Structure and Dynamics of Several Rare Gas-Halogen van der Waals Molecules

Citation

Evard, Dwight David (1988) Structure and Dynamics of Several Rare Gas-Halogen van der Waals Molecules. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/90wr-zj81. https://resolver.caltech.edu/CaltechTHESIS:01222013-092417239

Abstract

The structure and dynamics of several rare gas-halogen van der Waals molecules have been studied in the six laser-free jet expansion experiments which are described in this thesis. High resolution (0.01 cm⁻¹ spectra were obtained for one B ← X transition of both NeBr₂ and NeCl₂, in order to determine the structure and lifetime of these complexes in the ground and excited states. NeCl₂ was studied extensively at moderate resolution (0.05 cm⁻¹ to probe the potential energy surface and the correlation of the van der Waals bond with the covalent bond. The lifetime of metastable vibrationally excited NeBr₂ X(ν = 1) was determined directly by measuring its concentration as a function of distance from the source to the detection region. A pump-probe technique was used to study ArCl₂ to probe the structure and dynamics of the complex. ArₙCl₂ (n = 1, 2, 3) was studied to test the validity of the bond-bond additivity model of binding for the complex. This set of experiments has provided a great deal of information on the nature of the structure and dynamics of the complexes.

Item Type:

Thesis (Dissertation (Ph.D.))

Subject Keywords:

Chemistry

Degree Grantor:

California Institute of Technology

Division:

Chemistry and Chemical Engineering

Major Option:

Chemistry

Thesis Availability:

Public (worldwide access)

Research Advisor(s):

Janda, Kenneth C.

Thesis Committee:

Beauchamp, Jesse L. (chair)
Grubbs, Robert H.
Bercaw, John E.
Janda, Kenneth C.

Defense Date:

21 September 1987

Record Number:

CaltechTHESIS:01222013-092417239

Persistent URL:

https://resolver.caltech.edu/CaltechTHESIS:01222013-092417239

DOI:

10.7907/90wr-zj81

Related URLs:

URL	URL Type	Description
https://doi.org/10.1063/1.448610	DOI	Article adapted for Chapter II.
https://doi.org/10.1063/1.450200	DOI	Article adapted for Chapter III.
https://doi.org/10.1021/j100294a014	DOI	Article adapted for Chapter IV.
https://doi.org/10.1016/0009-2614(87)80223-3	DOI	Article adapted for Chapter V.

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7415

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CaltechTHESIS

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22 Jan 2013 17:39

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05 Nov 2021 20:04

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STRUCTURE AND DYNAMICS OF SEVERAL RARE GAS-HALOGEN VAN DER WAALS MOLECULES Thesis by Dwight David Evard In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1988 (Submitted 21 September 1987) ii To the Memory of My Father iii ACKNOWLEDGMENTS I would like to express my appreciation to my research advisor, Ken Janda, throughout my graduate and excitement about fly, or so it for his patience student years. His science have helped seems. Alberto and guidance ideas, insight to make Beswick the and time Nadine Halberstadt gave me some appreciation for theoretical work, and I will certainly remember their cooking. I have enjoyed working and sharing the past five years at Caltech and Pitt. with many peop,le The postdocs and fellow graduate students I have worked with have helped to make life enjoyable usually, them are Dave Brinza, and bearable always. Joe Cline, Sally Hair, Some of Brian Reid, N. Sivakumar, Fritz Thommen and the youngest, Craig Bieler. Thank you Fritz, of raclette. Beauchamp Joey, I group, Craig, for helping also 1 ike to for greatly the Sally, to introducing enjoyed Sparks group, type and Rob tape Coal son to the wonders associating and the Siva and Brian deserve read, thank the group this for the with the Pratt lads. special credit thesis. kind I use would of his laser printer to print the "final" copy of this thesis. Finally, I would like to love, understanding and support. thank my family for their And that's the way it is. iv ABSTRACT The structure and dynamics of several rare gas-halogen van der Waals molecules have been studied in the six laser-free jet expansion experiments which are described in this High thesis. obtained for in order complexes one resolution B~X to determine in the (0 . 01 the the structure and ground and excited der Waals ) spectra bond with lifetime of resolution the were and NeC1 2 states . the potential energy surface and van -1 transition of both NeBr studied extensively at moderate probe em 2 . these NeC1 2 1 (0.05 cm- ) was to the correlation of covalent bond. lifetime of metastable vibrationally excited NeBr The = 1) X(u 2 was determined directly by measuring its concentration as a function of region. A pump-probe technique was used to study ArC1 probe (n the distance the source structure and dynamics = 1, 2, 3) was additivity This of detection complex. to test the validity of binding for the has provided a great information on the nature of the complexes. the the model experiments to of studied bond-bond set from 2 of to the complex. deal of the structure and dynamics of v TABLE OF CONTENTS Page Dedication ii Acknowledgements iii Abstract iv List of Figures vii List of Tables ix Chapter I. Introduction 1 Chapter II. Rotational Resolution of the NeBr 2 B~X (10~) Transition 20 Chapter III. Rotational Resolution of the NeC1 2 B~X Transition (9~1) 30 Chapter IV. Molecular Beam-Laser Spectroscopy of the NeC1 2 van der Waals Molecule 51 Chapter V. Direct Measurement of the Vibrational Predissociation Lifetime of NeBr 2 in the Ground Electronic State 82 vi TABLE OF CONTENTS, continued Page CHAPTER VI. The Structure and Dynamics of the ArC1 2 van der Waals Molecule 103 CHAPTER VII. A Test of Atom-Atom Additive Interactions: Arnc1 2 . n = 1, 2, 3 147 APPENDIX I. SHAPE: A Working Manual 164 vii LIST OF FIGURES Chapter II. Figure 1. Chapter III. B~X The {10~) 2 LIF spectrum Rotational Resolution of NeC1 Figure 1. LIF spectrum of Cl Figure 2 . LIF spectrum of NeC1 Chapter IV. {10~) Rotational Resolution of NeBr Spectroscopy of NeC1 B~X 2 2 {9~1) 2 B~X {9~1) B~x {11~1) Cl 2 Figure 2. NeC1 2 near Cl 2 Figure 3. NeC1 2 near c~ 2 Figure 4. NeC1 Figure 5. Momentum gap plot for NeC1 Chapter V. near Cl 2 region 63 67 {10~) ()9 (13~) 70 2 Br Figure 2. Intensity ratio NeBr /Br vs r 2 2 Energy gap plot for NeBr 2 Figure 3. Chapter VI. 2 X(u=1) 4 and 11 mm Structure and Dynamics of ArC1 Figure 1. Experimental apparatus Figure 2. ArC1 Figure 3. Cl Figure 4. Odd Figure 5. Even Figure 6. ArC1 Figure 7. Au (6~) 2 Au 2 73 2 Figure 1 . 2 42 (7~) Lifetime Measurement for NeBr and NeBr (9~1) 37 2 Figure 1. 2 25 90 93 97 2 excitation spectra 110 114 = -1 fragment spectrum 119 excitation spectrum 121 excitation spectrum 122 (7~) (7~) rotational energy levels 124 = -1 rotational distributions 130 2 viii LIST OF FIGURES. continued Figure 8. Cl Figure 9. Av 2 Au = -2 fragment spectrum 133 135 Figure 10. = -2 rotational distributions Av = -2 energy levels Figure 11. Av = -2 energy levels in detail 141 Chapter VII. 139 Atom-Atom Additive Interactions Figure 1. Ar c1 fragment Cl spectrum 2 2 2 154 Figure 2. Ar c1 fragment Cl spectrum 2 2 3 157 Appendix. Figure 1. SHAPE: A Working Manual Axi.s system for an asymmetric top 168 ix LIST OF TABLES Chapter II. Table I. Chapter III . Rotational Resolution of NeBr Spectral Constants for NeBr Rotational Resolution of NeC1 Table I . 2 Spectral Constants for Cl Table II. Spectral Data for NeC1 Chapter IV . Table I. Chapter VI. Spectroscopy of NeC1 Data for NeC1 2 39 2 , Structure and Dynamics of ArC1 Table II. Bond Energies for ArC1 Appendix I. (9~1) 46 Transitions Structure of ArC1 Table I. 2 26 2 2 Table I. Chapter VII. (10~) 2 66 2 118 2 127 2 Atom-Atom Additive Interactions Arnc1 SHAPE: 2 Bond Energies 159 A Working Manual Table I. ·Rotational Constants for ArC1 Table II. Character Table for D2 . 172 Table III . Asymmetric Rotor Symmetries 172 2 169 1 CHAPTER I Introduction 2 Introduction The purpose of chemical physics is basic nature of physical phemonema at a to explain fundamental the level. Originally this was done by observing the behavior of bulk material nature and of basing largely recently, unobserved has microscopic molecular atoms allowed scientists the statistical molecules. interactions theoretical directly which More are study the responsible the bulk properties of There are still many difficulties associated with the study of a and to the macroscopic observations of matter. but upon the availability of experimental and techniques for explanations chemical variety experiment of and reactions model on the microscopic systems may theory provide meet . to level, examples explain where physical phenomena at a basic level . Van der Waals test mo-lecules provide theory against a convenient system to experiment, their structure and dynamics has Several groups are studying triatomic so become model the study of very popular. van der Waals molecules consisting of a rare gas atom bound to a diatomic h a 1 ogen mo 1 ecu 1 e, 1,2 experiment and adjustable parameters. easily formed for theory in can 3 4 5 • The van be the comparison between made with a few complexes are triatomic These molecular 1 2 probed spectroscopically • techniques. which beam only expansions and may be or by molecular beam resonance der Waals bond in the rare 3 gas-halogen complex is very weak; typically less than the energy of a quantum of vibration of the halogen stretch for He and occur Ne if compounds. energy molecule is from Vibrational the transferred vibrational predissociation vibrational to mode the van der predissociation process is of the will halogen Waals modes. thought to The proceed on a single adiabatic potential energy surface which makes the predissociation process example of intramolecular Studies of the for the rare may span vibrational accessible relaxation (IVR). gas-chlorine complexes indicate from to to progression dynamics theoretically a HeC1 the . range 2 from NeC1 simple 2 V--+T ArC1 that the 2 vibrational predissociation to IVR. Background The first studies of rare gas-halogen van molecules by Klemperer et al. and KrClF 5 bound to the Cl considering the rare electrons orbital (LUMO), the molecule. geometry fails to of techniques. They gas into rationalize atom the to be lowest a the Although this model unoccupied the geometries of Waals the acid which molecular the Cl end of rationalizes interhalogen van der predict These structure by Lewis which is mainly localized at the 4 linear geometry with the rare gas atom atom . donates Waals involved detection of ArClF by molecular beam resonance ClF complexes have a der the linear molecules, observed it rare 4 gas-homonuclear diatomic halogen complexes. 2 homonuclear halogen dimers are T-shaped; der Waals atom-atom additive model for apparent that more experimental development of appropriate the most important These indicating a the binding. van It is data is necessary for theories the to determine which interaction in the formation of is the van der Waals bond. Levy et al. rare were gas-homonuclear directly monitor the first to study van Waals der the structure of complexes and the vibrational predissociation dynamics. They carried out a detailed study, probing the Hei by laser induced fluorescence. of the both B+--X system of total laser induced fluorescence. be band heads -1 of I 6-9 made 2 for to possible the fluorescence spectral blue of Analysis free 4.5 A distance from Homogeneous the linewidths He were to complex detection and 2 the (3+--0) of the was shown to the found I 2 to appearing to (29+--0) rotational ~he of dispersed features contours yielded a T-shaped structure for a 2 The strong fluorescence The van der Waals molecule Hei responsible 3.4 - 4.0 em to band complex with center of mass . vary with the vibrational state excited, corresponding to predissociation lifetimes ranging from 220 picoseconds = 26. 7 v rates showed quadratic upper state vibrational v = 12 to 38 The vibrational predissociation picoseconds for a for plus linear quantum number. dependence on the A study of the 5 dispersed fluorescence state B { v' ) showed r 2 in the B(v' - that with Ne. 10 of Hei excited 2 to the f 1 uorescence was domina ted by 8 This led to a statement of the = -1 for this predissociative process. Brinza et al. 2 the 1) state. propensity rule Au Cl spectrum studied The the van der Waals complexes structure of the NeC1 2 van der of Waals molecule was determined to be T-shaped . in both the ground and broadening excited observed states . in X(v" = 1, 2) However, NeC1 = 1) sta te the over X( v" ten no homogeneous (0.2 em the -1 ) spectroscopy observation of of in metastable vibrationally excited states was very interesting. in was low resolution the complex. the There times lives 2 even for though the energy necessary der Waals bond. This was more than 10 the -5 seconds co mp 1 ex con t a i n s to dissociate the van the first observation of a long lived metastable vibrationally excited complex. Janda and cdworkers studied the van der Waals molecule laser using Spectra were recorded at transitions {30~) tee h n1ques. low resolution (0.2 em of -1 ) {11~) van der Waals molecule associated with the the . fluorescence induced for 2 the through The Br . 11 NeBr 2 bands showed increasing spectral shifts of the complex from the free 8.8 em Br -1 features with 2 The natural increased of 0.10 em -1 increasing from for NeBr 2 v ' • linewidths the of the laser bandwidth {16~) 5.5 from ranging van der to Waals limited value to 3.1 cm- 1 for the (27~) 6 band, corresponding lifetimes of estimated the 64 ± 4 em -1 to 84 and vibrational 1.7 picoseconds, dissociation from the respectively. They in the B state to closing of the one quantum = 27 . The data follow energy apparent predissociation predissociation channel near v' be the trends predicted by the gap models discussed below. Heaven molecule {0.05 em HeBr -1 ) coworkers in a structure for 12 observed system B~X 2 at several bands was bands mass distances are 3.7 respectively. picoseconds 1.8 ± 0.2 (38~) bands of He 1 23 cm- · for was the 79 HeBr for · the respectively . provided by observation of the v' = 40 vibrational level. again consistent with with analysis center 2 a > 100 Lifetimes ranged from in limit of the B state rapid predissociation The simple and {12~) An upper dissociation energy 2 rotational The He to Br picoseconds Br . 2 Waals A and 3 .. 8 A in the ground and excited states, to der resolution and resolved consistent with aT-shaped structure. of van Spectra were obtained {38~) through the moderate free jet expansion . {11~) the for and from lifetimes reported are energy gap excitation study model for of rare vibrational predissociation. The first laser induced complex was a gas-interhalogen van der. Waals reported by Skene and Lester . 13 A spectroscopic feature approximately 3.6 cm- 1 to the blue of the expected band origin of the ICl B(v' = 3)~X(v" = 0) transition was attributed to HeiCl. 7 This is from uncomplexed ICl level because subnanosecond of particularly the of ICl. interesting was This predissociation of because observed fluorescence this vibrational electronic indicates the for no HeiCl that van predissociation the der vibrational Waals bond competitive with the electronic predissociation of molecule. 150 Analysis yields a picoseconds for Drobits lifetime. optical-optical dynamics of the et double the ICl lower bound estimate of 550 ± vibrational al. 14 resonance predissociation report the use of techniques to study the the vibrational predissociation process in the NeiCl van der Waals complex. A pump laser excites the transition, then at up probe laser scans while the fluorescence lifetime for a time to through several NeiCl in from the is 15 nanoseconds E~A A~X later transitions of the E state is collected. A state (uA = 14) is a ICl The 3 ± 2 nanoseconds based on experimental and theoretical ratios of the complex signal A state 44 em (uA = 14) to free ICl as a function of binding was determined of the energy time. The to be -1 theoretical The treatment vibrational predissociation in rare gas-halogen van der Waals complexes is based on the assumpti.on that the stretch vibration of the halogen molecule and the van der Waals stretching mode are only calculated weakly th~ coupled . vibrational Beswick and predissociation J or t ner of 15,16 T-shaped 8 complexes the where interaction between the diatomic halogen molecule and the rare gas atom was represented by a sum of Morse atom-atom close-coupling scattering analytically, but predissociation resonances. rates have difference final a from model strong between dissociated describes Au dependence of the the inverse This on the by of the of the be bound resulting predissociation the complex rule and solved vibrational the ·on the vibrational the energy and the correctly superlinear quantum number. the absolute predissociation Ewing has proposed a momentum gap Beswick and Jortner the qualitative basis of v~T rate . the ability of to the Waals van der the couple intermode the to the f requ~ncy is proportional to mom en tum in 1 eads products coupling matrix element · both models, a ny clearly v~T rate is limited perturbation part u = 0 nodeless stretch and the momentum gap constraint the the wavefunction of rapid integrand and a rotational plane wave Since the plane wave product to of oscillating that represents dissociated products. the analysis In both models the Hamiltonian For not for vibrational predissociation which contains many features shows resulting energy gap model propensity 2. The gave dependence state. rates observed in Hei 17 that initially but did not correctly predict model widths predicts rate on could solutions the = -1 the equations numerical rates The potentials. momentum. higher dephas i ng of slower v~T excitation of the rate. the 9 dissociation products momentum gap and would thereby serve to increase lower the the energy dissociation or rate, but rotational excitation would also be limited by angular momentum constraints. determined by the The final dynamics will interplay between momentum gap, be angular momentum gap and IVR constraints . Current Work The experimental and provided the original presented in this resolution (0 . 001 theoretical work discussed above motivation thesis. em -1 ) for Chapter experiment (10+--0} transition of NeBr . much II of the describes performed on work a high the B+--X Detailed rotational structure 2 in the spectrum was observed which allowed us to determine the the vibrational The experimental structure of the complex precisely. lifetime predissociation resolution was limited to 0.017 cmbut the spectrum was fit natural well to a linewidth of 0.015 em fit to this and 1 by Doppler broadening, rigid T-shaped model -1 linewidth, . with a The entire spectrum was corresponds which to a vibrational predissociation lifetime of 355 picoseconds. The NeC1 2 B+--X high resolution, (9+--1} as described previously confirmed the metastable vibrationally and provided a transition was also more in Chapter reported This geometrical state of study of observation excited ground precise III. studied at NeC1 structure of 2 a . 10 the 10 Although molecule. the energy X state stretching vibration is an order of magnitude larger the Ne-Cl the on in the than dissociation energy, no dissociation is observed 2 microsecond time scale. Despite Doppler and homogeneous broadening, several rovibronic transitions were nearly unblended and a detailed made which allowed the accurately determined. rotational structure of the The structure of is 3 . 536 ± 0.036 3.565 ± 0 . 035 A in predissociation to in the excited lifetime 258 ± 42 be the A in was complex be the NeC1 Waals molecule is T-shaped and the Ne to Cl distance assignment van der 2 center of mass 2 ground state. to state The vibrational the B(v' = 9) state was on basis of picoseconds the and found homogeneous broadening. IV Chapter describes resolution {0.06 em the -1 experiment using moderate in which we studied eleven bands of ) system of NeCl B~X an 2 in a free jet expansion. We were able to determine the vibrational predissociation lifetime as a function of vibrational on intermode the momentum on rotational the coupling of NeCl 2 T-shaped rigid Hami 1 ton ian model excited states. Homogeneous the lifetimes B(v' = 9) to ranged 33 ± 2 from to set upper the and As lifetime. structure level and effect of limits angular was seen previously. was well simulated for both broadening 258 ± 42 picoseconds for the was the by a ground and observed and picoseconds for = 13). The B(v' 11 B(v' = 7, 8) levels have longer lifetimes since the spectra were not broadened Another goal of at the reso 1 uti on the experiment was of the experiment. to evaluate the extent of coupling between the van der Waals mode and the halogen covalent stretching mode. as a This coupling could be measured change in the van der Waals bond length as a of· halogen data vibrational showed momentum that effects quantum the on the lifetime trends for NeC1 number. Analysis result has fact that efficient 2 coupling and dynamics are small. quite 2 . 18 directly rotational than HeC1 2 measure lifetime of NeBr 2 . to excitation . This 2 be due to the is much 2 in the was more 19,20 vibrational performed predissociation the ground electronic state with one vibrational quantum in the halogen stretch. technique The For a given Chapter V describes an experiment which we to angular dissociates much faster then HeC1 product NeC1 the could be fit to the gap laws, but 2 subsequently been determined fo~ of intermode showed a very different behavior than HeC1 energy gap, NeC1 function employed to monitor the The pump-probe decrease in the population of the vibrationally excited level as a function of distance from a supersonic metastable state is prepared. fluorescence signal due to to to (X, v that from the due nozzle. Br 2 This nozzle source ratio the We measured the ratio of the excitation of = 1) where as a cancels NeBr function the 2 (X, v of = 1) distance effects of the 12 geometrical rate of expansion vibrational measured. for NeBr of Analysis (X, 2 molecular jet, predissociation of the data that of = 1) u the is 8 showed ± 3 microseconds. so the that the can be lifetime This 1 if e time is in fairly good agreement with a prediction based on the energy gap extrapolation vibrational levels of of lifetimes of the B electronic state . several Apparently, both the vibrational predissociation mechanisms and the van der Waals potential energy surfaces are similar for the two electronic states. VI Chapter describes designed to study van Waals der structure and rotational vibrational of initial quite channels. laser pump-probe molecule. the bond We were energy of able the excited states. complex, The interesting number which is quantum the ArC1 2 numbers the Cl atoms. Cl for a numbe~ distributions Au = -2 to aspect of the that parity is a throughout the initially rare good the 2 j prepared symmetric with respect Cl the molecule product due the figure axis, Conversely, Also, 2 the is produced with even 2 when complex is two-fold rotation about of determine those conserved vibrational predissociation. state of 2 rotational particularly the ArC1 complex. the Cl gas-homonuclear halogen complexes is rotational to predissociation were measured An quantum experiment the structure and dynamics of state distributions of of were a to a i.e .. an exchange is produced with odd j 13 when the initially excited state of ArC1 is antisymmetric 2 with respect to an exchange of the Cl atoms. This symmetry selection makes excitation states. it to spectra by detecting record only transitions. B+-X (6+--0} E+-B (0+-5) =9 j structure of or j molecule 2 The structure of similar to HeC1 vibrational 2 individual of the ArC1 obtain odd 2 2 and even The spectra were top fitting routine. The is T-shaped with an Ar A in to the ground state 2 van der Waals molecule . but the dynamics are very different. 2 mechanism in at all 2 ArC1 is 2 is The v~T.R ± 0.3 in blue the X(u shift distributions for Cl process are which levels in the B state. is open studied, for closes The bond energy, van der Waals molecule is determined to 2 -1 em in the B(u = 7) state and 187.9 ± 178.4 -1 vibrational = 8 and u = 9 the Ar-Cl -1 Au= -1 channel, The product. for .3 em product significant amount of energy going into rotation of between u 0 . 4 em the ArC1 predissociation and NeC1 2 odd A in the excited state. and 3.70 HeC1 simplified laser detecting Cl spectra. rigid asymmetric the ArC1 to center of mass distance of 3.72 the Cl or taken the probe = 10 excitation modeled with a with a even Spectra were transition with parity-selected 2 greatly This provides easier identification of rovi bronic Cl possible not 2 at = 0} from state, free because Cl 2 of The . the 9.5 ± rotational formed in the Au = -2 predissociation all statistical in nature. The 14 distributions may show some signs of resonance effects with = -1 bound level. the intermediate Au (B, = 11) u van der The Waals lifetime of molecule are not applicable here where the The gap laws = -1 Au 83 ± 10 is picoseconds based on homogeneous broadening. the channel is described in closed. (n = us to examine bonding which is dominant in larger complexes. The Chapter the study VII, of the highest the observed Cl level cutoff due kinematic is 1, atom-atom In unobserved is 2 the bond energy of Waals molecules. the Arnc1 enabled validity determining of Arnc1 case 2 nature between level and the lowest we believe bond of that the energy and not energies given by state through either of shows which gives 2Ar + Cl X(u = 0) that the state, experimental the approximation dynamics 2 as bond the products while the energy. the can sum of proceed -1 . for is 458 ± 3 pair-pair predicts a value of 460.6 ± 0.4 em Ar c1 2 2 were two paths: The the is which interactions . 2 distribution van der 2 off that the Ar-Ar and Ar-Cl by cut so potential tested the to intermolecular the interaction obtained experimentally were compared the of We three Arnc1 conservation The constraints . the these sharp, to 3), additive fragment 2 quite strictly 2, Ar c1 2 2 em additive -1 in model The bond energy for is predicted by the simple bond-bond additivity, so 15 this model appears to accurately describe the bonding in this system. Suggested Future Work The rare provided gas-halogen model a theoretical van system der for study of energy Waals the transfer molecules have experimental and from a to a weak van der Waals bond. However, have spectroscopy been studied shown to have a excited states. by optical T-shaped structure 2 It would complex which is linear, covalent van der and be the complexes which have all been in both the ground and interesting because Waals covalent bond to study the coupling between modes should be much a the more efficient. ArClF and KrClF both have linear structures in the state, the ground but the excited electronic state. der Waals molecule the T-shaped structure 4 5 · is should be quite different complexes . blue-shifted respectively , from shift to is due known The dynamics of a B-x The approximately the from that of of and in the well the ground and the excited states and the potentials will be This experiment may require a similar for great it the deal 2 cm- 1 12 corresponding halogen bands. the difference the Ne and Ar with Cl 6 3, in linear van transition T-shaped van der Waals complexes of He, are not 1 The depths between is not linear of known if complexes . searching to 16 find the transitions, but the results should be well worth the effort. The triatomic rare gas-halogen complexes have only one covalent vibrational bend modes. The mode and van substition of a der Waals stretch and second covalently bonded species as the van der Waals partner would add a great deal complexity of to the experimental The van der considerations. COC1 could be 2 studied discussed previously, However the in Waals and complexes experiments NOC1 analogous B~X exciting the theoretical to process. predissociation as a A function study of of this stretching the process. probe the final in 2 . the vibrational frequency the partner would help to elucidate the important of those transition of c1 second covalent bond could participate predissociation and 2 of features The pump-probe technique could be used to vibrational and rotational state of each partner of the complex. A great deal of information has been obtained studying the rare gas-halogen van der Waals molecules. potential energy surfaces have been studied through and the bond energy. detailed information process. It is of several de termination Pump-probe on the interesting of of the experiments dynamics that these of the by The molecules s true ture have given dissociation the complexes which have been studied using LIF and pump-probe techniques have been T-shaped even though the first complexes studied, ArClF and 17 KrClF, were studied linear. using Certainly pump-probe dynamics. different The these molecules should be techniques to examine the difference in lifetimes and dynamics seen already in the rare gas-halogen van der Waals mo 1 e c u 1 e s is varying over simply the to the halogen. several in t r i gu i ng . five orders difference In colleagues and of in it is different despite their with 2 studies that , NeC1 superficially 2 lifetimes apparently vibrational clear predissociation dynamics of HeC1 have 2 magnitude, the conjunction NeC1 due frequency of performed by the vibrational and ArC1 similar 2 are very structures. A great deal of progress has been made in recent years, but it is clear that there is more exciting research to be done by the next generation of graduate students. 18 References 1. D.H. Levy, Adv. Chern. Phys. 47, 323 {1981). 2. K.C. Janda, Adv. Chern . Phys. 60 , 201 {1985). 3. J.A: Beswick, and J. Jortner, Adv. Chern . Phys 47 , 363 {1981) . 4. S.J. Harris, S.E. Novick, W. Klemperer, and W. E. Falconer, J . Chern. Phys. 61, 193 {1974). 5. S.E. Novick, S.J . Harris, K.C . Janda, and W. Klemperer, Can. J. Phys. 53, 2007 {1975). 6. R.E. Smalley , D. H. Levy, and L.J. Wharton, J. Chern . J . Chern . and D. H. Levy , Levy, Chern. Phys . 64, 3266 {1976). 7. K. E. Johnson, L . . Wharton, and D. H. Levy, Phys . 69, 2719 {1978). 8. W. Sharfin, K.E. Johnson, L. Wharton, J. Chern. Phys . 71, 1292 {1979). 9. K.E. Johnson, W. Sharfin, and D.H. J. Phys . 74, 163 {1981) . 10. D.E . Brinza. C.M. Western, B . A. Swartz, and K.C. Janda, D. D. J. Evard, F. Phys . Chern. Thommen, 88, 2004 {1984) . 11. B.A. Swartz, D.E. Brinza, C.M . Western , and K . C . Janda , J . Phys. Chern . 88, 984 {1984) . 12. L.J. van de Burgt, J .P. Nicolai, Chern. Phys. 81, 5514 (1984). and M.C. Heaven , J. 19 13. J.M. Skene, and M.I . Lester. Chern. Phys . Lett. 116, 93 ( 1985). 14 . J.C. Drobits, J.M. Skene, and M.I. Lester, J. Chern. Chern . Phys. Phys. 84, 2896 (1986). 15. J.A. Beswick, and J.J. Jortner, J. 69, 512 (1978). 16. N. Halberstadt, and J.A. Beswick, Faraday Discuss. Chern. Soc. 73, 357 (1982). 17. G.E. Ewing, Faraday Discuss. Chern . Soc. 73, 325 ( 1982). 18 . J.I. Cline, D.D. Evard, F. Thommen, and K.C. Janda, J. Chern. Phys. 84 , 1165 (1986). 19. J.I. Cline, N. Sivakumar, D . D. Evard, and K.C. Janda, J. Chern . Phys . 86, 1636 (1987). 20 . J.I. Cline, N. Sivakumar, D.D. Evard, Phys. Rev. A 36, 1944 (1987). and K.C. Janda, 20 CHAPTER II Rotational Resolution of the NeBr B~X (10~) Transition 2 21 Rotational Resolution of the NeBr 2 B~X {10~) Transitiona) Fritz Thommen, Dwight D. Evard and Kenneth C. Jandab) Arthur Amos Noyes Laboratory of Chemical Physics California Institute of Technology Pasadena, California 91125c) a) This manuscript was published in modified form in J. Chern. Phys. 82, 5295 (1985). b) A.P. Sloan Research Fellow. Camille and Henry Dreyfus Teacher-Scholar . c) Contribution No . 7115. 22 Abstract The B~X molecule was {10~} studied Detailed rotational which allowed us transition of the NeBr at high 2 resolution van der Waals (0.01 em -1 ) . structure in the spectrum was observed to determine the geometrical structure of the comp 1 ex. 3.67 ± 0 . 01 A in the ground state and 3.65 ± 0.01 A in the B state. corresponds The Ne to Homogeneous to 355 picoseconds. a Br 2 center broadening vibrational of was mass distance observed predissociation is which lifetime .of 23 Since the first observation of fluorescence spectrum by Wharton, gas-halogen vibrational valuable· model system energy redistribution. is a for process sections can be however, potential energy Smalley, 2 for laser excited and Levy, predissociation has understanding 1 rare become a intramolecular The dissociation of these molecules which obtained Recently, the Hei detailed state-to-state from both experiment and it surfaces has become for these apparent cross theory. that the systems are not known well enough for accurate calculations of the dynamics . 2 Smalley, Wharton, and Levy reported well resolved P, R branches characteristic of an near a~type prolate top for 3 They noted that the spectrum suggests a T-shaped molecule. Further resolution the (10~). transition of Hei B~X . 2 of the spectrum is precluded by the large I atomic mass and the homogeneous _ linewidth of the transition. Unlike Hei 2 , highly asymmetric details of about the this a T.-shaped NeBr molecule 2 oblate top spectrum. Resolving spectrum can both remove any molecule and structure of the lead rotational homogeneous quantum structure linewidth numbers. characteristic of a As as a allows us function discussed below a to a the ambiguity to refined In addition, information on the potential energy surface. detailed produces determine the the rotational single linewidth, of 355 picosecond lifetime, fits both the 24 low J and high J data. The observed spectrum, recorded on a Coherent CR 599-21 illustrated spectrometer dye in described laser, Figure elsewhere. obtained Francisco Laser Center , was used as from was 1, 4 A the San the excitation source. The Rhodamine 6G dye was pumped with an Ar+ laser to obtain a bandwidth -1 The 1 was recorded of em of 0.001 segment the NeBr 2 in 9 cm- was 1 tunable divided over into minute sequences. 1 em -1 segments . 1024 data points and Overlapping segments spectrum were recorded simultaneously with an r 2 spectrum for frequency calibration. · Twenty such scans were combined to produce the spectrum as shown in Figure 1. The model used to simulate the NeBr of a T-shaped rigid and excited to be Thus, the on.ly mass rotor Hamiltonian for electronic taken unchanged free separation states. from those of uncomplexed the Ne-Br for transition. and a The are the 2 bond the ground Br in each state, temperature, both The parameters rotational the spectrum consists 2 lengths 2 center bandhead position, single homogeneous values obtained are of the linewidth for these parameters are given in Table I. The two Ne-Br different bond 2 electronic increases by about the Ne-Br 2 separation length bond 30% in decreases increases from is remarkably states. The Br similar 2 in bond the length the electronic excit a tion while 0. 5 %. The Ne-Br 3.80 A to 4.10 A, or by atomic 8% , upon 25 Ne Br2 8- X ( 0-Q) DATA STICK 17,313 Figure 1. fluorescence The 17,314 NeBr spectrum. 2 The stick ( 1 0+-{)) laser excited spectrum is same as the the fitted spectrum except that the homogeneous and Doppler widths have been removed from the calculation. 26 Table I. R , Br 0 R 10 X state (Reference 5) 2 . Br Spectral constants for NeBr 2 B state (Reference 5) 2 B~X. {10~) 2.284 A 2 . 821 A X state 3.67 ± 0.01 A R , Ne-Br B state 0 2 3 . 65 ± 0.01 A r {homogeneous linewidth} 0.015 ± 0 . 005 em -1 T (rotational temperature) 3.345 K R . Ne-Br 0 2 Bandhead shift from free Br 2 6.045 em -1 27 transition. The atom separation in both states is somewhat larger the 3.58 in than A NeKr equilibrium distance . 6 scattering experiments. The similarity of measured the ground and excited state bond lengths accounts for the weakness of vibronic bands motion. We involving searched for the van der such bands Waals stretching to the blue to assert of the that the reported transition without success. The observed homogeneous spectrum linewidth of dependent on the J The allows this transition is at most weakly and K quantum numbers of entire spectrum is homogeneous linewidth, 0.015 em was negligible 0.017 em -1 Although as the homogeneous the very dependent measured shape of on well on study linewidth this -1 . {The the linewidth in corresponds to Doppler bandwidth width was transitions.) and Doppler width the convoluted spectrum is are still By reducing the spectra it will be possible more a single a laser the homogeneous width . effect by adjacent Doppler contribution to future to the molecule. simulated comparison, in , comparable, us detail. lifetime of The homogeneous 355 picoseconds . This agrees well with an extrapolation of data from higher vibrational . reso 1 ut1on . if extracted obtained from spectra such as reported of much lower 7 Spectra useful levels accurate from them. those potential energy Not is only it here will be can sur~aces necessary to most be obtain 28 the shape of for the the potential, interaction of pre sen ted here show perhaps riot easily. molecules results the observed rigid rotor but also detailed cross the two bond lengths. that this can First, the T-shaped structure of these goal The terms be results reached, in a highly congested spectrum . spectrum is mode 1. This vibrations probably span a surprisingly Second , well fitted that zero indicates limited range of but by a point the potential. Third, the weak dependence of the van der Waals bond length on halogen the bond length results in very weak vibronic overtone transitions . This work was Department of Energy . Francisco Foundation. Petroleum Laser supported United States The laser was obtained from the San Center funded Acknowledgement Research Chemical Society, by Fund, the by the National is made to the donors of administered by the for partial support of this work. Science the American 29 References 1. R.E. Smalley, D. H. Levy , and L. Wharton , J. Chern. Phys. 64, 3266 {1976). 2. D. W. Schwenke and D. G. Truhlar, Chern. Phys. Lett . 98, 217 {1983). 3. R . E. Smalley , L. Wharton, and D.H. Levy, J. Chern . Phys. 68, 671 {1978). 4. D.E. Brinza, C . M. Western, B.A . Swartz, and K. C . Janda, D.D. J. Evard, Phys. F. Chern. Thommen , 88, 2004 {1984). 5. R . F . Barrow, T.C. Clark, J.A. Coxon, and K. K. Yee, J. Mol . Spectrosc. 51, 428 {1974) . 6. C.Y. Ng, Y. T . Lee, and J.A. Barker , J. Chern. Phys . 61, 1996 {1974) . 7. B.A. Swartz, D. E. Brinza, C . M. Western, and K.C . Janda, J. Phys . Chern . 88, 6272 {1984). 30 CHAPTER III Rotational Resolution of the NeC1 B~X {9~1) Transition 2 31 Rotational Resolution of the NeCl 2 B~x {9~1) Transitiona) Dwight D. Evard, Fritz Thommenb) and Kenneth C. Jandac) Department of Chemistry California Institute of Technology Pasadena CA. 91125 a) This manuscript was published in modified form in J. Chern . Phys . 84, 3630 {1986). b) Present address: c) A.P. CIBA-Geigy, Basel , Switzerland. Sloan Research Fellow. Teacher-Scholar. Camille and Henry Dreyfus 32 Abstract High resolution (0 . 01 em spectra of the (9~1) system of Cl and NeC1 have been 2 2 spectrum of NeC1 the free Cl ) laser induced fluorescence rovibronic band of the associated obtained in a van free der jet band origin of the previously vibrationally uncomplexed Cl reported excited 2 . Although the energy in the Cl order magnitude larger The transition of -1 to the blue of study of electronic 2 molecule expansion. This observation ground Waals (9~1) associated with the 2 2 molecule was observed 5.46 em the of -1 confirms a metastable state of . NeC1 2 . stretching vibration is an than the Ne-Cl 2 dissociation energy , no dissociation is observed on the microsecond time scale. Rotational resolution was achieved and a detailed rotational assignment was made which allowed the Ne to Cl center of mass distance to be determined. 2 This distance is 3.565 ± 0.035 A in the ground state, and 3.536 ± 0.036 A in the excited state. Waals molecule moment lying asymmetric lifetime in is The T-shaped, along top the structure the Cl spectrum. B(v' = 9) 2 of the NeC1 with the dipole bond axis , van 2 der transition giving a b-type The vibrational predissociation state to was found be picoseconds on the basis of homogeneous broadening. 258 ± 42 33 Introduction We recently fluorescence reported spectrum of a NeC1 contains ·one quantum of Cl state is metastable, with molecule contains over to dissociate existence of the strongly supports in which which The the vibrational van der Waals state predict van der present paper, we report of NeC1 B+-X NeC1 theories of long the high lived energy bond. of Waals (9+-1) even though the times current triatomic excited stretching excitation. 1 · 2 metastable the the > 10- 5 seconds, T laser state 2 the excited the 2 resolution initial ten necessary predissociation low The = 1} X(u' 2 vibrational vibrationally molecules. 3 ' 4 In the resolution spectroscopy transition, gives more detailed information of the structure and dynamics of this van der Waals molecule. The rotational structure serves to remove the assignment the any 2 doubt as vibrationally to excited metastable which of the state. spectrum to Analysis of the spectrum also determines the average distance of the Ne atom from the Cl 2 center of mass to 1% precision. Experimental The free jet expansion apparatus employed in measurements is similar to the system described . 1 y. 2 preV10US The spectra were obtained 90%/10% Ne/He gas mixture at a total by pressure these passing of a 200 psi 34 over liquid Cl with a 2 vapor pressure of torr 60 (-70 C) through a 35 micron nozzle. The Ne/He gas mixture and Cl gas were used as supplied by A Coherent Innova purification . Matheson 18 with no argon ion 2 further laser supplied 6 W of continuous power at 488 nanometers to pump a Coherent 599-21 continuous wave (cw) high resolution dye The dye laser, on loan from the San Francisco Laser laser. Center, was actively stabilized to provide radiation with a bandwidth of 0.001 segments. The em -1 laser continuously was operated which gave 100 mW of power of interest. baffles into The dye the vacuum laser was tuned to excite the (9~1) c1 and . 2 The directed to -1 1 em 6 dye, region through 1 igh t intersect The laser associated van der fluorescence was collected the total Coumarin the spectral apparatus right angle. of with throughout molecular beam at a band tunable over the radiation was Waals molecule at right angles to the laser and molecular beams by a 75 mm diameter aspheric lens variable defining the point of The beams. (f/0.7), which projects the approximately 35 slits intersection defining slits for the and a fluorescence centimeters laser Schott and OG-530 to from molecular cut off filter served to reduce the scattered laser light. The by an laser IBM interface PC and data acquisition microcomputer card. The system are controlled through a microcomputer Tecmar Labmaster operates in an 35 interrupt-driven Laboratory mode using Microsystems, the in to de teet photons counted seconds, was stored frequency was incremented . separated into during -1 from RCA 7265 cooled photon counting mode f 1 uorescence. The a preset the microcomputer time, The total so that segment of 2 Figure overlapping 1 em system a number of typically and em 1 was -1 the 0 .5 laser segment single scan was took Approximately 80 scans were averaged obtain each 1 em in A the points, 1024 about 9 minutes. shown to tal in PC-Forth Inc. photomultiplier operating used the -1 was regions, the spectrum . obtained by to The spectrum scanning three piecing the individual spectra together and averaging the intersecting portions. Absolute wavelength calibration was achieved by simultaneously recording the absorpt i o n spectrum of iodine. A small fraction of the laser beam was diverted with a beam splitter and temperature . passed The through beam was an iodine detected by a cell at ambient photodiode, and the signal was stored concurrently with the molecular beam fluorescence spectrum of spectrum, 6 The experimental absorption in the computer. was iodine which gave matched absolute the with the published wavelength of A miniature train wavemeter individual iodine transitions. 7 similar in design to one described by Hui-Rang et al. used scan . to monitor This the method laser required the frequency a large while setting fraction of was up a the cw 36 laser light, so it was not used while data was being collected. Results and Discussion The laser induced fluorescence vibronic (9-1) of Cl spectrum transition , continuous expansion Figure 1 . The transition moment for the 2 Ne, and of of He the in is shown a in B-x system of the halogens lies along the axis of the bond and the transition is allowed due to spin-orbit the B-X transition 1 than in Cl in the heavier in 2 coupling was modeled to a least squares is band origin for 5 the fit. 8 . The strength of orders of magnitude of greater the molecule . The larger spin-orbit chlorine spectrum rigid rotor Hamiltonian using a nonlinear fitting B states, several because 2 0.2417 and 0.1342 cmX and coupling. 9 routine. 1 The the values of for the-rotational constants for the respectively, for literature 35 c1 2 and 18963.43 em were used as The rotational -1 initial temperature, for the estimates laser bandwidth, band origin, and both rotational constants were allowed to vary during the isotopic three 20 em -1 , paper because forms allowing d ea 1 s of on 1 y the The band origins of fitting process . of Cl excitation wi t h 35c 12 . extensive are 2 of the signal obtain a high quality spectrum. separated any one most the by nearly species. This abundant averaging isotope, necessary to 37 Cl2 8-X (9-1) FIT DATA 18962 Figure 1. (9~1) 18963 cm-1 18964 Laser excited fluorescence spectrum of vibronic band for Cl 2 . the B~X The upper line is the fit to the experimental data, which is shown in the lower trace. 38 The rotational high resolution Cl constants determined by fitting the spectrum in Figure 1 are obtained from 2 a different rotational regime than the literature values of Coxon. 9 · Rather differences, of the than employing Coxon performed observed line method of direct least squares frequencies necessary to include a H J 3 (J+1.) 3 , the for C1 2 . combination He fitting found second centrifugal distortion term, to fit the higher vibrational levels of state. Thus, the molecular extracted the J u high strongly region where influenced constants the are rotational centrifugal by energy it the B from levels are distortion . The molecular beam experiment discussed in this paper produces c1 of with 2 the population also it lar.ge fraction region ne·ar the low 1 shows the spectrum is clear that some higher The the J so a the populated. within is temperatures, in Figure origin. though low rotational of Cl 2 with rotational band < 4, J states are rigid rotor approximation is valid of this experiment, so the accuracy determination of the rotational constants is a much simpler process. The values for in this work Table I. It are is compared seen experimental values are although they are the rotational constants obtained that to the literature the literature values values and in our the same within experimental error obtained by different from different portions of the spectrum. means using data 39 Table I. Spectral Constants for Cl Literature 2 , B~X (9~1). Experimental a) B. Cl 2 X State 0.2417 em - 1 b) 0.2419 em B. Cl 2 B State 0. 1342 em -1 b) 0. 1344 em -1 c) 18 963.47 em 18 963.44 em Band Origin a) From this work . b) From reference 9 . c) From reference 5. -1 -1 -1 40 not The rotational be fit temperature of accurately using the Cl this spectrum could 2 generalized routine. The mass 35 isotope of chlorine is a nuclear spin alternation I of = 3/2, which degeneracies rotational levels of effect was clearly resolution lasers, should for visible 2 in however, spectra it is to odd 35 Cl the homonuclear fermion with lead the 5:3 a and even molecule . 2 taken not fitting This using readily j lower apparent A reasonable fit to the experimental data could be here. obtained by and the was never starting with any final temperature reached significantly temperature. There are several The data faT taken one a experimental week conditions, expansion conditions, average any over by to 7 3 fitting from possible the K, routine initial explanations for the spectrum in Figure 1 were period, during in particular varied. such from the different this behavior. over temperature which time the the · laser power and The reported spectrum is an variations in experimental conditions. The premise that the rotational temperature of a beam molecular expansion may be modeled by a Boltzmann distribution has been contested by a number of experiments where non-Boltzmann distributions of rotational states have been observed. more heavily 10,11 populated Boltzmann population problem we that Typically, are than the would distribution. sampling higher be predicted Finally, different states j we by have portions of are a the the 41 expansion. spectrum number With only consists of of different agreement in Table demonstrates that distribution is limited contributions expansion I spatial not from molecules conditions. between our precise filtering critical to of in However , data and Coxon's knowledge the the a the values population the determination of of a feature observed band origin of the is shown in spectroscopic constants of interest. The 5.46 em high -1 resolution spectrum the of to blue the transition This Figure 2. feature of is observed only in expansions of gas mixtures containing Ne, as well as He and Cl 2 . and has · 1y prev1ous to . 1. 2 individual b een attr ib ute d NeC1 2 The transitions are not well enough resolved to avoid having to simulation spectral use transition In frequencies. extract to fitting the individual the NeC1 spectrum we 2 assume that the van der Waals bond has little effect on the c1 2 ground state potential energy surface so the transition moment remains along the Cl-Cl bond axis. fit using a Hamiltonian model for consisting both bond lengths for taken to identical be the of The spectrum was a T-shaped rigid rotor the ground and excited states. The Cl-Cl distance in complex were to in those the the free Cl 2 molecule. The Ne was assumed to lie on the line perpendicular Cl-Cl bond p a ssing species. through the In our previous work, center the of mass of spectrum of to the the Cl 2 the free 42 Figure 2. associated Laser with the stick spectrum is linewidth has excited th~ been B+--X fluorescence (9+--1) same as spectrum transition of of Cl removed frequency of each individual transition. to 2 . The but the show the the fitted spectrum, artificially NeC1 2 The peaks labeled A and B were used to determine the ground state rotational constants. See the text for details. 43 NeCI2 8-X (9-1) _5 5 t t _Q rJ" 8 N A FIT DATA STICK 18968.5 189690 em- I 18969.5 44 C1 2 was used fitting the to associated independently, single rotational der Waals the temperature molecule. temperature since the Cl rotational the van situation, present a determine In must the be fit could not be adequately fit 2 temperature. The major in to contributions to the linewidth of the transition are from the homogeneous linewidth and was the Doppler broadening. negligible 0 . 0125 em -1 in comparison taken from with the The the laser bandwidth Doppler spectrum. width The width was generated using a Gaussian line shape, natural linewidth shape. The was convoluted spectrum was fit the rotational temperature, origin, the and the Ne ground and to Cl 2 excited by using a varying Doppler while Lorentzian five of the line parameters, the natural linewidth , the band center of mass distance in both states and defined as RX RB' respectively. The rotational were used constants obtained from to generate a this procedure stick spectrum similar to that in Figure 2 to show which transitions contributed to each peak in the For spectrum. structure of the NeC1 2 the symmetric T-shaped van der Waals molecule molecular the moments of inertia are IA = 1-Lm r 2 IB = 1-LMR 2 where 1-Lm is the Cl 2 reduced mass, 1-LM is the Ne-Cl 2 rc = IA + IB r is the Cl reduced mass and R is center of mass distance . The rotationa l 2 bond length, the Ne atom to Cl 2 energy levels are 45 labeled as JK . K -1. , where K_ 1 is the K quantum number in 1 the prolate top limit and K < 4, For J oblate top limit. is the quantum number in the 1 these energy levels for the X and B states can be written in closed form in terms of the rotational constants A. B. and C for each transition moment lies along the Cl-Cl bond, axis, and follows b-type of individual Assignment that the two primarily to the 1 ines, rotational and could determine entire marked unblended excited B asymmetric be the ground spectrum was then rotational transitions shows in Figure remaining parameters van der bond which the to length. have are a due common between A this used to rotational squares determine The 2, splitting accurately, least four Waals rules. Since state the b inertial selection transitions measured The top A and B state. state . was constants. The fitted varying the the final excited values state for the parameters are given in Table II . The Ne to Cl the ground and only 8% while electronic 2 center excited the Cl 2 of mass distance is similar in electronic states, decreasing by bond The excitation. length increases Ne-Cl atomic 3.70 A in the ground state and increases the excited state. larger than the r m scattering data. 12 These atomic value of 3.43 The r m to by 34% upon separation just 3.78 separations are is A in both A for Ne-Ar obtained from value corresponds to the minimum 46 Table II. Spectral Constants for NeC1 2 B~X {9~1). R • Ne-Cl X State 2 0 3.565 ± 0.035 A B State 3.536 ± 0.036 A R • Ne-Cl 2 0 r {homogeneous linewidth) T (rotational 0.02186 ± 0 . 0022 em temperature) Bandhead shift from free C1 0.949 K 2 5.460 em -1 -1 47 of the potential well, while the Ne-Cl atomic separations reported here are vibrationally averaged distances. The vibrational estimate-d from homogeneously the predissociation natural broadened. lifetime linewidth The if the vibrational may be spectrum is predissociation lifetime is T where r is the linewidth . 1 from errors transitions in by lifetime. A more obtained and natural linewidth 0 . 0196 ± 0.0020 2 natural linewidth of 0.0219 ± lifetime frequencies the gives of 243 the which the B state. two lifetime ± 24 individual natural linewidth further a estimate for low the area points by gives the of the lifetime of the spectrum labeled A and B. The this is fitting a lifetime region of 272 ± 28 We conservatively report lifetimes of of determination fitting obtained cm- 1 these predissociation NeC1 the the entire spectrum we obtain line accurate including, picoseconds for of which by between, average the broadening correct, be to predissociation is may fit natural maximum of The fitting routine appears to compensate for picoseconds. than the the vibrational small width at half Usirig 0.0022 cmthe full = [21rcf] -1 giving 258 ± 42 a vibrational picoseconds van der Waals molecule in the B(v' = 9) the state. for the 48 Conclusions The B~X (9~1) molecule has been techniques the rotationally unblended studied 0.001 at transition of em -1 were laser spectrum used to van der Waals 2 induced resolution. resolved lines by the NeCl The were fluorescence transitions assigned accurately in and two determine the absolute value of the Ne to Cl the ground state. The structure is T-shaped and the Ne to Cl · 2 center of mass 2 center of mass distance in distance ground state and 3.536 ± 0.036 is 3.565 ± 0.035 A in the A in the excited state. The vibrational predissociation lifetime in the B(v' = 9) state is 258 ± 42 picoseconds based on the homogeneous broadening of the spectrum . Acknowledgments This work was Department of Energy. supported Petroleum Acknowledgment Research Chemical Society, the United States The dye laser was obtained from the San Francisco Laser Center Foundation. by Fund, funded by the National Science to the donors of administered by the is made for partial support of this work . the American 49 References 1. D.E . Brinza , B . A . Swartz, C.M. Western, and K.C. Janda, J . Chern. Phys . 79, 2. 1541 {1983) . D.E. Brinza, C.M. Western, D.D. B.A. Swartz, and K.C. Janda, ]. Jortner, J . Evard, Phys. F. Chern. Thommen, 88, 2004 {1984) . 3. ].A. Beswick, and J . Chern. Phys. 69, 512 {1978) . 4. G.E. Ewing, Faraday Discuss. Chern. Soc . 73, 325 {1982). 5. J.A. Coxon, J. Quant. Spectrosc. Radiat. Transfer . 11. 1355 {1971) . 6. S. Gerkenstorn, and P. Luc , AtLas du Spectre D'Absorption de la MoLecule D'Iode (CNRS, Paris, 1978). 7. X. Hui-Rang, S . V. Benson, and T.W. Hansch, Laser Focus March, 54 (1981). 8. R . S. Mulliken, Phys. Rev 36, 699 {1930) . 9. ].A. Coxon , ]. Mol. Spectrosc. 82 , 264 (1980) , and references therein. 10. R.E. Smalley, D.H . Levy, and L . Wharton, J . Chern. Phys. 64, 3266 (1976). 11. S . G. Kubolich, D.E. Oates, Phys. 61, 4686 (1974). and J . H.S. Wang , J. Chern . 50 12. C.Y. Ng, Y. T. Lee, and J.A. Barker, J. Chern. Phys 61, 1996 (1974). 13. F. Thommen, D.D. Evard, and K.C. Janda, 82' 5295 ( 1985) . j. Chern . Phys. 51 CHAPTER IV Molecular Beam-Laser Spectroscopy of the NeC1 2 van der Waals Molecule 52 Molecular Beam-Laser Spectroscopy of the NeC1 2 van der Waals Moleculea) Dwight D. Evard, Fritz Thommen,b) Joseph I. Clinec) and Kenneth C. Jandad) Arthur Amos Noyes Laboratory of Chemical Physics California Institute of Technology, Pasadena CA 91125 and Department of Chemistry, University of Pittsburgh Pittsburgh, PA 15260 a) This manuscript was published in modified form Phys. Chern. 91, 2508 {1987). CIBA-Geigy, Basel, Switzerland. b) Present address: c) National Science Foundation Predoctoral Fellow. d) Camille and Henry Dreyfus Teacher-Scholar . in J . 53 Abstract fluorescence Laser-induced eleven bands of excitation 1 ~+ sys tern o f ~ ~ B 3 rr(O+)~x u g the spectra for Cl the 2 an d associated van ~er Waals molecule NeC1 have been obtained 2 at 0.06 cm-l resolution in a free jet expansion of Ne, Cl . 2 and He. The observed rotational are of Hamiltonian model The vibrational simulated well for both by picoseconds for = 13). for The momentum effects were too a the spectra T-shaped, rigid the ground and excited states . predissociation 258 ± 42 B(v' structure of B(u' = 9) intermode small lifetimes to 33 ± 2 coupling ranged picoseconds and angular to be determined with resolution achieved in this experiment. from the 54 Introduction The study of the structure and dynamics of Waals molecules has become an active area for chemical physics . The van der research in triatomic van der Waals molecules, particularly those consisting of a rare gas atom bound to a distomic halogen molecule, and theoretical have been of interest because their both experimental relative simplicity may allow a quantitative comparison between experiment and theory few with adjustable parameters. complexes are easily formed and spectroscopically may be fluorescence probed or by very weak; of the less than halogen in the beam van der process is Waals induced techniques. is quantum of vibration and occur if compounds. Ne energy from the the halogen molecule is transferred to The mode. thought to vibrational proceed on potential energy surface which makes theoretically laser resonance He for Vibrational predissociation will the by rare gas-halogen complex the energy of a stretch vibrational mode of triatomic in molecular beasm expansions molecular The van der Waals bond These example accessible a predissociation single adiabatic the predissociation a intramolecular of vibrational relaxation (IVR). The first studies of al. involved detection of beam resonance techniques. these molecules by Klemperer ArClF 1 These and KrClF ClF 2 et by molecular complexes have a 55 1 inear geometry atom. They with the rationalize rare gas atom to be a rare the gas a tom structure bound by to the Cl considering the Lewis acid which donates electrons into the halogen a orbital, which is molecular (LUMO) ClF . This of interhalogen predicts orbital the linear of geometry Waals molecules, but fails observed rare indicative of a. binding. It is necessary for the determine which diatomic halogen van der apparent the Waals that most halogen complexes development is the model correctly van der to predict the geometries of the gas-homonuclear homonuclear These the lowest unoccupied are additive more of complexes. T-shaped, · model experimental appropriate important of the data are theories interaction in to the formation of the van der Waals bond. A detailed induced r2 3-6 made induced der probing The strong possible the fluorescence Waals molecule the {3~) the rotational for the distance. the to {29~) with Homogeneous vibrational Levy and the detection shown of 4.5 A He both B~X system total laser fluorescence. to be The van responsible for - 4.0 em -1 to the blue of band heads of free to linewidths were state laser of band contours yielded a complex by fluorescence structural features appearing 3.4 the complex by was 2 2 out and dispersed Hei Hei carried was fluorescence coworkers . of study excited, I2. 3 Analysis of T-shaped r2 center found structure of mass to vary with corresponding to 56 predissociation lifetimes ranging = 12 u to 38 dependence A study on of for u = 26. 4 showed a quadratic picoseconds predissociation rates the upper the from 220 picoseconds The state vibrational dispersed fluorescence for vibrational plus linear quantum number. spectrum of Hei 2 excited to the B(u') state showed that the fluorescence was r2 dominated by statement of in the B(u' propensity the state . 1) rule 5 This = -1 Au led to a for this predissociative process. The theoretical treatment of the vibrational predissociation in rare gas-halogen van der Waals complexes is based on the assumption that the normal vibration of the halogen molecule and the van der Waals stretching mode are only weakly Beswick and coupled. Jortner 7 8 ' studied the vibrational predissociation of T-shaped complexes where the interaction between rare gas atom was equations diatomic resulting could not be vibrational widths of resulting that the dependence predissociation on the close-coupling scattering but numerical predissociation rates from resonances. The model predicts rates a strong inverse have energy difference between bound complex and the final dissociated state. gap model correctly describes and super linear the the sum of Morse atom-atom solved analytically, solutions gave the halogen molecule and represented by a The potentials. the the Au dependence of = -1 the the the initially This energy propensity rate on rule the 57 vibrational quantum number, but did not the absolute predissociation rates potential energy surface used by observed 10 9 of is The Jortner has the Beswick and Jortner analysis momentum gap constraint on rate . Ewing has proposed a and gives a qualitative understanding for v~T 2 for vibrational predissociation which contains many features the in Hei Beswick and been shown to be quite unrealistic . momentum gap model correctly predict the limited by v~T the basis of rate. the In both models the ability of the intermode perturbation part of the Hamiltonian to couple the nodeless v = 0 wavefunction oscillating products. to the leads plane Since product to of rapid integrand and a the van der that wave higher dephasing of slower to the dissociated frequency is proportional momentum in the rate. V~T stretch represents the plane wave momentum, Waals coupling the products matrix element For both the Ewing and the Beswick and Jortner models any rotational excitation of the dissociation products would serve to lower the momentum (or energy) gap and thereby increase the IVR rate . Janda and coworkers using molecule 11.12 . tee h n1ques. (0 . 1-0 . 2 with em the -1 ) for the laser The of the the van der Waals induced fluorescence recorded at low resolution van der through of shifts studied Spectra were ( 11+-0) transition spectral have Waa 1 s the NeBr 2 complex molecule associated (30+-0) bands from showed the free increa sing Br 2 with 58 increasing v ranging from 5.5 to 8.8 em , -1 The natural linewidths of the van der Waals features increased from the bandwidth laser limited value of 0.10 em -1 for (16~) to 3 . 1 cm- 1 for the (27~) band, corresponding to vibrational predissociation picoseconds, respectively. energy in the B state closing v of = 27. the one be to be 64 ± 4 cm- quantum 12 ± 0.005 0.015 -1 1 the B+-X giving and 1.7 the dissociation from predissociation (10~), The homogeneous em 84 of They estimate One transition, high resolution. lifetimes the apparent channel near was studied at linewidth was found an e s t i rna t e of to ± 120 355 picoseconds for the vibrational predissociation lifetime of v. = 10. of the This low lifetime agrees well resolution data. The with an extrapolation data follow the trends der Waals predicted by the gap models discussed above . Heaven complex HeBr and 2 using B+-X system at jet expansion. 13 laser moderate observed the van induced fluorescence resolution Spectra (38~) through coworkers were of (0 . 05 cm- 1 ) obtained for the Br in a 2 free the (11~) bands and rotational structure for several bands was resolved with analysis consistent with a T-shaped structure. The He A 3.8 A 3.7 and respectively . to in Br Lifetimes respectively . center of ground and the ranged 1.8 ± 0 . 2 picoseconds for He 79 Br . 2 2 the from (12~) An upper mass distances states, excited > 100 picoseconds and 1 imi t (38~) of 23 em - are to bands of 1 for the 59 He-Br 2 dissociation energy in the B state was provided by observation of rapid vibrational 1 eve 1. predissociation The consistent with a lifetimes from the reported simple energy gap model = 40 u are for again vibrational predissociation. The first laser gas-interhalogen van Skene and Lester. 3.6 cm- 1 induced der 14 excitation Waals molecule transition This is interesting from uncomplexed particularly level because of This indicates van ICl was was by that for HeiCl. no fluorescence this vibrational der the iibrational predissociation of electronic predissociation of the yields a because to subnanosecond electronic predissociation . is Waals competitive ICl with molecule. the the Analysis lower bound estimate of 550 ± 150 picoseconds for vibrational 15 rare reported attributed observed bond al., a to the blue of the expected band origin of the ICl = 3)~X(u" = 0) the was of A spectroscopic feature approximately B(v' He-ICl study report techniques to predissociation the use of study the Drobits, lifetime . optical-optical dynamics of double the et resonance vibrational predissociation process in the NeiCl van der Waals complex. A pump laser excites the A~X transition, then at a time up to 15 nanoseconds later a probe laser scans through several E~A transitions of state is collected. (uA = 14) is 3 ± 2 ICl while the fluorescence The lifetime for NeiCl nanoseconds based on from the E in the A state experimental and 60 theoretical ratios of function of time. the complex signal to free ICl as a = 14} binding energy was The A state (uA determined to be 44 cm- 1 . Previously, complexes of Cl information was we have studied 16 with He obtained in NeC1 2 the spectroscopy of the observation of N eC 1 vibrationally excited states for than NeC1 exists 2 state even though necessary energy High more rovibronic of Cl -1 ) limited lifetime by der No resolution Waals lifetime (0.2 em However , in very 10- 5 -1 ) the metastable interesting. The in the X(v" = 1) over ten times the seconds the van der Waals bond. spectra of the B+-X (9+-1} the associated Waals molecule were obtained . was 17 18 · = 1 , 2) was and 2 van complex. 2 dissociate (0 . 01 em bands low X ( v" 2 Ne. the complex contains to resolution and the NeC1 2 van der The experimental resolution and Doppler broadening, with analysis leading to an estimate of 258 ± 42 picoseconds for the B(v' = 9} state. The Ne to Cl in RX' the ground experimental state, line nearly unblended lines in both and NeC1 the HeC1 2 of the 2 center of mass distance 3.565 ± 0.035 A based is positions 2 two the rotationally assigned, The structure of spectrum. van on der Waals complexes is T-shaped in both the ground and excited electronic states. In this paper we report state lifetimes as a the dependence of function of vibrational The observed trends are compared to HeC1 2 the NeC1 2 B excitation. and to the energy 61 gap and momentum gap laws . That the basic notion of energy gap rare laws applies to the beyond doubt. What energy surface parameters function of remains vibrational gas-halogens is to predissociation and rotational Ideally, theory . both and which are accurate enough to test available obtain seems we to be potential rates quantum as a numbers the details of presently want to have experimental measurements to evaluate the extent of coupling between the van der Waals bond the and covalent molecules . This would be measured as a der bond length Also , we want Waals vibration . of individual progress rotational toward meeting band width spectra of {9~1) to ( 12~1) lowest excited upon In l evels. those vibronic electronic clearly resolved excitation to be able the NeC1 2 of the halogen to measure lifetimes this paper we (7~) The 0.06 to em report -1 laser {13~) spectra vibrational and for the levels show transitions which can be used the desired information. shows both the the van B~X to extract that these in via bands . in change goals state rotational bonds intermode Analysis of coupling and this dat a the angular momentum effects on the dynamics are qu i te small. Experimental Section The basic design of the molecular beam apparatus used in these exper i ments has been described previously, therefore only a brief summary is given here . as 17 A supersonic 62 beam was pressures formed by varying from . 200 K where passing 100 a mixture of to 300 psi the vapor pressure of Cl 2 over the vacuum chamber maintained below 10liter/second diffusion pump backed by and He at liquid Cl at 2 is approximately 60 The mixture was expanded through a 35 torr. Ne 4 a pinhole into J.L torr by a roots 10,000 blower and mechanical pump. Molecules were excited with a pulsed dye laser (Lambda Physik FL2002E) which was pumped by an XeCl This dye (Lumonics 861-S). laser, excimer laser which is equipped with an air spaced Fabry-Perot over a range of 20 cm- 1 with a bandwidth of 0.05 cm- 1 and a pulse energy total fluorescence was detected by an S-20 photomultiplier and of appropriate etalon, 1-3 milliJoules cutoff filters is using were continuously tunable Coumarin 503. used to The reduce the stray laser light. The data were recorded on line by means of a signal averager multi-channel microcomputer. The laser transition of Cl through a experiment connected consists 2 of and further to an IBM-PC scanning to the the blue while detecting the total fluorescence form the halogen and associated van der Waals molecules. Results The B~X laser-induced ~ spectrum of the The feature transition is shown in Figure 1. 35 -1 c1 band is to the blue of the 5.5 em 2 (11~1) observed fluorescence 63 (11-1) 19262 19264 ~ 19256 19260 19258 19262 ~ 19264 cm- 1 Figure 1. (11~1) Laser excited fluorescence spectrum of vibronic band Waals molecule NeC1 2 . the transition for NeC1 for CI 2 and the associated the van B~X der The inset shows an expanded view of 2 with the fit to the data . 64 attributed basis of to the Ne pressure shows a 35 c1 van 2 der dependence Waals studies. molecule 17 18 · The on the feature nearly quadratic dependence upon backing pressure and disappears entirely in expansions consisting of only He and Cl 2 . {13~) through system Excitation spectra were obtained 35 c1 of {9~1) and 2 and {12~1) through the associated Ne 35 c1 for (7~) the band of the B~X van der Waals 2 molecule. The 35 c1 rotor model. B~X excitation spectra were fit to a rigid 2 which temperature and included nuclear the nonlinear least constants for inhomogeneous squares both The Cl 0.06 the ground and -1 which consist bandwidth (0.05 em The NeC1 2 -1 of a the excited states by a rotational and the the literature values. 19 linewidths of about convolution of the ) with the Doppler width {0.01 em spectra were fit The fit while transitions have inhomogeneous 2 em linewidth were routine band origin were held constant at spin statistics. laser -1 ). to a model consisting of a rigid T-shaped Hamiltonian for both the ground and excited The Cl-Cl bond distances, states. to be unchanged constant at inhomogeneous the by the free linewidths, presence Cl 2 RX and RB. of the literature Ne were assumed and values. were 19 held The with laser bandwidth and Doppler contributioh, were held at the values obtained from fitting t h e spectra o f uncomp 1 exe d 35Cl2. From the high resolution 65 spectrum reported of 18 contains the NeC1 we know the most B+--X 2 that (9+--1) the portion of structural the blue of individual transitions were best resolved, other is in the region The portion of the spectrum the band origin consists of a blend of many o . 040 A. • spectra and is Since rotational constants. 3 . 532 ± previously the spectrum which information to the red of the band origin. to transition less useful (7~) the for extracting (8~) and spectra they were fitted to obtain RX(u" This value was originating at then used = 0. v = 0) = in fitting all Rx ( v" = 1) = 3. 536 ± 0.035 as previously determined 18 was used in fitting of each spectrum originating at u" = 1. were the rotational temperature, band origin and RB(u'). The fitted parameters the natural linewidth, R, r and T the are given in Table I. The quality of the fits is shown in Figures 2, 3 and 4. too The natural linewidths for small determined from to be the linewidth (7~) these can and (8~) are For the spectra. to a seen in Figures 3 and 4 as decreased resolution of the spectra. We other bands, the be converted vibrational predissociation lifetime via the formula T The are effect limited of to = (2~cf(FWHM))- 1 lifetime estimating broadening the is readily vibrational rates for levels in the B state with u' predissociation < 13 because higher levels are dominated by electronic predissociation . 22 66 linewidths and lifetimesa) lengths, 2 Bond Table I. NeC l Band RB (A) r (em -1 ) 7+--0 3.52 ± 0 . 05 8+--0 3.51 ± 0 . 05 ----------------- ----------- 9+--0 3 ..53 ± 0.05 0 . 022 ± 0 . 003 240 ± 30 10+--0 3 . 51 ± 0 . 05 0 . 029 ± 0 . 003 180 ± 20 11 +--() 3.51 ± 0.05 0 . 052 ± 0.003 100 ± 6 12+--0 3 . 51 0 . 081 ± 0.005 66 ± 4 13+--0 3.55 ± 0.05 0.16 9 -1 3 . 55 ± 0.04b) 0.021 ± 0.003b) 258 ± 42b) 10 -1 3.54 ± 0 . 06 ------- - ------ 11-1 3.51 ± 0 . 06 0 . 053 ± 0 . 003 100 ± 6 12- 3 . 54 0 . 070 ± 0.004 76 ± 4 a) 1 ± 0 . 05 ± 0 . 06 ± 0.01 Rx(u"=O) 3 . 57 ± 0.04 A Rx(u"=1) 3 . 53 ± 0.04 Ab) In ea ch case the rotat i onal s p e c t rum was 0.67 ± 0 . 03 K . b) From r eference 18 . T (ps) 33 ± 2 temperature used to f it th e 67 Figure Laser 2. associated lower trace excited with the B+-X is the fit fluorescence (7~) and the The labeled transitions give the energy levels for spectrum of NeC1 2 transition of Cl . The upper trace is the data. J rotational K_lKl the ground and excited states. 2 The similar linewidths demonstrate the apparent independence of lifetime details . on rotational quantum number . See the text for 68 I E IOl _oil-+ u <oz-"z'l oo _11 0 u - 1 ~ co Q) 0 (\J I r'- l() rt') Q) z X + CD - ·LL.- 69 Ne - 35 8+-X (/) CI 2 (10-0) - . .0 lo... 0 0 c 0'1 (f) 19674 Figure 3. Laser associated with lower is trace excited the B-X the fit and 19676 fluorescence (10--o) spectrum transition the upper trace is of of Cl 2 NeC1 . the data . 2 The 70 Ne - - 35 CI 2 (/) 8+-X c (13-0) :::l ~ llo... 0 llo... .a lo... 0 0 c Ol ·(f) Data Fit 20068 Figure 4. associated decreased is due Laser with 20070 excited the rotational to homogeneous B+-X fluorescence {13+-0) structure spectrum transition compared to lifetime bro a denin g . of of Cl 2 Figures 2 NeCl . 2 The and 3 71 Discussion The dimers of vibrational predissociation of rare is particularly interesting because high resolution spectroscopy and gas-halogen the combination inelastic scattering data for the isovalent series of molecules provides a more detailed test of IVR molecules. The predissociation rate which number we theories than dependence of NeC1 report of on 2 here for the other classes the vibrational vibrational completes possible combinations of He and Ne with c1 We and predicted by molecules. can gap now see models how are The next phase of the of quantum matrix of 17 18 · . Br 11 · 12 2 2 we 11 the general obeyed by this trends group of this project will be to make more quantitative predictions based on realistic intermode coupling parameters and understanding of effects on the IVR dynamics. Analysis of puts of limits on the magnitude these angular momentum the present effects d~ta discussed below. Ewing's dynamics . 10 ana 1 ys1s indicates of vibrational that vibrational state predissociation lifetimes should be correlated by the formula -log(T) = b(2~AEv~T) 1/2 /an + c T is the lifetime, (2~AEv~T) 1 / 2 momentum of the dissociated products where range parameter for the dimer bond. and is the a is relative the Morse The constants b and c 72 should be independent the molecule at Figure 5 shows how the NeC1 approximation. here compare of this correlated in this manner. D 0 for of data reported 2 the previously reported HeC1 to level 2 data 16 when the complexes have been estimated by a one dimensional zero point energy correction of the D values reported by Reid, et al. e excited electronic state were 23 Values for the obtained by subtracting the dimer band origin shift from the free halogen band origin . As predicted molecule has a momentum gap . by Ewing's model, the nearly linear dependence of Although the slopes of the are somewhat different , data this could be corrected by a the Morse range parameters of For momentum given rates of NeC1 magnitude. 2 and HeC1 In fact , log(T} gap, 2 however, each on the two sets of data adjustment of a for the slight the molecules. predissociation are different by several orders of the lifetime is better correlated with the vibrational state quantum number than with the momentum gap. By and Cl 2 examining , specific we can compare vibrational the levels lifetimes of r 2 . Br 2 of the Ne complexes of the halogens in states for which the product energy ( a nd less accurately , momentum} halogen is bonded to is nearly the Ne atom. independent For instance of which = 12 r2 . v the stated while Cl , = 107 em . Br 2 , v = 16 has w = 108 em 2 - 1 The vibrational predissociation v = 14 has w = 110 em lifet i mes - 1 -1 has w for Ne bonded to each halogen in 73 II 6 -..... - 10 13 c 12 NeCI 2 12 ~ c II 0 0'1 0 ~ HeCI 2 ~ 10 -I f ~ 40 ~,I HeC1 the 2 . 16 Plot of -log(T) momentum 95% for det ai ls . 9 30 (2,u.~Ev-r) 2 of ~ 8 20 Figure 5. 10 9 f 9 II gap law confidence versus for {2~AEv~T) NeC1 limits a 2 are and a shown. 1/2 /a as a test comparison See the to text 74 levels vibrational p1cosecon d s 25 Thus, when 30 ± 10 and 0 229 ± 118 are compared in picoseconds, picoseconds, this fashion 26 24 93 ± 10 respectively. the correlation of lifetime with the vibrational energy which might have been inferred from Figure 5 is no longer the energy gap should be similar for Several gap law explanations correlation obviously, we of have predissociation as a only does this for the the data been simple, ignore the dissociation dynamics, evident, even though the three molecules. deviations are treating from simple possible. Most the vibrational one dimensional process. role of angular momentum on the it also ignores the wide amplitude van der Waals motions within the molecules. In fact, rigid would T-shaped structure Ewing's analysis 10 that the dissociation rate would be zero; from that couple. geometry It is not improve the models energy surfaces allow the hard, in weak and for a predict only deviations strong bonds to how principle, see to to to account for both realistic potential and angular time, however, we have such corrections. The intended Not momentum insufficient remainder data of At this proceed with effects. to the discussion to outline what data is needed and to is illustrate the experiments necessary to obtain such data. A fairly realistic representation of the NeC1 u =0 potential energy surface can be obtained 2 X state from the 75 analysis of differential inelastic scattering data with constraints on the well position imposed by spectroscopy. 23 What remains is which relate the bond . One experimental source of such information would be to determine in van the the c1 length on seen to determine Table 2 I, der the Waals intermode coupling bond to of vibrational quantum number . a van Cl dependence such the the dependence der is too terms covalent 2 Waals As bond can be small to be measured with the present data which only determines RX and RB to 0 . 04 A at best . To estimate the extent to which this precision must be improved, consider the approximation that the Ne to Cl atom distance is independent of vibrational level. The increase in the u (r7 (r10 length in going from = 2.612 A) 19 of B state to = 2 . 722 A) would Waals Cl bond 2 bond levels. length Thus, determine precision the of the lead a the extent potential, rotational the decrease 0.02 A between of to to the that modest constant u =7 level = 10 level of the the two vibrational atom atom properties improvements van in determination will der the start to provide the desired coupling information. Another source complexity of in the vibrational predissociation is the effect of angular momentum . momentum may effects as molecules help have couple been the IVR postulated like formaldehyde. 21 Angular process via coriolis IVR in covalent for The present data show that 76 angular momentum is not a IVR the rate for the dominating effect in determining NeC1 molecule . 2 Each of the and 4 assumes that the calculated spectra in Figures 2, 3 natural linewidth independent of j . If the were increase as some function of J to is one would expect for the lowest strong the calculated spectrum frequency transitions The same J dependence would lead to a for the J these of is observed in NeC1 2 too narrow Figures sharp, or J2 • ,e.g ., to be and 3. 2 intense spike = 0 line near the origin of . Figure 4. effects linewidth the Neither of other rare gas-halogens . Finally, the deviation from simple gap laws which are observed may be due to rotational excitation of the halogen molecule during dissociation . which might halogens due be considered to mass Such rotational more matching probable of the excitation , for "half the light collision" partners, would serve to lower the momentum gap and thereby also reduce · the predissociation lifetime. little rotational excitation of the I Hei 2 Levy reported 2 upon dissociation of Preliminary measurements in our laboratory .6 2 excitation of upon rotational slight and Ari indicate NeBr . 2 dissociation of reported NeC1 for 2 . Such measurements Thus the role of have yet product to be rotation remains open. It is interesting to note that Drobits et al ., observe substantial rotational excitation of the ICl product of 77 vibrational predissociation of even the quite though Unfortunately, lifetime little is the NeiCl A long, information is 3 state = 14 v nanoseconds . 15 available on the potential energy surface of this molecule. It is obviously considerably more anisotropic the homonuclear than that of halogen dimers. Summary this In dependence state. paper of the Comparison reported we IVR rate of for this the NeC1 data to 2 vibrational in the B the s ta .t e electronic momentum gap law shows that while the law predicts the correct dependence of lifetime on gas-halogen vibrational molecules, molecules will the require a type of have been discussed. level comparison and intermode coupling Better lifetimes terms individual of rates rare between more sophisticated analysis . measurements necessary positions for are in for more The complete analysis measurements of high J line necessary to obtain the the potential energy surface and the angular momentum effects on the IVR rate. Product state measurements are necessary role of to determine the product angular momentum in lowering the momentum gap. 78 Acknowledgements This Foundation. Petroleum work was supported Acknowledgement Research Fund by the is made to administered National Science the donors of by the Chemical Society for partial support of this work. the American 79 References 1. S . J. Harris, S . E. Novick, W. Klemperer, and W. E. Falconer, J . Chern. Phys. 61, 2. 193 (1974). S . E. Novick, S.J. Harris, K.C. Janda, and W. Klemperer , Can. J. Phys . 53, 2007 (1975) . 3. R.E . Smalley, D.H. Levy, L . J. Wharton, J . Chern. Phys . 64, 3266 ( 1976) . 4. K.E. Johnson, L. Wharton, and D.H . Levy, J. Chern. and D. H. Levy; D. H. Levy , J. Chern. J. Chern. Phys. Phys. 69, 2719 (1978) . 5. W. Sharfin, K. E . Johnson, J . Chern. Phys . 71, 6. K. E . Johnson, W. L. Wharton, 1292 (1979) . Sharfin, and Phys. 74, 163 (1981}. 7. J.A . Beswick, and J.J. Jortner, 69, 512 (1978) . 8. N. Halberstadt, and J.A. Beswick, . Faraday Discuss . Chern. Soc . 73, 357 (1982). 9. D.W. Schwenke, and D.G. Truhlar, Chern . Phys . Lett . 98. 217 ( 1983) . 10 . G.E. Ewing, Faraday Discuss. Chern. Soc . 73, 3 25 (1982} . 11. B . A. Swartz, D.E . Brinza, C . M. Western , and K. C . Janda, J. Phys. Chern. 88 , 6272 (1984}. 12 . F . Thommen, D. D. Evard, and K.C. Janda , J . Chern. Phys. 82, 5295 (1985) . '· 80 13. L.J. van de Burgt, J.P. Nicolai, and M. C . Heaven, J. Chern. Phys. 81, 5514 {1984} . 14. J.M. Skene, and M. I. Lester, Chern. Phys. Lett. 116, 93 ( 1985). 15. J.C . Drobits, J . M. Skene, and M.I. Lester, J. Chern. Phys. 86, 2896 {1986). 16. J . I . Cline, D.D. Evard, F. Thommen, and K.C. Janda, J . Chern . Phys. 84, 1165 {1986) . 17 . D.E. Brinza, C.M. Western, B.A. Swartz, and K.C. Janda, D.D. J. Evard, Phys . F. Chem. Thommen, 88, 2004 (1984). 18. D.D. Evard, F. Thommen, and K. C . Janda, J. Chern. Phys. 84. 3630 ( 1986) . 19. J.A. Coxon, J. Mol. Spec. 82, 264 {1980). 20. M.A.A. Clyne, and S.I. McDermid , J . Chern . Soc. Faraday Trans. 21. II 75, 1677 {1979). H.L. Dai, C.L. Korpa, J . L. Kinsey, and R . W. Field , J. Chern. Phys. 82. 1688 (1985}. 22 . M. C. Heaven, Trans. 23. B . P. and M.A.A. II 78, Reid, Clyne, J. Chern . Soc. Faraday 1339 {1982}. M. J. O'Loughlin, and R.K. Sparks, to be K . E. Johnson, Sharfin, and D.H. Levy, published. 24. J.E. Kenny. W. J. Chern. Phys. 72, 1109 {1980} . 81 25. Unpublished data. 26 . The value given the data in for Table I . Cl 2 v = 14 The is extrapolated extrapolation ignores from the electronic predissociation which affects this level. 82 CHAPTER V Direct Measurement of the Vibrational Predissociation Lifetime of NeBr 2 in the Ground Electronic State 83 Direct Measurement of the Vibrational Predissociation Lifetime of NeBr 2 in the Ground Electronic Statea) N. Sivakumar, D.D. Evard, J.I. Cline, and K.C . Janda Department of Chemistry University of Pittsburgh Pittsburgh, a) PA 15260 This manuscript was published in Chern. Phys. Lett. 137, 403 {1987). modified form in 84 Abstract The vibrational predissociation life t ime of NeBr 2 in the ground electronic state with one vibrational quantum in the halogen expansion . stretch was NeBr (X, 2 u measured directly in The NeBr (X, 2 from the vibrational u free jet = 1) was detected by optical-optical double resonance to monitor the population as a distance a nozzle to the laser predissociation function of interaction region . lifetime = 1) was determined to be 8 ± 3 microseconds. for 85 Introduction The vibrational predissociation has to molecules proved tractable process energy trans f er. for 1,2 electronically a studying simple the rate of intramolecular is perhaps best characterized are excited metastable rates in the levels 1 3 9 • - ground limit of 10 microseconds for NeC1 stretch of Waals theoretically the halogen 2 . of 3 the rare The vibrational electronic these molecules have not been measured, the der and gas-halogen van der Waals molecules . predissociation van The systems for which the vibrational predissociation dynamics the be of states aside from a .o f lower Direct excitation of covalent bond within these complexes is difficult because the infrared frequencies lie in an inconvenient region transitions are containing the homonuclear vibrational molecule in vibrational expected to quantum the be very halogens. predissociation the of and weak complexes We lifetime ground electronic in Br-Br the spectrum for the report here the Ne of state stretching the 79 with mode . Br 2 one This measurement was performed by monitoring the decrease in the population of the vibrationally excited level as a function of the distance from a supersonic nozzle metastable state is prepared. source where the 86 Experimental A gas (natural mixture of isotopic ::::: Br 0. 05% abundances) 50 micron nozzle at a in 90% 2 was Ne and expanded 10% He through a backing pressure of ::::: 175 psi, vacuum system previously described. 3 The Ne 79 into a = 1) Br (X, u 2 molecules formed in the expansion were detected downstream from nozzle by the an optical-optical double resonance The symbol X indicates the electronic state of technique. NeBr 1 + 2 associated with the ground X ~g state of Br 2 and u is the number mode. of vibrational quanta A pump laser _pulse promotes NeBr (X, u 2 electronically excited state, 3 B IT{O:) electronic state of Br in the Br-Br stretch. molecule Ne blue of 79 Br 79 the (B, u Br 2 pulse, 14 state. 11 determined The fluorescence intensity is then of level a to NeBr (B, u 2 the 10 nanoseconds of with transition . by pulse =2 to an the the van der Waals dissociate as u = 1) observed ::::: 6 cm- 1 is lifetime the stretching with 10 vibrational quanta The laser Br-Br correlates The absorption of Approximately to , molecules probe a 2 the B 3 IT{O+)~x 1 ~+ {10~1) u g = 10) 355 picoseconds, linewidth . which ( 10~1) 2 in of the measure the the E(O+) g ultraviolet of the 10 the The Ne and = 10) is homogeneous after excites to the pump product electronic (UV) number E~B of 87 = 1) NeBr (X, u 2 molecules in density of a the collection volume within the expansion. The will number decrease nozzle, 2 as the Vibrational density r. falling · Measuring off the ratio of to Br (X, u = 1) as a 2 the predissociation vibrational Br 2 from the predissociation of 1/r 2 than the populations function of r rate. with Comparison of yields of the = 1) UV fluorescence signal to the Br 2 (X. u = 1) fluorescence nozzle distance faster NeBr (X, u = 1) 2 NeBr (X. u 2 such as = 1) to form Ne and Br 2 (X, u = 0) will result in number increasing 1/r increases. r' NeBr (X, u 2 its roughly with stable molecule signal separates as the a function effect of of distance from the dissociation from the decrease due to the geometrical expansion of the jet . Two XeCl dye lasers excimer laser (Lambda (Lambda frequency pulse. co 1 i nearly the jet. The doubled pump through The in KDP the vacuum probe pulse pumped MSC) to generate laser chamber was 10 nanoseconds from the pump photomultiplier tube (EMI 9558QA) the beams 90 ° to delayed pulse. A detected by a generated The output of one dye probe and FL2002) Physik EMG 201 pump and probe laser pulses. was Physik UV laser probe propagated the axis of approximately UV sensitive fluorescence . The signal was preamplified (LeCroy VT100B) and averaged by a boxcar integrator (Stanford Research Systems SR250) using 88 a 300 nanosecond wide gate . The laser UV intensity was monitored by a photodiode viewing a dye cell illuminated by a reflection from the laser beam. A second integrator averaged the photodiode signal. and doubling crystal were scanned by a also controlled the synchronization boxcar The dye lasers microcomputer which of the laser trigger and detection electronics and stored the data. Fluorescence was collected at 90 beams and laser jet axis by a focal length, f/0.7). laser beam was 0 to the plane of quartz the (75 millimeter lens The scattered light from the visible filtered by a Corning 7-54 filter. An adjustable aperture placed between the photomultiplier and lens defined the area from which fluorescence was collected and also rejected collected from a scattered UV light. F 1uorescence was 2 millimeter diameter cylinder defined by the probe laser beam. The aperture defined the cylinder to be 5 millimmeters in length. The probe laser wavelength was tuned (2~9) head of laser wavelength was scanned through the transmits filter fluorescence the recorded band and 79 Br 2 transition. band and 7-54 the R branch to from the excited v Br (X, v = 1) with fraction a 2 the B~X (10~1) the = 10 vibrational excitation double of spectrum resonance the . pump Since the visible level of could be spectrum of 89 v = 1) NeBr (X. 2 in the same scan. Negligible visible fluorescence due to the decomposition product Br (B, v = 9) 2 was observed. Visible fluorescence excitation spectra of the reference Br (X, v = 1) and double resonance spectra of 2 = 1) were obtained at distances ranging from 4 NeBr (X, v 2 to 11 millimeters from the nozzle. Double resonance spectra were normalized to the probe laser intensity . Results Figure 1 distances, and 4 the show shows spectra millimeters 11 decrease to the Br (X. v = 1) 2 confirm that the change only decay in the probe the study of intensity of is observed NeBr (X, v 2 over the v the to of ( 10~) same as change that in similar B~X 2 to indicates population, B~X No = 0) range These order intensities = 1) 2 = 1) : NeBr (X, 2 In the uncomplexed Br transition used was the different nozzle. population. NeBr 2 (X, v NeBr (X, v 2 the two population the · corresponding NeBr laser from in relative spectra were recorded for band and at the in relative a obtained (10~) band. The that used in the relative of Br (X, v 2 distances for = 0) which = 1) was studied. The density of NeBr (X, 2 a distance r v = 1) molecules in the jet at from the nozzle can be written as p(r)=p 0 (r) exp(-rR/u) (1) 90 The spectra in this figure are of Br Figure 1. 2 and NeBr 2 taken at a distance of 4 and 11 millimeters from the nozzle to the laser obtained by spectra are interaction laser induced taken using region . intensity . NeBr to Br 2 NeBr (X, u 2 2 The is due = 1). to Br 2 spectra are fluorescence while the optical-optical double resonance. The spectra are normalized such that equal The observed the Br decrease 2 in NeBr 2 peaks are of the ratio of the vibrational predissociation of 91 ~ ()) ()) N L.. <.0 ~ en Q) z ~ I 0 ~ X I co N !....._ co ~ ~ I E E E ~ E E ~~ ()) <.0 ~ ~ ~ ~ 2) Q) c w bJ ()) <.0 ~ L.() co ()) c..o ~ o_ E ::J Q_ 92 where p 0 (r) is the density of r in the absence of distance velocity of NeBr integrated by the at r NeBr 2 molecules u dissociation, in the jet, and k 2 constant for the dissociation. in p 0 (r) as the at is the is the first order rate To correct for the decrease the distance from the nozzle is increased, intensity of ratio of the Br the NeBr feature at r 2 integrated 2 a the is divided fluorescence intensity to that at the smallest distance !?tudied. Figure 2 a plot of the logarithm of corrected intensity the distance from the shows versus interaction nozzle The slope of this plot gives a value for k/u. fit to the jet region. the is determined to be the to best the laser straight line The velocity of approximately 7.4 X 10 5 millimeters/second using the equation <K.E.> and assuming that (2) the temperature of the gas equilibrated to room temperature after travelling 7 from the Br 2 trap to accurate since small. The lifetime the extent of cluster formation T = 1/k is found to microseconds. The obtained different using dependence. meters This equation should be the nozzle. fairly has quoted error sets of reflects data for be the the is 8 ± 3 spread distance 93 • • • • 0 • L() ~ -+-----------.----------.-----------~--------~r---------~ 6 4 8 12 10 Distance (mm) The intensity ratio of Figure 2. feature, normalized to the NeBr the feature to the intensity at 4 2 millimeters, is plotted versus the distance from the nozzle to interaction region . for the h./u laser where expansion and u is the velocity h. is the rate predissociation. The of constant slope gives a the for molecules the value in the vibrational 94 Discussion Several experimental lifetime factors determination. ± 0.5 miflimeters in the introduce error into the uncertainty of There is an distance at which the intensity The correction for the decrease in ratios were determined. p 0 {r) should include the fact that the photomultiplier does not view· a point source of fluorescence . The pump probe beam diameters . which determine the volume of from which fluorescence is detected are a the distance from the nozzle. The and the jet large fraction of intensity of the NeBr 2 feature should be given by Jv (r) exp(-rk/u) dV I - (3) p0 where V is the collection volume in the jet. Another vibrational source temperature formation may However, the Br constant over that the of be a error as well function rotational 2 is that the as the degree of position distance in of cluster the value apertures for which the used lifetime change the jet. is far This indicated enough downstream from the nozzle source that no further cooling occurs. same and temperature distributions were the range of distances used. smallest rotational is obtained dimension of The using different the collection 95 volume perpendicular Since not the above result analysis greatly applied vibrational estimated from a of (X. ratios same Use of for a ~ v the these factors do not decay from ~ and NeBr fraction the of also be ratio of intensity assuming the nozzle did would not studied, gives However, a ratio that these be the dissociate. 2.5 respectively) measured value for the the assumption that = 1) concentrations should Br (X. v = 0) and Br (X. v = 1), 2 2 v be valid. of not to (X. 2 may intensity molecules 0.04 and distance lifetime v = 1)] 1 microsecond . = 0) same = 1) v (~ smallest NeBr (X , 2 does the v = 0)] distance NeBr (X. 2 the ratios lifetime of be given the the = 0) observed of v = 1)]/I[NeBr (X. 2 for if v NeBr (X. 2 decay, comparison v .= O)]/I[NeBr (X, 2 2 lens. predissociation I[Br (X, 2 I[Br the to the to the axis of = 1). v The the plane of in any artifactual contribute NeBr (X. 2 to respectively, need 8 microseconds to be closer of the difficulties to Therefore, the actual we value view of the above, the lifetime. In reported view lifetime should magnitude determination. this result law 2 · 12 which is an be regarded Even at interesting adequately discussed predicts as this level test of the vibrational predissociation rates for an order of of precision , the observed energy trends gap in the rare gas-halogens 96 in excited electronic presented an linewidth of parameters, including states. intriguing an Beswick correlation observed the and of the transition amount of Jortner have homogeneous with several energy which must deposited into product translational kinetic energy. 12 a The r. may be expressed as resonance half-width, r be unw exp[-{2~AE) 1 / 2 /an] {4) Ip this equation u is the vibrational quantum number of · the hw is the harmonic oscillator vibrational energy, halogen, AE is the energy of the vibrational quantum expended in the dissociation minus the energy required to break the van der Waals bond, ~ is the reduced mass of and a is the Morse range parameter system, atom-diatom stretching . predissociation coordinate. lifetime, homogeneous linewidth, c is the can atom-diatom The be for the vibrational related to the r. by the equation = (27rcT)- 1 T where T, the speed of (5) Homogeneous light. linewidth measurements have been used to study the lifetimes of NeBr with various quanta of excitation in the Br-Br 2 stretch . Increasing vibrational excitation corresponds to decreasing values of AE of of the . 1 4,13,14 potentia . stretc h ing value because 355 picoseconds anharmonici ty of The range from to ± 0.3 lifetimes ± 100 picoseconds for for u = 30. Figure u = 10 3 shows the 2.8 a Br-Br plot a of 97 • r-1~ 3 > ~ L~ L-....J c • _j I 0 ~ •• • ••• •• •• L() 4 Figure 3. 8 6EV2/ ex em -1/2 A A plot of -ln[f/uw] versus AE the energy gap model 12 for The state 12 determined points in 112 16 20 1a as a test of the vibrational predissociation the lower 4 14 previously · while left are from the single the B point in the upper right is from the g round state determined in this p a per . 98 versus -ln{r/uhw) agreement with Equation proposed for show to Note {4). the that the predissociation of a experimental Equation (4) was linear van der Waals The extrapolation from one vibrational frequency molecule. to another depends very sensitively on the range parameter, Although a. the form of the coupling molecule is expected to be different the it is B electronic correlation, lifetimes in the value of AE for NeBr 2 v still for from to T-shaped that assumed in to compare the the appropriate instructive state the = 1 in the ground electronic state. The value obtained, 0.6 microseconds, by extrapolating from the lifetimes in the B electronic state is nearly within an order of magnitude the experimentally lifetime of 8 ± 3 microseconds. The variation of determined the two values may be explained by differences in the shape of the potentials in the ground and excited in states. studies to determine the lifetimes of NeBr (u 2 Further· = 2, 3) would help to clarify the question. The analysis above assumes energy, that all of the available AE, goes into relative translational kinetic energy of the atom and diatom . The product Br (B) vibrational and 2 rotational quantum state distributions predissociation of recently. 13 available the B state of NeBr for 2 the vibrational have been measured Very little rotational excitation{~ 5% of the energy) of the Br 2 is observed, and thus the 99 v~T mechanism is inferred to be a nearly pure far no measurements vibrational of the product predissociation of process. So state distribution for rare gas-halogen van der Waals molecules on the ground electronic surface have been performed. Any significant participation of the rotational degree freedom of predissociation rate would be expected over that estimated to increase from the the energy Since the measured rate for the ground electronic gap law. surface is longer than predicted by extrapolating data from the state, B important we in conclude the that rotation vibrational is probably predissociation occuring on the the ground state surface. not process Instead it seems reasonable that the coupling between the covalent and van der bonds is on Waals surface. simply excited state potential the entire the very difference state to similar the two states Waals 14 potential between the excited state The Morse range parameter must be 25% larger for the excited stronger the energy surface found the ground van der to account for in extrapolating from the state lifetimes . Along with measured for Waals bond lengths this result suggests that both the van der energy covalent surface stretch and and the the anharmonic van der Waals are quite similar for the X and B electronic states. terms modes 100 Conclusions We have reported a value of 8 ± 3 microseconds for the vibrational predissociation lifetime of the ground electronic state NeBr 2 . of = 1 level of The lifetime the v measurement shows good agreement with a prediction based on the energy vibrational gap extrapolation levels of lifetimes of of the B electronic state. several Apparently, both the vibrational predissociation mechanism and the van der Waals potential energy surface are similar for the two electronic states. Acknowledgement We would like to acknowledge the financial support of the National Science Foundation (N.S., J.I.C., and the United Energy (D. D. E). wish to thank Beswick for States Department Professor of Alberto and K.C . J.) We helpful discussions and Professor Michael Golde for the loan of the KDP crystal. 101 References 1. D.H. Levy. Adv. Chern. Phys. 47, 323 (1981}. 2. J.A. Beswick and J . Jortner, Adv. Chern . Phys. 47, 363 (1981}. 3. D.E. Brinza, B.A. Swartz C.M. and Western. K.C. D.D. Janda, Evard, J. Phys. F. Thommen, Chern. 88,2004 (1984). 4. B.A. Swartz, D.E. Brinza. C.M . Western. and K. C. Janda, J. Phys . Chern . 88, 6272 (1984). 5. D.D. Evard, F. Thommen, and K.C. Janda, J. Chern. Phys. 84. 3630 ( 1986) . 6. J.I. Cline, D.D. Evard, F. Thommen, and K.C. Janda, J. Chern. Phys . 84, 1165 (1986). 7. L.J. van de Burgt, J.P. Nicolai, and M.C. Heaven, J. Chern. Phys. 81, 5514 (1984}. 8. J.C. Drobits, J.M. Skene, and M.I. Lester, J. Chern. and M.I. Lester, J. Chern. Phys. 84, 2896 (1986). 9. J.M. Skene, J.C. Drobits, Phys. 85, 2329 (1986). 10 . R . F . Barrow. T.C. Clark. J.A. Coxon and K. K. Yee, J. Mol. Spectrosc. 51, 428 (1974} . 11. P. Berwanger, K.S. Viswanathan, and J. Tellinghuisen, J. Mol. Spectrosc. 91, 275 (1982). 12. J. A. Beswick, 2277 (1978). and J. Jortner, J. Chern. Phys .. 68, . 102 13. J.I. Cline, D.D. Evard, B.P. Reid, N. Sivakumar, F. Thommen, and K.C . Janda, Proceedings of the NATO Advanced Research Workshop on Weakly Bound Molecular Complexes, Maratea, 14. Italy, September, 1986, in press. F. Thommen, D.D. Evard, and K.C. Janda, J. Chern. Phys. 82, 5295 ( 1985). 103 Chapter VI The Structure and Dynamics o£ the ArC1 van der Waals Molecule 2 104 The Structure and Dynamics of the ArC1 2 van der Waals Molecule Dwight D . Evard, Joseph I . Cline, N. Sivakumar and Kenneth C. Janda Department of Chemistry University of Pittsburgh Pittsburgh, PA 15260 105 Abstract The ArC1 laser van der Waals molecule was studied by a 2 pump-probe technique. The complex has a two T-shaped geometry in both the ground and excited states, with a bond energy, o0 , 187.9 ± 0.4 em of 178.4 ± 0.3 em 1 inewidth of -1 the in the B(u ArC1 2 B(u -1 in = 7) state. = 11) band indicates that the prepared state has a psec. · The one quantum = 0) the X(u state and The homogeneous was measured and lifetime of 83 ± 10 predissociation is the preferred channel when it is energetically accessible. The rotational distributions of the Cl 2 process fragment formed in the two vibrational quantum dissociation are not smooth and are nonstatistical in relaxation the to nature. The intermediate distributions bound level indicate with one vibrational quantum transferred to the van der Waals modes . 106 Introduction It has been over a decade since the pioneering work on Hei 2 past first was published by Levy and ten years a the In number of . studies have been performed on 2 3 · The rare system for the study the rare gas-halogen van der Waals molecules . gas-halogen complexes provide a model of 1 coworkers. intramolecular energy transfer experimental and theoretical studies. and are amenable 2-4 Recent pump-probe to studies of rare gas-halogen van der Waals molecules will be described to outline the application of this technique. Lester and coworkers have used optical-optical double techniques resonance predissociation of state. to study the NeiCl van der Waals complex pump laser 5,6 The transition of 0) free jet expansion. the NeiCl vibrational in the excited the formed in a A second dye laser, delayed by 0 to 15 nsec from the pump laser pulse, was scanned through several transitions E~A As detected. was the while increased, they transitions. observed several excitation of the Ne!Cl state. The vibrational in the A(v to increased intensity was lasers of the dissociation fragment Simultaneously, of intensity fluorescence the delay between the pump and probe spectroscopic feature due E~A state E features a ICl they noted a decrease in attributed complex from the A state predissociation = 14) state is 3 ± 2 nsec . to lifetime direct to the E of Ne!Cl 107 The Ne!Cl features complex to attributed to the constitute E state direct excitation a of progression the in the van der Waals stretching mode. Ne!Cl in The bond energy, D , of 0 1 based on a state is 87 . 6 ± 0.8 cm- = 1) the E(u Birge-Sponer analysis of 48.2 ± 0.5 is em -1 the em -1 in the progression. the = 0) X(u The bond energy state and 43.3 ± 0.9 in the B(u = 15) state as determined by the shifts of spectroscopic features. The progression observed in the van der Waals stretching mode indicates that there is . a significant change in geometry in going from the A to the E states. Skene ICl et fragment der Waals al. report rotational distributions of the in the predissociation of Ne!Cl and He!Cl van complexes excited the B( 3 rr +) 0 to state. 7 These distributions are relatively narrow, are highly peaked and are He!Cl the rotational while for Ne!Cl nonstatistical. distribution is In the case peaked at j of = 8, rotational distribution is peaked at to 6. 1 and fragment, 25.9 em -1 respectively. of of rotational j = 17, the corresponding energy in the !Cl The classical impact parameter for the dissociation He!Cl and Ne!Cl ranges from 2.1 A, which is quite reasonable for an impulsive model of 0 .7 to dissociation. Janda and predissociation techniques. 8 9 · coworkers have of and studied the vibrational using pump-probe The rotational distribution for Cl 2 formed 108 in the dissociation of NeC1 but has a c1 flat fragment 2 tail 2 = 11) B(u extending out rotational state bond energy for Ne-Cl 2 to high j. corresponds allowed by the available energy. the is peaked at low j , The highest to the maximum They were able to bracket and 44 between cm- 1 52 by subtracting the centrifugal barrier height and the fragment rotational vibrational also energy quantum observed an from the expended even/odd in energy the of Cl dissociation. intensity 2 They alternation which depended upon the position of the pump laser. Cline et dissociation al. of studied HeC1 constants of HeC1 2 2 . 9 the The parity constraints relatively large of the rotational permitted excitation of a specific HeC1 rotational state, which decayed to give Cl 2 2 fragments which possessed the same symmetry with respect to exchange of the Cl atoms . and j had = 7. well The rotational distribution was peaked at j = 9, 10 with The distribution extended out to j = 14, a below second the maximum near limit which is j a =2 node a which is energetically allowed. The node in the distribution may be due to a rotational rainbow or quantum interference effects in the dynamics. In the present paper we several bands of the ArC1 obtained parity-selected 2 report pump-probe spectra of van der Waals molecule. excitation spectra We have which reduce spectral congestion and allow a more accurate determination of the geometry of the complex . We report the ArC1 2 bond 109 dissociation energy distributions of The dynamics of discussed and in the fragment B states and X and Cl 2 formed in rotational the dissociation. the vibrational predissociation process is compared to previously reported is work on other rare gas-halogen systems. Experimental schematic A apparatus is through the representation shown in Figure n~x transitions of the The pump 1. of ArCl 2 experimental laser over . is tuned the range 490 - 530 nanometers. preparing the complex in a particular level mode. of quanta in The Waals bond 10 product the the B state with u Cl E~B The 2 weak is van der probed by transition in the fluorescence photomultiplier. tuning the the Cl second of stretching ruptures is and laser 250 - 260 range 2 the through nanometers. detected by 11 a An ~xcitation spectrum may be obtained by scanning the pump laser while the probe laser is tuned to a particular transition. E~B distribution of the Cl the probe laser while 2 Alternately, the rotational product may be obtained by scanning the pump laser excites some initial levels of the complex in the B state. The . l y. 12,13 preVl.OUS Ar in He Waals apparatus vacuum over described been The backing gas is formed by passing 2.5% liquid molecules has are Cl held at -78 prepared in a 2 K. ArCl pulsed, van der free jet 2 110 Figure 1. A apparatus. The (BS1) coated nm. The (BS2) coated light. beams, dye schematic reflect and to probe reflect Folding mirrors and a cell portion of (DC) and phototransistor {PT). detects E~B the experimental split by a beam splitter 60% of the incident light at beams are combined by excimer beam to pump diagram the UY is light of and (FM) are used transmit to direct the probe pulse is sent fluorescence an is 308 optic visible the laser through a detected by a A UY sensitive photomultiplier {PMT) fluorescence of Cl . 2 An IBM-PC controls lasers and boxcars and accumulates the signal. the 111 Cl.) c ·r1 ..J "'ru C.D C\J en CD en - ..J .a ..J Cl.) 0 Cl.) L Cl.) ru ~ Cl.) r-t ::J - >- c c - L Cl.) "'ru r-tca m ~ - c>- w ~ CJ') m L G.) "'m ~ ~ L c..J a_ C) ....u E X UJ 112 expansion through a 150 stagnation pressure of ~ orifice J.Lm 320 psi. (General The gas Valve) pulse is at a probed 5 centimeters downstream of the nozzle. Two dye a lasers, pumped by XeCl probe laser some experiments operating with Coumarin 503 dye, exc imer pulses. The with Fabry-Perot etalon to from ~ 0 .2 em -1 laser to generate first dye laser an the is tuned, angle reduce linewidth The output of the the pump and equipped in air to are spaced 0. 05 em ~ second dye -1 laser .is doubled in KPB to generate the probe laser pulse, while the fundamental is rejected by a Schott UG-5 filter . The pump and probe beams are combined with an optic which relects UV and passes visible co 11 i nearly radiation . through Brewster chamber. The nanoseconds from each is pulse probe laser The beams then windows in to and is the pump pulse and ~ 20 to an with a imaging quartz lens ( f /0.7) . This sensitive photomultiplier lens the focusses experiment is of the approximately 10 uv is free by jet axes focal fluorescence (EM! width of fluorescence 75 millimeter the out temporal laser and tube Corning 7-54 filter attenuates The the nanoseconds. collected perpendicular light. delayed propagate 9558QA), onto a UV while a the scattered visible controlled which scans the pump and probe lasers, by a length laser microcomputer triggers the excimer laser , pulsed valve and boxcar, and stores the data. 113 Results and Discussion The Structure: rare gas-halogen van der Waals molecules provide a model system to compare the results of theory and experiment. In order to do quantitative calculations it is necessary to have a surface. energy experimentally and lengths theoretical realistic potential This potential must agree with determined parameters, such as bond dissociation the energy. the This section describes the determination of these two parameters for the ArC1 van der Waals molecule. 2 The NeC1 shown 2 and HeC1 to have . 10. 12 geometries . studied at van der Waals molecules were both 2 T-shaped The structures ArC1 r e s·o 1 u t i on moderate laser and the spectrum of Figure 2. The ArC1 rotational structure asymmetric top electronic states. Cl-Cl bond axis, thus ArC1 2 The complexes 2 the which may for both The Waals em (0.06 B~X spectrum model der their -1 ) equilibrium molecule was of pump the band is shown in (6~) contains a be assuming fit the ground transition dipole which is parallel great and lies to the b deal a of rigid excited along the inertial axis; has a b-type asymmetric top spectrum. parity is predissociation rotational van 2 in of rare the throughout conserved process. quantum 9 is numbers wavefunction of the ArC1 2 gas-homonuclear when the produced the halogen vibrational with initially even j prepared complex is symmetric with respect 114 Excitation Figure 2. spectrum of the ArC1 2 (6+--0) B-X transition detected using a pump-probe technique. The dots are are the rigid experimental rotor fits to data and the data. the solid · curves Trace (a) is the the spectrum obtained by positioning the probe laser on the bandhead of the E-B (0+-5) Cl 2 transition. Trace transitions to odd parity states of ArC1 2 (b) B(v consists of = 6) detected by positioning'the probe laser on the P(5) line. Trace (c) consists states of of transitions to even parity ArC1 detected by positioning the probe laser on the P(6) line. 2 115 ,....--...,. • =>• ~ (a) Q) u cQ) u (f) ~ (b) 0 :J LL > ~ (c) 19000.5 19002.5 Pump Energy/em_, 116 to a two-fold when j the the ArC1 initially the ArC1 simplifies excitation 2 on spectra Figure in j ArC1 ~ay . structure for rotational temperature, 2 which is produced with 2 state of to an exchange of spectra 2 axis, ArC1 2 is the Cl atoms. the otherwise complex spectrum of = 10 and positioned Cl excited van der Waals molecule. 2 figure Conversely, antisymmetric with respect This greatly the about the Cl atoms. exchanges odd rotation when = 9, j Figures 2b and 2c show the probe respectively. all be fit During the fitting the natural origin were allowed to vary . laser The three the same assuming procedure linewidth and The Ar to Cl 2 is the the band center of mass distance in both the X and B states was varied over a wide range to find the minimum, allowed to vary from Cl 2 . 10 atom Recent changes complex. The observed the and the Cl 2 bond literature values work by Reid et the Cl-Cl effective al . was for uncomplexed suggests bond length that length the Ar in the structure was 15 most for well resolved the ArC1 B+--X 2 rotational (6+--0) band. The rotational constants for the X(u = 0) state were determined by fitting the Figure spectra bands, other shown than in the 2. For fitting ( 6+--0) band, the vibrational ground state rotational constants were fixed at the values determined in the fit to the (6+--0) band parameters were allowed to vary . while the excited state The final values for each 117 These distances represent vibrationally averaged structure of the ArC1 complex. band are given in Table Bond Energy: molecule may I. The bond energy of be determined distribution of Cl and 2 the ArC1 by analysis branch head, 2 van der Waals the rotational the excitation spectra. Figure 3 shows the rotational distribution of Cl the dissociation of ArC1 2 B(u = 7). 2 of B(u 2 = 6) formed in The spectrum has an R and an extended P branch. The P(6) the last line with significant intensity, however some and measurable intensity in the P(7) Excitation spectra obtained by setting the P(5) and P(7) lines of product pump laser are shown in Figure 4. Cl P(S) and spectrum we are symmetry states lines. laser scanning that particular j only have those sufficient state of Cl determination examination of many more level of However, the the Cl 2 of spectra metastable the Similar spectra obtained 2 initial energy lines the Ar-Cl fragment to populate of ArC1 than 2 to the basis for bond energy. By it is clear that decay to the 2 in Figure 5, states odd/even . The spectra in Figures 4 and 5 provide an accurate on In each parity-selected excitation detecting which is there is the probe 2 1 ine with the probe laser positioned on the P(6) and P(S) are shown in Figure 5. the the j =8 j =6 1 eve l. in Figure 4, most lines in the excitation spectrum which contribute to the intensity of the P(5) line are seen 118 Table I. ArC1 2 Bond Lengths State B(u = 11) 2.81 ± 0.05 3 . 72 ± 0.05 B(u = 9) 2.68 ± 0 . 05 3.61 ± 0 . 05 B(u = 7) 2.53 ± 0.05 3 . 67 ± 0 . 05 B(u = 6) 2.55 ± 0.05 3.70 ± 0.05 X(u = 0) 1.98 ± 0.05 3.72 ± 0 . 05 119 Figure 3. The c1 = 6) formed in the dissociation of ArC1 2 B(u rotational distributions of the 2 fragment B(u = 7). The spectrum is obtained by scanning the probe laser while positioning B~X (7-.Q) the pump laser transition . on the bandhead The P(B) line product rotational state which is populated. is of the the ArC1 2 highest 120 • • 38668.6 38672.6 Probe Energy/em_, 38676.6 121 (a) (b) -2 -3 -1 0 1 2 Shift from Band Origin Figure 4. Excitation spectra transition with the probe and (b) P(5) of the ArC1 2 B.-X laser positioned on the lines in the Cl 2 E.-B (0+-6) (7+-0) (a) transition . P(7) 122 (a) (b) -3 -2 -1 0 1 2 Shift from Band Origin Figure 5. Excitation spectra of the ArC1 2 B+--X (7+-0) transition with the probe laser positioned on the (a) P(8) and (b) P(6) lines of the Cl 2 E+--B (0+--6) transition. These spectra are due to even parity states of ArC1 2 . 123 also ArC1 in the Figure in ArC1 2 energy sufficient energy The j P(7) state of is D , 0 spectrum =7 of then in the energy c1 As . 2 internal the gives D for ArC1 . 0 and from the the the Cl (j 2 vibrational 2 minus = 7) 8.112 product, energy = 7, as a from rigid rotor assignment energy of the levels . The height of the than 0.04 em The dotted and is less Figure 6 corresponds to the -1 energy of fragment centrifugal line fragment Since the centrifugal barrier is very small rotational levels dissociate to produce Ar + states are the B(v = 7) is 178.4 ± 0.3 em -1 ·, the barrier of product, by given bond 185.222 em -1 rotational j 2 Cl Ar and is energy The the = 7) fragment lowest energy between (j rotor of derives the translational B(j=8). the that uncertainty transitions relative -1 produce determined . the dissociation, lowest the to to was plus where free j B(v = 7) which was observed in 2 of 2 B 0 00 state does not transition energy 1. 0 ± 0. 3 em ArC1 2 available rotational -1 2 = 6) B(v fragment populate is ArC1 excitation complex c1 the The ArC1 to = 7. with quantum expended em levels. energy energy, the with sufficient rotational the The internal energy is increased the threshold is reached 2 where Cl along 6, rotational have P(7). 2 = 7) rigid asymmetric top energy levels are shown B(v 2 excitation spectrum detecting Cl which lie above this line in Cl 2 the may fragment Cl 2 B(j = 8) . imbedded in the Ar + Cl 2 continuum, 124 Figure 6. The light lines are the ArC1 levels the were in B(u = 7) determined by state. fitting of ArC1 2 B(u = 6, produce B(u j = 7) . = 6) Cl {u 2 B(u ArC1 but = 6, 2 j rigid rotor energy rotational excitation spectra constants similar = 6) formed in the dissociation 2 B(u does not = 7). = 7. have The J = 0) can produce Cl sufficient ArC1 2 energy rotational levels above the dotted line can produce fragment Cl j = 8, provided the .t o The dark lines depict free rotor those shown in Figure 2. states of fragment Cl The 2 symmetry of the initial 2 to energy 2 state correct, since parity is conserved in the dissociation. with is 125 ArCI2 B(v = 7) -----= .......-..-.=:::=:-----------------=::.::....--==-=-= -= =- -- ---+---=------ 0 0123456 7 8 9 -4 -3 Cl2 B(v = 6) t~, J 0 ~ I 126 since the relative translational energy of the dissociated complex is not quantized. The shift uncomplexed binding Cl of the band 2 energy in ArC1 origin the band origin relative is measure of 2 two a electronic the states. to relative The B~X (6~) transition is blue-shifted 9.5 ± 0.2 cmthe free c1 B~X 2 (7-0) than in reported in X(v = 0) level energy in the bands other elsewhere, B the Table 8 state. A series II, bands for provides excited than and the (7~) The data in Table energies and a nearly shifts error of linear function The lineshape the instrumental varied lifetime during The in X the as the concerning the bond bond energies barriers as are are all consistent spectra was for the described taken into the measured bond within the The band shift seen with Lifetime were inhomogeneous fitting broadening was transitions. that from that linewidth the from measurements, determined as 2 is the Hei a Voigt 2 16 excitation function . stronger show v, 1 indicates II of ArC1 originating the measurements. van der Waals molecule. Lifetime: are centrifugal account. experimental The -1 of information state. the band which is 9.5 ± 0.2 em the van der Waals bond state band origin, the and the fit width was natural procedure . observed for broadening the was with fixed at linewidth was No measurable (6~) observed or (7~) for the 127 Table II . ArC1 2 Bond Energies and Band Shifts n0 (em -1 ) Band Shift 176 ± 4 13 ± 0.5 B(u = 9) 176 ± 5 11.3 ± 0.5 B(v = 7) 178 . 4 ± 0.3 9 . 5 ± 0.4 B(v = 6) 177 . 8 ± 1.8 9 .3 ± 0.4 X(u = 0) 187 . 9 ± 0.4 State B(v = 11) 128 (11+-0) transition , (0.06 resolution inhomogeneous c~ Doppler which em width 0. 01 em The natural -1 ) was also studied of the pump includes the and laser -1 ) linewidth of the at moderate laser. The contributions c~ 0.05 em -1 the of ) widths . the ArC1 (11+-0) transition was 2 determined to be 0.064 ± 0 . 018 cm- 1 , which corresponds to a predissociation vibrational lifetime 83 ± 10 of picoseconds. Dynamics: The rotational distributions which are observed using pump-probe the information give the dynamics of the process. Levy al . observed on predissociation channel technique in which transferred to complex = -1) (Av one quantum was Beswick and Jortner of great deal of vibrational that the stretch is dissociate the the halogen Waals modes to dominant when this process wa·s 2 result was explained by the van der accessible. energetically et a This in terms of an energy gap model which predicted that the most efficient channel would be the one which least put the amount of energy relative translation of the products. The the Av = -1 B state spectrum is of channel ArC1 2 . shown in is for A typical Cl 3, the sharp cut off in the where rotational v < 8 fragment 2 Cl 2 formed in the predissociation of ArC1 2 B(v a rotation and 4 open Figure into levels rotational B(v = 7) . of = 6) was There is distribution, which 129 energetic the indicates The excitation. number, jmax' channel "because limit highest is of observed typically breaking Cl quite the nearly all of the energy of fragment the Cl rotational 2 low Ar-Cl rotational for Au = -1 the bond 2 quantum accounts for stretching vibrational 2 energy in j =6 is nearly 90% of the available energy and corresponds to a classical quantum. The rotational A. parameter of 5.2 in B(u = 11) the rotational · For the NeC1 state, the distribution corresponding classical to van der Waals molecule product Cl extending out and parameter of 7.2 A. 8 The inverted (Au = -1) preferred j is energetically allowed. The rotational in initial states accounts for < = -1 Au the is = 24, j energy kinematically 2 to has . a available for Cl = 10) the 85% distribution fragment B(u 2 of ~ impact 2 impact implies much that higher is distribution of The Au for two = -2 channel of the dissociation of ArC1 B(u = 7) and is closed completely for ArC1 B(u 2 2 formed in the = 6). The energy of a Cl the Cl 2 10% 2 product the than dissociation of ArC1 shown in Figure 7. a 2 vibrational quantum decreases with u and u = 7 and u = 8 for ArC1 2 with J = 0. Au= -1 channel cannot dissociate through expect the to vibrational see two is energetically closed between Since ArC1 2 B(u = 9) the loss of one quantum we would quantum channel predissociation process and this dominate is the the case. 130 35 Figure 7. the Au= -1 c1 2 fragment rotational state populations for channels. The circles and triangles are the distributions for the even and odd parity rotational states of ArC1 2 , trace were respectively. The populations determined by fitting the spectrum (0+--6) spectrum trace in spectroscopic constants of 10 and E+--B Ref. for the upper trace is at 50%. for Figure 11. 3 the in the CI using The upper 2 the baseline 131 0 0 ~ ~/ 0 OJ 0 co · 0 R~ / / "--/ 0 cw Oo L1") v'~v'-1 0 ~ 00 5_~ &~ o-----o~-6- ~ ~~5 0 ~ 0 2 4 6 8 10 Rotational state, j 12 132 The Cl 2 E.--B {0.---7) the ArC1 exciting The Figure 8. quite sharp distribution accessible j of NeC1 2 where and, as which rotational was the to observed j classical ArC1 distributions show and rotational are 2 in Figure of the out HeC1 2 . the of The fragment two quantum Figure to the transfer the in to from The 9. state populations populated is available s i mi 1 a r the from 8 impact parameter energy. shown rotational are is is limit distributions of distribution distinctly different constraints dissociation 90% Th i s dissociation. into in energetically to a energy shown highest corresponds but is the over the by for observed for kinematic smooth the obtained transition accounts rotational not in highest distributions, vibrational distribution {94---0) out The A for 7.2 off extends This energy. B.--X 2 cut j. = 32. max rotational which are energetically allowed limit. The compared product to rotational those reported state distributions for 2, HeC1 NeC1 2. can be HeiCl and NeiCl. 5 - 9 The vibrational predissociation of each of these complexes is dominated by the Au= -1 channel. The rotational distributions of ICl in B(u = 1) state following vibrational HeiCl NeiCl and distributions predissociation B(u = 2) are distribution is at quite j the show different narrow and the of Both behavior. the = 8 for HeiCl and at complexes j peak of the = 17 for NeiCl. 133 Figure 8. probe laser through the E~B positioning the pump laser on the band head The intensities B~X {9+-0) Pump-probe transition. lines are not a the Av spectrum obtained {1~7) smooth function of j, = -2 spectra observed for ArC1 2 . by scanning transition of of the while the ArCl 2 rotational which is typical of 134 ,--..... • ::J• g Q) u c Q) () (f) ~ 0 . =:; LL > => 38445 38470 Probe Energy/em- 38495 1 135 35 Figure 9. the Au = -2 Cl 2 fragment channels. rotational state populations for The circles population of the even and odd respectively. The highest j and triangles states fragment c1 2 of j fragment constraints. The baseline offset by 20% on the vertical axis. for the Cl state which observed is determined by the available energy, kinematic are 2 . is rather than each plot is 136 v'--7v'-2 12--710 0 <.0 ~ ~0 1..() c .o 0 +--' 0 ~ =:Jo Q_('f') &o N 0 5 10 15 20 25 30 35 40 Rotational state, j 137 The impact complexes parameter ranges from distribution shows a j max = 16, energy, Only for the gradual The decrease in for corresponds to are for A. 0.7- 2.1 which accounts and dissociation all HeC1 the ICl rotational 2 intensity out nearly 24% of an of to the available impact parameter of fragment rotational 3 A. states consistent with conservation of energy and angular momentum For populated. = 24, J. max (3+-10) available = -2 B+-X 2 which energy half-collision Au NeC1 in to ~ of are similar that most every to energetically populated and the distribution shows a E+-B 2 of the classical a 7.2A. parameter Cl 85% approximately corresponds distributions distributions is and impact detecting (11+-0), The ArC1 the NeC1 allowed 2 2 is j sharp cut off above that limit. large The dissociation impact of predissociation A possible indirect half from the Cl that may be collision stretching that 2 the and the NeC1 NeC1 distributions 2 2 mode to the a in van Au the the this vibrational = -2 vibrational direct V---+T-.R behavior is an there is which relaxation der Waals (IVR) modes The major difference between product rotational distributions is distribution are for mechanism followed by predissociation. the ArC1 not explanation intramolecular 2 for indicate mechanism process. preliminary parameters quite is smooth structured and complex structure is observed when the Au while the ArC1 2 complex. = -1 channel This for 138 ArC1 a is closed, where preliminary IYR leading to ArC1 2 metastable state of highly excited van der Waals 2 in modes becomes possible. These through distributions cannot analysis, additional unusual any simple and be explained theoretical work will be necessary to fully understand the dynamics of the system. One possible explanation for behavior this of complex simplify the discussion, the is follows. = 0. may which the into highly is closed, having be described as excited, the ArC1 number of 2 metastable 10. The Figure 11, where region of levels are shown. only 1 state/em two such as overall J. for those each vibrational levels . population distribution stretching is shown = 0 2 IYR shown in fn detail in B(v and bending vibrational = 8) potential well is general, the initially limited number of rotational in Figure 6, the bending unusual The of in bending is 2 = 0) (J of In . of via and stretching density shown process state decays interest prepared state can couple to a states, the less energy step ArC1 J -1 = 9), The predissociation for the The -1 states states near the top of the ArC1 approximately to complex van der Waals modes. B(v = 8) vibrational Figure order B(v 2 12 em a spectroscopically prepared levels of The then In For ArG1 than needed to dissociate the complex . process interesting consider initially the case where total angular momentum J one quantum channel as the the Cl 2 (v having and the stretching rotational = 7) same state fragment may 139 Figure 10. Energy levels for ArC1 The B(u=7. 8, 9). energy levels for ArC1 dotted 2 are shown . lines which were , techniques of Reid et a1. 2 15 B(u = 7, 8, 9) and Cl are 2 continuum . vibrational calculated using the Only the]= 0 levels of ArC1 The solid lines are the Cl in the Ar + Cl the 2 2 2 free rotor states The energy scale is relative to the energy of the prepared J = 0 state of ArC1 2 B(u = 7) . 140 0 0 N =========~ Cl2 mmm B(v=9) Utili tit 111111111 111111111 l!!!!!l!! iiiiiiiii 0 0 ltUIIIII ......... ;:;:;;;;; ......... 111111111 ~ iiiiiiiii ......... ~ 1....... 1 ~ 0 t ArCI2 B(v=9) 111111111 111111111 ......... 111111111 111111111 Cl2 B(v=8) II II IIIII !!!!!!::: iiiiiiiii II II IIIII 111111111 ......... ......... iiiiiiiii 111111111 ::::::::: - t 0 0 N I _ArCI2 B(v=8) 0 0 Cl ~~2 mmm · 111111111 numn 111111111 111111111 B( v -:1) ········· ~~:::::~: ii iiiiiii ......... ::::::::: mmm ......... ......... I") I t 0 ~ I ArCI2 B(v l) ·/ 141 Figure B(u J 11. Energy = 7, 8). = 0) The energy however 2 The the Ar + Cl 2 2 for ArC1 lines are while the = 8, 9) the ArC1 solid Au = -1 2 lines and Cl B(u =8, 9; indicate IVR 2 the 2 dissociation channel is to excited vibrational highly B(u = 8) may occur, B(u B(u 2 free rotor states imbedded in the Ar+Cl preliminary levels of ArC1 B(u dotted levels, enrergy of the c1 continuum. levels = 7) continuum. closed, followed by coupling to Alternatively, the ArC1 2 = 9) complex may dissociate by coupling directly to the Ar + Cl 2 B(u = 7) competitively. continuum, or both processes may occur 142 0 N B(v=8) B(v==9) B(v =1) • J - 35 - 34 Direct --------------------------~ I.V.R. 33 ::::::::a: 0 ~ I ~ I - 32 . 143 coupling relative reflect the prepared ArC1 = 9) B(u 2 between the states and rotational initially the excited van der Waals vibrational levels of ArC1 Following the quantum is transferred highly excited ArC1 B(u = 7) Cl 2 preliminary to B(u 2 the IVR second Cl 2 highly B(u = 8). 2 vibrational the van der Waals modes and = 8) complex decays Alternatively, continuum. prepared state may decay directly into to the the the ArC1 the Ar + initially 2 = 7) B(u continuum. Halberstadt et al. have performed a three dimensional quantum mechanical study tor vibrational predissociation of NeC1 . 2 17 The lifetimes and product Cl 2 rotational distributions were calculated from the wave functions using the Fermi golden The rule. calculated lifetimes and rotational distributions were in qualitative agreement with experimental results. performed ArC1 on 2 Similar which might interesting results would good model system to methods, and then test be coupling which a would allow complex systems. which calculations we have calculations to to serve reported study with various be could be explain the here . This exact close approximations performed on more 144 Conclusions The ArC1 van der Waals complex has been studied using 2 a pump-probe technique to obtain excitation spectra of the and rotational predissociation of the distributions of complex. ArC1 The following geometry 2 is T-shaped with an Ar to Cl center of mass distance of 3.72 2 ± 0.04 A states, and 3 . 70 ± 0 . 04 A respectively. the in ground The bond energy, Do· and excited of the complex -1 in the X state and varies with u in the is 187.9 ± 0.4 em B state. B(u = 11) The state lifetime is of the spectroscopically 83 ± 10 picoseconds. whether this corresponds to an IVR rate, this complex . in the The rotational predissociation It are not clear or the lifetime of distributions process is prepared very of Cl 2 formed complex, non statistical in nature. The distributions extend out to the energetically allowed limit structured distributions to dissociation. and, for indicate that Au= -2, the highly IVR may occur prior 145 References 1. R.E. Smalley, D.H. Levy, and L. Wharton, J. Chern. Phys. 64, 3266 (1976). 2. D.H. Levy, Adv. Chern. Phys. 47, 323 (1981). 3. K.C. Janda, Adv. Chern . Phys. 60, 201 (1985) . 4. J.A. Beswick and J. Jorter, Adv. Chern. Phys. 47, 323 (1981). 5. J.C. Drobits, J.M. Skene, and M. I. Lester, J. Chern. Phys. 84, 2896 (1986). 6. J.C. Drobits, and M.I. Lester, J . Chern. Phys. 86, 1662 (1987). 7. J.M. Skene, J.C. Drobits, and M.I. Lester, J. Chern . J.I. Cline, N. Sivakumar, D . D. Evard , and K.C. Janda, Phys. 86, 2329 (1986) . 8. J. Chern. Phys . 86, 1636 (1987). 9. J.I. Cline, N. Sivakumar, D.D . Evard, and K.C. Janda, Phys. Rev. A 36, 1944 {1987) . 10. J.A. Coxon , J. Mol. Spectrosc. 82, 264 {1984). 11. T. Shinzawa , A. Tokunaga, T. Ishiwata, and I. Tanaka, J. Chern. Phys. 83, 5407 {1985) . 12. D. E . Brinza, C . M. Western, B . A. Swartz, and K.C. Janda, D.D. J. Evard, Phys . F. Chern. Thommen, 88, 2004 {1984) . 13 . N. Sivakumar, D. D. Evard, J.I . Cline, and K. C . Janda, Chern. Phys. Lett. 137 , 403 (1987). 146 14. J.I. Cline, D.D. Evard, F. Thommen, and K. C. Janda, J. Chern. Phys. 84, 1165 (1986). 15. B.P. Reid, Phys., 16. J.E. K.C. Janda, Halberstadt, J. Chern. and D.H. Levy, in press. Kenny, K.E . J. Chern . Phys. 72, 17. and N. Johnson, W. Sharfin, 1109 (1980). N. Halberstadt, J.A. Beswick, and K.C. Janda, J. Chern. Phys., in press. 147 CHAPTER VII A Test of Atom-Atom Additive Interactions: Arnc1 2 . n = 1. 2. 3 148 A Test of Atom-At6m Additive Interactions : ArnC1 2 , n = 1, 2, 3 Dwight D. Evard, Joseph I. Cline, N. Sivakumar and Kenneth C . Janda Chemistry Department, University of Pittsburgh Pittsburgh, Pennsylvania 15260, U.S.A . 149 Abstract We have determined dissociation energies der Waals molecules Arnc1 2 . where n = 2, 3. for the van These values are compared to those obtained from the approximation that the intermolecular Ar-Ar and Ar-Cl 2 potential interactions. is given by the sum Within experimental of the error the Ar c1 bond energy is identical to the predicted value . 2 2 The measurements are precise enough to illus·trate a deviation from complex. simple bond-bond additivity for slight the Ar c1 3 2 150 Introduction A simple approach to constructing an intermolecu l ar potential for a weakly bound cluster is to employ a additive atom-atom potentials. This model is set of attractive because accurate atom-atom potentials are often available. However, model there is has been some debate correct for all van as to der whether Waals 1 this molecules. Klemperer and coworkers have studied the ArClF 2 and KrClF 3 van der Waals resonance molecules spectroscopy . using The molecular s true ture of beam electric each of these complexes is linear with the rare gas atom on the Cl end of the halogen. This the rare gas atom electrons into the lowest unoccupied structure to is predicted be a Lewis halogen a orbital, molecular orbital by acid considering which which (LUMO) is of donates the the the ClF . This model does not correctly predict the structure of the rare gas-homonuclear der Waals molecules are halogen complexes . T-shaped , indicative These of van an atom-atom additive model of the binding. The dissociation energy of the van der Waals indicative of the type of bonding which i s camp 1 ex. able Waals to 4 Levy and bracket bond potential. the coworkers have dissociation 2 a nd were der of the van the of the anharmonicity of By dispersing the fluorescence fragment because they were able is important in the studied He r energy bond of r2 to determine the last I 2 stretching quantum 151 which had sufficient energy to dissociate the complex. The energy of that quantum served as an upper limit to the bond energy while the next smaller quantum determined the lower limit. Janda and coworkers have Waals molecule at 0.05 em . 5 tee h n1que. fragment Cl -1 of formed 2 ArC1 resolution using a in the vibrational van 2 der pump-probe The initial as allowed by internal complex allowed two additional Cl populated. By analysing shift from Cl the predissociation of transition of Cl E~B state was populated, energy. be 187.9 the They determined the rotational distribution of the complex by scanning the rotational studied 2 energy . Every cons~rvation of rotational 2 the ArC1 states to be spectra and adding the blue they determined the bond energy of ArC1 2 2 2 to ± 0.4 cm- 1 in the X{u = 0) state. We have determined dissociation energies der Waals molecules Arnc1 2 where n • for the van ranges from 2 to 3, to test the approximation that the intramolecular potential is given by the sum of Ar-Ar and Ar-Cl 2 potentials . The determination is performed by interpreting the fragment Cl rotational distribution predissociation of ArnC1 2 produced in the 2 vibrational . Experimental A gas mixture was over liquid Cl 2 prepared by passing 2. 5% Ar at -77 C. in He The van der Waals molecules were 152 formed in a free jet expansion of stagnation pressure of 320 psi. of the clusters molecules were technique. 6 7 8 · · was For to 9 The band shift excited. level vibrational a laser n~x the 3 pump-probe (11~) lie approximately 12, 24 and 33 cm3 Cl2. K. 2, 1, the associated B U(O the blue of uncomplexed 2 1.5 using = n from a The rotational temperature approximately detected transitions for Arnc1 the gas mixture + )~X u is 1 + Lg transitions of dependent The 1 product upon the rotational distribution is obtained by setting the visible pump laser on an Arnc1 transition 2 and through the region of the c1 scanning the probe UV laser 3 10 2 E(O:)~B U(O:) transition. Results Narrow limits can be placed on the dissociation energy of the complexes by measuring the internal energies of products. The van der Waals bond energy is between the in highest the total dissociation. 8 cluster energy and fragment Since Cl in the Arnc1 between the highest observed fragment unobserved fragment the is cutoff due level is strictly very to the difference the energy remaining rotational 2 the 2 state case following the cut off level and the lowest sharp, we conservation believe of that energy and not due to kinematic constraints. There are two small, but significant argument . corrections clusters have to this some distribution of rotational First, the energy (< 5 153 cm- 1 ) before barrier to which approximately is Second, excitation. dissociation on the there of order incorporated is into a centrifugal -1 or less 2 em the calculations below. Figure c1 shows the produced by v = 11) . Three 2 (B, 1 (1+--8) E+--B vibrational quanta spectrum of predissociation of the halogen fragment of Ar c1 2 2 stretch are necessary to dissociate the complex. An upper limit may be placed by on the Ar c1 2 2 energy rotational bond energy (B. v = 8, of subtracting = 12) j (~ and the height of the centrifugal barrier the barrier in Ar c1 2 2 potential is to Calculation ambiguous but a is the calculated (458 . 39 energy available -1 because by adding the centrifugal of barrier dissociation good estimate can be made. unobserved rotational this method the ArC1 to be 434 ± 2 em The Ar c1 2 2 ) from centrifugal centrifugal the -1 2 ) The the polarizabilities the -1 ). The level of which Ar and c1 for Ar c1 mechanism lower dissociation energy is obtained by doing first -1 .25 em em long range van der Waals potential from of estimated em (21. 52 the 2 is 2 2 . 11 is unknown, limit for the the same for the fragment Cl 2 . B(v = 11} bond energy der Waals Using is determined . van molecule may dissociate through two processes to produce different products; Ar Cl (B,v , J) * 2 2 Ar Cl (B,- v, 1) * 2 2 - 2Ar + Cl (B , v",j) 2 (1) Ar (v',j) + Cl (B,v",j') 2 2 (2) 154 Figure 1. Pump-probe formed in the spectrum was dissociation obtained positioning the B~x band. (11~) spectrum pump by of of Ar c1 2 2 scanning laser on fragment the Cl 2 B(v probe = B(v = 8) 11). The laser wh i le the bandhead of In this figure j = 12 is the maximum j allowed energetically to produce 2Ar + Cl in the dissociation process . 2 the ArC1 2 as the products 155 r--..... =>. ~ Q) u cQ) u (f) j == 12 t ~ 0 => ~ .> ~ 38547.8 38557.8 Probe Energy/em- 38567.8 1 156 where and v represent j the vibrational The Cl excitation of the products. and rotational product state spectrum 2 shown in Figure 1 suggests that both of these processes are important. j A sharp decrease in intensity is observed above = 12 due to the closing of channels for in Equation producing but 1, states there to at least > 12 appear possessing j is a small = 22. j the process shown probability The Cl of fragments 2 to be products of the dissociation shown in Equation 2 for which the Ar-Ar bond remains intact so that extra energy can be released to Cl B(v The rotational = 6) produced in Ar c1 B(v 3 2 = 11) which observed was distribution. drops off the state the The vibrational Ar c1 of fragment Cl predissociation 2 of The sharp cut off this The population decreases gradually and then decay bond is rotation. in 2 2 also visible = 20. There is no evidence for processes which were for steeply above j different distribution is shown in Figure 2. for 2 energy for the Ar c1 3 2 observed complex may be determined by using the procedure which was outlined above. The total cluster binding energy for = 11) state is 754 ± 4 em -1 . the B(u In Table energies are bond- bond additivity , 84 . 8 I, the the compared em -1 . 12 ' 13 error, the Ar c1 complex in 3 2 total It experimental with where total values 0 0 is observed for cluster obtained Ar-Ar that, is by taken binding simple to be within experimental binding energy of Ar c1 2 2 is identical to 157 Figure 2. Pump-probe formed in the spectrum was dissociation obtained positioning the B~x band. (11~) spectrum pump by of of on Cl B(v = Ar c1 3 2 scanning laser fragment the the probe bandhead B(v = 6) 11). The laser while 2 of the ArC1 2 158 . ~ :J. 0 Q) u c Q) u (J) ~ 0 :J j == 20 ~ LL > ~·~ 38653.7 38666.2 Probe Energy/em- 38678.7 1 159 Table I. Arnc1 2 Bond Energies (em -1 ) a) Ed.1SSOC (calc) n m State Edissoc(exp) 1 0 X(v=O) 187.9 ± 0 . 3b) 1 0 B(v=7) 178.4 ± 0.3b) 2 1 X(v=O) 458 ± 3 2 1 B(u=11) 434 ± 2 - - - 3 3 X(v=O) 787 ± 5 818 . 1 ± 0.5 3 3 B(u=11) 754 ± 4 - - - - 460.6 ± 0.4 - - - a) Ed.1SSOC (calc) = nD 0 (Ar-Cl 2 ) + mD 0 (Ar-Ar). b) From reference 5. 160 + 2D (Ar-Cl } 2 0 D0 (Ar-Ar) while that of Ar 3 c1 2 from free is 4% less measures the than 3D 0 (Ar-Cl 2 } + 3D 0 (Ar-Ar). Discussion The band shift of Arnc1 2 Cl 2 difference in binding energies of the complex between the X and the B states . the ArnC1 2 We have determined the bond energy for complexes in the B state, but we can obtain the shif~. bond energy in the ground state if we know the band The spectroscopic features attributed to the Arnc1 Waals complexes are the blue shifted from well deeper potential is free Cl in van der 2 2 , the which implies that ground state. In Table I, we also list the bond energies for the X state of the complexes, which were obtained by adding the band shift to the B state binding energy. Kenny Ne n I et , for n 2 . which has al. = 1 - six 14 6, observed a constant equivalent sites the in the first model, sites in equatorial positions about the Cl structure, shell. has 2 for One equivalent bond axis. We 12 em observe shifts shift from which they inferred a geometry "belt" consistent band while Ar c1 2 3 has only Ar c1 is T-shaped, 1 2 consistent with the distorted tetrahedral "belt" 5 a 9 em -1 blue shift -1 from and the Ar c1 bond energy is 2 2 model arrangement which would predict a of four atoms. A the "belt" model for Ar c1 . however, would allow for two Ar-Ar 3 2 161 bonds. while the three . There bonds while experiment is by structure The total allowing Ar der of such a structure allows Waals atoms clustered perpendicular to the Cl energy there may three be Ar-Ar perpendicular van the that which maintaining configurations. maximized no indicates 2 to form axis . will be attraction a is triangle The total binding slightly less than predicted by simple bond-bond additivity. Conclusion In Arnc1 to 2 conclusion, the bond have been measured. illustrate slight relationships . Levy coworkers 14 for the complexes The results are precise enough deviations additivity and energies The for Nei from "belt " 2 simple model correctly bond-bond suggested by predicts the structure of Ar c1 . but not Ar c1 . 2 2 3 2 Acknowledgments This work was supported Department of Energy (D.D . E . ) Foundation ( J. I. C. , made to the donors by and the the N. S . . and K. C. J . ) . of Petroleum the partial support of this research. United States National Science Acknow 1 edgemen t is Research for Fund, 162 References 1. K.P. Huber, and G. Herzberg, Constants of Molecules (Van Nostrand Reinhold, New York, 2. Diatomic 1979). S.J. Harris, S.E. Novick, W. Klemperer, and W.E. Falconer, J. Chern. Phys. 61, 193 {1974}. 3. S.E. Novick, S.J. Harris, K.C. Janda, and W. Klemperer, Can. J. Phys. 53, 2007 {1975). 4. J.A. Blazy, B.M. DeKoven, T.D. Russell, and D.H. Levy, J. Chern. Phys. 72, 2439 (1980). 5. D.D. Evard, N. Sivakumar, J.I. Cline, and K.C. Janda, manuscript in preparation. 6. J. C. Dr obits, J. M. Skene, and M. I. Lester, J. Chern. and M.I. Lester, J. Chern . and K.C. Janda, Phys. 84, 2896 (1986). 7. j.M. Skene, J.C. Drobits, Phys 85, 2329 {1986). 8. J.I . Cline, N. Sivakumar, D.D. Evard, J. Chern. Phys. 86, 1636 {1987). 9. J.A. Coxon, j. Mol. Spectrosc. 82, 264 {1980}. 10 . T. Ishiwata, T. Shinzawa, T. Kusayanagi, and I. Tanaka, j. Chern. Phys . 82, 11. B. P. Reid, Phys., 12. N. Halberstadt, 1788 {1985). and K.C. Janda, j. Chern. J. Chern. Phys . in press. J.M . Parson, P.E. 56, 1511 ( 1972) . Siska, and Y.T. Lee, 163 13. R.A. Aziz. and H.H. Chen, J. Chern. Phys. 67, 5719 {1977) . i4. J . E. Kenny, K.E. Johnson, W. Sharfin, J . Chern. Phys. 72, 1109 {1980) . and D. H. Levy, 164 APPENDIX SHAPE: A Working Manual 165 Introduction rotational The structure of electronic excitation spectra of rare gas-halogen van der Waals molecules can be very complex. Although HeC1 2 has the least complicated spectrum, because of its large rotational constants, as the mass of rare the gas atom increases the rotational constants decrease and the number of accessible rotational states increases rapidly, Also, homogeneous and even in a supersonic expansion. inhomogeneous broadening tend to smooth the spectra and eliminate the possibility of making definitive frequency assignments to individual transitions. It would spectra be very simply difficult by to try to line positions. fit NeBr Instead, spectrum fitting program is essential or 2 ArC1 2 an automated to interpretation of the spectra. Colin Western, a postdoctoral fellow, spectrum fitting program for routines which he obtained our assembled such a research group. from Herb Pickett, He used at the Jet Propulsion Laboratory, and made the necessary additions and modifications. These routines, known collectively SHAPE, are the basis of the spectrum fitting program. appendix first provides a theoretical basis for as This the routines in SHAPE by outlining the quantum mechanics of the asymmetric instructions rigid for rotor. SHAPE, as Following this well few as a are operating suggestions for 166 common modifications to this program. Beyond this, you are on your own. Quantum Mechanics of the Asymmetric Rigid Rotor The rare gas-halogen van der Waals molecules are not actually rigid rotors, but a reasonable description of the system may be made by assuming that the deviations from the equilibrium geometry are small . be valid for complexes of Ne and Ar as In these cases and rotation perturbation may be This assumption appears to We have quite been of the quantum rotors will follow . halog~ns mechanics accurately quite treating these molecules as rigid rotors discussion the the interaction of vibration treated theory. with 1 of by successful and thus a brief rigid asymmetric There are several very good references for the description of asymmetric tops, 2 3 ' so the following discussion will not be in complete detail . The van der Waals molecule ArC1 an asymmetric system of ArC1 by a 2 in a the and good example of excitation free jet expansion have been obtained the ArC1 ground is a The laser pump-probe technique. indicate that both top. 2 2 4 spectra of Analysis of the B+--X the spectra complex has a T-shaped geometry in excited states. The spectra can be reproduced using a rigid rotor Hamiltonian for both states. The ArC1 for 2 van der Waals molecule will this discussion . serv~ as an example 167 The geometry of Waals molecule is the symmetry then the three principal moments of inertia are Iz = J.L mr 2 I = JJ.MR X {1a) 2 {1b) = IX + Iz Iy where van der If we take the z axis as shown in Figure 1. axis, the ArC1 2 is J.Lm {1c) reduced reduced mass. The mass and is standard notation defines the Ne-Cl 2 Ia ~ Ib ~ Ic and correlation of a, b, and c with x, y and z depends up~n the values of the moments of inertia. If none of the three moments the of inertia asymmetric top. are equal then molecule The rotational constants, A, is an B and C, may be obtained from the moments of inertia by the expression h A = 4Z1I {2) a and analogous expressions the is molecule for B and C. quantified by an The asymmetry of asymmetry parameter expressed as 1(. where K. = 2A - B - B - C {3) C ranges from a value of -1 in the case of a prolate symmetric top {B = C) (A= B). The rotational ArCI = 0) and 2 X{u that ArC1 2 B(u to a value of +1 for constants and K. = 7) in Table I. an oblate top are given for can be seen It is a near prolate top in the ground state and is more asymmetric in the B state . 168 z R y Figure 1 . This is the axis system for the ArC1 2 van der Waals molecule in the body-fixed frame . The symmetry axis is handed taken to be system is used. the z axis and a right coordinate 169 Table I. Rotational Constants for ArC1 2 X(v = 0) B(v = 7) -1 0. 1500 em A 0.2461 em B 0.0479 em c 0.0410 em -1 0.0371 em -0.933 -0.784 IC. -1 0.0493 em -1 -1 -1 170 The issue next calculating the address to energy levels of is the an problem asymmetric of rotor. First select a body fixed axis system as shown in Figure 1, with the origin at the axes The quantum the center of mass of coinciding with mechanical the the molecule and principle Hamiltonian for axes the of inertia. rotation of a rigid asymmetric top is then HR = AJ; + BJ~ + C J~ where J The n is (4) the angular momentum about a energy are . levels obtained by particular axis. solution of the Schrodinger equation (5) where '41 JM are eigenvalues, the wave are the functions and E, rigid asymmetric the cor responding top energies. The rotational Hamiltonian is such that Equation (5) cannot be solved directly, so there are no analytical expressions for the wavefunctions. The asymmetric rotor wavefunctions may be linear expressed as a combination of symmetric rotor wavefunctions, (6) IJKM>. the symmetric rotor wavefunctions are IJKM> = 2J+1]1/2 [ 8I12 J DMK(~.a.x) and 5 J are the Wigner functions. DMK and (7) ~. 9, and x are t.he Euler (7) In both Equations (6) angles the describing rotation of the body fixed axes with respect to some set of 171 Substituting Equation (6) space fixed axes. into Equation (5), left-multiplying by <JK'MI and integrating we can see that the energy levels may be determined by solving the 2J+1 by 2J+1 secular determinant (8) This is the brute force where oK'K is the Kronecker delta. method to determine rotor, but the problem can be greatly simplified by taking advantage of the the energy symmetry levels of inherent in the asymmetric the rotational Hamiltonian. The Hamiltonian asymmetric rotor determined by describing has symmetry considering its ellipsoid of inertia belongs consists the of identity the rotation properties ellipsoid to the D element and 2 of of which a rigid can be inertia . The point group, which two-fold rotations, c a2 . c b2 and c c2 . about each of the three principal axes. The character table Table II. Ideally, the have wave functions with the same symmetry as and Be of the of the D 2 basis set which D 2 group . group This is is given used in should the species A, will simplify the Ba . entire problem because the only nonvanishing matrix elements would This result occurs because the symmetry species are orthogonal to each arise between states of the same symmetry . other and the Hamiltonian has A symmetry, thus the integral 172 Table II. Character Table of the D point group 2 Symmetry Species Symmetry Element E A 1 1 1 1 B a 1 1 -1 -1 Bb 1 -1 1 -1 B 1 -1 -1 1 c Table III. Submatrix K Jeven E+ e 0 A (ee} Ba (eo) E e 1 Ba (eo} A ( ee} 0+ 0 0 Bc (oe} Bb(oo} 0 0 1 Bb(oo} B c (oe) 173 Thus symmetry . the secular determinant factors into belong to four separate subdeterminants. The point symmetric group and basis set for rotor thus wave are an functions inappropriate choice the D00 for the Wang suggested an appropriate this problem. 6 linear combination of symmetric rotor wave functions, I JK?th> = I JKM> for K>O (9) for K=O, -r=O (10) where K is now non-negative. These linear combinations do belong to the D point group. 2 The four blocks are labeled E or 0, depending + also or upon the depending correlation of the four Even or Odd nature upon the value of of symmetry species of D 2 K, and The "Y . is given in Table III. The energy levels of the asymmetric top may be written as JK -1 K , where K_ 1 and K1 represent the K value in the 1 prolate and oblate top limits, respectively. K is no.t a quantum number, but this labeling is convenient because the symmetry state may be determined of the easily. value corresponds to the symmetry of the wave function with respect to a c2 rotation about the a inertial axis, since this is the symmetry axis in the prolate top limit. is odd, respect then the wave to the two-fold denoted by the label labeled "e." function is antisymmetric rotation about "o," Similarly K 1 while the the axis, symmetric corresponds to with which is species is the symmetry of 174 the wave axis, function while the with respect product of K_ to a rotation about with K 1 the c to a corresponds 1 By examination of the character rotation about the b axis. table of the n2 point group given in Table II, correlations may be made regarding the associated the nature symmetry species. appropriate submatrix and combinations of for appropriate K_ K 1 1 of the K_ K 1 1 labels and Table III lists the species for the top. The most symmetry the representation for prolate the oblate top will change the entries in this table. The elements in the next step is the calculation in each submatrix. right handed of The diagonal prolate top basis the individual matrix elements are given by the expression ( 11) while the off diagonal elements are expressed as <JKM~IHRIJK±2M~> = 1/4{B-C)[J(J+1)-K{K±1)] 1 / 2 X [J(J+1)-(K±1)(K±2)] 1 / 2 (12) Since we are working in the prolate top basis the K in the matrix element associated with expressions K in the is the limit K_ of 1 value the which prolate is top. The energy levels may be calculated from the equations The first which are given here. step is symmetry of the particular energy level, determinant subblock to be used to to determine the which defines the calculate The energy may be. calculated using Equations the energy. (11) and (12) 175 when the wave functions have been levels determinant J = 3, the of is a same 2x2 or there are 3 2x2 writ ten as If there are two or more shown in Equations {9) and {10). energy correctly symmetry, then the larger matrix. For example, secular .determinants and secular one for 1x1. This represents a great simplification from solving the 7x7 matrix which results if .we do not take advantage of the symmetry inherent in the Hamiltonian . The spectrum of the asymmetric rotor is determined not only by the energy levels of the ground and excited states, but is also governed by the selection rules which is transitions are allowed. non-zero. integral and ~ ~i then and ~f the transition allowed. In this are the initial and final wave functions the transtion. diatomic molecule Cl is the axis for 2 The transition moment for lies along the Cl-Cl bond axis. the transition moment in ArC1 since it is the b inertial axis, character <AIBbiBb> totally and table. Thus <B a IBbiB c > symmetric since ee - AK -1 00 =± 1 with AJ = o. ±1. allowed these This as well and - and eo and AK 1 = ± 1 transitions products The A representation. The 2 the transforms as Bb in the ~ the are written as or is is the transition dipole which carries the oscillator strength for D 2 that determine give selection are the rules oe line frequencies of the transitions 176 may be used simulated to assign by the spectrum or the spectrum may be calculating the intensities and convoluting the transitions with the laser and homogeneous linewidths. In summary, there are a number of steps which must be performed to generate the spectrum of an asymmetric top. structure must be assumed and the rotational calculated for the ground and excited states. of each energy elements for level each is determined, subdeterminant submatrix is diagonalized. are constants The symmetry then the matrix calculated and The energy A each levels are ordered according to the J and K labels and the allowed transitions are determined. spectrum The intensities are is generated by convoluting calculated the and individual the lines with a Voigt profile. SHAPE The routines which make up the SHAPE spectrum fitting package are currently found in the directories of USR4:[11742.210165.SHAPE] on the PITTVMS VAX cluster. The subdirectories and [ . . . SPECOPT], [ .. . V20PT]. [ ... SPLBOPT] [ ... SLIB] contain the source code for the respective object libraries which are necessary making an executable file . At to you make an executable because we do interactively. file not have The current to link to the present must sufficient file SHAPE.OBJ time, submit memory which will a to in in order batch job link SHAPE perform this 177 task is LINK.COM. and the important line is $LINK SHAPE, SPECOPT/LIB,V20PT/LIB,SPLBOPT/LIB,LIB/LIB,PRG:DISPLA/LIB. The order in the library list way in which the linking routine performs subroutines. . We do have library not PRG:DISPLA.OLB, is critical any which is because of its the search for source code for the supported by the VAX SHAPE. two system. In addition to the executable version of files are necessary for fitting spectra. The first file the which contains atomic masses, as initial format frequencies, guesses of this SHAPE.DOC and der Waals information for file is parameters outlined different complexes. Hamiltonian, fitting regions, the is about when Samples in to fitting of etc., be the is the as well fit. The reference file diatomics each are or van given in DIATSMP.DAT and VDWSMP . DAT in the [ .. SHAPE] directory . The second file is file program a parameters and the this given file format of are this which is which necessary to contains the experimental fit. Samples spectrum you want in file to DIATSMP. SPC and is determined by run the VDWSMP.SPC. the SHAPE of The subroutine RSPCT.FOR, which reads the spectrum from the ___ .SPC file. The is on machine data obtained program written the free jet in PC-FORTH by Colin Western. been a number of modifications using a There have to the original PC program, most recently by Joe Cline to allow use of two dye lasers, 178 one doubled and the other with an angle-tuned etalon. __ .SPC file, generated can be transferred from by the data collection the experimental FORTH emulator files The routines, to using the whi~h is transferred to the VAX contains only the number of data points, program entitled VAX. the VAX the beginning and ending wavelengths and data . A file header example which fits the current modify the header with the beginning The and ending can be constructed RSPCT number wavelengths and the from an existing format. of f i 1e data the You must points, the first and last points, e.g . , 0, 299 near the end of the __ .SPC file. The program is ready to be run once __ .DAT files are in the correct form. the __ .SPC and On the VAX system, the files must be assigned to FORTRAN logical unit numbers before program can be run. using The first assignments are made the A.COM and AP.COM command files which are [ .. COM] subdirectory. The following are the in the necessary commands. $ assign _ plotdev ( _ is the graphics output device number in the graphics routine GSTART . $ PC defines the PC running one of the FORTH emulator routines.) $ a _.spc 4 (assigns __ .SPC to FOR004) $ ap - - (assigns __ . DAT to FOR009 and various output devices as necessary.) $ rshape (RUN USR4:[11742.210165 . SHAPE]SHAPE) 179 The first thing is which a that SHAPE linewidth for asks for as input artificially is sigma. broadening the experimental spectrum to help obtain an intial fit. If you do <cr>. not The want to use spectrum is points and point read feature from the wavelength is displayed. displayed is this FOR004 (em -1 ) return, then the number the maximum of rotational the entire spectrum screen, after which temperature, the natural the scaling the factor. the structure. distances these or leave the typing in parameters rotational constants, (cr>. initially, intended new be be either depending to vary. of that changed to the first pass . a for bond on · which of Any parameter may unchanged, parameter temperature. rotational must for value the six parameters can parameters These are the band shift, the appropriate number of intermediate The than 1 . . typing the origin and These the program is be changed by band twelve linewidth, experimental (laser and Doppler) linewidth, a intensity (cr) parameters which may be varied are printed out. the of Following a the on simply hit On subsequent and to then followed which positive commas. by / is negative value, greater iterations the temperature may be set less than 1. The second set of screen controls the fitting of parameters by program. The value the number parameters first numbers is which is displayed of vary when fitting the experimental spectrum. the on the SHAPE to The remaining 180 spaces are For the example, natural parameters to float linewidth the and <c r >. 3, 1 . 2, 6/ listed which are the The rotational band final be varied. temperature, origin three to one numbers would which the input can be changed are the accuracy required in fitting the spectrum, the initial step size to be used when varying the parameters and the maximum step. The fitting process begins by fitting eye, varying offset, the band origin parameter {4}. used to vary the as many The times as rotational obtain the because SHAPE necessary sum is of employing fitting. some to fitting obtain a be squares to and routine may to fit the vary satisfactory fit . varied manually of deviations, this the parameter to widely The entire process is an iterative manual fitting as computer The program is terminated by entering a negative rotational temperature. This SHAPE is to and experimental parameters should the unwi 11 ing from its initial value. one, experimental The fitting process may be repeated temperature best the the the SHAPE structural experimental spectrum. or After calculated spectra overlap, be {6} the spectrum by essential as well is the correct way to stop close the files created when using SHAPE to generate a plot file or a data file. There are several problems which occur can be easily solved. The header between the in FOR004 and RSPCT, file first is a commonly difference the in that the routine 181 The two must be compatible and which reads this file. is simply a matter of editing the ___ .SPC file that is the header has that the the correct format. experimental spectrum do not overlap spectrum is being frequency region. program to stop. spectrum and the calculated the calculated all, i.e.' generated over an This fatal a to be sure The next problem at is entirely error and (6), (4), offset, is near the experimental spectrum as printed at the Finally, rotational must the the This may be remedied easily by checking the calculated spectrum, the different causes that the band origin of minus it temperature paramet~r maximum of the the run. greater than start of be one degree, and yes that means it must be positive. There are the several SHAPE program. The _____ .SPC file format to make simply the with the parameters which are is the done by RSPCT to be READ header statement of currently FIRSTP, the The title is not essential, This of ____ .SPC used SPCT. object if is convenient. ENDSPC, the modify RSPCT more START, running SHAPE. to the need the compatible first to is changed and someone feels process modifying modifications which can be made are file. TITLE, The SPCTSI, LASTP and the spectrum is read into but is printed out when If a new version of RSPCT is prepared then module must be placed SPECOPT.OLB for linking with SHAPE. in the object library 182 Another modification which has been made fitting the spectra by varying the rather than the structural parameters. is rotational to allow constants This new version of SHAPE is entitled ROTCON.FOR and the source code is in the [ .. SHAPE] directory. You may peruse the changes which were necessary . modification. but I being quite complex, that program to see This was a fairly simple think that any other changes may end up so I wish you the best. Finally, the source code for all of the subroutines is somewhere in the laboratory, SHAPE. compiled in a notebook entitled, oddly enough, 183 References 1. D.D. Evard, F. Thommen, and K . C. Janda, J . Chern. Phys . 84 , 3630 {1986). 2. W. Gordy , and R.L. Cook, Microwave Molecular Spectra , 3rd Ed. {John Wiley & Sons, Inc . , New York , 1984). 3. R.N. Zare, Angular Momentum in Quantum Mechanics {manuscript in preparation) . 4. D. D: Evard, J.I. Cline, N. Sivakumar, and K.C . Janda, manuscript in preparation. 5. 6. E.P . Wigner, York, 1959). Group Theory {Academic Press, S . C. Wang , Phys. Rev. 34, 243 {1929). Inc., New