Infrared Photodissociation of Van der Waals Molecules Citation Casassa, Michael Paul (1984) Infrared Photodissociation of Van der Waals Molecules. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/n43s-1339. https://resolver.caltech.edu/CaltechTHESIS:10262018-123200794 Abstract Infrared photodissociation of van der Waals molecules is investigated using low power cw infrared lasers. Information gained concerns the dynamics of vibrational predissociation and the van der Waals interactions. Clusters formed in supersonic molecular beams are irradiated for approximately 0.5 msec and the fraction of clusters remaining intact is measured as a function of laser wavelength and power. Detailed homogeneous and inhomogeneous line shape models are presented and used to analyze the results. Effects such as fluence broadening and orientational inhomogeneity are described. Van der Waals molecules studied include dimeric clusters of ethylene with rare gases, hydrogen halides and non-hydrogen bonding polyatomic molecules. Homogeneous widths of clusters excited near the ν 7 frequency of free ethylene correspond to lifetimes ranging from 0. 44 psec for (C 2 H 4 ) 2 to greater than 10 psec for Ne•C 2 H 4 . These are attributed to vibrational predissociation constrained by conservation of angular momentum. Other conceivable broadening mechanisms are discussed. Spectra obtained by exciting the ν 7 mode in different types of ethylene clusters are quite dissimilar. Lineshape analysis indicates that the ν 7 transition in (C 2 H 4 ) 2 occurs as a hybrid band. The same transition in (C 2 H 4 ·HF occurs as a perpendicular band. The rare gas-ethylene clusters are less rigid than the others and excitation of hindered internal rotation of C 2 H 4 accompanies the ν 7 absorption. All of the ethylene clusters exhibit blue shifts and intensity enhancement, as compared to ν 7 absorption by free ethylene, which are attributed largely to electrostatic interactions. 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): Beauchamp, Jesse L. Thesis Committee: Beauchamp, Jesse L. (chair) Janda, Kenneth C. Kuppermann, Aron Samson, Sten Otto Defense Date: 18 November 1983 Funders: Funding Agency Grant Number Caltech UNSPECIFIED NSF UNSPECIFIED Shell Companies Foundation UNSPECIFIED Procter and Gamble UNSPECIFIED Atlantic Richfield Foundation UNSPECIFIED ACS UNSPECIFIED Department of Energy (DOE) UNSPECIFIED Record Number: CaltechTHESIS:10262018-123200794 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10262018-123200794 DOI: 10.7907/n43s-1339 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 11249 Collection: CaltechTHESIS Deposited By: INVALID USER Deposited On: 26 Oct 2018 21:05 Last Modified: 31 Oct 2025 21:42 Thesis Files Preview PDF - Final Version See Usage Policy. 72MB Repository Staff Only: item control page

INFRARED PHOTODISSOCIATION OF VAN DER WAALS MOLECULES Thesis by Michael Paul Casassa In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1984 (Submitted November 18. 1983)_ ii ACKNOWLEDGEMENTS It is a pleasure to thank Ken Janda for his guidance during the past five years. The many successes described in this thesis are largely attributable to his help and encouragernent. I would also like to thank Ahmed Zewail for his help in understanding line broadening mechanisms which are central to the interpretation of our experiments. I thank Jack Beauchamp for the loan of both his co laser, without 2 which there would be no experiments, and his studentr David David Bornse. provided the boost which got me and this project started, and together we relished the first ethylene dirner success. Since then I have enjoyed working closely with Francis Celii and Colin Western, both of whom helped to accomplish the work described in this thesis. Many fellow graduate students have given up valuable time to help with various problems. Among them are Sam Batchelder, David Brinza, Sally Hair, Bill Lambert and Barry Swartz. Members of the technical staff who have been excep- tionally helpful are Dee Barr, Sr. Bill Schuelke Jr. Torn Dunn and Bill Schuelke deserves credit for building our Thanks also go to Gwen Anastasi molecular beam apparatus. for typing this thesis. Organizations research Procter DOE. are & who have helped support Caltech, NSF, Shell Companies Gamble, Atlantic Richfield me and this Foundation, Foundation, ACS and iii Finally, my heartfelt thanks and love to my wife, Joanne, and to many close friends who have enriched my life. iv ABSTRACT Infrared photodissociation of van der Waals molecules is investigated using low power cw infrared lasers. mat ion gained concerns the dynamics of Infor- vibrational predissociation and the van der Waals interactions. Clusters formed in supersonic approximately 0.5 remaining intact wavelength and molecular msec is beams and the measured as power. are irradiated fraction a of clusters function Detailed of laser homogeneous and inhomogeneous 1 ine shape models are presented and used analyze the results. for to Effects such as fluence broadening and orientational inhomogeneity are described. Van der Waals molecules studied clusters of ethylene with rare gases, non-hydrogen widths bonding polyatomic of clusters excited near include hydrogen halides and molecules. the dimeric Homogeneous v frequency of free 7 ethylene correspond to lifetimes ranging from 0. 44 psec for <c 2 H4 ) 2 to greater than 10 psec for Ne • c 2 H4 • attributed conservation to vibrational of angular predissociation momentum. These are constrained Other by conceivable broadening mechanisms are discussed. Spectra obtained by exciting the v 7 mode in different types of ethylene clusters are quite dissimilar. Lineshape transition in <C H > occurs 2 4 2 as a hybrid band. The same transition in c H ·HF occurs as 2 4 a perpendicular band. The rare gas-ethylene clusters are analysis indicates that the v 7 v less rigid than the internal rotation of All of the ethylene others and excitation c 2 H4 accompanies clusters exhibit intensity enhancement, as compared to v ethylene, which interactions. are attributed the 7 largely v 7 blue of hindered absorption. shifts and absorption by free to electrostatic vi TABLE OF CONTENTS CHAPTER 1. Introduction . 1 CHAPTER 2. Infrared Photodissociation Spectra of Clusters of c H with c H , c F , Ar, Kr 2 4 2 4 2 4 and Ne 7 Isotopic Selectivity in van der Waals Molecule Photodissociation. Infrared Photolysis of Ar · BC1 _ 62 Homogeneous Photodissociation and Photodesorption Lineshapes 77 CHAPTER 3. 3 CHAPTER 4. CHAPTER 5. Infrared Photodissociation of HydrogenBonded Clusters: c H ·HF and 2 4 C H ·HC1 . 2 4 CHAPTER 6. CHAPTER ?. CHAPTER 8. CHAPTER 9. Inhomogeneity in the Infrared Photodissociation Spectra of (C H ) , c H ·HF 2 4 2 2 4 and c H ·Hcl 2 4 113 138 Infrared Photodissociation of the Hindered Internal Rotors Ne·C H and Ar·C H 2 4 2 4 170 Decay Mechanisms in Vibrationally Excited van der Waals Molecules 200 Summary 216 1 Chapter 1 Introduction 2 The quintessential photodissociation Klemperer van der waals experiment was originally 1974. 1 in He proposed molecule that infrared described infrared by active constituents of weakly bound clusters formed in molecular beams using narrow could be vibrationally The quantum of lasers. larger than the van excited vibration der Waals would, bond in band general, energy. be Subsequent intramolecular vibrational energy redistribution would lead to fragmentation of the complex which could be detected as beam loss by using a mass spectrometer. The information gained from such experiments is important in two major areas of chemical physics. First, since the dynamics of the _initially excited state are reflected in spectral linewidths, direction of discerned. factors vibrational which energy control flow the in molecules the the success of laser existence butions. be The of metastable second area information, On the other selective chemistry depends on vibrational energy is understanding the weak interactions between molecules. ical can and Fast randomization of this energy is ·a postulate of statistical unimolecular reaction theories. hand, rate photodissociation distri- nature of In addition to dynamspectra contain, in principle, all of the types of information found in traditiona! spectroscopies. Structure, frequencies and intens- ities observed are all a consequence of the intramolecular potential. 3 Based on an empirical half-collision model, Klemperer estimated that 1 psec. At HF · · ·HF( v =1) the same should time, dissociate vibrational within 50 predissociation theories 2 were unable to account for the widths of diffuse bands in hydrogen-bonded liquids. Soon afterward, Child 3 and Ewing 4 calculated lifetimes on the order of seconds for some clusters. Theoretical work of Beswick and Jortner 5 was successful accounting in vibronically excited Hei 2 for the widths of levels of observed by Levy and coworkers, but (at the same time) their theory also predicted very long lifetimes for other clusters. Before 1979, two direct . observations of infrared photodissociation of van der Waals molecules had been reported. clusters inhomogeneous, precluded Gentry al. 6 by Gough et and and analysis. The first was a study of N o 2 These spectra were evidently uncertainty the in cluster size The second experiment was performed by coworkers 7 on ethylene dimer. They observed intense photodissociation over a range of nearly 200 cm- 1 , suggesting an incredibly fast decay rate. The incongruity of the results listed above were the motivation for the work presented in this thesis. The chapters, which are arranged roughly in chronological order, reflect an effort to vary the intramolecular potential to see how it influences the photodissociation spectrum. are interspersed which became with sections on the lineshape increasingly detailed as measurements They analysis became 4 Using very detailed lineshape analysis, more precise. we have discovered that it is possible to learn a great deal, even from spectra which appear as broad featureless blobs. Chapter 2 contains our original results, including ethylene dimer. stration of infrared photodissociation the facility and of ethylene cluster Chapter 3 is a demonisotopic weakly selectivity bound of complexes. Chapter 4 describes the homogeneous lineshape analysis which reconci1es the dimer width originally observed by Hoffbauer et a1. 7 and the 12 cm-l width observed in our laboratory. Chapter 4 also includes an application of a similar line- shape laser model to test the feasibility desorption experiment analogous photodissociation. to van of a induced der Waals molecule Chapter 5 contains our measurements on c 2 H4 • HF and c 2 H4 • HCl which exhibit significantly narrower widths than <C H > • 2 4 2 The observed blue shifts and intensity enhancement _of the cluster-bound c H vibration, as compared 2 4 to free c H , are interpreted using an electrostatic inter2 4 action model. Since the hydrogen-bound clusters' spectra are narrow, it is possible affects the band profile. Chapter 6 where presented. With an that inhomogeneous broadening This possibility is addressed in inhomogeneous this model, lineshape model is seemingly disparate measure- ments of the <c H > width over a wide range of laser powers 2 4 2 have been quantitatively reconciled. Spectra of Ne·C H and 2 4 Ar • c H are reported in Chapter 7. These are rich in 2 4 structure and Ne·C H has the narrowest lines yet observed 2 4 5 in ethylene cluster spectra. The structure hindered internal rotation by the ethylene. is due to Evidently the other clusters mentioned above are rigid when compared to Ne·c H and Ar·c H • Comparison of results obtained for all 2 4 2 4 of the ethylene clusters indicates that widths are due to vibrational predissociation constrained by angular momentum conservation. Chapter 8 discusses line broadening mechan- isms and their importance in van der Waals molecule photodissociation spectra. These considerations are crucial to interpretation of our experiments since linewidths only give a decay r~te, while the decay mechanism must be inferred. Chapter 9 summarizes highlights of the previous chapters. 6 REFERENCES 1. W. Klemperer, Ber. Bunsenges. Phys. Chern. ~, 128 (1974). 2. c. A. Coulson and G. N. Robertson, Proc. R. Soc. London A342, 289 (1975). ~, 307 4. G. Ewing, Chern. Phys. 29, 253 (1978). 5. J. A. Beswick and J. Jortner, J. Chern. Phys. ~, 3. M. S. Child, Faraday Discuss. Chern. Soc. (1977). 512 (1978). 6. T . . E. Gough, R. E. Miller and G. Scoles, J. Chern. Phys. 69, 1588 (1978). 7. M. A. Hoffbauer, W. R. Gentry and C. F. Giese, in Laser-Induced Processes in Molecules, edited by K. L. Kempa and S. D. Smith (Springer-Verlag, Berlin, Heidelberg, New York, 1979). 7 Chapter 2 Infrared Photodissociation Spectra of Clusters of c2 a 4 with c2 a 4 , c 2 F 4 , Ar, Kr and Ne. 8 Infrared Photodissociation of van der Waals Molecules Containing Ethylene Mike P. Casassa,a David S. Bomse,b and Kenneth C. Janda Arthur Amos Noyes Laboratory of Chemical Physics,c California Institute of Technology Pasadena, California 91125 aNational Science Foundation Predoctoral Fellow. b Josep h'1ne d e Karman Fe 11 ow an d Monsanto Fe 11 ow. cc ontr1. b ut1on . No. 6351 . 9 Abstract Vibrational region of the predissociation lineshapes in ethylene spectrum are measured Waals molecules of ethylene bound to Ne, Ar, c2 F 4 • of v the for van 7 der c 2 H4 and Kr, The predissociative rate is very fast for this group The molecules. . lifetimes of vibrationally 0. 89xl0 -12 excited state (c H ) and 2 4 2 That the observed lineshapes are homogeneous is is c 2 H4 ·c 2 F 4 . range 0. 44 to seconds for demonstrated by the fact that a low-power, narrow frequency bandwidth laser initial ensemble transition ethylene can dissociate of ethylene probability. subunits ethylene subunits. for is a large clusters. proportional clusters fraction to containing These observations are The of the observed the number three or of fewer interpreted in terms of intramolecular energy flow directly from ethylene v7 to ·the weak van der Waals modes of motion. 10 I. INTRODUCTION Van systems der for Waals molecules studying present intramolecular relatively simple vibrational energy Klemperer 1 originally speculated that vibrationally flow. excited (HF) 2 an empirical thereafter, lif.etimes should dissociate within 5xlo- 11 sec based on half-collision V-T transfer model. using Fermi's Golden many orders Rule, of magnitude Meanwhile, . theoretical models 3 Child 2 longer Shortly calculated for Ar · HCl. were unable to account for diffuse bands in infrared absorption spectra of gas phase complexes. 4 hydrogen-bonded These disparate themes have been reechoed for the most part in considerable subsequent experimental 5-18 and theoretical 19-30 work to understand energy transfer rates in weakly bound molecules. a1. 17 found efficient In one such study Gentry et dissociation of ethylene clusters with a pulsed co operating anywhere suggested the between possibility ciation process. power , cw co of Subsequent 900 an and 1100 laser 2 cm-l This exceedingly fast dis so- . 31 exper1ments . h w1t a low- laser showed that the vibrational process is 2 indeed fast, but at least an order of magnitude slower than suggested by the pulsed laser experiments. In this the cw 950 cm-l co 2 To paper we present a complete description of laser of dissociation provide additional ethylene insight we dimer at have also studied lineshapes for 950 cm-l vibrational predissociation 11 c 2 F 4 and l~rger ethylene of ethylene bound to Ne, Ar, Kr, clusters. Rates .for this set of molecules are all in the range of 3xl0 12 sec -1 to 10 12 sec -1 indicating that energy transfer out of the initially excited v 7 mode of ethylene controls the order of magnitude of the rate. The quali- tative partner variation of rate versus bonding is reasonable with regard to the theories of Beswick 19 - 23 and . 24-26 Ew~ng. Unfortunately, this class of molecule is much too complicated to yield to a detailed application of theory. II. EXPERIMENTAL sonic Van der Waals molecules were synthesized in super- expansions molecular beams. which were skimmed to form Molecular beam composition was determined by mass spectroscopy and controlled by varying the composition and pressure of the expanding gas cooling of internal degrees massive condensation containing a constituents few in was helium of Nearly complete freedom was avoided percent of a mixture. the carrier ensured, and by expanding mixtures van der Waals molecule gas. Infrared laser irradiation of the molecular beam using a low-power cw co 2 laser resulted in photodissociation of a large fraction of the van der laser-induced Waals complexes. change in In these experiments the molecular beam composition was monitored as a function of laser wavelength and power. 12 A. Apparatus A schematic of the molecular beam instrument is shown in Figure 1. Four levels of pumping are used so that low background pressures required for van der Waals molecule spectroscopy despite the and high mass spectrometry throughput of the are maintained, supersonic nozzle. Quartz nozzle sources were constructed by sealing one end of a quartz tube (0.8 em OD, 0.2 em ID) and then gently grinding until a pinhole of the desired size was formed. Flat nickel utility pinholes mounted on the end of a stainless steel pipe were also used as nozzle sources. The metal nozzles generally provided more van der Waals molecule intensity but were less durable and dependable than the quartz nozzles. The source chamber (at the far left in Figure 1) is pumped by an unbaffled 4-inch Pennwalt Stokes booster pump backed by a Leybold-Heraeous El50 mechanical pump. Throughput of this configuration is 2800 torr cm 3 sec-l at 10- 2 Torr. a skimmer diameter. The first aperture downstream of the nozzle is (Beam Dynamics Model 2) Optimum nozzle-skimmer distance Nozzle position stream is 'Vl. 0 em. is completely adjustable while all down- apertures are Typically, gases at through 35- l.l m pinhole a with a 0.1-cm entrance fixed in optical alignment. 5 to 10 a tm and 300 o K are - expanded while maintaining a background 13 MOLECULAR BEAM SPECTROMETER (TOP VIEW) :fSe window - I l ..J r'l"'l"" t-~ .. I= ,. ninlet -o-: gas == skimme~ mass spectrometer D\__,lo- /collimators " " - -F=- -1- - - - ~------- -- ---~ nozzle/ laser beam ZnSe window lanizer '" FIGURE 1. &.. Schematic diagram of the molecular beam spectrometer. See Experimental Section for details. 14 pressure of the order of 10 -3 Torr in the source chamber. The molecular beam emerging from the skimmer (moving left to right in Figure 1) traverses a 4.8-cm region of differentia! pumping before encountering a cone-shaped collimator with an entrance diameter of 0.2 em. Differential pumping is supplied by an unbaffled 6-inch Varian VHS-6 diffusion pump which maintains a pressure in this Torr during operation. Passing through 'Vl0- 5 region of the first colli- mator, the molecular beam enters the largest vacuum chamber and travels 40.5 em further to a second collimator. Pressure in the main chamber is maintained at 10- 6 Torr by an Edwards 160/700 diffusion pump having an internal watercooled baffle. After the second collimator, the molecular beam enters a fourth vacuum chamber (far right in Figure 1) which houses an Extranuclear quadrupole mass spectrometer equipped with a crossed-beam electron channeltron particle chamber pumped is equipped with multipler. by an The Edwards internal water and The second collimator, ionizer and mass spectrometer CR-760 diffusion nitrogen-cooled which provide ambient pressures of 'Vl0iments. impact 8 with a pump baffles Torr during exper0 . 2 4 em aperture, defines the diameter of the molecular beam detected by the mass spectrometer. to the Total distance from the nozzle source ionizer of the mass spectrometer is 60 em spending to a molecular msec. flight time of the order correof 0. 5 15 An Apollo Laser Model SSOA grating-tuned cw co was used in these estimated by infrared experiments. the manufacturer photodissociation The laser 2 laser linewidth to be rv 50 MHz. studies, the unfocused is For most laser beam was directed into the apparatus through a ZnSe window (supplied by II-VI Incorporated) indicated at the far right in Figure colinear 1. in The this laser beam and molecular configuration and irradiation species in the molecular beam was maximized. iment the unfocused laser beam was beam were time of In one exper- directed into the apparatus through the auxiliary window (Figure 1, top) and crossed the molecular beam at right angles before being absorbed by a graphite beam stop. Laser beam quality Engineering Model was 22A thermal monitored with an imaging plate. Optical When opti- mized (by visual inspection on the imaging plate), the beam profile was nearly Gaussian (FWHM = 6 mm) as determined by measuring the power transmitted through pinhole translated across the beam. variations in mode a However, reproducible structure were observed wavelength was changed. As 1-mm diameter dec.r ibed above, as the laser the detected molecular beamis 0.24 em in diameter and thus only interacts with the central portion of the laser beam. Measurements of the infrared beam intensity within the largest chamber of the apparatus indicated that 4 to 7% of the total incident laser power was transmitted through the mass spectrometer chamber apertures. This attenuation 16 was only partly due transmitted power apertures the in to losses at loss was molecular op~ical mainly surfaces. due to beam apparatus The the and small was thus extremely sensitive to the transverse mode structure of the laser beam. Irradiances were calculated using calibration constants obtained for each set of photodissociation experiments. Power Precision Corporation meter. measurements Model were RkP-345 made with a Laser pyroelectric radio- Temporal fluctuations in laser power were less than ±5% during an experiment. Infrared laser wavelengths were measured with Engineering an Optical Model 16A spectrum analyzer. For infrared photodissociation experiments performed with colinear laser and molecular beams, the laser beam was mechanically chopped (usually 100-150 Hz). of a the molecular given peak in measured both in radiation using a the presence two-channel The intensity beam mass spectrum was and absence boxcar. of infrared Direct electronic division of the two values gave the fractional change in mass spectrometer diation. signal intensity due laser irra- Fine adjustments in laser beam position were made to maximize extent of photodissociation. ment to performed with the crossed-beam For the experiarrangement, the infrared beam was chopped at 1000 Hz, and resulting changes in mass spectrometer signal were measured using a lock-in amplifier. 17 Infrared measuring tuning photodissociation attenuation co 2 the of laser constant laser power. mass from spectra were spectrometer line to line obtained signals and by while maintaining Beam quality and power were optimized with each change of wavelengths by adjusting laser optics. Laser power was then brought to some standard adjusting the discharge current in the laser. value by Most spectra were recorded using 5.0 W total laser power corresponding to irradiances of 4. 0 to 6. 7 W em - 2 mode structure) transmitted to (depending on transverse the molecular beam. The dependence of infrared photodissociation intensity on laser power at fixed laser frequency was also measured. 2 Irradiance was varied in the range of 0 to 11 W cm- in the power dependence experiments. B. Characterization of Detected Clusters As indicated above and in Figure 1, molecular beams using characterized were a mass quadrupole spectrometer equipped with an electron impact ionizer. A typical molecular beam mass spectrum is shown in Figure 2. The crossed-beam ionizer was set to deliver 2.5 rnA electron current at 50 fragmentation eV of electron kinetic van Waals der energy. molecules Considerable resulted upon electron impact ionization under these conditions. Careful analysis to of unambiguous mass spectra was needed in order identification of neutral cluster make molecules 18 Ar+ 2 ~ X I --H- X 100 -H-- X 500 - - - - - t 20 I I 40 60 80 ION MASS FIGURE 2. Molecular beam mass spectrum indicating formation of ethylene clusters. Note changes in detector sensitivity. Molecular beam formed by expanding 7.7 atm of a mixture of c 2 H4, Ar, and He (0.8:10:90). Nozzle diameter is 50 ~m. 19 present in the molecular beam. Figure 3 shows a plot of mass as spectrum ion intensities a function of source pressure for a c H -Ar-He (ratio 0.75:20:80) mixture. 2 4 Figure 3 both scales are logarithmic. produced by ionization considered. the parent of c H 2 4 ion of argon dimer, next group of is ions detected as Data points for (Figure a +, ethylene Ar Ar + at m/e 2 3) with slopes The dimer parent ion a 3 5 2.6 ion (m/e not formed from ethylene dimer. with reported is described The + and m/e _ 55 <C H + ). 4 7 and 2.3 notionally 56) shows identified a higher . pa~r. order ( c H ) + 1s . 2 4 2 + the 32 where principal those shown in Figure 3 were obtained mixtures above as This result is consistent + that Data such as gas the increased ion-molecule reactions of ethylene, observed all are As > and C4H7 are C3H5 . products of the react1on o f c H + with c H . 2 4 2 4 for 80. the pressure is pressure depen d ence t h an t h e c H +; c H + 3 5 4 7 it monomers these two species lie on nearly parallel respectively. 4 7 or Ar +c H is observed. 2 4 increased, further are the two at m/e 41 <c c Only those ions not At low pressures the most abundant species is backing pressure lines In used. determined Analysis identity similar of to that molecular beam constituents and optimum source conditions for production of a desired van der Waals cluster. Except as noted, in studies molecules the gas of selected van der Waals mixtures and pressure were adjusted so that large clusters were not present and interfering cluster concentrations 20 Ar 2+ 6 1000 • ArC2H4+ 0 C3Hs+ • C4H7+ 0 C4Hs+ 100 > E r ten z w t- z 10 C2 H4 :Ar: He = 7.5:200: 800 35fLm NOZZLE 25 50 SOURCE PRESSURE FIGURE 3. 75 100 (PSI) Variation of van der Waals molecules mass spectral intensity with source pressure. Both scales are logarithmic. Data for Ar!, ArC2H4+, C3H 5 +, C4H7+ and c 4 H8 + are included. Gas m1xture is 0.75% c H , 20% Ar and 80% He. 2 4 21 Complications occur if different van der were minimized. Waala clusters present in the molecular beam contribute to For example, ArC H + and fragments 2 4 the same mass signal. of pure ethylene clusters <c H +> 5 8 contributed to the mass spectrum signal intensity at m/e 68 observed in molecular beams formed from He-Ar-c H mixtures. 2 4 The intensity of the m/e 68 signals observed in molecular beams formed by expansion of generally about fragments. pure ethylene 10% of and the He-c H 2 4 intensity m/e was 69 Accordingly, conditions employed in the study of Ar · c H were such that the m/e 69 2 4 than 2% of the m/e 68 signal. were so adjusted intensity was less A similar situation arose in In this case, the expansion condi- the study of Kr-c H • 2 4 tions of mixtures that ratios of signals corresponding to isotopic Kr·C H van der Waals molecules 2 4 were identical occurring Kr to the relative isotopes. abundance of naturally These considerations ensure that the Krc H + , ArC H + and NeC H + signals measured reflect 2 4 2 4 2 4 behavior of species containing only one ethylene molecule. Such a determination with respect to the number of rare-gas atoms present is more difficult. Recent work, presented in Chapter data 7, indicates and that presumably the for reported here are to due for photo- dissociation of clusters which contain at least two noble gas atoms. The problem of maximizing production of mixed bimolecular clusters and cooling their internal degrees of 22 freedom while minimizing other cluster concentrations is It has proved usefu1 33 to think somewhat of an art form. in terms of a kinetic scheme such as: Ar + Ar + He - Ar 2 + He + c H Ar·C 2 H4 + Ar 2 4 2 Ar·C H + c H --- (C 2 H4 ) 2 + Ar 2 4 2 4 Ar Insofar as this picture is correct, important because the He carrier gas is it can provide cooling collisions that only rarely produce clusters containing He. In a fluor- escence complexes excitation study of van der Waals of tetrazine and noble gases, addition of a few percent argon to helium inhibited carrier gas formation containing of helium a trace of tetrazine complexes and only Ar complexes were observed. 34 The role of Ar in the expansion is seed reaction for cluster formation, the condensation process. to provide the in effect catalyzing Ethylene-containing clusters are formed by exchange reactions with Ar . It is empirically 2 observed that when Ar is not in the mixture, the formation of ethylene dimer raising the is source inhibited. pressure If this or the is overcome by concentration of ethylene in the expansion mixture, large ethylene clusters are produced before the dimer experiences enough collisions to be rotationally cooled. It is especially important to 23 optimize source parameters in van der Waals dissociation experiments because individual states are not resolved in the spectroscopy. C. Molecular Beam Velocities knowledge A of molecular beam velocity and hence the period of time molecules are irradiated is necessary for interpretation of photodissociation intensities. Velocities model, were since our calculated apparatus using ·a supersonic is equipped not expansion to directly molecular beam velocity distributions. measure We assume that the molecules in the beam achieve the terminal velo. c~ty o f t he . expans~on 35 . g~ven by 1 = (2C p T s /M) ~ where C p the (1) is the heat capacity of the expanding gas, T source temperature, and M is ' the molecular s is weight. Since expansions of gas mixtures were used in these experiments, the molecular weight is replaced by an mass: M e = 1:i m.F. 1 1 ( 2) effective 24 F. ~ is the mole fraction and m. is the mass of a component ~ of the expansion mixture. eq. (1) Similarly, the heat capacity in is replaced by an effective heat capacity: ( 3) (3), k is Boltzmann's constant and N. In eq. ~ is the number of relevant degrees of freedom in an expansion component. N. ~ includes only translational freedom since vibrational and rotational degrees degrees of freedom are of not expected to participate strongly · in the cooling process. The heat of formation of van der Waals molecules is neglected in this analysis, since only a small fraction of molecules are allowed to condense. Also, the high pressure expansion conditions will minimize the gas a toms and van der Waals slip molecules. between This rare velocity analysis is borne out in velocity measurements of Janda et al. 36 Irradiation times were determined from the 60-cm flight distance and calculated velocities. III. RESULTS Infrared photodissociation ethylene-containing van der was Waals observed molecules for all studied. Identities of the clusters along with ion fragments monitored and calculated irradiation times are listed in Table I. Also tabulated are gas mixtures and source conditions TABLE I. Experimental Conditions for Production of Ethylene-Containing Clusters in Molecular Beams. Nozzle Diam. ( m) Pressure (psi) Irradiation Ti.Ire Ion (ms) Detected -- Cluster Gas Mixture (C2H4) 2 0.7% C H4 + 20% Ar + 80% He 35 51.5 0.57 C3H5 (C2H4) 3 0.7% c H4 + 20% Ar + 80% He 2 35 51.5 0.57 C4H8 (C2H4) 5 11% c H + 39% Ar + 50% He 2 4 25 290.0 0.75 c10H20 (C2H4)7 11% c H4 + 39% Ar + 50% He 2 25 290.0 0.75 cl4H28 C2H4·C2F4 0.7% c H4 + 0.5% c F + 20% Ar + 80% He 2 4 2 35 111.0 0.58 C H F+ a) 3 4 Ne·C H 2 4 0.5% c H + 89.5% Ne + 10% He 2 4 35 215.0 0.76 20NeC H + 2 4 Ar·C H 2 4 0.3% c H + 20% Ar + 80% He 2 4 35 215.0 0.57 ArC2H4 Kr·C H4 2 0.5% c H4 + 22% Kr + 78% He 2 50 65.0 0.79 Kl:C H + b) 2 4 2 . a) Identical results obtained when rronitoring c H F +. 3 3 2 + . th 37 C2H4 W1 Cr4· b) Sum of all Kr isotopes. These ions are major products of the reaction of + + + + + N V1 26 used to produce the complexes. ethylene 4 shows infrared dirner and ethylene photodissociation spectra trimer. this figure as well as Data for of Figure for all spectra shown below were obtained using coaxial laser and molecular beams. Note that the spectra are plotted with logarithmic The reason for this choice is presented in the ordinates. discussion section. are nonlinear The solid lines shown in the spectra least-squares fits of described in the discussion section. Figure 4 'V 952 consist of a ern -1 and single both a line shape Both spectra shown in symmetric band, exhibit function the same centered at width. The photodissociation cross section of ethylene trimer is larger than that for <c 2 H4 > 2 at all laser wavelengths sh9wn. Only 6.7 W cm- 2 was used to obtain data shown in Figure 4, yet it was possible to dissociate 25% of the dirner and 50% of the trimer. Figure 5 shows photodissociation ethylene cluster, notionally nearly identical photodissociation monitoring spectra large <C 2 H4 > 5 and <C 2 H4 > 7 which have photodissociation cross of sections. bandshapes and Spectra obtained <c 2 H4 > 5 and <C 2 H4 > 7+ are thought to be typical of large clusters and not due solely to <C H > and <C H > • 2 4 5 2 4 7 These spectra exhibit essentially the same width as ethylene dirner and trimer spectra. Irradiation of ethylene clusters in the crossed laser beam-molecular beam configuration yielded the same wave- length dependence observed iri the colinear-geornetry experi- 27 1.0 C2H4=Ar:He =7.5:200:800 35 f'm nozzle c 0.8 50 psi 0.6 0 N C3H5+ 0 u 0.4 c C4He+ 0\ 0 I 0.2 0.0 940 960 v FIGURE 4. 980 ( cm-1) Infrared photodissociation spectra of (C2H 4 )2 and (C2H4) 3 . The solid lines are least-squares best fits of Eq. (6). The dirner is detected as c 3 H5 + and the trimer is detected as c 4H8 +. No photodissociation of either species 1s observed at co 2 laser wavelengths > 1000 cm-1. Laser intensity is 6.7 W cm-2. Molecular beam conditions are listed in Table I; lc 0 12 is the fraction of undissociated van der Waals molecules. 28 0.6 c N -0 0.4 (.) Cl 0 I 0.2 0.0 930 940 950 , FIGURE 5. 960 970 980 (cm-1) Infrared photodissociation s~ectra of large clusters detected as (C 2 H4)5 and (C2H4)7+. The solid lines are least-squares best f1ts of Eq. (6). No photodissociation of either species is observed at co 2 laser wavelengths >1000 crn-1. Laser intensity is 6.7 W crn-2. Molecular beam conditions are listed in Table I. 29 In ments. the crossed-beam experiment photodissociation yield of ethylene trimer was only ~.005 at 953 cm-l due to Relative cross sections for the short irradiation time. dissociation of cc 2 H4 > 3 and <C 2 H4 > 2 are identical for both types of experiments. This indicates inhibition of cluster formation caused by heating of the expansion by the laser beam does not occur. Consideration of the relative proba- bilities for photon absorption and quenching collisions in the expansion also vitiates expansion heating as a cause of cluster Observed loss. infrared is photochemistry the result of excitation and decomposition of isolated van der Waals molecules. Changes in laser intensity in the range of 1 to 10 W em -2 do not alter photodissociation bandwidths. Further- more, the width and position of photodissociation profiles are independent of expansion conditions as ethylene concentration is varied from 0.5% to 5% and stagnation pressure is varied from 65 to 115 psi. Figure logarithm of 6 . shows the the laser power dependence of the fraction of undissociated van der Waals The molecules. laser wavelength is fixed at a frequency close to the peaks of the photodissociation spectra. Similar data were obtained for all of the van der Waals clusters listed in Table I. data In each case, points lie on straight L aw-type re 1 at1ons h 1p. 31 0 0 semilog plots of power dependence lines suggesting a Beer's 30 0.8 0.6 c 0 u c '- LL 0.4 -c ...c CP 0 0 en en "t:J 0 (C2H4)2 c (C2H4 )3 c :::> 0.2 C2 H4 =Ar: He= 7.5=200:800 35 p.m 0 FIGURE 6. 2 nozzle 50 psi 4 6 8 Irradiance (W·cm- 2 ) 10 Measured power dependence of infrared photodissociation of (C2H4)2 and (C 2 H 4 )~. Ordinate is logarithmic. Laser wavelength ~s nearly identical to Arnax for infrared photodissociation spectra of these van der Waals molecules. 31 The wavelength dependence for dissociation is shown in Figure 7. are also shown for c F • c H 2 4 2 4 photo- Data for ethylene dimer comparison. The spectra exhibit characteristic width, position, and photodissociation efficiency. The c F ·c H spectrum is narrower and shifted to 2 4 2 4 the blue compared to pure ethylene clusters. Qualitative differences appear in the spectra of complexes of ethylene and noble gas atoms shown in Figure 8. As in the symmetric peak pure ethylene cluster spectra, is observed near 950 cm-l in a the broad spectra However, in the spectra shown in Figure 8 a second broad feature of lower intensity is discernible near 970 cm- 1 • For KrC H + this appears as 2 4 a peak, broad shoulder of the main while it is clearly resolved in the ArC H + data. 2 4 more enticing. Unfortunately, the signal-to-noise ratio in the NeC H experiments is q?ite low since it is difficult, 2 4 even in strong expansion to synthesize Ne-c H clusters in 2 4 detectable concentrations. Results presented in Chapter 7 indicate that the broad envelope in the c H Ar+ data is due 2 4 to Arn·c H , with n 2 4 due to Ar· c H . 2 4 ~ 2, while the underlying structure is Presumably this occurs for c H Kr + as 2 4 well. No dissociation was detected at energies higher than 1000 cm-l for any of the van der Waals molecules listed in Table I. Therefore, data for only half of the co wavelength range are presented. 2 laser Resolution of the spectra 32 0.6 N 0 0.4 0 C3Hs+ A C3H4F+ u 0\ 0 0.2 0.0 940 FIGURE 7. 960 980 Infrared photodissociation spectra of (C2H4)2 and C2H4·C2F4. (C2H4)2 data as in Figure 1. The solid curves are least-squares best fits of Eq. (6). c 2 H4 ·c 2 F 4 is monitored using C3H4F+. No photodissociation at co 2 laser wavelengths > 1000 cm-1 is observed. Laser intensity is 6.7 W cm-2 Molecular beam conditions are listed in Table I. 33 0.2 0 0 0 .1 0.0 N - u 0 0' 0 Ar · C2 H4 + 0.1 ~ox:o 0 .0 0.1 oo ~OcP0 0 .0 930 FIGURE 8. g 940 950 960 970 980 Infrared photodissociation spectra observed monitoring of KrC2H 4 +, ArC2H4+ and NeC2H4+. The solid curves are least-squares best f1ts of Eq. (6) to data obtained at frequencies less than 960 crn-1. No phot~dissociation at C02 laser wavelengths > logo em- is observed. Laser intensity is 4.0 W ern- • Molecular beam conditions are listed in Table I. 34 is limited by the discrete tunability of the co The large gap spectra from presented 955 cm-l to 965 corresponds to em-l laser. 2 in all of the weakly populated or forbidden transitions of the 00°1-10°0 band of co • Scat2 ter in the data is mainly due to changes in laser mode structure and hence changes in irradiance along the molecular beam with tuning. IV. DISCUSSION The · broad, obtained in symmetric bandshapes observed in spectra this study broadened transitions. are characteristic of lifetime- Linewidths are determined by rates of predissociation of the vibrationally excited states of the van der Waals molecules. This interpretation requires. that the nature of the initially prepared state and broadening mechanisms be understood. Furthermore, homogeneity of the observed spectra must be well established. These points are taken up individually in the discussion below. Together, these considerations lead to a simple model and lineshape formula for the photodissociation process which are in excellent agreement with our observations. By comparing vibrational predissociation lifetimes of similar molecules some of the criteria that govern intramolecular vibrational energy transfer can be determined. to vibrational predissociation rates, In addition transition moments 35 for infrared absorption can be extracted from data presented. A. Vibrational Transitions in Ethylene Clusters The ethylene molecule has four modes of vibra(v , tion v , v 7 4 8 and v 10 frequency range of the co ) which are within or near the laser. The vibrational modes and 2 frequencies of ethylene and perfluoroethylene are listed in Table II for convenience. All other modes are not relevant to this experiment since they are higher in energy and far The v removed from the observed absorption frequencies. mode is neither infrared nor Raman active. 4 Consistent with this we see no dissociation of ethylene clusters for laser frequencies near 1027 em there was efficient -1 • For all molecules studied dissociation near 950 em -1 corresponds to strongly allowed excitation of the v in ethylene. This 7 mode In this mode the hydrogen a toms are moving together above and below the equilibrium plane. the nearly degenerate infrared inactive v 8 Motion of mode is similar except that opposite ends of the molecule are out of phase. This mode becomes weakly infrared active as molecule is perturbed by general, this perturbation van der Waals is weak and v 8 expected to be insignificant compared to v c 2F the 4 the ethylene bonding. In absorption is absorption. 7 has no modes (Table II) which absorb in the range of co 2 laser. We thus conclude that for Ar, Kr, Ne, and 36 TABLE II. Fundamental Frequencies of c H4 and C2F4. 2 M::>de SyntTEtry \)1 ~g \)2 \)3 Frequency C2H4 -1 (on ). 3019.3 a) C2F4 Description R 1872 778 1342.4 394 ~u 1027.0 \)5 ~g 3272.3 Inactive R 1236.0 \)6 Frequency (ern-1) 1623.3 \)4 190 1340 551 Blu 949.2 IR,s 406 \)8 B2g 940. Oc) R,w 508 \)9 B2u 3105.5 IR 1337 825. 9C) w 218 2989.5 IR 1186 \)10 \)11 ~2 B3u 1443.5 a)Ref. 38, except as noted. b)Ref. 39. c)Ref. 40. b) 558 37 c F 2 4 mode bound to ethylene the laser photon is absorbed by a similar requirements, an to v in free ethylene. Due to symmetry 7 the absorbing mode in ethylene dimer must be infrared active combination of partner. the v 7 motion of each The nature of this combination is discussed more fully below. for c 2 F4 · c H , the observed absorption band 2 4 center is shifted only slightly from the v fundamental of 7 Except free It thus et~ylene. seems justified that the vibra- tional mode excited in cluster-bound ethylene be considered as only slight perturbed. The excited state of the complex can then be considered to be a discrete state imbedded in a dissociative continuum. See Chapter 5 for a discussion of an electrostatic mecha~ism for the frequency shifts. B. Nature of the Lineshape for Cluster Excitation It is crucial to the arguments of this study and of other similar studies that the nature of observed spectral broadening be reported exper imerits have initial population are unambiguously the determined. advantage observed that directly. The changes in When the ethylene dimer is irradiated with 11 W/cm 2 of laser flux, 50% of the initial population is lost from the molecular beam even though the laser linewidth is ~so MHz. In a plot of fraction dissociated versus laser irradiance, as shown in Figure 6, a Beer's Law relationship is seen with no 38 leveling off laser of the fraction dissociated at irradiance available to us. narrow laser bandwidth ensemble of molecules. is the highest It is clear that the interacting with the whole The transition must be dominated by homogeneous broadening. Unfortunately, measurement although of our experiment rotational similar or experimental gives no translational temperature, conaitions known are produce rotational temperatures of less than 1 K . a measurement would be useful ( N o) 16 2 2 comparing and of In dissociated, a large fraction it is possible of ethylene to use very dilute mixtures comparable to those dimer is {down to This allows 0.5%) mixtures of ethylene behind the nozzle. for very efficient rotational cooling. our al. 16 , 41 we experimental conditions to those of Gough et since Such that 2 X that 34 to in light of the fact spectra predissociation vibrational {CO ) 41 are plainly inhomogeneous. note direct Using 10% ethylene used by Gough et al. 16 in their N o study leads to formation of large fractions of 2 higher polymer. Under these conditions, it would be likely that ethylene dimer is not effectively cooled. In molecular beam electric resonance experiments of large van der ethylene dimer, could be Waals molecules e.g. BF observed even P 800 conditions, 0 = 3 similar in complexity to ·co, 42 no van der Waals hot bands though Torr, relatively mild were used. expansion Finally, when ethylene concentration was varied from 0.5% to 5% and P 0 39 was varied from 4.3 atm to 7.7 atm, no change in the dimer lineshape was observed. All of the above observations sup- port the claim that the observed lineshapes for <C H > and 2 4 2 c2 H4 ·c 2 F 4 aredominated by homogeneous broadening. For (Kr)nC H there are clear features 2 4 (Ar)nC H and 2 4 These features to the high energy side of the main peak. cannot be ascribed to rotational structure due to a thermal distribution of initial state rotational levels. of such an The width inhomogeneous rotationally broadened transition measured between maxima of the P and R branches is given by (8kTB)~ • Ar·C H , 2 2 43 Assuming a structure still to that of Ar·C H at 1 K would have an absorption bandwidth 2 4 of approximately 1.7 cm-l be analogous narrower. Larger (Ar)nC H clusters would 2 4 Conversely, Ar·C H 2 4 the rotational temperature calculated from the observed spectrum, assuming rotational inhomogeneity, unreasonable. observed, Together is greater with these considerations the than 100 K, efficient which is dissociation indicate that the main parts of these spectra are essentially homogeneous. C. Broadening Mechanism The most satisfying explanation of the observed linewidth is state limited is ciation. would For imply a that each the lifetime of the by the of vibrational of the rate molecules initially in vibrational predissociation this excited predissostudy rate of this greater 40 than 10 12 sec -1 These rates are one to two orders of a1. 5 - 15 in magnitude faster than any observed by Levy et their study of van der Waals molecules containing r • Even 2 for H • r , where the r and van der Waals bond-stretching 2 2 2 motions are of similar is sec only 5 frequenc~ -1 15 the predissociation rate The observed widths of the ethylene spectra are also an order of magnitude greater than those of Gough et <N 2 o> 2 16 and <co 2 >2 • 41 al. for Are such fast predissociation rates reasonable? as a First, it is useful to consider the molecule Ar·C H 2 4 In this case it is prototypical ethylene cluster. possible to make a structure by "T-shaped" reasonable comparison molecule 0.02 Debye, indicating unaffected by Ar. monomer Ar is located 3.2 0 A from a the The dipole moment of Ar·C H is 2 2 that acetylene bond angles are modes formation of a weak bond. are only weakly affected vibrational by Another interesting aspect of that the vibrational potential for the "T" is very flat. ground the molecular This supports the above supposition that vibrational Ar· c 2 H2 is of with with acetylene molecular axis. estimate bending of This may indicate that even in the state of the molecule the bending amplitude is such that there is direct interaction between the hydrogen atoms and the Ar atom. The Ar-ethylene interaction should be much the same as Ar-acetylene, with Ar above resulting the in a plane defined "T-shaped" by the configuration hydrogen a toms. 41 There are three normal modes of motion associated with the weak bond: to a stretch, and bends parallel and perpendicular the carbon axis. It is of interest to speculate how these weak modes interact with the vibrationally excited v 7 mode of ethylene. The change of vibrational amplitude upon excitation of v 7 can be bending angles, determined by comparing root mean square B, given by: ( 4) = in the ground and excited states. v b is the v 7 bending frequency, vb is the vibrational quantum number, and mb is an grn effective bending reduced mass Herzberg 44 gives the equation for (units of 2 ern ) . the frequency of the v 7 mode which defines rnb: = = The bending force constant is kb' and carbon masses, H-C-H angle. ~ ( 5) rnH and me are hydrogen 2 is the C-H bond length and a is the Putting in numbers leads to the result that 42 the rms amplitude due to zero point motion of v is 7 7 o, while the rms amplitude of the first excited level is 13°. corresponding displacements of the hydrogen atoms from the 0 0 molecular plane are 0.14 A and 0.24 A, respectively. The substantial out-of-plane bending amplitude for v 7 excitation may provide anharmonic terms necessary to efficiently couple vibrational dissociative pathway. that of energy out of v 7 Comparing the symmetry of the weak bond vibrational modes, that only the stretch is a into the v with 7 it would appear likely mode for the excitation enegy. This would certainly be true if the molecule was rigid. However, the average position of Ar is expected to be well off to one side of the equilibrium position above the center of the point motion. c-c bond because of large amplitude zero Data presented in Chapter 7 show that ArC H 2 4 is indeed a hindered internal rotor. tional possibility bending modes. of The direct end This opens the addi- coupling result in of either case with weak is rapid dissociation leaving the ethylene fragment in a high rotationa! state. The arguments applied to Ar ·C H would apply in an 2 4 Unfortunately, the structue Possibilities are a "T-shaped" structure or a parallel structure, and there ae theoretical calculations . 45 46 metr 1.es ' . in the literature supporting both geo- It is unlikely that any but the very best calculation would give a reliable structure or bond energy 43 for this molecule. Recent . deflection exper~ments 47 molecular using ions of beam electric 41 m/e to detect cc 2 H4 > 2 beams indicate that the. dipole moment of the complex is less 0.1 than D. This supports parallel configuration. However, also unable to detect a dipole moment a centrosymrnetric similar experiments were for Ar • c H • This 2 4 indicates that .the quadrupole moment of c H may be too weak 2 4 to induce an observable dipole moment in <C H > no matter 2 4 2 what structure is favored. the nature of coupling v In either case, an argument for cc 2 H4 > 2 and to the weak modes of 7 other van der Waals molecule studies would be analogous to those presented for Ar·C H • 2 4 Up to this broadening rather point it has been argued in these complexes is due than other types of intramolecular redistribution. There are two predissociation nondissociative broadening modes, but creation of a long-lived orbiting complex; and 2) within vibrational With regard rotation, to dephasing the possibility transfer energy weak conceivable: Energy spectral the mechanisms 1) to that to covalently bound of enegy _internal high modes. note that the radial van der Waals potential is highly anisotropic with respect to internal rotation. equilibrium bond length of centers the of mass ethylene changes rotates. 45 The cc 2 H4 > 2 with respect to ethylene by more than This type half of an Angstrom as anisotropy would certainly couple bending and stretching degrees of freedom. · Several hundred wavenumbers of excitation deposited in such 44 an orbiting resonance would result in a subpicosecond rotational period and rapid coupling to dissociative modes. Intramolecular energy transfer within bound ethylene modes is also unlikely. The v and v modes of ethylene are 7 8 close in energy but are of different symmetry, and remain so in the coupling reduced might be symmetry of ethylene expected to be low clusters. on this The basis. Experiment argues against such fast dephasing processes. The spectrum of ethylene in an Ar matrix at l0°K exhibits linewidths of less by site inhomogeneity rather than matrix-induced dephasing. 48 The special case of t~e All of than 0.25 crn-l determined cc 2 H4 > 2 is considered below. above evidence gives strong support to the conclusion that the observed homogeneous linewidths are due to vibrational predissociation on the subpicosecond time scale. D. Absorption Profile and Intensities A model for vibrational excitation followed by predissociation, which for some circumstances leads to purely lifetime broadened absorption, is a two-level system in which the upper state undergoes unimolecular decay. In our experiments the v = 0 and v = 1 states of the ethylene v7 mode correspond to the states of the two level system. Derivation of an exact lineshape equation from this model is described in Chapter 4. In the present study, uni- 45 molecular dissociation rates of vibrationally excited van der Waals molecules are more than 5 orders of magnitude faster than rates of stimulated absorption and stimulated Spontaneous emission. in emission the is even infrared Thus it is possible to make simplifying approxi- slower. mations to the lineshape function (see Chapter 4) from which we obtain eq. 2 jc (w,t) (6): T = 0 -2 4(w- w ) 2 0 jC 0 ( w, t) 1 2 molecules, + T -2·} (6) is the fraction of undissociated van der Waals is t the irradiation w time, is the laser frequency, wR is spacially averaged the Rabi frequency (see Chapter 4), Tis the dissociation rate of molecules in the is the band center. excited state, and w 0 w 0 in eq. is the (6) Note that Eq. are in units of angular frequency. exponential of a scaled w and Lorentzian ( 6) curve. Typically, 2 wR -r t < 1 implying that I C0 ( w,t) I 2 is nearly Lorentzian but is Lorentzian lineshape . ca t 1on. slightly narrower than in previous reported our the simple communi- 31 Solid lines drawn in the infrared photodissociation spectra (Figures 4, 5, 7 and 8) are results of a nonlinear, least-squares fit of eq. (6) to the data points. 46 Predissociative lifetimes are calculated from the fitted spectra using eq. (7). -r(sec) = Values of w and 0 1 (7) 2nc{FWHM(crn -1 )] -r for each ethylene containing van der Waals molecule studies are listed in Table III. shape function with remarkable consistency. While agree- ment with a lineshape is not usually strong enough evidence to assert homogeneity, does serve as the lineshape of these transitions additional evidence that inhomogeneous noble gas-ethylene effects are not observed. Note that in the case of cluster a reasonable fit of eq. is are not possible. obtained occurring in However, ArC H and 2 4 the P emission are used. (6) to the entire spectrum statistically reasonable for branch each of KrC H 2 4 the data co 2 if fits only points (00°1-10°0> laser This is consistent with the discussion in the previous sections and, for the purpose of comparing spectral linewidths, we ignore the high portions of the rare gas-ethylene spectra. frequency Values of w 0 and T for (Ar)nC H and (Kr)nC H listed in Table III were calculated 2 4 2 4 in this way. Results in Chapter 7 suggest that these are 47 TABLE III. Parameters· Obtained from Lineshape Fit to Photodissociation Spectra and Photodissociation Power Dependence Dataa) T (psec) Cluster (Ar) C H b) n 2 4 952.3 ± 0.5 0.44 0.05 96.0 ± 18.0 952.3 ± 0.5 0.50 0.07 141.0 ± 33.0 953.2 ± 0.9 0.33 0.05 100.0 ± 19.0 953.2 ± 0.9 0.33 0.05 100.0 ± 19.0 950.0 ± 0.5 0.59 0.13 43.0 ± 16.0 949.1 ± 0.7 0.55 0.14 39.0 ± 15.0 954.7 ± 0.2 0.89 0.10 43.2 ± 3.3 a) The errors tabulated are three standard deviations. b) These results apply to clusters which contain at least two rare gas a tans. See Chapter 7 for further investigation of Ar·C H and Ne·c H4 . 2 2 4 48 representative of clusters with n > 1. signal-to-noise ratio low. in the ~ntriguing However, Unfortunately, the Ne· c H experiment was very 2 4 and reproducible features in the Ne·C H spectrum suggest that the broadening mechanism is 2 4 significantly weaker for Ne·c H than for any of the other 2 4 See Chapter 7 for a closer molecules which were studied. look at Ne·c H • 2 4 Eq. ( 6) predicts that the logarithm of the undissociated fraction of clusters decreases linearly with increasing laser power _ since wR 2 is proportional to laser inten~ity. power This is in excellent agreement with the observed dependence of infrared photodissociation shown in Figure 5. The Rabi frequency, wR is also a function of the transition moment two-level system. < ll > for infrared absorption by the Results obtained from photodissociation wavelength dependence combined with power dependence data allow determination of <l.l> for the van der Waals cluster The square of the transition moment is propor- studied. tional absorption to probability. Values with or of <ll>2 are listed in Table III. Among transition clusters probabilities proportional to the cluster. The average (4.5±1.2) x 10- 2 0.21 D. The three calculated number of fewer using ethylenes, eq. (4) are in the ethylene is ethylene molecules contribution per o 2 corresponding to a transition moment of transition moment for infrared absorption by the v 7 the v = 0 -+ v = 1 mode in ethylene monomer is 49 0.188 D. 49 The excellent agreement with observed photo- dissociation bandshapes and power dependences as well as consistency of the various transition moments leads us to conclude that eq. (6) and the underlying model adequately characterize the photodissociative behavior or (Kr)nC 2 H 4 , <C 2 H 4 > 2 , E. 3 vibrational to and c 2 H 4 .c 2 F 4 • detailed predissociation qualitative theoretical in Jortner 19 present treatments simple model generalizations comparison of predissociation rates. and 2 4 Comparison with Theoretical Models Recent led (C 2 H 4 > (Ar)nC H , of systems have may guide which For example, Beswick approximate relations for vibra- tionally predissociative lifetimes of molecules of the type AB •X. AB is a well-characterized, diatomic and molecule. of the X represents a vibrationally excited rare gas atom or simple An energy gap law predicts that close matching high frequency molecular frequency and the low stretching of the van der Waals bond enhances vibrational predissociation rates. Furthermore, with other parameters fixed,the predissociation rate is expected to increase with decreasing mass of X or as the van der Waals bond energy is decreased. ciation that . 1.n Theoretical treatments of vibrational predissoh y d regen- b on d e d internal molecule degrees of constituents . 25 Ew1.ng comp 1 exes by freedom the can in enhance van . d 1.ca . te 1.n der Waals vibrational 50 predissociation rates by six orders of magnitude. In parti- cular, enhancement compared to V - T processes is observed when a V ...... V channel is operative. momentum gap tially rule which states excited bound state and Ewing 24 has derived a that overlap of the ini- continuum wave functions determines the predissociation rate. Although no theoretical treatment exists for mole- cules as complicated as ethylene clusters, some features of calculations with simpler systems are borne out in trends in the observed lifetimes listed in Table III. The bonding c 2 F 4 and ethylene is expected to be stronger than between interactions in other bimolecules Indeed, studied. ethylene absorption frequency in c H the blue by 5 Cm-l. ' th e mos t mass1ve . 1s par t ner 2 4 Al so, C F 2 4 •c the F is 2 4 shifted to used in construction of ethylene complexes. Insofar as the previous discussion is correct, both of these factors contribute to the observed extension of the c H • c F life2 4 2 4 time compared to other clusters. ficantly Waals as the partners internal are Rates do not vary signi- degrees changed in of freedom of van der the series of clusters studied. This ciation channel studied, and that energy transfer rates depend mainly on the mode implies that the same efficient predissois excited in operative ethylene. in all For of the example, several vibrational frequencies (Table II) which might be acceptor modes. candidates for molecules c2F4 has below 949 em the -1 slow dissociation rate of C2H 4 • c 2 F relative to other van der 4 51 waals molecules studied suggests that such acceptor modes are not coupled to v 7 • decomposition is not expected to be vibrationally excited. The dynamics of ethylene qimer predissociation are of special interest because of degeneracies introduced by symmetry. the type strong in Exactly analogous is the decomposition of dimers of AB • BA. Beswick and Jortner 22 have that intramolecular coupling of degenerate bound states such molecules can lead to linewidths dephasing rather than decomposition lifetimes. of shown the ethylene dimer symmetry adapted wave in o h 2 symmetry, functions can be dominated In the case nearly degenerate constructed symmetric and antisymmetric combinations of the v mode motion of monomeric ethylene. by 7 from normal Designating the van der Waals partners arbitrarily as A and B, and the localized v motions are A and 7 a7 , with one quantum of v., excitation are and 7 corresponding dimer wave functions 52 vibrational degenerate Nearly states obtained from inspection of Table II are {+)v8 and (-)\) 8 We assume that only such discrete states carry oscillator Consideration of dipole strength from the ground state. moment derivatives indicates that optical transitions from the ground state to only <+>v (+) v we expect that absorption by the compared to the <+>v 7 <+>v 8 are allowed, and 7 8 mode will be weak Assuming that <+>v mode. and 7 motion is excited, we need to consider whether energy flow into the other three transitions Morse nearly into degenerate the potential modes dissociative coupling term can continuum. derived by compete with Using the Beswick and Jortner, 22 the only nonzero matrix elements couple the discrete state (+) v 7 and (+) v 8 . However, widths due to coupling between discrete states compete with the width due to decomposition only in special cases. Calculations for such a case, 22 collisionally excited F -F , predict widths 2 2 of less than states. The 4 x 10~ 3 cm-l due to coupling of discrete ethylene dimer width must be domina ted by 53 vibrational predissociation much than larger 4 x 10 since -3 em -1 the and observed is width is not dramatically different than widths observed for other clusters. Calculated vibrational predissociation rates are dramatically affected by slight changes in molecular parameters. 19 26 ' In contrast, lifetimes listed in Table III vary by only a factor of three through the series of seven ethylene clusters studied. This is an extremely small range of lifetimes compared to those calculated for simpler molecules, perhaps reflecting a narrow range of bond energies and frequencies among the dimeric species studied. In addition, observed faster erably than predissociation those rates generally are consid- calculated for theoretical models. Photodissociation spectra of pure ethylene clusters (Figures 4 and 5) all show maxima blue-shifted compared to = 949.2 ern-1 in ethylene monomer (Table II). This trend v 7 in wavelength shifts condensed ethylene. in the crystal v 7 is observed but is more marked in Liquid c H exhibits v = 961 cm-l and 2 4 7 50 1 = 970 crn- • One expects the infrared frequency of absorption band maxima in ethylene clusters to increase with increasing cluster size until a value characteristic of the liquid or solid is However, in the homologous series <C H > , 2 4 2 and reached. <C H > , <C H4 > 5 2 4 3 2 cc 2 H4 > 7 photodissociation bands are shifted, by 5 cm-l relative to the monomer fundamental. ipated progression towards 970 ern -1 is limiting not at most, The anticobserved. 54 Photodissociation efficiencies do not scale with the number of molecules constituting clusters beyond <C H ) , implying that photodissociation spectra of 2 4 3 clusters may not mimic absorption spectra. large dissociation spectra pure with ethylene transition probabilities comparable to ethylene dimer. Assuming that all consti- tuents be of large clusters can excited locally, this suggests that excitation at only a few sites will lead to decomposition on the time scale of our experiment. For example, fast predissociation may be detected only when an ethylene molecule at the cluster "surface" is activated by infrared excitation. Decomposition following excitation · of molecules embedded in consuming multiple bond the cluster may require time- cleavage or extensive energy predissociation of van der Waals a single redistribution. V. SUMMARY Vibrational molecules has been observed. Absorption of infrared photon (950 cm- 1 > by a slightly perturbed normal mode of ethylene is sufficient weakly bound complexes. (less than 10 W to photodissociate Use of relatively low laser power em - 2 ) avoids saturation. dissociation spectra such Infrared photo- (925-1080 cm- 1 > are characterized by lifetime broadened homogeneous lines. Observed wavelength 55 dependences and power dependences show excellent agreement with a lineshape derived from a a two-level-plus- model. Predissociative lifetimes lie in the range of 0. 3 psec for large ethylene clusters to 0.9 psec for These correspond to 9-26 vibrational periods decay c 2 H4·c 2 F 4 . prior to dissociation. Low-power infrared irradiation removes large fractions of clusters from the molecular beam in all of the experiments presented in this study. Photodissociation spectra of clusters in molecular beams are simplified due to supersonic cooling and generally consist of single homogeneously infrared broadened lasers absorptions. may be used This to modulate suggests that van Waals der molecule intensity for phase-sensitive detection in other An isotope separation scheme molecular beam experiments. based on infrared molecules in photodissociation molecular beams may . examp 1 e, 1n a recent stu d y o f Ar ·BC 1 using the technique explored of prove van der Waals feasible. For . . p h oto d.1ssoc1at1on, 3 50% here, of the 51 11 B containing van der Waals molecular were removed from the molecular · beam without effecting species containing 10 a. Efficient selective photodissociation of 10 B species was also observed. Qualitative applied to aspects ethylene predissociation of simple clusters lifetimes. are However, theoretical useful in observed models comparing rates are much greater than these models would imply, and the range 56 of predissocia tion rates expected as molecular parameters This suggests that among the are varied is not observed. species dime ric studied, predissociation rates are controlled by the nature of the vibration initially excited This may reflect a narrow range of van der in ethylene. waals bond-types and available predissociation channels. Alternatively, to applicable theory the developed more thus far complex may not prove polyatomic species transition moments containing ethylene. Absolute are obtained. roughly magnitudes of infrared The transition moment per ethylene unit is constant over the series The molecular technique used in general for method this study measuring appears to be an infrared beam excellent transition inten- sities. Larger ethylene clusters, <C H > and <c H > exhibit 2 4 5 2 4 7 infrared photodissociation behavior similar to the dimer. It is inferred that present fraction of clusters. Excitation of a ethylene experiments molecules sample constituting only a larger c 2 H4 unit which is bound to many other ethylene molecules may not yield cluster dissociation on the time scale of the experiment. 57 ACKNOWLEDG"EMENTS The authors for his Thanks ideas, are gratefully acknowledge J. advice, and the use due D. D. Smith also to curve-fitting routines. of set an upper Dr. Berkeley, generously isolation Heinz spectra acknowledge W. C. for Frei, the the <c 2 H4 > 2 and Ar·C 2 H4 dipole moments University supplied of of in Ar. Schuelke for work It is in these California prepublication c 2 H4 of providing Robert Altman, Harvard University, limit species. Beauchamp co 2 laser. his for kindly measured electric deflection of to L. a at matrix pleasure to constructing our apparatus. This work was supported by the Research Corporation and the Division of Chemical Sciences, Office of Basic Energy Sciences, U. S. Department of Energy under contract no. DE-AS03-76SF00767. Acknowledgement is made to the Donors of the Petroleum Research Fund, administered by the American research. Chemical Society, for partial support of this 58 REFERENCES 1. W. Klernperer, Ber. Bunsenges. Phys. Chern. 78, 1281 (1974). ~, 2. M. S. Child, Faraday Discuss. Chern. Soc. 307 (1977}. 3. C. A. Coulson and G. N. Robertson, Proc. Royal Soc. (London), Ser. A 342, 289 (1975). 4. J. S. Lassegues and P. V. Huang, Chern. Phys. Lett. 17, 444 (1972). 5. R. E. Smalley, L. Wharton and D. H. Levy, J. Chern. Phys. 64, 3266 (1976) • 6. M. S. Kim, R. E. Smalley, L. Wharton and D. H. Levy, J. Chern. Phys. 65, 1216 (1976). 7. R. E. Smalley, L. Wharton and D. H. Levy, J. Chern. Phys. 66, 2750 (1977) . 8. G. Kubiak, P. H. Fitch, L. Wharton and D. H. Levy, J. Chern. Phys. 68, 4477 (1978). 9. D. H. Levy, J. Chern. Phys. 68, 2524 (1978). 10. K. E. Johnson, L. Wharton and D. H. Levy, J. Chern. Phys. 69, 2719 (1978). 11. W. Sharfin, K. E. Johnson, L. Wharton and D. H. Levy, J. Chern. Phys. 71, 1292 (1979). 12. J. E. Kenny, D. v. Brumbaugh and D. H. Levy, J. Chern. Phys. 71, 4757 (1979). 13. J. A. Blazy, B. M. DeKoven, T. D. Russell and D. H. Levy, J. Chern. Phys. 72, 2439 (1980). 14. J. E. Kenny, K. E. Johnson, w. Sharf in and D. H. Levy, J. Chern. Phys. 72, 1109 (1980}. 59 15. J. E. Kenny, T. D. Russell and D. H. Levy, J. Chern. Phys. 73, 3607 (1980). 16. T. E. Gough, R. E. Miller and G. Scoles, J. Chern. Phys. 69, 1588 (1978). 17. M. A. Hoffbauer, W. R. Gentry and C. F. Giese, Laser-Induced Processes in Molecules, edited by K. L. Kampa and S. D. Smith (Springer-Verlag, Heidelberg, 1979). 18. H. S. Kwok, M. F. Vernon, D. J. Krajnovich, Y. R. Shen and Y. T. Lee, Lawrence Berkeley Laboratory Report No. 10566; H. S. Kwok, M. F. Vernon, D. J. Krajnovich andY. T. Lee, Lawrence Berkeley Laboratory Report No. 10288. 19. J. A. Beswick and J. Jortner, J. Chern. Phys. ~, 2277 ~, 512 (1978). 20. J. A. Beswick and J. Jortner, J. Chern. Phys. (1978). 21. J. A. Beswick, G. Delgado-Barrio and J. Jortner, J. Chern. Phys. 70, 3895 (1979). 22. J. A. Beswick and J. Jortner, J. Chern. Phys. 71, 4737 (1979). 23. J. A. Beswick and G. Delgardo-Barrio, J. Chern. Phys. 73, 3653 (1980). 24. G. Ewing, J. Chern. Phys. 71, 3143 (1979). 25. G. Ewing, J. Chern. Phys. 72, 2096 (1980). 26. G. Ewing, Chern. Phys. 29, 253 (1978). 60 21. R. Ramaswamy and A. E. DePristo, J. Chern. Phys. 72, 770 (1980) . 28. S. B. Woodruff and D. L. Thompson, J. Chern. Phys. 71, 376 (1979). 29. J. W. Brady, J. D. Doll and D. L. Thompson, J. Chern. Phys. 73, 292 (1980). 30. L. S. Bernstein and C. E. Kolb, J. Chern. Phys. 71, 2818 (1979) . 31. M. P. Casassa, D. S. Bomse, J. L. Beauchamp and K. 32. c. Janda, J. Chern. Phys. 72, 6805 (1980). M. T. Bowers, D. D. Elleman and J. L. Beauchamp, J. Phys. Chern. 72, 3599 (1968). 33. K. C. Janda, Ph.D. Thesis, Harvard University (1977). 34. R. E. Smalley, L. Wharton, D. H. Levy and D. · w. Chandler, J. Chern. Phys. 35. ~, 2487 (1978). L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon Press, New York, 1959). 36. K. C. Janda, J. E. Hurst, C. A. Becker, J. P. Cowin, D. J. Auerbach and L. Wharton, J. Chern. Phys. 72, 2403 (1980). ~ 37. A. J. Ferrer-Correia and K. R. Jennings, Int. J. Mass Spectrom. Ion Phys. 11, 111 (1973). 38. R. L. Arnett and B. L. Crawford, Jr., J. Chern. Phys. 18, 118 (1950). 39. D. E. Mann, N. Acquista and E. K. Flyer, J. Res. Natl. Bur. Stand. 51, 69 (1953). 61 40. J.· L. Duncan and E. Hamilton, J. Mol. Struct. ~' 65 (1981). 41. R. E. Miller, Ph.D. Thesis, University of Waterloo (1980). 42. K. C. Janda, L. S. Bernstein, J. M. Steed, S. E. Novick and W. Klemperer, J. Am. Chern. Soc. 100, 8074 (1978). 43. R. L. DeLeon and J. S. Muentor, J. Chern. Phys. 72, 6020 (1980). 44. G. Herzberg, Infrared and Raman Spectra (Van Nostrand and Reinhold, New York, 1966) . 45. K. Suzuki and K. Iguchi, J. Chim. Phys. 75, 779 (1978). 46. R. Lochmann and P. Hobza, Int. J. Quant. Chern. 15, 73 (1979). 47. R. Altman, Harvard University (unpublished results). 48. H. Frei, University of California at Berkeley (unpublished results). 49. T. Nakanaga, S. Kondo and S. Saeki, J. Chern. Phys. ~' 2471 (1979). 50. C. Brecher and R. S. Halford, J. Chern. Phys. 35, 1109 (1961) . 51. M. P. Casassa, D. S. Bomse and K. C. Janda, J. Phys. Chern. 85, 2623 (1981). 62 Chapter 3 Isotopic Selectivity in van der Waals Molecule Photodissociation. Infrared Photolysis of Ar•BC1 3 63 IR PHOTOLYSIS OF ArBC£ Michael P. Casassaa, DavidS. Bomse, 3 and Kenneth C. Janda * Arthur Amos Noyes Laboratory of Chemical Physicsb California Institute of Technology Pasadena, California 91125 64 ABSTRACT The infrared photodissociation spectrum of Ar·BCi Spectra obtained using a cw co reported. ated by homogeneous dissociation of broadening excited van predissociation lifetime of due der Ar~Bct is 3 laser are domin- 2 to vibrational pre- Waals molecules. The 3 containing one quantum psec and 3 psec. v mode is between 1 3 3 Results presented are discussed in terms of and of vibrational excitation in the BCi the efficiency isotopic selectivity of the photo- dissociation process. INTRODUCTION In recent studies of the infrared photodissociation of van der Waals molecules, ethylene clusters formed in supersonic molecular power cw co to 2 beams 1 2 laser. ' characterize simplified photodissociated spectra using a low The object of these experiments was intramolecular weakly bound molecules. and were vibrational energy flow in The large fractional dissociation observed in these studies suggest that an isotope separation scheme based on infrared photodissociation of van der Waals molecules would be both highly selective and efficient. The isotopic selectivity and quantum efficiency of photochemical processes are of fundamental interest, though 65 certainly not the only practical considerations in designing laser isotope separation schemes. 3 enrichment studies, loss of In both cw 4 and pulsed 5 selectivity often occurs by isotope scrambling due to reactions of excited intermediates or thermal Selectivity heating. is also spectra of different isotopes overlap. diminished This if is often the case in multiphoton infrared photodissociation spectra which are generally broader than infrared absorption spectra. corresponding single photon Multiphoton excitation, which is the key photochemical process in many enrichment studies, represents an inefficient use of laser The cross power. section for mul tiphoton excitation is typically two orders of magnitude smaller than the cross section for step. 6 absorption Overall quantum the first efficiency is also reduced by collisional quenching of reactive intermediates. In Waals contrast to covalently bound molecules, molecules undergo infrared photon 1 2 7 8 complex. ' ' ' rapid bond cleavage absorption by a Consistent with this upon constituent simple van der single of the mechanism, observed photodissociation spectra exhibit frequencies and cross sections characteristic of the uncornplexed species. Supersonic molecular beams provide a collisionless environment in which molecules exist in their lowest rotational and vibrational states. Thus, dissociation spectra are Doppler-free and, cluster photo- in the case of ethylene clusters, 2 are dominated by homogeneously broadened absorption lines. Linewidths determined by vibrational 66 predissociation lifetimes are of the order of 10 em-1 molecular beam study of · or 2 9 less. ' In this paper we present a infrared photodissociation of co 2 laser. Ar•BC~ 3 using a low power cw In addition to characterizing vibrational pre- dissociation for this species, we have examined the isotopic selectivity and efficiency the of photodecomposition process. EXPERIMENTAL SECTION The apparatus for studying infrared photodissociation of van der Waals molecules has been described in detail in . . 2 anot h er pu bl 1cat1on. Waals clusters are formed mixtures of helium. A quadrupole mass from the constituent the nozzle source composition. Ar•BC~ Briefly, by 3 and other van der supersonic gases in a spectrometer expansion larg~ excess positioned is used to monitor of molecular 60 of em beam Uniform infrared irradiation along the mole- cular beam is provided by an unfocused cw co 2 laser directed through the ionizer of the mass spectrometer and propagating colinearly with the molecular beam. The laser beam is chopped and the intensity of a given peak in the molecular beam mass spectrum is measured both with and without laser irradiation using a two-channel boxcar. The fractional change in mass spectrometer signal intensity due to photo- 67 dissociation of is recorded as a van der Waals molecules function of laser power and wavelength. Characterization of clusters is complicated molecular by beams chlorine electron impact ionization of Ar•BC.t leads to extensive fragmentation. 3 containing BC .t isotopes, and because and pure BCt clusters 3 The most prominent ions observed are BCt + and BCt + which evidently arise from Bct 2 3 3 3 monomers and polymers. No parent Ar•BC.t + is detected, nor are containing any fragment observed. clusters 3 ions both argon and boron Ionic species definitely attributable to parent containing Ar and BC .t observed at m/e 75 and 77, 3 are Ar 35 c.t + and Ar 3 7 c t+ respectively. Relative intens- i ti_es of these two fragments are consistent with chlorine isotope natural abundances. The photodissociation results described below are also consistent with the assignment of these ions to Ar•BC.t • 3 RESULTS AND DISCUSSION A photodissociation spectrum obtained by measuring the fractional attenuation Ar 35 c t + of signal intensity function of laser wavelength is shown in Figure 1. example, 0. 5% BC .t the molecular 3 - 25% Ar - through a 50 11m nozzle. . 1n a 0 •62 msec beam was 75% He formed mixture 7 atrn a In this by expansion at as of a pressure These expansion conditions result . d 1a . t 1on . 1rra . l O t1me. Th e da t a s h own were 68 0.0 940 960 w FIGURE 1. 980 1000 (em- I) Infrared photodissociation spectrum of Ar·BC23. Ar·BC2 3 is detected as Ar35c2+. The line spectrum represents absort~ion by BC23 dissolved in solid argon at 75.8 K. 2 Note that widths of the Tatrix absorption lines are less than 0.1 em- . 69 obtained with 2.4 W total laser power which after losses at surfaces and apertures provided 3.2 W crn- 2 in the molecular beam. A strong feature is 954 observed at ern attribute to selective photodissociation of Ar• v band position corresponds to the mental of free l! BC~ 3• 11 -1 11 which BCi 3 we The • in-plane-bending funda- 3 Results of ethylene cluster photo- dissociation experiments indicate that the frequency shift by caused van . . f.1.cant. 1' 2 s1.gn1. Waals der should bonding not The irregular shape of the band may be due Ar·BC~ to dissociation of chlorine isotopic variants of . '1 ar 1 y, Ar• 10 Bct S1.rn1. v 3 absorption frequency of 10 BC ~ 3 (994 crn- 1 >; 11 thus dissociation of Ar· 10 the weak feature observed at 987 crn- 1 • and range of the of the accurately spectra isotope measured of reported. 12 in variants of the gas in dissolved For a are lirni ted by the laser. infrared absorption by the v know~edge, chlorine 2 sc~ 3 contributes to Unfortunately, both spectrum discrete tuning capability of the co To our 3• . t.1.on 1.s . expec t e d t o occur p h o t o d.1.ssoc1.a 3 close to the gas phase resolution be BC~ 3 mode has never phase. High resolution solid argon given boron isotope, 3 have been been there are several lines, spaced by approximately 1.3 crn-l due to chlorine isotope shifts, exhibiting widths of less than 0.1 ern -1 • These lines, reproduced in Figure 1, approach the unperturbed gas phase BC ~ 3 absorption frequencies with increasing lattice temperature, presumably because the lattice expands and the 70 BC R. is less 3 Results presented here perturbed. indicate that the gas phase limit is achieved at low temperatures if the bonding interaction is limited to a single argon atom. Figure 2 shows the variation of the logarithm of the undissociated fraction of molecules with laser power at fixed wavelength. Data shown were obtained by measuring the fraction total Ar c t + surviving irradiation with the laser tuned to 954.55 cm-l, close to 3 the 35 intensity the v of fundamental of 11 sct . 3 ion The plot of the raw data is nonlinear and at the highest laser power attained approaches a limiting value of 42%. Note that Ar 35 c R. + arises .from ionization of six isotopic variants of Ar·Bct • Data such 3 as shown in Figures 1 and 2 thus represent a sum of photodissociation probabilities of six dist·inct species. • • .t . d ue to Ar •10 BCR. t h e Ar 35 c~n+ ~on ~ntens~ y ~s sitive to 954.55 cm-l irradiation. 3 20% of . an d ~s in sen- The additional 22% not dissociated by 954.55 cm-l radiation must be due to isotopic and rotational inhomogeneity. Still, the homogeneous widths of the underlying absorptions must be of the same order as the inhomogeneous structure since it is possible to induce 72% attenuation of the irradiation at 954 cm- 1 • Ar • 11 sct flux with 9.5 W cm- 2 3 Data presented indicate that the homogeneous broadening is comparable to the chlorine isotope shifts but much less than the separation of boron isotope absorption frequencies. 71 1.00 0.50 c 0 .... (.) c ~ LL -c Q,) +- c u 0 (/) (/) 0.10 "'0 c:: ::::> 0.05 w = 954.55 cm- 1 2 4 6 8 Irradiance FIGURE 2. Power dependence of the photodissociation yield. Expansion conditions are identical to those used in generating Figure 1. The nonlinear plot corresponds to measured fractional attenuation of total Ar35ct+ ion intensity. The linear Elot is generated by assuming that 42% of the Ar3 ct+ signal is insensitive to 954.55 crn-1 radiation and treating this as background. 72 A simple two-level-plus-decay model yields a lineshape formula for homogeneous photodissociation under our experimental conditions: 2 lc 0 (w,t) I 2 T 4(w-w ) -2 2 + 0 IC (w,t) 1 2 T -2 ]· is the fraction of van der Waals molecules in the 0 molecular beam which survive irradiation for a light ( 1) with angular frequency Laser w • infrared transition moment enter equation time t, power ( 1) by and the through the Rabi frequency wR • . The complex has a resonant absorption at frequency w and excited state vibrational predissociation lifetime 't. Note that equation (1) confirms the intuitive 0 prediction increases that with narrowing). the extent increasing of photodissociation lifetime (and Consideration of equation at concomitant ( 1) indicates w 0 line that inhomogeneity such as observed in these experiments can be washed out by increasing the laser fluence. Attributing the full width of the dissociation spectrum to predissociative broadening, the minimum lifetime of Ar•BC~ containing one quantum of v mined to be 1. 2 psec. periods. larger 3 excitation is deter- This corresponds to 34 vibrational Alternatively, the minimum width must certainly be than the separation of co 2 laser lines which 73 corresponds to a maximum vibrational predissociation lifetime of 2.7 psec. Results presented are consistent with a highly effi- cient, isotopically selective photodissociation process. The quantum pre- yield is near dissociation process unity since the is extremely fast, vibrational and intensities are comparable to single photon infrared absorption intensities. Isotopic selectivity absorptions is limited only by the overlap of by different isotopic species and hence depends on the vibrational predissociation rate. implement selective dissociation is Equipment used to relatively energy effi- cient and inexpensive. The feasibility of this technique as a practical method for isotope separation is most limited by the intrinsically small scale of the method. Ar~ remove 70% of the only a fraction beam. The van expansions are gas 10 of 10 BC£ the der 3 from the molecular beam, this is 10 total Waals typically a concentration. Although it may be possible to Thus, sc £ 3 concentration in the dimer concentrations in our few percent of the total parent the of one separation mole of Bct from a natural isotopic mixture would require several 3 years of constant irradiation, recirculation, and fragment collection under present operating conditions (105 PSI behind a 35 ~m nozzle) of our apparatus. However, the throughput of such a device could easily be increased by a factor of 100 by using larger pumps, nozzles and apertures. decrease the required time to several days. This would 74 SUMMARY We have reported a one photon infrared dissociation spectrum for Ar•BC£ • The predissociation lifetime of the v 3 3 excited state is between one and three picoseconds. The homogeneous chlorine spectral isotopic isotope shift. isotope widths shifts, are but of much the same less magnitude than the as boron The implications of these findings to laser separation using van der Waals molecules are discussed. ACKNOWLEDGEMENT The authors thank J. L. Beauchamp for providing the co 2 laser used in the experiment. This work was supported by the Research Corporation and the Division of Chemical Sciences, Sciences, U. S. DE-AS03-76SF00767. the Department of Off ice of Energy, under Basic Energy contract no. Acknowledgement is made to the Donors of Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. 75 NOTES AND REFERENCES a. National Science Foundation Predoctoral Fellow. b. Contribution Number 6396. 1. M. P. Casassa, D. S. Bomse, J. L. Beauchamp and K. C. Janda, J. Chern. Phys. 2. ~, 6805 (1980). M. P. Casassa, D. S. Bornse and K. C. Janda, J. Chern. Phys. 74, 5044 (1981). 3. V. S. Letokhov and C. B. Moore in Chemical and Biochemical Applications of Lasers, Vol. III, edited by c. B. Moore (Academic Press, New York, 1979). 4. T. J. Manuccia and M. ·D. Clark, J. Chern. Phys. ~' 2271 (1978). 5. v. Arnbartsurnyan, v. s. Letokhov, E. A. Ryabov and N. v. Chekalin, JETP Lett.· 20, 273 (1974). R. v. Arnbartsurnyan, Yu. A. Gorokhov, v. s. Letokhov and R. G. N. Makarov, JETP Lett. 21, 171 (1975). J. L. Lyman, R. J. Jensen, J. Rink, c. P. Robinson and s. D. Rockwood, Appl. Phys. Lett. ?:]_, 87 (1975) . J. L. Lyman and s. D. Rockwood, J. App1. Phys. 47, 595 (1976). S. Bittenson and P. L. Houston, J. Chern. Phys. ~' 4819 (1977). C. T. Lin and T. D. Z. Atvars, J. Chern. Phys. 68, 4233 (1978). A. Hartford, Jr. and S. A. Tuccio, Chern. Phys. Lett. 431 (1979). ~' 76 6. E. R. Grant, P. A. Schultz, A. A. Sudb¢, M. J. Coggiola, Y. R. Shen and Y. T. Lee, Multiphoton Processes, Proc. In t . Con f • , 19 7 7 , 3 59 ( 19 7 8 ) • 7. M. A. Hoffbauer, W. R. Gentry and c. F. Giese, Laser-Induced Processes in Molecules, edited by K. L. Kompa and S. D. Smith (Springer-Verlag, Heidelberg, 1979) • a. T. E. Gough I ~' 9. R. E. Miller and G. Scoles; J. Chern. Phys. 1588 (1978). K. E. Johnson, W. Sharfin and D. H. Levy, J. Chern. Phys. 74, 163 (1981), and references contained therein. 10. Molecular beam velocities are calculated using effective masses and heat capacities for each expansion mixture and the known expansion conditions as in reference 2. 11. L. P. Lindeman and M. K. Wilson, J. Chern. Phys. ~' 242 (1956). 12. W. B. Maier, II and R. F. Holland, J. Chern. Phys. 72, 6661 (1980). 13. Natural abundances 10 B=l9.78%, 11 B=80.22%, Handbook of Chemistry and Physics, edited by R. c. Weast, 52nd edition (Chemical Rubber Co., Cleveland, 1971). 77 Chapter 4 Homogeneous Photodissociation and Photodesorption Lineshapes 78 PHOTODISSOCIATION AND PHOTODESORPTION LINESHAPES Michael P. Casassaa, Francis G. Celii, and Kenneth C. Janda Contribution No. 6577 from the Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, derived based Pasadena, California 91125 Abstract Photodissociation lineshapes two-level-plus-decay models. The are simplest model on involves only dissociative decay of the upper level and applies to laser-induced vibrational predissociation of van der Waals molecules. A more general model which includes quenching processes that compete with dissociation is presented in a form applicable to laser-induced desorption. Both models yield insightful lineshape expressions with explicit dependence on laser power and frequency, irradiation time, absorption strength, and phenomenological rate constants. Implications of the lineshape formulae for several recent experiments as well as feasibility of studying more complex systems are discussed. aNational Science Foundation Predoctoral Fellow. 79 I. INTRODUCTION Van der Waals molecule photodissociation spectroscopy has developed in recent years as an elegant technique .for studying intramolecular characterized photodissociation example, those of iodine and pure vibrational clusters 1 energy spectra Well include, for and ethylene containing clusters, 2 co 2 3 and HF. 4 of flow. Using narrow band lasers, excitation can be localized in covalent constituents of weakly bound complexes. Subsequent intramolecular vibra- tional energy flow leads to dissociation since van der Waals bond energies are generally vibrational excitation. narrow distributions smaller than the Excitation spectra, of initial states quanta of simplified by produced upon formation of clusters in molecular beams, exhibit widths and time evolution which may be ular Rates are also amenable to detailed rate processes. theoretical approach defined, in and potentials precise for 5-7 many van relationship interpreted in terms of molec- cases, der of the since Waals the excitation structures clusters observed line are is and relevant known. profiles well The and time evolution of excitation spectra to molecular rate processes has not appeared in the literature, but is crucial to the interpretation of experiments. Laser induced desorption of molecules from surfaces is currently an nascent stage. active research area, though still in its It is anticipated that energy transfer rates 80 for surface processes might analogous to experiments be occurring at desorption lineshapes from desorption der Waals molecule van Additional nondissociative photodissociation spectroscopy. processes extracted surfaces would, and however, influence Analysis intensities. of laser-induced desorption spectra would of necessity include consideration of these various rates. Two models are discussed in detail. pure case--applies predissociating to ensemble clusters. formulae, line-shape an two-level-systems, In based may which of this on The first--the non-interacting, paper we present ensembles of simple be used in modeling photodissociation spectra to unambiguously extract rates for decay processes. isola ted is appropriate for molecules This model in molecular beams interpretation of . t s. 2 exper1.men The and has ethylene cluster second model--the general and may be applied been employed in the photodissociation mixed case--is to an ensemble of more interacting species in which decomposition must compete with quenching of excited states. A layer of molecule·s physisorbed on a surface constitutes such an ensemble. The dependences of vibrational state populations and photodissociation yield on laser power, wavelength phenomenological quenching and rate pure and irradiation time, constants dephasing, are for as well as decomposition, explicit. Detailed 81 lineshape formulae are reduced to simpler expressions valid for conditions experiments. generally employed in photodissociation Finally, results of photodissociation experiments performed to date and feasibility of studying more complicated chemical processes, in particular, that of laser-induced desorption, are discussed in terms of the models presented. II. MODEL An insightful model characterizing vibrational predissociation induced by light . absorption consists of an ensemble of two-level systems interacting with a radiation field, in which upper decaying into a conceivable state population has dissociative situation--the continuum. pure the option of In the simplest case--members of the ensemble are completely independent and the two levels are coupled exclusively by the light. Time evolution of population, and hence photodissociation spectra, are then completely coherent, rates up- and the depending down-pumping and molecules. Van der Waals only on predissociation molecules of rate for isolated formed in supersonic expansion of gases conform to this simplest model. 82 A more include general situation--the nondissociative decay mixed pathways case--ought for the to excited state, perhaps ultimately serving to repopulate the ground state, as well as the possibility coherence in the ensemble. of decay of phase The system of interest here is a collection of infrared-absorbing molecules weakly bound to a surface. Upon complexes may radiation field, or reservoir of solid. occur absorption either the a photon, surface-adsorbate decompose, release a lose of energy to the Decomposition of by ejection of the adsorbed species, photon to the infinite heat complexes may chemisorption, or chemical reaction. We start the description of this problem with standard e~pressions from time dependent quantum mechanics. Our approach and notation closely parallel those given by Lamb et al. 8 The state function for a two-level system evolving in time can be written as a linear superposition of the two time-independent eigenfunctions with time-dependent coefficients. (1) 1JJ(_r,t) = c (t)¢ (r) + cb(t)¢b(r) a a - ¢a and ¢ b are eigenfunctions of unperturbed molecule, the Hamiltonian representing the upper levels, respectively, of the two-level system. for and the lower The complete 83 time dependence of the system is contained in the c. • If l. the upper state is predissociative, then c corresponding In exponential perturbation, the time decay. dependence of will contain a a the presence the c. can l. of a be decon- voluted into factors due to the perturbation interaction and the inherent time evolution of stationary states, c. (t) = c. (t) l. l. -iw.t (2) l. e th e energy o f th e 1.. th state 1.n . un1.ts . . wh ere w. 1.s o f angu 1 ar l. frequency. formulae The mathematical development of lineshape is simplest using interaction picture probability amplitudes, in the pure case, C. , l. and Schrodinger picture probability amplitudes, c.' in the mixed case. l. Pure Case In the situation that completely noninteracting, ensemble correspond amplitudes. to members of the ensemble are the populations of states in the the isolated If initially ICa(Q) 1 2 molecule + lcb<O>I 2 probability = 1, then the fraction of the molecules remaining in the ensemble at some later time is given by F P (t > = I c (t > I a 2 + Icb ( t) I 2 (3) 84 The time evolution of C and Cb in the presence of a pertur- bation two-level-plus-decay . a in the simplest model, 2 ' 9 is given by c c a ( 4a) a ( 4b) The first equation exponentially radiation. by the -y D -2- so that constant Y0 in includes with rate I the C a 1 2 decays absence of The matrix elements for coupling of the states radiation field are given in the rotating wave . . 8 by approx1mat1on = = Here ~ is the transition moment, intensity, and w is ( 5) E 0 is the electric field the angular frequency of the 1 ight. Substituting eq. (5) into eqs. (4) gives the rate equations = e = e i~wt -i~wt c b - ca (6a) ( 6b) 85 = wa -wb -w where b.w Solution of eqs. a (t) cb(t) = -z = ll•E = - h -o is the Rabi frequency. ( 6) subject to initial = conditions Ca ( 0) = 1 yields 0 and Cb(O) c and w R exp (it::.wt/2) exp (-y t/4) sin (zt/2), 0 UYo/ 2 : it.w) sin(zt/2) X exp(-i!::.wt/2) (7a) + cos(zt/2>] ( 7b) exp(-y t/4) 0 where z = + The populations of the individual states are irradiation at frequency w for the t are lc a (w,t) I 2 ( 9a) xt) -cos 2 2 lzl2 + I :12 [(~ x + t.w0 X sinh sin x2t cos x2t + J 'Yf cosh ¥f + (cosh 2 Gy + t.wx) ¥f - sin 2 x2t)} ( 9b) 86 where x and y are the real Explicit expressions for x and and y imaginary appear parts of z. in Ref. 2. The fraction of the total initial population remaining at time t is given by unnecessarily eq. ( 3). However, cumbersome and the does exact not solution directly physical insight into long-time observations. is yield In the case that wR < y , eq. (3) can be reduced to a simpler form 0 F p ( w, t) = Equation (10) exp [ -w R2 v'D -lt • (10) is the exponential of a Lorentzian multiplied by a factor proportional to laser power, decomposition lifetime transition moment. and the square irradiation time, of the absorption The width of the Lorentzian term (FWHM) is related to the decomposition rate by (lla) The full width at half minimum of eq. (10) is given by FWHM' ( llb) 87 where FWHM' is Lorentzian term to be distinguished from the width of (FWHM) (lla). appearing in eq. the Equations (10), (11), and associated restrictions apply to most photodissociation experiments performed to date. Mixed Case In order systems and matrix approach is ensemble to repopulation to more approach used for for the include the interaction or feeding problem appropriate a = -(iw a cb = -iw b cb Equations of motion + y /2) c evolution than the isolated molecule The equations of motion Schrodinger picture probability (2) and (6): i (12a) K vab cb a for (12b) the - the corresponding en em * density matrix are easily derived from ( 13a) i (Vabpba- Vbapab) =+ K ( 13b) Pab = Pba of i Paa = -ypaa pbb density i - K vba c a elements, defined as P nm eqs. ( 12) : . a time amplitudes are obtained from eqs. c processes, molecular of the pure case. isolated molecule between - K (Vabpba - vbapab) i -[i(w -w ) + y/ 2 ]Pab + flvab (paa -pbb) a b = Pab * ( 13c) ( 13d) 88 Equations ( 13) are completely equivalent to eqs. 10 1s . . so 1 ut1on somew h at more comp 1'1cated . density matrix modified to feeding terms. formalism is in that phenomenologically For example, though The utility of the eqs. include suppose ( 4) are (13) other that Y easily decay is and actually composed of a sum of nondissociative quenching rates, Y Q' as well as decomposition rates, r 0• Excited state population which is quenched should reappear incoherently in the ground state population. Another incoherent effect due to inter- molecular interactions is increased rate for loss of ensemble phase coherence. than Y/2) Although of This appears as more rapid decay (greater the off-diagonal density the formalism presented here rna tr ix elements. is designed specifi- cally to deal with the problem of laser-induced desorption, eqs. ( 13) may be further modified to apply to different or more complicated include, for physical example, systems. 11 additional Simple coherent modifications and incoherent feeding and decay paths for both states. Recasting eqs. {13) to include these effects produces i paa = -(y Q + yD)paa - R [Vab Pba - • = pbb v ba Pab] i YQPaa + ¥i [V ab Pba - v ba Pab] . YT) Pab + Ki vab (paa - pbb) (14a) ( 14b) Pab = - (iw 0 + 2 (14c) * Pba = Pab ( 14d) 89 where = wa - wb. wo YT is the total phase relaxation rate 2 defined such that ( 15) In NMR parlance, where Ypo is the rate for "pure" dephasing. y Q + y 0 can be associated with l/T is again given by eq. (5). 1 YT and 2 The initial conditions are taken to be Paa = Pab = Pba = 0 and Pbb = 1 as are appropriate for molecules in a supersonic molecular beam, or on a cold surface. Solution of eqs. procedure, as used in (14) is accomplished by an iterative Lamb's semiclassical laser theory, whereby it is noted that the population difference, pbb, is slowly varying solution of eq. compared to p ab. The first 8 p aa order (14) is then -i = 2 wR (paa - Pbb) e -iwt ~i~(-w----w~)--+_y_T~/~2- 0 (16) Substitution of eq. (16) into (14a) and (14b) yields = (17a) = (17b) 90 where = L ( 18) Integration of eqs. (17) is performed by the Laplace trans- form method to give second order solutions for Paa and Pbb. The fraction of population remaining at time t F m is = ( t) = exp [-(L + (yQ + y 0 )/2)t] . X [L + ( y Q + y D) /2 sinh(z~t) J + cosh(z~t) (19) z' where z ( 2 0) = In the case that wR < yQ + y Frn (w, t) = exp Substituting eq. 0 , eq. (16) simplifies to (-L • YQ y +D YD ) ( 19) into eq. (21) (21) yields a form of F (t) m 91 which can be compared to eq. ( 10) (the isolated two level solution): y 2 F m (w,t) -1 t -~::--T_ _--:::YT 4llw2 + 2 YT = exp (-wR2 ( 2 2) The width of the Lorentzian is increased by the added decay and dephasing processes as compared to eq. also includes quenching a rate scaling factor overwhelms ensemble remains intact. Y 0 /( Y Q ( 10). Eq. ( 2 2) if the processes, the + decomposition In the absence of pure dephasing and quenching eq. (22) reduces to eq. (10). III. DISCUSSION The pure case two-level-plus decay model to many recent vibrational predissociation is applicable studies since these have involved coherently excited van der Waals mole- cules formed in molecular beams. There growing body of experimental and devoted to these well-defined systems. formalism is appropriate increased complexity and for has is a theoretical The photochemical been presented substantial, literature mixed-case systems in a of form 92 describing laser-induced desorption of physisorbed molecules. Due to the increased difficulty are, of studying suc·h systems, unfortunately, relatively few examples laser-induced desorption for comparison. In both the pure there of and mixed cases, photodissociation profiles and yields depend explicitly on decomposition rates. Physical details, such as coupling mechanisms and product distributions are intimately related to these rates but may remain unspecified in modeling photodissociation spectra. In the discussion below, we consider the interpretation of spectral profiles and intensities observed in several van der Waals surface molecule experiments, experiments. In light and those of the anticipated models in presented, extraction of lifetimes from spectral data generally requires ~onsideration of factors such as irradiation time, power, and the possibility of saturation. The same considerations apply in determining feasibility of lifetime measurements or optimizing experimental conditions. chemical systems, these For more . complicated photo- considerations must also include competing rate processes. Ethylene containing clusters The pure case two-level-plus-decay model is in excellent agreement with the observed power and wavelength dependence . 2 d 1mer. of infrared photodissociation yields for ethylene Lifetimes and transition probabilities for a series 93 of ethylene containing success of the model for clusters <C 2 H4 > 2 have been obtained. · The dissociation makes this an attractive system for exploring the nature of the lineshape in different regimes of power and irradiation time. In one cc 2 H4 ) 2 set of photodissociation experiments, dimers were formed in supersonic expansions and detected 60 em downstream with a mass spectrometer. Colinear excitation co 2 laser provided low-power (6.7 W cm- 2 > uniform with a cw irradiation of the beam with moderate fluences (3.7 mJ cm- 2 ) due to a long irradiation time (0.57 msec). The irradiation time corresponds to the flight time from the nozzle to the detector. Plots frequency exhibit symmetric, close the out-of-plane bending frequency Photodissociation spectra are to ethylene. broadened. v of 7 fractional dissociation nearly Lorentz ian vs. laser line-shapes of free homogeneously A Lorentzian fit to these raw data, however, leads to an error in the lifetime. Eq. for (10) and associated interpreting the restrictions are appropriate experiment described. Note (10) is the exponential of a scaled Lorentzian. that eq. Thus, a plot of the logarithm of the undissociated fraction of molecules exhibits Lorentzian shape with width directly associated with the predissocia tion rate using eq. transition moment for mined from absolute {10), since ~ Rabi frequency. ( lla) . In addition, the infrared absorption is readily deterfractional dissociation data using eq. appears in the scaling factor as part of the 9'4 The departure of eq. (10) from Lorentzian behavior 2 increases with the scaling factor wR y - 1 t and is not readily 0 2 -1 t<l. observable for wR y 0 ment described, least-squares y - w R2 0 Lorentzian 1 t For the ethylene dimer experi- = 0. 389, fit to and the the raw width data of a yields a predissociation rate which is only 11% greater than obtained using eq. (10). Experimental 2 y -lt D trimer. comparison, probability absorption WR In = 0.389 for trimer has that the dimer. which yield times 1.5 identical conditions ethylene to of those w 2y -lt (C2H4)2 give R D an = 0.795 for the In the latter case a simple Lorentzian fit implies a dissociation rate which is high by 24%. Thoughthese discrep- ancies the relative quality are consistent with eqs. (11), of statistical fits to experimental data is not sufficient to This is illustrated obviate use of either functional form. in Figure 1, which shows nearly identical least-squares Lorentzian fits to ethylene trimer dissociation spectra for f r actio na 1 d i s soc i at ion undissociated fraction frequency. which ( so 1 i d 1 in e ) (dashed line) and as 1 og a r i t hm functions of of the laser Arrows indicate widths of the two fitted curves differ by The 24%. statistical quality of the Lorentzian fit to the raw data shown in Figure 1 (solid line) is misleading and alone lends no justification to inter- preting its width as a lifetime. As laser power and irradiation time are increased,the lineshape, shape. eq. At some (10), point, exhibits increasingly non-Lorentzian saturation dramatically affects the 95 1.0 ( C2H4} 3 0.6 0 0 2 -1 C&IR Yo t = 0.795 0.8 w ~ <( u 0 en en 0.6 0.4 0 ---- - z 0 -In F 0.4 1-F-- ~ u <( a:: 0.2 0.2 u... 0.0 0.0 930 FIGURE 1. 940 950 960 970 980 Photodissociation profiles for (C2H 4 )3. The solid and broken lines are nonlinear leastsquares fits of a Lorentzian and Eq. (10) , respectively, to experimental measurements (circles). Arrows indicate widths of the profiles at half maximum on their respective scales. 96 profile, appearing as a plateau of complete attenuation of van der Waals molecule intensity. Such a situation is easily accessible for cc 2 H 4 >. 2 dissociation and with determined (10) parameters broad, the dimerexperiment above. from eq. ( 10 > using the same measured predissociation life- time and transition time, t moment, intense in eq. described but spectrum with is shorter obtained irradiation = 10 ll sec, ' and higher power so that the fluence is J/crn 0.5 The in is depicted 2 conditions attainable TEA co with a laser. 2 Lifetimes can be extracted from saturated spectra using the same procedure described above for ment. the low-fluence experi- Note, however, that detailed analysis of pulsed laser photodissociation profiles is complicated considerably by temporal and spatial variations in laser power not included in the models presented here. The width of the profile predicted for the pulsed laser experiment is an order using the cw laser. broadening varies dependent on magnitude Inspection of eq. with laser of the fluence a than observed ( llb) shows that the 2 wR t product for greater and is therefore given molecule. We have dubbed this effect fluence broadening in order to distinguish it from power broadening and interaction-time The power-broadened width of a Rabi frequency, given by the 1 0- 2 em-l (2 x pulsed laser while the reciprocal and 5 x experiment transition interaction irradiation 10 -7 em -1 , depicted is time time. broadening. given by the broadening is widths These respectively, for the in 2 are Figure 97 1.0 T =0.44 psec fL =0.18 D 0 .8 - "C Q) .2 (.) 0.6 0 (/) (/) 0 0.4 3.8 mJ · cm- 2 c: · 0 ( .) c ~ LJ... 0.2 0.0 -200 FIGURE 2. -100 0 100 200 Photodissociation profiles for (C2H4)2 cal~ulated using Eq. (10) for pulsed laser (0.5 J em- ) and . cw laser (3.8 mJ cm-2) experiments. 98 insignificant compared to the lifetime and fluence broadened width. The infrared photodissociation spectrum of ethylene dimerconsists of an isolated, homogeneously broadened line. Because of this simplicity, fluence and saturation effects on the profile do not appreciably complicate extraction of the photodissociation rate from the spectrum. sociative lifetime were somewhat longer, If the predisit is conceivable that inhomogeneous structure would begin to emerge, obscuring the saturation plateau and fluence broadening, and perhaps lead to an incorrect assessment of the nature of the broadening mechanism. He•! --2 Vibrational tative of a been predissociation series of investigated reported by Levy He • I 12 2 iodine-rare gas thoroughly and of with co-workers. 1 is represen- clusters which have innovative experiments these experiments, In He ·1 formed in molecular beams is pumped optically to an 2 electronically and vibrationally excited state of iodine. Fluorescence observed is emitted exclusively from uncornplexed 1 , 2 and .therefore fluorescence intensity is proportional to the fraction of irradiated molecules which predissociate. Spectral lines are significantly narrower than observed in the ethylene experirnents,so that the possibility of observing saturation and fluence effects is more acute. Individual 99 bands are inhomogeneous and consist of overlapping homo- In the analysis, 12 the geneously broadened rotational lines. rotational lines were assumed to be Lorentzian, with width corresponding to the predissociation rate, and a convolution procedure was employed to determine lifetimes. Are conditions employed in the He·I that the valid? choice Two of of a Lorentzian many He • 1 X( u =0)-+ B(u =12) and . 1 y. 13 · Measured widths 5 em/sec, the configuration is yield scaling factors, wR 2 0-12 and 0-25 transitions, lifetimes of 221 time 10- ~0.1 y - 1 t, of 0 in 7 the crossed sec. mJ em -2 • The conditions 0.33 and respectively, 0.65 for the so that lineshapes the measured widths, beam Each molecule basis (llb), 43 Assuming a veloci.ty of 2 x However, eq. and was approximately 0. 3W are quite similar to Lorentz ian profiles. of 2 respec- in the order of then experiences a fluence of are He • 1 o2 and ~2 x 10- 2 o2 , laser power irradiation is squared yield which form have focused to a 0.2 rnm beam waist. 10 functional X(u =0)-+ B( u =25), The single mode psec. a transitions measured 2 transition moments of ~2 x 10- 3 t~ve as experiments such 2 and on the approximate conditions, actual predissociation lifetimes are ~9% and ~17% larger than reported. This discussion by no means vitiates results or significance of the He ·1 2 experiment. Discrepancies calculated certainly represent an upper limit and are reduced to 3% and 6% by factor 2 simply decreasing the estimated product, w R t, of 3. Improved interpretation of the data by a would 100 require more precise knowledge perhaps consideration of of conditions spatial variations of employed, laser power and irradiation time, but would probably not change lifetimes reported by more than ten percent. We emphasize that such considerations will be crucial to extraction of lifetimes in the case that any one of four factors--laser power, irradiation and lifetime--is increased. to completely colinear excitation. transition moment, For example, it would be trivial He •I remove time, from 2 In general, a molecular beam using the prospect is excellent for observing large attenuation of cluster intensity in molecular beams using visible lasers and molecules with moderately allowed fractional electronic attenuation--as transitions. in the Measuring ethylene absolute experiments-- permits direct determination of transition moments, which are important in line shape analysis, as well as . straightforward assignment of spectra to particular clusters. The visible laser induced fluorescence technique is complimentary in that it is extremely sensitive and can be used to probe product state distributions as well a excitation spectra. Combination of the two techniques would seem to be ideal for fully characterizing vibrational predissociation of van der Waals molecules over a wide range of vibrational excitation. 101 The first dissociation Scoles for performed spectrum (N20)2. with oscillating co 2 • 3 infrared near was 14 pure the laser reported Similar co 2 by Gough, experiments clusters (101) vibrational inducea and using (021) have an pre- Miller and since been F-center combination laser bands of In these experiments, the molecular beam was directed into a bolometer which produces a signal proportional to the energy imparted to the detector surface by collisions with molecules. The observed signal includes contributions from all degrees of freedom of all molecular beam components. Laser-excited predissociation of clusters scatters fragments out of the field of view of the detector and reduces bolometer signal by an amount which is assumed to be proportional to the fractional The disso~iation of van der Waals molecules. <co 2 > 2 photodissociation spectrum exhibits a broad, nearly symmetric band, near the {101) absorption frequency of co 2 , with full width at half maximum of 2.3 cm-l providing a lower limit of 2.3 psec for the lifetime. The slight asym- metry and suggests inhomogenity longer lifetimes. in the band consequently In order to provide an upper limit, Miller has modeled the rotational structure and obtained a similar profile composed of ~10 mechanism laser. imposed 5 other rotational lines with no broadening than the 1 MHz bandwidth of the However, the finite flight time of particles from the 102 irradiation region to the detector further limits the together with reduce the life-time to less than 3 x 10- 4 sec. The lineshape dissociation expression, eq. data considerably yield uncertainty in the co spectra similar F-center laser in dimer lifetime. We have obtained dimer 2 to those the spectrum. 15 described colinear by Miller arrangement complete moni taring The maximum fractional dissociation i~tensity of approximately 0.16 W/cm 2 and an irradiation time of 0.82 msec. assuming an the molecular observed is 0.6% using laser and and using cco 2 > 2 intensity in fractional attenuation of beam mass can (10), homogeneity, these Using eq. conditions (10) yield 0.6% dissociation if the lifetime is 4.0 psec accounting for the full width of substantially the observed spectrum. inhomogeneous, it would If be the band is impossible to dissociate 0.6% of the total population at a given frequency, because the laser linewidth is extremely narrow. An inter- mediate degree of inhomogeneity may exist such that the laser probes subensembles frequencies. to varying An estimate of extent at different laser the minimum homogeneous width which is consistent with observations is 0.6% of the observed width. This corresponds to a maximum predissociation life- time of 700 psec. With improved characterization of the co 2 dimer spectrum and modeling, it should be possible to further reduce the uncertainty in the to one order of magnitude. cco 2 > 2 predissociation lifetime 103 Laser-Induced Desorption The use of radiation to effect desorption of adsorbed species is a topic which encompasses a wide range of experiments. Included are cases in which species bound to semi- conductor surfaces are desorbed with bandgap excitation, 16 or where the radiation enhances desorption by surface heating. 17 The subset of particular interest in this paper consists of the case in which coherent radiation directly excites vibrations within an adspecie to induce resonant desorption. The problem is conceptually similar to the case of van der Waals molecule vibrational predissociation 18 with one partner of the van der Waals complex being replaced by a surface. The adspecie excited subsequently molecular localized substrate-adsorbate bond. particularly of a metal, other van der desorbs Waals upon coupling vibration Unfortunately, is not partners to a of the solid weak surface, strictly analogous previously the to the discussed. The presence of additional fast decay channels not present in the gas phase experiments may serve El ectron- h o 1 e . pa1r t.1on 20 . exc1ta examples such quenching considered of when dealing quench to an d phonon mechanisms with excited desorption. . . em1ss1on which species 21 must in are be close proximity to a solid surface. Relatively few experiments desorption of condensed . spec1es. have demonstrated 22-24 Resonant resonant molecular absorption of radiation followed by local heating has been 104 advanced as the mechanism for the evaporation of thick c H N 5 5 24 layers on KCl or Ni. A similar explanation for the case of cH F multilayers on NaCl (100) seems reasonable, as the wave3 length dependence of the desorption yield mimics the solid-phase CH F adsorption spectrum. 23 An additional broad 3 1 ('V 25 cm- > desorption feature for CH F on a NaCl film 23 has 3 been interpreted as indicative of the layer bound directly to As there the surface. computed results, are few our data with which to compare discussion feasibility of future experiments. presented here desorption can given be used to reasonable thus deals with the The mixed-case formalism estimate rates for the the probability of different decay processes. Vibration-vibration interactions coupling a high frequency (localized adatom) mode with low frequency surface (phonon) modes 10 11 10 -10 sec -l has b een a 1 so has been modeled, 2 0b, 2 l yielding The rate of electron-hold pair cons1. d ere d20 the for case of rates of excitation vibrationally excited CO bound to Cu and was · computed to lie in the range of 10 9 -10 systems 10 1 sec- . derived The 0.2 to 3.5 psec lifetimes of similar from IR reflection-absorption lineshapes 25 have been explained by invoking energy loss to charge oscillation in the CO-metal bond. 26 These results seem to indi- cate that, in general, rates of energy transfer to the metal may not be as fast as is commonly speculated. We consider radiation from a the example low power of a (10 mW) molecule which cw laser at absorbs 'V3100 cm-l 105 <<~> (8.9 kcal/rnole), with one-tenth the absorption strength = CH 0.01 D) 4 of CO on Cu (100). 27 A model sys tern would be <v 3 = 1) adsorbed on a metal surface, or NH 3 <~ 1 = 1) on an inert (e.g., sapphire) substrate. glancing A angle of incidence is used to interact with the component of molecular vibration normal to the surface, the laser power density. sion, eq. which also serves to lower The mixed-case lineshape expres- (22), is used to examine the dependence of the peak desorption mentally 28 signal w determined dependent rates, y 0 = wo ) as a irradiation , and y Q' will be presented elsewhere, 29 function of the experi- and the system A more detailed account time, Ypo· t, but some important results are summarized here. Figure 3 demonstrates that desorption may be induced, even with quenching rates faster than 10 13 sec -1 if the ensemble of molecules on the surface can be irradiated for a sufficiently long time. The fraction remaining surface after the indicated irradiation time, t, vs. the quenching rate, on a logarithmic scale. desorption rate rates, is parameters sec -1 . 4 10 assumed result in a 12 sec -1 consistent negligible, Rabi and frequency the is plotted The. assumed with gas-phase the example system (wR) of x 1.47 10 5 The maximum value of t, set by the cleanliness of the vacuum chamber, <10 is on could probably not be greater than rv 3 hr s sec). Figure 4 examines the desorption response of the model system upon change of various molecular parameters. The 106 1.0 0 (a) 20 0.8 0.6 LJ...:E. fT1 ::0 I x 10- 12 SEC (') T = w = I. 5 X 105 SEC-I D R , 40 fT1 z -i 0 0.4 60 fT1 (f) 0 ::0 OJ fT1 0 0.2 80 (b) 0 .0 107 108 ' 109 10 10 11 10 1012 1013 1014 100 15 io o0 (QUENCHING RATE, SEc-l ) FIGURE 3. Fraction of adspecies rema1n1ng on the surface for a range of quenching rates. ~he irradiation time is: (a) 10; (b) 102; (c) 10 ; (d) 104 sec. Other parameters are given in the text. 107 0 20 0.8 ~ t 0.6 w ~ u.. R rT'I = I x 103 SEC :::0 () 40 = I. 5 X 105 SEC-I rT'I z --f 0 rT'I 0.4 60 (/) 0 :::0 CD rT'I 0 0.2 80 O.Ot---~~~~~~~--~~~~~~==~~----~--~100 106 107 10 8 '6 FIGURE 4. 109 0 1010 10 11 ( PREDISSOCIATIVE 1012 1013 1014 10 15 RATE, SEC-I) Fraction of adspecies remaining on the surface for a range of d~sorption rates. The quenchin2 rate is: (a) 1010; (b) 1012; (c) 1013; (d) 101 sec-1. Other parameters are given in the text. 108 fraction of adspecies remaining on the surface is plotted vs. the logarithm of the desorption rate, rates. The Rabi frequency for various quenching and dephasing rate are as set previously, while the irradiation time is fixed at 1000 sec. A variety of predissociative rates lead to observable attenuation of the overlayer, including cases with quenching rates sec of -1 The key to experiments of the type described lies with 2 wR t the term in eq. (22). Even with a low-power laser, desorption may be observed since t ·can be made large, and the 2 wR t 2 overwhelms the quenching rate Y • Note that 0 scales linearly with both the laser fluence and the product wR ~ square of the transition dipole moment. with a cw co 2 calculated. greater higher laser may occur more readily than for the case Assuming the lower energy of vibration remains than the available strengths Desorption induced of 2 increase wR t adsorbate-substrate bond power stronger and fundamentals generally in this spectral strength, the absorption region would by a factor of 10-100, which would facilitate desorption over a wide range of dynamic rates. We conclude that resonant laser-induced photodesorption of weakly-bound adspecies should be an observable phenomenon. 109 Acknowledgement This work was supported by the Division Sciences, Office of Basic Energy Sciences, of Energy. u. 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Fayer and C. B. Harris, Phys. Rev. A 13, 383 (1976). 12. K. E. Johnson, L. Wharton and D. H. Levy, J. Chern. Phys. 69, 2719 (1978). 111 13. J. Tellinghuisen, J. Quant. Spectrosc. Radiat. Transfer 19, 149 (1978), and A. Chutjian and T. C. James, J. Chern. Phys. 51, 1242 (1969). 14. T. E. Gough, R. E. Miller, G. Scoles, J. Chern. Phys. 69, 1588 (1978). 15. M. P. Casassa, F. G. Celii and K. C. Janda, unpublished results. 16. D. Lichtman, Y. Shapiro, in "The Chemistry and Physics of Solid Surfaces", Vol. II (eds., R. Vanselow, S. Y. Tong), CRC Press, Cleveland (1979). 17. J. P. Cowin, D. J. Auerbach, Surf. Sci. 18. ~, c. Becker, L. Wharton, 545 (1978). This analogy has also been utilized by Ewing (ref. 19) to extract photodesorption rates. ~' 19. D. Lucas and G. E. Ewing, Chern. Phys. 20. a) B. ·N. J. Persson and M. Persson, Surf. Sci. 97, 609 (1980). 385 (1981). b) T. Korzeniewski, E. Hood and H. Metiu, J. Vac. Sci. Tech. 20, 594 (1982). ~, 21. H. Metiu, W. E. Palke, J. Chern. Phys. 2574 (1978). 22. N. V. Karlov, R. P. Petrov, Yu. N. Petrov and A. M. Prokhorov, JETP Lett. 24, 258 (1977); see, however, B. Davies, M. Poliakoff, R. P. Smith and J. J. Turner, Chern. Phys. Lett. 23. ~, 28 (1978). J. Heidberg, H. Stein, E. Riehl and A. Nestmann, Z. Phys. Chern. Neue Folge 121, 145 (1980). 24. T. J. Chuang and F. A. Houle, J. Chern. Phys. 76, 3828 (1982) • 112 25. See Table 1, ref. 26, and associated references therein. 26~ B. N. J. Persson and M. Persson, Solid State Cornmun. 36, 175 (1980). 27. s. Andersson, Surf. Sci. 89, 477 (1979). 28. R. G. Greenler, J. Chern. Phys. 44, 310 (1966). 29. F. G. Celii, M. P. Casassa and K. C. Janda, submitted to Surf. Sci. 113 Chapter 5 Infrared Photodissociation of Hydrogen-Bonded Clusters: c 2 a 4 ·HF and c 2 a 4 ·HC1 114 Infrared Photodissociation and Hydrogen-Bonded Clusters: Michael P. Casassa,a Colin M. Western, Francis G. Celii, David E. Brinza and Kenneth C. Jandab Arthur Amos Noyes Laboratory of Chemical Physics,c California Institute of Technology Pasadena, California 91125 ABSTRACT Infrared Parameters photodissociation determined are spectra absorption of frequencies, w , 2 initial-state lifetimes, T, transition ~oments, <~> : ~ T <~>2 psec 10- 3 D2 974.8(1) 1.57(19) 44.2(28) 964.3(1) 3.27(16) 51.9(34) 951.5(5) 0.72(10) 50.9(48) w 0 ern c 2 H4 ·HF c 2 H4 ·HC1 c 2 H4 ·NO -1 aAtlantic Richfield Foundation Fellow and Proctor & Gamble Fellow bAlfred P. Sloan Fellow cContribution No. 6827. 0 115 All are blue-shifted relative to the 949 em -1 monomer v c 2 H4 • HF While the frequency for absorption frequency. close to that observed in an Ar matrix, 7 is the frequency for c 2 H4 ·HC1 is shifted 6.8 cm-l further than that observed in a matrix. The results are discussed in terms of the bonding interaction and the photodissociation mechanism. INTRODUCTION Spectroscopy applled of van to understanding der the Waals nature tional transfer for quantum in a weak served as model systems 'for energy attractive of this within purpose has been interactions Recently, van der Waals between molecules for many years. clusters have molecules studying vibra- molecules. because a covalently bound partner 1 They single in a are vibrational van der Waals complex is generally larger than the weak bond energy and can lead to dissociation. Ideally, factors which control the rate and direction of vibrational energy flow, as well as the fragmentation mechanism, can be determined. Experimental studies of vibrational predissociation of van der Waals molecules were first performed by Levy and coworkers on Hei • 2 Since then vibrational predissociation 2 spectra have been obtained for many clusters, both in the visible and the spectral widths infrared. 3 range from 6 Lifetimes subpicosecond inferred for from ethylene 116 dimer 4 ' 5 to greater than 10 nsec for HF dimer. 6 Theoretical workers of have examined the relative importance affecting vibrational predissociation rates. factors These studies show that rates are strongly dependent on the nature of the interaction between van der Waals partners and on the availability of internal degrees of freedom to absorb excess energy. 7 Several experiments on vibrational predissociation of ethylene-containing clusters have been reported. Spectral widths observed for <c H > , <C H > and c H ·c F all indi2 4 2 2 4 3 2 4 2 4 cate similar lifetimes (less than excited with one quantum in the v mode. 4 (Spectra of Ar- and 7 1 psec) for clusters out-of-plane C-H bending Kr-containing clusters also exhibited broad widths but closer examination has revealed additional structure in the case of Ar·C H • 2 4 be presented in a future publication.) ~ 10 in-plane bending mode leads to This work will Excitation of the significantly longer . 5 d ecay t1.mes. 5 8 h Scatter1.ng experl.ments ' ave s h own t h at t h e fragments of ethylene dimer and trimer dissociation carry most excess of the isotropically. energy as rotation and are scattered These results imply that the same efficient decay mechanism operates in each of these clusters and that predissociation may be indirect. Here we report photodissociation spectra of c H4 • HF 2 and c H4 • HCl obtained by exciting the 2 partner. v 7 mode of the c H4 2 Lifetimes measured are significantly longer than previously observed for other ethylene-containing clusters. 117 The frequencies absorption compared to the other strongly are ethylene blue-shifted complexes. These obs er- vations are discussed in terms of differences in the bonding interaction and the decay mechanism. photodissociation spectrum of We also report the c 2 H4 ·No, which is similar to those obtained for the nonhydrogen-bonded ethylene clusters. EXPERIMENTAL The molecular beam apparatus used in obtaining photodissociation spectra of c 2 H4 • HF, c 2 H4 • HCl been described previously. 4 and c 2 H4• NO has Van der Waals molecules were synthesized in seeded supersonic expansions. Clusters were detected 60 em downstream from the skimmed gas jet, using a quadrupole mass impact ionizer. entire flight spectrometer equipped with an electron The molecular beam was irradiated over the path by infrared laser beam. a counterpropagating, unfocused cw This arrangement ensured that the van der Waals complexes were bathed in ~ uniform radiation field for a period of approximately 0.5 msec, corresponding to the flight time dissociation, was from source to the detector. Photo- induced by mechanically chopped laser light, detected as mass spectrum. the modulation of cluster intensities in the 118 Two modifications ion improved the experimental The first improvement was to measure the molec- procedure. ular greatly beam intensity by counting ions, rather than measuring current. accumulated Under in computer two channels and laser-off ion counts corresponding to were the laser-on phases of the chopper blade. the molecular beam was accumulated. control, Periodically, blocked and background counts were These three count totals determine the abso- lute fraction of van der Waals molecules dissociated by the infrared laser. to statistical analysis of cluster Uncertainty in this result counting errors the measurement was intensities, or so that wa~ mainly due statistical straightforward. weak counting time corresponding to a dissociation error For low signals, a time constant of several minutes was required to keep statistical uncertainties to an acceptable level. The second improvement was to inside the molecular beam apparatus, measure laser power eliminating artifacts caused by variation of laser mode structure with wavelength and power. This was done by moving a mirror into the path of the molecular beam to deflect the laser beam into a calibrated thermoelectric detector dissociation measurement. the molecular before and after each The mirror also served to block beam for molecular beam background measure- ments. The experiments were performed with a cw co 2 laser, although for some experiments the same laser was operated as 119 an N o laser by using a different gas mixture. Both lasers 2 are discreetly tunable with the N o laser filling in some of 2 the gaps in the tuning curve of the co laser. 2 Spectra were taken by monitoring the photodissociation of the mass peaks <C H HF) + , <C H HC1) + and <C H NO) + as a 2 4 2 4 2 4 function of laser wavelength and power. For some expansion conditions, these spectra did not reflect photodissociation of the simplest dimeric large species, ciation of dimeric species were obtained, spectra and mass peak the clusters. To but rather ensure the photodisso- that spectra dependences intensities on the of of the expansion conditions were thoroughly investigated. RESULTS Figures obtained for show 1-3 HF, HCl expansion conditions. the photodissociation and NO mixtures All three under a spectra variety of show significant changes with concentration but each converges on a single peak with a fixed intensity at the lowest concentration. Experiments with lower concentrations were not feasible because of the low count rates. Furthermore, the spectra taken at the lowest concentration did not show a pressure dependence over a range of source pressure of about 5-15 atm. This leads us to believe that these limiting spectra are mainly due to the mixed dimers with little contribution from higher polymers. 120 HF CzH4 Ar He 2 400 600 130 PSIG 10 200 800 150 PSIG 10 200 800 1.0 0 PSIG 5.0 200 800 150 PSIG 2.5 200 800 150 PSIG 0.063 1.3 200 800 200 PSIG 0.2 1.0 200 800 195 PSIG Q.l 0 .5 200 800 200 PSIG 0 .5 u.. I - "'0 Q) 0 '(3 ss 0 0.4 (/) 0.2 5 += u 0~ LL --=- 1t =- --= 0.0 920 940 960 980 w(cm- 1 ) FIGURE 1. Photodissociation spectra of (C2H4)m(HF)n clusters observed at m/e 48 (C2HsF+) for a variety of expansion conditions. The lowermost spectrum best represents c 2 H4 ·HF. Solid curves are best non-linear least-squares fits of the line shape formula described in the text. Data points shown are averages of several measurements, taken over a range of powers and scaled using the 2 fitted parameters to a laser fluence of 2.4mJ/cm . Error bars correspond to ± cr. Where spectra appears to consist of more than one peak, fitted curves are weighted superpositions of line shape formulas, F = 1: X. F. i ~ ~ where the mole fractions, X., are adjustable parameters constrained by ~ r x. i ~ = 1 121 Ar He 5 200 800 175 PSIG 1.1 2.8 210 800 250 PSIG 0.55 1.4 210 800 300 PSIG HCI lL I \J (l) .Q u 0 (/) (/) 0 0.2 c: 0 n 0 ~ l.J..... 0.0 940 960 980 w(cm-1) FIGURE 2. Photodissociation spectra of (C2H4)m(HC1)n observed at m/e 64 (C 2 H5 c1+) with a laser fluence of 3.7 mJjcm2. The lowermost spectrum best represents C~H 4 ·HC1. See Figure 1 and the text for deta1ls of the data manipulation and curve fitting. 122 Ll... Ar He 8 400 600 120 PSIG 10 300 700 70 PSIG 10 210 800 135 PSIG 0.4 I .......... - NO "'0 Q) 0 ·u 0 C/) C/) 0.2 0 c - .Q u 0 Lt 0.0 940 960 980 w(cm- 1) FIGURE 3. Photodissociation spectra of (C2H4)m(NO)n observed at m/e 58 (C 2 H4 No+) with a laser fluence of 1.9 mJ/cm2. The lowermost spectrum best represents C2H4·NO. See Figure 1 and the text for details of the data manipulation and curve fitting. 123 It should be noted that the pressure dependence of molecular beam intensities, which has also been used as a diagnostic tool for determination of cluster sizes contri4 5 buting to a given mass, ' was of limited use- in this work. The mass peaks used in these smooth pressure dependence, mixture used. The mass experiments 2 rv P , always regardless spectrum did, showed a of however, the gas serve to reject obviously unsuitable mass peaks and to aid minimization of the concentration of unwanted species such as ( c H ) n. For example, the pressure dependence of m/e 66 2 4 (notionally c H H37 cl+) was of higher order than that of m/e 2 4 35 64 cc H H cl> so m/e 66 was not used for photodissociation 2 4 spectra of the dimer. The line shape found in previous experiments onethylene were successfully described by a formula derived from a two-level-with-decay model. it must geneous. this be demonstrated The point 9 In order to apply the model, that observed spectra are in previous paper discussion given applies here, and our furthermore, Gentry homo4 on and coworkers have verified experimentally that ethylene cluster spectra are homogeneous. The lineshape formula is: F(w,t) = exp -w . R [ 4(w-w 2 0 yt ) 2 + (1) 124 where F is the fraction of molecules remaining undissociatd after irradiation at angular frequency w for a time t. central frequency of the transition is w and the decay rate 0 for molecules in the excited state is is simply y- 1 . The y. The lifetime, T , The Rabi frequency, wR, is given by: = ( 2) where H is the transition dipole moment, field, and E is the electric e is the angle between ~ and E. The result of . . averag1ng cos 2e 1s: ( 3) = This factor of 3 was not taken into account in our previous work on ethylene clusters, and our moments were a factor of 3 too small. reported transition Our results and those of Gentry are now in agreement. 5 The irradiation time, t , was calculated using the effective heat capacity and molecular weight of the expansion mixture assuming all the thermal rotational and translational energy is converted to translational energy of the molecular beam. 4 Values of w , 0 T and <~ >2 obtained by a nonlinear least-squares fit to the above line shape formula are shown · in Table I. The uncertainties shown are 95% confidence 125 TABLE I. Parameters obtained from line shape fit to photodissociation wavelength and power-dependence data.a b 1" <1J>2 ) (psec) (10- 3 o 2 ) 952.3(5) 0.44(5) 96.0(18) 952.3(5) 0.50(7) 141.0(33) 951.5(5) 0.72(10) 50.9(48) 954.7(2) 0.89(10) 46.2(63) 974.8(1) 1.57(19) 44.2(28) 964.3(1) 3.27(16) 51.9(34) w 0 Cluster (ern (C2H4)2 -1 949.0 35.5(14) aErrors reflect 95% nonlinear confidence limits. b Values for <1J> 3. c 2 reported in ref. 4 have been multiplied by See text for discussion on this point. Ref. 16. 126 limits. In the case of c 2 H4 •HC1, the spectrum used shows definite evidence for a higher cluster in the small feature at ~943 cm-l and in a smaller-than-expected dissociation at higher power. To account for this, was to the 959 was introduced restricted parameter, x, fraction of c 2 H4 •HCl - 970 the least-squares fit em-l range and a corresponding to in the molecular beam. fourth the mole The observed fraction remaining, F , is then given by: 0 F 0 + xF = 1 (4) X For this case x was found to be 0.69(3). In the spectra of c 2 H4 ·HF and c 2 H4 ·NO there is less evidence for the presence of other observed species, for the and full exponential range of power power dependence available was ( 1-10 W cm- 2 >. In any case uncertainties in the mole fraction only affect the quoted transition moment, not the center frequency or lifetime. We can also make tentative assignments of the other peaks in the spectra. All show an 950 cm-l at high ethylene concentration, halide complexes show small peaks of the dimer peak. Earlier work 4 intense peak near and the hydrogen higher frequency than indicated that ethylene poly- mers absorb around 953 cm-l and are typically more intense than dimer species. In mixtures large clusters are formed, in an experiment rich in ethylene where most clustered ethylene will be similar to that in pure ethylene 127 clusters, so that the spectrum should approach that of ethylene polymers. Note, This is in fact observed in all three cases. however, that the clusters whose spectra are observed at 950 cm-l must contain at least one HF (or HCl, NO) to be detected on the mass peak which was monitored. From the spectra taken at low concentrations we see that ethylene bound to one hydrogen halide has a significant frequency shift. two or shift. more We might suppose that ethylene bound to hydrogen halides might have an even greater In the case of c H ·HC1 the mixtures relatively high 2 4 in HCl do indeed show a peak to the blue of the dimer peak which we can assign to c HCl. There is some 2 H~WC1> 2 and other polymers rich in evidence c 2 H4 ·<HF> 2 but, unfortunately, of the range of the co 2 for a similar peak due to this seems to occur just out laser. DISCUSSION ~ are qualitatively different clusters. Inspection than of Table I those of other ethylene shows lifetimes that of nonhydrogen-bonded clusters are grouped below 1 psec, while c 2 H4 ·HC1 and c 2 H4 ·HF are considerably longer lived. Central absorption frequencies in the nonhydrogen-bonded species are all slightly blue-shifted from the monomer absorption 128 blue-shifts However, of 15.3 despite the 25.8 range lifetimes of observed, transition moments for v subunit show remarkable listed in Table I. -1 crn-l ·and ern respectively. and blue-shifts absorption per ethylene 7 similarity -for all the In the discussion below, clusters we consider these observations in terms of the interaction between partners, and their implications for the dissociation mechanism. A. The Bonding Interaction of 2 4 and are unique c ~ ·HF 2 4 •HCl c ~ among ethylene-containing clusters in that their rnicrowave matrix-isolated infrared spectra microwave spectra show the that 11 the ethylene 10 and have been observed. The axis is in the the diatom perpendicular to structure, with the hydrogen of the dia torn directed toward the n clouds of the C=C bond. plane of equilibrium The distances between centers 0 0 of mass of the partners are 3.097 A for c H ·HF and 3.67 A 2 4 for c 2 H4 ·HC1. The v absorption frequencies of c H •HF and c H •HC1 7 2 4 2 4 11 in matrices are both blue-shifted relative to c H but not 2 4 to the extent observed The blue-shifts of here. 1 . 8 ern em -1 -1 and 6 • 8 less than the gas phase shifts. This difference is presumably due to matrix-induced constraint on the act on c 2 H4 • HCl geometry. some While the same forces should 129 c 2 H4 • HF, their manifestation may not be as large, since the interaction between c H and HF is stronger than that 2 4 between c H and HCl. 2 4 A blue shift for the ethylene v vibration in 7 c 2 H4 ·HF and c 2 H4 • HCl is expected on electrostatic grounds alone. The v 7 motion leads increase as to an electrostatic potential energy the ethylene hydrogen-bound proton and a hydrogens decrease as approach they move the away. Since the electrostatic interaction is roughly proportional to l/r 2 , the net result is a narrowing of the v potential and an increase in frequency. vibrational 7 An implicit assumption in this picture is that aside from the electrostatic interaction, the bending force constant is unchanged in hydrogen bonding. This simple picture is supported by infrared spectra of matrix-isolated c H • HF 2 4 and c H •HC1 show no measurable shifts of infrared active CH 2 4 the fact that bending or stretching modes in c 2 H4 other than the treating the out-of-plane bend. 11 Considering only atoms as point charges, the v 7 vibration the effective v 7 and potential can be written as: q.q. l. J lr. ·I -l.J ( 5) 130 12 is the v bending force constant, s and S are 2 1 7 out-of-plane bending angles (constrained to be equal), and i where ks and j are atom ~ndices on the ethylene and hydrogen halide fragments, respectively. of th 1. s . 1 po t en t 1a were The eigenvalues and eigenfunctions f oun d . us 1ng given estimates of the parameters in eq. distances, above. r .. , 1] were taken from the 13 t ec h n1ques . s t an d ar d (5). Interatomic structures described The atomic charges, qk, were formal charges deduced from isolated molecule properties or those reported in an ab initio study of c 2 H4 ·~X electronic structure. 14 The iso- lated molecule properties used were the HX dipole moments 15 and C-H bond-dipole moments which reproduced the measured . t ens1ty. . 16 c 2 a 4 v7 1n with For comparison, the electrostatic pair-wise similar Lennard-Jones term calculations of eq. (5) potential, charge-induced dipole potential, were performed replaced plus a with a pair-wise to approximate the inter- action in the nonhydrogen-bonded cluster, c H ·NO. The ArNe 2 4 ' 17 and ArHe Lennard-Jones parameters were chosen to model the interactions of NO with C and H, izability of NO was approximated respectively. with that of The polarAr. 18 The geometry was taken to resemble the structures of the hydrogen-bonded complexes. Results of these are listed in Table II. and calculations, and parameters Calculated blue-shifts for used, c 2 Hi HF c 2 H4 ·HC1 are in qualitative agreement with the observed , values. Comparison of shifts calculated using parameters TABLE II. Parameters used and results of the frequency shift calculation. HX C2H4 Cluster qH a qc R em D qH qx __j_& e_l (em ) o_l (em ) (em -1) <lJ>2 2 o x10- 3 w ~w Isolated molecule properties: C2H4 .1375 -.2750 -- -- -- -- 947.98 -- 35.3 c H ·HF 2 4 .1375 -.2750 .4130 -.4130 3.097 - 939.28 957.60 9.62 35.0 c H ·Hcl 2 4 .1375 -.2750 .1786 -.1786 3.670 - 375.49 952.29 4.32 35.2 c H ·NO 2 4 .1375 -.2750 b 3.299 - 326.08 948.11 .13 35.3 Ab initio properties: ........ w C2H4 . 1631 -.3263 -- -- -- 0.00 947.98 -- 49.7 c H ·HF 2 4 .1770 -.3494 .3894 -.3985 3.097 -1075.27 959.36 11.38 57.6 c H ·HC1 2 4 .1720 -.3416 .2167 -.2214 3.670 - 549.70 954.42 6.49 54.8 c H ·NO 2 4 .1631 -.3263 b 3.299 - 388.64 947.97 -.01 49.7 aThe harmonic part of the potential was the same for all calculations and used the following 19 parameters for c 2 H4 : kB = .289 mdyne A/rad 2 , RC-H - 1.081 A, Rc-c = 1.334 A, <HCH = 117.37°. D is the potential minimum and R is the distance between the centers of mass e em of the partners. bThese calculations were performed with a pair-wise Lennard-Janes potential with induction 3 -1 forces. :~e parameters used were: aN =1.64A ; NO-C: £=48.7 em ; Re=3.43 A; NO-H: 0 £=20.4 em , R =3.47 A. e ........ 132 from isolated molecule properties and the ab initio values shows that the calculated shifts are sensitive to the values of the formal charges which in themselves approximation to the true distribution. are only an Thus, calculations with a more detailed charge distribution might reproduce the c 2 H4 • HF observed adjusting kS. The blue-shift calculated for NO·C H is very 2 4 shows that induction and dispersion forces, slight, but in c 2 H4 • HCl blue-shifts and without which would cause a red-shift, can be compensated by valence forces to produce a blue-shift. The experiments reported dissociation energy, D , 0 em-l A ssum1ng demonstrate that the c 2 H4 •HF must be less than 975 of zero-po1n t a 0 here 0 energy of 50 em-l f or th e stretching vibration of the van der Waals bond, this dissociation energy published ab is lower than initio value of would the be inferred bond energy, from D e the = 1180 em -1 , 14 or from the 1075 cm-l bond energy listed in Table II. These exaggerated bond energies, which would preclude dissociation, reflect the approximate character of the calculations. Infrared transition moments are characteristic of the charge distribution on c 2 H4 . If the charge distribution on c 2 H4 and the is held fixed, if influence of the polar- izability of the partner is neglected, then only changes in the vibrational motion can affect the transition moment. The this calculations effect to using be isolated-molecule negligible even for properties show strongly bound 133 clusters. A more pronounced, though still relatively small, change in the transition moment occurs if the c 2 H4 charge density is redistributed upon hydrogen bonding, as shown by the calculations using ab initio parameters. transition moments in Table I moment of ethylene monomer, slightly larger. This are close to the transition 16 may The measured although we note that all are be due to polarizable partner in the clusters. the presence of For example, if the contribution of the polarizability of NO is included, transition moments calculated are 13% larger a than the those listed in Table II. These considerations imply that the electronic structure of the C-H bonds of c H is not strongly perturbed 2 4 by -hydrogen bonding and that the blue-shift is electrostatic in origin. The magnitude of the blue-shift reflects the change in the distribution of electron density in the C=C bond and in the hydrogen halide upon hydrogen bonding. B. Decomposition Mechanisms Photodissociation linewidths have implications for the predissociation mechanism but only reflect decay of the initially excited state. The mechanism could, indeed, be indirect involving other states before dissociation. If the mechanism is direct and does not involve excitation of · internal degrees of freedom, one might expect c 2 H4 ·HF and 134 c 2 H4 ·HC1 to exhibit the fastest decay since they are more strongly bound than consequently offer fact, The the a nonhydrogen-bonded clusters and smaller momentum or energy gap. In c 2 H4 •HF and c 2 H4 ·HC1 availability of have the slowest decay rates. degrees of freedom to absorb excess energy would also affect the measured lifetime regardless of the nature of the dissociation mechanism. variety of degrees of freedom of listed in Table I not is However, the the passive constituents reflected in the range of life- times, and no clear trends are apparent. Another factor which may influence decay rates is the In particular, one shape of the intermolecular potential. may expect hydrogen-bonded narrower wells than internal rotation the could clusters other be to have deeper and clusters. The barrier to is perhaps as substantial large as the dissociation energy. and Velocity-resolved angular 5 8 distribution experiments ' on <C H > indicate that most of 2 4 2 the excess energy appears in the fragments as rotational energy. Excitation of rotation then appears to be important in decomposition process the and on this basis expect decay of rigid clusters to proceed slowly. one might 135 ACKNOWLEDGEMENTS The authors thank J. L. co 2 laser and D. S. Beauchamp for the use of his Bomse for helpful discussions. One of us (M.P.C.) thanks the Shell Companies Foundation for summer fellowship support. This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, U. S. Department of Energy. 136 REFERENCES 1. For a comprehensive bibliography of work in this field published prior to 1980, see: J. A. Beswick and J. Jortner, Adv. Chern. Phys. 2. !2, 363 (1981). R. E. Smalley, D. H. Levy and L. Wharton, J. Chern. Phys. 64, 3266 (1976). 3. D. H. Levy, Ann. Rev. Phys. Chern. 31, 197 (1980); T. E. Gough, R. E. Miller and G. Scoles, J. Phys. Chern. ~' 4041 (1981); J. Geraedts, S. Stolte and J. Reuss, z. Phys. A - Atoms and Nuclei 304, 167 (1982); J. M. Lisy, A. Tramer, M. F. Vernon and Y. T. Lee, J. Chern. Phys. 75, 4733 (1981}; M. F. Vernon, J. M. Lisy, H. S. Kwok, D. J. Krajnovich, A. Trarner, Y. R. Shen andY. T. Lee, J. Phys. Chern. 85, 3327 (1981); M. P. Casassa, D. S. Bornse and K. C. Janda, J. Phys. Chern. 85, 2623 (1981); M. F. Vernon, D. J. Krajnovich, H. S. Kwok, J. M. Lisy, Y. R. Shen andY. T. Lee, J. Chern. Phys. 4. M. P. Casassa, D. S. Bornse and K. C. Janda, J. Chern. Phys. 5. 2!, 5044 (1981). M. A. Hoffbauer, K. Liu, C. F. Giese and W. R. Gentry, J. Chern. Phys. 6. 22, 47 (1982); also see ref. 1. A. ~' 5567 (1983). s. Pine and W. J. Lafferty, J. Chern. Phys. 78, 2154 (1983}. 7. G. E. Ewing, Chern. Phys. 63, 411 (1981}; D. A. Morales and G. Ewing, Chern. Phys. 53, 141 (1980}; also see ref. 1. 137 8. D. S. Bomse, J. B. Cross and J. J. Valentini, J. Chern. Phys. ~, 7175 (1983). 9. M. P. Casassa, F. G. Celii and K. c. Janda, J. Chern. Phys. 2§_, 5295 (1982). 10. P. D. Aldrich, A. c. Legan and W. H. Flygare, J. Chern. Phys. 75, 2126 (1981); J. A. Shea and w. H. Flygare, J. Chern. Phys. 76, 4857 (1982). 11. L. Andrews, G. L. Johnson and B. J. Kelsall, J. Chern. Phys. 76, 5767 (1982). 12. G. Herzberg, Infrared and Raman Spectra (Van Nostrand Reinhold, New York, 1966). 13. J. W. Cooley, Math. Comput. 15, 363 (1961). 14. A. Hinchliffe, Chern. Phys. Lett. 15. R. Weiss, Phys. Rev. 131, 659 (1963); E. J. Chern. Phys. 16. ~, ~, 531 (1982). w. Kaiser, 1686 (1970). T. Nakanaga, S. Kondo and S. Saeki, J. Chern. Phys. 70, 2471 (1979). 17. G. Scoles, Ann. Rev. Phys. Chern. 18. A. Dalgarno and E. A. Kingston, Proc. Roy. Soc. ~, 81 (1980). (London) A259, 424 (1961). 19. J. L. Duncan and E. Hamilton, J. Mol. Struct. 2§_, 65 (1981). 138 Chapter 6 Inhomogeneity in the Infrared Photodissociation Spectra of (C H > , 2 4 2 c 2 H4 •HF and c 2 H4 •HC1 139 INHOMOGENEITY IN THE INFRARED PHOTODISSOCIATION SPECTRA OF CC H > , 2 4 2 c 2 H4 •HF AND c 2 H4 •HC1 Michael P. Casassa,a Colin M. Western, and Kenneth c. Jandab Arthur Amos Noyes Laboratory of Chemical Physics,c California Institute of Technology Pasadena, California 91125 ABSTRACT A general inhomogeneous lineshape model for describing predissociation spectra is presented. . The model is appli- cable to systems of noninteracting molecules for which the predissociation rate is greater than the Rabi frequency. The multilevel lineshape formula reported results for is used to analyze previously cc 2 H4 > 2 , c 2 H4 ·HF and c 2 H4 ·HC1. The infrared photodissociation spectra of these van der Waals aAtlantic Richfield Foundation Fellow and Proctor & Gamble Fellow. bAlfred P. Sloan Foundation Fellow. cContribution No. ---- 140 molecules are homogeneous in appearance. v However, the broad 1 spectrum of <C H > is shown to be significantly affected 2 4 2 by orientational hybrid band. The i~ narrower spectrum of a perpendicular c 2 H4 • HF or exhibits to dispersion of rotational transitions, inhomogeneity due the c H • HCl 2 4 while and inhomogeneity, Other sources of spectrum is essentially inhomogeneity, homogeneous. including Fermi resonance, are discussed in terms of their effects on band shapes and intensities. INTRODUCTION In recent years spectroscopists studying dynamics of molecules, and in particular those s ,t udying the infrared photodissociation of van der Waals molecules, have observed broad, featureless bands. 1-5 absorption Strictly, the widths of such bands can only provide an upper limit for the rate of an transition. sity, in unspecified decay process involved in the The profile of the observed band and its inteninstances in which the fraction of molecules dissociating is measured, are used to assert that such bands are essentially distribution of homogeneous. initial 1 2 4 ' ' states Broadening (and, indeed, due to a absorbing species) and to the inevitable distribution of final states is asserted to be negligible compared to the natural width of the transition. Thus, by taking into account laser power 141 and fluence effects, the decay rate of the initial state can be deduced from the spectral width. Of course, the procedure described above hinges on the assertion of complete homogeneity within a band. laboratories, In several two-laser experiments have been performed to confirm the assumption of initial-state homogeneity in the photodissociation of van der Waals molecules. 2 a, 2 b,Sb However, such experiments do not demonstrate the absence of final state inhomogeneity. There are notable instances for which such arguments are tenuous. constants 6 c 2 H4 • HF of and For example, c 2 H4 • HCl are of rotational the order . . . one-tent h o f t h e o b serve d p h oto d 1ssoc1at1on w1'd t h s. lb that finite all photodissociation temperature, the experiments question of are G'1ven performed homogeneity of at in these and co- type of cases requires closer examination. Using workers5b a classical have shown diatomic convincingly model, Reuss that ·another inhomogeneity--orientational inhomogeneity--is important and have used this model to reconcile disparate measurements on However, for experiments performed at low temperatures, a full quantum mechanical description is necessary to describe quantitatively the effects of orientational inhomogeneity. In this paper we present a phenomenological model for photodissociation of multilevel systems, which includes the types of inhomogeneity described above. It is a general- ization of described a two-level-with-decay model earlier 142 for interpretation ciation spectra. 7 of van der Waals molecule photodisso- In Section II the model is presented with equations of motion for the density matrix. Approximations are described which lead to an analytical formula for photodissociation spectrum. the The result, which is applicable to experiments in which the decay rate is greater than the Rabi frequencies, shows the relationship between lineshapes, intensities and inhomogeneity. In Section III observed photodissociation spectra of cc 2 H4 > 2 , c 2 H4 • HF inhomogeneous and c 2 H4 ·HCl are lineshape model. In interpreted each case, with the the photo- dissociation profiles are essentially single Lorentzians. ( c 2 H4 ) 2 has been while there question . stud1.ed by several groups is qualitative agreement, about differences la 2a Sb 8 ' ' ' there has observed. In the and been some discussion below, which was motivated by the work of Geraedts et al., ------ disparity full in the inhomogeneous measured widths is reconciled photodissociation spectra so fluences the initial and is dispersion the the model. narrower states using Sb most of important source that final of at moderate rotational inhomogeneity. Limits on the inhomogeneity, decay rates and temperature for these clusters consistent with observations are deduced from the multilevel model. discussion of the Section infrared III also includes a transition moments clusters and other sources of inhomogeneity. of brief ethylene 143 2. PHOTODISSOCIATION MODEL Figure 1 depicts a simple model which includes essential features experiment. of an The model molecular systems, inhomogeneous is an photodissociation ensemble of non-interacting each with a manifold of lower and upper states designated by the indices Z and u. Only transitions between the two manifolds are allowed and these occur only by interaction with radiation. folds are forbidden. Transitions within the mani- Interaction matrix elements are given by vnm = (1) with n nm = ( 2) where v is the frequency of the applied field and ~ nm is the Rabi frequency of the n -+ m transition. includes the intensity E1 transition and moment orientational The Rabi frequency the electric field -- nm 1 effects. In addition to l..l population being pumped between the manifolds, population in the upper sublevels can decay, ultimately cia t i ve con tin u urn at rates given by the necessarily equal. w.1, while the manifolds is y u, into a disso- which are not The energy of any sublevel is given by separation The of the lowest splitting of levels of sublevels the is two small 144 Yu• {I u>} -wu.~ 4i' w0 1J { Lt >} FIGURE 1. Multilevel photodissociation model. 145 compared by w0 , while the frequency of the applied radiation w~ is comparable to A. Density Matrix The general . form of the equations of motion for density matrix elements in the Schrodinger the representation . 9 ~s .Pnm where of = -(iw nm ( 3) wn- wmand Ynm = ~<Yn +ym ). wnm= This definition for which population relaxation is the only 'nm 1 dephasing mechanism, is appropriate for ensembles of simple v non-interacting systems. n,m basis can be selected Hamiltonian is traceless. consequence of the This is because in such a case an 10 inherent for which the interaction Rapid oscillation, which is a time dependence of stationary states, can be reduced with the substitition: = With eqs. (1), e ivt ( 4) (4), and the rotating wave approximation 9 the rate equations become (Sa) . 146 (Sb) . (Sc) Pzz' = where !1ul In photodissociation experiments the signal which is measured is proportional to the fraction of molecules which dissociate time t. or remain undissociated after irradiation for The fraction of molecules remaining undissociated at any time is given by the trace of the density matrix. Initially the phases of the constituent systems of the ensemble are randomly distributed and population is distributed according to the Boltzmann distribution. Thus appropriate initial conditions for the integration of eqs. {5) are p nm ( 0) = -wn/kT -w·/kT ~e -z, 8 n=m (6) i = B. 0 nlm Lineshape Formula Consideration of typical experimental conditions leads to a useful formula for the inhomogeneous photodissociation lineshape. When fit to a two level model, the results of the 147 ethylene cluster experiments ra t es ot- t h e or d er o f y ~ u described w 0 manifold >> kT and sec are y u is large, populated. yield decay 10 12 sec -l wh.1 1 e Ra b.1 f requenc1es . are of the order of Since below Under -1 i.e., yu only states in the lower such conditions numerical solution of eqs. (5) shows that the lower state populations, p ll ~ vary 2 slowly with a decay rate of the order of nul I Yu • Upper state populations achieve small steady state values of the order of and puu' p uu < n 1 /y ~ u"' oscillate at u > 2 • Off-diagonals of the type 0...1, · &"' frequencies wll' or small with amplitudes of the order (Q 1 u"' /y u wuu' > 2 but remain • With these considerations eq. (5b) can be approximated by ( 7) = Noting that Pz,z, changes negligibly in time 1/Y u ~ eq. ( 7) can be integrated to give ( 8) = Substituting this result into eq. (5c) and integrating gives for the diagonal elements p ll ( t) = J ( 9) 148 where p Zz< 0) is given by eq. r~maining ( 6). The fraction of molecules after irradiation time t is then This lineshape formula is an intuitive generalization of that derived for a two-level system, 7 in which the sums The sum over Z , which accounts collapse to single terms. for initial state inhomogeneity, is a superposition of the spectra for each lower level weighted by their initial populations. on This leads to a non-exponential dependence of F(t) laser power, in contrast to the two-level case. over u in eq. The sum ( 10), which accounts for final state inhomo- geneity, is the sum of the rates at which population of level 1 is lost to each upper level. In addition to decay rates, it includes detailed transition moments for each sublevel. The lineshape, formula in two ways. is comparable to y of a u Lorentzian, experimental in (10), differs from as might be inferred Secondly, frequency, even overlapping from of comprising a single transition moments rotational causes degenerate line. sublevels limited negligible transitions dence intensities the with An example is the two-level Firstly, if the spread of transitions different transition moments. of a the lineshape is not a simple exponential data. dispersion eq. to have the M2 depentransitions The variation in · be depleted at 149 different rates; this may ·be thought of hole burning in the case of M levels. dissociated, system; as orientational With large fractions results resemble the behavior of a however, two level parameters obtained with such an analysis differ from those determined using eq. orientational hole burning model (10). The classical of Geraedts et al. Sb, Sc includes only the second effect and is restricted to linear molecules (or K = 0 states in non-linear molecules). Figure 2 shows power dependence curves exhibiting the orientational light. inhomogeneity induced by linearly polarized The slope of the line from the two level model gives the vibrational transition moment. obtained from eq. transitions of a (10) for molecule at constants (see below). The two solid curves are perpendicular 4°K with and parallel <C H > rotational 2 4 2 In order to show only orientational effects the transition frequencies were adjusted to coincide with w 0 in these plots. dependences for inhomogeneous two-level model The dashed curves are the power a classical plots show with dramatic deviation. the linear molecule. The four positive curvature from the parallel bands showing Since this is a saturation only apparent at moderate-to-high fluences occurs with concomitant linebroadening. quantum mechanical curves differ the most effec~ it is <>10mJ/cm 2 > and The classical and significantly for the parallel bands but much less so for the perpendicular bands. 150 1.0 ~ This work u. - C7' c c 10- 1 E CD a:: ... 0 \ 0 \ '' ' ·-c c Geraedts et .QJ \ Two -level model b ' 10- 2 --Parallel bands]---- - - u --- c ~ u. bands 0.1 FIGURE 2. 0.2 0.3 Fluence (J/cm 2 ) 0.4 Power dependences on resonance showing orientational inhomogeneity. To facilitate comparison, the parameters used were the same as used in Figure 1 of reference Sb. 1 These were <~>2 = 0.071 o2 and y = 11.0 ernThe solid curves used, in addition, the rotational constants of (C H ) (see text) 2 4 2 and T = 4°K. (a) References Sb and Sc. (b) Reference 7. 0.5 151 The quantum mechanical results are a function of temper- in general, a super- ature, while the classical plots are not. Power dependences will reflect, position of effects described, and will show positive curvature in all cases. A transition moment derived assumin~ the than two-level actual from model transition integrated would yield moment. a value Transition intensities will transition moment since, from eq. be lower moments less the determined than the true (10) (11) The equality, which is rigorously true for a two-level system, is satisfied if the fraction dissociated is small. 3. APPLICATION Here we interpret photodissociation spectra of <c 2 H4 > 2 , c 2 H4 ·HF and c 2 a 4 •HCl using the multilevel model. Photodissociation exciting the v 7 has been measured in these clusters out-of-plane bending mode of ethylene. by In each case a single broad symmetric profile in the region of the v 7 frequency of free ethylene analyzed using two-level models. has been observed and · 152 Each spectrum was calculated using eq. over all band. rotational transitions in a (11) with sums single vibrational We also allowed that signals measured were not due purely to hi-molecules by including an undissociating mole fraction in the calculations. Finally, all predissociating levels were assumed to decay at the same rate. its Ethylene dimer generated remarkably broad, intense, considerable interest photodissociation was first observed by Gentry and coworkers. 2 d recent experiments are listed in Table I. when spectrum Results of a1 5 b Geraedts et have reconciled the differences in these results, using the classical model for orientational averaging. Their analysis of the disparity in widths suggests that the transition is a parallel band with both transition moments nearly parallel to the dimer axis. Below we interpret the various measure- ments using the full inhomogeneous lineshape model. Establishing the structure of ethylene dimer is first step in calculating the inhomogeneous spectrum. the The geometry has not been determined experimentally, but several ab initio calculations have been performed. 11 These indicate that the structure resembles the packing of c H in 2 4 crystals with configuration. ethylene the partners in a skewed-parallel For this discussion we will assume that the molecules are locked with planes parallel and 153 y(cm -1 ) w (cm -1 0 ) Fluence (rnJ /crn2) Reference Previously reported results: 17.5±1.4 87.6±10.9 952.8±0.2 40.0 2a 12.2±1.2 96i ±18a 952.3±0.5 3.8 la 10.9±0.8 53 ±10 952.4±0.2 0.50 Sb This work: ab (degrees) 12.0 87.0 952.55 25.0 16.0 12.0 87.0 952.55 90.0 22.0 aThis value is 3 times the value reported in ref. la. be is the angle between the transition moment and the dimer axis. 154 0 This structure is at best an approx- separated by 4.1 A. (c H ) ima te ·picture of broad relatively it is The constants. 2 4 2 but since the insensitive important quantity spectrum to is the is very rotational the skew angle, 8 , which we define as the angle between the transition moments (normal to the ethylene planes) and the dimer axis. adjusted from 0° to 90° the v As 8 is spectrum will evolve from a 7 parallel band to a perpendicular band. for al. 2 a Figure 3 <C H4 > 2 2 photodissociation wavelength temperature 2 Lorentzian, transition, Table I. with valid Hoffbauer et beam with a and a f luence of 16 K for parameters by in a molecular The dotted curve through 0. 04 J/cm • fit of and power dependence data observed These data were obtained translational best shows a laser the spectrum is the completely listed in the homogeneous first line of The observed power dependence is reasonably well reproduced by the same parameters assuming a mole fraction of about 10- 3 is nondissociating. the spectrum dissociated approximately so that 95% Note that at the peak of of orientational the molecules are should be effects significant. The thick solid and dashed curves reproduce the high fluence data using the inhomogeneous model, with parameters obtained at low f luence. The two calculated curves were contrived to bracket the high fluence data by adjusting the temperature, the angle 8 and, within tainties, the low fluence parameters. their quoted uncer- The numbers used are 155 Two-level fit 22 1< , 8 • go• 16 K , 8 • 25 • c 10. 161< 8= 25° (-- -., ' .2 fluenc~ = 4 mJ-tm 2 ) u tJ ., ~ 5. ~ (.) 940. 980. 1.0 ( b) 0.0 0.1 u • 947.8 cm-1 0.2 Fluence FIGURE 3. 0.3 (J/cm 2 0.4 0.5 ) Comparison of the inhomogeneous model and results for (C 2 H4 ) 2 at l6°K~ (a) Spectrum with a fluence of 0.04 J/cm . (b) Power dependence at 947.8 cm-1. Experimental data are reproduced from reference 2a. The dotted curve was generated using a two-level model with parameters listed on the first line of Table I, assuming a nondissociating mole fraction of 0.001. The thick solid and dashed curves were calculated using eq. (10) with parameters listed in Table I and a nondissociating mole fraction of 0.001. The thin solid curve in Figure 3a was calculated with a fluence of 4 mJ/cm2 and e = 25°. 156 shown in Table I. The dashed curve corresponds to 0 e = 25 • Since the power dependence would show more pronounced positive curvature as the parallel band limit is approached, 25° e. The thick solid curve corresponds to the upper limit, 8 = 90°. The temperatures determ~ned in is the lower limit of the calculations are close to the translational temperature of the beam, which is expected; however, we caution that the spectra are sensitive to the rotational state distribution, which is known to be non-Boltzmann in molecular beams. 12 Ref. 2a also states different at 4K or that as the the observed fluence is lineshape changed. is no The thin solid curve shown in Figure 3a was calculated at 0.004 J/cm 2 and 16K with similar, e = 25 °; the calculated curve at 4K shows a but smaller discrepancy. The experiment is such that these were measured with poorer signal to noise so that differences may not have been evident. Figure 3 shows that the high and low fluence data can be reconciled quantitatively. skew angle e is between 25 ° Our conclusion is that the and 90° brackets the which angles predicted by theoretical calculations. v 7 The <C H ) 2 4 2 spectrurnis certainly not a parallel band and has a strong perpendicular component. earlier work remain intact. The essential conclusions of 157 Results of recent measurements on c H •HF and c H ·HC1 2 4 2 4 in supersonic molecular beams are listed in Table II. Equilibrium structures determined from rotational constants are t-shaped with ethylene plane the and diatomic the towards the C=C bond. 6 axis hydrogen The v 7 perpendicular of the diatom to the pointed photodissociation spectra of these clusters lb are significantly narrower and more blue shifted than (c H ) as 2 4 2 indica ted by the two-level para- meters listed in Table II. The geometry and microwave exper iments ening to due significant. rotational nuclear indicate disperson of constants that determined inhomogeneous rotational transitions in broadmay be Even if the temperature were very low, initial state spins do complexes, 6 rotational inhomogeneity not if rigid, persists The equilibrate. require that the v since the structures of 7 c 2 H4 the transition occurs as a parallel band. The solid lines in Figure 4 and 5 are least squares fits . of the inhomogeneous lineshape model to c H • HCl · and 2 4 c 2 H4 ·HF photodissociation data. The parameters and their upper and lower limits are listed in Table II. are true 95% non-lineari ties confidence and limits parameter taking correlation These limits into in the account model. They reflect the high degree of correlation among the pararneters (with the exception of w0 ) . For this reason more 158 -1 y(cn ) c2H4 ·HF 'IW:> level paraneters: b 3.38±0.37 44.2±2.8 974.8±0.1 76.8 974.4 Multilevel pa.rarreters: best values 1.59 upper limits 2. 40 ~ 0.95 lbnits 0.59 1.5 102. 0.73 0.7 55.2 0.51 1.9 c2H4 ·HCl 'IW:> level par arreters :b 1.62±0.24 51.9±3.3 964.3±0.1 0.69±0.03 1.57 49.7 964.1 0.73 0.4 upper limits 1.80 67.6 1.00 2.6 lc:Mer limits 36.1 0.65 0.0 Multilevel pararreters: l:est values 0.90 ~ is the rrole fraction of the dissociating van der Waals nolecule. b Reference lb. 159 0 . 5~---------------------... 04_ (a l 03_ :~ Fk.Jence = 2 2 mJicm 2 02f- i// \, 01_ .............. :;.;!/ _, 00 ········· ·· 965 FIGURE 4. / I 970 I~ ·. f · ..... I I 975 900 985 Comparison of multilevel and two-level fits to experimental results for c 2 H4 ·HF. (a) Spectrum at 2.2 mJ/cm 2 . (b) Power dependences at three wavelengths. The dotted line is the best two-level fit. The solid line is the best multilevel fit. See Table II for parameters. Error bars are one standard deviation. 160 ~ "'@ Q ~ IJl IJl (a) 04 2 Fluerce = 3.7 mJ/cm 03 0 ~ ·n e u.. 02 01 00 965 960 955 975 1/ (em-') 10 Q G: ·~~ '""~I (b) ~ c ~ <1.> ~~ 2· 0:: 11 = 964 78 em-' c Q -g 96326 L.t 04 FIGURE 5. ~! Q 0" c ~ ~~2. ' !~f . Comparison of multilevel and two-level fits to experimental results for c 2 H4 ·HC1. (a) Spectrum at 3.7 mJ/cm2. (b)Power dependences at two wavelengths. The solid line is the best multilevel fit. See Table II for parameters. Error bars are one standard deviation. 161 significance should be attached to the range of acceptable values rather than the best fit values. -It is not likely that than rotational temperatures were lower fact that the least-squares fits permit 1 K but the lower temperatures indicates that the spectra are nearly homogeneous. There are differences in the parameters obtained with the inhomogeneous model and those originally obtained using a two-level homogeneous model. These original parameters are listed in Table II and were used to generate the dotted c 2 H4 ·HF data were originally curves in Figure 4 and 5. The fit molecules assuming that the The multilevel fit sample. Therefore, multilevel fit is detected were purely strongly indicates an impure the transition moment obtained in higher. rotational constants c 2 H4 • HCl, than c 2 H4 • HF Since exhibit inhomogeneous effects. it is has the larger more likely to This explains why the width obtained in the multilevel fit is a factor of two lower than that obtained in the two-level multilevel fit in Figure 4 fits. Indeed, the best shows asyrrunetry associated with rotational inhomogeneity. The differences in the fits to the smaller for two reasons. fit to a fraction. other First, the data were originally two-level model This justified since species was present c 2 H4 •HC1 data are with with an undissociating there different mole appeared to be spectra (e.g.' 162 constants inhomogeneous effects are expected to pronounced than in c H •HF. 2 4 In summary, we see that the essential results of previous analysis slightly. widths of c 2 H4 • HF and c 2 H4 ·HCl are narrower than that of have changed comparable (c H ) • 2 4 2 The and be less significantly The transition moment of c 2 H4 •HF is larger than thought previously and may be greater than that of c H ·HC1. Both transition moments~re enhanced 2 4 compared to c H • 2 4 C. Vibrational Transition Moment We have observed that ethylene clusters have greater v 7 vibrational transition moments than would be expected based on the 0.188 D transition moment of free ethylene. 13 We propose an electrostatic model to explain enhancement vibrational transition moments in 7 c 2 H4 •HF and c 2 H4 •HCl, and, by extension, that in (C 2 H4 ) 2 . In of the model, the v which has the observed qualitatively predicted the shifts, 1 b the van der Waals partners are viewed as acting collections of point charges. 7 inter- If the polarizability of the passive partner, e.g., HF or HCl, clear that v blue is included it is will cause oscillation of the induced dipole and thereby enhance the v 7 transition moment. Because of the geometry, the magnitude of the induced dipole depends on the component of polarizability parallel to the diatomic axis. Using formal charges based on isolated molecule proper- 163 . lb t ~es, . exper~menta 1 6 . geome t r~es, c 1 us t er = 0.99 ~ 3 and izabilities14•15 et;;<HFJ po 1 ar- an d et;;IHCll = 2.79 ~3 the calculated v transition moments are 0.210 and 0.240 for 7 The agreement between the calculated and observed values is only qualitative but it shows ficant. about that the polarizability effect should be signi- Since blue shifts predicted by this model are only one-third of those measured, it is likely that the interaction leading to enhanced transition moments is underestimated in this model. ethylene to redistribute Allowing upon charge hydrogen bonding certainly enhance the polarizability effect. that same the mechanism accounts density in would It is likely for the observed enhancement of ethylene transition moments in <C H > which, 2 4 2 assuming the squared transition moments sum, are 0.210. resonance, Fermi amplified by the perturbative presence of partners in ethylene clusters has been proposed as the mechanism underlying the blue shifts. inactive cases 16 v mode of ethylene occurs at 940 em 8 c 2 H4 • HF of and c 2 H4 • HCl this The infrared -1 17 In the explanation is implausible given the large observed shifts, indicative of a very strong interaction, and the fact that no new bands have been measured. active mode, A decrease in intensity which is certainly there were Fermi not in the occurring, resonance with an infrared would expected if mode. 18 In addition to showing intensity enhancement, be inactive the 164 Thus, a weak-bonding-induced Fermi resonance in the ethylene constituents is less likely. D. Sources of Inhomogeneity In the analysis of the photodissociation spectra above, we have considered only rotational and orientational inhomogeneity as is appropriate for a distribution transitions in a single vibrational band. There are other sources of inhomogeneity which should be discussed. resonance of the type described above of Fermi involving perturbed c H vibrational modes could introduce final state inhomo2 4 geneity but, for reasons outlined above, is not operative in Another sort of final state inhomogeneity, resonance, which would combinations of may arise v 7 with be viewed a if it the low frequency librational van der Waals modes. were as type possible of to Fermi excite stretching and Hindered internal rotation has been observed in the loosely bound Ar·c H and Ne·c H 2 4 2 4 19 molecules. In the latter example a 12.5 em-l barrier causes spli ttings band of the order of 10 em-l 7 with relative intensities approximately given by rotational transition moments. in the v Corresponding excitation of the tightly bound clusters described here would tings, with intensities selection rules. better involve described Such transitions have larger splitby vibrational · not been observed 165 and are expected to be only weakly allowed. source of . initial state inhomogeneity, tional populations, in addition to rota- is initial population in van der Waals modes which would give rise to hot bands. the populations A conceivable of such low frequency We expect that modes reflect the rotational temperature in supersonic expansions and are thus not significantly populated. 4. SUMMARY - A general inhomogeneous lineshape model for describing predissociation spectra has been presented. The model restricted the the under to study cases are where molecules non-interacting and of where is ensemble the pre- dissociation rate is greater than the Rabi frequency. Application of the model to <C H > photodissociation 2 4 2 shows that orientational inhomogeneity is an important effect at moderate fluences. Reconcilation of high and low f luence the data has shown that v 7 ethylene mode in the dimer occurs as a perpendicular or hybrid band. Application of photodi s soc ia t ion has regime the model shown that to c 2 H4 • HF these and s pee i es in which inhomogeneity becomes important. c 2 H4 • HCl bridge the Although the c H ·HF spectrum is empirically homogeneous, the natural 2 4 width width. is a factor of two smaller than the inhomogeneous In contrast, rotational inhomogeneity has an insig- nificant effect on the appearance of the c 2 H4 ·HC1 spectrum. 166 ACKNOWLEDGEMENTS The authors thank W. R. Gentry and J. Reuss for helpful comrnunica tions publication. and for This work was Chemical Sciences 1 providing supported by results the Division of Off ice of Basic Energy Sciences 1 Department of Energy. before U. S. 167 REFERENCES 1. (a) M. P. Casassa, D. S. Bornse and K. C. Janda, 1!, 5044 (1981). J. Chern. Phys. (b) M. P. Casassa, C. M. Western, F. G. Celii, D. E. Brinza and K. C. Janda, J. Chern. Phys. 79, 3227 (1983). 2. (a) M. A. Hoffbauer, K. Liu, c. F. Giese and W. R. Gentry, J. Chern. Phys. 78, 5567 (1983). (b) M. A. Hoffbauer, K. Liu, C. F. Giese, and W. R. Gentry, J. Phys. Chern. 87' 2096 (1983). (c) M. A. Hoffbauer, c. F. Giese and w. R. Gentry, J. Chern. Phys. 79, 192 (1983) . (d) M. A. Hoffbauer, w. R. Gentry and c. F. Giese, in Laser Induced Processes in Molecules, edited by K. Kompa and S. D. Smith, Springer Series in Chemical Physics (Springer, Berlin, 1978} , Vol. 6. 3. M. F. Vernon, J. M. Lisy, H. S. Kwok, D. J. Krajnovich, A. Trarner, Y. R. Shen and Y. T. Lee, J. Phys. 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Casassaa and Kenneth c. Jandab Arthur Amos Noyes Laboratory of Chemical Physics,c California Institute of Technology Pasadena, California 91125 ABSTRACT Infrared photodissociation spectra of the Waals molecules Ne·C H and Ar·C H are reported. 2 4 2 4 obtained near the v sharpest and most ethylene-containing 7 der Spectra frequency of free ethylene exhibit the complex structure van Waals der yet Proctor & Gamble Fellow. bAlfred P. Sloan Fellow. ---- observed molecule. aAtlantic Richfield Foundation Fellow and cContribution No. van for an Calculated 172 spectra based satisfacory on a hindered-internal agreement with those rotor model observed. The are in barrier heights for hindered rotation of c H about the C=C axis are 2 4 -1 -1 12.5 em and 30 em for Ne•C 2 H4 and Ar·C H , respectively. 2 4 The natural linewidths, 0.5 cm-l for Ne•C H and 3.0 cm-l 2 4 for Ar • c 2 H4 , are compared to those of other ethylenecontaining reflect clusters and vibrational is it concluded predissociation, that the widths constrained by conservation of angular momentum. INTRODUCTION During recent years, tra of a series of infrared photodissociation spec- ethylene- containing molecules have been reported. van der Waals These include ethylene bound to C H4 , 1-4 c o , 2 SF , 3 HF, HCl, NO, 5 Ne, Ar, Kr 1 and Xe. 3 2 4 2 6 With the exception of the Ne, Ar and Kr clusters, excitation of these weakly bound molecules at frequencies near the ·gs 0 em -1 v mode of ethylene leads to dissociation in a single, 7 symmetrical band of frequencies. The widths of such spectra, convoluted with orientational and saturation effects, are a measure of the decay of the initially excited state other i.e., transfer of energy from the v modes of the molecule. The vibration to 7 observed position, intensity and band-type give information about the van der Waals interaction. 173 The appearance of the bands, for the most well-characterized clusters, indicates that these molecules have rigid structures. hydrogen For example, bending the v occurs c 2 H4• HF- and c 2 H4 • HCl, 5 as 7 a motion simple an out-of-plane parallel band · in (C H ) • 6 and as a hybrid band in 2 4 2 These observations are consistent with known and calculated If geometries. rotors, the the spectra distinct subbands, structures would be were hindered expected resembling the v to internal have several 7 perpendicular band of free ethylene. Here we report photodissociation spectra Ne • c H of 2 4 and Ar·C H which exhibit the complex band-type expected for 2 4 hindered model rotors. A hindered internal rotation is presented which satisfactorily reproduces experi- mentally eters internal measured line determined with internal rotation decay rate. by positions this model and intensities. include ethylene about the Param- barrier its C=C axis and to the The decay time for Ne·C H is the longest yet 2 4 observed for ethylene clusters. We note that structure in both these spectra has been observed before, clusters in 1 although partially the previous Ar • c H 2 4 obscured experiments. by larger The broad symmetrical absorption observed in our previous experiments was mistakenly attributed to Ar·C H • 2 4 the case structure. for Kr • c H 2 4 which also We presume this to be exhibited underlying Higher sensitivity and resolution in the present experiments has made these new assignments possible. 174 EXPERIMENTAL The . v~ous experimental 1 y. 1,5 supersonic d er Van molecular spectrometer. procedure Waals beams ('ViO been molecules and described were detected pre- formed with a in mass Throughout the 0.5 msec flight time from the source to the detector, power has W/cm 2 > cw the beam was irradiated by a infrared laser. The laser low induced attenuation of the cluster signal was measured as a function of laser wavelength, power, and Sensitivity and precision were experiments by source improved over our earliest sophisticated more conditions. techniques and by monitoring the lase~ action volume with each data point. signal averaging power in the interExpansion gases were c 2 H 4 in Ne, Ar and He, all available from dilute mixtures of commercial sources. Spectra parent ion although, reported spectrometer mass to here help were monitoring the signals in assignment, were also surveyed. obtained spectra at other masses In both cases the expansion conditions were made increasingly dilute in c H and milder (lower stag2 4 nation pressures) in order to ensure correct assignment of observed signals to Ar·C H • 2 4 A co molecules. In 2 the laser the simplest was case of used complexes in Ne • c H , 2 4 Ne • c H 2 4 measurements the same and on both laser was operated as an N o laser by using a different gas mixture. 2 The N o laser fills in some of the gaps in the tuning curve 2 175 of the co laser and helped to resolve some of the extra- 2 ordinarily sharp structure in the Ne•C H spectrum. 2 4 RESULTS Figure 1 shows the photodissociation spectrum of Ne•C H obtained measuring the NeC H + signal (m/e 48) in a 2 4 2 4 beam formed by expansion of c H in Ne and He. This spec2 4 trum shows no significant dependence on source conditions over the range possible with our apparatus. Using the nozzle and mixture shown in Figure 1, it was vary the pressure from 50 to 300 psig. Over this range, the possible to spectrum remains constant while the NeC H + signal varies 2 4 over an order of magnitude, and passes through a maximum. <C H >2, also grow 2 4 By using a larger nozzle ('VlQO ll m diameter), we The intensities of other clusters, e.g., steadily. have extended the pressure range over which spectrum remains constant down to 800 torr. the Note also that this spectrum is identical to the Ne•C H spectrum reported 2 4 ~reviously 1 , except that the N o laser has afforded higher 2 resolution. Molecules contributing to dissociation at m/e 48 are evidently the same under all of these conditions. Since the spectrum persists even with the weakest expansions, we conclude that these spectra are in fact due 176 0 . 20--------------------------------------------------------~ 0 .15 Ne ·C2 H4 Fluence = 1.9 mJ/cm 2 "0 Q) 0 u 0 ~ 0 .10 0 c 0 "5 0 Lt 005 000..,___... 940 960 980 Wavenumber (cm-1 ) FIGURE 1. Photodissociation spectrum of Ne·c 2 H with a 4 laser fluence of 1.9 rnJ/cm2. The gas mixture was 0.5% C2H4, 10.0% He and 89.5% Ne, and was expanded through a 35 ~rn pinhole at 95 psig. The solid curve was calculated using the parameters listed in Table I. 177 Figure 2 shows the spectrum of Ar • c H 2 4 obtained by monitoring the c H Ar + signal (m/e 68) produced by expansion 2 4 of c H in Ar and He. The spectrum shown in Figure 2 is the 2 4 low pressure limiting spectrum for Ar·C H • The intensities 2 4 features experimental strongest are, within the of certainty, constant in the range 400 torr to 1000 torr. As further evidence that this spectrum is due to Ar·C H , the 2 4 same spectrum has been obtained at high pressures in an extremely dilute expansion (0.01% c H , 20% Ar, 2 4 He at 200 psig). 72% Ne, 8% Unlike the Ne·C H spectrum, the Ar·C H measurements 2 4 2 4 by influenced changes in source significantly are . . con d ~t~ons. 7, 8 If the pressure is increased, or if the ethylene concentration is reduced relative to Ar, the broad feature at intensity. 956 em -1 shifts to 950 em -1 and grows in By noting the absence of pure ethylene clusters in such expansions, this broad feature which grows in can be c H Arn where n ~ 2. 2 4 Dissociation of these clusters, which partially obscured the attributed to clusters of the type structure shown in Figure 2, was wrongly assigned to Ar·c H 2 4 1 in our previous work. The l~miting spectrum reported here occurs near the limits of experimental sensitivity. conceivable that apparent breadth of the feature It is near 956 cm-l in Figure 2 is due to small residual concentrations of 178 0 .2 Ar·C 2 H4 Fluence = 5.2 mJ/cm 2 "0 Q) 0 ·u 0 1/) 1/) 0 § n0 0.1 Lt 940 960 980 Wavenumber . (cm- 1 ) FIGURE 2. Photodissociation spectrum of Ar·C2H4 with a laser fluence of 5.2 mJ/cm 2 . The gas mixture was 1% c 2H4 , 20% Ar and 79% He and was expanded through a 100 ~m pinhole at 5 psig. 179 Hindered Rotor Model The observed spectra of Ne • c 2 H4 and Ar • c H do not 2 4 resemble any of our previous ethylene cluster spectra. particular, the spectra are too complex to assign a molecular structure, as we did for of c 2 H4 •HC1. In rigid The splittings 5-10 cm-l are too small to be considered as conventional vibrational combination bands so it becomes necessary to use a hindered internal rotation model. In the model described below, we treat only rotation about the C=C axis as internal rotation, the other two van der Waals modes. the ignoring Normal mode calculations using estimated atom-atom potentials for Ne • c H , 2 4 with Ne symmetrically positioned about the c H plane, indicate that 2 4 this simplification is reasonable. With Ne-Ne and Ne-He Lennard-Janes potentials used to approximate the Ne-e Ne-H interactions, the rotation about the C=C axis and has a vibrational frequency of 5 cm-l and the other two van der Waals modes stretching- are 28 and 46 cm- 1 , respectively. two modes would be best treated as These latter simple vibrations. We note that this distinction is less clear in Ar ·C H where 2 4 1 the corresponding normal model frequencies are 31 cm- , 35 em-l and 45 cm-l (The normal mode calculations involve infinitesmal changes in atomic positions about the equilibrium geometry, and as such may internal rotation barrier heights.) not reflect the actual 180 The approach we use follows that of Bauder et al. ---- The coordinate system is shown in Figure 3. atoms into two sets: 9 We divide the top atoms, and frame atoms. In our picture of Ne•C H , Ne is the frame atom and the atoms of 2 4 c 2 H4 are the top atoms. There are two corresponding axis systems with origins fixed in the molecule: the frame axes - xf' yf' zf - which correspond to the usual body fixed axis system, and the top axis system - xt' yt, zt - which has its origin at the center of mass of the top and is fixed with respect to the top atoms. We choose these axes such that the z-axes are parallel to each other and to the C=C bond, The frame y-axis, the Ne • c H bond and the 2 4 is along y-axis is perpendicular to the c 2 H4 plane. Y top is the angle Thus, y=O corresponds to Ne lying between the two y-axes. above the c H plane. 2 4 The theory for this type of hindered rotor has been al.9 given by Bauder et Unfortunately, their paper appears to contain several errors in the equations, so it was necessary to rederive them. The classical kinetic 2 -I cosysiny -I cosysiny 2 Iyy-I sin y 0 0 0 0 energy is given by I 2T = ( WX I Wy I (.UZ I)) XX +I sin y I 0 0 0 0 zz I w X w y I w z I y . ( 1) 181 FIGURE 3. Coordinate system for the hindered internal rotor model. 182 where wX , wy and wZ are the projections onto the frame axes of the angular velocity of the frame. I and I are xx' yy zz the usual moments of inertia of the system at y=O. I is the moment of I inertia of the top about the top z axis. For Ne·C H the moments of inertia are 2 4 I I I I = XX 2 ~e y Ne + 2 + Ie = I + I e yy (2) 2 = m Ne Y Ne zz e meye = 2m 2 c z c + m ye e + 2 + I 2 4mH z H = 4mH xtH 2 I where xtH is the x coordinate of the hydrogen in the top system. All other coordinates are in the frame system with Y=O. y mass. m is the ethylene mass. e The quantum mechanical Hamiltonian for this system is H = e is the frame coordinate of the ethylene center of ~~ +~ X where -B A -B qq q=x,y,z -~ A qg [A zz -B zz cos2y) A [Jy [JY- -Bcos2y + cos2y cos2y C sin2y A 2 2 2 2 J 2 + ~ xy (J J + J J ) A-Bcos2y X y y X q A J y + Jy (A zz -B zz . cos2y) J A -Bcos2y ~(Jyln(A-Bcos2y)~ (A -B cos2y) . yy yy ~(Jyln(A-Bcos2y))J + v (y} Jy = -ina;ay J z A -Bcos2y ( 3) 183 The symbols containing A and B are algebraic functions of the moments of inertia, eq. (2), which arise from inverting the coefficient matrix in eq. usual body momentum. fixed (1). projections of Jx' Jy and Jz are the the The hindering potential, V { Y), overall angular is expanded as a series in cos2jy for ease of calculation of matrix elements: V(y) = (4) 1: j The symmetry of the expected equilibrium structure is c 2 v. However, the fact that ethylene can rotate within the complex must be taken into account and using the methods of . . Longuet-H~gg~ns morphic to Furthermore, 10 o2 h' . . t h e symmetry group o f t h e mo 1 ecu 1 e ~s ~so- the point the molecule has group four of ethylene distinct itself. nuclear spin states with statistical weights 7, 3, 3, and 3, as has c 2 H4 . The basis functions chosen were products of internal rotor wavefunctions. The internal rotor basis was 1/ J rr , 1/{TicosY, l/{ITcos2y ... 1/fiT cos2ny 2 1/fiTsiny, l/{ITsin2y ..• 1/ff sin(2n+l)y The overall rotation wavefunctions were Wang symmetrized top wavefunctions with L=O or 1: 184 1- (-1)2J+L ( ( -1) K IJ-KM> - ( -1) J+L IJKM>) , IJKLM > = ~ and, for K=O, jJOLM > = The matrix !JOM > eleme·nts with J+L odd only. of the Hamiltonian can be evaluated analytically using these basis functions. For a given total angular momentum, J, and irreducible representation of ations of the matrix was o2 h, we made up a matrix using all combin- above that transformed truncated at some and as value of diagonalized the the to above. The internal rotor quantum number, · n, give levels. This maximum value of n was chosen by checking for convergance in the eigenvalues of the matrix. was sufficient for barriers of 10 em -1 the energy A value A check on 'V 5 the computer program consists of making certain that the energy levels are reasonable in two 1 imi ting cases of V ( Y ) . the limit of zero barrier for rotation, For the J=O states have the energy levels of a diatomic molecule with a moment of inertia of <~1000 em I (I -1 zz - I) /I zz • As the barrier becomes large for Ne·c H > the energy levels become those of 2 4 an asymmetric rotor with slightly anharmonic vibrations. Calculation of Photodissociation Spectra The transitions observed are due to absorption by the v 7 mode of dipole for v ethylene. 7 The orientation of the transition is perpendicular to the ethylene plane. The 185 frame-fixed ( -11siny, components 11cosy, 0) and of the dipole the interaction moment with are an thus electric field polarized along the z-axis is !!·~ IElllll {2 = [ (-DO-l 1* ( w) . 1* - ~<Do-l ( w) + + 1* DOl (w))siny 1* DOl ( wl l cosy J ( 5) J* where the DKM(w) are the rotation matrices defined by Brink and Satchler. 11 in our The matrix of the dipole operator, eq. (5), basis can be evaluated by standard means, and the transition dipole moments of · the system are found by transforming the matrix using the eigenvector from diagonal- ization of the Hamiltonian. These transition dipole moments are then convoluted into a photodissociation spectrum using 6 (6) Equation (6) geneous is a general lineshape formula for an inhomo- vibrational predissociation spectra. F is the fraction of molecules remaining after irradiation for time t. The sums are over all rotational sublevels, the M sublevels, of final state (f). The ground state levels the vibrational ground state p. 1 and including ( i) and are the Boltzmann factors for the include weighting factors for 186 non-equilibrated nuclear spins. The nif are the Rabi frequencies, defined as ( ~f·~)/fi, for the system transition moments described above. The Yf are the decay rates for the upper vibrational levels and are assumed to be equal in the calculations below. Finally, ~if is the difference between the laser frequency w, and the resonant frequency wif of the i-f transition. Spectra were calculated for Ar•C H and Ne•c H for a 2 4 2 4 v2 , range of values of the double well potential parameter the decay rate y, the separation of the partners, R, and the temperature. Calculated spectra which best agree with observed spectra, as ascertained by visual inspection, shown in Figures 1 and 2. given in Table I. are The corresponding parameters are The agreement in the case of Ne·C H is 2 4 quite good, with a one-to-one correspondence between position of most comparable observed and intensities. calc.ula ted Peaks in maxima, the as well as calculated Ar · c H 2 4 spectrum also coincide with those observed, but the distributions of intensity disagree. The calculated spectra are most sensitive to the absolute value of the double well potential parameter, v , which 2 determines the separation of the most intense subbands. For both Ne•C H and Ar·C H the best agreement with experiment 2 4 2 4 was obtained planar with equilibrium molecules, negative v2 , structure with a intensity throughout the band with is less which corresponds y =90 ° • uniformly positive· v 2 For to a both distributed than with negative 187 TABLE I. Parameters used in calculated photodissociation spectra. v2 Cluster a (ern y -1 R -1 0 ) (ern -12.5 0.5 949.1 -30.0 3.0 Reference 13. ) T (A) (K) 35.3 2.92 3.0 953.9 35.3 3.30 5.0 949.0 35.3 188 v2 • While this indicates that the structure is planar, the simplicity of the model and the sparse experimental data preclude definite determination of the geometry. However, the existence of a two-fold barrier to internal rotation of ethylene about is C=C bond is well established. The calculated spectra were values of the other parameters. of the rare-gas atom from mined using rare-gas pair-wise symmetrically less sensitive to the The equilibrium separation c 2 H4 was taken to be that deter- Lennard-Janes disposed potentials above with c 2 H4 the the plane. Spectra calculated with bond lengths 10% shorter or longer than this longer were bond subtly lengths different tending to in appearance concentrate with the end-over-end rotational substructure within the principle subbands. This narrowing effect could be compensated in part by adjusting the temperature or natural width. In the calculations, rotational temperatures were assumed to be in the range of those determined sions2'5'12 and for other natural clusters widths were in similar taken to expanbe the approximate widths of the narrowest observed spectral peaks. As such, these are upper limits for the homogeneous widths. The vibrational transition moment was assumed to be that of free ethylene. 13 Because of the limited experimental data, these parameters could not be more precisely determined. Similarly, consideration of potential terms of higher order than v was not warranted. 2 189 DISCUSSION A. The van der Waals interaction Unlike ethylene clusters previously observed, Ne·C H and Ar·c H must be considered as hindered internal 2 4 2 4 rotors. The corresponding internal motion in c H • HF, 2 4 c 2 H4 ·HCl, <C 2 H4 > 2 or c 2 H4 •c 2 F 4 may be better described as a vibration since observed for along with no internal rotor these molecules. subbands Excitation of have this been motion v would then be described as a vibrational 7 band, with corresponding low intensity, and combination would be well shifted from the v 7 In the cases of origin. <C H > and c H ·c F , the internal motion may be restricted 2 4 2 2 4 2 4 The bonding · interactions in c H • HF and 2 4 are quite strong, evidently pose a sub- by ster ic effects. c 2 H4 • HCl, which stantial barrier to internal rotation by c 2 H4 • The slight blue shift of the band origin in the rare gas clusters from that of free ethylene <v to repulsive = 949 em-1 ) 13 may be attributable interaction of hydrogen atoms. course, 7 the The extent of rare-gas this and the wagging interaction will, of depend on the actual equilibrium geometry and the hindered rotor level. The observed spectra are in qualitative agreement with those calculated with a double-well hindered internal rotor model. As noted above, the agreement is much better for While the explanation for this must await more experimental data and a more detailed model, we 190 can point out factors which have not been considered in this work. The model includes only internal rotation about the C=C axis in complexes where this bond is perpendicular· to the line joining the rare gas and the ethylene center of This structure is analogous to that of Ar·c H , and 2 2 by analogy with c H • HF and c H • HCl, the noble-gas is 2 4 2 4 expected to be above the c H4 plane. It is therefore 2 mass. surprising that the calculations predict a planar sfructure. v2 , while the gross appearance of the spectra depend only on I V2 I , we Since this prediction depends on the sign of hesitate to dismiss the non-planar structure. As noted above, only the interaction term v2 was considered because this led to good agreement between the calculated and observed subband positions. While this indi- cates that the internal rotor potential is well approximated by ~ 2 <1-cos2Y), it is likely that higher order terms would be necessary for quantitative agreement. We did not explore this open-ended question because of uncertainties because of the limited data and introduced by the approximations described below. The consideration of a single dimension of internal rotation is justified in the case of Ne·c H because, based 2 4 on Lennard-Janes pair-wise potentials, the librational motion of c H about the C=C axis is considerably freer than 2 4 end-over-end motion of c H or the van der Waals stretching. 2 4 (The normal mode frequencies are 5 cm- 1 , 28 cm-l and 46 cm-l 191 respectively.) As such one could expect the low frequency mode to dominate the spectrum. In contrast, the corres- Ar • c H4 modes are comparable. (The normal mode 2 frequencies are 31 cm- 1 , 35 cm-l and 45 cm- 1 .> Thus, in the pending case Ar·C H , the other internal modes might also have to be 2 4 considered. Two factors which have been ignored. polariza~ility could influence peak intensities First is the influence of the Ne or Ar on the v transition moment. The oscillating 7 dipole induced on the rare gas by ethylene v motion can 7 enhance the vibrational transition moment. This effect, which has been observed for other ethylene clusters, should be a function of internal rotor level and should be more pronounced in Ar·C H than in Ne•C H4 • 2 2 4 type which has been observed in The second effect, a 14 ( c H2 ) 2 spectra, is a 2 rotational-level dependen~ decay rate. B. Photodissociation dynamics The homogeneous linewidths of van der Waals molecule photodissociation spectra reflect the lifetime of the initially excited state. measure of the flow, mechanism the interest. rate for for Since these lifetimes are a intramolecular vibrational energy the decay is of considerable There has been some question about whether the decay mechanism is best described as a direct dissociative 192 process or as energy transfer to other modes which is fast compared to subsequent dissociative steps. The upper limits for the homogeneous linewidths of Ne • c H make this the longest lived ethylene complex yet 2 4 observed. Previous studies have produced linewidths in a surprisingly narrow range. c 2 H4 • HF em -1 6 and c 2 H4 • HCl For example, observed c2 H4 for perhaps two orders of magnitude. these constrained indicates data are by angular that transfer modes of cc 2 H4 > 2 and c 2 H4 ·c 2 F 4 are 12.0 em-1 and 6.0 em-1 , respectively. 1 in 7 exhibit widths of approximately 1. 6 The widths observed for linewidths the v widths clusters now encompasses As discussed below, trends consistent with momentum are Thus, the range of indeed predissociation conservation. determined to the weakly bound modes. Such This by energy trans£ er would lead to rapid dissociation of the complex. This conclusion is of consistent with predi ssoci_a tion from general, excited while many observations electronically excited clusters are not vibrational states . 15 observed, In their fragments are observed. Energy pumping v , 7 . d , 16 pre d ~cte conservation requires that the cannot be vi bra tionally excited. and 2 17 measured, ' that fragments of It has been translation is a relatively inefficient channel for dissipation of energy in excess of the dissociation energy. Rotation principal channel for product energy release. is then the 193 Ewing has presented a model for energy transfer into rotation which is analogous to his momentum gap model for v~T relaxation. 16 Some conclusions are 1) a perturbation to couple the excited vibration to rotation the rate is enhanced if l::lJ, is necessary; 2) the rotational quantum number change, is small; 3) the energy gap, E - D v o - EJ (where E 7 and EJ are the energies of the tively), should be small to minimize translational energy , D initially excited o 7 mode, the van der Waals bond and product rotation, respecv Also, release. since initial states little angular momentum, the final of the complex have angular moment of the products must cancel. · Ethylene dimer excited in the v 7 criteria for rapid V-T,R dissociation. mode meets the above The coupling between the wide amplitude motion of v and fragment rotation ought 7 to be quite efficient, since the dimer is thought to have a staggered planes-parallel structure. 6 about E v 7 the - D 0 serving carbon-carbon axis can be angular of By exciting rotation each ethylene the released as rotational energy momentum. The rotational final entire while con- quantum numbers need not be greater than 10. c H4 • HCl is less able to satisfy the above criteria for 2 two reasons. The molecule pointing reducing any impulsive coupling may be involved are large. structure of between the c 2 H4 • HCl carbon has the HCl atoms 18 thereby coupling from v 7• electrostatic since the Second, E v 7 Instead bond the dipoles - D0 for c 2 H4• HCl is esti- 194 mated to be 400 cm- 1 • 5 evenly between c of excess the and HCl would require HCl ~o accept most energy with = 4 and 5, between n result a 2 4 To divide the final angula_r moment.um = 4 J or fortuitous The energy gap is over 100 em-l with the however, that translation must provide a sink unless a 5. substantial energy The same resonance is involved. statements apply to c H •HF, except that in this case energy 2 4 release, E - D , is expected to be smaller. 0 'V7 In Ne-c a and Ar·C H only orbital angular momentum 2 4 2 4 Thus decay can offset any ethylene rotational excitation. channels cient. available to Ne·C H 2 4 and Ar·c H are least effi2 4 Because of its lower mass, Ne can carry more kinetic energy with less orbital angular momentum than Ar. Thus, if all else were equal, we would expect the Ne·c H width to be 2 4 greater than the Ar·c H width. Unfortunately, our model has 2 4 permitted determination only of upper limits of the widths. The above arguments are consistent with the inverse linewidths for the series cc H > , c H ·HF and Ne·C H which 2 4 2 2 4 2 4 are 0.44, 3.4 and ~10 psec, respectively. The above model . - affords a physical interpretation of the data and leads to qualitative predictions which can be tested. product velocity distributions For instance, stantial translational energy Ne·C H may show sub2 4 release. In the case of C2 H4 •HCl a or C2 H4 • HF perhaps for structured time of flight "spectrum" of the fragments would be observed due to widely spaced rotational energy levels. Two other broadening mechanisms which are dismissed in the following discussion are pure dephasing and resonant 195 energy transfer molecule. of to other strongly bound modes of the Both mechanisms would mimic the density of states internal modes which are not involved in the initial on the parti- spectroscopic excitation (the "bath" modes). The pure dephasing mechanism depends 19 tioning of degrees of freedom into system and bath modes. For the clusters whose bands- CC H > , 2 4 2 spectra exhibit single symmetric c 2 H4 ·C 2 F 4 , c 2 H4 •HCl and c 2 H4 •HF- the bath modes would include all degrees of freedom other than v • 7 For the rare gas clusters which exhibit separate bands for internal rotation, the internal rotor levels may be excluded from the bath. In this picture, dynamics within the bath modes cause broadening, i.e., pure dephasing, of transitions among the observed degrees of freedom. 19 However, dephasing depends on population numbers in such a way 20 pure that this mechanism may be ruled out as the origin of the line broadening in these clusters at low temperatures. The non-dissociative resonant energy transfer mechanism is likely to be inoperative because it has been shown that increased densities of effect on the widths. strongly bound bath modes that of no cc 2 H4 > 3 and For example, widths of than have cc 2 H4 > 2 • 1 Also, a recent study of OCS-alkane clusters has shown no correlation of the widths and the alkane vibrational state density. Finally, modes the fact fragments that into cc 6 H6 ) 3 (c H ) + 6 6 2 excited c 6 H6 in C-H instead of 21 stretching 3 ( c 6 H6 > 22 196 argues against uniform redistribution of energy before infrared photodissociation spectra dissociation. Summary Highly structured of the van der Waals molecules Ne·C H and Ar·C H have been 2 4 2 4 A hindered rotor model for internal rotation by reported. cluster-bound c H about its C=C axis has been presented. 2 4 Absorption frequencies calculated from this model are in excellent agreement with observations, intensities are in qualitative agreement. while absolute Barrier heights for hindered rotation of c H are 12.5 cm-l and 30 cm-l 2 4 Ne·C H and Ar·c H , respectively. The upper limits for 2 4 2 4 natural linewidths are 0.5 cm-l for Ne·c H and 3.0 cm-l 2 4 These correspond to lifetimes of ~ 10 psec for the for for Ne·C H and ~1.7 psec for Ar·C H . Comparison to widths of 2 4 2 4 other ethylene containing clusters leads to the conclusion that the widths reflect vibrational predissociation constrained by conservation of angular momentum. 197 ACKNOWLEDGEMENT The authors thank J. L. Beauchamp for the co 2 laser, and the Division of Chemical Sciences, Office of the Basic Energy Sciences, support. U. S. Department of Energy for on-going Finally, we would like to thank Professor George Ewing for numerous helpful suggestions. 198 REFERENCES 1. M. P. Casassa, D. S. Bomse and K. C. Janda, J. Chern. Phys. 74, 5044 (1981). 2. M. A. Hoffbauer, K. Liu, C. F. Giese and w. R. Gentry, J. Chern. Phys. 78, 5567 (1983). 3. J. Geraedts, M. Snels, S. Stolte and J. Reuss, Chern. Phys., in press. 4. G. Fischer, R. E. Miller and R. 0. Watts, Chern. Phys., ~, 5. 147 (1983). M. P. Casassa, C. M. Western, F. G. Celii, D. E. Brinza and K. C. Janda, J. Chern. Phys. 79, 3227 {1983). 6. M. P. Casassa, c. M. Western and K. C. Janda, J. Chern. Phys., submitted for publication. 7. Note that even as the spectrum is a function of expansion pressure, log-log plots of cluster intensity vs. pressure would imply the cluster signal is reasonably pure. Because of fragmentation we have found that mass spectroscopy is of limited utility in assigning spectra. See reference 8 for demon- strations of this point. 8. A. van Deursen, and J. Reuss, Int. J. Mass. Spectrom. Ion Phys. 23, 109 (1977). 9. A. Bauder, E. Mathier, R. Meyer, M. Ribeaud and Hs. H. Gunthard, Molecular Physics 15, 597 {1968). 10. H. c. Longuet-Higgins, Molecular Physics ~, 445 (1963). 199 11. D. M. Brink and G. R. Satchler, Angular Momentum (Clarendon Press, Oxford, 1975). 12. (a) D. E. Brinza, Ph.D. Thesis, California Institute of Technology, Pasadena, California (1983). {b) B. A. Schwartz, Ph.D. Thesis, California Institute of Technology, Pasadena, California (1983). 13. T. Nakanaga, S. Kondo and S. Saeki, J. Chern. Phys. 70, 2471 (1979). 14. R. D. Pendley and G. E. Ewing, J. Chern. Phys. 78, 3531 (1983). 15. K. C. Janda, Ace. Chern. Phys., 16. G. E. Ewing, Faraday Discuss. Chern. Soc. 73, 325 (1982). 17. D. S. Bornse, J. B. Cross and J. J. Valentini, J. Chern. Phy$. 18. ~, in press. 7175 (1983). (a) P. D. Aldrich, A. C. Legon and W. H. Flygare, J. Chern. Phys. 75, 2126 (1981). (b) J. A. Shea and W. H. Flygare, J. Chern. Phys. 76, 4857 (1982). 19. s. Mukarnel, Chern. Phys. 31, 327 (1978). 20. A. H. Zewail, Ace. Chern. Res. 13, 360 (1980). 21. M. A. Hoffbauer, C. F. Giese and W. R. Gentry, J. Chern. Phys. 79, 192 (1983). 22. M. F. Vernon, J. M. Lisy, H. S. Kwok, D. J. Krajnovich, · A. Trarner, Y. R. Shen andY. T. Lee, J. Phys. Chern. 85, 3327 (1981). 200 Chapter 8 Decay · Mechanisms in Vibrationally Excited van der Waals Molecules 201 I. Introduction In the previous chapters, van der Waals molecule photodissociation spectra were interpreted using as a model pairs of discrete levels, coupled in the presence of light. For chemical determined dynamics are the the most interesting phenomenological decay Though this type of model provides a parameters constants. reasonable physical picture . of the photodissociation process, as evidenced by generation of a consistent set of parameters variety of experiments, there is ence the decay on the nature of little for a wide intrinsic depend- mechanism. In this chapter, conceivable decay processes are defined in a very schematic way and their importance in van der Waals molecule photodissociation is discussed. description physical of decay picture one observed linewidths We shall see that the processes depends chooses. We largely conclude on the that the of ethylene containing van der Waals molecules can be interpreted unambiguously as the result of population relaxation processes. Before proceeding, a vocabulary must be agreed upon. The phenomenological homogeneous rates linewidth mentioned are determined measurements (having from considered contributions due to saturation and inhomogeneity) and as such, give the rates of decay of the off-diagonal density matrix elements for these are a two optically coupled states. measure of the phase coherence Since of the 202 excitation of the dephasing rates. processes (DP) ensemble, these There two which are contribute to rates types are of called dephasing the dephasing rate. These are population relaxation (PR), which also appears as decay of the diagonal elements of the density matrix, and pure dephasing processes (PDP) by which phase coherence is lost without concomitant population loss. In Section II, presented with a the simplest discussion of its application) for decay processes. lineshape model stipulations is (in our Included is a discussion of the population ·relaxation mechanism. Sections II and III draw heavily from a profound article by Mukamel 1 on the nature of dephasing in isolated molecules. Section II addresses the nature of DP in a global description of the van der Waals molecule system. by many This is the picture adopted theoreticians calculating PR rates Waals molecules. for van der In Section III, reduced descriptions of the van der Waals molecules are proposed and, with the help of the work of Zewail et al, 2 the implications of these pictures for DP in van der Waals molecules are discussed. II. The Lineshape Model The lineshape model derives from a highly idealized system described by a Hamiltonian of the form H = H 0 + H' + V (1) 203 The zero order Hamiltonian has two discrete eigenfunctions, Ia> and ib>, and continuum eigenfunctions JE,s>. E denotes the total energy of the continuum level and B denotes a set of other parameters which uniquely specify the state. The I time-independent interaction couples the upper level V represents the Hamiltonian, H ' weakly Ia>, and states of the continuum. interaction of an oscillating electric field which couples Ia> and lb>. The most general state function of the system is L:c llJJ (_t) > = n n (t) In> = L:bn{t)e-iwntJn> (2) n where the sum is over all eigenfunctions of H 0 for the continuum treating the states). continuum We can avoid in the density explicitly matrix by noting that the rate of decay of the discrete state I a> resonantly ignoring V for the (t) ( 3) coupled to states (an integral the continuum, moment, is given by . b a Equation (3) the ( t) follows from (2) 3 4 Schrodinger equation. ' stant is given by b a and approximate solution of The first-order decay con- 204 = which { 4) resembles decay ticians primarily element in ( 4) gap formulas Beswick used 5 an d by several E w1ng. 0 6 The theorematrix leads to the familiar momentum and energy propensity rules for state-to-state rates. The density of states and integration over internal degrees of freedom cause the final states. rate to depend on the availability of The quantity oE is simply the shift of the discrete state energy due to coupling with the continuum and henceforth will be ignored. Using ( 2) , element, matrix and the definition of the density ( 3) = c n * c m, P nm the density matrix rate equations are . Paa = -yPR Paa. - . Pab = K (Vabpba - c. c.) i + K (VabPba - c. c.) pbb = . i i -(iwo + Yop)Pab + K Vab (paa (5) - pbb) We have added Y PDP for generality, although there has been no 205 explicit mechanism introduced which could be responsible for PDP. The fraction of molecules remaining undissociated under our experimental conditions is (6) where wR is the Rabi frequency, and ~w t is the irradiation time is the difference between the laser frequency and w • 0 With regard to the decay mechanisms, the stipulations of the model in the approximation of (6) are: (i) The width (FWHM) of ln Tr(P) which is measured in our experiments is 2Yop· (ii) The PR rate is much greater than the Rabi frequency. In our experiments, wR is typically 10 7 sec- 1 . (iii) directly to The PR is irreversible, the "dissociated" state. but It need is not be conceivable that there are states of the continuum for which the fragments have little relative kinetic energy. ever the initial decay, However, what- it must inevitably lead to disso- ciation. Stipulations (i) and (ii) indicate that the limit for YPR is 2YDP' while the lower limit is wR. upper Stipu- lation (iii) indicates that the upper limit for the dissociation rate, 7 as determined by our experimental geometry, 206 is of the order of 10- 4 sec -1 argued that both the widths, In our analyses we have 2 YDP' and the dissociation rate are given by YpR• The physical picture of van der Waals molecule photodissociation described above is appealing in its simplicity and has been applied successfully in many cases. been used as an essentially phenomenological model parameters adjusted to fit experimental results.) cuss ion of YPR has constant in theory. firmly rooted the first {It has with The dis- order decay The following sections are aimed at understanding the physics underlying Ypop· III. Dephasing in a Complete Description of the System. Theoretical work on line broadening in van der Waals 5 6 molecules ' has for the most part employed global Hamiltonians of {usually idealized) complexes with all degrees of · freedom treated on equal footing. part of the Hamiltonian is that of eq. The time independent <1>, but now H have many bound levels and adjacent continua. 0 may In calcu- lations on model van der Waals molecules, eigenfunctions of H have involved the internal degrees of freedom ( vibrao tion and rotation) of the constituents and degrees of freedom of the van der Waals bond. only includes residual terms freedom. The interaction Hamiltonian involving no new degrees of 207 In the basis of eigenfunctions of H 0 0 ~s the Hamiltonian 1 H rim> = o m < mj E ( 7) H' In the lrn > Vrnn < nl = view - of the calculations mentioned, off-diagonal I terms in H induce transitions ( PR) in the { j m> } basis. Diagonal terms merely cause energy shifts in the and could in principle be included there is no PDP in this complete lm> levels in H • In any case, picture. The only DP 0 corresponds to PR. The complete description, with the Hamiltonian partitioned as in (7), reduces to the lineshape model Cor, more precisely, the density Chapter if the optical Hamil toni an only connects dis- crete 5) levels of H • 0 matrix That is, superposition of discrete states function itself). There is for multilevel the prepared system state is in a (not generally an eigen- some experimental evidence, though not conclusive, that the optically prepared state in van der Waals molecule experiments appreciable continuum component. and HCl ·c H , 2 4 for example, does not include an In the spectra of HF·C H 2 4 only vibrational fundamentals 208 are observed, the transition moments are comparable to that of free ethylene and the lines are symmetrical. superposition prepared continuum character, Fano lineshapes. states did have If the substantial one might expect to observe instead 8 This description preserves the distinction between PR and actual dissociation outlined in Section II. Experi- mental attempts to determine if the dissociation mechanism is in fact the line-broadening PR have been inconclusive. 9 Trends in widths measured in van der Waals molecular spectra are consistent with propensity rules for dissociation calculated with increase in reflecting full the descriptions. series dissociation For Ne ·c H 2 4 example, < constrained widths < by angular momentum conservation. In practice, adoption of the picture described is most useful (i.e., allows us to draw physical insight from experiments) if it is possible in the excitation step to keep track of all degrees of freedom of the ·complex. the case this of the simple van der Waals is arguably the case. In molecules studies, Structure in the spectra of Ar•c H and Ne•c H , for example, is due to combinations of 2 4 2 4 vibration and hindered rotation of c H , giving a measure 2 4 of the spacings and populations of these levels. As described in the next section, including unobserved degrees of freedom in the model can lead to pure dephasing. 209 As an aside, we note that the Hamiltonian ( 7) need not be partitioned and, in principle, the basis of eigenfunctions of the full Hamiltonian could be determined. In this new basis the time evolution of the optically prepared superposition state could only be described without PR. This alternative picture, as dephasing though completely equivalent to the one described above, would be preferable (i.e., would lend more physical insight) if the initially prepared superposition state was appreciably mixed with the continuum levels of H • 0 IV. Dephasing in a Reduced Description of the System In a reduced description, the Hamiltonian is parti- tioned into terms which operate in two distinct spaces 1 (8) where Q represents the degrees 8 of freedom which are of interest Q (the "system") while degrees of freedom (the "bath"). 8 represents the other Modes may be relegated to the bath if they are only weakly coupled to system variables - this is especially helpful if the bath is enormous or be can treated in some approximate way. From the experimental standpoint the bath may be thought of as an unobserved part of the system. 210 F.o cussing attention on the system variables alone, the system properties are determined by the reduced density matrix p where the right s hand = TrB{p) side is { 9) the partial trace of the density matrix of the global system, over the space of the bath system. 10 By performing the partial trace, the if correlated to activity in Q , 5 5 implicitly included in p . In particular, dynamics properties of the bath, are . p·S 1,2,11 occurring in the bath appear as PDP terms ~n arises as a therefore result of adopting a could, in principle, PDP reduced description and be removed by expanding provided an insightful Qs. 1 Zewail and colleagues 2 have description of PDP which is qualitatively applicable here. Let s and b label the eigenfunctions of H5 and HB. p:s' ±s 2 decay rate of the off-diagonal element = The PDP TT 2 K ~,b' wbl<sbiH 5 Bisb'>- <s'biH 5 Bis'b'>l 6lEb-Eb,l (10) The form of (10) indicates that PDP in lation flow amongst the bath levels. ps is due to popu- Aside from the matrix elements in (10) important features are the delta function, by which a large density of states near Eb would enhance 211 y PDP, and the Boltzmann factor, Wb, which permits only populated bath levels to contribute to PDP. The question of how to partition the Hamiltonian in a reduced description of van der Waals molecules is an interesting one. We propose that the partitioning should reduce ps to an extent consistent with the observations of experiments. Below, the implications of this type of parti- tioning and eq. (10) for ethylene cluster experiments are discussed. It should be emphasized that the discussion is qualitative and derived 2 that approximations by which (10) is do not strictly apply here. Spectra of Ar·C H and Ne ·C H show combinations of 2 4 2 4 ethylene the v v vibration and hindered rotation. 7 coordinate 7 and rotational ethylene constitute Q • 5 degrees Therefore, of freedom of Remaining degrees of freedom rele- gated to QB are all other ethylene vibrational modes, the end-over-end coordinate rotation for of the separation of complex, the and the partners. 12 radial Under our experimental conditions, kT ~ 3 cm-l so that the only bath modes populated would be rotation of the complex. 13 Together these do not contain enough energy to excite the other bath modes, and in any case constraints forbid such population flow. in this reduced description of angular momentum We conclude that c 2 H4 •Ar and c 2 H4 • Ne that PDP does not appreciably affect the measured linewidth. In the spectra of c 2 H4 • HF and c 2 H4 • HCl vibrational transition is observed so that 0 8 only the is reduced to 212 the v7 coordinate. QB absorbs the degrees of freedom of both partners. ience, remaining internal Based on our exper- we expect that librational frequencies of these molecules are greater than kT (i.e. , c 2 H4 greater Furthermore, in than the libra- tiona! frequency of HF in c H ·HF is thought to be of the 2 4 1 14 order of 400 cm- • Again, we conclude, based on equation (10) in this reduced description, that PDP does not in 0 • Little is known about 5 cases, but it is expected that the contribute to the observed linewidths. also include only v potentials in these 7 the density of states in the bath modes is higher than that in the previous examples, frequencies are lower. and that all the bath Although ( 10 > shows that mode Ypop is larger in these cases, experimental results imply that YPDP does not significantly influence example, the homogeneous width of 4 K 16 K·, 15 and factor in (10). that of c 2 H4 , frequencies. that for modes. despite the measured widths. cc 2 H4 > 2 is influence of For the same at the Boltzmann The spectrum of c H •c F is narrower than 2 4 2 4 even though the former has lower bath Finally, the width for cc 2 H4 > 3 is less than cc 2 H4 > 2 despite increased density of resonant bath 213 V. Summary Dephas ing processes in several descriptions of van der Waals complexes have been outlined, along with expressions for heretofore Consideration of phenomenological these expressions rate and constants. experimental measurements has led to the conclusion that observed linewidths are best pure dephasing. interpreted as population decay and not As this conclusion is based on a quali- tative discussion, there is need for a good experiment or theory to further elucidate van der Waals molecules. the problem of dephasing in A direct measurement of popu- lation evolution would be of great significance. theoretical standpoint, it would the matrix elements in equation 10. be From a interesting to study 214 REFERENCES l!' 327 (1978). 1. S. Mukamel, Chern. Phys. 2. a) K. E. Jones and A. H. Zewai1, in Springer Series in Chemical Physics, Vol. 3: Advances in Laser Chemistry, edited by A. H. Zewail (Springer, Berlin, Heidelberg, New York, 1978), p. 196. b) K. E. Jones, A. H. Zewail and D. J. Diestler, ibid, p. 258. c) D. J. Diestler and A. H. Zewail, J. Chern. Phys. 71, 3103 (1979). 3. C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics (Wiley-Interscience, Paris, 1977), Vol. 2, p. 1350. 4. Equation (4) gives a first-order decay rate valid for all time t >> 1/ ~ where n ~ is the width of the right hand side of (4) . as a function of E (replace E=E a withE in (4)). As such (4) is more general than Fermi's golden rule which predicts linear decay valid for t 5. << YPR -1 • See ref. 3. J. A. Beswick and J. Jortner, Adv. Chern. Phys. !2, 363 (1980). 6. G. E. Ewing, Faraday Discuss. Chern. Soc. 73, 325 (1982). 7. We define dissociation rate as the effective firstorder decay constant one would observe if directly measuring dissociation. This could in fact be due to a rate-limiting intermediate step. 215 8. U. Fano, Phys. Rev. 124, 1866 (1961). 9. D. S. Bomse, J. B. Cross and J. J. Valentini, J. Chern. Phys. ~, 7175 (1983). 10. Reference 3, Vol. 1, p. 305. 11. U. Fano, Rev. Mod. Phys. 29, 74 (1957). 12. Since dissociation is observed, one might suggest that the dissociation coordinate should be included in the system space. However, dynamics af£ecting the spectrum occur in time t ~ YDP-l while practical restrictions prevent detection of dissociation until t 13. ~ 10- 4 sec. Manifestations of end-over-end rotational inhomogeneity have been observed (Chapter 6), but individual sublevels have not been resolved. 14. L. Andrews, G. L. Johnson and B. J. Kelsall, J. Chern. Phys. 76, 4857 (1982). 15. M. A. Hoffbauer, K. Lin, C. F. Giese and W. R. Gentry, J. Chern. Phys. ~, 5567 (1983). 216 Chapter 9 Summary 217 The important parameters determined by lineshape fits to spectra predissociation vibrational of ethylene- containing clusters are listed in Table I. All of these data were obtained from bands observed near the frequency of the v in-phase out-of-plane bending mode of ethylene. The 7 parameters are the band origin, w , the homogeneous width, 0 y, and corresponding moment for lifetime, T, infrared absorption, internal rotation, y • 2 the squared transition < 1..1> 2 , and the barrier to Observations that have been made can be divided into three categories pertaining to the spectroscopic transition, the van der Waals interaction and the dynamics of dissociation. A. Spectroscopy There are dramatic differences in some of the ethylene cluster c 2 H4 mode, as illustrated in Figure 1. v 7 spectra, the appearance of all excited in the However, all of the observed spectra can be interpreted using as a model two groups of levels with the upper group experiencing irreversible decay. In many cases, it is possible to reduce the model to a homogeneous two-level system. The most detailed model inhomogeneity to incorporated rotational and spatial reconcile ethylene dimer results over a wide range of laser powers and temperature. The position, intensities and appearance of the bands are consistent with the idea that the spectroscopically 218 TABLE I. Parameters determined photodissociation. for ethylene cluster Wo y Cluster (an-1) (an-1) Ne·C H 2 4 949.1 ~0.5 ~10.0 -12.5 Ar·C H 2 4 953.9 ~3.0 ~ 1.7 -30.0 c2H4 ·HF 974.4(1) 1. 59 (81) 3.3 (22) 77. (25) c2H4 ·HC1 964.1(1) 1.57(67) 3.4 (25) 52. (16) c2H4 ·NO 951.5(5) 7.4 (12) 0.72(10) 50.9(48) - C2H4·C2F4 954.7(2) 6.0 (8) 0.89(10) 46.2(63) (C2H4)2 952.3(5) 12.0 (2) 0.44(5) 96.0(18) (C2H4)3 952.3 (5) 11.0 (2) 0.50(7) 141.0(33) a 949.0 C2H4 ~ference 14. T <1J>2 psec (l0- 3o2 ) 35.5(14) v2 (an-1) 219 0.4 r - - - - - - - - - - - - - - - - - - - - - - - - - - - • 04 0 .2 0.2 "0 Q) 0 8 Ill Ill 0 .~ u tt 0 10 0.0 0 .05 000 920 940 960 980 w(cm- 1 ) FIGURE 1. Comparison of (C2H4)2, c 2H4 ·HC1 and C2H 4 ·Ne infrared photodissociation spectra. Note the different intensity scales and fluen~es: 3.8 mJ/cm2, 3.7 mJ/cm2 and 1.9 mJ/cm , respectively. 220 excited motion ethylene. closely resembles the v mode 7 of free As indicated by the spectral profile and known structures, this motion occurs as a parallel band in clusters with HF and HCl, and as a hybrid band in <C H > . 2 4 2 These clusters Ne·C H and 2 4 exhibit single Ar • c H The structured. whose 2 4 combinations of v 7 structure symmetric spectra results bands, unlike more richly are from excitation of motion and hindered internal rotation by ethylene. All of the spectra exhibit a the v fundamental 7 bonded clusters larly, the of free having non-rare ethylene, the most gas blue shift relative to with pronounced clusters the hydrogen shift. show enhanced bands for Simi- intensity relative to the monomer. B. The bonding interaction The observation of parallel c H 2 4 • HF and c H ·HC1 is expected since the measured structures of these 2 4 clusters have the diatomic above the ethylene plane. order to reconcile measurements different laser powers must be hybrid parallel band. or and of <c H > 2 4 2 temperatures, perpendicular. It 2-4 is 1 In widths at the band type certainly not a A hybrid band would be expected based on the 6 . . ca 1 . crysta 1 structure 5 an dab '1n1t1o cu1 at1ons. Ne • c H and Ar • c H are evidently quite 2 4 2 4 complexes compared to the other clusters in Table I. loose They 221 are the only internal clusters wherein The rotations. it others is may possible be rigid to excite because of strong, directional hydrogen bonds, or because the internal motion is sterically hindered. In the case of the hydrogen-bonded clusters, the blue shifts are attributable to an electrostatic rather than stiffening of the C-H bonds redistribution upon hydrogen bonding. induced by charge This is supported by the fact that only the out-of-plane modes of shift in clusters. the 7 infrared The spectra slight blue bonded clusters may be due action which compensates dispersion interactions. interaction c 2 H4 exhibit a of the matrix shifts in the to a for repulsive isolated non-hydrogen valence red-shifting inter- induction and The slight blue shift observed for ethylene dimer could be due to resonant dipole coupling. The small actions shift nearly suggests cancel, that which planes were parallel but the resonant dipole would occur the skewed with the conclusion above that v 7 55 ° • if This is 8 inter- ethylene consistent occurs as a hybrid band. The observed intensity enhancements are largely attributable to interaction of the c 2 H4 v 7 oscillation and the polarizable, but otherwise passive, van der Waals partner. The oscillating induced dipole provides the enhanced intensity. Note that the transition moments listed in Table I are quite uniform, with the exception of c 2 H2 ·HF, with an average squared transition moment per ethylene subunit equal to 48.3 x 10 -3 D2 • The large enhancement for c 2 H4 ·HF may 222 reflect a change in the charge distribution in the C-H bonds upon hydrogen bonding, although not so large as to effect the observations mentioned in the previous paragraph. c. Photodissociation dynamics The range of the observed lifetimes of ethylene clusters is relatively narrow compared to range expected on . t h e b as1s of are 9 ' 10 . ear 1 y t h eor1es. consistent with . momentum conserva t 1on. . 4,12 o b servat1on that However, dissociation 11 tren d s o b serve d constrained This is also consistent with the fragment rotation is an degree of freedom absorbing the excess energy. encouraging to note that Ewing has dimer dissociation rate, angular using a important It is also calculated an ethylene curve crossing model for V~R,T energy transfer,13 which is comparable to the observed rate. It has been inferred from the observed widths that the broadening mechanism is in fact vibrational predissociation. Two other decay mechanisms cannot be categorically dismissed until the population evolution is observed directly. are relaxation to ~ other states not These immediately leading to dissociation and pure dephasing processes. Nondissociative relaxation has been ruled out in ethylene clusters since it would involve transfer of substantial vibrational energy to weakly bound Conservation modes of and energy multiple and angular quantum transitions. momentum alone would 223 severely restrict such a process. The pure dephasing mechanism has been ruled out because pure dephasing depends on occupation numbers in such a way that it is precluded in these molecules at low temperatures. In either case, trends expected have not been observed. D. The future Clearly, there is a great deal yet to be learned. This work at the very least provides a strong methodological foundation for dissociation ethylene obtaining spectra cluster of and van interpreting der measurements also body of data on which to build. types of trends. clusters and Waals the photo- molecules. provide a The substantial More spectra of different vibrations are needed to discern Direct measurements of the time evolution of the initially excited state would be of tremendous significance. The same can be fragments for Previously distributions. translational said energy should be described reported content in product measurements state of the photodissociation in of hybrid this of cc 2 H4 >2 of reexamined saturation effects and the transition measurements view nature of orientational the dimer Higher thesis. v 7 resolution spectra of Ne·C H and Ar·C H are needed. 2 4 2 4 The molecules studied here are probably too compli- cated for detailed theoretical study. However, data are now 15 available for (HF> and are likely soon to be available for 2 224 a molecule _like Ar~HF. These should give impetus to thea- retical· work in this field. Finally, our absolute intensity measurements reflect the charge distributions in the van der Waals clusters. Such measurements could serve as a for calculated charge distributions. check 225 REFERENCES 1. (a) P. D. Aldrich, A. C. Legan and w. H. Flygare, J. Chern. Phys. ~' 2126 (1981). (b) J. A. Shea and W. H. Flygare, J. Chern. Phys. 76, 4857 (1982). 2. M. A. Hoffbauer, W. R. Gentry and C. F. Giese, in Laser-Induced Processes in Molecules, edited by K. L. Kampa and S. D. Smith (Springer-Verlag, Berlin, Heidelberg, New York, 1979). 3. M. P. Casassa, D. S. Bomse and K. C. Janda, J. Chern. Phys. 74, 5044 (1981). 4. M. A. Hoffbauer, K. Lin, C. F. Giese and W. R. Gentry, J. Chern. Phys. 78, 5567 (1981). 5. G. J. H. van Hes and A. Vos, Acts. Cryst. B33, 1653 (1977). 6. A. van der Avoird, P. E. s. Wormer, F. Mulder and R. M. Berns, Topics in Current Chemistry ~' 1 (1980). 7. L. Andrews, G. L. Johnson and B. J. Kelsall, J. Chern. Phys. 76, 5767 (1982). 8. J. Geraedts, S. Stolte and J. Reuss, z. Phys. A304, 167 (1982). 9. G. Ewing, Chern. Phys. 29, 253 (1978). 10. J. A. Beswick and J. Jortner, J. Chern. Phys. ~' 2277 (1978). 11. G. E. Ewing, Faraday Discuss. Chern. Soc. 73, 325 (1982). 12. D. S. Bomse, J. B. Cross and J. J. Valentini, J. Chern. Phys. 78, 7175 (1983). 226 ~' 13. G. E. Ewing, Chern. Phys. 411 (1981}. 14. T. Nakanaga, S. Kondo and S. Saeki, J. Chern. ·Phys. 70, 2471 (1979}. 15. A. S. Pine and w. J. Lafferty, J. Chern. Phys. 2154 (1983}. ~'