 3.2). Some dependence of the c.m. translational energy distribution on the c.m. angular distribution was observed in the 16 O TOF data; the forward-convolution simulations became increasingly faster than the data at larger laboratory and c.m. angles (e.g, Θ = 18◦ , 28◦ , and 42◦ in Figure 3.16). We also note that, like for 16 O (see Sections 4.4.2.1 and 4.5.2), the c.m. angular distribution for inelastically scattered 16 O 2 at θc.m. ∼ 0 ◦ is an extrapolation because of high background from the hyperthermal source at the small laboratory angles corresponding to small c.m. angles for 16 O2 . Most of the 16 O2 probably scatters forward through high-impact-parameter collisions, but the limited constraints on the θc.m. ∼ 0◦ angular distribution (e.g., the laboratory-frame angular distribution, which only probes Θ = 6◦ ) increase the uncertainty in that part of the c.m. angular distribution. The experiment mainly observed 12 C18 O2 scattered opposite its initial direction in the c.m. frame (see Newton diagram in Figure 3.2). Detected 12 C18 O2 products (m/z = 48) showed best-fit c.m. translational energy distributions that were both broader and lower in energy, on average, than that obtained for forward-scattered 16 O2 . A single pair of P(ET ) and T(θc.m. ) distributions was not sufficient to describe the m/z = 48 TOF distributions (see Sections 4.4.2.1 and 4.5.2), and a second pair of P(ET ) and T(θc.m. ) distributions was 93 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 included in the fit; five representative laboratory-frame TOF distributions, the c.m. angular and translational energy distributions, and the laboratory-frame angular distribution obtained from 12 C18 O2 product detection are shown in Figure 3.17, along with the c.m. velocity-flux diagram in Figure 3.18. The first P(ET ) and T(θc.m. ) pair for inelastically scattered 12 C18 O2 described the scattering at θc.m. < 125◦ . In this region, the angular distribution was peaked near θc.m. = 60◦ , though the probability of scattered products was roughly constant for 0◦ < θc.m. < 40◦ . The probability of finding these products decayed steadily at θc.m. > 60◦ . The corresponding translational energy distribution was peaked at 60 kcal mol−1 with an average hET i = 62.8 kcal mol−1 , or 40% the available energy. The second P(ET ) and T(θc.m. ) pair for inelastically scattered 12 C18 O2 described the scattering at 60◦ < θc.m. < 125◦ (corresponding to the maximum θc.m. observed in the experiment), although there was a small component 0◦ < θc.m. < 60◦ . This angular distribution overlapped, in the sideways-scattering region, with the first pair. For θc.m. > 60◦ the distribution increased rapidly until it peaked near θc.m. = 120◦ and decayed quickly at θc.m. > 120◦ . This part of the distribution, however, is uncertain because our experiment did not probe it directly. The translational energy distribution was peaked at 103 kcal mol−1 with an average hET i = 100.8 kcal mol−1 , or 64% the available energy. The similarity in product c.m. angular and translational energy distributions in the O2 + CO2 system and the O(3 P) + CO2 system (see Sections 4.4.2.1 and 4.5.2) suggests that the collisional energy transfer mechanism is similar in both cases. Ryali et al. [1982] found that CO2 collisions with N2 , O2 , and Ar near at high collision energies all had similar translational-to-vibrational energy transfer cross-sections for the excitation of CO2 (ν3 ), so they suggested that energy transfer sampled the repulsive part of the intermolecular potential in all cases. Transfer of vibrational energy from O2 to CO2 cannot be ruled out in our experiments because we did not characterize the vibrational temperature of the hyperthermal O2 . Consequently, the similarity in inelastic scattering dynamics of O(3 P) and O2 collisions with CO2 could also be coincidental. 94 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.16: Laboratory scattering data detected at m/z = 32. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for scattered 16 O2 products from 16 O2 + 12 C18 O2 collisions at hEcoll i = 158.1 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines (orange and brown) are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). These data indicate that 16 O2 is scattered mainly in the forward direction with little change in its initial direction or velocity. 95 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.17: Laboratory inelastic scattering data detected at m/z = 48. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for inelastically scattered 12 C18 O2 products from 16 O2 + 12 C18 O2 collisions at hEcoll i = 158.1 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). The dark blue and cyan lines correspond to products of 16 O(3 P) + 12 C18 O2 collisions, and they are discussed in Section 4.4.2.1. A single c.m. translational energy and angular distribution for each collision partner was insufficient to describe the TOF distributions of inelastically scattered 12 C18 O2 , suggesting a scattering dependence on impact parameter. 96 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 Figure 3.18: Velocity-flux contour diagram for inelastically scattered 12 C18 O2 from 16 O2 + 12 C18 O2 collisions in the center-of-mass frame. The white arrows are the initial 16 O2 and 12 C18 O2 velocity vectors and dashed white line is the maximum recoil velocity for 12 C18 O (v 2 max ). Only the c.m. angles for which the experiment were sensitive are shown; inelastically scattered 12 C18 O2 from high-impact-parameter collisions are not shown, as their flux would be off-scale. Strong coupling of the P(ET ) and T(θ c.m. ) distributions was observed. 97 L. Y. Yeung 3.B Oxygen isotope exchange reactions of CO2 Chapter 3 MATLAB program for generating Newton diagrams A series of programs (linked as functions) was written in MATLAB so meaningful Newton diagrams could be generated with little effort. This proved to be quite useful during data analysis because the program could display expected product times-of-flight, speeding up the forward-convolution fitting process considerably. The programs included here (NewtonD.m, NewtonDcalc.m, and NewtonDplot.m) use parameters specific to the MSU crossedbeam apparatus, but the code is general and the parameters adjustable for use with any crossed-beam apparatus with arbitrary crossing angle. Figure 3.19 shows a sample input and output. Figure 3.19: Sample output of the NewtonD.m program. Predicted c.m. angles are defined relative to the slow product’s c.m. velocity vector. 3.B.1 NewtonD.m % Program for generating Newton diagrams for molecular scattering. % Command line input is NewtonD(observed,labangle) function NewtonD(observed, labangle) clear m1 m2 v1 v2 theta e DEint observed=observed; labangle=labangle; % observed product (1 or 2) as inputted below % lab angle of observation relative to initial v1 % vector, in degrees 98 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 % Begin input section m1=16; v1=8262; % mass of particle 1 in g/mol % initial velocity of particle 1 in m/s m2=48; v2=800; % mass of particle 2 in g/mol % initial velocity of particle 2 in m/s theta=0.5; % angle between v1 and v2 in pi radians, e.g. 0.5 −−> 0.5*pi % = 90 degrees e=0.5; DEint=0; % elastic scattering efficiency 0 < e ≤ 1) % gain of internal energy upon reaction in kcal/mol mp1=16; mp2=48; % mass of product 1 in g/mol % mass of product 2 in g/mol minangle=6; maxangle=54; % minimum lab angle relative to v1 vector, in degrees % maximum lab angle relative to v1 vector, in degrees length=33.66; % distance between interaction region and ionizer in cm if observed == 1 IFT=0;2.44*sqrt(mp1); % ion flight time (delay) in microseconds else if observed == 2 IFT=0;2.44*sqrt(mp2); end end delec=0;3; % electronics delay in microseconds dlaser=0;174; % laser firing delay in microseconds otravel=0;(0.99/v1)*10ˆ6; % O−atom travel time from nozzle to % interaction region in microseconds % End input section % Input error check if observed 6= 1 && observed 6= 2 disp('Invalid input, "observed" must equal 1 or 2'); return; end % Begin calculations hold off format short g disp('Observed m/z'); % Display observed mass if observed == 1 disp(mp1); else if observed == 2 disp(mp2); end end disp('Lab angle (degrees)'); disp(labangle); 99 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 disp('Predicted center−of−mass angles (degrees)'); disp(' Fast channel | Slow channel'); % Iterate; first round includes specified change in internal energy, % second round sets the internal energy change to zero, i.e. % elastic scattering. for i = 1:2 [vc, thetavc, vrel, u1, u2, vrelp, up1, up2, Ecoll, phi, vd, chi]= NewtonDcalc(m1, m2, v1, v2, theta, e, DEint, mp1, mp2, labangle, observed); NewtonDplot(v1, v2, vc, thetavc, up1, up2, e, minangle, maxangle, labangle, vd, length, IFT, delec, dlaser, otravel, chi); if DEint == 0 return; else DEint=0; end end disp('Collision Energy (kcal/mol)'); disp(Ecoll); 3.B.2 NewtonDcalc.m % Function for calculating center−of−mass quantities function [vc, thetavc, vrel, u1, u2, vrelp, up1, up2, Ecoll, phi, vd, chi]=NewtonDcalc(m1, m2, v1, v2, theta, e, DEint, mp1, mp2, labangle, observed) % reactant parameters mu=m1*m2/(m1+m2); vc=sqrt((m1/(m1+m2)*v1)ˆ2+(m2/(m1+m2)*v2)ˆ2); vrel=sqrt(v1ˆ2+v2ˆ2−2*v1*v2*cos(theta*pi)); u1=m2/(m1+m2)*vrel; u2=m1/(m1+m2)*vrel; thetavc=asin((u2/vc)*(v1/vrel)*sin(theta*pi)); Ecoll=(1/2)*mu/1000*vrelˆ2/4.184/1000; % reduced mass % CM velocity % relative velocity % velocity of particle 1 % in CM frame % velocity of particle 2 % in CM frame % angle between CM % velocity and v2 % CM collision energy % reactive product parameters mup=mp1*mp2/(mp1+mp2); % reduced mass vrelp=sqrt(((mu/1000)*vrelˆ2−2*(DEint*1000*4.184))/(mup/1000)); %relative velocity up1=mp2/(mp1+mp2)*vrelp; % velocity of product 1 % in CM frame up2=mp1/(mp1+mp2)*vrelp; % velocity of product 2 % in CM frame phi=labangle*pi/180−(theta*pi−(thetavc)); % case structure determining output parameters if observed == 1 100 % angle between lab % detection vector and % CM velocity L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 up=up1; u=u1; v=v1; else if observed == 2 up=up2; u=u2; v=v2; end end % product velocity in lab frame with case structure for removal of % imaginary roots. if imag(roots([1 −2*vc*cos(phi) vcˆ2−(up*sqrt(e))ˆ2])) == 0 vd=roots([1 −2*vc*cos(phi) vcˆ2−(up*sqrt(e))ˆ2]); % Solve for product velocity observed at detector if vd(1) ≤ 0 && vd(2) ≤ 0 vd(1)=0; vd(2)=0; else if vd(1) > 0 && vd(2) ≤ 0 vd(2)=0; else if vd(1) < 0 && vd(2) > 0 vd(1)=0; end end end % Product scattering angle relative to CM velocity vector of reactant 2 if phi > 0 chi=(acos((diag(vd*vd')−vcˆ2−diag(up*up')*e)/(−2*vc*up*sqrt(e)))− asin(v2/u2*sin(thetavc)))*180/pi; else chi=360−(acos((diag(vd*vd')−vcˆ2−diag(up*up')*e)/(−2*vc*up*sqrt(e)))+ asin(v2/u2*sin(thetavc)))*180/pi; end if imag(chi(1)) 6= 0 chi(1) = 0; end if imag(chi(2)) 6= 0 chi(2) = 0; end if chi(1) > 180 chi(1)= chi(1)−360; end if chi(2) > 180 chi(2)= chi(2)−360; end % In case of imaginary roots else vd(1,1)=10000; vd(2,1)=10000; chi=1; disp(' N/A end N/A') %((1/2)*(mp1/1000)*(up1)ˆ2*e)/4184 %((1/2)*(mp2/1000)*(up2)ˆ2*e)/4184 3.B.3 % Display lack of solutions % CM Translational energy of % product 1 % CM Translational energy of % product 2 NewtonDplot.m 101 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 function NewtonDplot(v1, v2, vc, thetavc, up1, up2, e, minangle, maxangle, labangle, vd, length, IFT, delec, dlaser, otravel, chi) % Messy plotting code for pretty pictures x1 = vc*cos(thetavc); y1 = vc*sin(thetavc); N=256; t=(0:N)*2*pi/N; plot(sqrt(e)*up2*cos(t)+x1, sqrt(e)*up2*sin(t)+y1, '−.r'); % Newton circle for product 2 hold on grid on plot(sqrt(e)*up1*cos(t)+x1, sqrt(e)*up1*sin(t)+y1, '−.b'); % Newton circle for product 1 legend('Particle 2', 'Particle 1') % text(1,1,'Collision energy = \Ecoll kcal/mol') x0 = 0; y0 = 0; x1 = 0; y1 = v1; plot([x0;x1],[y0;y1]) alpha = 0.05; % Particle 1 % Size of arrow head relative to the length of % the vector beta = 0.2; % Width of the base of the arrow head relative to % the length hu = [x1−alpha*((x1−x0)+beta*((y1−y0)+eps)); x1; x1−alpha* ((x1−x0)−beta*((y1−y0)+eps))]; hv = [y1−alpha*((y1−y0)−beta*((x1−x0)+eps)); y1; y1−alpha* ((y1−y0)+beta*((x1−x0)+eps))]; plot(hu(:),hv(:)) % Plot arrow head x0 = 0; y0 = 0; x1 = v2; y1 = 0; plot([x0;x1],[y0;y1],'r') % Particle 2 alpha = 0.4; % Size of arrow head relative to the length of % the vector beta = 0.5; % Width of the base of the arrow head relative to % the length hu = [x1−alpha*((x1−x0)+beta*((y1−y0)+eps)); x1; x1−alpha* ((x1−x0)−beta*((y1−y0)+eps))]; hv = [y1−alpha*((y1−y0)−beta*((x1−x0)+eps)); y1; y1−alpha* ((y1−y0)+beta*((x1−x0)+eps))]; plot(hu(:),hv(:),'r') % Plot arrow head x0 = v2; y0 = 0; x1 = 0; y1 = v1; plot([x0;x1],[y0;y1],'m') % vrel alpha = 0.05; % Size of arrow head relative to the length of % the vector beta = 0.2; % Width of the base of the arrow head relative to 102 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 3 % the length hu = [x1−alpha*((x1−x0)+beta*((y1−y0)+eps)); x1; x1−alpha* ((x1−x0)−beta*((y1−y0)+eps))]; hv = [y1−alpha*((y1−y0)−beta*((x1−x0)+eps)); y1; y1−alpha* ((y1−y0)+beta*((x1−x0)+eps))]; plot(hu(:),hv(:),'m') % Plot arrow head x0 = 0; y0 = 0; x1 = vc*cos(thetavc); y1 = vc*sin(thetavc); plot([x0;x1],[y0;y1],'g') % vc alpha = 0.1; % Size of arrow head relative to the length of % the vector beta = 0.25; % Width of the base of the arrow head relative to % the length hu = [x1−alpha*((x1−x0)+beta*((y1−y0)+eps)); x1; x1−alpha* ((x1−x0)−beta*((y1−y0)+eps))]; hv = [y1−alpha*((y1−y0)−beta*((x1−x0)+eps)); y1; y1−alpha* ((y1−y0)+beta*((x1−x0)+eps))]; plot(hu(:),hv(:),'g') % Plot arrow head x1=10000*sin(minangle*pi/180); y1=10000*cos(minangle*pi/180); plot([0;x1],[0;y1],'k') % minimum lab angle x1=10000*sin(maxangle*pi/180); y1=10000*cos(maxangle*pi/180); plot([0;x1],[0;y1],'k') % maximum lab angle if chi == 1 return else if chi 6= 1 x1=vd*sin(labangle*pi/180); y1=vd*cos(labangle*pi/180); plot([0;x1],[0;y1],'k') % observed lab angle x0=vc*cos(thetavc); y0=vc*sin(thetavc); x1=vd*sin(labangle*pi/180); y1=vd*cos(labangle*pi/180); plot([x0;x1],[y0;y1],'k') % center−of−mass scattering end end xlabel('Velocity of Particle B (m/s)') ylabel('Velocity of Particle A (m/s)') axis([−9000 11000 −5500 9500]) % Relevant quantities disp(chi'); if vd(1) == 0 && vd (2) == 0 TOF=[0 0]; else if vd(1) == 0 TOF=[((length/100)/vd(1))*10ˆ6 0]; 103 % Predicted TOF times in % microseconds L. Y. Yeung Oxygen isotope exchange reactions of CO2 else if vd(2) == 0 TOF=[((length/100)/vd(1))*10ˆ6 0]; % Predicted TOF times in % microseconds else if vd(1) == 10000 && vd(2) == 10000 TOF=[0 0]; else if vd(1) > 0 && vd(2) > 0 % Predicted TOF times in microseconds TOFfast=((length/100)/vd(1))*10ˆ6; TOFslow=((length/100)/vd(2))*10ˆ6; TOF=[TOFfast TOFslow]; end end end end end % Display TOF on graph next to Newton circle text(x1(1),y1(1),[' \leftarrow ',num2str(round(TOF(1)+IFT+delec+dlaser+ otravel)), ' \mus'],'FontSize',14) % Only display second TOF value if there is a product to display if TOF(2) 6= 0 text(x1(2),y1(2),[' \leftarrow ',num2str(round(TOF(2)+IFT+delec+ dlaser+otravel)), ' \mus'],'FontSize',14) else return end 104 Chapter 3  L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Chapter 4 Dynamics of O(3P) + CO2 collisions at hyperthermal energies In collaboration with Mitchio Okumura, Jianming Zhang, Timothy K. Minton, Jeffrey T. Paci, Jan M. L. Martin, Jon M. Camden, and George C. Schatz; parts of this will be submitted to Journal of Physical Chemistry A for publication. 105 L. Y. Yeung 4.1 Oxygen isotope exchange reactions of CO2 Chapter 4 Abstract The dynamics of O(3 P) + CO2 collisions at hyperthermal collision energies near 100 kcal mol−1 were investigated experimentally and theoretically. Crossed-molecularbeam experiments at hEcoll i = 98.8 kcal mol−1 were performed with isotopically labeled 12 C18 O 16 3 12 C18 O ] from 2 to distinguish products of non-reactive scattering [ O( P) + 2 products of reactive scattering (18 O + 16 O12 C18 O and 18 O16 O + 12 C18 O). 16 O products were detected mainly in the forward direction, i.e., in the initial direction of the hyperthermal oxygen beam in the center-of-mass (c.m.) frame, and they contained ∼87% of the collision energy in translation, on average; the amount of energy transfer during non-reactive scattering depended on impact parameter. 16 O12 C18 O products from the oxygen isotope exchange reaction were scattered mainly in the backward direction with 35% of the available energy in translation, on average. 18 O16 O products from the oxygen-atom abstraction reaction were detected in the forward direction, with 56% of the available energy in translation, on average. Stationary points on the lowest triplet potential energy surface of the O(3 P) + CO2 system were characterized at the CCSD(T)/aug-cc-pVTZ level of theory. Quasi-classical trajectory (QCT) calculations of O(3 P) + CO2 collisions at energies between 1.0 – 6.5 eV (23 – 150 kcal mol−1 ) were performed at the B3LYP/6-311G(d) and BMK/6-311G(d) levels of theory, and both reactive channels observed in the experiment were also predicted by the theory. In addition, trajectories leading to the formation of 18 O2 + 12 C16 O products were predicted. The c.m. translational energy and angular distributions derived from the QCT calculations show qualitative, but not quantitative agreement with experimental results. The theoretical relative product yield for the oxygen isotope exchange reaction also agreed well with the experiment. The isotope exchange reaction demonstrates a new pathway through which oxygen isotopes may be cycled in the upper atmosphere, where O(3 P) atoms with hyperthermal translational energy distributions can be generated through the photolysis of ozone and molecular oxygen. 106 L. Y. Yeung 4.2 Oxygen isotope exchange reactions of CO2 Chapter 4 Introduction Atomic oxygen radicals in the atmosphere play an important role in regulating Earth’s oxidative and radiative balance. Photodissociation of molecular oxygen and ozone by solar ultraviolet radiation produces not only electronically excited O(1 D) and O(1 S), but also ground-state O(3 P) with velocities as high as 6 km s−1 [Matsumi and Kawasaki, 2003; Stranges et al., 1995]. O(3 P) has received less attention than O(1 D) and O(1 S), however, because it is less reactive at low collision energies. Yet, its important role in the terrestrial mesosphere and thermosphere is widely recognized; for instance, its collisions with CO2 significantly influence the population of CO2 (010), whose emission at 15 µm cools the atmosphere and regulates the height of the mesopause [Sharma and Roble, 2002]. O(3 P) can also interact with CO2 from space vehicle exhaust streams at relative velocities near 8 km s−1 and collision energies near 100 kcal mol−1 , well above those expected at local thermodynamic equilibrium. These high collision energies exceed barriers to (1) CO3 formation, leading to oxygen isotope exchange, and (2) oxygen-atom abstraction on the triplet potential energy surface (PES) [Averyanov et al., 1999; Bennett et al., 2004; Froese and Goddard, 1993; Mebel et al., 2004; Yang et al., 2005]. The enthalpies associated with these reactions are: 3 1 + O(3 P) + CO2 (1 Σ+ g ) → O( P) + CO2 ( Σg ) 1 + → O2 (3 Σ− g ) + CO( Σ ) ∆H ∼ 0 (4.1) ∆H = 8 kcal mol−1 (4.2) A reaction analogous to reaction 4.1, between O(1 D) and CO2 in the stratosphere [Baulch and Breckenridge, 1966; Chakraborty and Bhattacharya, 2003; DeMore and Dede, 1970; Johnston et al., 2000; Mebel et al., 2004; Perri et al., 2003, 2004; Shaheen et al., 2007; Wen and Thiemens, 1993; Yeung et al., 2009a], alters the stable isotope composition of stratospheric CO2 , allowing the isotopic composition of stratospheric CO2 to be used as a tracer of O(1 D) [Thiemens et al., 1995; Yung et al., 1991, 1997] and atmospheric transport [Boering et al., 2004]. The isotopic composition of CO2 has also been proposed as a tracer of biogeochemical cycles on annual and decadal timescales [Hoag et al., 2005]. Consequently, the dynamics of reactive channels that could alter the isotopic composition of 107 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 upper atmospheric CO2 are also of interest [Perri et al., 2003, 2004]. Early studies on the O(3 P) + CO2 system were primarily theoretical and focused on the vibrational-state-specific energy transfer [Bass, 1974; Garrett, 1983; Harvey, 1982; Schatz and Redmon, 1981]. The mechanism was found to be primarily impulsive at high collision energies, like that of collisions between CO2 and noble gases [Billing and Clary, 1983; Harvey, 1982; Schatz and Redmon, 1981]. More recent quantum calculations on the O(3 PJ ) + CO2 (010) system indicate that vibrational-to-translational energy transfer is sensitive to the total angular momentum J at thermal collision energies, although the importance of spin-orbit coupling decreases with increasing collision energy [de Lara-Castells et al., 2006, 2007]. Two experimental studies also focused on state-specific excitation in O(3 P) + CO2 collisions, specifically to CO2 (001); both studies also reported evidence that reaction 4.2, which is important in combustion chemistry [Tsang and Hampson, 1986] yielded vibrationally excited CO products [Oakes et al., 1994; Upschulte and Caledonia, 1992]; no mechanism was proposed, however. We recently confirmed the presence of reaction 4.1 at hyperthermal collision energies [Yeung et al., 2009b], and we intend now to investigate its dynamics. Mebel et al. [2004] suggested that the dynamics of CO3 formation on the triplet (3 A0 ) PES with hyperthermal O(3 P) atoms might be complicated by a nearby 3 A0 –1 A0 intersection seam, which could lead to non-adiabatic effects along reactive trajectories. Indeed, many low-lying electronic states of CO3 (e.g., 3 A00 ) lie within several eV of CO3 (3 A0 ), so vibronic [Kowalczyk and Krylov, 2007] and/or spin-orbit [Mebel et al., 2004] coupling could result in unexpected curvature and dynamics on the triplet PES. Here, the results of theoretical and crossed-molecular-beam studies of O(3 P) + CO2 collisions at hyperthermal collision energies will be presented. Theoretical direct dynamics calculations using the QCT method on an adiabatic PES were compared with the results from an experimental dynamics study obtained for an average collision energy hEcoll i = 98.8 kcal mol−1 . The oxygen isotope exchange and oxygen-atom abstraction reactions were observed in both the QCT calculations and the laboratory experiment, and center-of-mass (c.m.) angular and translational energy distributions for the oxygen isotope exchange reaction were 108 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 obtained. Their implications for atomic oxygen cycling through CO2 in the atmosphere will be discussed. 4.3 Theoretical studies 4.3.1 Electronic structure calculations Geometry-optimization, single-point, and vibrational-frequency calculations were performed on stationary points of the lowest triplet PES of CO3 , 3 A00 ; a discussion of the relative energetics of the 3 A0 and 3 A00 surfaces can be found in Section 4.5. Stationary points for reactions 4.1 and 4.2 were characterized using electronic structure calculations at the B3LYP/6-311G(d) [Becke, 1993; Frisch et al., 1984; Lee et al., 1988], BMK/6-311G(d) [Boese and Martin, 2004], and CCSD(T)/aug-cc-pVTZ [Kendall et al., 1992; Raghavachari et al., 1989] levels of theory/basis using the MOLPRO electronic structure code [Werner et al., 2006]. Confirmation of transition-state character was achieved by inspection of the associated vibrational frequencies. Other reactive channels were not characterized because reactant energies in excess of 250 kcal mol−1 are required to open them, according to our B3LYP/6-311G(d) calculations. Here, we report three transition-state structures and one bound-state structure on the CO3 (3 A00 ) PES; the results are shown in Figures 4.1 and 4.2 and Table 4.1 [Mebel et al., 2004]. All structures are planar. One transition state (TS1) and the bound state (CO3 ) were associated with the O(3 P) + CO2 isotope exchange reaction. Two transition states (TS2 and TS3) were associated with the oxygen-atom abstraction reaction producing O2 and CO. Two additional bound states and two associated transition states were also found; they resemble the Cs minima reported in previous work [Bennett et al., 2004; Froese and Goddard, 1993; Mebel et al., 2004], but they will not be discussed here because neither of the bound states were bound when zero-point energy (ZPE) was considered. For this reason, we are also not reporting minima in the van der Waals region of the PES, e.g., the quadrupole-induced minimum (∆E ∼ 335 cm−1 ) at the RCCSD(T)/aug-cc-pVTZ level of theory [de Lara-Castells et al., 2006, 2007], because the binding energies were below the ZPE of the system. Further 109 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.1: Stationary-point structures for O(3 P) + CO2 reactions below 100 kcal mol−1 calculated at the CCSD(T)/aug-cc-pVTZ level of theory on the 3 A00 . The relative energies have been corrected for zero-point energy. comparisons of the structures with previous work on the lowest triplet PES will be presented in Section 4.5. Of the levels of theory and basis examined in this study, CCSD(T)/aug-cc-pVTZ is probably the most accurate combination; however, multi-reference character in the stationary points may be important because several electronic surfaces are within several eV of the PES that is the subject of this study [Bennett et al., 2004; Kowalczyk and Krylov, 2007; Mebel et al., 2004]. Multi-reference CCSD(T) calculations, unfortunately, were not computationally affordable. Still, our CCSD(T)/aug-cc-pVTZ geometries are nearly identical to those obtained in recent calculations using the W4 method [Karton et al., 2006] near the full-configuration-interaction and complete-basis-set limits, with transition-state energies within 2 kcal mol−1 and the bound-state energy within 4 kcal mol−1 (J. M. L. Martin, per- 110 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Table 4.1: Energies (kcal mol−1 ) for the stationary points on the lowest triplet CO3 potential energy surface for 16 O(3 P) + 12 C16 O2 → 16 O + 12 C16 O2 collisions B3LYP 6-311G(d) BMK 6-311G(d) w/ZPEC† O(3 P) + CO2 TS1 CO3 TS2 TS3 O2 + CO 0.0 18.0 11.8 56.2 70.3 9.7 0.0 17.7 11.3 55.2 69.2 7.9 CCSD(T) aug-cc-pVTZ w/ZPEC† 0.0 25.2 20.2 65.3 80.0 14.3 0.0 25.0 19.0 64.5 78.9 12.6 CCSD(T) 6-311+G(3df)∗ w/ZPEC† 0.0 25.2 21.8 63.0 76.5 10.2 0.0 25.0 20.2 62.1 75.3 8.3 0.0 35.2 22.0 ∗ From Mebel et al. [2004] using a 3 A0 geometry optimized at the CASSCF(16,13)/6-311G(d) level of theory. The authors noted that the more ideal MRCI+Q/6-311+G(3df) energy calculation was not affordable. † Zero-point-energy correction (ZPEC). sonal communication). Thus, we used the CCSD(T)/aug-cc-pVTZ geometries and energies as benchmarks for comparison with those calculated by the density-functional methods, which are more affordable for QCT calculations. In addition to using the B3LYP and BMK levels of theory, we characterized the transitionstate structures at the MP2 [Møller and Plesset, 1934], M06-2X [Zhao and Truhlar, 2008], and CCSD [Purvis and Bartlett, 1982] levels using the 6-31G(d,p), 6-311G(d), and cc-pVTZ [Dunning, 1989] basis sets during our search for an appropriate level of theory for QCT calculations (optimizing computational cost and accuracy). The density-functional methods B3LYP/6-311G(d) and BMK/6-311G(d), however, were found to have the best balance between computational cost and accuracy, so we will only report the results of those calculations here along with the results of CCSD(T)/aug-cc-pVTZ calculations (see Figure 4.2). The results of the lower-level B3LYP and BMK calculations, along with the MP2, M06-2X, and CCSD calculations, are shown in Figure 4.3. TS1 had Cs symmetry in all cases. Mild compression of one C–O bond and stretching of the other C–O bond in the parent CO2 , along with moderate bending (∼30◦ ) of the O– C–O bond angle, was found at all levels of theory. The geometries were similar to that calculated at the CCSD(T) level of theory, which had C–O bond lengths of 1.24 Å, 1.18 Å, and 1.60 Å and bond angles of 87◦ , 123◦ , and 150◦ (see Figure 4.2). The B3LYP geometry 111 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.2: Comparison of CO3 stationary point geometries relevant to the QCT calculations. Our geometry optimizations at the CCSD(T)/aug-cc-pVTZ, B3LYP/6-311G(d), and BMK/6-311G(d) levels of theory (bold) are shown with Mebel et al.’s CASSCF(16,13)/6311G(d) geometries for CO3 and TS1. Figure 4.3: Comparison of TS1 and TS3 geometries and energies at various levels of theory. ZPE-corrected transition-state (∆E ‡ ) and reaction (∆E) energies are shown. 112 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 generally agrees well with that at CCSD(T), deviating by < 0.02 Å in the two shorter C–O bond lengths and by < 3◦ in all the bond angles. The longest bond length, however, is 0.06 Å longer at B3LYP than at CCSD(T). Its ZPE-corrected energy is also 7.3 kcal mol−1 lower. At the BMK level of theory, the TS1 geometry agrees with the CCSD(T) geometry within 0.02 Å in all the bond lengths and within 3◦ in all the bond angles, and with the CCSD(T) energy within 0.1 kcal mol−1 . The CO3 bound state had C2v symmetry at the B3LYP and CCSD(T) levels of theory and Cs symmetry at the BMK level of theory. C–O bond lengths were larger than typical CO2 bond lengths (1.21 Å), consistent with an overall decrease in C–O bond order upon CO3 formation. The B3LYP geometry agreed within 0.04 Å and 1◦ with the CCSD(T) geometry, which had C–O bond lengths of 1.27 Å, 1.27 Å, and 1.30 Å and bond angles of 118◦ , 118◦ , and 123◦ (see Figure 4.2). The ZPE-corrected B3LYP energy, however, is 8.9 kcal mol−1 lower than that at CCSD(T). At the BMK level of theory, moderate agreement in the CCSD(T) geometry was observed; in addition to displaying lower symmetry, the C–O bond lengths calculated at BMK were different from CCSD(T) bond lengths by up to 0.07 Å, while the bond angles were different by up to 8◦ . The lower symmetry for CO3 using the BMK functional may be a consequence of the large amount of Hartree-Fock exchange mixed into the functional [Boese and Martin, 2004], which can result in orbital symmetry-breaking [Sherrill et al., 1999]. The ZPE corrected CO3 energy at BMK is in better agreement, however, at 1.2 kcal mol−1 below the energy at CCSD(T). Both B3LYP and BMK theories do show a CO3 potential well of 6.4 and 6.0 kcal mol−1 , respectively, in reasonable agreement with the CCSD(T) well depth of 4.8 kcal mol−1 . TS2 and TS3 were associated with an oxygen-atom abstraction reaction producing O2 + CO. They had Cs symmetry at all levels of theory. In both transition states, one C–O bond on the parent CO2 was compressed, while the other C–O bond, which is eventually broken, was stretched (see Figure 4.2). The O–C–O bond angle was bent ∼40◦ , and the only qualitative difference between the structures was the C–O–O bond angle: The C–O–O angle bent inwards to form a ‘C’-shape in TS2, whereas it bent outwards to form a ‘S’-shape in TS3. Both B3LYP and BMK geometries agreed with the CCSD(T) geometry with a maximum dis- 113 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 crepancy of 0.04 Å in the O–O bond length at the BMK level. The two bond angles agreed to within 2◦ . Resulting ZPE-corrected barrier heights showed larger discrepancies: B3LYP and BMK energies for TS2 differed from CCSD(T) values by –6.9 and +2.4 kcal mol−1 , respectively, while they differed from CCSD(T) values by +6.1 and –3.6 kcal mol−1 , respectively, in TS3. We note that BMK overpredicted the endothermicity of the O(3 P) + CO2 → O2 + CO reaction by ∼4.5 kcal mol−1 ; this disagreement is again probably a consequence of the large amount of Hartree-Fock exchange mixed into the BMK functional, which was included to improve the performance of the functional when predicting transition state properties. 4.3.2 Reaction dynamics calculations QCT calculations were run on the 3 A00 PES with both B3LYP/6-311G(d) and BMK/6311G(d) methods. Both methods showed reasonable agreement with the geometries and energies of the stationary points calculated at CCSD(T)/aug-cc-pVTZ and were computationally affordable for direct dynamics calculations. Four hundred trajectories were run at collision energies of 1.0, 1.5, 2.5, 3.5, 4.5, 5.5, and 6.5 eV (23.0, 34.6, 57.6, 80.7, 103.7, 126.7, and 149.8 kcal mol−1 , respectively) using the B3LYP level of theory for a total of 2800 trajectories. This range of energies was selected because the ZPE-corrected barriers for TS1, TS2, and TS3 according to this level of theory were 17.7, 55.2, and 69.2 kcal mol−1 (0.77, 2.4, and 3.0 eV, respectively). In addition, four hundred BMK trajectories were run at collision energies of 1.5, 2.5, 3.5, 4.5, 5.5, and 6.5 eV for a total of 2400 trajectories. At this level of theory, the ZPE-corrected reaction thresholds were 25.0, 64.5, and 78.9 kcal mol−1 (1.1, 2.8, and 3.4 eV, respectively) for TS1, TS2, and TS3, respectively. The collision energy of 1.0 eV (23 kcal mol−1 ) was not considered because it is below the threshold for both reactions 4.1 and 4.2, according to the BMK level of theory. Trajectories were integrated using a standard fifth-order predicator, sixth-order corrector integration algorithm [Bunker, 1970; Press et al., 1992] with an integration time-step of 10.0 a.u. (0.24 fs). The energy and gradient were calculated at each point using the Q-Chem software package [Shao et al., 2006], and the initial orientation and impact parameter was sampled randomly. To simulate the ZPE, an intermolecular trajectory starting from CO2 in its equilibrium configuration was run 114 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 with kinetic energy corresponding to the ZPE in each normal mode, and the atomic coordinates along this trajectory were used to sample the initial CO2 vibrational phase randomly in subsequent trajectories. An estimate of a reasonable value for the maximum impact parameter for reactive scattering, bmax , was calculated using the expression [Levine, 2005]: 1  E0 2 bmax = d 1 − ET (4.3) where d is the distance in the transition-state structure between the center of mass of the reactant CO2 and the colliding oxygen atom, E0 is the transition-state energy, and ET is the collision energy. Because large collision energies were of principal interest, we chose to consider the largest value for bmax suitable for trajectories with unlimited collision energy by setting ET = ∞ in Eq. 4.3. Reaction 4.2 had the larger of the two d values, with a value of d ∼ 4.3 a0 (2.3 Å). This d value, combined with a ∼15% safety margin, suggested a bmax = 5.0 a0 (2.6 Å); thus, the trajectories were sampled with impact parameters 0 < b < 5.0 a0 . Trajectories were stopped when the distance between any two atoms exceeded 12 a0 (6.3 Å). Energy conservation and spin contamination were checked at each time-step. Trajectories in which energy was not conserved to within 3 kcal mol−1 or spin contamination rose above hS2 i = 2.5 were flagged. Less than 1.3% and 10% of the B3LYP and BMK trajectories, respectively, failed to meet these acceptance criteria. Most problems were related to energy conservation, and were attributed to self-consistent field convergence to an excited electronic state. Trajectories that initially did not meet the criteria were run again using a different set of self-consistent field convergence tools, which improved the energyconservation or spin-contamination problem in many cases. Results of the re-run trajectories were compared to their initial-run analogues, and the one that met or came closest to meeting the acceptance criteria was included in the analysis. To do otherwise would have resulted in an underestimate of the reaction cross-sections, as most of the problematic trajectories were reactive ones. Reactive cross-sections (σR ) were calculated from the QCT data using the expression: 115 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 N σR = π R (2li + 1)lmax ∑ Ntotal p2 i=1 (4.4) 1 where p = (2µET ) 2 is the momentum of the reactant system, li = bi p is the angular momentum of the ith trajectory, and lmax = bmax p. NR is the number of reactive trajectories in the set of Ntotal trajectories run. The total collision cross-section, σtotal , was estimated using the Lennard-Jones parameters for O and CO2 according to the expression for the total cross-section: σtotal = πb2total (4.5) where btotal is the radius beyond which no elastic, inelastic, or reactive scattering occurs. This radius can be estimated using the Lennard-Jones potential [Hirschfelder et al., 1964]: V (r) = 4ε   r 12 e r −  r 6  e r (4.6) where ε and re correspond to the well depth and the separation distance, respectively, at the potential minimum for an interaction between a pair of like atoms or molecules. The separation distance, re , is a measure of the atomic or molecular size. The values for the O-atom and for CO2 have been estimated to be re (O) = 2.78 Å and re (CO2 ) = 3.897 Å, respectively [Hirschfelder et al., 1964; Némethy et al., 1983]. Combining these radii with the usual method [Hirschfelder and Meath, 1967], i.e., re (O + CO2 ) = 1 [re (O) + re (CO2 )] 2 (4.7) we calculated an intermolecular interaction distance re (O + CO2 ) = btotal of 3.34 Å and a total collision cross-section of 125.2 a20 , which we used to calculate the relative product yields in Section 4.4.2.4. The theoretical reactive cross-section was divided by three for the comparison with experiment because the O(3 P) + CO2 surface is triply degenerate at large O(3 P)–CO2 separation distances (see Section 4.4.2.4). Trajectories corresponding to oxygen isotope exchange were observed at all collision 116 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.4: Reactive scattering cross-sections for the O(3 P) + CO2 isotope exchange reaction obtained from the QCT calculations. energies (see Table 4.2), and the resulting excitation functions were calculated from the QCT data (see Figure 4.4). These excitation functions had the same shape at the B3LYP/6311G(d) and BMK/6-311G(d) levels of theory. The BMK excitation function was shifted to slightly higher energies compared to the B3LYP prediction, consistent with the 7.3 kcal mol−1 (0.32 eV) higher ZPE-corrected transition-state barrier for isotope exchange. Opacity functions for the isotope exchange reaction showed a slight decrease in reaction probability at smaller impact parameters as the collision energy increased (see Figure 4.5). P(b) also appeared to reach a maximum near b ∼ 1.5 – 2 a0 (1 Å). The O2 + CO channel appears to open at higher energies than the exchange channel (see Table 4.2), consistent with the higher ZPE-corrected transition-state barriers for the oxygen-atom abstraction reaction of 37.5 kcal mol−1 (1.63 eV) and 39.5 kcal mol−1 (1.71 Table 4.2: Number of reactive QCTs observed at different collision energies. Theory/Basis Products 1.0 B3LYP/6-311G(d) BMK/6-311G(d) O + CO2 O2 + CO O + CO2 O2 + CO 1 0 117 Collision energy (eV) 1.5 2.5 3.5 4.5 5.5 6.5 16 0 2 0 78 11 80 8 54 0 37 0 66 0 66 0 68 1 80 0 80 4 76 5 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.5: Opacity functions for the O(3 P) + CO2 isotope exchange reaction and for inelastic scattering of the two reagents obtained from QCT calculations at the B3LYP/6311G(d) and BMK/6-311G(d) levels of theory. eV) higher than the exchange channel barrier according to the B3LYP and BMK predictions, respectively. The B3LYP threshold is slightly higher than that calculated using BMK, which is consistent with a ZPE-corrected barrier 9.3 kcal mol−1 (0.40 eV) larger at BMK than at B3LYP. Because only a small number of oxygen-atom abstraction reactions were observed, even at collision energies significantly in excess of the calculated reaction barrier, the amount of mechanistic insight available from the O(3 P) + CO2 → O2 + CO reaction is limited. A full discussion of the trajectory calculations, including the resulting product angular and translational energy distributions, can be found in Sections 4.4.2 and 4.5; they will be analyzed with the experimental data to elucidate the possible reaction mechanisms for each channel. 118 L. Y. Yeung Oxygen isotope exchange reactions of CO2 4.4 Experimental studies 4.4.1 Methods Chapter 4 Crossed-molecular-beam experiments were performed with an apparatus equipped with a hyperthermal atomic oxygen beam source at Montana State University, which was described in the preceding chapter. Briefly, a pulsed, hyperthermal beam of ∼87% 16 O(3 P) and ∼13% 16 O 3 − 16 O using a high-energy CO 2 ( Σg ) was generated by laser-induced detonation of 2 2 TEA laser (6 – 7 J pulse−1 ). Though initially broad in velocity distribution (6 – 9 km s−1 ), a portion of the overall beam was velocity-selected with a chopper wheel (see Figure 3.1) at an average velocity hvi = 8262 m s−1 . The resulting beam was crossed at a right angle with a pulsed supersonic expansion of 98% 12 C18 O2 . The scattered products were detected with a rotatable quadrupole mass spectrometer that collected number-density distributions for each product as a function of arrival time at the ionizer, N(t), at a given laboratory angle, Θ, the angle at which the product scatters with respect to the direction of the reagent oxygen beam. Time-of-flight (TOF) distributions for 16 O, 18 O16 O, 16 O12 C18 O, and 12 C18 O2 were collected over a range of laboratory angles; at each angle, the TOF distribution was integrated to give a laboratory angular distribution, N(Θ). A forward-convolution method was then used to derive c.m. translational energy P(ET ) and angular T(θc.m. ) distributions from the laboratory N(t) and N(Θ) distributions [Lee, 1988], where θc.m. is the angle at which a product scatters with respect to the reagent oxygen direction in the c.m. frame. The canonical Newton diagrams used in this analysis are shown in Figure 4.6. Laboratory TOF product distributions were measured every 2◦ between Θ = 6◦ – 54◦ . Scattered product TOF distributions were collected for 200 beam pulses for m/z = 16 (16 O+ ) and 32 (16 O2 + ), for 1000 beam pulses for m/z = 46 (16 O12 C18 O+ ), and for 500 beam pulses for m/z = 48 (12 C18 O2 + ). Scattered products at m/z = 34 (18 O16 O+ ) were collected for 12000 beam pulses at Θ = 6◦ and 10◦ and 6000 beam pulses at Θ = 14◦ . Dwell time for each channel at the MCP was 1 µs. At a representative laboratory angle of 10◦ , integrated count rates were 1.1 × 107 s−1 for m/z = 16, 1.3 × 107 s−1 for m/z = 32, 1.4 × 104 s−1 for m/z = 34 (18 O16 O+ ), 1.8 × 105 s−1 for m/z = 46 , and 4.2 × 106 s−1 for 119 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.6: Canonical Newton diagram for 16 O + 12 C18 O2 collisions at Ecoll = 98.8 kcal mol−1 The 16 O-atom beam velocity is 8262 m s−1 and the 12 C18 O2 beam velocity is 800 m s−1 . The shaded region indicates the range of laboratory angles probed. The radii of each circle represent the maximum recoil velocities of the following products of 16 O(3 P) + 12 C18 O collisions: 12 C18 O (blue solid) + 16 O (blue dashed), 16 O12 C18 O (red solid) + 18 O 2 2 (red dashed), and 18 O16 O (green solid) + 12 C18 O (green dashed). m/z = 48. Three signal corrections were made before data analysis. First, we corrected for beam divergence at Θ = 6◦ – 16◦ . The divergent intensity with the 12 C18 O2 beam turned off was measured by obtaining TOF distributions at m/z = 16 and 32 from Θ = 6◦ – 16◦ . These TOF distributions were then scaled and subtracted from the corresponding experimental TOF distributions at m/z = 16 and 32 that had the 12 C18 O2 beam turned on. Uncertainties in the non-reactive and reactive scattering signals due to collisions of the divergent hyperthermal oxygen could not be quantified, however; they were instead considered in the analysis of the laboratory data, where collisions at crossing angles of 88◦ , 89◦ , 90◦ , 91◦ , and 92◦ were included during forward-convolution fitting. Adding more crossing angles did not affect the forward-convolution fits significantly. Second, we measured that the 12 C18 O2 beam contained 2% 16 O12 C18 O using the instrument’s mass spectrometer. Thus, 2% of the inelastic scattering signal (m/z = 48) at each laboratory angle (Θ = 6◦ – 54◦ ) was subtracted from 120 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 raw m/z = 46 (16 O12 C18 O+ ) TOF distributions to obtain reactive-scattering-only distributions. Last, the hyperthermal O2 beam contained 0.4% 18 O16 O (at natural isotopic abundances), so 0.4% of the non-reactive scattering signal (m/z = 32) was subtracted from the raw m/z = 34 (18 O16 O+ ) TOF distributions to obtain reactive-scattering-only distributions. 4.4.2 Results 4.4.2.1 Non-reactive scattering of 16 O(3 P) and 12 C18 O2 The experiment mainly observed signals due to 16 O scattered with little deflection from its initial direction; these signals corresponded to the sum of elastic and inelastic scattering collisions of 16 O, which we could not resolve, so they will be referenced collectively as “scattered 16 O.” Five representative laboratory-frame TOF distributions (m/z = 16), the c.m. angular and translational energy distributions and the laboratory-frame angular distribution are shown in Figure 4.7. Scattered 16 O had 85.6 kcal mol−1 total translational energy, or 87% of the available energy (see Figure 4.7B), on average. The experimental translational energy distribution was peaked at ∼97 kcal mol−1 . The c.m. angular distribution for 16 O was highly peaked in the forward direction with little scattered intensity for θc.m. > 20◦ ; however, the velocity and angular range for 16 O product detection in the experiment prevented the detection of backward-scattered 16 O (see Newton diagram in Figure 4.6). Some dependence of the c.m. translational energy distribution on the c.m. angular distribution was observed in the 16 O TOF data; the forward-convolution simulations became increasingly faster than the data at larger laboratory and c.m. angles (e.g, Θ = 20◦ , 30◦ , and 40◦ in Figure 4.7A). We also note that the c.m. angular distribution for scattered 16 O at θ c.m. ∼ 0 ◦ is an extrapolation because of high background from the hyperthermal oxygen source at the small laboratory angles corresponding to small c.m. angles for 16 O. Most of the 16 O probably scatters forward through high-impact-parameter collisions, but the limited constraints on the θc.m. ∼ 0◦ angular distribution (e.g., the laboratory-frame angular distribution, which only probes Θ = 6◦ ) increase the uncertainty in that part of the c.m. angular distribution. This extrapolation had a small effect on the relative product yield measurements (see Section 4.4.2.4), but did not alter the results qualitatively. 121 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.7: Laboratory inelastic scattering data detected at m/z = 16. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for inelastically scattered 16 O products from 16 O + 12 C18 O2 collisions at hEcoll i = 98.8 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). These data indicate that 16 O is scattered mainly in the forward direction with little change in its initial direction or velocity. 122 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 The experiment mainly observed 12 C18 O2 scattered opposite its initial direction in the c.m. frame (see Newton diagram in Figure 4.6). Detected 12 C18 O2 products (m/z = 48) showed best-fit c.m. translational energy distributions that were both broader and lower in energy, on average, than that obtained for forward-scattered 16 O. Furthermore, a single pair of P(ET ) and T(θc.m. ) distributions was not sufficient to describe the m/z = 48 TOF distributions. Consequently, a second pair of P(ET ) and T(θc.m. ) distributions was included in the fit of inelastically scattered 12 C18 O2 ; five representative laboratory-frame TOF distributions, the c.m. angular and translational energy distributions, and the laboratory-frame angular distribution obtained from 12 C18 O2 product detection are shown in Figure 4.8, along with the c.m. velocity-flux diagram in Figure 4.9. The first P(ET ) and T(θc.m. ) pair for inelastically scattered 12 C18 O2 described the scattering at θc.m. < 120◦ . In this region, the angular distribution was peaked near θc.m. = 60◦ , though the probability of scattered products was roughly constant for all θc.m. < 60◦ before decaying steadily at θc.m. > 60◦ . The corresponding translational energy distribution was peaked at ∼39 kcal mol−1 with an average hET i = 40.1 kcal mol−1 , or 41% the available energy. The second P(ET ) and T(θc.m. ) pair for inelastically scattered 12 C18 O2 described the scattering at 60◦ < θc.m. < 125◦ (corresponding to the maximum θc.m. observed in the experiment); this range overlapped, in the sidewaysscattering region, with the first pair. The second T(θc.m. ) distribution increased rapidly from θc.m. = 60◦ peaked near θc.m. = 120◦ . It decayed quickly at θc.m. > 120◦ , although this part of the distribution is uncertain because our experiment did not probe it directly. The translational energy distribution was peaked at 65 kcal mol−1 with an average hET i = 63.8 kcal mol−1 , or 65% the available energy. Mechanistic implications of the additional P(ET ) and T(θc.m. ) distributions will be addressed in Section 4.5. While the forward-convolution laboratory fitting method produced c.m. angular and translational energy distributions that yielded good fits to the data in Figures 4.7 and 4.8, they may not be unique fits to the data because of the temporal and angular width of the incident O(3 P) source beam and the low resolution and SNR in the resulting TOF distributions. Small changes to the c.m. angular and translational energy distributions still produced good fits to the data that were within the uncertainty bounds of the laboratory-frame 123 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.8: Laboratory inelastic scattering data detected at m/z = 48. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for inelastically scattered 12 C18 O2 products from 16 O + 12 C18 O2 collisions at hEcoll i = 98.8 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines (dark blue and cyan) are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). The orange and brown lines correspond to products of 16 O + 12 C18 O collisions, and they are discussed in Appendix 3.A. A single c.m. transla2 2 tional energy and angular distribution for each collision partner was insufficient to describe the TOF distributions of inelastically scattered 12 C18 O2 , suggesting a scattering dependence on impact parameter. 124 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.9: Velocity-flux contour diagram for inelastically scattered 12 C18 O2 from 16 O(3 P) + 12 C18 O collisions in the center-of-mass frame. The white arrows are the 2 initial 16 O(3 P) and 12 C18 O2 velocity vectors, and the dashed white line is the maximum recoil velocity for 12 C18 O2 (vmax ). Only the c.m. angles for which the experiment were sensitive are shown; inelastically scattered 12 C18 O2 from high-impact-parameter collisions are not shown, as their flux would be off-scale. Strong coupling of the P(ET ) and T(θ c.m. ) distributions was observed. angular distribution (see Figures 4.7D and 4.8D), but larger, qualitative changes to the c.m. angular and translational energy distributions did not. Consequently, general statements regarding the scattering direction and degree of energy transfer in the c.m. frame can be made with some certainty. The c.m. angular and translational energy distributions derived from the QCT calculations at Ecoll = 4.5 eV (103.7 kcal mol−1 ) are shown in Figure 4.10 for comparison with the experimental results for scattered 16 O. Center-of-mass angular and translational energy distributions for inelastic scattering obtained from the QCT calculations were in qualitative agreement with the laboratory data, although there are noticeable quantitative disagreements. The theoretical c.m. angular distribution showed fewer scattered products at θc.m. < 20◦ and more scattered products at 40◦ < θc.m. < 90◦ . In addition, the theoretical c.m. translational energy distribution had a sharper peak at high energies and a broader tail at low energies, although the average translational energies were similar (hET i = 85 and 86 kcal mol−1 for B3LYP and BMK, respectively). However, forward convolution of these dis- 125 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.10: Comparison of laboratory and theoretical c.m. (A) angular and (B) translational energy distributions for inelastic scattering of O(3 P) and CO2 at hEcoll i ≈ 100 kcal mol−1 . Distributions obtained from the inelastic scattering of 16 O and from the QCTs are shown here. They were binned (midpoints are shown, connected by spline curves) to provide better statistics for comparison. Both B3LYP and BMK theories show fewer forwardscattered products than were observed in the experiment. Also, the theories predict a translational energy distribution that is more highly peaked at high energies and that has a longer tail at low energies. 126 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 tributions resulted in simulations of the laboratory data that underestimated the proportion of products scattered to low laboratory angles (i.e., Θ = 6◦ , 8◦ , and 10◦ ) and overestimated the low-energy tail in the TOF distributions. Some of this disagreement may be attributable to the ∼14 kcal mol−1 width of the initial collision energy distribution, the inability of the experiment to resolve elastic- from inelastic-scattering contributions to the 16 O signal, and the observed coupling between the c.m. angular and translational energy distributions (see Section 4.5). Still, these laboratory results are consistent with previous studies of hyperthermal O(3 P) scattering from small molecules; a forward-scattering preference and minimal energy transfer was also observed in our earlier studies of D2 , CO, and C2 H6 collisions [Brunsvold et al., 2008; Garton et al., 2006, 2009]. 4.4.2.2 16 O(3 P) + 12 C18 O 2 → 18 O + 16 O12 C18 O As we reported in the preceding chapter, some of the fastest reactively scattered 16 O12 C18 O was attributed to an O-atom exchange reaction between fast-moving 16 O2 and 12 C18 O2 at Ecoll ∼ 160 kcal mol−1 . We describe here the results for the remaining product signal at m/z = 46, which we attribute to the O(3 P) + CO2 isotope exchange reaction. Products of the isotope exchange reaction near 100 kcal mol−1 scattered mainly in the backward direction (θc.m. = 180◦ ), as implied by the five representative laboratory-frame TOF distributions, the c.m. angular and translational energy distributions, and the laboratory-frame angular distribution shown in Figure 4.11. The product c.m. velocity-flux diagram is shown in Figure 4.12. Significant forward and sideways scattering of products was also observed in addition to backward scattering; the T(θc.m. ) distribution indicates that products scattered to 0◦ < θc.m. < 90◦ do so with nearly equal probability, and that scattered products become increasingly more probable as θc.m. approaches 180◦ . On average, the two products had 34.8 kcal mol−1 of total translational energy, or 35% of the available energy (see Figure 4.11B). The peak of the experimental translational energy distribution, P(ET ), was ∼30 kcal mol−1 . These results indicate a significant transfer of translational energy to internal degrees of freedom of the products, which is characteristic of reactions with significant barriers (e.g., ∼25 kcal mol−1 ). 127 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.11: Laboratory reactive scattering data detected at m/z = 46. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for 16 O12 C18 O products of the 16 O(3 P) + 12 C18 O2 → 18 O + 16 O12 C18 O reaction at hEcoll i = 98.8 kcal mol−1 . The circles in (A) and (D) are experimental data, while the lines are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. In (A), the best-fit forward-convolution simulations of 16 O12 C18 O products from 16 O(3 P) + 12 C18 O2 collisions (black dot-dashed lines) are shown with those from 16 O2 + 12 C18 O2 collisions at hEcoll i = 158.1 kcal mol−1 (blue dashed lines). The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). 128 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.12: Velocity-flux contour diagram for 16 O12 C18 O products of 16 O(3 P) + 12 C18 O2 collisions in the center-of-mass frame. The white arrows are the initial 16 O(3 P) and 12 C18 O velocity vectors, and the dashed white line is the maximum recoil velocity for 2 16 O12 C18 O (v 16 O12 C18 O products are scattered mainly in the same direction as the max ). initial 12 C18 O2 velocity vector. The theoretical c.m. angular and translational energy distributions derived from the QCT calculations at Ecoll = 4.5 eV (103.7 kcal mol−1 ) are plotted with the experimental data for comparison in Figure 4.13. In general, good agreement between experiments and the theoretical predictions was observed. The experimental best-fit c.m. angular distribution agreed nearly quantitatively for products scattered in the forward direction (small θc.m. ), while only qualitative agreement was found for products scattered in the backward direction (large θc.m. ). The preference for backward-scattered 16 O12 C18 O products suggested by the QCT calculations is also observed in the experimental data. hET i for the experimental P(ET ) is in good agreement, within uncertainty, with those obtained from the B3LYP (hET i = 43 ± 15%) and BMK (hET i = 47 ± 16%) trajectories. Qualitative aspects of the energy transfer during reactive scattering collisions appear to be reproduced in the QCT results, namely, that the product 16 O12 C18 O has a significant amount (≥ 50 kcal mol−1 ) of internal energy, on average. The experimental peak ET , however, is slightly less than the most probable translational energies predicted by the QCT calculations, ∼40 kcal mol−1 . This mild disagreement in the shape of the P(ET ) distribution may arise from uncer- 129 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.13: Comparison of laboratory and theoretical c.m. (A) angular and (B) translational energy distributions for the O(3 P) and CO2 isotope exchange reaction at hEcoll i ≈ 100 kcal mol−1 . Distributions obtained from the inelastic scattering of 16 O and from the QCTs are shown here. They were binned (midpoints are shown, connected by spline curves) to provide better statistics for comparison. Both B3LYP and BMK theories predict fewer backward-scattered products than were observed in the experiment. Also, the theories predict a translational energy distribution that is peaked at slightly higher energies. 130 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 tainties in the experiment and in the forward-convolution analysis. First, the broad O(3 P) velocity distribution in the experiment, and the resulting broad collision energy distribution, could mask any underlying structure in the P(ET ) distribution if the location of the peak in the P(ET ) distribution depends on collision energy. Indeed, the theoretical excitation functions indicate that the reaction cross-section is sensitive to collision energy in near Ecoll = 100 kcal mol−1 (see Figure 4.4). Second, the presence of the O2 + CO2 isotope exchange channel, which was not resolved from the forward-scattered 16 O12 C18 O peak in the laboratory TOF, renders the higher-ET portion of the P(ET ) less certain. Constraints from the backward-scattered component of the laboratory TOF distributions were also limited due to the t −3 dependence of the scattered product intensity in the laboratory-to-c.m.frame Jacobian transformation (see Eq. 3.3), which reduces the instrument’s sensitivity to backward-scattered products. Consequently, the angular distribution of products near θc.m. = 180◦ is less certain, and the observed disagreement between experimental and theoretical c.m. angular and translational distributions could be refined with additional measurements. Last, some uncertainty in the average and peak of the product translational energy distribution in the QCT data arises from the binning process used to obtain better statistics in the distribution; the width of each ET bin was ∼11.5 kcal mol−1 , so disagreements in the P(ET ) peak locations between theory and experiment on the order of 10 kcal mol−1 are not unreasonable. 4.4.2.3 16 O(3 P) + 12 C18 O 2 → 18 O16 O + 12 C18 O Reactively scattered products at m/z = 34 were clearly resolved at Θ = 6◦ , barely detectable at Θ = 10◦ , and not detectable at Θ = 14◦ (see Figure 4.14). While this laboratoryframe angular dependence may imply that 18 O16 O products are mainly forward-scattered, we cannot rule out backward scattering because the experiment was not sensitive to it (see Newton diagram in Figure 4.6); the signal corresponding to the counterproducts at m/z = 30 (12 C18 O+ ) could not be resolved because of high background signal from 12 C18 O2 fragmentation at the ionizer. We obtained a c.m. translational distribution peaked at 56 kcal mol−1 from the laboratory data, which indicated that 18 O16 O + 12 C18 O products had 55.0 131 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.14: Laboratory reactive scattering data detected at m/z = 34. (A) Laboratory TOF, (B) c.m. translational energy, and (C) laboratory angular distributions for 18 O16 O products of the 16 O(3 P) + 12 C18 O2 → 18 O16 O + 12 C18 O reaction at hEcoll i = 98.8 kcal mol−1 . The circles in (A) and (C) are experimental data, while the lines are the best-fit forwardconvolution simulations of the experimental data derived from the c.m. translational energy distribution shown in (B). Experimental sensitivity was not sufficient to obtain a full c.m. angular distribution, so a T(θc.m. ) distribution is not shown. The error bars in (C) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). kcal mol−1 translational energy, or 61% of the available energy, on average. No products were detected at m/z = 36 (18 O2 + ), which would have corresponded to an oxygen-atom abstraction mechanism more complex than simple stripping. Qualitatively, these results are consistent with the QCT results, which predicted a lower reactive cross-section for the oxygen abstraction channel than for the isotope exchange channel. 4.4.2.4 Relative product yields Experimental relative product yields for 16 O(3 P) + 12 C18 O2 collisions at hEcoll i = 98.8 kcal mol−1 were calculated from the integrated cross-sections for each channel, which were obtained from the forward-convolution simulations of the TOF data. Because the signal at m/z = 46 contained contributions from both 16 O(3 P) + 12 C18 O2 and 16 O2 + 12 C18 O2 collisions, 132 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Table 4.3: Comparison of experimental and theoretical yields for the products of O(3 P) + CO2 collisions near 100 kcal mol−1∗ Experiment B3LYP/6-311G(d) BMK/6-311G(d) Non-reactive scattering Oxygen isotope exchange 98.4% 98.2% 98.1% 1.6% 1.8% 1.9% ∗ Uncertainty bounds in the experimental estimates are probably less than ± 0.25%, based on the uncertainties in the integrated count rates at m/z = 46. Uncertainties in the QCT-derived relative yields are less than ± 0.1%. the forward-convolution fits for 16 O2 + 12 C18 O2 isotope exchange were subtracted from the laboratory TOF data before the 16 O(3 P) + 12 C18 O2 cross-section was calculated. Resulting integrated cross-sections were scaled by their electron-impact ionization cross-sections and fragmentation patterns for the comparison; the transmission through the quadrupole mass filter was assumed to be similar for all the small molecules examined here. Using this method, we calculated branching fractions for non-reactive scattering (98.5%), oxygenatom abstraction (0.0004%), and oxygen isotope exchange (1.6%) based on the integrated cross-sections obtained at m/z = 16, 34, and 46, respectively. The oxygen-atom abstraction yield is a lower limit because only a portion of the Newton sphere was observed. The oxygen isotope exchange yield is an upper limit because we compared the integrated cross-section of 16 O12 C18 O products to the yield of scattered 16 O only; the strongly coupled P(ET ) and T(θc.m. ) distributions for inelastic scattering make momentum-matching of 16 O and 12 C18 O2 products difficult. Our experimental branching fractions for the isotope exchange reaction at hEcoll i = 98.8 kcal mol−1 and those calculated from the QCT calculations at Ecoll = 4.5 eV (103.7 kcal mol−1 ) agree within 0.3%, despite a difference of 5 kcal mol−1 in the collision energy (see Table 4.3). This agreement could be coincidental because both the theoretical and laboratory data have significant uncertainties when defining the total cross-section, but our analysis suggests that the agreement persists in spite of these uncertainties. First, Eq. 4.4 shows that the theoretical calculation for the total cross-section depends on the square of maximum impact parameter sampled for reactive scattering (bmax ), but examination of the theoretical opacity function for the oxygen isotope exchange reaction (Figure 4.5) indicates 133 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 that no reactions occur beyond b = 3.5 a0 , so the reactive cross-section should be sufficiently converged with a bmax = 5.0 a0 . Second, the accuracy of the laboratory integrated cross-sections depends on the accuracy of the best-fit c.m. angular and translational energy distributions, but our sensitivity study on the θc.m. → 0◦ extrapolation we used for scattered 16 O resulted in the non-reactive scattering and oxygen isotope-exchange branching fractions fluctuating ∼0.5% when the scattered intensity at θc.m. < 4◦ was varied between twice the best-fit value and zero. Third, the oxygen-atom abstraction reaction contributes to the overall reactive cross-section, but this channel had a negligible contribution to the overall product yield based on the small number of reactive trajectories observed in the QCT calculations and the small amount of 18 O16 O detected in the experiment. Consequently, the agreement between the theoretically derived and experimental relative product yields for the oxygen isotope exchange reaction should be robust. The theoretical reactive cross-sections (Eq. 4.4) were divided by three for the comparison with experiment because the O(3 P) + CO2 surface is triply degenerate at large O(3 P)–CO2 separation distances;. All three electronic states were probed by the experiment, but only one (3 A00 ) was probed in the QCT calculations. Whether the two additional states (e.g., 3 A0 ) lead to reaction under our experimental conditions is unknown, but the good agreement between theory and experiment is consistent with the other two electronic surfaces being either repulsive or unimportant for producing 16 O12 C18 O at these collision energies. If the barrier to isotope exchange on the 3 A0 surface is close to the one the 3 A00 surface, isotope exchange on the 3 A0 surface could also contribute to the experimental product yield; the current theoretical product yield, therefore, should be treated as a lower limit when compared to the experimental value. Degenerate triplet states were also a concern in our study of O(3 P) + C2 H6 collisions, but the laboratory relative product yields there also agreed, within uncertainty, with those derived from QCT calculations [Garton et al., 2009]. 134 L. Y. Yeung Oxygen isotope exchange reactions of CO2 4.5 Discussion 4.5.1 Theoretical studies Chapter 4 Our electronic structure calculations yielded some disagreements with previous work [Bennett et al., 2004; Froese and Goddard, 1993; Mebel et al., 2004; Yang et al., 2005]. First, we reported a geometry and energy for TS1 structure that was significantly different from that predicted by Mebel and coworkers calculated at the CASSCF(16,13)/6-311G(d) level of theory (see Figure 4.2) [Bennett et al., 2004; Mebel et al., 2004]. For example, in Mebel et al.’s 3 A0 TS1 structure, the longest C–O bond was 0.08 Å shorter, the shortest C–O bond was ∼0.02 Å longer, and the most acute bond angle was 17◦ smaller than in our CCSD(T)/aug-cc-pVTZ structure. Interestingly, our 3 A00 TS1 structure shows smaller disagreements with the 3 A0 TS1 structures calculated by Froese and Goddard at the HF/6-31G* and MP2/6-31G* levels of theory. These differences in geometries and the difference in symmetry yielded a TS1 energy 11 kcal mol−1 higher in Mebel et al.’s CCSD(T)/6-311+G(3df) calculation than in our calculation. Mebel et al. did note that their truncated (16,13) active space was a clear shortcoming of their study; it was chosen over the full-valence (22,16) active space due to computational limitations. Second, our calculations indicated that the lowest-energy triplet PES near TS1 had 3 A00 symmetry, not 3 A0 symmetry, as others had reported [Bennett et al., 2004; Froese and Goddard, 1993; Mebel et al., 2004]. We examined this discrepancy first by calculating the single-point CCSD(T)/aug-cc-pVTZ energy of Froese and Goddard’s “T9” structure at both orbital symmetries. In this case, the 3 A0 energy was ∼10 kcal mol−1 above the 3 A00 energy. We also attempted to optimize a TS1-like 3 A0 structure at the CCSD(T)/aug-cc-pVTZ and W4 levels of theory, but we found self-consistent field convergence problems similar to those reported by Froese and Goddard and thus could not locate any stationary points. The 3 A00 state of CO3 near TS1, then, appears to be lower in energy than the 3 A0 state. We argue that these discrepancies were caused by the differing treatment of dynamical correlation in this study and others. The electronic structure of ground singlet CO3 displays vibronic coupling with an array of Jahn-Teller states [Kowalczyk and Krylov, 2007; Liu et al., 135 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 2009], and the resulting energy minima required a high level of dynamical correlation to represent correctly; because of the large number of electronic states within several eV of the lowest triplet PES, vibronic coupling (and therefore dynamical correlation) is likely important here as well. Multiconfigurational self-consistent field methods like CASSCF (used by Mebel et al. for geometry optimizations) do not treat dynamical correlation, and this shortcoming has been implicated in the poor representation of the singlet-CO3 , NO3 , and parabenzyne radicals with these methods [Crawford et al., 2001; Eisfeld and Morokuma, 2000; Kowalczyk and Krylov, 2007]. High-level dynamical correlation is included in coupledcluster methods, which generally yield more accurate thermochemical properties for this class of problems. Furthermore, the agreement between our TS1, TS2, and CO3 energies and those calculated using the W4 method (J. M. L. Martin, private communication) suggest that single-reference calculations with high-level treatment of dynamical correlation can describe the triplet stationary points appropriately. Multi-reference character on other regions of the PES could still be important, however, and is not ruled out by the correspondence between the CCSD(T) and W4 calculations at the stationary points. If strong vibronic coupling on the low-lying electronic states of CO3 is important during reactive trajectories, it could lead to a misrepresentation of the PES curvature by the B3LYP and BMK methods during the QCT calculations. Russ et al. [2004] noted that B3LYP underestimated the magnitude of vibronic interactions in the B–N–B and C3 + model systems, and attributed this tendency to the behavior of the Kohm-Sham molecular orbital Hessian near conical intersections. Because the Kohm-Sham Hessian is common to both B3LYP and BMK theories, both functionals are subject to the same tendency. Large fractions of Hartree-Fock exchange mixed into the BMK functional for improved barrier height prediction may also result in unintended symmetry-breaking on the CO3 PES [Sherrill et al., 1999], as was the case for the CO3 minimum (see Figure 4.2). The results of these calculations are compared with the experimental results below. 136 L. Y. Yeung 4.5.2 Oxygen isotope exchange reactions of CO2 Chapter 4 Non-reactive scattering of O(3 P) and CO2 Non-reactive 16 O(3 P) + 12 C18 O2 collisions mainly scattered products with little change in the initial direction or speed, although some products scattered in directions sideways and opposite their initial direction; these products had lower average velocities. Products showing little deflection from their initial trajectories probably arise from high-impactparameter collisions, while products that are highly deflected probably arise from lowimpact-parameter collisions. These two molecular regimes were supported qualitatively by the theoretical opacity functions (see Figure 4.5), which display separate peaks at low (1.75 a0 ) and high (3.25 a0 ) impact parameters. While large impulsive energy transfer was observed for hyperthermal collisions of Ar and O(3 P) with C2 H6 at low impact parameters [Brunsvold et al., 2004; Garton et al., 2009; Tasic et al., 2007], large energy transfer was also observed for “failed” reactive collisions of hyperthermal O(3 P) and CO; the CO2 * complex resulting from these collisions can dissociate to yield products corresponding to isotope exchange or inelastic scattering, depending on the identity of the dissociating oxygen atom. This mechanism resulted in a low-energy tail in the translational energy distribution for inelastic scattering of O(3 P) + CO [Brunsvold et al., 2008]. Our analysis of inelastically scattered 12 C18 O2 molecules indicated that one pair of P(ET ) and T(θc.m. ) distributions was insufficient to simulate the laboratory data accurately. This observation corresponds to a breakdown of the assumption that the c.m. angular and translational energy distributions are separable. Our use of two pairs of P(ET ) and T(θc.m. ) distributions to fit the laboratory data is similar to previous studies where inelastic scattering of Cl + C3 H8 and hyperthermal O(3 P) + C2 H6 were investigated [Blank et al., 1998; Garton et al., 2009]. In both the previous cases and in the present case, the polyatomic species had a large number of degrees of freedom into which translational energy can be transferred upon collision. Consequently, a dependence of energy transfer on the impact parameter is not unexpected; different impact parameters may preferentially excite different degrees of freedom. In the system studied here, the product translational energy decreases as 12 C18 O2 becomes more forward-scattered (small Θ, corresponding to low-impact-parameter collisions), implying that 12 C18 O2 becomes increasingly internally excited as O–CO2 collisions 137 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 become more rebound-like. The type and mechanism of internal excitation are uncertain, however, because the “failed” reaction might also contribute to the observed c.m. angular and translational energy distributions of forward-scattered 12 C18 O2 . We note that our experimental data did not display a slow tail in the 16 O TOF distributions characteristic of the “failed” reaction in the O(3 P) + CO system. 4.5.3 Oxygen isotope exchange, O(3 P) + CO2 → O + CO2 Laboratory data for the isotope exchange reaction at hEcoll i = 98.8 kcal mol−1 shows a backward-scattering preference, and thus is evidence for a direct reaction mechanism. The isotopically exchanged products also had relatively low translational energy (hET i = 35% Eavail ). These two observations suggest that the reaction involves a short-lived CO3 ∗ intermediate and/or occurs at low impact parameters where the transfer of energy to internal degrees of freedom of the products is efficient. With 74 kcal mol−1 excess energy, the O(3 P)–CO2 collision need not be head-on to have enough energy to surmount the TS1 activation barrier. The long C–O bond length (1.6 Å) and mild O–C–O bending angle (150◦ vs. 180◦ for CO2 ) in TS1 also suggests that the entrance and exit barriers are neither particularly early nor late. Hence, the CO3 ∗ complex could exist for several vibrational periods. Efficient transfer of energy into vibrational modes of the CO3 ∗ intermediate would be required for an isotope exchange event to occur because inefficient coupling of that energy would increase the probability of redissociating the incident oxygen atom, resulting in an inelastic collision. A direct isotope exchange mechanism through a short-lived CO3 complex is qualitatively in agreement with our QCT calculations (see Figure 4.15). For O(3 P) + CO2 collisions Figure 4.15: Snapshots of a quasiclassical trajectory for O(3 P) + CO2 isotope exchange through a short-lived CO3 ∗ complex at 1.5 eV (34.6 kcal mol−1 ) collision energy. The incident oxygen atom is highlighted for clarity. 138 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 resulting in oxygen isotope exchange, a CO3 ∗ complex forms when the incoming oxygen atom interacts with the carbon atom on CO2 (see also the opacity functions in Figure 4.5). In some cases, the CO3 ∗ complex existed for less than one vibrational period (the reaction is nearly direct) while in others it existed for many vibrational periods. After some time (typically leq 200 fs), one of the oxygen atoms initially part of the CO2 detaches to leave behind a new CO2 molecule. Head-on collisions at higher collision energies tended to form complexes existing for shorter times than those formed similarly at lower energies. Higher energies also tended to form CO3 ∗ complexes that tumbled ≥ 360◦ in the plane of the reaction. In all cases, however, the CO3 ∗ complex lasted less than a picosecond. These data support an isotope exchange reaction mechanism that begins with an interaction between O(3 P) and the carbon atom of CO2 to form a short-lived CO3 ∗ reaction complex. The identity of the dissociating oxygen atom determines the reaction’s classification. If the dissociating oxygen atom is one originally on CO2 , then the trajectory is reactive; if it is the incident oxygen atom, then the trajectory is inelastic. The lifetime of the CO3 reaction complex determines the c.m. angular and translational energy distributions of product CO2 . Longer-lived CO3 complexes should yield smaller average translational energies because they will have more time to redistribute the initial translational energy to internal degrees of freedom. This mechanism for the O(3 P) + CO2 isotope exchange reaction is different from that observed by Perri et al. for the O(1 D) + CO2 → O(3 P) + CO2 isotope exchange reaction at Ecoll = 4.2 and 7.7 kcal mol−1 , which samples part of the same PES [Perri et al., 2003, 2004]. In those molecular-beam experiments, the reactively scattered CO2 products had an isotropic (forward-backward symmetric) angular distribution and ∼50% of the available energy in translation; these results were evidence for a CO3 ∗ intermediate complex that lasted for at least several rotational periods (> 1 ps). These dynamics are not inconsistent with our O(3 P) + CO2 results, however, because the two studies may sample different parts of the 3 A00 and/or 3 A0 PESs. O(3 P) + CO2 collisions on the 3 A0 surface could, in principle, cross onto the 1 A0 surface to yield reactively scattered O(1 D) + CO2 products. One possible triplet-singlet crossing mech- 139 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 anism could be through spin-orbit coupled radiationless transitions, i.e., the reverse of what Mebel et al. had suggested for the O(1 D) + CO2 reaction, because the spin-orbit coupling terms and Franck-Condon factors are favorable [Mebel et al., 2004]. Thus, we evaluated the general possibility of intersystem crossing (ISC) during our experiments by performing forward-convolution fits of the laboratory data that included the ∼45 kcal mol−1 endothermicity of O(1 D) vs. O(3 P). Satisfactory fits of the laboratory TOF and angular distributions were obtained (see Figure 4.16); the peak and average of the P(ET ) distribution were 34 and 30.7 kcal mol−1 (63% and 58% Eavail ), respectively. Consequently, ISC cannot be explicitly ruled out by the experimental data. The diabatic radiationless transition probability, however, decreases exponentially as a function of velocity [Landau, 1932], and no evidence for ISC has been observed during our previous dynamics studies at hyperthermal velocities [Brunsvold et al., 2007]. The qualitative agreement between the experimental and QCTderived dynamics on the lowest triplet PES is consistent with the oxygen isotope exchange reaction exiting on a triplet surface, although more dynamics studies will be necessary to test this hypothesis. 4.5.4 Oxygen-atom abstraction, O(3 P) + CO2 → O2 + CO Our laboratory observation of the oxygen abstraction reaction in the forward direction with a moderate amount of energy transfer (∼50%) could arise from early-barrier strippingtype mechanisms through TS2 or TS3. Hammond’s postulate states that for endothermic reactions, the transition state should be late and product-like. However, the small endothermicity relative to the barrier height (see Figure 4.1 and Table 4.1) for oxygen-atom abstraction suggests that TS2 and TS3 should be more reactant-like. Indeed, the bond lengths of CO and O2 are significantly longer in TS2 and TS3 than at equilibrium for the isolated molecules, which are 1.14 and 1.21 Å, respectively, at CCSD(T)/aug-cc-pVTZ. Theoretical trajectories yielding O2 + CO products occurred generally in one of two ways: through a stripping-type mechanism and through a CO3 ∗ complex. In the strippingtype mechanism (see Figure 4.17A), the incoming oxygen atom interacts principally with one of the oxygen atoms on CO2 to form TS3 directly. The C–O bond then breaks, releas- 140 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.16: Laboratory reactive scattering data detected at m/z = 46, fit assuming an ISC mechanism. (A) Laboratory TOF, (B) c.m. translational energy, and (C) c.m. and (D) laboratory angular distributions for 16 O12 C18 O products of the 16 O(3 P) + 12 C18 O2 → 18 O16 O(1 D) + 12 C18 O reaction at hE −1 coll i = 98.8 kcal mol . The circles in (A) and (D) are experimental data, while the lines are the best-fit forward-convolution simulations of the experimental data derived from the c.m. translational energy and angular distributions shown in (B) and (C), respectively. In (A), the best-fit forward-convolution simulations of 16 O12 C18 O products from 16 O(3 P) + 12 C18 O collisions (black dot-dashed lines) are shown 2 with those from 16 O2 + 12 C18 O2 collisions at hEcoll i = 158.1 kcal mol−1 (blue dashed lines). The error bars in (D) represent 2σ uncertainties in the integrated experimental TOF distributions (see Appendix 4.7). 141 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.17: Snapshots of quasiclassical trajectories for the O(3 P) + CO2 → O2 + CO reaction. (A) A stripping-type mechanism through TS3 at 6.5 eV (149.8 kcal mol−1 ) collision energy calculated at the B3LYP/6-311G(d) level of theory. (B) A CO3 reaction-complex mechanism through TS2 at 5.5 eV (126.7 kcal mol−1 ) collision energy calculated at the BMK/6-311G(d) level of theory. The incident oxygen atoms are highlighted for clarity. ing O2 + CO products. Of all the QCTs run, only two of these stripping-type trajectories were observed, and they occurred at Ecoll = 6.5 eV (149.8 kcal mol−1 ) using B3LYP/6311G(d). The remaining 27 O2 + CO-producing trajectories proceeded through a CO3 ∗ complex mechanism (see Figure 4.17B). In that mechanism, the incoming oxygen atom interacts first with the carbon atom of CO2 to form a short-lived CO3 ∗ complex, similar to that observed in the isotope-exchange trajectories. This complex rarely survived more than one vibrational period. An oxygen atom is then released and then interacts with a CO2 bound oxygen atom as the CO2 rotates. Last, an O–O bond forms as the adjacent C–O bond breaks to form O2 + CO products. A key difference between the two O2 + CO-producing mechanisms is that the CO3 ∗ complex mechanism requires a slow recoil of the oxygen atom that dissociated initially. Following complex formation in a high-energy collision, the nascent CO2 will have sufficient internal energy (∼70 kcal mol−1 ) to form the O2 + CO products only if the O atom dissociates with low translational energy. When the O atom escapes the CO3 ∗ complex with high translational energy, the nascent CO2 rotates too slowly for any further reaction to take place (in these cases, the trajectory results in either inelastic scattering or isotope 142 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 exchange). With so much excess energy, however, the reaction need not take the lowest energy path [Zhang et al., 2008]; the slow recoiling oxygen atom in the CO3 ∗ -complex mechanism resembles the “roaming’ H-atom and methyl group in formaldehyde [Townsend et al., 2004] and acetaldehyde [Houston and Kable, 2006] photodissociation, respectively. We note that the stripping-type mechanism would have produced 18 O16 O molecules in the experiment exclusively, whereas the CO3 ∗ -complex mechanism can produce 18 O2 in addition to 18 O16 O. Our laboratory observation of m/z = 34 products is consistent with both oxygen abstraction mechanisms, but the lack of signal due to m/z = 36 products in the forward direction (where there was negligible background) is evidence against the CO3 ∗ complex mechanism. The CO3 ∗ -complex mechanism, however, comprised 27 of the 29 oxygen-atom abstraction trajectories obtained from the QCT calculations, and only one of those trajectories would have produced m/z = 34 products. The two remaining trajectories proceeded through the stripping mechanism. This preference for the CO3 ∗ -complex mechanism observed in the QCT calculations may be a consequence of the ∼50 kcal mol−1 lower barrier for CO3 formation and the ∼13 kcal mol−1 lower energy of TS2, both relative to the energy of TS3. Additional experimental and theoretical studies with a higher SNR, perhaps at higher collision energies, will be required to elucidate the mechanisms of this reaction. 4.6 Conclusions We have investigated the dynamics of O(3 P) + CO2 collisions at hyperthermal collision energies. Non-reactive scattering was dominated by high-impact-parameter collisions, which did not perturb the initial velocity of the reactants significantly. Lower impact parameters resulted in increased translational-to-internal energy transfer. Both the oxygen isotope-exchange and the atom-abstraction reaction channels were observed directly by our crossed-molecular-beam apparatus. The oxygen isotope exchange reaction displayed an anisotropic angular distribution with a large amount of translational-to-internal energy transfer, suggesting that the reaction occurs at low impact parameters through a short-lived intermediate CO3 ∗ complex. The mechanisms for both non-reactive scattering and oxygen isotope exchange were supported qualitatively, but not quantitatively, by the QCT calcula143 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 tions on the 3 A00 surface. Nonadiabaticity during inelastic and reactive trajectories cannot be ruled out and its effects should be investigated; both inelastic and reactive trajectories may be sensitive to the coupling between the lowest triplet (3 A00 ) PES and nearby (e.g., 3 A0 ) electronic surfaces. With ∼100 kcal mol−1 collision energy, the experiment may probe regions of the PES far from the TS1, TS2, TS3, and CO3 structures; the presence of several other surfaces (both triplet and singlet) within this energy range [Kowalczyk and Krylov, 2007; Liu et al., 2009], the possibility of vibronic effects due to Jahn-Teller-like distortion, and the failure of densityfunctional methods to capture the dynamics quantitatively all suggest that a higher-level treatment of the PES would be desirable. While the transition states and stationary points on the lowest triplet PES may be described well with density-functional calculations, this may not be the case in other regions of the PES where vibronic interactions can affect its curvature. A more complete, high-level description of the PES, along with more dynamics experiments, will be required to describe the dynamics of isotope exchange on the lowest triplet PES quantitatively. 4.7 Acknowledgements We thank Ned F. Lindholm for experimental assistance. This work was supported by the Missile Defense Agency under cooperative agreement HQ0006-05-2-0001. L. Y. Y. was supported by the Davidow Fund, and G. C. S. was supported by the Air Force Office of Scientific Research grant FA955D-07-1-0095. 144 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Appendices 145 Chapter 4 L. Y. Yeung 4.A Oxygen isotope exchange reactions of CO2 Chapter 4 Differential scattering cross-sections from 1.0 – 6.5 eV Theoretical center-of-mass differential scattering cross-sections for the oxygen isotope exchange reaction (Figure 4.18) showed a preference for backward scattering at all collision energies. The incident oxygen atom, attached to the product CO2 molecule, appeared to prefer scattering in a direction opposite its initial direction. As the collision energy increased, however, the angular distribution of products showed little qualitative change: Reactively scattered products showed a slight preference for backward scattering up to Ecoll = 6.5 eV (149.8 kcal mol−1 ), the highest collision energy considered in this study. The theoretical c.m. product translational energy distributions showed significant (≥ 50%) transfer of the available energy into internal degrees of freedom of the products at all collision energies = 2.5 eV (57.6 kcal mol−1 ). The QCT data below Ecoll ≥ 2.5 eV did not contain statistically significant number of reactive trajectories, i.e., > 30, so they were not included in this analysis. P(ET ) distributions became broader as the collision energy increased, though the proportion of energy remaining translation was similar at all collision energies. A bimodal distribution of translational energies may exist in the products of BMK trajectories run at 2.5, 3.5, and 4.5 eV collision energy (57.6, 80.7, and 103.7 kcal mol−1 , respectively); for instance, separate peaks were observed at ∼50% and ∼80% of the available energy for the 2.5-eV trajectories, although there is considerable uncertainty in the theoretical translational energy distribution (see Figure 4.18). Additional QCT calculations will be required before structure in the product translational energy distributions can be determined conclusively. 146 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 4 Figure 4.18: Center-of-mass angular and translational energy distributions for the O(3 P) + CO2 isotope exchange reaction derived from QCT calculations at the (A and B) B3LYP/6-311G(d) and (C and D) BMK/6-311G(d) levels of theory. Distributions with more than 30 reactive trajectories are shown. At both levels of theory and all collision energies shown, reactive scattering shows a preference for backward scattering (θc.m. > 90◦ ) with a moderate (≥ 50%) transfer of translational energy to internal degrees of freedom of the products. 147 L. Y. Yeung 4.B Oxygen isotope exchange reactions of CO2 Chapter 4 Estimating uncertainty in the laboratory angular distributions For this analysis we treat the TOF distribution at a given laboratory angle Θ as a type of Monte Carlo integration of the ‘true’ TOF distribution, and we estimate the variance in the integrated area accordingly. Under this approximation, the integrated area, I(Θ), is equivalent to the area of a rectangle with a width equal to the total time range, ttotal , and height equal to the average number density over that time range, hN(t)itotal . More formally, this relation can be written as a discrete sum over the channels on the MCP, each of which corresponded to a 1 µs dwell time: ttotal I(Θ) = 1 ttotal ∑ N(ti ) = ttotal [ ttotal ∑ N(ti )] = ttotal hN(t)itotal i=1 (4.8) i=1 The variance of I(Θ), however, must be evaluated as a function of time because the number density at a given arrival time at the detector, N(t), varied with flight time in each TOF distribution. Consequently, the TOF distribution was further divided into a set of bins for which the variance was calculated and summed over the total TOF distribution using the following relation: 2 σN(t) bin = 1 f [tbin N(ti )]2 − [tbin hN(t)ibin ]2 tbin ∑ i 2 σI(Θ) = 2 ∑ σN(t) bin (4.9) (4.10) bins where i and f represent the first and last members of each data bin. The standard deviation, σI(Θ) , was calculated by taking the square root of the variance. We note some degree of sensitivity in the calculated σI(Θ) values on tbin because the N(t) distributions show significant structure; consequently, we have reported conservative estimates of σI(Θ) using the 2 minimum bin size of tbin = 3 µs, or 3 data points per σN(t) bin 148 calculation.  L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 5 Chapter 5 Summary and outlook 5.1 New signatures, new reactions Presently, the large enrichment in 16 O13 C18 O we found in the stratospheric polar vortex is still unexplained. The laboratory photochemical experiments we reported in Chapter 2 seem to rule out O(1 D) + CO2 isotope exchange; stratospheric 16 O13 C18 O should get more depleted with increasing extent of isotope exchange, not enriched, and we observed this trend as a decrease in ∆47 in field samples from the mid-latitude stratosphere. What, then, could enrich 16 O13 C18 O in the polar vortex, and what might we be able to learn from future studies? We suggested in Chapter 2 that fast low-temperature isotopic equilibration of CO2 on stratospheric particles (e.g., PSCs) could be responsible for the high ∆47 values in the polar vortex. Our initial tests of the PSC-isotope-equilibration hypothesis suggested that isotopic equilibration on certain HNO3 ices and H2 SO4 :HNO3 :H2 O mixtures is slow, and is therefore unlikely to produce 16 O13 C18 O enrichments on timescales that would be consistent with our polar vortex data. The CO2 isotopic equilibration rate, however, could be sensitive to particle structure and composition. PSCs and cirrus clouds form under similar conditions, but they can differ in bulk and surface composition [Zondlo et al., 2000]; the structure, physics, and chemistry of these particles are still not understood [Dash et al., 2006; Lowe and MacKenzie, 2008], so the role of CO2 isotopic equilibration on ice particle surfaces remains uncertain. Future laboratory work on CO2 –ice surface interactions may shed light on the structure and composition of these and other atmospherically important particles. 149 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 5 We also identified three new reactions, O2 + CO2 and O(3 P) + CO2 isotope exchange and O(3 P) + CO2 → O2 + CO, in our crossed-molecular-beam experiments. Because of the ≈160 kcal mol−1 reaction barrier for O2 + CO2 isotope exchange, and the ≈75 kcal mol−1 barrier for O(3 P) + CO2 → O2 + CO, they are unlikely to be important in the stratosphere. O(3 P) + CO2 , in contrast, has a reaction barrier (≈ 25 kcal mol−1 ) that is atmospherically accessible, in principle. 5.2 Potential atmospheric importance of O(3 P) + CO2 The laboratory observation of O(3 P) + CO2 isotope exchange at hyperthermal energies may have implications for modeling the oxygen isotope cycling in the middle and upper atmosphere because current models do not include O(3 P) + CO2 reactions explicitly [Liang et al., 2007, 2008; Thiemens et al., 1995; Yung et al., 1991, 1997]. Here, I suggest that O(3 P) + CO2 reactions in the upper atmosphere could affect the oxygen isotope distribution in CO2 . The O(3 P) + CO2 isotope exchange reaction could yield isotope effects qualitatively different from those in the O(1 D) + CO2 reaction because its mechanism is direct, unlike the mechanism involving a long-lived CO3 ∗ intermediate for the O(1 D) + CO2 reaction [Chen et al., 2009; Perri et al., 2003, 2004]. Instead, like the O3 ∗ complex in the O(3 P) + O2 isotope exchange reaction [Van Wyngarden et al., 2007], the CO3 ∗ reaction complex formed from O(3 P) + CO2 does not live long enough for its energy to randomize; thus, dynamical isotope effects are likely to be important to its isotope-specific branching fractions. These types of non-statistical isotope effects are believed to be partly responsible for “anomalous” formation rates of stable O3 from the O3 ∗ complex for different isotopologues [Babikov et al., 2003; Gao and Marcus, 2001; Schinke et al., 2006]. Due to limitations in our apparatus, however, we were unable to investigate the O(3 P) + CO2 isotope exchange dynamics near the predicted reaction threshold, which is more relevant to the atmosphere. Our reactive trajectories at Ecoll = 1.0 and 1.5 eV (23.0 and 34.6 kcal mol−1 , respectively), however, suggest that isotope exchange is still direct near the calculated reaction barrier. The overall importance of the O(3 P) + CO2 isotope exchange reaction to reactive oxygen cycling in the atmosphere, however, depends on (1) the reaction’s excitation function 150 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 5 and (2) the proportion of O(3 P) in the atmosphere with sufficient translational energy to surmount the reaction barrier. In the absence of experimental data, high-level variational quantum calculations can assign an upper limit to the TS1 barrier. The CCSD(T)/aug-ccpVTZ energy for TS1 (25 kcal mol−1 ) reported in this work implies that relative velocities of ≥ 3 km s−1 in the ground-state reactants will be required to open the isotope exchange channel; ozone photolysis in the Hartley band (220 – 310 nm) and at shorter wavelengths yields O(3 P) + O2 (3 Σ− g ) photofragments having a total translational energy in excess of 25 kcal mol−1 and as high as 100 kcal mol−1 [Fairchild et al., 1978; Kinugawa et al., 1990; Shamsuddin et al., 1994; Stranges et al., 1995; Syage, 1995; Takahashi et al., 1998]. Our preliminary hard-sphere collision modeling (see Appendix 2.D) using cross-sections for the velocity relaxation of O(1 D) by N2 [Matsumi and Chowdhury, 1996; Matsumi et al., 1994b] suggests that the size of the reactive O(3 P) reservoir could be as high as several percent that of O(1 D). Future theoretical and experimental studies can elucidate the shape of the reaction’s excitation function, which is needed before an appropriate simulation can be constructed. Finally, we note that during our laboratory study of the O2 /O3 /CO2 photochemical system using a mercury lamp as an actinic light source (185 and 254 nm), we observed deviations from modeled results at long irradiation times (t ∼ days; see Figure 2.8); a minor O(3 P) + CO2 channel could address part of this discrepancy, as well as some of the disagreements between earlier studies [Chakraborty and Bhattacharya, 2003; Johnston et al., 2000; Shaheen et al., 2007; Wen and Thiemens, 1993]. The yield of hyperthermal O(3 P) during O3 photolysis depends on wavelength [Stranges et al., 1995; Takahashi et al., 1998], however, so this hypothesis awaits further testing with systematic studies of the O2 /O3 /CO2 photochemical system. Claims of hyperthermal O(3 P) + CO2 chemistry in the atmosphere based on laboratory data must be met with some skepticism, however. Both N2 and O2 are efficient energy quenchers for even the most reactive atmospheric species, and the steady-state population of fast-moving O(3 P) will be determined largely by its translational relaxation rate in air. In addition, thermal averaging collapses most reaction rates towards the chemical kinetic limit, so any atmospheric signature of the O(3 P) + CO2 reaction will be difficult to identify 151 L. Y. Yeung Oxygen isotope exchange reactions of CO2 Chapter 5 unless the associated isotope effect is large and unique. Previously published reports of hyperthermal chemistry in the atmosphere based only on laboratory evidence have been controversial due to the lack of an unequivocal signature in the field data [Li et al., 2008; Miller et al., 1994]. The stratospheric 16 O13 C18 O enrichment reported in Chapter 2 is a clear signature of some heretofore unknown process, but definitive tests of the hyperthermal O(3 P) + CO2 isotope-exchange hypothesis will have to take the form of well-characterized, rigorously modeled bulk photochemical experiments involving O3 and CO2 . 152  Photochemical and dynamics studies of oxygen isotope exchange reactions of CO2 Thesis by Laurence Yip-Lun Yeung In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2010 (Defended December 10, 2009) L. Y. Yeung Oxygen isotope exchange reactions of CO2 © 2010 Laurence Yip-Lun Yeung All Rights Reserved ii Copyright L. Y. Yeung Oxygen isotope exchange reactions of CO2 Inspiration Small quantities of different gases were added to separate portions of a non-inflammable mixture of dry carbonic oxide and oxygen, and the spark was then passed. In all cases where a gas containing hydrogen was introduced, the mixture exploded; in all cases where a gas containing no hydrogen was introduced, the mixture did not explode. — Harold Dixon, The Combustion of Carbonic Oxide and Hydrogen, 1886. iii L. Y. Yeung Oxygen isotope exchange reactions of CO2 Acknowledgements Acknowledgements This body of work would not have been possible without the intellectual, spiritual, and financial support from professor Mitchio Okumura, professor John Eiler, and Dr. William Davidow. Mitchio and John have taught me how to think critically and quantitatively about scientific problems; their unending creativity, enthusiasm, and wisdom continue to inspire me. Dr. Davidow’s generous endowment funded all of this research and much more not documented here. Only with his support was I able to pursue these risky projects. To my collaborators, professors Hagit Affek, Kristie Boering, Elliot Atlas, Tim Minton, Jon Camden, and George Schatz; Drs. Sue Schauffler, Jeff Paci, Weifu Guo, Kate Hoag, and Jianming Zhang; and Mr. Aaron Wiegel: This work was a collective effort, and I dare not take the credit for any more than my own modest contribution to it. Thank you for your time, patience, lab equipment, and fishing lessons. To the Okumura group, the Eiler group, and other mentors, professors Jack Beauchamp, Rudy Marcus, Geoff Blake, Yuk Yung, Zhengrong Wang, Julie Fry, Rose Came, Kate Huntington, Ben Passey, Naomi Levin, and Aradhna Tripathi; Drs. Pin Chen, Joe Hodges, Chip Miller, Linda Brown, Andrew Mollner, David Robichaud, Aaron Noell, Nathan Eddingsaas, and Mathieu Daëron; Mr. Bill Bing; fellow students Kana Takematsu, Matt Sprague, Kathleen Spencer, Dave Long, Sigrid Barklund, Aileen Hui, Thinh Bui, Nathan Honsowetz, and Heather Widgren: Most of my education here has been at your hands. Thank you for your time, wisdom, skepticism, and coffee. Finally, to my friends and family: You are the music of my life. You are the rhythm, the harmony, and melody. If music be the food of love, play on. Nothing I could say would ever be enough to express my gratitude. I am excited for whatever misadventures lie ahead. iv L. Y. Yeung Oxygen isotope exchange reactions of CO2 Abstract Abstract This dissertation describes laboratory studies of three oxygen isotope exchange reactions — O(1 D) + CO2 , O2 + CO2 , and O(3 P) + CO2 — and their importance to oxygen cycling in the upper atmosphere. First, we studied the isotope exchange reaction O(1 D) + CO2 , which is believed to govern the oxygen-isotope budget of CO2 in the stratosphere. Our combined field, laboratory, and modeling study of the exceptionally rare 16 O13 C18 O isotopologue revealed that O(1 D) + CO2 explains only part of the stratospheric CO2 isotopologue budget, not all of it as previously thought: O(1 D) + CO2 could not explain the large enrichments of 16 O13 C18 O (i.e., of the “∆47 ” tracer) at high Northern latitudes. Mesospheric and heterogeneous chemistry of CO2 were proposed as possible sources of this meridional variation in 16 O13 C18 O. Therefore, we performed crossed-molecular-beam experiments to investigate the chemistry of CO2 at hyperthermal collision energies; this class of reaction could be important in the upper atmosphere, where low gas densities and high rates of photochemistry increase the relative probability of hyperthermal reactions. Our experimental and theoretical study of the O2 + CO2 isotope exchange reaction showed that the reaction can occur through a short-lived CO4 reaction complex, which leads to O2 + CO2 products that are highly internally excited, but possibly still in their ground electronic state. Our study of O(3 P) + CO2 collisions at hyperthermal energies showed that O(3 P) + CO2 isotope exchange can occur in the upper atmosphere, proceeding through a short-lived CO3 reaction complex. The O(3 P) + CO2 → O2 + CO reaction was also observed, and our data suggest that it can proceed through a ‘stripping’ mechanism or a CO3 complex. These reactions demonstrate new ways in which oxygen can be cycled through CO2 in the atmosphere; their isotope effects, manifest in the isotopic composition of atmospheric CO2 , may impose independent constraints on atmospheric transport and biosphere-atmosphere interactions. v L. Y. Yeung Oxygen isotope exchange reactions of CO2 Table of contents Contents Acknowledgements iv Abstract v 1 Introduction 1.1 CO2 in the global carbon cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Stable isotopes, ‘clumped’ and otherwise . . . . . . . . . . . . . . . . . . . . 1.3 Anomalous isotopic enrichments in stratospheric CO2 . . . . . . . . . . . . . 1.4 Insights from the physical chemist’s toolbox . . . . . . . . . . . . . . . . . . 1.5 Executive summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 2 5 8 Appendices 1.A Isotopic notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.B Copyright declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 10 12 2 Large and unexpected enrichment in stratospheric 16 O13 C18 O 2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Field sample collection and analysis . . . . . . . . . . . . . . . . . . . . . . . 2.4 Field results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Laboratory photochemical experiments . . . . . . . . . . . . . . . . . . . . . 2.5.1 13 C/12 C kinetic isotope effect experiments . . . . . . . . . . . . . . . 2.5.2 Continuous-irradiation experiments . . . . . . . . . . . . . . . . . . . 2.5.3 Conclusions from laboratory measurements . . . . . . . . . . . . . . 2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 O(1 D)+CO2 only explains mid-latitude 16 O13 C18 O variations . . . . . 2.6.2 Effects of intra-stratospheric chemistry and mixing . . . . . . . . . . 2.6.3 Effects of mesospheric and heterogeneous chemistry . . . . . . . . . 2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 14 15 16 17 18 21 32 34 36 36 37 39 47 47 Appendices 2.A Mixing effects on isotopic composition . . . . . . . . . . . . . . . . . . . . . 2.B Practical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.B.1 IRMS long-term signal stability . . . . . . . . . . . . . . . . . . . . . 2.B.2 IRMS vs. optical methods . . . . . . . . . . . . . . . . . . . . . . . . 2.C Low-temperature cell for 13 C/12 C KIE experiments . . . . . . . . . . . . . . . 2.D MATLAB code for hard-sphere collision model . . . . . . . . . . . . . . . . . 49 50 52 52 53 58 67 vi L. Y. Yeung Oxygen isotope exchange reactions of CO2 Table of contents 2.D.1 montecarlo.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.D.2 scatter.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 69 3 A hyperthermal O-atom exchange reaction, O2 + CO2 3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Theoretical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Proposed mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 72 73 73 73 80 87 89 92 93 Appendices 3.A Non-reactive scattering of O2 and CO2 . . . . . . . . . . . . . . . . . . . . . 3.B MATLAB program for generating Newton diagrams . . . . . . . . . . . . . . 3.B.1 NewtonD.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.B.2 NewtonDcalc.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.B.3 NewtonDplot.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 96 101 101 103 104 4 Dynamics of O(3 P) + CO2 collisions at hyperthermal energies 4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Theoretical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Electronic structure calculations . . . . . . . . . . . . . . . . . . . . . 4.3.2 Reaction dynamics calculations . . . . . . . . . . . . . . . . . . . . . 4.4 Experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Theoretical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Non-reactive scattering of O(3 P) and CO2 . . . . . . . . . . . . . . . 4.5.3 Oxygen isotope exchange, O(3 P) + CO2 → O + CO2 . . . . . . . . . 4.5.4 Oxygen-atom abstraction, O(3 P) + CO2 → O2 + CO . . . . . . . . . 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 110 111 113 113 118 123 123 125 139 139 141 142 144 147 148 Appendices 149 4.A Differential scattering cross-sections from 1.0 – 6.5 eV . . . . . . . . . . . . 150 4.B Estimating uncertainty in the laboratory angular distributions . . . . . . . . 152 5 Summary and outlook 153 5.1 New signatures, new reactions . . . . . . . . . . . . . . . . . . . . . . . . . 153 5.2 Potential atmospheric importance of O(3 P) + CO2 . . . . . . . . . . . . . . . 154 Bibliography 157 vii L. Y. Yeung Oxygen isotope exchange reactions of CO2 Figures List of Figures 1.1 1.2 1.3 Schematic of atmospheric CO2 sources and sinks. . . . . . . . . . . . . . . . . Bulk oxygen isotope composition of stratospheric CO2 . . . . . . . . . . . . . . Potential energy surface for CO3 (3 A00 ) from Mebel et al. [2004]. . . . . . . . . 2.1 2.2 2.3 2.4 2.5 2.6 Meridional variation of ∆47 measured in stratospheric samples. . . . . . . . . 18 Correlation between ∆47 and stratospheric tracers. . . . . . . . . . . . . . . . 19 ∆17 O values vs. long-lived stratospheric tracer mixing ratios. . . . . . . . . . . 19 Schematic of O(1 D) + CO2 reaction-purification-analysis procedure. . . . . . 21 FT-IR spectrum of synthesized N2 18 O between 1100 cm−1 and 4000 cm−1 . . 24 Modeled O(1 D) + CO2 reaction collision energy distributions at different He bath gas pressure (T = 300 K). . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Changes in ∆47 vs. ∆δ 18 O after pulsed UV photolysis at 300 K and 229 K. . . . 30 Changes in ∆47 vs. ∆17 O of CO2 after continuous UV irradiation of O2 /O3 /CO2 mixtures with a Hg lamp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 How mixing two arbitrary reservoirs of CO2 can be nonlinear in ∆47 . . . . . . 51 Allan-variance plot of ∆47 over 40 IRMS acquisitions. . . . . . . . . . . . . . . 53 Schematic of conflat chamber used for low-temperature 13 C/12 C KIE experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Photograph of conflat chamber used for low-temperature 13 C/12 C KIE experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Cold cell assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Machining diagram for the OFHC copper tube. . . . . . . . . . . . . . . . . . 61 Machining diagram for the OFHC copper conduction block. . . . . . . . . . . 62 Machining diagram for the OFHC copper heat transfer block. . . . . . . . . . 63 Machining diagram for the brass heat transfer block. . . . . . . . . . . . . . . 63 Machining diagram for the OFHC copper connection to the liquid N2 feedthrough. 64 Cold cell assembly for O(1 D), OH + CH4 KIE experiments. . . . . . . . . . . . 65 Machining diagram illustrating the modifications made to the conduction block for O(1 D), OH + CH4 KIE experiments. . . . . . . . . . . . . . . . . . . . . . 65 Machining diagram for the OFHC copper heat transfer block designed for O(1 D), OH + CH4 KIE experiments. . . . . . . . . . . . . . . . . . . . . . . . 66 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 3.1 3.2 3.3 3.4 Crossed-molecular-beam apparatus with hyperthermal oxygen source. . . . . Canonical Newton diagram for hyperthermal 16 O2 + 12 C18 O2 collisions. . . . Velocity distribution of hyperthermal oxygen beam. . . . . . . . . . . . . . . . Laboratory TOF distribution of m/z = 46 (16 O12 C18 O+ ) at Θ = 6◦ , with the inelastic scattering signal removed. . . . . . . . . . . . . . . . . . . . . . . . . viii 3 5 6 74 75 77 80 L. Y. Yeung 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 Oxygen isotope exchange reactions of CO2 Figures TOF distributions for 16 O12 C18 O products at laboratory angles Θ = 6◦ and 8◦ with the inelastic scattering signal removed. . . . . . . . . . . . . . . . . . . . 82 TOF distributions for 16 O12 C18 O (m/z = 46) at various laboratory angles Θ with the inelastic scattering signal removed. . . . . . . . . . . . . . . . . . . . 83 Center-of-mass-frame (A) angular and (B) translational energy distributions from the 16 O2 + 12 C18 O2 oxygen isotope exchange reaction obtained from TOF fits of m/z = 46. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Velocity-flux contour diagram for 16 O12 C18 O products of 16 O2 + 12 C18 O2 collisions in the center-of-mass frame. . . . . . . . . . . . . . . . . . . . . . . . . 84 Energetically allowed neutral product channels from O2 + CO2 collisions. . . 86 Calculated energies and structures on the lowest triplet PES of O2 + CO2 . . . 87 Calculated stationary point geometries on the lowest triplet PES of CO4 . . . . 89 Calculated energies and structures on the lowest triplet PES of O2 + CO2 . . . 89 Singly-occupied molecular orbitals (SOMOs) in the CO4 (3 A00 ) and TS3 structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Molecular orbital diagrams for O2 and CO2 , adapted from DeKock and Gray [1980]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Electron-pushing diagram of an adiabatic CO4 (3 A00 ) isomerization through TS3. 92 Laboratory scattering data detected at m/z = 32. . . . . . . . . . . . . . . . . 98 Laboratory inelastic scattering data detected at m/z = 48. . . . . . . . . . . . 99 Velocity-flux contour diagram for inelastically scattered 12 C18 O2 from 16 O2 + 12 C18 O collisions in the center-of-mass frame. . . . . . . . . . . . . . . . . . . 100 2 Sample output of the NewtonD.m program. . . . . . . . . . . . . . . . . . . . 101 Stationary-point structures for O(3 P) + CO2 reactions below 100 kcal mol−1 calculated at the CCSD(T)/aug-cc-pVTZ level of theory on the 3 A00 surface. . . 114 Comparison of CO3 stationary point geometries relevant to the QCT calculations.116 Comparison of TS1 and TS3 geometries and energies at various levels of theory.116 Reactive scattering cross-sections for the O(3 P) + CO2 isotope exchange reaction obtained from the QCT calculations. . . . . . . . . . . . . . . . . . . . . 121 Opacity functions for the O(3 P) + CO2 isotope exchange reaction and for inelastic scattering of the two reagents obtained from QCT calculations at the B3LYP/6-311G(d) and BMK/6-311G(d) levels of theory. . . . . . . . . . . . . 122 Canonical Newton diagram for 16 O + 12 C18 O2 collisions at Ecoll = 98.8 kcal mol−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Laboratory inelastic scattering data detected at m/z = 16. . . . . . . . . . . . 126 Laboratory inelastic scattering data detected at m/z = 48. . . . . . . . . . . . 128 Velocity-flux contour diagram for inelastically scattered 12 C18 O2 from 16 O(3 P) + 12 C18 O2 collisions in the center-of-mass frame. . . . . . . . . . . . . . . . . 129 Comparison of laboratory and theoretical c.m. (A) angular and (B) translational energy distributions for inelastic scattering of O(3 P) and CO2 at hEcoll i ≈ 100 kcal mol−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Laboratory reactive scattering data detected at m/z = 46. . . . . . . . . . . . 132 Velocity-flux contour diagram for 16 O12 C18 O products of 16 O(3 P) + 12 C18 O2 collisions in the center-of-mass frame. . . . . . . . . . . . . . . . . . . . . . . 133 Comparison of laboratory and theoretical c.m. (A) angular and (B) translational energy distributions for the O(3 P) and CO2 isotope exchange reaction at hEcoll i ≈ 100 kcal mol−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 ix L. Y. Yeung 4.14 4.15 4.16 4.17 4.18 Oxygen isotope exchange reactions of CO2 Figures Laboratory reactive scattering data detected at m/z = 34. . . . . . . . . . . . 136 Snapshots of a quasiclassical trajectory for O(3 P) + CO2 isotope exchange through a short-lived CO3 ∗ complex at 1.5 eV (34.6 kcal mol−1 ) collision energy.142 Laboratory reactive scattering data detected at m/z = 46, fit assuming an ISC mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Snapshots of quasiclassical trajectories for the O(3 P) + CO2 → O2 + CO reaction.146 Center-of-mass angular and translational energy distributions for the O(3 P) + CO2 isotope exchange reaction derived from QCT calculations at the (A and B) B3LYP/6-311G(d) and (C and D) BMK/6-311G(d) levels of theory. . . . . . 151 x L. Y. Yeung Oxygen isotope exchange reactions of CO2 Tables List of Tables 2.1 2.2 2.3 2.4 2.5 2.6 Stratospheric air sample data . . . . . . . . . . . . . . . . . . . . . . . . . . . IR band assignments for the spectra in Figure 2.5 . . . . . . . . . . . . . . . . IRMS ion signals from the synthesized N2 18 O . . . . . . . . . . . . . . . . . . Results of pulsed photochemical experiments . . . . . . . . . . . . . . . . . . Results of continuous irradiation experiments . . . . . . . . . . . . . . . . . . Tropospheric-stratospheric-mesospheric mixing model results . . . . . . . . . 17 23 25 30 33 41 3.1 Energies of stationary points associated with the exchange reaction O2 + CO2 → O2 + CO2 on the lowest triplet potential energy surface . . . . . . . . . . . 88 4.1 4.2 4.3 Energies (kcal mol−1 ) for the stationary points on the lowest triplet CO3 potential energy surface for 16 O(3 P) + 12 C16 O2 → 16 O + 12 C16 O2 collisions . . . 115 Number of reactive QCTs observed at different collision energies. . . . . . . . 121 Comparison of experimental and theoretical yields for the products of O(3 P) + CO2 collisions near 100 kcal mol−1 . . . . . . . . . . . . . . . . . . . . . . 137 xi  L. Y. Yeung Oxygen isotope exchange reactions of CO2 Bibliography Bibliography Affek, H. P., and J. M. Eiler (2006), Abundance of mass-47 CO2 in urban air, car exhaust and human breath, Geochim. Cosmochim. Acta, 70(1), 1–12. Affek, H. P., X. Xu, and J. M. 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