Gas Kinetics & Energy Transfer (v. 3)

A Specialist Periodical Gas Kinetics and Energy Transfer Volume 3 (Volume 1 was published as “Reaction Kinetics - Vol...

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A Specialist Periodical

Gas Kinetics and Energy Transfer Volume 3 (Volume 1 was published as “Reaction Kinetics - Vol. 1”)

A Review of the Literature published up to early 1978

Senior Reporters P. G. Ashmore, Department of Chemistry, University of Manchester Institute of Science and Technology R. J. Donovan, Department of Chemistry, University of Edinburgh

Reporters R. T. Bailey, University of Strathclyde D. L. Baulch, University of Leeds A. B. Callear, University of Cambridge 1. M. Campbell, University of Leeds F. R. Cruickshank, University of Sfrafhclyde H. M. Frey, University of Reading J. N. Murrell, University of Sussex R. Walsh, University of Reading

The Chemical Society Burlington House, London, W I V OBN

British Library Cataloguing in Publication Data

Gas kinetics and energy transfer.(Chemical Society, Specialist periodical reports). Vol. 3. 1. Chemical reaction, Rate of 2. Gases, Kinetic theory of 3. Energy transfer I. Ashmore, Philip George II. Donovan, Robert John 111. Series 541l.39 QDSOl ISBN 0-85186-776-6 ISSN 0309-6890

Copyright @ 1978 The Chemical Society All Rights Reserved. No part of this book may be reproduced or transmitted in any form or by any means - graphic, electronic, including photocopying, recording, taping or information storage and retrieval systems - without written permission from The Chemical Society.

Printed in Great Britain by Billing & Sons Limited Guildford, London and Worcester

Foreword We indicated in the Foreword to Volume 2 of this series that we intended to publish Volume 3 in less than two years. In the interval there have been many exciting developments in gas phase reaction kinetics and energy transfer, allowing us to fulfil our intention. However, it is impossible to review all the developing areas in a volume of sensible length. We have selected topics for this volume that give the flavour of some important developments with the intention of covering other areas in succeeding volumes at short intervals. A major influence on the field has been the rapid expansion in the use of laser technology for both pumping and probing chemical reaction dynamics. 'This expansion will undoubtedly continue and we can therefore look forward to a period of even greater activity in the future. The themes of the title of this series are nowhere better linked than in studies of unimolecular reactions. In Chapter 1 Frey and Walsh review advances in theory and the experimental techniques for testing the theories, and laser technology has played a particular role here. They present a complementary view to those given in Volumes 1 (Robinson) and 2 (Quack and Troe); restriction on space precluded extensive tabulation of high pressure rate constants for molecular or radical reactions, but they point out the need for a critical review of such data, and also for review of data on the reactions of ions where precision of information is steadily improving. Chemiluminescent reactions have not been covered as a single subject in previous volumes although reference to them has been made in several earlier chapters. We therefore welcome the chapter by Campbell and Baulch which reviews the entire area from ultraviolet through to infrared chemiluminescence. Metal atom reactions have featured particularly in recent visible and ultraviolet studies of chemiluminescence, and this area is reviewed in some detail. In Chapter 3 Callear presents an overview of progress in studies of molecular energy transfer involving translational, rotational, vibrational, and electronic energies, with particular emphasis on work during the past decade. In Chapter 4 Bailey and Cruickshank give a full and detailed account, with extensive compilations of rate constants, of laser studies of translational, rotational, and vibrational energy transfer. For the final chapter, the author was invited to review work carried out by his group in recent years on potential energy surfaces for studying the reactions and dynamics of small polyatomic molecules. The review deals mainly with the methods used to construct such surfaces and initiates what we hope will be a developing theme. In future volumes we plan to cover the results obtained from trajectory calculations on these surfaces and their relationship to molecular beam and state-selected studies. July 1978

R.J. D. P. G . A.

Contents Chapter 1 Unimolecular Reactions By H. M. Frey and R. Walsh

1

1 Introduction

1

2 General Theoretical Considerations

3

% Energy Transfer

4 4 4 7 7 8

Intramolecular Energy Randomization Experiment Classical Trajectory Studies Theory Intermolecular Energy Transfer 4 Non-Thermal Activation Chemical Activation Multiphoton I.R. Photochemistry

10 10 13

5 Thermal Unimolecular Reactions in the Fall-off and Low Pressure Limiting Regions

16

6 Thermal Unimolecular Reactions in the High Pressure Region Cyclopropane, Cyclobutane, and their Derivatives (Table 2) Polycyclic Systems (Table 3) Heterocyclic Compounds (Table 4) Olefins and Polyenes (Table 5 ) Elimination Reactions (Table 6) Bond-fission Reactions (Tables 7 and 1) Miscellaneous Reactions

19 20 23 25 28 30 32 34

7 Radical Recombination and Addition Reactions

34

8 Mechanism

37

9 Computational Chemistry (Potential Energy Surfaces)

39

Chapter 2 Chemiluminescence in the Gas Phase By I. M. Campbell and D. L. Baulch

42

1 Introduction

42

2 Electronic Chemiluminescence

42 42 49 50 58 58 60

Towards a Visible Chemical Laser System New Spectra and States Reaction Dynamics of Metal Atomaxidant Systems Radiative Lifetimes ( z R ) Bond Strength Limits Miscellaneous Systems

Contents

vi Three-body Combination Reactions (i) O + N O (ii) H + N O (iii) N + O (iv) N + N (v) C + N I F Chemiluminescence Phosphorus Chemiluminescence O('S) Atom Emission C2 Chemiluminescence Ozone Reactions Dioxetane Decomposition 3 Infrared Chemiluminescence Three-atom systems Reactions of Atoms with Polyatomic Molecules HF Chemiluminescence Chemiluminescence from Polyatomics and Related Systems Miscellaneous Rovibrationally Excited Systems 0 cs2 F2 +H2 O(3P)+ Hydrocarbons (HI), + F2 Formation of Gaseous HNC O('D) H2

+

+

Chapter 3 A n Overview of Molecular Energy Transfer in Gases By A. B. Callear

1 Introduction 2 Vibrational-to-TranslationalEnergy Transfer 3 Vibrational-to-VibrationalEnergy Transfer 4 Electronic-to-TranslationalEnergy Transfer 5 Electronic-to-VibrationalEnergy Transfer 6 Electronic-to-Electronic Energy Transfer 7 Rotational-to-Tr anslational Energy Transfer 8 Rotational-to-Electronic Energy Transfer 9 Final Comment Chapter 4 Laser Studies of Vibrational, Rotational, and Translational Energy Transfer By R. T. Bailey and F. R. Cruickshank

1 Introduction 2 Experimental Techniques Discrete Frequency Lasers Helium-Neon

60 60 61 61 61 62 63 64 64 64 65 67 68 69 74 74 76 79 79 79 80 80 80 80 82 82 83 88 93 97 101 103 108 108 109 109 110 110 110

vii

Contents

111 113 113 113 114 115 117 117 117 119 119 119 120 121 122 123 124

Carbon Dioxide Chemical Lasers Tunable Lasers Semiconductor Diode Lasers Spin-flip Raman Lasers Non-linear Mixing High Pressure Gas Lasers Other Laser Systems Detectors CW and Low Frequency Studies Fluorescence Techniques Low Frequency Measurements High Frequency Measurements Double Resonance Techniques Non-linear Raman Techniques Matrix Isolation Techniques The Thermal Lens Technique The Evaluation of Energy Transfer Probabilities from Fluorescence Data

125

3 Theoretical Prediction of Energy Transfer Probabilities (PmJ General Techniques Techniques for Near-resonant Transfer The Vibrational Quantum Number Dependence of (PmJ The Effect of Rotation on (Pm,,) The Present Position and Future Trends

127 127 130 132 135 136

4 Data on Compounds Hydrogen V-T Transfer V-V Transfer Hydrogen Fluoride V-T, R Transfer Relaxation with Atomic Species Relaxation with Foreign Molecules V-V Transfer Hydrogen Chloride, Bromide, and Iodide V-T, R Transfer V-V Transfer Carbon Dioxide Relaxation from the (00'1) Level Relaxation from the (10'0) and (02'0) Levels Relaxation from the (01'0) Level Relaxation from the (10'1) and (02'1) Levels Nitric Oxide Carbon Monoxide V-T' Transfer V-V Transfer

136 136 136 139 144 144 146 148 151 154 154 157 157 157 159 161 161 162 163 163 164

Contents

viii CO Self Quenching CO Quenched by Hzand N2 CO with Miscellaneous Quenchers CO Quenched by Large Organic Molecules Sulphur Dioxide V-T and V-V Transfer Nitrous Oxide V-T Transfer V-V Transfer Ozone V-T Transfer V-V Transfer Carbonyl Sulphide V-T and V-V Transfer V-V Transfer Methyl Fluoride V-T Transfer V-V Transfer Rotational Relaxation Methyl Fluoride as an Energy Transfer Agent CD3F V-T transfer V-V transfer Methyl Chloride V-T Transfer V-V Transfer CD3CI V-T transfer V-V transfer Methyl Bromide V-T Transfer V-V Transfer CD,Br V-T transfer V-V transfer Methyl Iodide V-T Transfer V-V Transfer CDSI V-T transfer V-V transfer Comparison of the Methyl Halides V-T Transfer Rates Sulphur Hexafluoride V-T Transfer V-V Transfer Rotational Relaxation Summary

165 166 166 167 167 167 169 169 170 172 172 173 174 174 175 176 176 178 179 179 181 181 182 182 182 I83 183 183 184 184 184 185 186 186 186 187 187 187 188 188 188 189 190 190 191 192 192

Contents

ix Miscellaneous Compounds

cs2

V-V transfer C2N2 V-T transfer Boron Trichloride V-T transfer Nitrosyl Chloride V-T transfer V-V transfer SiF, Ammonia Methane V-T transfer V-V transfer CD4 V-T and V-V transfer Ethylene V-T transfer V-V transfer Difluoromethane V-T transfer V-V transfer Biacetyl 5 Conclusions Chapter 5 Potential Energy Surfaces for Studying the Reactions and Molecular Dynamics of Small Polyatomic Molecules By J. N. MurreN 1 Introduction 2 General Principles 3 Methods of Calculating Tri-atomic Potentials Cubic Spline Functions LEPS Surface DIM Approach Arbitrary Functions

HCN

so2 0 3

4 Special Features of Potential Surfaces cusps Saddle Points 5 Systems with more than Three Atoms 6 Conclusion Author Index

192 192 192 192 192 193 193 195 195 195 195 195 196 196 196 197 197 197 197 198 198 198 199 199 199

200 200 202 204 204 204 205 206 207 210 212 214 214 217 218 222 223

Un imolecu lar React ions BY H. M. FREY AND R. WALSH

1 Introduction In the first volume of this series Robinson presented a comprehensive account of the subject which together with his book brought together in tabular form most of the unimolecular reactions that had been reported and for which there were accurate Arrhenius parameters. Quack and Troe in Volume 2 did not attempt a complete compilation of experimentaldata but concentrated on progress in theory together with selected .experiments related to fundamental aspects of unimolecular reactions. The high standard set by these previous Reports has been hard to follow and the volume of work which has since been published difficult to digest. This Report is intended to be ‘consumer oriented’ in that coverage of theory, in the main, is limited to those theories which can be readily applied to practical calculation. In selecting topics for coverage we have if anything reverted to the pattern of Robinson’s article although inevitably with some modifications. For example, multiphoton i.r. photochemistry, a rapidly expanding area, is covered for the first time (although relatively briefly). Unfortunately we have found it too difficult to attempt a comprehensive tabulation of high-pressure rate constants since the Robinson Report (Quack and Troe covered a good deal although by no means all of these). In this area we have tried to cover most of what appeared in 1976 and 1977 and additionally we have included the relevant area of radical recombinations (the reverse of unimolecular dissociation). Diatomic molecules (and atom recombination) present special problems and have, therefore, been omitted. There has been a tendency in the past, which we have not been able to avoid, of giving undue emphasis to presenting data where Arrhenius parameters have been reported without a critical analysis of the likely errors in the quoted values. Such a critical evaluation (which would be extremely time-consuming) is now overdue; the work reported since Benson and O’Neal’s, ‘Kinetic Data on Gas-phase Unimolecular Reactions’ has probably equalled in volume all that available prior to 1969. We would like to reiterate a plea we have made previ~usly,~ that all rate constants should be reported as well as the Arrhenius parameters on which they are based, and again that values of the pre-exponential factor and the energy of activation should always be given even if values of AS* and AH* are presented. P. J. Robinson, in ‘Reaction Kinetics,’ ed. P. G. Ashmore (Specialist Periodical Reports), The Chemical Society, London, 1975, Vol. 1, p. 93. P. J. Robinson and K. A. Holbrook, ‘Unimolecular Reactions,’ Wiley, London, 1972. M. Quack and J. Troe, in ‘GasKinetics and Energy Transfer’,ed. P. G. Ashmoreand R. J. Donovan (Specialist Periodical Reports), The Chemical Society, London, 1977, Vol. 2, p. 175. S. W. Benson and H. E. O’Neal, ‘Kinetic Data on Gas-phase Unimolecular Reactions,’ NSRDS-NBS 21, 1970. H. M. Frey and R. Walsh, Chem. Rev., 1969, 69, 103. 1

Gas Kinetics and Energy Transfer

2

The number of recent reviews that have been published relevant to unimolecular reactions is not large. Troe’s chapter in ‘Chemical Kinetics’ and Tardy and Rabinovitch’s review on intermolecular vibrational energy transfer in unimolecular systems are required reading. However, there have been numerous reviews which have dealt with some aspects of particular series of unimolecular reactions which contain useful compilations of data, e.g. on the vinylcyclopropane rearrangements and azo decomposition~.~ Mechanisms of some specific cyclopropane rearrangements have been dealt with in great detail.” Other reviews have dealt with some thermal sigmatropic rearrangements and the decomposition of a number of heterocycles.’2 A comprehensive survey on strained organic molecules contains much useful information on data and theories and especially energetic^.'^ Other reviews on aspects of Transition State Theory (TST) l4 and use of local modes in the description of highly vibrationally excited molecules raise interesting ideas in relation to unimolecular reactions. Lee’s review on laser photochemistry of selected states l 6 outlines an area that may well become of great importance for testing theory in the future. After much debate it was decided not to devote a major section of this Report to the reactions of ions. We judged the time not quite ripe but it was a marginal decision. The area is growing very rapidly and as well as now covering a large number of species of a great range of complexitythe precision of the quantitative information is approaching that of conventional thermal studies. Williams ” has discussed how the unimolecular decompositions (and isomerization) of ions in the field free region of a conventional (magnetic sector) mass spectrometer can be studied to give detailed information on potential energy surfaces. It is often necessary for the construction of ‘unimolecular potential surfaces’ to use information obtained from ion cyclotron resonance experiments on bimolecular reactions. Indeed RRKM calculations have been helpful in the latter area.” Field isomerization techniques allow one to look at ion isomerizations occurring in the pic0 second time scale l 9 and the use of photoelectron-photoion coincidence spectrometry can give very precise values of the translational energy ielease during ion fragmentation reactions at specific energizations and time delays. Some of these techniques have yielded results which have provided searching tests of RRKM theory and later we mention phase-space theory.

’

’’

’

’ lo 11

l2 l3 l4

l6 l7

J. Troe, ‘Chemical Kinetics’ in International Review of Science, Physical Chemistry Series 2, Vol. 9, ed. D. R. Hershbach, Butterworths, 1976. D. C. Tardy and B. S. Rabinovitch, Chem. Rev., 1977,77,369. E. M. Mil’vitskaya, A. V. Tarakanova, and A. F. Plate, Russian Chem. Rev., 1976,45,469 (translation Uspekhi Khim., 1976,45,938). H. Meyer and K. P. Zeller, Angew. Chem. Internat. Edn. 1977,16,835. J. A. Berson, Ann. Rev. Phys. Chem., 1977,28,111. C. W. Spangler, Chem. Rev., 1976,76, 187. S. Braslavsky and J. Heicklen, Chem. Rev., 1977, 77,473. J. F. Liebman and A. Greenberg, Chem. Rev., 1976,76,311. W. H. Miller, Accounts Chem. Res., 1976, 9, 306. B. R. Henry, Accounts Chem. Res., 1977,10,207. E. K. C . Lee, Accounts Chem. Res., 1977, 10, 319. D . H. Williams, Accounts Chem. Res., 1977,10,280; see also R. D. Bowen and D. H. Williams, J.C.S., Perkin ZI, 1976, 1479; ibid., 1978, 68; R. D. Bowen and D. H. Williams, J. Amer. Chem. Soc., 1977,99, 3192,6822.

la

l9

W. N. Olmstead and J. I. Brauman, J . Amer. Chem. SOC.,1977,99,4219. R. P. Morgan, P. J. Derrick, and A. G. Harrison, J. Amer. Chem. SOC.,1977,99,4189.

Unimolecular Reactions

3

2 General Theoretical Considerations Despite many independent developments and much criticism it is still clear that RRKM theory occupies the centre of the stage of unimolecular reaction theory. This is partially because workers in this field have become familiar with its use and there are excellent textbooks describing it.292o But it is also because alternative and more fundamental theories, making fewer (or different) assumptions have not yet been fully developed to a point where they can be easily and practically applied. It is, however, true that the underlying assumptions of the RRKM theory have come increasingly under fire. The assumption of strong collisions is no longer regarded as integral to the theory, and indeed has been largely abandoned. RRKM calculationsare routinely carried out incorporating specific models of weak collisional behaviour. The related random lifetime and free intramolecular exchange assumptions, while still seemingly reliable under a variety of experimental conditions, are however being probed with increasing vigour. There has been considerable discussion in recent years of the application to unimolecular reactions of the ergodic hypothesis (which states that the time average of a system property is the same as the average of the property over all parts of the system at a single time instant). In this context, of course, ergodic behaviour may be identified with free and complete energy randomization, implying that a specifically energized molecule decays with a single rate constant irrespective of its initial mode of excitation. The limitations of this are being increasingly explored (see Section 3). However, it should be noted that ergodic behaviour is not necessarily synonymous with rapid intramolecular energy randomization since energy randomization may be brought about by collisions. The assumption of ergodic behaviour in collisions is also under investigation (see Section 3). The equilibrium hypothesis of the transition state theory (underlying the use of RRKM theory) has been the subject of criticism. In the earlier report Quack and Troe described the relationship of more fundamental dynamic theories to RRKM, and this is not repeated here. More recently Kay, on the basis of an earlier dynamic theory,21 has presented a statistical treatment for isolated molecules in which states near the critical surface for decomposition are not in statistical equilibrium with the bulk of reactant states.22 Nevertheless he has derived an RRKM-like expression for the rate constant with a correction factor y, roughly independent of energy, which must be < 1. Miller 23 has developed a unified statistical model for direct and complex bimolecular reaction mechanisms, which, in the former case, is the usual transition state theory but in the latter corresponds to the statistical phase space theories of Light 24 and Nikitin 25 for long lived complexes. This theory is clearly of interest to molecular beam specialists as is another version by Zvijac and Light 26 in which a hybrid quantum mechanical-statistical theory is developed for the purpose of deriving product energy distributions. For a model without any exit barrier product transitional energy distributions do not differ substantiallyfrom those of RRKM. Marcus 27 2o 21

22

23 24 25

26 27

W. Forst, ‘Theory of Unimolecular Reactions’, Academic Press,New York, 1973. K,G. Kay, J. Chem. Phys., 1976,64,2112. K . G. Kay, J. Chem. Phys., 1976,65,3813. W. H. Miller, J. Chem. Phys., 1976,65, 2216. J. C. Light, Discuss. Faraday SOC.,1967,.44, 14. E. E. Nikitin, ‘Theory of Elementary Atomic and Molecular Processes in Gases,’ Oxford University Press, New York, 1974, p. 391. D. J. Zvijac and J. C. Light, Chem. Phys., 1977,21,411. R. A. Marcus, Ber. Bmengesellschafi Phys. Chem., 1977, 81, 190.

4

Gas Kinetics and Energy Transfer

has addressed himself to a number of current problems in unimolecular reaction theory concerning energy distribution within a long-lived complex and amongst the products of its decomposition. Still in this area, Case and Herschbach 2 8 have published a statistical theory of angular distributions and rotational orientation. In the field of thermal unimolecular reactions, Troe has published a solution to the master equation at the low pressure limit, by incorporating an exponential model for energy transfer (for both vibrational only and coupled rovibrational cases).29 The theory presents the low piessure rate constant as a product of easily calculated terms comprising a strong collision rate constant, k y and a collisional efficiency factor analyticallyrelated to the parameters of the energy transfer model. In a second paper 30 the calculation of the various terms is discussed and the model is applied to a number of experimental decompositions. This is discussed in more detail in Section 5. Pritchard 3 1 has also addressed himself to the master equation solution but without any detailed model of collisional energy transfer. It is demonstrated that, not unexpectedly, a Kassel-like fall-off curve is predicted. The paper contains an interesting discussion of the case of a reactant with more than one decomposition channel. Other theoretical contributions have been made by Nordholm 3 2 and Grig~lini.~’ Finally we note that the successful application (and indeed tests) of RRKM depended on the availability of computer programs essentially to calculate values of sums and densities of states. Numerous approximate methods have been used and indeed are still being suggested,34but the development of fast and efficient procedures by Stein and Rabinovitch 3 5 to carry out exact state counting using the Beyer, Swinehart algorithm 36 would have been expected to have closed this area to further development. It was, therefore, worrying to note the letter of Hayward and Henry 3 7 on some difficulties in using exact count procedures to determine densities of states. These problems were certainly known to practitioners in the field but the choice by these authors of some rather unrealistic (pathological) situations highlighted them. However, with minimal care even these situations can be handled without more than minor program changes.38 3 Energy Transfer Intramolecular Energy Randomization.-Experiment. It is now seven years since Rynbrandt and Rabinovitch‘s seminal experimental determination of the limiting rate of intramolecular energy transfer in a carefully tailored chemical activation system.39 Many subsequent studies involving a bewildering variety of techniques have purported to shed further light on this subject, but it is probably still true that bulk chemical activation experiments of the original type have provided the most concrete evidence. D. A. Case and D. R. Herschbach, J. Chem. Phys., 1976,64,4212. J. Troe, J. Chem. Phys., 1977,66,4745. 30 J. Troe, J. Chem. Phys., 1977, 66,4758. 31 H. 0. Pritchard, Canad. J. Chem., 1977,55284. 32 S. Nordholm, Chem. Phys., 1976, 15, 59. 3 3 P. Grigolini, Chem. Phys., 1977, 21, 161. 34 A. W. Yau and H. 0. Pritchard, Canad. J. Chem., 1977,55,992, 3 5 S . E. Stein and B. S. Rabinovitch, J. Chem. Phys., 1973,58,2438. 36 T. Beyer and D. F. Swinehart, Comm. ACM, 1973,16, 379. w R. J. Hayward and B. R. Henry, Chem. Phys. Letters, 1976,38,158. 38 S . E. Stein and B. S. Rabinovitch, Chem. Phys. Lefters, 1977, 49, 183. 39 J. D. Rynbrandt and B. S. Rabinovitch, J. Phys. Chem., 1971,75,2164. 29

5

Unimolecular Reactions

Further chemical activation experiments by Rabinovitch's group involving substituted cyclobutanes have substantiated a time scale s for energy redistribution in these molecules just as in the earlier c y c l o p r o p a n e ~ . ~The ~ * ~recent ~ evidence arises from both positive and negative observations. Where high pressure turn-up can be observed in some of the plots of k ( = p o D / S ) against pressure, actual, although approximate, figures can be obtained. If no turn-up is observed even at high pressures (ca. 15 atm) then a lower limit to the rate of redistribution is obtained. The differences N

40941

in the behaviour of the system41 'CH, 'CH2 +

-

+

mpri

and that of the system4'

rfMe are rationalized on the assumption that non-random decomposition

will occur only for those excited molecules prepared with energy deposition near to the site of decomposition and then only if the molecule has a sufficient side chain (with poorly coupled vibrational modes). In i.r. chemiluminescence or beam experiments, product energy distribution measurements from reactions involving long-lived complexes were earlier thought to provide evidence of a breakdown in energy randomization. However, it is now widely recognized that non-statistical product energy distributions cannot per se be taken as evidence of non-randomized energy in a reaction intermediate, due to intermode vibrational coupling after the exit channel energy barrier (see for example refs. 3, 27) or other dynamical effects.43 Thus the experimental tests in this area have to be of a more penetrating kind than previously. Notable among the molecuiar beam studies bearing on this question is the study of Farrer and Lee,44 who extending earlier work 45 on the F + C2H4 system found that average product recoil kinetic energies constituted ca. 50 % of the total available independent of reactant collision energy (over a range 9-51 kJ mol -'). They then argued that although exit channel energy barriers can distort product energy distributions away from statistical, nevertheless a statistical energy redistribution ought to be more likely at increasing energies above the barrier and the observed invariance of the proportion of product kinetic energy argues against statistical energy randomization in the intermediate C2H4F. The shape of these distributions were also argued to be inconsistent with statistical (phase space) theory. It should be added that symmetrical product angular distributions were observed indicating a lifetime of greater than a rotation period (-lo-'* s) for the intermediate. In the i.r. chemiluminescence area a study by Durana and McDonald 46 (using the arrested relaxation technique) singled out the reaction C1*

+ CH,=CHCH,Br

* ClCH,CH=CH,

+ Br'

(1)

by observing a non-statistical vibrational energy distribution in the allylchloride product. As this reaction is thought to involve little or no energy barrier (for loss of Br' from the intermediate 1-chloro-3-bromo-Zpropylradical) this appears to support 40 41

42 43 44

45 46

F.-M. Wang and B. S. Rabinovitch, Camd. J. Chem., 1976,54,943. A. N. KO, B. S. Rabinovitch, and K.-J. Chao, J. Chem. Phys., 1977, 66, 1374. B. S. Rabinovitch, J. F. Meagher, K.-J. Chao, and J. R. Barker, J. Chem. Phys., 1974, 60,2932. D. J. Zvijac, S. Mukamel, and J. Ross, J. Chem. Phys., 1977, 67, 2007. J. M. Farrer and Y.T. Lee, J, Chem. Phys., 1976,65, 1414. J. M. Parson and Y.T. Lee, J. Chem. Phys., 1972,56,4658. J. F. Durana and J. D. McDonald, J. Chem. Phys., 1976,64,2518.

Gas Kinetics and Energy Transfer

6

a non-randomization of internal energy in the intermediate and confirms an earlier beam study 47 which found a very short lifetime for the radical (or complex) in this system. This reaction is unusual since other similar reactions (Cl' bromo-olefins) do give rise to statistical product vibrational distributions. It has been claimed that certain photochemical experiments provide evidence of non-randomization of vibration energy. In a beam-laser experiment Sander, Soep, and Zare 48 have concluded that internally converted pentacene (with ca. 200 kJ mol -') fails to redistribute its energy (initially preferentially stored in a C-C vibration) on a ps timescale. This result is to be contrasted, however, with a time-resolved study of internally converted cycloheptatrienes 49 where the vibrationally excited species (with ca. 430 kJ mol-') decay in the time scales (10-6--10-9 s) expected from RRKM calculations, thus implying effective internal energy randomization. It is possible that the different levels of excitation of these molecules account for the different results but in view of the possible complexities of interpretation we would caution against a too-ready acceptance of non-randomization in the pentacene experiment. Chloroacetylene offers another photochemical system where non-randomization of energy has been claimed but trajectory studies are in conflict with this c o n c l ~ s i o n . ~ ~ Work on the decomposition of ions and ion molecule reactions can also yield results germane to the problem of energy transfer. Application of Phase Space Theory (with conservation of energy and angular momentum) to the product kinetic energy distribution of the reaction C2Ht + C2H4 + C3Hz + CH,. by considering the potential energy surface in the region of the complex C 4 H i yields results in agreement with e~perirnent.'~This contrasts with the findings of Lee et aLS3who suggested that energy was not randomized in the collision complex. Similarly a detailed consideration 5 4 of the unimolecular reactions (2) and (3)

+

C,H,CN' C4H6'

-+ --*

+ HCN C3H3+ + C H 3 C,H4?

(3)

showed that R R K M theory yielded values for the lifetimes of the reactants in agreement with experiment, whereas the very loose transition state used for the application of Phase Space Theory (PST) produced upper limit values very much greater than observed. However, PST did give good values for the product kinetic energy distributions. These results contrast with earlier ones, and illustrate yet again in a very clear manner that conventional RRKM theory is only appropriate for calculating rates or distributions in the region of the transition state of the potential energy surface and will not in general be appropriate for calculating properties of the system in the product region of the surface.55 RRKM theory does not conserve angular momentum 47

** 49

52

" 54 55

J. T. Cheung, J. D. McDonald, and D. R. Herschbach, J. Amer. Chem. SOC.,1973, M, 7889. R. K. Sander, B. Soep, and R. N. Zare, J. Chem. Phys., 1976,64,1242. H. Hippler, K. Luther, J. Troe, and R. Walsh, J. Chem. Phys., 1978, 68, 323. K. Evans, R. Scheps, S. A. Rice, and D. Heller, J.C.S. Faraday ZZ, 1973,69,856. W. L. Hase and C. S. Sloane, J. Chem. Phys., 1977,66, 1523; ibid., 1976,64,2256. W. J. Chesnavich and M. T. Bowers, J. Amer. Chem. SOC.,1976,98,8301. A. Lee,R. J. LeRoy, Z. Herman, R. Wolfgang, and J. C. Tully, Chem.Phys. Letters, 1972,12,569. W. J. Chesnavich and M. T. Bowers, J. Amer. Chem. SOC.,1977,99, 1705. R. G. Cooks, K. C. Kim, T. Keough, and J. H. Beynon, Znternat. J. Mass Spectrom. Zun. Phys., 1974,15,271; C . E. Klots, 2.Naturfursch., 1972,27a, 553; J. Chem. Phys., 1976,64,4269; A. S . Werner and T. Baer, J. Chem. Phys., 1975,62,2900.

7

Unimolecular Reactions

or take account of long range potentials of the system.56 Other experimental studies using Photoelectron-photoion coincidence spectroscopy have shown that RRKM (or Quasi Equilibrium Theory) will account for the translational energy release in the formation of CFS from C2F6+but not for SFS from SF:. These observationsillustrate the points just made about the relationship between the range of applicability of the theories and the nature of the potential energy surface.

’’

Classical Trajectory Studies. This is an expanding area and calculations have been carried out recently on specifically energized CD,CI and CD,H 5 8 and HCmCC1.” Although the time evolution of energized molecules depends on the detailed input energy distribution the general conclusion from these studies appears to be that s, for initial vibrational energy randomization has occurred within < 5 x energies in excess of ca. 400 kJ mol -I. Bunker 5 9 has carried out a similar study on C2H6,the largest molecule yet investigated by this method, and found some discrepancies between the resulting decomposition rate constants and those given by an RRKM calculation. The conclusions of this study must be regarded as suspect, however, since both the trajectory studies and the RRKM calculations as presented suggest C-H dissociation becoming relatively more important than C-C dissociation as energy increases, contrary to reasonable expectation (viz. that at high energies rate constant ratios will tend towards the limiting ratio of their thermal A factors). An earlier study on MeNC 6o remains inconsistent with RRKM theory. Some errors in a TST treatment of earlier beam measurements have been pointed out.61

Theory. Oxtoby and Rice 6 2 have presented a dynamic theory of energy exchange within a polyatomic molecule based on resonant interaction between coupled anharmonic oscillators. At low energies vibrational energy is trapped in isolated nonlinear resonances giving rise to slow vibrational relaxation, whereas at higher energies these resonances overlap and rapid energy exchange and the random lifetime distribution results. Within the confines of the specific models used in their study the onset of rapid exchange appears to occur at about 80% of the dissociation energy. Other theories are not so clear cut or specific. A variational equations approach has been tried 6 3 and Freed 64 has discussed the parallel between intramolecular vibration and electronic energy relaxation. Three years ago Robinson 6 5 wrote that ‘one might draw the tentative and hopeful conclusion that while energy randomization may require times of 10-’2-10-” s in some or many systems, it will usually be rapid enough for randomization to be assumable in calculations for thermal reactions and for many chemically activated reactions’. A similar conclusion may be drawn with somewhat more confidence today. There are more supportive chemical activation results than before; some of 56 57

58 59

R. A. Marcus, Faraday Discuss. Chem. SOC.,1973,55,381. I, G. Simm, C. J. Danby, J. H. D. Eland, and P. I. Mansell J.C.S. Faraday ZZ, 1976, 72, 426; I. G. Simm and C. J. Danby, ibid., 1976,72, 860. J. D. McDonald and R. A. Marcus, J. Chem. Phys., 1976,65,2180. E. R. Grant and D. L. Bunker, unpublished work quoted by D. L. Bunker, Ber. Bunsengesellschaft

Phys. Chem., 1977,81, 155. D. L. Bunker and W. L. Hase, J. Chem. Phys., 1973,59,4621. L. Holmlid and K. Rynefors, Chem. Phys., 1977, 19,261. D. W. Oxtoby and S. A. Rice, J. Chem. Phys., 1976,65, 1676. 63 P. Brunner and J. W. Duff, J. Chem. Phys., 1976,653566. 64 K. F. Freed, Chem. Phys. Letters, 1976,42,600. a Ref. 1, p. 115. 6o

61

8

Gas Kinetics and Energy Transfer

the difficulties of interpretation of the beam experiments have been recognized; trajectory studies are no longer wholly at odds with the idea; and theory has advanced to a point where the energy threshold for randomization is beginning to be probed. Other, new, experimental techniques (such as i.r. multiphoton excitation, see Section 4) may be expected shortly to be brought to bear on this question. Intermolecular Energy Transfer.-There have been two recent reviews of this topic, one in the previous Report by Quack and Troe and a second by Tardy and Rabino~ i t c h .The ~ latter in particular is extremely comprehensive and so this subject will be touched on only briefly here. For the practical purpose of incorporating the effects of intermolecular (collisional) energy transfer as a part of unimolecular reaction theory, parameterized models offer currently the best method (realism tempered by ease of calculation). Most widely used are the purely numerical models of Tardy and Rabinovitch 66 in which collision transition probabilities can be cast into one of a number of forms (stepladder, exponential, Gaussian, Poisson) and the analytical exponential model of Troe recently simplified from a three 6 7 into a single parameter form.3*2 9 These models can be fitted to existing experimental data from either low pressure limit thermal reactions or chemical activation systems. The results may be expressed in terms of the single quantity, (AE), the energy transferred per collision, and broadly speaking results have shown a consistent pattern whichever method has been used, thus encouraging the belief that to a first approximation the multistep collisional process is not sensitive to the precise details of the model. Two qualifications seem worth making to this general picture. The definition of the quantity (AE) needs careful attention. It may be defined in terms of the down collision average, (&?)down as preferred by Tardy and Rabinovitch or of the average of all collisions, (AE) (both down and up) as used by T r ~ e . ~ These ’ averages are related but the relationship depends upon the model under discussion. For convenience we may illustrate this in terms of Troe’s model in the low pressure limit thermal case, equation (4), where FE is a factor representing the energy dependence of the density of states (usually =I-2 in magnitude). Thus for large values of (AE)downand low temperatures (AE) N -(AE)downbut for small values of and high temperatures

This difference needs to be borne in mind when comparisons with different models are made. The second qualification arising out of this concerns the temperature dependence (largely unknown) of collisional energy transfer. Both (AE) and are straightforwardly related to the collisional efficiency,&, although again the relationship depends on the model. Thus if the temperature dependence of either (AE) or (AE)down is specified, that for #Icfollows naturally. Conversely experimental measurements of flc as a function of T lead to information on the temperature dependence of (AE) or (AE>down. Rut clearly these two qualities, being connected by temperature, each have a direrent temperature dependence. 66 67

D. C . Tardy and B. S . Rabinovitch, J. Chem. Phys., 1966,45, 3720; ibid., 1968,48, 1282. J. Troe, Ber. BunsengesellschaftPhys. Chem., 1973, 77, 865.

Unimolecular Reactions

9

From an analysis of high temperature (shock tube) studies at the low pressure limit of a number of triatomic and tetra-atomic molecules, Troe 30 has concluded, on the basis of his model, that their collision efficiencies with Ar,B,(Ar), vary with temperature roughly as T“*5*0.5.This would imply that { A E ) is almost independent of temperature while (AE)d,,n actually increases slightly with temperature. If on the other hand is independent of temperature, (AE) will decrease weakly may actually decrease with temperawith temperature. Some evidence that (AE>down t ~ r e , ~comes ~ , ~ ’from the somewhat questionable high temperature ‘turn over’ effect in cyclopropane 7 0 and cyclobutane 71 shock tube pyrolyses as well as a reinterpretation of the decomposition of SF,.68 Some very recent isotope effect and other experiments in conventional systems appear to support this.72a*b However, the question of the temperature dependence of collisional energy transfer appears to us to be still very much open and more work in this area is certainly needed. Troe has extended his energy transfer model to allow for angular momentum restriction^.^^ Penner and Forst 74 have carried out some calculations of separated vibrational and rotational energy transfer for the low pressure limiting decomposition of H202. However it is doubtful that any experimental evidence yet exists which demonstrates conclusively separate rotational and vibrational energy transfer. It is interesting to note that Bunker 7 5 has extended his trajectory studies into this area. A study of collisional energy exchange of MeNC with various colliders was in agreement with experimental findings on energy removal, but the pattern of internal mode energizations of MeNC by collision was found to be non-random. Thus the trajectory calculations which earlier found incomplete intramolecular energy randomization 6o for MeNC cannot produce energy randomization by intermolecular means either. As opposed to modelling, a new ergodic theory of collisional energy exchange has been published by Nordholm et al.76 The ergodic assumption is certainly an oversimplified one, and as with earlier statistical theories of energy redistribution in the collision complex, the energy removed per collision is overestimated. Chemical activation studies of methylcyclobutane by McCluskey and Carr,77 and of spiropentane and other molecules by Frey et al.78* have given values of (Stepladder model) of ca. 16-30 kJ mol for deactivation by C4 hydrocarbons !relatively strong colliders). These figures are in line with similar data for other systems. Robinson 8o had noted earlier that amongst chemical activation systems methylcyclobutane and methylcyclopropane appeared to be anomalous and this study 77 demonstrates that for the former at least this is not the case. Frey et aL7*

’’

69

70

B. S. Rabinovitch, D. G. Keil, J. F. Burkhalter, and G. B. Skinner, ‘10th InternationalSymposium on Shock Tubes,’ Kyoto, 1975, 579. J. A. Barnard and T. K. Parrott, Internut.J. Chem. Kinetics, 1977,9,387. (a) Ref, 1, p. 113; (b) D. K.Lewis,S. A. Feinstein and P. M. Jeffers, J. Phys. Chem., 1977, 81 1887.

71

72

73 74 75 76

77 78 79

**

J. A. Barnard, A. T. Cocks, and R. K. Y. Lee,J.C.S. Furudzy Z, 1974,70,1782. (a)I. E. Klein, B. S. Rabinovitch, and K. H. Jung, J. Chem. Phys., 1977,67,3833; (b) I. E. Klein and B. S. Rabinovitch, J. Phys. Chem., 1977, 82,243. J. Troe, Ber. Bunsengesellschuji Phys. Chem., 1977, 81,230. A. P. Penner and W. Forst, Chem. Phys., 1976, 13,51. D. L. Bunker and S. A. Jayich, Chem. Phys., 1976,13, 129. S. Nordholm, B. C. Freasier, and D. L. Jolly, Chem. Phys., 1977, 25,433. R. J. McCluskey and R. W. Carr, jun., J. Phys. Chem., 1976,80,1393. H. M. Frey, G. E. Jackson, R. A. Smith, and R. Walsh, J.C.S. Furuduy I, 1975, 71, 1991. A. D. Clements, H. M. Frey, and R. Walsh, J.C.S. Faraday I, 1977, 73, 1340. Ref. 1, p. 119,

Gas Kinetics and Energy Transfer

10

have argued that methylcyclopropane is also not anomalous if a different value for AH",lCH,) is used. Chemical activation now presents a fairly uniform and self-consistent picture on collisional energy transfer, although a very recent study on ethylcyclobutane 81 has produced a seemingly low figure for (AE)down for a strong collider of between 12 and 15 kJ moll. It is possible that these values are underestimated because of the relatively wide energy distribution function employed for the activated ethylcyclobutane. Some beam studies yield information which link the area of inter- and intramolecular energy transfer. Thus Fisk and Crim 8 2 discuss the transfer of vibrational energy from KBr* (formed by the reaction of K with Br, in a molecular beam) to such molecules as MeOH, H,O, and NH,. The KBr* contains on average 170 kJ mol of vibrational energy (with an energy spread of -40 kJ mol-') and the collision complex has a lifetime of about s. In respect of the energy transferred on collision the complex behaves as if it has almost four vibrational modes. It is relevant to note that this is just the timescale where the assumption of complete intramolecular vibrational relaxation breaks down.

-'

4 Non-Thermal Activation

Chemical Activation.-In bulk chemical activation experiments rate constants are normally measured relative to the collisional clock, o. Interpretation in terms of specificrate constants, k(E), then depends on an appropriate collisional deactivation model (see Section 3). Thus one of the more significant recent studies was a direct measurement of k(E) in a time-resolved laser flash photolysis experiment (under collision free conditions) by Hippler et aL4' In this experiment a number of alkyl substituted cycloheptatrienes were photoactivated at 265 nm (ca. 433 kJ mol -') and life-times of vibrationally excited molecules (produced by internal conversion) were measured in the time range 10-9-10-6 s. In the most definitive case ethylcycloheptatriene was found to decay with k = 1.7 x lo6 s-' at an energy of 469 kJ mol-'. RRKM calculations were within a factor of two of this value (well within the uncertainty of the calculation). Further experiments of this kind which avoid the uncertainties of collisional deactivation efficiencies are obviously highly desirable. It is now abundantly clear that the strong collision assumption must be abandoned (except perhaps in wall activation) and, therefore, interpretations of chemical activation experimentsbased upon it must be regarded as approximate at best. A calculation by Tsang 83 based on earlier results of Mintz and CvetanoviC 84 on chemically activated alcohols formed by O('D) insertion into C-H bonds falls into this category. Tsang obtained k(E) between three and forty times less than observed, and suggested that O('D) might have been translationally hot. However, it appears to us much more likely that inefficient multistep collisional deactivation is the explanation for the discrepancy. 'CH, continues to be a popular species for preparation of chemically activated species via addition and insertion reactions. A number of studies are mentioned elsewhere in this Report. Richardson and Simons 8 5 have carried out a detailed study 82

83 84

R. J. McCluskey and R. W. Can, jun., J. Phys. Chem., 1977,81,2045. 0. A. Fisk and F. F. Crim, Accounts Chem. Res., 1977, 10,73. W. Tsang, Internat. J. Chem. Kinetics, 1976, 9, 193. K. J. Mintz and R. J. Cvetanovie, Canad. J. Chem., 1973, 51, 3386. T. H. Richardson and J. W. Simons, Chem. Phys. Letters, 1976,41, 168.

11

Unimolecular Reactions

+

of the system 'CH, cyclobutane using a number of different 'CH, sources. By means of a collisional model they obtained quantitative data on the distribution of excess energy in 'CH, (from CH,N,) prior to insertion. Interpretation of this and other systems depends on a knowledge of AH,"('CH2). This is still a matter of some dispute and recent laser photoelectron ejection measurements by Zittel et aZ.86have suggested that the existing value of 418 f 8 kJ mol-' may be up to 40 kJ mol-' too low. The interpretation of this latter experiment has been questioned 87 and other evidence strongly supports the existing value.78B 88-90 It would be very hard to fit at least some of the 'CH, activated systems with AH,"(CH,) much different from 418 kJ mol-', thus we are inclined to discount the new figure.86 However, until this matter is finally settled there must remain some uncertainty over the interpretation of the methylene prepared chemical activation systems. Robinson introduced a useful classification of chemical activation studies according to their objectives [determination of E,, E*, A,, and tests of theory (input data all available)]. There are insufficient recent results to warrant such a division here but obviously the studies which make the fewest assumptions are the most useful. An analysis by Holmes, Setser, and Pritchard 92 of earlier experimental data on of the CH2FCDF2*, formed by radical recombination, reveals substantial (-78 total energy released to the olefin (cis or trans CHF=CHF) foFmed via act elimination of DF. This supports the intermediacy of the carbene CH,FCF, and a best fit to the data suggests the aa elimination barrier to be -42 kJ mol-' greater than thf endothermicity (i.e. a barrier of 42 kJ mol-I for the reverse reaction of CH,FCF with DF). This is the latest in a number of ingenious studies by Setser and co-workers (reviewed earlier *,) where the secondary reactions are exploited to give information on energy disposal in the primary reaction. Activated alkyl fluorides may be produced by direct fluorination, viz. R F, + RF*, and when in the appropriate pressure region they decompose by elimination of HF. Cadman et ~ 1 . ' have ~ studied several molecules by this technique (R = C2HS, CH,FCHF, CH,CHF, CH,CF,, CH,CHCl, or CH2ClCH2) and hence estimated values of Eo based on assumed values of AS*. This procedure requires an additional assumption about what fraction of the exothermicity of the reaction resides in the alkyl fluoride. The same authors have also reported studies 94 in which activated alkyl fluorides have been produced by the recombination of alkyl and fluoroalkyl radicals and by methylene insertion reactions. It is thus possible to produce the same alkyl fluoride with energy contents of about 300, 380, and 450 kJ mol-'. Again the authors claim that application of RRKM theory allows the calculation of the critical energy for decomposition or, where this is available (from thermal studies), the extraction of quantitative information about the thermochemistry of the chemically activated molecule. Throughout, the strong collision assumption is used. For the 'high' energy species the value of Eo estimated is very sensitive to the assumed AS*,

z)

'

+

86 87

88 89

91

92

93 94

P. F. Zittel, G. B. Ellison, S. V. O'Neil, E. Herbst, W. C. Lineberger, and W. P. Reinhardt, J. Amer. Chem. SOC.,1976,98, 3731. L. B. Harding and W. A. Goddard, Chem. Phys. Letters, 1978,55,217. J. W. Simons and R. Curry, Chem. Phys. Letters, 1976,38,171. F. Lahmani, J. Phys. Chem., 1976,80,2623. H. M. Frey and G. J. Kennedy, J.C.S. Faraday 1, 1977,73, 164. Ref. 1, p. 120. B. E. Holmes, D. W. Setser, and G. 0. Pritchard, Internat. J. Chem. Kinetics, 1976, 8,215. P. Cadman, A. W. Kirk, and A. F. Trotman-Dickenson, J.C.S. Faraday I, 1976, 72,1428. P. Cadman, A. W. Kirk, and A. F. Trotman-Dickenson, J.C.S. Faraday I, 1976,72,996.

Gas Kinetics and Energy Transfer

12

whereas this will not be so for low excess energy. However, the uncertainty of the energy content in the low energy range is quite large. We believe studies of this kind are of interest (although these papers 9 3 * 9 4 contain a rather large number of errors) but unreliable for obtaining critical energies and that most workers underestimate quite appreciably the error limits of their results. In some of the earliest studies using chemical activation Rabinovitch and his co-workers 9 5 added hydrogen atoms to C4 olefins to produce vibrationally excited s-butyl radicals and then measured their fragmentation rate to methyl propene (by comparison with the collisional stabilization rate). The results obtained over a reasonable pressure range were consistent with RRKM calculations, but were limited to a relatively small temperature range. In a more recent study 96 the addition of hydrogen atoms to trans-but-Zene and but-l-ene has been studied from 300-670 K (but over a very limited pressure range). As before, values for the rate of decomposition of the s-butyl radicals were determined and the slope of the plots of k, against the temperature were found to give a good fit to theory, though the absolute rates are incorrect by a factor of about four. Chemically activated l-buten-l-yl have been produced by the addition of ethyl radicals (photolysis of diethyl ketone) to acetylene." They undergo a 1,4-hydrogen shift to yield l-buten-4-yl radicals which can themselvesundergo further isomerization to methylallylradicals by a 1,2-hydrogenshift. RRKM theory applied to the measured unimolecular rate constants obtained at both 75 and 123 "C yield apparently reasonable values for the threshold energies for these isomerizations. Chemically activated spiropentane has been produced 98 in the thermal decomposition of the pyrazoline (1) although it is not activated when formed from compound (2).

+

(2)

(1)

Lin and co-workers 99 have measured vibrational excitation in CO produced from the chemically activated product of O(3P) with both allene and methylacetylene. With assumptions of statistical energy partitioning they have been able to show that the C,H, produced probably comes directly in the allene system but indirectly via MeCH in the methylacetylenesystem. Amongst other studies are two on dichlorocyclopropanes,'"* lo' formed via 'CCl, addition to olefins, ethylallyl ether formed via radical recombination, O2 methyl cyclohexadienyl radical formed via H toluene '03 and Si2H6 formed via radical recombination '04 which appears to imply a rather low value for D,(SiH3-

+

95 96

97 98 99

loo

Io1 Io2 lo3 lo4

'

B. S. Rabinovitch, R. F. Kubin, and R. E. Harrington, J. Chem. Phys., 1963,38,405. 0. Horic and N. H. Hanh, J. Phys. Chem., 1976,80,1657. T. Ibuki, A. Tsuji, and Y. Takezaki, J. Phys. Chem., 1976,80,8. K.K.Shen and R. G. Bergmann, J. Amer. Chem. Soc., 1977,W, 1655. M. C. Lin, R. G. Shortridge, and M. E. Umpstead, Chem. Phyx. Letters, 1976,37,279;Chem. Phys., 1977,20,271. H.Heydtmann, W. BardorlT, and H. Rullmann, Ber. Bumengesellschaft Phys. Chem., 1976,80, 311. H.Rullmann and H. Heydtmann, Ber. Bmengesellschaft Phys. Chem., 1977,81,490. T. Ibuki and Y. Takezaki, Internat. J. Chem. Kinetics, 1976,9,201. A. Amano, 0. Horie, and N. H. Hanh, Internat. J. Chem. Kinetics, 1976, 8, 321. B. Reimann, A. Matten, R. Laupert, and P. Potzinger, Ber. Bumengesellschaft Phys. Chem., 1977,81, 500.

Unimoleeular Reactions

13

SiH3). A study of C4Hi fragmentation (which fits RRKM theory) is interesting as the first example involving photoionization in an ICR spectrometer.' O 5 Multiphoton I.R. Photochemistry.-The last three years have seen a rapid growth of papers in this new area of chemical interest stimulated by the observation of isotopically selective decomposition of SF, and other molecules following absorption of i.r. radiation from a C 0 2 laser.'06-'08 An interesting account of the early work has appeared log as well as a general review of lasers in chemistry."' Since such decompositions may occur in the absence of collisions (although in some situations they may also be collisionally induced) it is clear that this topic falls well within the ambit of unimolecular processes. It is less clear whether such processes should be regarded as special in themselves or merely involving a special form of energization which is immediately followed by all the normal processes which otherwise occur in collisionally induced unimolecular decompositions. If the latter is true then we expect RRKM theory (or ones similarly based) to be applicable. It appears to us that the field is still too young for a coherent picture to be presented and accordingly we limit this section to a few brief and selected comments. Much of the discussion so far has been reminiscent of an earlier stage of the development of thermal unimolecular reaction rate theory on the relative merits of Slater versus RRK theory."' The question of the extent to which intramolecular energy flow takes place followingthe initial absorption of the photons and prior to decomposition is hotly debated. The multi-photon absorption, which is a certain requirement for decomposition in the collision free region, is not well understood.'12 One of the simplest models of the isolated molecule multiphoton decomposition process, due to Bloembergen,' envisages it as occurring in two stages. In the first place, excitation occurs from the absorbing ground state vibration mode via its anharmonic ladder, the laser field effectscompensating for the energy mismatch due to anharmonicity. At v = 3-4 the vibrational density of states is sufficiently large to constitute a quasi-continuum and vibrational energy will spread out into the molecule providing effective redistribution in the second stage. Provided the absorbed number of photons is sufficient then the molecules can reach the energy threshold and decomposition results. It should be noted that, in practice, because the time between collisions is limited and coflisional processes can modify (by quenching) the energy distribution it may be necessary for the original absorption process to provide sufficient energy to raise molecules substantially above threshold in order to see decomposition. That excitation well above threshold may occur anyway has been shown for SF, in a recent molecular-beam, COJaser experiment by Lee and co-workers. The SF6 was probably excited up to

'

lo5

Io6 lo' lo*

Io9 110 lil l l2

113

114

M. Riggin, R. Orth, and R. C. Dunbar, J. Chem. Phys., 1976,653365. R. V. Ambartzumian, A, Gorokhov, V. S. Letokhov, and G. N. Makarov, J.E.T.P. Letters, 1975, 21, 375. J. L. Lyman, R. J. Jenson, J. Rink, C. P. Robinson, and S. D. Rockwood, Appl. Phys. Letters, 1975, 27, 87. G. Hancock, J. D. Campbell, and K. H. Welge, Opt. Commun., 1976,16,177. R. V. Ambartzumian and V. S. Letokhov, Accounts Chem. Res., 1977, 10,61. S. Kimel and S. Speiser, Chem. Rev., 1977, 77,437. E. K. Gill and K. J. Laidler, Proc. Roy. SOC.,1959, A250, 121. (a) D. S. Frankel, J. Chem. Phys., 1976,65, 1696; (b)S. Mukamel and J. Jortner, ibid., 1976,65, ibid., 1976,65,5052, 5062. 5204; (c) M. F. Goodman, J. Stone, and D. A. DOWS, N. Bloembergen, Opt. Commun., 1975,15,416. M. J. Coggiola, P. A. Schulz, Y . T. Lee, and Y . R. Chen, Phys. Rev. Letters, 1977, 38, 17.

14

Gas Kinetics and Energy Transfer

ca. 100 kJ mo1-l beyond its dissociation threshold (if free intramolecular energy transfer in SF, was assumed). This latter study provided unambiguous evidence of the production of SF, and F as the only products, as well as information on their scattering and recoil energies. A large number of chemical systems have been looked at by Grunwald and his co-workers."5~''7 Many of their results have been shown to fit the equation f = Aexp(-E,/E,,J and other workers have found a similar variation,"' where f is the conversion per laser pulse, Eabsis the radiant energy absorbed and A and E, are constants. It has been argued that if RRKM theory applies to the processes being observed then E, should be equal to the reaction threshold or critical energy and Eabsrelated to the 'vibrational temperature T,' given by Eabs = skT, where s is the number of the vibrational modes. However, in order to fit the data, E, values well in excess of the known threshold energies for the reaction under investigation were required. The authors argued that the internal energy could not be equilibrated amongst all the vibrational modes of the molecule and an effective value s considerably less than the total number was implied. Indeed s might be equal to unity,li7~11' implying that the energy was stored in just one vibrational mode. These arguments are reminiscent of those produced to rationalize the experimental findings with some thermal unimolecular reactions at the time of RRK theory. At that time fast intramolecular energy flow between vibrational modes was assumed but limited to a certain number of 'active' modes s, where s < 3N-6. Because of its clear success in many other areas, we feel that at this early stage in the study of multiphoton processes it is wiser to accept the assumptions of RRKM-like theories and assume free intramolecular vibrational energy relaxation among all vibrational modes (at least near to and above the reaction threshold*). There may well be special situations where free intramolecular energy transfer is limited and the 12' but rather stronger evidence is appropriate theories are being developed required than exists at present. Some studies i22 which originally reported large differences in reaction rates of CF,ClCF,Cl induced by laser radiation for two frequencies (921 and 1051 cm -') suggesting significant 'compartmentalization of energy in vibrational modes was taking place, despite (intermolecular) V-V transfer' have since been reinterpreted as a result of further work.'23 Further, while Grunwald's work on CCI,F, suggests non-RRKM behaviour, that of King and Stephenson does not. The latter report a most elegant piece of work which probes the initial energy distribution of CF, produced by the multiphoton decomposition of CF2CI, and CF,Br, under collision free pressure conditions. By the use of u.v. laser excited fluorescence they are able to determine the initial vibrational populations of CF,. Their measurements show that the energy is distributed statistically in the CF, according to the relationship P(Ev) = exp(-Ev/kT,) where P(E,) is the relative 115

116

11' 118 119

120 lZ1

12*

*

D. F. Dever and E. Grunwald, J. Amer. Chem. SOC.,1976,98,5055. E. Grunwald, K. J. Olszyna, D. F. Dever, and B. Knishkowy,J. h e r . Chem. SOC.,1977,99,6515. G . A. Hill, E. Grunwald, and P. Keehn, J. Amer. Chem. SOC.,1977,99,6521. J. M. Preses, R. E. Weston, jun., and G. W. Flynn, Chem. Phys. Letters, 1977,46,69.

E. Grunwald and K. J. Olszyna, Laser Focus, 1976,12,41. I. Shamah and G. Fiynn, J. Amer. Chem. SOC.,1977,99,3191. S . Mukamel and J. Ross,J. Chem. Phys., 1977,46,5235. R. N. Zitter and D. F. Koster, J. Amer. Chem. SOC.,1976,98, 1614. R.N, Zitter and D. F. Koster, J. Amer. Chem. SOC.,1977,99, 5491. D. S. King and.J. C. Stephenson, Chem. Phys. Letters, 1977,51,48. There is no doubt that at low vibrational excitation a very different situation can exist and indeed one may get trapped metastable vibrational energy distributions.120

Unimolecular Reactions

15

probability that an initially formed CF, will have a vibrational energy content E,, and T, is the vibrational temperature characteristic of the parent molecule. For CF,CI,, T . = 1050 K and is the same whether dissociation is produced by 929 cm-’ or 1082 cm radiation (which excite a rocking and stretching vibration respectively), The results certainly suggest strongly that vibrational equilibrium takes place in the CF2C1, molecule (and CF,Br,) prior to decomposition. We further note that the RRKM model has had some success 125apb in explaining the observed product yields in the multiphoton decomposition of SF, provided a somewhat higher (and in our view more reasonable S-F bond dissociation energy than hitherto believed is assumed.125a A higher dissociation energy is also required to fit an RRKM model for the shock tube (thermal) dissociation of SF6.68 A straightforward study of the laser-induced isomerization of methylisocyanidehas appeared 127 as well as the decomposition of some alkyl halides.’28 An interesting note has also been published on the laser-induced Cope rearrangement in deuteriated hexa-1,5-dienes which indicates a possible route for isotope separation via an isomerization pathway.12’ Most of the published work, which has involved studies of small polyatomic molecules (four to seven atoms) which decompose to give radical products, has been concerned with isotope separation or with determining the dependence of yield on laser intensity. This is not an area which seems likely to interact strongly with current unimolecular rate theory (and indeed such experiments may not be appreciably more easily interpreted with the aid of such theories). Molecules with two channels for decomposition, however, offer the possibility of probing its internal energy in terms of a vibrational temperature directly. Such work is beginning to be published. A recent experiment by Rosenfeld, Brauman, Barker, and Golden 130 is of this .type. The conventional pyrolysis of ethylvinyl ether yields acetaldehyde and ethylene by a unimolecular process involving a cyclic transition state with a low A factor and low energy of activation (186 kJ mol-I). Under ‘laser conditions’ another pathway iiivolving simple bond fission also occurs. The estimated Arrhenius parameters for such a process are IOl5 s-l and 275 kJ mol-’. At low temperatures the retro-ene reaction with its low energy of activation will predominate, whereas at sufficiently high temperatures the bond fission pathway with its high pre-exponential factor will assume increasing importance. Thus the relative rates of the two processes provide a value for the ‘internal or vibrational’ temperature of the system. Golden et al. report such rate ratios for multiphoton decomposition under a range of pressure conditions and obtain a unique temperature which they attribute to collisional thermalization by V-V transfer. Similarly Richardson and Setser 13’ have reported work on the laser induced decomposition of MeCF,, MeCH,F, and CH2FCH,Br. For the last molecule there are two decomposition pathways of interest,

-’

lz9 130

(a) J. L. Lyman, J. Chem. Phys., 1977, 67, 1868; (b) J. G. Black, E. Yablonovitch, and N. Bloembergen, Phys. Rev. Letters, 1977, 38, 1131. S. W. Benson, Chem. Rev., 1978,78,23. C . Kleinermanns and H. Gg. Wagner. Ber. Burtsengesellschaft Phys. Chem., 1977,81,1283. W. Braun and W. Tsang, Chem. Phys. Letters, 1976,44,354. I. Glatt and A. Yogev, J. Amer. Chem. SOC.,1976,98,7087. R. N. Rosenfeld, J. 1. Brauman, J. R. Barker, and D. M. Golden, J. Amer. Chem. Soc., 1977,99,

lJ1

T. H. Richardson and D. W. Setser, J. Phys. Chem., 1977,81,2301.

125

126

12‘ 128

8063.

Gas Kinetics and Energy Transfer

16 HF

+ CH,=CHBr

CHZFCH2B HBr

+ CH2=CHF

On the basis of RRKM theory, yields of HBr should exceed HF since that reaction pathway has the lower threshold energy. However, if intramolecular relaxation was in any way rate-determining then the reverse might be expected since the initial laser excitation occurs in a C-F stretching frequency. In fact there was a pronounced favouring of the HBr elimination over H F (- 1O:l) consistent with an excitation energy (assuming RRKM behaviour) of about 314 kJ mol If energy randomization is also assumed to occur in MeCF, and MeCH2F then the results suggest that these molecules have acquired energies of about 356 and 293 kJ mol respectively, well in excess of the threshold energies. Richardson and Setser are careful to eliminate any significant contribution from intermolecular energy transfer or 'thermal' heating by addition of a second non-absorbing gas to the system. For part of the work they used cyclopropane. They found no direct laser-induced decomposition of cyclopropane which is at variance with other reports in the literature 132 and which may reflect more severe focusing conditions (and hence high power densities) in the other work, though the possibility of heterogeneous effects should also be borne in mind. Such a warning has been sounded by Karny and Zare 133 and it will certainly strike a sympathetic note in all those kineticists who work or have worked with 'aged' reaction vessels. These last two studies are in an area that seems likely to develop rapidly and may well lead to an increase in our understanding of unimolecular reactions.

-'.

5 Thermal Unimolecuiar Reactions in the Fall-off and Low Pressure Limiting Regions There have been relatively few studies of thermal reactions in their fall-off regions during the period of this Report. It is useful here to draw a distinction between the true second-order limiting rate region and the region of pressure dependence intermediate between the limiting high and low pressure regions. Of course, the RRKM theory in conjunction with a suitable model of collisional energy transfer is well capable of encompassing both regions,' 3 4 however relatively few experimental studies span them. Many static bulb pyrolysis experiments have revealed fall-off with kuniup to approximately a modest factor of ten below k,, certainly well away from the second-order limit, while shock tube experiments tend to provide data at the second-order limit. Thus the experimental bias as well as the complexity of RRKM combined with collision energy transfer calculations has led different groups to apply unimolecular theory in somewhat different ways. Troe 29 has formulated a solution of the master equation at the low pressure limit in which the rate constant is expressed as a set of separable and multiplicative terms :

where the factors Fj refer to anharmonicity, energy dependence of the density of E. Grunwald, Eng. News, 1976,54,18; M. L. LeSieckl and W. A. Guillory, J. Chem. Phys., 1977,

lJZ

133

66,4317. Z. Karny and R. N. Zare, Chem. Phys., 1977,23,321.

17

Unimolecular Reactions

states, rotation, and internal rotation, respectively, and the other terms have their usual significance. The assumption of separability of rotation and vibration is thought to produce no serious error. van den Bergh has in fact tested this assumption and shown that though errors are usually small they can be up to a factor of two. Use of this equation has the merit that each term is explicitly evaluated and one can see very quickly its relative importance. The greatest source of error in practical calculations lies in uncertainty as to the value of E,. Troe has applied this theory using E, values available from spectroscopic and other non-kinetic sources to obtain 3/, values for a number of decompositions of three and four atomic molecules in shock tubes at high temperatures.30 The collisional energy transfer information derived is discussed in Section 3. Troe’s approach to the intermediate region of pressure dependence is to fit between the high and low pressure limits with an empirical two parameter version of the Kassel integral adapted for weak collision effect~.”~This procedure gives falloff curves differing little from RRKM predictions. Another simplificationof RRKM theory is the method due to Forst 13’ wherein the specific rate constant, k(E) is approximated by

k(E) = A,N(E--E,)/N(E)

E > Em

where the terms have their usual significance. Use of this method avoids the necessity of making a vibrational assignment of the activated complex and is thus relatively simple to carry out. The fall-off curve derived is, however, equivalent to that from a full RRKM calculation. The method tends to be attractive for fitting fall-off data near the high pressure limit and has been applied recently by Dill and Heydtmann ”* to a variety of experimental curves. In order to fit the curves precisely the authors, as is commonly done, introduced an arbitrary collisional inefficiency 1 (not the same as &) which ranged from 0.2 for HCI elimination from alkyl chlorides to 1.0 for cyclopropane and other small rings. Unfortunately the efficiencies cannot be taken too seriously as the calculations are sensitive to a number of input parameters such as the high pressure Arrhenius Parameters, collision diameter, and the inclusion of rotational effects, although the authors argue that errors from some of these should not be serious. Pritchard et al.’ 39 have discussed earlier fall-off curves for fluorocyclopropane, a molecile with four reaction channels and using their master equation approach demonstrated how the reaction channels with higher critical energy should show sharper fall-off characteristics, in accordance with observation, although it should be said the authors of the original work 140 felt that the experimental observations were probably due to the differential polymerization of the monofluoropropene products, since at low pressures there was a poor carbon balance. At all events theoretically this situation is to be expected since the depletion of states above the lowest energy threshold will severely reduce the probability of reaction by upper channels at the low 134

13s 136

137 13*

IJ9

I4O

Ref. 2, Chapter 10. H. van den Burgh, Chem. Phys., 1977,22, 131. J. Troe, Ber. Bunsengesellschaft Phys. Chem., 1974,78,478. W. Forst, J. Phys. Chem., 1972, 76, 342. B. Dill and H. Heydtmann, Znternat. J. Chem. Kinetics, 1977, 9, 321. M. H. Baghal-Vayjooee,A. W. Yau, and H. 0. Pritchard, Canad. J. Chem., 1977,55,1595. F. Casas, J. A. Kerr, and A. F. Trotman-Dickenson,J. Chern. SOC.,1964,3655.

Gas Kinetics and Energy Transfer

18

pressure limit. Such a situation is interesting, however, from the point of view of the study of specific weak collision effects.141* 142 Barnard and co-workers 143* 144 have reported several reflected shock wave studies in which at temperatures above ca. 1100 K decompositionrate constants fall drastically below those anticipated from extrapolation of lower temperature data. These are further examples of a phenomenon first observed for cyclopropane 7 0 some years ago. This high temperature ‘turn-over’ appears too sharp in most cases to be attributed simply to ‘fall-off and the explanation favoured by Barnard involves both fall-off and high temperature decrease of collisional efficiency.68 We remain unconvinced that this is wholly a unimolecular reaction phenomenon but note the accumulating need for some independent corroborative evidence. Forst and co-workers 145 have discussed some specific low pressure limiting behaviour in the H202decomposition, noting amongst other features curvatures that arise in the Arrhenius plots due to weak collision effects. Shock tube studies of MeCHO 14‘ MeCOCH3,146and C2H,C1 14’ give results in the intermediate fall-off region for decompositions of these molecules. These results have been extrapolated to the high and low pressure limits using theory. However, with neither limit fixed the extrapolated results must be regarded as having higher than average uncertainty. At the low pressure limit rate constants for the shock tube decompositions of HCN,148 N20,14’ and NF315’ have been obtained, the data for the latter decomposition The shock tube study of the decomposition of giving rise to some dispute. NCNO (0.4 % in Ar) has been studied from 1400-1700 K and at total pressures up to 2.1 atmospheres. Calculated rate constants using RRKM are in good agreement with the experimental results and suggest the reaction is near its low pressure limit.lS2 A conventional (static bulb) pyrolytic study l S 3of the decomposition of l,;?-epoxypropane has shown that there are four simultaneous isomerization pathways (to propanal, propanone, methylvinyl ether, and allylol) as well as a process leading to fragmentation products (reduced by the addition of nitric oxide). In the pressure region 25-326 Torr the rate constant for the formation of propanone shows an appreciable decline, whereas the effect on the other isomers is much smaller. This could be attributed to the fact that the reaction channel leading to propanone has the highest energy of activation (and hence the pseudo equilibrium concentration of energized molecules is depleted by the presence of the other reaction channels). However, Flowers produces an alternative explanation. Propanone produced from epoxypropane is chemically activated by about 40 kJ mol-’ in excess of the minimum required for its decomposition. RRKM calculations using this datum as well as an

’”*”’

141

142 143

144 145 146

14’ 148 149

151

lS2 53

Ref. 7, p. 405. Th. Just, P. Roth, and R. Damon, ‘XVIth International Symposium on Combustion’, The Combustion Institute, Pittsburgh, 1976, p. 961. J. A. Barnard, A. T. Cocks, and T. K. Parrott, J.C.S. Faraday I, 1976,72,1456. J. A. Barnard and T. K. Parrott, J.C.S. Faraday I, 1976,72,2404. A. P. Penner, R. C. Bhattacharjee, and W. Forst, Internat. J. Chem. Kinefics, 1977,9,371. J. Ernst, K. Spindler, and H. Gg. Wagner, Ber. BunsergesellschaftPhys. Chem., 1976,81,645. F. Zabel, Internat. J. Chem. Kinetics, 1977, 9, 651. P. Roth and Th. Just, Ber. Bunsengesellschafr Phys. Chem., 1976,80, 171. A. M. Dean, Internat. J. Chem. Kinetics, 1976,8,459. P. J. Evans and E. Tsuikow-Roux, J. Chem. Phys., 1976, 65,4202; ibid., 1977’66,4253. E. A. Dorko, U. Grimm, and G. W. Mueller, J. Chem. Phys., 1977,66,4252. E. A. Dorko, R. H. Flynn, U. Grimm, K. Scheller, and G. W. Mueller, J. Phys. Chem., 1977, 81, 811. M. C. Flowers, J.C.S. Faraday I, 1977,73, 1927.

19

Unimolecular Reactions

assignment of the activated complex to agree with high temperature results, gave fall-off curves in satisfactory agreement with the experimental curve. It was also shown that similar effects for propanal would not be expected until much lower pressures were reached. Another conventionalstudy by Bailey and Walsh,' 5 4 of cyclopropene isomerization covered more than two orders of magnitude of fall-off (five orders of magnitude of pressure). The VLPP method has been used to obtain the data in Table 1, although it should be pointed out that in some cases the A factors were estimated and RRK rather than RRKM used to process the results. It is worth repeating that the strong collision assumption so commonly assumed ten years ago has now been largely abandoned by workers in this field. Table 1 Arrhenius parameters from VLPP Reaction CsHsCHzCHzNHz --t CsHsCHz CH2NHz C6HsSCH3 --t C6H5S CH3 CsHsCH2SCH3 C6H5CH2 SCH3 CsHsOCHzCH=CHz CsHs0 CHZCH=CH2 CsHsOCzHs -+ C6HsO C2Hs CsH5CH2OCH3 C6H5CHz OCHJ MeOOMe --t 2Me0 cycloheptatriene toluene Bu'CN --+ Me MezCCN -+ Me2C=CH2 HCN

+

--+

+

+

--+

+

--+

+

--f

+

+

+

log(A/s-1)

E/kJ mol-l

14.7 15.3 14.7 14.6 15.3 14.5 15.7 13.6 15.9 14.1

267 266

234 203 253 273 155 218 313 310

Ref. a b b C

C C

d e

f f

(a) A. J. Colussi and S. W. Benson, Internut. J. Chem. Kinetics, 1977,9, 307; (b) A. J, Colussi and S. W. Benson,Internat.J. Chem.Kinetics, 1977,9,295; (c) A. J. Colussi, F. Zabel, and S. W. Benson, Internut. J. Chem. Kinetics, 1977, 9, 161; ( d ) J. R. Barker, S. W. Benson, and D. M. Golden, Internut. J. Chem. Kinetics, 1977, 9, 31; ( e ) B. J. Gaynor, R. G. Gilbert, K. D. King, and J. C. Mackie, Internut. J. Chem. Kinetics, 1976, 8, 695; (f) K. D. King and R. D. Goddard, J. Phys. Chem., 1976,80,546.

6 Thermal Unimolecular Reactions in the High Pressure Region This section deals with kinetic and, to a limited extent, mechanistic studies of unimolecular reactions (but see Section 8). The layout of data follows approximatelythat used by Robinson and Holbrook2 and the same comments made by Robinson apply.'55 The data is presented here in terms of Arrhenius parameters A , and Em, but there are many workers who report it in terms of AS' and AH*. This has been converted at some labour particularly where AS* has been reported incorrectly, or without a specified temperature. This practice is unfortunate, and from the point of view of readers, reporting in terms of A, and E, is much to be preferred! For the calculation of Arrhenius parameters, CvetanoviC and Singleton 156 have criticized the usual procedure of a linear least squares fit to the logarithmic form of the Arrhenius equation and suggested alternatives. Although other procedures yield different Arrhenius parameters, it is our view that discrepancies are only serious for ls4 lSs

I. M. Bailey and R. Walsh, J.C.S. Furaduy I, 1978, 74, 1146. Ref. 1, p. 121. R. J. CvetanoviC and D. L. Singleton, Internut. J. Chem. Kinetics, 1977, 9, 481.

Gas Kinetics and Energy Transfer

20

experimental data of rather poor quality and that for more precise work errors in rate constants tend to be proportional to the rate constants themselves, thus justifying the usual procedure. Cyclopropane, Cyclobutane, and their Derivatives (Table 2).-General developments in our mechanistic understanding of these pyrolyses are discussed in the section on mechanism. Among specific studies given in Table 2, one or two are of particular Table 2 Recent high pressure Arrhenius parameters for small ring isomerizations and decompositions Reactant

v

CN CN

Ref.

13.86 13.73

186 191

a a

14.89

208

b

14.75

210

b

14.7

208

C

15.23

212

d

11.86 11.86

167 179

e

CN b

forward reverse

N

$' JoMe

E,/kJ mol-l

log(A,/s-')

Product (s)

OMe OMe

Pe

pe OMe

K

W g F

forward

F3C> F

+ reverse

+ CF,

forward reverse

21

Unimolecular Reactions

Table %continued Reactant

EJkJ mol-I

Ref.

10.58

131

f

14.66

156

g

12.79

116

g

13.56

142

13.27

131

13.21

224

h

14.57

193

i

log(A,/s-')

Product (s)

6' 4

racemization

OEt

+e

JoMe

+e

L + CH$O

(a) W. von E. Doering, G. Horowitz, and K. Sachdev, Tetrahedron, 1977,33,273; (6) W . Kirmse and M. Zeppenfeld, J.C.S. Chem. Comm., 1977, 124; (c) W. R. Dolbier, jun., and H. 0. Enoch, J. Amer. Chem. SOC.,1977,99,4532; (d) E. D. Quero, J. C. Ferrero, and E. H. Staricm, Internut. J. Chem. Kinetics, 1977, 9, 339; (e) J. J. Gajewski, R. J. Weber, R. Braun, M. L. Manion, and B. Hymen, J. Amer. Chem. SOC.,1977, 99, 816; (j') H. G. Richey and D. W. Shull, Tetruhedrun Letters, 1976, 575; ( g ) W. Kinnse and H.-R. Murawski, J.C.S. Chem. Comm., 1977, 122; (A) A. D. Clements and H. M. Frey, J.C.S. Furuuizy I, 1976, 72, 1637; ( i ) H. M. Frey and R. A. Smith, J.C.S. Perkin 11, 1977, 752.

kinetic interest. Dolbier's study 157 of the reaction of (3) to (4) strongly suggests the intermediacy of the biradical(5). The measured activation energy of the reaction thus

(3

(4)

(5

indicates a probable remote bond-weakening effect of the difluoro substituent of ca. 40 kJ mol relative to the analogous non-fluorinated molecule. This is a sur15'

W. R. Dolbier, jun., and H. 0. Enoch, J. Amer. Chem. Soc., 1977, 99,4532.

22

Gas Kinetics and Energy Transfer

prisingly large value for a remote substituent effect which was predicted qualitatively some years ago by H~ffmann.'~' The low A factor and energy of activation observed in the reaction of (6) to (7)are

A

COOEt

(61

(7 )

almost certainly indicative of the homodienyl 1,5-shift process occurring via the intermediacy of compound (8) as proposed.15' What is interesting here is that this

h HO

OEt

(8)

hydroxyolefin (enol form) does not ketonize via a 1,3-H shift but lives long enough to revert to a cyclopropane (in conflict with a previous similar system). The data enables a conservative lower limit of 188 kJ mol-' to be placed on the activation energy for enol + keto 1,3-H shift.15' The [1,3]sigmatropiccarbon shift which occurs in the degenerate rearrangement of methylene cyclobutane was earlier alleged by Baldwin to occur predominantly antarafacially.160 Gajewski161has recently reinterpreted Baldwin's data to show that this unlikely process is not in fact significant. Gajewski's paper is illustrative of the difficulties of dealing with kinetics in such systems. Severe problems arise because of the complexity of the network of partially inter-related rate constants as shown in Scheme 1.

scheme 1

Gajewski's refinement involved solution of the coupled differential equations by a Runga Kutta procedure. This produced rate constants differing in some cases by up to 50% from the original. It is not easy to assess the dependence of individual rate constant values on the refinement procedure but what is certain is that analytical data of high quality are required (with kinetic runs from each possible precursor) in order to have rate constants of good precision. Even then, some of them may be ill deterlS9

R. Hoffmann, Tetrahedron Letters, 1970,2907. J. J. Gajewski, R. J. Webex, R. Braun, M. L. Manion, and B. Hymen, J. Amer. Chem. SOC.,

160 161

J. E. Baldwin and R. H. Reming, J. Amer. Chem. SOC.,1973,95, 5249, 5256, 5261. J. J. Gajewski, J. Amer. Chem. SOC.,1976, 98, 5254.

lS8

1977,99, 816.

Unimolecular Reactions

23

mined. Amongst simpler systems Back and co-workers have succeeded in studying the kinetics of the formation of cis- and trans-dimethyl cyclobutanefrom ethylene and cis- or trans-but-Zene. These reactions are not unimolecular but it is interesting that the results fit precisely the biradical mechanism proposed for the reverse processes studied originally by Gerberich and Walters.' 63 The rearrangement of diethynylcyclobutane produced some interesting products, with probable diallenylcyclic intermediate^.'^^ Another noteworthy result is the direct detection, by nanosecond flash photolysis of a 1,4-biradi~al,~'~ analogous to the cyclobutane intermediate (although formed in a Norrish Type I1 photochemical process). Polycyclic Systems (Table 3).-These cover a great mixture of possible processes although undoubtedly many mechanisms resemble those in simpler systems. The contrasts may be illustrated by studies of two of the valence bond isomers of benzene which have recently appeared. Benzvalene (9) isomerizes, with no discernable intermediate, in a concerted process to benzene,' 66 whereas 3,3'-dicyclopropenyl isomeriza-

tion occurs in a number of stages, as shown in Scheme 2. In a discussion dominated by experimental results it is pleasant to report what looks like a very carefully constructed flow pyrolysis apparatus by Meyer and de Meijere which has been tested

'''

Scheme 2

with some kinetically well characterized isomerization reactions and used to study several new reactions. Solly and Cain ' 1 5 ~have studied some more substituted bicyclo[2,2,0]hexane systems and while no new mechanistic information is derived they note that methyl and ethyl substitution at the reaction site serves to increase the activation energy. They attribute this to ground state stabilization effects. This finding serves as a reminder that substituents do not only modify transition state behaviour. A number of spirodiene rearrangements have activation energies too low to fit biradical mechanisms.170* 171

164

166

G. Scacchi, C. Richard, and M. H. Back, Internat. J, Chem. Kinetics, 1977,9,513. H. R. Gerberich and W. D. Walters, J. Amer. Chem. SOC.,1961,83,3935,4884. L.Eisenhuth and H. Hopf, Chem. Ber., 1975,108,2635. R. D. Small jun., and J. C. Scaiano, Chem. Phys. Letters, 1977, 50,431. N. J. Turro, C. A. Renner, T. J. Katz, K.B. Wiberg, and H. A. Connon, Tetrahedron Letters, 1976,4133.

168

169

J. H. Davis, K. J. Shea, and R. G. Bergmann, J. Amer. Chem. SOC.,1977,99,1499. L.-U. Meyer and A. de Meijere, Chem. Ber., 1977,110,2745. R. K. Solly and E. N. Cain, Internat. J. Chem. Kinetics, 1976, 8, 563. M. F. Semmelhack, H. N. Weller, and J. S. Foos,J. Amer. Chem. SOC.,1977, 99, 292. A. de Meijere and L.-U. Meyer, Chem. Ber., 1977,110,2561.

24

Gas Kinetics and Energy Transfer

Table 3 Recent high pressure Arrhenius parameters for reactions of polycyclic compounds Reactant Product(s) Cyclopropane ring reactions

"g

log(A,/s-')

I

forward R=Me &reverse R=Et

racemization

EJkJ mol-I Ref.

13.7

112

a

14.06

154

b

14.48 13.26

168 161

C

12.75

118

d

14.90

175

d

13.53

158

f

14.6

132

g

14.6

147

g

14.6

151

g

c

Unimolecular Reactions

25

Table Scontinued Reactant Proakct (s) Cyclobutane ring reactions

+

COaMe

C0,Me

4

a CLe

4J

133 138

h

12.1

107

h

13.9

171

g

13.9

147

14.0

165

{:::$

m

C0,Me

c;

C0,Me

c3

101

R

00

122

Miscellaneous

00

i

151

141

26

Gas Kinetics and Energy Transfer

Table Scontinued Product (s)

Reactant

log(A,/s-')

E,/W mol-'

Ref.

11.9

115

k

12.8

113

k

(a) In n-heptane solution; N.J. Turro, C. A. Renner, T. J. Katz, K.B. Wiberg, and H.A. Connon, Tetrahedron Letters, 1976, 4133; (b) H. M. Frey, H.Hopf, and R. A. Smith, J.C.S. Perkin IZ, 1976, 1865; (c) J. J. Gajewski and S. K.Chou, J. Amer. Chem. Sac., 1977,!W, 5696; ( d ) C. W . Jefford, J. Mareda, J. C. E.Gehret, T. Karbengele, W. D. Graham, and U. Burger, J. Amer. Chem. SOC.,1976, 98,2585; (e) D. H.Aue and M. J. Meshishnek, J. Amer. Chem. SOC.,1977,99,223; (f) In dodecane solution; K.Heger and W. G r i m e , Angew. Chem. Internat. Edn., 1976, 15, 53; (g) L.-U. Meyer and A. de Meijere, Chem. Ber., 1977,110,2545; (h) Liquid phase; H.-D. Martin and M . Hekman, Angew. Chem. Internat. Edn., 1976,15,431; (i) M. J. Goldstein, R. S. Light, and M. S . Lipton, J. Amer. Chem. Soc., 1976, 98, 5717; (j) A. de Meijere and L.-U. Meyer, Chem. Ber., 1977, 110,2561 ; (k) M. F. Semmelhack, H. N. Weller, and J. S . Foos,J. Amer. Chem. SOC.,

1977,99,292.

Heterocyclic Compounds vable 4).-Many different processes are illustrated by the data in Table 4 and these are not discussed in detail here. A useful review of earlier work on both thermal and photochemical reactions of heterocyclics has appeared,12 as well as a specific review of azo compo~nds.~ Table 4 Recent high pressure Arrhenius parameters for reactions of heterocyclic compounds Product(s)

Reactant Three-membered rings

MeCHzCHO MeCOCHj (extrapolated) MeOCH=CH2 CH2=CHCHZOH

10g~~(d,/s-~) E,/kJ mo1-I

Ref:

14.39 14.23 13.51 12.90

245 254 246 239

a a a a

14.1

200

b

13.53

185

b

10.8'1

109

C

A + co

6 -0,

-0,

(racemization)

Unimolecular Reactions

27

Table &continued Reactant

wo

0

X iN

C1

Product(s)

LoJ

O

W

X,Y

= Ph,

Me

X,Y = Ph,Bu” CHjNC

EJkJ mol-I

Ref.

14.9

177

d

11.29

110

e

13.45 13.26

119 117

12.20

136

13.36

144

14.47

247

12.9

120

13.0

103

15.1

120

15.1

152

13.3

99

0

+ N2

Me&l

loglo(A,/s-l)

+ CH~=N-BU’

Four-membered rings CHzO 2H4

+ CH2=CHEt

+ EtCHO

2R2CO R = Me0

Five-membered rings

i

28

Gas Kinetics and Energy Transfer

Table &-continued Reactant

logl&4,/s-')

Product (s)

E,/kJ mol-I

Ref.

202

m

Six-membered rings

CH2=CHCHO

+ CHz=CHOEt

14.47

M. C . Flowers, J.C.S. Faraday Z, 1977, 73, 1927; (b) R. J. Crawford, S. B. Lutener, and R. D. Cockcroft, C a d . J. Chem., 1976, 54,3364; (c) N. Manisse and J. Chuche, J. Amer. Chem. SOC.,1977,99,1272; (d) D. E. Penny, J.C.S. Perkin ZZ, 1976,36; ( e ) W . H . Archer and B. J. Tyler, J.C.S. Faraahy Z, 1976, 72, 1448; (f) In DMSO solution; M.T. H. Liu and B. M. Jennings, C a d . J. Chem., 1977, 55, 3596; (g) In benzene solution; H. Quast and P. Schifer, Tetrahedron Letters, 1977, 1057; (h) M. J. Clark and K.A. Holbrook, J.C.S. Faraday Z, 1977,73,890; ( i ) In benzene solution; T.Wilson, D. E. Golan, M. S. Harrison, and A. L. Baumstark, J. Amer. Chem. SOC.,1976,98, 1086; 0)In benzene solution; J. A. Berson, C. D. Duncan, G. C. O'Connell, and M.S . Platz, J. Amer. Chem. SOC.,1976,98,2358; (k) N. J. Turro, C. A. Renner, W.H. Waddell, and T. J. Katz, J. Amer. Chern. SOC., 1976, 98, 4320; (I) M. P. Shneider and B. Csacsko, J.C.S. Chem. Comm., 1977, 330; (m)1. M. Bailey and H. M.Frey,J.C.S. Perkin ZZ, 1977, 870. (a)

Olefins and Polyenes (Table 5).-The data presented in this section illustrates cis-trans isomerization processes, Cope reactions, and retro Diels-Alder reactions, as well as a few other reaction types.

-

Table 5 Recent high pressure Arrhenius parameters for reactions of olefins and polyenes Reactant

Product (s)

+ H,

'R

log(A,/s-')

E,/kJ mol-'

Ref.

13.6

259

a

13.0

274

a

13.04

133

b

12.3

83

C

13.6

218

d

15.16

274

e

15.79

262

e

R' = Ph, R' =PhCH,CMe,

0 0 CT

w 2-

+ C,H,

29

Unimolecular Reactions

Table %continued Reactant

Product(s)

10g(A,/s-~) E,/kJ mol-'

ReJ

14.26

186

f

12.98

194

g

15.34

217

h

16.46

236

h

12.6

139

i

9.6

110

i

10.68 10.72

135 151

i i

10.92

126

i

8.86

92

i

9.68

107

i

CHO

Cope-type rearrangements \

Ph

Ph

ph3

Ph

Gas Kinetics and Energy Transfer

30 Table %continued Reactant

PdUCt(S)

R

R CN (2) (El R =COzMe (2) (E) R

=

10.20 9.85 11.11 10.21

100 105 108 97

k k

k k

R R (a) D. Masson, C. Richard, and R. Martin, Znternut.J. Chem. Kinetics, 1976,8,37; (b) W. R. Roth and H.-D. Exner, Chem. Ber., 1976, 109, 1158; (c) In solution; K. Bertsch, G. Karich, and J. C. Jockims, Chem. Ber., 1977, 110, 3304; (d) B. J. Gaynor, R. G. Gilbert, K. D. King, and J. C. Mackie, Internut. J. Chem. Kinetics, 1976, 8, 695; (e) J. A. Barnard and T. K. Parrott, J.C.S. Farachy Z, 1976, 72, 2404; (f) R. Walsh and J. M. Wells, J.C.S. Perkin IZ, 1976, 52; (g) G. Huybrechts, G. Paternoster, and P. Baetens, Internut. J. Chem. Kinetics, 1976, 8, 241; (h) G. Huybrechts, L. Luyckx, Th. Vandenboom, and B. Van Mele, Znternut. J. Chem. Kinetics, 1977, 9, 283; ( i ) L.-U. Meyer and A. de Meijere, Chem. Ber., 1977, 110, 2545; 0') In solution; M. J. S.Dewar and L. E. Wade, jun., J. Amer. Chem. SOC.,1977,99,4417; (k) In decane solution, some other rate constants listed; R. Wehrli, D. Bellus, H.-J. Hansen, and H. Schmid, Helv. Chim. Actu, 1977, 60, 1325.

For the simple allene to methylacetylene isomerization, Walsh has shown, using existing data, that cyclopropene is a possible intermediate.17* The complexity of the formally Cope-type rearrangement has been revealed in the studies of Dewar 173 and S~hmid."~Although the concerted process appears in many cases to proceed via a chair-like transition state (10) neverthelesswith appropriate substitution (2,5 diphenyl) the biradical(l1) seems to be favoured. Because of probable structural distortions of

(10)

(1 1)

the latter (based on theory) Dewar has termed them biradi~aloids."~There seems, however, to be no experimental way of verifying these distortions and we favour using the term biradical to include all possible biradicaloids(see section on mechanism). We note elsewhere that the debate over the mechanism of the Diels-Alder (and therefore the retro Diels-Alder) reaction is as yet not resolved. There has been a comprehensivereview of thermal sigmatropic rearrangements."

Elimination Reactions (Table @.-Many of the studies shown in Table 6 are for wellestablished reaction types and little discussion is therefore necessary. On the basis of earlier compilations and some of the data presented here one should expect A factors of the following orders of magnitude.

1'14

R. Walsh, J.C.S. Faruhy I, 1976,72,2137. M. J. S.Dewar and L. E. Wade, jun., J. Amer. Chem. SOC.,1977,99,4417. R. Wehrli, H. Schmid, D. Bellus, and H.-J. Hansen, Helv. Chim. Actu, 1977,60,1325; Chimiu,

l'lS

M.J. S. Dewar, G.P. Ford, M. L. McKee, H. S.Rzepa, and L. E.Wade, jun., J. Amer. Chem.

1'12 1'13

1976, 30,416.

Soc., 1977,99,5069.

Unirnolecular Reactions

31

three-centre elimination four-centre elimination five-centre elimination six-centre elimination

log,,(A/s -9 13.5 f 1 13.5 & 1 13.0 f 1 12.5 & 1

Such magnitudes are obviously broadly consistent with transition state theory. Not all the data in Table 6 falls within these confines and it is probable that in some specific cases distortion of Arrhenius plots has occurred. This is hardly an original comment yet papers still appear where the authors apparently feel little or no anxiety over the (anomalous) magnitudes of A factors. Attention should be drawn to the work of Taylor in obtaining numerous correlations between gas phase and solution rates in ester eliminations.

'''

Table 6 Recent high pressure Arrhenius parameters for three- and four- five- and six-centre eliminations Reactant Product (s) Three-centre eliminations MeoSiSiH3 Me3SiH SiHz Me3SiGeH3 MesSiH GeHz Me3SiSiMezH (MesSkH + SiMez MeSiH3 + SiMez MezSiH%HzMe MezSiHz SiHMe Me3SiCl SiMez Me3SiSiMezCl MezSiCIz + SiMeCl MeSiCIzSiMezC1 MeSiClzSiMeClZ MeSiC13 + SiMeCl CICOzMe MeCl COz

+ +

+

+

+

Four-centre eliminations MezCHCMe=CHz HzO MezC=CMe2 + HzO Me3CCHMeOH Me3CCH=CHz 3- HzO

+

{

CHzClCHzOH MeCOCl Bu'OEt Bu'OCDzMe CeDDCzHs EtONO

+ + + + + +

CHsCHO HCl CHzCO HCl Me2C=CHz EtOH MeC=CHz MeCD,OH (CD3)zC=CDz EtOD MeCHO HNO

Five-centre eliminations CHz=CHCMezCHO MezC=CHMe

+ CO

log(A,/s-') 14.48 13.56 12.93 12.5613.66 11.69 12.45 12.06 14.26

Ref.

201 143 198 193 193 210 196 192 151

a a b b b C C C

d

14.17 13.66 <14.0

269 272 284

e e e

12.9

243

f

12.8 12.42 12.20 12.37 13.37 13.7

230 169 216 219 240 157

g

13.4

185

k

170 190-193

1 m

200-214

m

141

n

Six-centre eliminations Acetates (etc.) 14.22 Et(Pr')(Me)COAc HOAc olefins (various) RCsH4CHZCHzOAc HOAC RCsH4CH=CHz 12.39-12.55 R = various 12.5-12.9 RCHzCHzOAc HOAC RCH=CHz R = various 12.9 Bu'ONO HONO MezC=CHz ' 7 6 R.Taylor and M.P.Thorne, J.C.S. Perkin II, 1976, 799.

+ + + +

EJkJ mol-'

h i i

i i

'

32

Gas Kinetics and Energy Transfer

Table ':continued Reactant Anhydrides

Ac~O (Et C0)zO (Pr'C0)20 Acids

Product ( s )

+

HOAC CHzCO EtCOOH MeCH=CO Pr'COOH Me2C=C0

+ +

log(A,/s-l) 11.27 11.38 11.81

E,/kJ rno1-I

Ref.

135 140 152

0

0 0

+ + +

HC= CCH2COOH CH2=C=CH2 CO2 11.34 159 P 11.38 161 MeC= CCH2COOH MeCH=C=CH2 C02 P 11.35 153 HC= CCMe2COOH CH2=C=CMe2 C02 P CH2=C= CH2=CH--CH= CHCHaCOOH CH2 C02 11.08 168 4 CHp=C= CHz=CH--CH= 11.26 162 CHCMe2COOH CMe2 C02 4 CH?=CH--CH= CH2=CHCH2CH= 13.16 195 CHCMe2COOH CMe2 C02 4 (a) D. P. Paquin and M.A. Ring, J. Amer. Chem. SOC.,1977, 99, 1793; (6) I. M.T. Davidson and J. I. Matthews, J.C.S. Farudzy Z, 1976, 72, 1403; (c) I. M. T. Davidson and M. E. Delf, J.C.S. Faraday Z, 1976, 72,1912; (d) R. L. Johnson and V. R. Stimson, Austral. J. Chem., 1977, 30,1917; ( e ) W. Tsang, Internat.J. Chem. Kinetics, 1976,8,173; (f) J. L. Gamett, W. D. Johnson, and J. E. Sherwood, Austral. J. Chem., 1976, 29, 589; (g) D. C. Skingle and V. R. Stimson, Austral. J. Chem., 1976, 29, 609; (h) V. R. Stimson and J. W. Tilley, Austral. J. Chem., 1977,

+ + +

30, 81 ; ( i ) H. Kwart and J. J. Stanulonis, J. Amer. Chem. Soc., 1976,98, 5249; 0') L. Batt and R. T. Milne, Znternut. J. Chem. Kinetics, 1977, 9, 549; ( k ) R. J. Crawford, S. Lutener, and H. Tokunaga, Canad.J. Chem., 1977,55,3951; ( I ) A. Cuenca and 0.Chuchani, Internat. J. Chem. Kinetics, 1977,9,379; (m) S . de B. Norfolk and R. Taylor, J.C.S. Perkin ZZ, 1976,280; (n) L. Batt and R. T. Milne, Internut. J. Chem. Kinetics, 1976, 8, 59; ( 0 ) P. G. Blake, A. Craggs, and M. B. Vayjooee, J.C.S. Perkin IZ, 1976,986; (p) D. B. Bigley and R. H. Weatherhead, J.C.S. Perkin ZZ, 1976,592; (4)D. B. Bigley and R. H. Weatherhead, J.C.S. Perkin ZI, 1976, 704.

Bond-fission Reactions (Tables 7 and l).-The implication from radical recombination studies (see Section 7)that transition state theory offers a poor description of these processes is that at sufficiently high temperatures slight curvatures should.be observed in Arrhenius plots (not arising from fall-off effects). There is as yet no evidence for this in direct dissociation studies. Much of the impetus behind measurements in this area is the determination of bond strengths and radical heats of formation. There are several suggestions from these data 177 and others 1789 17' that the derived alkyl radical heats of formation (particularly t-butyl) are slightly too low and that upward revision of C-H bond strengths in simple alkanes (by 1-2 kcal mol-') may be appropriate. If so this is important since many thermochemical arguments are based on these data. Further evidence on this point would be welcome. The data on nitrite bond-fissions are worth singling out as they form part of more comprehensivekinetic and mechanisticreinvestigationsby Batt and co-workers,l 82 in which a number of other rate constants, previously in error have been corrected.

179

R. M. Marshall, J. H. Purnell, and P. D. Storey, J.C.S. Faraday Z, 1976,72,85. D. A. Parkes and C. P. Quinn, J.C.S. Faraday I, 1976,72, 1952. K.Y. Choo, P. C. Beadle, L. W. Piszkiewicz, and D. M. Golden, Internat. J. Chem. Kinetics, 1976, 8,45.

I8O 181 la2

L. Batt and R. T. Milne, Znternut. J. Chem. Kiktics, 1976, 8,59; ibid., 9, 141, 549.

L. Batt, R. T. Milne, and R. D. McCullough, Znternut. J. Chem. Kinetics, 1977,9, 567. L. Batt and R. D. McCullough, Znternut. J. Chem. Kinetics, 1976,8,911.

Unimolecular Reactions

33

Table 7 Recent high pressure Arrhenius parameters for bond-fission reactions Product(s)

Reactant Carbon-Carbon bonds

neo-GH12

But

log(A,/s-')

+ Me

16.1 16.52 iso-GHs Me C3H5 18.26 ------...-_-______I--* MeCH2CMe=CH2 Me CH2CMeCH2 16.6 R'R2R3CCR'R2R3 2R'R2R3C R' = R2 = R3 = Et 16.6 R1 = R2 = Me; R3 = Et 16.4 R' = R2 = Me; R3 = cyclo-C6Hi1 19.4 R' = Me; R2 = Et; R3 = CYC~O-C~HII 17.4 MezCHCMe20H Pr' CMe20H 16.24 Me3CCHMeOH Bu' CHMeOH 16.33 CFjCHO CF3 CHO 16.63 Other C-X bonds MeOMe Me OMe 15.33 CsHsI CsHs + I 15.0 EtzZn EtZn(?) Et 14.3 Et4Sn Et3Sn(?) Et 16.0

+ +

+ + + +

+

+

0-0 and 0-N b o d MeOOMe Bu'OOBu' (CF3)3COOC(CF3), RO NO R = Me Et Pr' Bu' But Miscellaneous R1-N=N-R2 R' R' = R2 = Et R' = Et; RZ = Pr' R' = R2 = Bu'

+ N2 + R2

E,/H mol-I

Ref.

3 30 336 375 297

a b c d

218 268 261 21 3 31 1 312 335

e e e e

320 270 205 248

f

f g

h i

i

k 1

15.5 15.33 16.2

155 152 149

15.8 16.0 16.2 16.2 16.3

172 175 172 171 169

14.2 16.5

186 206 170 175

U

120-1 31

v

{ Z 4

RCH2CMe2CO20Bu' RCH2CMe2+ COz + Bu'O R = various 14.1-1 5.5

m n 0

P 4

r S

t t t

(a) R. M. Marshall, J. H. Purnell, and P. D. Storey, J.C.S. F'ruhy I, 1976,72,85 ; (6) J. N. Bradley and K. 0.West, J.C.S. Faruduy I, 1976,72,8; (c) J. N. Bradley and K. 0.West, J.C.S. Faruhy I, 1976, 72, 558; ( d ) A. B. Trenwith and S. P. Wrigley, J.C.S. Furu&y I, 1977, 73, 817; (e) In solution; H.-D. Beckhaus and C. Ruchardt, Chem. Ber., 1977, 110, 878; (f) W. Tsang, Internut. J. Chem. Kinetics, 1976, 8, 173; (g) M.T. H. Lui, L. F. bucks, and D. G. Hooper, Internut. J. Chem. Kinetics, 1977, 9, 589; (h) D. Aronowitz and D. Naegeli, Internat. J. Chem. Kinetics, 1977, 9, 471 ; ( i ) R. J. Kominar, M. J. Krech, and S. J. W. Price, Cunud. J. Chem., 1976, 54, 2981 ; ( j ) A. A. Koski, S. J. W. Price, and B. C. Trudwell, Cunud. J. Chem., 1976,54,482; ( k ) M. Daly and S. J. W. .Price, Cunud. J. Chem., 1976, 54, 1814; ( I ) L. Batt and R. D. McCullough, Internut. J. Chem. Kinetics, 1976, 8,491; (m) D. K. Lewis, Cunad. J. Chem., 1976, 54, 581; (n) R. Ireton, A. S. Gordon, and D. C. Tardy, Internut. J. Chem. Kinetics, 1977,9,769; ( 0 ) L.Batt, R. T. Milne, R. D. McCullough, Internut. J. Chem. Kinetics, 1977,9, 567; ( p ) L.Batt and R. T. Milne, Internat. J. Chem. Kinetics, 1977, 9, 549; (q) L. Batt and R. T. Milne, Internut. J. Chem. Kinetics, 1977, 9, 141 ; (r) L. Batt and R. D. McCullough, Internut. J, Chem. Kinetics, 1976, 8, 911 ; (s) L. Batt and R. T . Milne, Internut. J. Chem. Kinetics, 1976, 8, 59; (t) G. Martin and A. Maccoll, J.C.S. Perkin II, 1977, 1887; (u) 0. McKay, J. M. C. Turner, and F. a r b , J.C.S. Furuday I , 1977, 73,803; ( v ) D. D. Tanner, H. Yabuuchi, and H. Lutzer, Cunud. J. Chem., 1977,55,612.

Gas Kinetics and Energy Transfer

34

Miscellaneous reactions.-Methyl isocyanide, as a result of the work of Rabinovitch, may be regarded as a well studied molecule. Nevertheless Collister and Pritchard lE3 have reinvestigated its high pressure isomerization mainly with a view to testing for an earlier suggested radical pathway. None was found and the high pressure Arrhenius equation obtained for the isomerization was in good agreement with the original one. This reaction can thus be safely re-categorized as well understood. There has been very little activity in the field of radical unimolecular reactions. An isotopic labelling experiment suggestsa 1,2-H shift process in ethyl radical competitive with its decomp~sition.'~~ A rate constant of log(k/s-') = 12.8 - 170kJmol-'/ RTlnlO was obtained for this process. There are continuing reports of methyl formation from isopropyl radical,18sa process also requiring a prior 1,2-H shift. Nevertheless the proposed rate constant is in conflict with other evidence for this process.'86 Alkoxy radicals can apparently undergo ready internal 13-H shifts giving Chydroxyalkyl radicals, a process previously observed for alkyl and peroxy radical^.'^' 7 Radical Recombination and Addition Reactions Since such reactions are the reverse of unimolecular decomposition processes and are, therefore, amenable to unimolecular reaction theory, it is natural to include them in this Report. Recent data both in the high-pressure (second-order) limit and in the low pressure (third-order) region are included in Table 8. The much studied methyl recombination (ethane dissociation) reaction appears now to be reasonably well understood certainly as far as the high pressure limiting rate constant and its temperature dependence are concerned.'" It is, however, worth emphasizing here that transition state theory with its built-in concept of a specifically located activated complex has proved inadequate to fit the data. This is because the true bottleneck of the ethane dissociation (and indeed other dissociations) is a function of the vibration-rotational energy of the molecule whether defined in terms of a minimum density of states '13' or maximum

Table 8 Recombination and related reactions Reaction

2C&

C4HlO

T/K

300 860

2Pr'

+ MezCHCHMel

300

2Bu'

-+

Me3CCMe3

300-473

700 28-methallyl --t C8Hl4 CH3 H +CHI

+

CzHs

+ H + 2CH3

295

321-521 308 321-521

k,,,

+ comments'

8.4 x 109(k,) 4.5 x 109(
2.4 x 109(T/300K)-l*s(k,) 6.3 x 108(k,) 2.6 x 10io(k,) pressure and temperature dependent 2.3 x 101l(k,) 2.0 X 10'3(ko,C&6) 4.7 x lO'O(k,)

Ref. b C

b b d e

f g

f

J. L. Collister and H. 0. Pritchard, C a d . J. Chem., 1976,54,2380. A. S.Gordon, D. C. Tardy, and R. Ireton, J. Phys. Chem., 1976,80, 1400. L. Szirovicza and F. Marta,Internat. J. Chem. Kinetics, 1976,8,897. lB6 W. M. Jackson and J. R. McNesby, J. Chem. Phys., 1962,36,2272. Is' W. P. L. Carter, K. R. Darnall, A. C. Lloyd, A. M. Winer, and J. N. Pitts, jun., Chem. Phys. Letters, 1976,42,22. 188 Ref. 3, p. 229. D.Bunker and M. Pattengill, J. Chem. Phys., 1968,48,772.

ln3

lS4 Ins

Unimolecular Reactions

35

Table "continued CH3

Reaction 0 2 + CHjOz

+

TIK 300

259-399 296 CHI

+ NO + CHJNO

298

+ NO + EtNO + NO NOCl

325-521 295 295-521 300

O+NO-+N02 OHfNO-tHONO

217-50 295

Et Cl

OH

C10

--+

+ CO + H + COz

+ NO2

+

ClNOj

2NH2 + N2H4( ?) OH

+ C2H4

--+

HOCHzCHz

296 299 213-300 220-358 220-550 296 296 250-356 300 29-25 296

+

k,,, comments" 7.2 x 1O8(k,) 1.1 x 10"(ko,Nz) 5.4 x 1011(ko,neO-C5H12) pressure and temperature 6.4 x 10'O(ko,N2) 3.4 x 10'O(ko,He) pressure dependent 7.2 x 109(k,, by extrapolation)} pressure dependent 2.2 x 1O"(k0,He by extrapolation) 1.4 x 108(k,) pressure dependent 1.8 x 10IO(k,) 2.1 x 10'O(ko,He) pressure dependent pressure dependent 1.1 x 10IO(k, by extrapolation) weakly pressure dependent pressure independent (k = 9.3 x lo') 3.6 x 1011(ko,He,300K) 1.5 X 10'2(ko,C02,300 K)} pressure dependent pressure and temperature 9.8 x 109(k, by extrapolation) 9.4 x 101'(k,,N2, by extrapolation) 3.0 x 10'0(ko,He,300K) 5.5 X 101'(ko,N2,297 K)} 1.5 x lO'O(k,) 2.5 x 10L'(k0,N2)} pressure dependent pressure dependent 6.0 x 109(k,) pressure dependent

Ref. h i

i k

k I m n 0,P B

r S

t U

V W X

Y

Units of k,,,; k,/dm3mol-' s-' or ko/dm6 mol-2 s-'; third body given where appropriate; (b) D. A. Parkes and C. P. Quinn, J.C.S. Furaday Z, 1976,72,1952; (c) D. M. Golden, K. Y.Choo, M. J. Perona, and L. Piszkiewicz, Internut. J. Chem. Kinetics, 1976, 8, 381; (d) K. Y . Choo, P. C. Beadle, L. Piszkiewicz, and D. M. Golden, Internat. J. Chem. Kinetics, 1976, 8, 45; ( e ) F. Rayrakqken, Chem. Phys. Letters, 1976, 43, 183; (f) G. Pratt and I. Veltman, J.C.S. Faruaky Z, 1976,72,1733; (g) J.-T. Cheng and C.-T. Yeh, J. Phys. Chem., 1977,81,1982; (h) D. A. Parkes, Internut. J. Chem. Kinetics, 1977, 9, 451; ( i ) N. Washida and K. D. Bayes, Internat. J. Chem. Kinetics, 1976, 8, 777; (j)M. J. Pilling, J. A. Robertson, and G. J. Rogers, Internut. J. Chem. Kinetics, 1976,8,883; (k) G. Pratt and I. Veltman,J.C.S. Fmaday I, 1976,72,2477; (2) H. Hippler and J. Troe, Internut. J. Chem. Kinetics, 1976, 8, 501; (m) J. V. Michael, W. A. Payne, and D. A. Whytock, J. Chem. Phys., 1976,65,4830; (n) R. Overend, 0. Paraskevopoulos, and C . Black, J. Chem. Phys., 1976, 64, 4149; (0) R. Overend and G. Paraskevopoulos, Chem. Phys. Letters, 1977,49,109; ( p ) W . H. Chan, W. M. Uselman, J. 0.a v e r t , and J. H. Shaw, Chem.Phys. Letters, 1977, 45,240; (4)R. Atkinson, R. A. Perry, and J. N. Pitts, jun., Chem. Phys. Letters, 1976, 44, 204; (r) K. Erler, D. Field, R. Zellner, and 1. W. M. Smith, Ber. Bunsengeseiischaft Phys. Chem., 1977, 81, 22; (s) C. Anastasi, P. P. Bemand, and I. W. M. Smith, Chem. Phys. Letters, 1976, 37, 370; ( t ) C. Anastasi and I. W. M. Smith, J.C.S. Faraday IZ, 1976,72, 1459; (u) M. S. Zahniser, J. S.Chang, and F. Kaufman, J. Chem. Phys., 1977, 67, 997; (v) P. V. Khe, J. C. Soulignac, and R. Lesclaux, J. Phys. Chem., 1977, 81, 210; (w) R. Overend and G. Paraskevopoulos, J. Chem. Phys., 1977,67,674; (x) R. Atkinson, R. A. Perry, and J. N. Pitts, jun., J. Chem. Phys., 1977,66, 1197; ( y ) D. G. Keil, K.P. Lynch, J. A. Cowfer, and J. V. Michael, Internut. J. Chem. Kinetics, (a)

1976, 8,825.

36

Gas Kinetics and Energy Transfer

free energy criterion.lgO The bottleneck tends to occur at shorter C-C distances at higher energies. Using transition state theory language, although obviously in an unsatisfactory way, the activated complex gets tighter at higher energies. The practical effect of this is to produce a different temperature dependence for methyl recombination compared with the simple transition state theory. Hase l g l has reproduced the experimental data by the device of selecting an actual complex structure representing a Boltzmann average of minimum state density configurations. Quack and Troe have applied their more rigorous adiabatic channel theory l g 2 to fit the known results. Adiabatic channel theory is, however, difficult and complicated to apply and so Quack and Troe have presented a simplified maximum free energy adaptation of it.' 93 Mainly with a view to accounting for recombination rates of larger alkyl radicals, Benson and Golden l g 4 have used a restricted Gorin model (but within the confines of transition state theory) in which rotational freedom of recombining radicals is limited by an excluded volume. This will produce a temperature dependence of recombination which is different from that of an unrestricted Gorin model but suffers from the disadvantage that there is no reliable apriori way of knowing how to choose the 'excluded volume'. Whatever the best method it is clear that simple transition state theory (as implied in any fixed complex RRKM calculation) is no longer adequate to model bond fission or radical recombination processes. Using the molecular modulation technique, Parkes and Quinn 78 have obtained new data on the recombination of ethyl, isopropyl and t-butyl radicals. The value for the t-butyl radical at room temperature is consistent with the 'high' value suggested by liquid phase studies using electron spin resonance,195and not the very low value obtained by the radical buffer technique.lg6 Also, the observation of a relatively large negative temperature coefficient rationalizes the smaller value of the rate constant for recombination obtained from high temperature VLPP studie~.''~What is now clear is that the t-butyl radical recombination is in no way anomalous but that earlier values of either or both its entropy and enthalpy of formation are appreciably in error.' 77-1 7 9 Pratt and Veltman l g 7 have measured the rate of addition of methyl and ethyl radicals to nitric oxide in the presence of helium. RRKM calculated fall-off curves suggest that the addition of ethyl radicals is substantially slower than methyl radicals at the high pressure limit. Studies of NH2 recombination l g 8 are not in good agreement with the RRKM calculations of Tsang lg9 based on the decomposition of H2NNH2. More recent calculations give a good agreement with the shape of the fall-off curve but the absolute value is wrong by an order of magnitude. It is possible that N2H4decomposition yields NH3 and NH rather than 2NH2. Smith2'' has pointed out that in order to observe pressure dependence in the 190

Igl lg2

Ig3 194

lgS 196 19' 198

Ig9

W. A. Wong and R. A. Marcus, J. Chem. Phys., 1971,55,5625. W. L. Hase, J. Chem. Phys., 1976, 64,2442. M. Quack and J. Troe, Ber. Bmengesellschajl Phys. Chem., 1974,78,240. M. Quack and J. Troe, Ber. Bunsengesellschaft Phys. Chem., 1977, 81, 329. D. M. Golden and S. W. Benson in 'Physical Chemistry. An Advanced Treatise', Vol. VII, ed. H. Eyring, Academic Press, New York, 1978 chapter 2, p. 57. D. Griller and K. U. Ingold, Internat. J. Chem. Kinetics, 1974, 6,453. R. Hiatt and S. W. Benson, Internat. J. Chem. Kinetics, 1973, 5, 385. G. Pratt and I. Veltman, J.C.S. Faraday Z, 1976, 72,2477. P. V. Khe, J. C. Soulignac, and R. Lesclaux, J. Phys. Chem., 1977, 81, 210. W. Tsang, N.B.S. Report 10904, 1972, 171. I. W. M. Smith, Chem. Phys. Letters, 1977,49, 112.

Unimolecular Reactions

37

OH + CO 4 H + CO, reaction, the COOH radical intermediate must decompose with nearly equal facility to either H + CO, or OH + CO. It seems likely that the OH + CO reaction is weakly pressure dependent despite one report to the contrary (see Table 8). Thus decomposition studies on the COOH radical would clearly be useful. The reaction OH + NO, + M -+ HNO, + M is of importance in atmospheric modelling, as is the analogous reaction C10 + NO, + M + ClNO, + M. Two theoretical calculations ,01*,02 of the pressure dependence have been carried out recently on these systems. RRKM theory has also been applied to the pressure dependent acid-base reaction between BF, and amines.,03 8 Mechanism It is always difficult in a review of this kind to draw a hard line between kinetics and mechanism and since mechanism determination has been the motivation of many unimolecular reaction studies, some discussion seems appropriate. It is now about a decade since Benson’s ‘Thermochemical Kinetics’ was published.204 This book brought together many of the ideas that had guided gas kineticists up to that time, and has had, and continues to exercise, great influence. At the time R. M. Noyes 2 0 5 wrote: ‘Dr. Benson has attempted to show how to estimate the rate for any hypothetical reaction involving reasonably conventional compounds. . . . Probably today nobody could do better.’ In view of the breadth of the task it is perhaps not surprising that some of the simpleideas contained in the book have since come under considerable fire. The famous ‘biradical meachnism’ for cyclopropane isomerization has been the subject of a sharp critique by Berson.” Berson’s thesis is that the biradical mechanism contains a number of ad hoc postulates and cannot predict the stereochemical outcome of cyclopropane isomerization. Additionally quantum mechanical calculations of a very detailed kind 206 have failed to find the necessary minimum in the potential surfacefor cyclopropane stereoisomerizationwhich would correspond to the biradical. The most compelling stereochemical evidence on cyclopropane transformations comes from subtle labelling experiments by Berson ,07 himself. In these he has shown by means of a study of optically active trans-l,2-[2H2]cyclopropane that the stereomutation process requires synchronous rotation of two carbon centres (in either con- or dis-rotatory fashion). The results cannot be accommodated by a stereorandomized (biradical) intermediate from which products arising via both formally single and double rotation of carbon centres, would be anticipated. Similar results were obtained with optically active trans-l-phenyl-2-[2H]cyclopropane,207 but here the picture becomes clouded because an earlier experiment by Wilcott and Cargle 208 with anti- l-~inyl-2,3-cis[~H,]cyclopropane indicated a stereorandom intermediate and does not support synchronousdouble rotation. Thus if we accept the data, phenyl and vinyl substituents produce opposite extremes of coupling of the two rotating carbon centres, a result which appears to us somewhat surprising. Other studies of substituted *01

202

203 204 205 206

R. Zellner, 2.Nutwforsch., 1977, 32a, 648. D. M. Golden and G. P. Smith, Internat. J. Chem. Kinetics, in the press. D. R. Chen, Internat. J. Chem. Kinetics, 1976,8, 795. S. W. Benson, ‘Thermochemical Kinetics,’ Wiley, New York, 1968. R. M. Noyes, J. Amer. Chem. SOC.,1969,91, 3110. J. A. Horsley, Y. Jean, C. Moser, L. Salem, R. M. Stevens and J. S. Wright, J. Amer. Chem. SOC., 1972,94,279.

207 208

J. A. Berson, L. D. Pederson, and B. K. Carpenter, J. Amer. Chem. SOC.,1976,98, 122. M. R. Willcott and V. H. Cargle, J. Amer. Chem. Soc., 1969, 91,4310.

38

Gas Kinetics and Energy Transfer

optically active or otherwise labelled cyclopropanes 209-2 l4 produce a mixture of geometric isomerization and racemization and require neither complete coupling of rotating carbons, nor completely random single carbon rotations, but are consistent with a view of uncoupled rotations in which the more massively substituted centre rotates more slowly.215 Thus apart from cyclopropane itself and possibly phenylcyclopropane, the results do not rule out intermediates with some semblance of biradical character. Put in another way the correlation of motion of the rotating carbon centres attenuates rapidly with substitution. While observations of stereoisomerizationwere undoubtedly one of the experimental foundations of the biradical mechanism, equally the magnitudes of substituent effects on rate constants were also important 204 (the constancy of energy of activation reduction, and of structural modification of A factors). What is significant here are the large effects such as are induced by vinyl substitution, leading to allylic stabilization of radical centres (by -50 kJ mol-’) and structural stiffness of transition states (lowering of A factors by an order of magnitude) and not the smaN and, in some cases marginal, effects of methyl substitution. These effects cannot be denied and it would seem to us very unlikely that they should be identical for a concerted (or coupled motion) process. It is however true, as Berson emphasizes, that precise agreement between observed activation energies and ‘biradical mechanism’ estimates rests on the introduction of an arbitrary ring-closure activation energy (of 39 kJ mol -’) which is set for cyclopropane itself but not subsequently modified for substituted cases. Although on occasion this ring-closure barrier has been taken literally, in one sense it is only an empirical device and, therefore, if precise quantum mechanical calculations show that no such barrier exists then the recipe for calculating the activation energy for biradical formation can be modified, and can attribute this 39 kJ mol-’ to electronic interaction not otherwise allowed for in the estimation of the energy of the biradical. One now has the biradical at the top of the energy barrier-the ‘continuous biradical’ concept of Doering.211 In extending the ‘biradical idea’ from 1,3-biradicals(the cyclopropaneintermediates) to 1,4 and larger species, it is clear that the ‘electronic interaction’ energy which is required to correct the simple additivity estimate of the biradical heat of formation, must decrease as the electron separation increases. This is, of course, just what is observed and was rationalized by Benson 204 as a ring closure activation energy diminishing with ring strain. Returning to Berson’s double rotation process, another seeming problem is the s -’). The transition magnitude of the A factor for stereoisomerization216 (ca. state is essentially loose and this does not suggest any sharply channelled concerted process (with a furrow in the potential surface) such as might be implied by a ncyclopropane intermediate 217* 218 (where a lower A factor s -1 might have

-

N

-

209 210 211 212

213

214 215

*I6 217

z18

R. J. Crawford and T. R. Lynch, Canad. J. Chem., 1968,46,1457. R. G. Bergmann and W. Carter, J. Amer. Chem. SOC.,1969,91,7411. W. von E. Doering and K. Sachdev, J. Amer. Chem. SOC.,1974,96, 1168. A. Chmurny and D. J, Cram, J. Amer. Chem. SOC.,1973,95,4237. J. A. Berson and J. A. Balquist, J. Amer. Chem. SOC.,1968,90,7343. W. Kirmse and M. Zeppenfeld, J.C.S. Chem. Comm., 1977, 124. H. E. O’Neil and S. W. Benson, J. Phys. Chem., 1968, 72,1866. E. W. Schlag and B. S. Rabinovitch, J. Amer. Chem. SOC.,1960, 82,5996. R. J. Crawford and A. Mishra, J. Amer. Chem. SOC.,1966,88,3963. R. Hoffmann, J, Amer. Chem. SOC.,1968,90, 1475.

Unimolecular Reactions

39

been anticipated). Rather an accidental coupling of phases of rotation, associated with the dynamics of the process, seems to us more in keeping with the looseness of 220 structure. Such an explanation has been offered by Chapuisat and In summary, then, the concept of a biradical intermediate still has some value (even for cyclopropane isomerization) but as an addition to the original concept it appears that the dynamics of its formation may give rise to coupled motion of its parts. It might reasonably be termed 'a biradical with a memory'. Furthermore, the prescription for the biradical's energy estimation must be differently regarded (even though the value obtained for the reaction activation energy involving it is the same). It might be objected that such a diluted form of the original biradical hypothesis is of no use and it should be abandoned. For the small energetic effects which determine stereochemistry this criticism has some validity, however for the assessment of larger rate effects and for the prediction of rate processes within an order of magnitude the biradical hypothesis remains very useful. It can certainly still be used to validate the existence of a concerted pathway where the observed rate of reaction is significantlygreater than the biradical estimate. For the case of cyclobutane and its intermediate there is less controversy." However, in one case,22l that of the optically active trans-l,2-dipropenylcyclobutane, Berson et al.have again found evidence militating against a stereorandom intermediate in the ring expansion process to 3-methyl-4-propenylcyclohexene,a formal [1,3]sigmatropic carbon shift. The product stereochemistry is consistent only with a suprafacial migration across the allylic carbon frame although with nearly equal propensity for inversion and retention at the migrating carbon. The energy of activation for this process is again consistent with the biradical hypothesis and so this result again calls for a qualification to the freedom of biradical motion. Maybe once again dynamic constraints may render this another case of a biradical memory effect, although an electronic explanation, viz. the operation of subjacent orbital control, has been proposed.222 The transition state is not so loose here if the isomerization of vinylcyclobutane to cyclohexene 223 may be taken as the guide (A = s -') and so the electronic effect cannot be ruled out. This system is interesting because the intermediate is the octa-1,7-dien-3,6-diyl biradical (dimethyl substituted version) which is also implicated in the rearrangements 225 vinylcy~lohexene,~~~* 225 and the Diels-Alder reaction of cyclo-octa-1,5-diene,224* of butadiene.22'*226-228 Much work has been done on these systems recently, but there remain, as might be expected, substantial arguments between biradical intermediates and concerted processes. These arguments are too involved to go into here. Another system where a dynamic explanation of stereochemical change is called for is that of the decomposition of 3-ethyl-5-methyl- 1-pyrazolinegiving l-ethyl-2-methyl219

220 221

222 223 224

Y.Jean and X. Chapuisat, J. Amer. Chem. SOC.,1974,%,

6911.

X. Chapuisat, Ber. Bunsengesellschaft Phys. Chem., 1977, 81,203. J. A. Berson, P. B. Dervan, R. Malherbe, and J. A. Jenkins, J. Amer. Chem. SOC.,1976,98,5937. J. A. Berson and L. Salem, J. Amer. Chem. SOC.,1972,94,8917. H. M. Frey and R. Pottinger, J.C.S. Faraday I, 1978, 74, 1827. W. von E. Doering, M. Frank-Neumann, D. Hasselmann, and R. L. Kaye, J. Amer. Chem. Soc., 1972,943833.

225

226

W. von E. Doering and D. M. Brenner, Tetrahedron Letters, 1976, 899. G. Huybrechts, L. Luyckx, Th. Vandenboom, and B. Van Mele, Znternat. J. Chem. Kinetics, 1977,9, 283.

227 228

L. M. Stephenson, R. V. Gemmer, and S. Current, J. Amer. Chem. SOC.,1975,97, 5909. J. A. Berson and R. Malherbe, J. Amer. Chem. SOC.,1975, 97, 5910.

Gus Kinetics and Energy Transfer

40

cyclopropane studied by Bergman.229 The pattern of stereochemistry of products from optically active reactants is again such as to rule out any long lived stereorandomized intermediate. Many other interesting and subtle labelling experiments are currently being carried out on systems which were once the mechanistic preserve of the gas kineticist. What seems to be emerging in a number of cases is a requirement for the application of molecular dynamics to account for the precise details of reaction pathways. We have selected only a minute fraction of studies for discussion from the large number reported. They have been chosen because they illustrate a major area of interest of many physical-organic chemists and have involved an unusual (and difficult) combination of experimental skills coupled with most careful analytical discussions of the resultant findings. We add one note of caution. Most reactions of polyatomic molecules take place on a potential energy hypersurface of enormous complexity, the more so when several (distinguishable) pathways have similar rate constants in the temperature region of interest. Mechanistic investigations seek to define the detailed nature of what may only be a very thin ‘section’ in two or three dimensions through the hypersurface. However valid this may be for the particular compound studied there can be no certainty that it will be transferable to another closely related molecule. It is not unlikely that the more subtle the experiment and the more closely defined the ‘section’ the more easily will a substituent, apparently well removed from the reaction centre, move the transition state out of the defined region of the hypersurface. Thus here, as in so many other areas of chemistry, if we strive too hard for precision we may have to sacrifice simplicity, generality, and transferability. If we prefer these latter three then we may have to forgo the quest for precision. 9 Computational Chemistry (Potential Energy Surfaces) In some respects this area represents one of the fastest growing ‘experimental’areas in kinetics. The shift from attempts to calculate equilibrium properties of molecules to determining activated complex geometries, energies, and details of reactive potential energy surfaces for complex systems has been very noticeable in the past two years. Unfortunately it appears to be at least an order of magnitude more difficult to obtain a quantitative estimate of the likely errors in a calculation than in doing the calculation itself. Further, there is no guarantee at all that the quantity of experimental interest, which is usually obtained indirectly as a difference between the calculated values, will be obtained with greater accuracy as the sophistication of the calculation increases. A nice demonstration of this occurs in the attempts to calculate the kinetic and thermodynamic stability of the oxirene molecule, a probable intermediate in the Wolff rearrangement of HCOCH to keten, where successive calculations over the years have produced no real convergence in the value of experimental interest.230 In the past few years extended Huckel calculations have by and large given way to CNDO followed by MINDOIn (n = 1-3) and there has also been a very significant growth in the use of various ab initio methods. While in some cases the calculated results have been a spur to more experimental work and this has often led to real advances in understanding, few reliable predictions seem to have been made. 229

230

T. C. Clarke, L. A. Wendling, and R. G. Bergmann, J. Amer. Chem. SOC.,1977,99,2740. 0. P. Strausz, R. K. Gosavi, A. S. Denes, and 1. G. Csizmadia, J. Amer. Chem. SOC.,1976, 98,4784.

Unimolecular Reactions

41

The Diels-Alder reaction (and its reverse, the unimolecular decomposition of for example cyclohexene) has been of considerable experimental and theoretical interest for several decades. In 1968 Salem 231 studied the addition of ethylene to butadiene (the simplest and most symmetric case) using a perturbational version of the extended Huckel method. This would now be considered a very crude treatment with only z-electrons considered and two geometrical lengths varied. He concluded that the reaction was concerted with a symmetrical transition state. In 1971 Kikuchi carried out a CNDO/2 calculation of the symmetrical reaction path and even though 11 degrees of freedom were optimized no activation barrier was revealed. In 1972 a MINDO/2 calculation predicted a non-symmetrical transition state 233 as did a MIND0/3 calculation 234 in 1974. In this latter calculation all 42 internal geometric co-ordinates were optimized and the calculated energy of activation agreed well with the experimentally determined value. However, an ST0/3G calculation 235 with limited CI in 1975 suggested a nearly symmetrical transition state and a similar but even more extensive calculation 236 in which more internal co-ordinates were varied gave a similar result. Finally, Basilevsky et aL2” have discussed why MIND0 type calculations yield a non-symmetrical transition state for the reaction and would always favour a non-symmetrical reaction pathway. [Nevertheless a recent Dewar MIND0/3 calculation on the unimolecular decomposition of but-3-enoic acid 238 does yield a symmetrical six-membered ring transition state in agreement with earlier mechanistic (experimental) studies.] We have chosen to discuss in some detail this one particular type to illustrate that while it is apparently possible to produce aposi-hoc rationalization of the structure of a TS (and hence a description of a reaction pathway) we are still a long way from being able to rely on computational predictions. It is extremely doubtful if a calculated energy of activation for any unimolecular decomposition can replace an experimental determination except in just those cases where one might expect an informed ‘estimate’ based on analogous reactions or the thermochemical kinetic arguments developed by Benson 204 to be reliable. For these reasons we do not report on the large number of papers published in the field we designate computational chemistry. We do, however, not wish to record a completely pessimistic note and indeed believe that some of the elaborate calculations being performed at present do suggest that we may be approaching a time when choice between reaction mechanisms will be helped by such work. In the end one must aim by these procedures at obtaining information that is either very difficult (or expensive) to obtain by conventional experiments.

”’

231 232

233 234

235

236

237

L. Salem, J. Amer. Chem. SOC.,1968,90,553. 0. Kikuchi, Tetrahedron, 1971,27,2791. J. W. Mclver jun., J. Amer. Chem. SOC.,1972,94,4782. M. J. S. Dewar, A. C. Griffin,and S. Kirschner, J. Amer. Chem. SOC.,1974,96,6225. L. A. Burke, G. Leroy, and M. Sana, Theor. Chim. Actu, 1975,40,313. R. E. Townshend, G. Ramunni, G. Segal, W. J. Hehre, and L. Salem, J. Amer. Chem. SOC., 1976,98,2190. M. V. Basilevsky, A. G. Shamov, and V. A. Tikhomirov, J. Amer. Chem. SOC.,1977,99, 1369. M. J. S. Dewar and G. P. Ford, J. Amer. Chem. SOC.,1977,99,8343.

2 Chemiluminescence in the Gas Phase BY 1. M. CAMPBELL AND D. L. BAULCH

1 Introduction Prior to this Report reviews by Carrington and Polanyi,’ Golde and Thrush,2 and Smith have appeared. Accordingly publications from 1975 to mid-1977 are covered in this review. In electronic chemiluminescence, metal atom reactions have come to the fore, with less interest in the more traditional areas such as afterglows, which largely reflects the search for visible chemical laser reactions. Interest continues in i.r. chemiluminescence from highly exothermic atom/molecule reactions, partly due to their importance in laser technology, but with increasing attention paid to larger organic molecules. An important development has been the application of i.r. chemiluminescence techniques to some endoergic reactions. 2 Electronic Chemiluminescence A visible chemical laser reaction can be defined as a system where an electronic state population inversion is produced by simple mixing without use of electrical discharge or optical pumping. Accordingly many studies have been concerned with photon yields produced in reaction systems of substantial complexity, with less interest in the underlying mechanism. However, there has been interest in molecular dynamics and, at the same time, new spectra and emitting states have been discovered in several reaction systems being investigated for the first time. Towards a Visible Chemical Laser System.-An extensive review of the theory and practical aspects of the chemical laser has been given by Zwillenberg, Naegeli, and Gla~sman.~ A sufficient density of inverted population (i.e. the excited-statepopulation larger than the lower-state population) must be generated in the optical cavity if stimulated emission is to result in amplification. Transition probabilities for stimulated emission are lo3 to lo4 times larger for most electronic transitions than for vibrational transitions, so that the minimum inversion density is lower for the former. Spontaneous radiative lifetimes are, however, generally in the reverse order, so that radiative leakage is more significant for most electronic inversions. At the same time collisional deactivation must be comparatively slow. The formation of electronically excited states is less common than vibrational excitation, and moreover, a preferential population of only a few vibrational levels of one particular state is required since T. Carrington and J. C. Polanyi in ‘MTPInternational Review of Science, Physical Chemistry Series I,, ed. J. C. Polanyi, Butterworths, London, 1972, vol. 9, p. 135. M. F. Golde and B. A. Thrush in ‘Advances in Atomic and Molecular Physics’, Academic Press, London, 1975, vol. 11, p. 361. I. W . M. Smith, Advances in Chemical Physics, 1975, 21, 1. M. L. Zwillenberg, D. W. Naegeli, and I. Glassman, Combustion Sci. and Tech., 1974, 8, 237.

42

Chemiluminescence in the Gas Phase

43

laser action can usually only be based upon a transition from one particular (w’,J’) level. Vibrational relaxation is a relatively slow process; molecules formed in just a few v’ levels will be preserved but molecules from other v’ will not be able to replenish that which is lasing. Rotational equilibration is generally fast enough to replenish the lasing J’ levels and also to preserve the inversion by rapidly depleting the excess population of J”. Circumstances which will favour a visible chemical laser reaction are summarized as follows. (i) Reactants with weak bonds such as 03,N,O, and halogens will be most likely to match with the exothermicities in excess of 170 kJ mol-l required of the elementary reaction to ground state products. Energy pooling in more complex reactions may overcome this restriction. (ii) The radiative lifetime of the excited state should exceed lO-’s to minimize spontaneous radiative leakage. (iii) The reaction should preferentially populate the excited state(s) at the expense of the ground state if the latter is (as usual) the lower state of the laser transition. Also the excited state potential energy curve should be displaced with respect to the ground state curve, generating larger transition probabilities to V” > 0, usually less populated than v” = 0. (iv) The effective channelling of chemical energy into a radiative channel which can be tuned to an optical cavity will be favoured by production of excited atoms rather than molecules. (v) Rare gases, He and Ar, will generally be the best carriers since they usually quench excited states least rapidly. Before considering what has been achieved in reaction systems, some of the newer experimental systems of interest are described. The flame-viewing apparatus shown in Figure 1 has been developed at the University of California and shown to be applicable to a wide variety of reaction systems. The vapourized metal is evaporated from the ceramic crucible and entrained in the inert gas flowing around it. The reactant gas is mixed a short distance above the orifice and, with excess oxidizer present the resultant flame is compact. The advantages of this method are the formation of high densities of product molecules in the viewed region with little thermal excitation. Usage has been restricted to binary systems. A system which is amenable to ternary systems has been developed at the Stanford Research InstituteY6-*with the typical design shown in Figure 2. This consists of stainless steel tubing (4 inch diameter) with a wick of five layers of stainless steel screen (60 mesh) saturated with alkali metal; in operation this evaporates along the wick, condenses at the watercooled ends and returns along the wick by capillary action. High pressures and large excesses of metal vapour could be produced in the wick region with Ar serving as the end buffer gas. In the case of Figure 2, both CC14 and N20 were added at the nozzle. The alkali metal atoms stripped down the polyhalide to generate the central atom reactant (difficult to volatilize itself in many cases) for reaction with the oxidizer. This apparatus has been termed the ‘Heat Pipe Oven Reactor’ (HPOR). A variant has used crossed-pipes to produce a large volume (- 0.02 dm3) of chemiluminescence from BaO in the reaction Ba + N20. An outstanding feature concerning the development of a simple chemical laser system is that no mechanical pumping is needed; apparently Ba is an efficient getter for the N, product and BaO simply condenses on the walls of the chamber. Involatile atoms can also be generated by J. B. West, R. S. Bradford jun., J. D. Eversole, and C. R. Jones, Rev. Sci. Zmtr., 1975,46, 164. M. Luria, D. J. Eckstrom, and S. W. Renson, J. Chem. Phys., 1976, 64,3103. ‘I M. Luria, D. J. Eckstrom, and S.W . Benson, J. Chem. Phys., 1976, 65,1581. M . Luria, D. J. Eckstrom, and S. W. Benson, J. Chem. Phys., 1976, 65, 1595. M. M. Hessel, R. E. Drullinger, and H. P. Broida, J. Appf. Phys., 1975,46,2317.

Gas Kinetics and Energy Transfer

44

I

To Monochromator-

-

I I- - +

Burner Oxidant ___)

Crucible--,

I'

I -

L

Figure 1 Flow system for the production of diatomic metal oxides and halides (Reproduced by permission from Rev. Sci. Instr., 1975, 46, 166)

CROSS-SECTIONAL VIEW

Vacuum

Figure 2 Heat pipe oven reactor (HPOR) I. A new device for flame studies (Reproduced by permission from J. Chem. Phys., 1976,64, 3104)

45

Chemiluminescence in the Gas Phase

laser blow-off from the reverse side of a thin target; Tang, Utterback and Fruchtenicht l o have used this method to produce beams of B and Ho atoms which give chemiluminescence from presumably the diatomic oxides in reaction with N 2 0 in crossed beams. Some of the most spectacular results from the search.for a visible chemical laser system are now discussed. The highest molecular photon yield (a) achieved so far is 0.70 (with respect to oxidant) from SmF emitters in the reaction of Sm atoms with NF, in an argon carrier at high pressures (hereafter described as pressures of the order of 0.1 to 1 kPa).* The chemical efficiency calculated as the total visible radiant flux energy divided by the total reaction exothermicity was -12%, a remarkable value. A not much lower maximum Q, of 0.64 was measured for Sm + F2 flames, with chemical efficiency still higher at -16%.” It was proved that the emitter was SmF by a similar spectrum arising from the Sm + F2 reaction under low pressure conditions l 2 (hereafter described as pressures of < lo-’ Pa) when the time scale of residence of species in the observation region would allow only a primary reaction resulting from a ‘single collision’ to be effective in generating an emitting state. However, the almost continuous spectra, with only slight evidence of structure and that broad, show the unsuitability of these systems as chemical lasers. The grouiid state Sm(7F)atom has a high degeneracy and with F(2P)correlates with 24 states of SmF;” the spectrum arises from a multitude of emitting states and vibrational levels and the high photon yields could be explained on a statistical basis, which need not produce any inversions of particular levels. The effect of secondary energy conversion processes at high pressures is marked by Q, 0.01 at low pressures.’ The flame from Ba + N 2 0 has been found to yield @ 0.3 at high pressures,11 and the only strong emission is BaO(A1~+X1~) with a radiative lifetime l 3 of (3.56 0.07) x s for v1 = 0. Again secondary energy conversion must be important since the low pressure Q, is 3.9 x 10-3.’4 But most importantly, around one-third of the photons originate” from v’ = 1 and the potential curve of the A state is displaced to larger internuclear distances than that of X.16 Revelli, Wicke, and Harris l 7 have carried the assessment further by measuring the X-state populations in the Ba + N 2 0 system by laser-induced fluorescence. The Ba O2 reaction, which produced concentrations of BaO(X) of about five times larger than Ba + N20, mol dmS3 of BaO(X) v” = 7 was was used to show that a concentration of detectable; since this level was undetectable in the Ba + N20 reaction, under conditions when [BaO(A) v’ = 11 could be estimated to be approximately 2 x mol drn-,, this proved that a population inversion existed in the Ba0(1,7) band at 791 nm, the transition with the most favourable Franck-Condon factor. The Ba + N 2 0 system has been reported to show evidence of laser action

’’

-

-

* lo

l1 l2 l3 l4 l5

l6

1 Pa

=

-

+

lNm-’.

S. P. Tang, N. G . Utterback, and J. F. Fruchtenicht, J. Chem. Phys., 1976,64,3833. D.J. Eckstrom, S. A. Edelstein, D. L. Huestis, and S. W. Benson,J. Chem. P h p . , 1975,63,3828. C.R. Dickson and R. N.Zare, Chem. Phys. Letters, 1975,7,361. J. G.Pruett and R. N. Zare, J. Chem. Phys., 1975,62,2050. A.Yokozeki and M. Menzinger, Chem. Phys., 1976,14,427. C . R.Jones and H. P. Broida, J. Chem. Phys. , 1974,60,4369. R. W.Field, C. R. Jones, and H. P. Broida, J. Chem. Phys., 1974,60,4377. M. A. Revelli, B. G. Wicke, and D. 0. Harris, J. Chem. Phys.,1977,66,732.

Gas Kinetics and Energy Transfer

46

in optical cavity experiments,” but Felder, Gould, and Fontijn have shown that N 2 0 quenches BaO(A) at almost every collision, which must be a severe restraint. Another route of approach to a visible chemical laser system is to look for a three-level species, where the transition is to a non-ground state which might be expected to have a low population. Benard, Slafer, and Hecht 2o have found such a system in the flames of N,O/CO mixtures with Mg, Ca, or Sr atoms in He carriers at high pressures. In addition to chemiluminescences from singlet states to ground states of the diatomic oxides, they also measured Q, 0.01 in narrow bands (MgO, 370-375 nm; CaO, 548-555 nm; SrO, 592-602 nm) identified as ’A - a’ll and CP 0.05 in broader bands (CaO, 585-625 nm; SrO, 638-678 nm) identified as IA, ‘E - A ” l l , with the Q, based on metal atom flux. An indication of laser action was obtained when Ca/N,O/CO or Sr/N,O/CO flames were enclosed in an optical cavity, when bright luminous discs appeared on the end-mirrors and the cavity output was critically sensitive to the tuning of the mirrors. Neither the magnitude nor the sign of the gain coefficients could be determined, but it was suggested that values of the order of lo-’ m-’ might be maintained with the 0.1 Pa metal vapour partial pressures used in this study. Moreover in Mg/N,O/CO flames, a large fraction of added Mg(’S) atoms pass through the metastable Mg(’P) state The mechanism was con(264 kJ mol-’ excitation) prior to their sidered to involve an excited (probably vibrationally) intermediate, denoted MgO*, with the elementary steps:

-

-

+ N 2 0 + MgO* + N2 MgO* + CO + CO, + Mg(3P)

Mg(lS)

The measured concentration profiles showed clearly that CO was consumed in the generation of both Mg(3P) and CO,. The correlation diagram2, showed that the singlet and triplet states emitting MgO chemiluminescence were populated by Mg(’P) + N20. Despite the efficiency of Mg(’P) formation, the steady-state concentration deduced from the intensity of Mg(’P, - ‘S)emission at 457.1 nm was only 1.5% of all Mg-containing species in a typical flame because of strong quenching. Similar, but less efficient production of 3P atoms was observed in the Ca and Sr based flames but no Ba(’P) was produced in Ba/N,O/CO flames; it seems that the decreasing validity of spin conservation with increasing atomic mass must account for the observed trend. Catalytic enhancement of Na emission from Na/N20 flames on addition of CO has also been observed 23 but with a maximum of only -0.02. A similar excitation mechanism to the above for Mg was proposed with the additional possibility that transfer of energy from vibrationally-excited C 0 2 could be important. Benard, Love, and Slafer 24 have found another laser possibility based upon reaction of Mg(’P), generated by a.c. discharge of Mg vapour in flowing Ar, with K vapour. Not only was intense K atom emission observed, but also molecular emission in a band with continuously oscillating spectral structure ( 5 8 0 4 8 0 nm),

-

l8

l9 2o z1

22

23 24

M. Steinberg, unpublished results cited in ref. 20. W. Felder, R. K. Gould, and A. Fontijn, J. Chem. Phys., 1977, 66, 3256. D. J. Benard, W. D. Slafer, and J. Hecht, J. Chem. Phys., 1977, 66,1012. D. J. Benard, W. D. Slafer, and P. H. Lee, Chem. Phys. Letters, 1976, 43, 69. D. J. Benard and W. D. Slafer, J. Chem. Phys., 1977, 66, 1017. R. C. Benson, J . Chern. Phys., 1977, 66, 3879. D. J. Benard, P. J. Love, and W. D. Slafer, Chem. Phys. Letters, 1977,48,321.

Chemiluminescence in the Gas Phase

47

the most intense peak being at 658.2 nm: the emission appeared as a salmon-pink flame issuing from the K-effuser and the intensity bore a quadratic relationship to the K atom intensity and a linear one to [Mg(3P)]. The maximum c9 was -0.2 per Mg(3P) atom. The observations were consistent with the formation of a KMg* emitter in the reaction of the potassium dimer:

K2 + Ms(~P)+ KMg*

+K

(3)

The continuous emission was explained in terms of an unstable KMg ground state, (Van der Waals forces only) but chemically bound KMg*. The spectral appearance suggested near-complete vibrational relaxation of the emitter so that the radiative s. For laser action, rapid thermal dissocialifetime was likely to be longer than tion of the ground state promotes population inversion so that it is highly favourable to have an unstable ground state. This situation is analogous to the emission from rare gas oxides and halides found by Golde 2 5 in the reactions of ("p,,,) metastables with halogen-containing molecules. The emission was continuous and showed oscillations to the short wavelength side of a main peak. For example, Xe(3P) + C1, showed six peaks, whereas Kr(3P) CH,Br, showed only one strong peak. It was proposed that the transition concerned is from a strongly bound excited XeCL* etc. state [correlating with the Xe(3P) etc. state] to a lower state [correlating with the Xe('S) ground state], which is almost unbound. The oscillating structure was attributed to particular vibrational distributions in the emitting states, which would be expected to vary from reaction to reaction. An analogy was drawn between these excited state species and the corresponding ground states of alkali hJides (e.g. ArF* =KF, KrC1* ERbCl) so that the dissociation energies were expected to be similar. Moreover, by analogy with the reactions of alkali metals a high degree of vibrational excitation in the initially-formed rare gas halide from halogen reactants would be expected (for a more detailed discussion of this area, see Volume 2, Chapter 4 of this series). A spectacular channelling of reaction exothermicity into states of Sn atoms has been observed by Sridharan and McFadden,26 using a coaxial diffusion burner with H,/SnMe, in the inner, and F,/Ar in the outer tube. At a pressure of 7.5 kPa, all emission was in Sn lines between 280 and 380 nm. With respect to SnMe,, the ten most intense lines gave CP 7, with one at 326.2 nm having CE, = 1.81, without compensation for radiation trapping. Accordingly it is apparent that each Sn atom may be excited many times and in principle Q, could be many orders of magnitude greater than unity in such systems. Here reactions (4) and (5) could be responsible

+

-

+ H + Sn H2+ Sn* HF(w % 0) + Sn + HF + Sn* H

--*

(4)

(5)

for the excitation. It is interesting to note that without H, the flame gave emissions mainly from C,,CH, and possibly CF2 with weak Sn lines and low @ of With H, present it is likely that the heat release from H, + F2 facilitated the pyrolysis of SnMe, and F,. It has not been established whether a population inversion is established between Sn states in this system but there is evidently a strong possibility. 25 26

M. F. Golde, J. Mol. Spectroscopy, 1975, 58,261. U.C . Sridharan and D. L. McFadden, J. Chem.Phys., 1975,63,5061.

Gas Kinetics and Energy Transfer

48

Attempts to find a chemical laser system based on alkali metal emissions have generally failed to achieve worthwhile population inversions. Hall 27 has shown that 37 states of Cs are excited when a flow of Cs vapour (10%) in He is concentrically injected within an equal flow of F2 (10%) in He to form a Bunsen-type flame with a reaction zone 1 mm thick at 0.27 kPa total pressure. The mechanism postulated was that the primary Cs + F, or Cs, + F reactions generated highly vibrationally excited CsF which then transferred its energy to Cs atoms. Such an energy carrier would have a substantial lifetime so it is not surprising that there was no selective excitation of any of the Cs states, and the primitive state populations decreased in a statistical pattern with increasing excitation energy. A high fraction (34 & 17%) of the reaction exothermicity was converted into radiant energy with Qi, = 1.3 0.6, unlikely to be much attenuated by radiation trapping in the thin reaction zone. Krenos and Tully 2 8 have developed a statistical approach to explain the partitioning of electronic energy in the exchange between vibrationally-excited CsF and Cs. Although the primitive populations of Cs states are statistical, they showed that it was nevertheless possible to have population inversions created by subsequent radiative cascading. In fact, Hall's steady-state population analysis revealed 28 inversions of above the experimental uncertainty. Other systems for generating alkali metal atom emissions have been less successful in producing high @, in part because of extensive radiation trapping effects. For example, Luria et aZ.29 have used the HPOR technique to generate alkali atom emissions from Li/Na/Cs NF, and Cs F2 systems. The situation of radiation emanating from within a thick metal-rich zone was hardly conducive to high Qi, and, in contrast to Hall's result above for Cs + F,, Qi, was only -0.005. The 0 from NF3 systems were -0.02 with Na + NF, highest at 0.03;these showed evidence also of energy transfer from a high energy N, species formed by conjunction of stripped-down N atoms since the distributions over emitting states were not completely statistical, in contrast to Cs + F,. However, the smooth variation of the degeneracy-corrected photon fluxes versus orbital binding energy could not be interpreted in terms of direct interaction of metal atoms with a series of different N2 species; one explanation could be that the initial interaction produced ionization and subsequent ion-electron recombination resulted in electronic excitation. Capelle and Suchard 30 have explored the potential of CN emission from the reaction of active nitrogen with C2F4 (the most efficient additive) as a partial chemical laser system. The maximum values of Qi, were 0.185 in the CN(A211 - X2Ec+) red system and 0.03 in the CN(B22+ - X 2 C + )violet system. The Av = 0 sequences in the red system were calculated to require a minimum of 81 % of CN to be formed in the A state for zero gain; but Au c 0 transitions were more promising since reactive branching ratios as low as 25% into the A state would be required for zero gain, and furthermore with v' < d' the lower state will be less populated. The vibrational distributions in the A state were Boltzmann, corresponding to To 4500 K;it was calculated that a vibrational temperature some 2000 K lower could meet the laser requirement. But since T, is determined by primitive population rates and relaxation could not be achieved by additions of C 0 2 or SF,, this system seems unpromising.

-

+

+

-

27 28

29

30

L.H. Hall, J. Chem. Phys., 1977,66,2435. J. R. Krenos and J. C. Tully, J. Chem. Phys., 1975,62,420. M.Luria, D. J. Eckstrom, S. A. Edelstein, B. E. Perry, and S. W. Benson, J. Chem. Phys., 1976, 64,2247. G . A. Capelle and S. N. Suchard, IEEE J. Quantum Electronics, 1976,QE12,417.

49

Chemiluminescence in the Gas Phase

In conclusion to this section, it may be said that there has been little return on massive investment in the search for the visible chemical laser as yet.

New Spectra and States.-In

the course of experiments in both high- and low-pressure systems, many new states, or considerable vibrational extensions of previously known states, have been observed in emission. Table 1 presents such a summary showing whether the reaction was conducted at high (H) or low (L) pressures and, where the spectra have been analysed, the highest 0‘ (vh) observed. Table 1 Observed states in chemiluminescence Too/m-’

‘h

21 18

-

8340

{1:&3/2) 9980(1/2)

0 5 14 12 3

2

6

-

--

State A10(A211) SiO (A’II) SiO(c311) SiO(E’C +) ~eo(b3n) PbO(A 0+) AsO(Ar211) BiO(A ‘II) 31 32

33 34

Reactants (HI O/SiC14/Ar(H) O/SiC14/Ar(H) O/SiCI4/Ar (H) Ge/NZO (H) Pb/N20/N (H) AsC13/02/K (H) Bi/NzO (H)

-

33

-

33

-> ->

633.3 478.4 441.o 855

15 072(5/2) 14 965(3/2)

-

-

-

14 870(5/2) 14 531(3/2)

-

11 871(0) 19 621 15 591

Ref. 31 32

9921(3/2) 9268(1/2) 10 417 33 409 27 733 16 025 16 315 16 413

5 2 16

0Jrn-l

545.8 472.8

-

-> -

33 33 34 34,35 36,37 36,37 38 39 39 40 41

z::} -

40

924.2

42

535 380.5

43 44

‘6

Ref.

17 10 5 12 10 15 6 8

45,46 47 47 47 35 48 38 49

41

R. W. Field, G. A. Capelle, and C. R. Jones, J. Mol. Spectroscopy, 1975,54, 156. G. A. CapelIe, H. P. Broida, and R. W. Field, J. Chem. Phys., 1975, 62, 3131. R. S. Bradford, C. R. Jones, L. A. Southall, and H. P. Broida, J. Chem. Phys., 1975,62,2060. G . Hager, R. Harris, and S. G. Hadley, J. Chem. Phys., 1975, 63, 2810.

Gas Kinetics and Energy Transfer

50

Reaction Dynamics of Metal Atom-Oxidant Systems.-Elementary reaction dynamic Pa) in order to inhibit studies are best carried out under low total pressure (< secondary processes in the viewed region. Two main types of experimental systems have been used. In crossed molecular beam (CMB) studies, two well-collimated effusion beams are crossed and chemiluminescence in the intersection zone is detected. In beam/gas (BG) studies a well-collimated metal vapour beam enters a chamber filled with gas and chemiluminescence is observed in the beam track. In CMB experiments the crossing region is sufficiently small and background pressures sufficiently low that only primary processes produce chemiluminescence. But Gole and co-workers have demonstrated that no such certainty attaches to BG experiments. Gole, Preuss, and Chalek 39 have found that the variation of chemiluminescent intensity with chamber gas pressure serves as a test. A first order (linear) onset (i.e. at the lowest pressures) indicated the ‘single collision’ (elementary step) formation of the radiating species. This would be expected for a species such as LaO(C211), where the radiative lifetime (zR) of 20-30 ns would be several orders of magnitude shorter than the mean time between collisions under BG conditions: in confirmation a CMB study and a BG study 39 showed identical spectral structure of LaO(C + X) emission from the reaction La + 02. However, when the emitter s), it may undergo secondary collisions before is more metastable (zR > 2 x emitting and the intensity or spectral distribution usually changes as a consequence: such situations are indicated by more than first order variation of intensity with chamber pre~sure.~’For example, Dubois and Gole have observed emission from TiO(C3A) v‘ = 0-6 in a BG study of Ti + 02,but only v’ = 0 - 4showed linear onsets, while v’ = 5,6 showed quadratic onsets. Thus w‘ = 4 is the highest energy level resulting from the exothermicity of a single Ti + O2 collision, an important point for the subsequent determination of Dg(Ti0). The reaction Sr + F2 generates chemiluminescence from SrF(C’l3) and (D2X’), but only the first showed a linear onset,” suggesting a considerable degree of metastability of the latter with s, as opposed to lO-’s for the C state. This explained the relative zR weakness of D -+ X emission which would otherwise be difficult since the energy separation of the C and D states is only 12 kJ mol-’; both are accessible from the reaction exothermicity and neither population route involves a substantial activation energy barrier.52 Further instances of interest were reactions of Sc or Y atoms with 39950

’’

-

35

36

37

G. A. Capelle and J. M. Brom, J. Chem. Phys., 1975, 63,5168. R. C. Oldenborg, C. R. Dickson, and R. N. Zare, J. Mol. Spectroscopy, 1975,58,283. M. J. Kurylo, W. Braun, S. Abramowitz, and M. Krauss, J. Res. Nat. Bur. Stand., Sect. A 1976, 80, 167.

38

39 40

41 42

43 44

45 46

47 48

49

51 52

V. S. Kushawaha, Chem. Phys. Letters, 1975,30,130. J. L. Gole, D. R. Preuss, and C. L. Chalek, J. Chem. Phys., 1977,66,548. C. L. Chalek and J. L. Gole, J. Chem. Phys., 1976,65,2845. C. L. Chalek and J. L. Gole, Chem.Phys., 1977, 19, 59. C. Linton and H. P. Broida, J. Mol. Spectroscopy, 1977, 64, 382. J. B. West and H. P. Broida, J. Chem. Phys., 1975, 62,2566. J. W. Birks, S. D. Gabelnick, and H. S. Johnston, J. Mol. Spectroscopy, 1975,57,23. S. Rosenwaks, R. E. Stele, and H. P. Broida, J. Chem. Phys., 1975,63,1963. D. M. Lindsay and J. L. Gole, J. Chem. Phys., 1977, 66,3886. R. Shanker, C. Linton, and R. D. Verma, J. Mol. Spectroscopy, 1976, 60,197. C. Linton and H. P. Broida, J. Mol. Spectroscopy, 1976,62, 396. K. Sakurai and H. P. Broida, Chem. Phys. Letters, 1976, 38,234. L. H. Dubois and J. L. Gole, J. Chem.Phys., 1977, 66,779. D. M. Manos and J. M. Parson, J. Chem. Phys., 1975,63, 3575. J. L. Gole and D. R. Preuss, J. Chem. Phys., 1977, 66,3000.

Chemiluminescence in the Gas Phase

51

F, or Cl, studied in BG experiment^.^^ ScF and YF emissions showed linear onsets but ScCI, ScCI,, and YCl emissions showed above-first order onsets; the mechanism for the last three was considered to involve two steps with collision-inducedvibrational relaxation within the emitting states. It should be pointed out that in many other cases BG experiments showed linear onsets so that the chemiluminescence observed results from a simple elementary reaction and secondary collisions exert no influence. Examples are LaS(C211-, X 2 X + ) emission from La + OCS,53 PbO(a3Xc+[1],b3X:'[O-]-, X'X+[O']) emission from Pb + 03,36 SmO and EuO emissions from Sm/Eu 03/N,0/N02, respectively,'2 MO and MCl emissions (M = Mg, Cay Sr, or Ba) from the reactions M C102,54 ScO and YO emissions from Sc/Y 02/N02/N20/03reactions4' and La0 emissions from La + 0,/N02/ N,O/O, reaction^.'^ Both CMB and BG types of experiment have yielded results on energy pathways of reactions. In a CMB experiment, Wren and Menzinger 56 have shown that chemiluminescence from BaO formed in the reaction Ba + N20 was strongly enhanced by increased vibrational energy in the v, mode (bending) of N,O, effectively 'frozen' into the gas beam using a heated nozzle (270-620K). This is strong evidence for a rate-determining 'electron jump' mechanism, analogous to the As Ba and N20 'harpooning' mechanism of alkali metal/halogen reactions. approach they transfer to an ionic Ba' + N20- potential energy surface and the electron-transfer distance (and so the square root of the reaction cross-section) is inversely proportional to the difference between the metal atom ionization potential and the gas electron affinity. The electron affinity of linear N20is slightly negative but becomes positive on bending, thus explaining the above enhancement. The electron jump mechanism appears to be of wide applicability in metal atom/oxidant reactions, as will be seen in other examples to follow. Subsequently in the Ba N 2 0 reaction, rearrangement of the ion pair yields the electronically excited products. Yokozeki and Menzinger 5 8 have applied a similar CMB technique to show that SmO chemiluminescence cross-sections from Sm + N,O rise with increasing N,O nozzle temperature from a low-energy threshold, pass through a primary maximum, and then show a secondary rise (not seen with Ba + N20) as the nozzle temperature approaches the upper temperature of 613 K. The emission spectrum was unstructured with broad maxima in the blue (-470 nm) and red (- 640 nm) ; this near continuous nature reflects the fact that 36 states of SmO correlate with the ground state atoms l 2 (cf. SmF, p. 45). By seeding the N,O beam with He or H,, the kinetic energy (only) was varied, but the spectral distribution was unaffected showing that no new reaction channel opened up. At the same time, the difference between the vibrationally hot and cold N 2 0 cross-sections (together with the slope of the secondary rise) was greater for the blue than the red band. It appeared likely that the red emitter was fed by radiative-cascading from the blue emitter since the averaged state-to-state cross-sections, corrected for statistical bias, were identical for both emitters with and without vibrational excitation of N,O. It is worth noting that almost identical SmO emission was obtained from Sm + N20in both BG studies l2 and in high-pressure

+ +

+

''

+

s3 54

s5 56 57 s8

R. W. Jones and J. L. Gole, Chem. Phys., 1977,20,311. F. Engelke, R. K. Sander, and R. N. Zare, J. Chem. Phys., 1976,65, 1146. J. L. Gole and C. L. Chalek, J. Chem. Phys., 1976,65,4384. D. J. Wren and M. Menzinger, J. Chem. Phys., 1975'63,4557. D. R. Herschbach, Adv. Chem. Phys., 1966,10,319. A. Yokozeki and M. Menzinger, Chem. Phys., 1977,20,9.

Gas Kinetics and Energy Transfer

52

-

flames,” with the influence of secondary collisions shown clearly by the peak CD 0.4 in these last studies as opposed to 0.003 in the low pressure The CMB emission then confirms that the high-pressure flame emitter is SmO, the only possible single collision product. Engelke, Sander, and Zare 54 have found that reactions of Group IIa metals with C102 in BG experiments provide a complement in the spectroscopic sense to the reactions with N20. For example, with Ba reaction with N20 produces the visible BaO(A’X - X’C) emission overwhelmingly, although Hsu et aLS9have shown that there is weak BaO(A’’n - X’X) emission in the U.V. region also, in part reflecting the zR of -0.35 ps of the A state and -9 ps for A‘.13 However, Ba C102 showed overwhelming BaO(A’ + X ) emission, with v’ < 22 and populations peaking at v’ = 15-1 8 in a distinctly non-Boltzmann distribution indicating a direct reaction. Associated BaO(A + X ) emission was an order of magnitude weaker, which allowed identification of new A’ -,X bands, obscured by A --* X emission in the Ba + N20 system. The differences between the two systems have been interpreted in terms of the electron jump mechanism, promoted in the first place by the comparatively low ionization potentials of the Group IIa metal atoms. The electron affinity of C102 is large (3.43 eV) as opposed to the near zero value for N20, so that the electron jump will take place at a longer range for C102 reactions. It was then argued that since BaO(A) has less c and more n bonding than BaO(A’), the energy of the latter state will be lower at the distances at which the electron jump occurs in Ba C102, encouraging its population. Another pathway also occurs in the C102 reactions resulting in emissions from the diatomic metal chlorides; evidently this is a ‘snap-out’ reaction, s.g.

+

+

Ba

+ Cl(

0 -+

BaCl

+ O2

0 The species ClO; formed by the electron jump was predicted 5 4 to be more bent than C102, promoting the combination of the two 0 atoms, and may have a double minimum in potential energy to accommodate the two pathways of approximately equal rates. The total CD from Ba + C102 is low in BG experiments (-0.01). Similar chemiluminescent features appeared in the reactions of the other metals. have investigated chemi-ionization in the Ba + C102 system Diebold et amongst others and have shown that the chemi-ionization channel is generally very much faster than the chemiluminescence channel, which will partly explain the low nm2 or values of a. Chemiluminescence reaction cross-sections are usually less, whereas for Ba C102 the chemi-ionization cross-section was nm2, nm2 for Ca F2 and 1.4 x rising to 2 x nm2 for Ba + C1,. Perhaps the most unusual molecular dynamics have been discovered by Engelke and Zare 61 in the reactions of Group IIa metal atoms with S2C12in crossed beams with the gas poorly collimated. In the Ba reaction, the dominant chemiluminescence was from S2(B3C; -+ X’C,) bands, which is unusual because the excitation appeared

+

59

+

C. J. Hsu, W. D. Krugh, H. B. Palmer, R. H. Obenauf, and C. F. Aten, J. Mol. Spectroscopy, 1974, 53, 273.

6o

G. J. Diebold, F. Engelke, H. U. Lee, J. C. Whitehead, and R. N. Zare, Chem. Phys., 1977,

61

F. Engelke and R. N. Zare, Chem. Phys., 1977, 19, 327.

20,265.

Chemiluminescence in the Gas P h e

53

in the 'old' S-S bond. Weak BaCl and BaCl, emission was also observed. The intensities showed linear onsets with increasing pressure, showing that only single collision processes were involved. Moreover, all the reactions showed large reaction cross-sections suggestingan electronjump mechanism. To explain the three channels, it seems likely that a five-atom cyclic complex intermediate was formed. The small values of CP (-0.01) may also reflect the spin-forbiddennature of the reaction forming S2(B). Total CP increased with the mass of the metal atom as Ca : Sr : Ba; 0.03 : 0.08 : 1.0 while those for S2 emission were as 0.02 : 0.12 : 1.0. Several interesting molecular dynamic aspects of reactions have been revealed in high-pressure work, generally using Ar carrier, although clearly the initially-formed species will be subject to many collisions before radiating under these conditions. Collision-induced transfer between states makes it likely that the internal energy stored in a reaction product will find its way into states with comparatively short zR so that Q, will be higher than in low-pressure work. Some examples of this have been given (see p. 4 9 , but in some instances the effect is only minor, e.g. EuF emission from Eu + F, showed @ rising from -0.01 at low pressure l 2 to -0.025 at high pressures," probably reflecting the low degeneracy of Eu(*S) which in combination with F(2P) only correlates with four states of EuF. The influence of electron jump mechanisms has been observed by Lindsay and Gole 46 in the reactions A1 + 03/N20. A10(B2X+)from A1 + O3 shows a markedly non-Boltzmann vibrational distribution with maxima at v' = 6, 8, 12, and 14; in contrast A1 + NzO produced an approximately Boltzmann distribution. Three critical features could be identified: (i) the positive electron affinity of O3 (2.5 eV) would promote a long-range electron jump mechanism, (ii) the AIO(A211) state (the dominant emitter) lies below A10 (X'X') at large internuclear separations (both correlate with ground-state atoms) and (iii) the inner limbs of the potential energy curves of A and B states are nearly coincident. Therefore Lindsay and Gole46 considered that a likely primary A1 + O3 reaction populated AlO(A) with subsequent collision-induced crossing into AIO(B) levels with the almost isoenergetic processes giving the maximum populations. This was evidenced by the marked pressure dependence of B -, X bands which indicated a gas kinetic hard sphere collision rate for A + B crossings between levels most perturbed by spin-orbit interaction. Conversely the near zero electron affinity of N 2 0 suggested a more covalent approach, in line with the smaller reaction cross-section (0.15 nm2 as opposed to 0.54 nm2 for A1 + 0,) and direct population of AlO(B). Under similar conditions, Rosenwaks, Steele, and Broida 4 5 estimated CP 0.01 for A1 + N 2 0 and about five times larger for A1 + 0,, taking into account the extension of AlO(A -,X) emission into the i.r.: here weak emissions from AIO(C211), A1 atoms and A10, were observed and two unidentified band systems in the U.V. region. The Group IIa metal reactions with oxygen-containing species at high pressures also show evidence of collision-induced crossings and decreasing @ from BaO to CaO can be interpreted on this bask3, The postulate is that a significant fraction of products are trapped in a metastable a311 precursor, itself probably populated from high vibrational levels of X'X' formed by the primary reaction.62 The a311 and emitting A'X curves cross at vibrational levels (wa) and (wA) respectively in BaO at (0)(1), Sr0(4)(0), and Ca0(7)(0). In CaO and to a lesser extent in SrO there will be vibrational relaxation within a311 in competition with crossing to A'X, while

-

R. W. Field, G. A. Capelli, and M. A. Revelli, J. Chem. Phys., 1975,63, 3228.

Gas Kinetics and Energy Transfer

54

only the latter can occur in BaO. The pressure dependences of Q, reflect these secondary processes. An interesting demonstration of the effect of secondary collisions has been performed by Lee and Zare 6 3 in a study of Yb + F2 at low and high pressures. Only YbF(A211, B2X+) emissions were seen in a BG experiment but in Ar at 0.4 kPa not only were the rotational structures of A 3 X and B --* X bands sharpened by rotational relaxation, but emissions from YbF(C'l3, D2Z+) states appeared in the U.V. evidently due to collision-induced crossing. The upper v' had energies corresponding to the reaction exothermicity of simple F atom exchange and the resemblance to the Group IIa metal (also ' S ground state atoms) reactions below is clear. Reaction of Yb with ClO, produced only YbCl emission, in partial analogy to Group IIa metals above. Under BG conditions the emission was broad and rather unstructured, but sharpened markedly at high pressures owing to relaxation of initial high rotational excitation. As with YbF, only YbCl(A,B --* X ) emission was observed under BG conditions but YbCl(C,D + X ) emissions appeared at high pressures. Several studies of Group IIa metal atom reactions with halogens have indicated that a simple exchange reaction occurs with F1,whereas the others involve a two step mechanism with long-lived MX, intermediates. With Ca,64 Sr,33 and Ba3, + F,, the highest energy MF state observed in emission lies within the exothermicity of the simple F atom exchange reaction. Also the electronic temperatures were high e.g. 12 OOO K for CaF 64 and the vibrational distributions were either moderately inverted as for CaF,64 or very high Boltzmann temperature e.g. -6700 K for BaF,33 all consistent with a direct mechanism. In contrast, for Cl,, Br2, or 12, emissions from states with excitation energies above the exchange reaction exothermicity were seen,33electronic temperatures were substantiallylower e.g. 1900 K for BaCl 3 3 and CaCl 64 and vibrational distributions were Boltzmann with comparatively low vibrational temperature (< 3000 K). Moreover these reactions gave rise to strong continuum emissions, ascribed to MX: species, whereas the F, systems showed little such emission.64 CMB experiments have shown that even at very low pressures the MX* (X = Cl, Br, or I) emitters are formed mainly in a two-step mechanism involving MX, as intermediate:64a key to the second step is the observation in Ba + CI, systems that the intensities from the highest energy BaCl states increased relative to that from the lower states with increasing flowrates of Ba, suggesting the reaction :

-

-

Ba

+ BaClt + BaCl* + BaCl

(7)

Even with F, systems, collisional effects were evident in the rise of Q, from low to high pressures, e.g. for Ba + F, from 1 x lo-' (ref. 55) to 7 x 10-3.33 Along the was found for Sr in contrast Group IIa series, for F, the maximum Q, (1.1 x to the steady rise through Mg, Ca, Sr, to Ba for the other halogens. Again this suggests a different mechanism for F, and the trend for the others can be explained in terms of the easing of interstate crossings with increasing atomic mass owing to less effective selection rules. In several other systems reaction at high pressures has involved secondary H.U. Lee and R. N.Zare, J. Mol. Spectroscopy, 1977, 64,233. 64

M. Menzinger, Chem. Phys., 1974,5,350.

Chemiluminescence in the Gas Phase

55

excitation processes which generate states with energies well above the primary reaction exothermicity. Examples are Pb + N20/0,/02 A1 halogen flames 6 5 and TI + F2 flames studied by Maya and Nordine.66 Only in the last case was a definite mechanism advanced, although clearly all demand an energypooling scheme. TI has (in contrast to alkali metal atoms) a low-lying electronic state (6,P3/2) 93.3 kJ mol-' above the ground state (62P1/2); it was considered that a statistical population ratio of these was generated by energy transfer from vibrationally excited TIF produced in the primary exchange reaction. Direct production of the highest emitting states seen, T1(62D3/2,5/2) and TIF(A311,B311), would have required -419 kJ mol-' as against the primary F atom exchange reaction exothermicity of 280 kJ mol-l. Tl(62P3,2)was considered as the effective primary reactant, with the additional energy required to form the emitters being derived from vibrationally excited TIF. The most obvious secondary energy transfer processes occur when NF, is used as oxidant; the range of emitters can only be explained in terms of a metastable N2 species formed when the F atoms have been stripped off. Photon yields not unexpectedly are usually higher than those for the corresponding F2 system, e.g. at while Q, 0.5 for Ba + NF,," although high pressures Q, 0.01 for Ba + F211933 the emitting species were the same. However A1 + NF, in Ar carrier showed strong and was similar to that produced A1 atom emission up to the ionization limit by A1 active nitrogen; but such high energy states were not produced by A1 F2, which showed stronger AlF emission. The likely significant reaction

+

-

-

65*67968

+

N

+ NF -+

N,

+

+F

is sufficiently exothermic to produce N2(A3Xi) o)' = 2 and it is noteworthy that spin conservation in N2(A) + AIF(X'Z) energy transfer collisions should favour production of triplet AIF emitters over singlets, as was observed. Spin conservation arguments have been applied by Felder and Fontijn 69 to explain the high Q, 0.5 from mainly triplet states of SnO in the reaction

-

Sn(3P)

+ N 2 0 + SnO + N2(X'Z:)

(8)

The study was performed in a high temperature, fast flow reactor using Ar carrier and very oxidant-rich conditions at lo00 K. The overall rate constant corresponded to a collisional efficiency of These observations could be consistent with the spin-forbiddennature of SnO(XIX) production, since no emission was observed from states with excitation energies above the elementary reaction exothermicity. Unfortunately this postulate does not accord with observations on Ge + N,O 35 where spin conservation should be more binding. Under similar, but lower temperature, conditions Q, has a value of only, with all observed levels within the reaction exothermicity. Here the pressure dependences of relative emission intensities showed clear evidence for the importance of secondary collisions, a point emphasized in Ge + O2 where the same three emitting states were observed but the elementary reaction was not sufficiently exothermic to populate any of them.

-

65 66

67

69

S. Rosenwaks, J. Chem. Phys., 1976,65,3668. J. Maya and P. C. Nordine, J. Chem. Phys., 1976, 64,84. S. Rosenwaks and H. P. Broida, J. Opt. SOC.Amer., 1976, 66, 75. S. Rosenwaks, R. E. Stele, and H. P. Broida, Chem. Phys. Letters, 1976,38,121. W. Felder and A. Fontijn, Chem. Phys., Letters, 1975, 34, 398.

Gas Kinetics and Energy Transfer

56

Reactions of B atoms with alkali fluorides in merged flows of He carriers have led to alkali atom emission 7 0 originating from reactions B('P)

+ MF + BF + M*

(9)

The Q, were -0.5 and the low concentrations of alkali atoms would not have led to significant radiation trapping effects. Such high chemiluminescent efficiencies could be predicted by the argument that the reactants can approach on three potential surfaces corresponding to the degeneracy of the P state; only one of these can yield a ground state alkali atom. Similar arguments have been applied by Struve et aL71 to interpret high photon yields from alkali dimer reactions with halogen atoms. The main doubt concerning the B atom work above is the cleanness of the procedure of discharging B2H, in flowing He as a source of B atoms. Information on chemiluminescence originating from reactions of electronically excited atoms has been provided mainly by the low pressure techniques. In a CMB system, Loh and Herm 7 2 have measured the emission intensities from Li(2*P) and Na(32P) atoms resultant from the crossing of a beam of Hg(3P'',2) atoms with velocity-selected beams of LiI, NaI, and NaBr. These halides were chosen since the channel represented as Hg('P)

+ MX + HgX + M*

(10)

was only exoergic for all three systems with Hg(3P2). The significant features observed were a reproducible increase in Li emission near the threshold for kinetic energy compensation of the endoergicity of the Hg(3P0)+ LiI reaction and a rapid decrease in reaction cross-sections for alkali atom emission with further increase in relative velocity, particularly steep for NaI and NaBr. The first feature indicates effective conversion of kinetic energy, the second could indicate the opening of an alternative reaction channel, perhaps the ionization process represented as

When a beam-source metal is rather involatile and consequently requires a high temperature effusive source, low-lying electronically-excitedstates can be present in substantial equilibrium concentrations. For example, at 2400K only 0.645 of La atoms are in the ground ('D) state with the bulk of the remainder in the excited (4r;)manifold. Evidently this may result in mixed chemiluminescent reactions being studied, as would have been the case in Manos and Parson's CMB study 5 1 of L a 0 emission from La + 02.However, here there is no spin restriction upon either La state forming the doublet emitters observed; since the population ratios of emitters were independent of the beam source temperature from 2275 to 2550 K, there was no detectableeffect of the different proportions of La species. BG experiments have given a more quantitative insight into the roles of atomic reactants in different states. Preuss and Gole 73 have shown that the variation of a chemiluminescent intensity as a function of beam source temperature will reflect the U. C. Sridharun, D. L. McFadden, and P. Davidovits, J. Chem. Phys., 1976,65, 5373. W. S. Struve, J. R. Krenos, D. L. McFadden, and D. R. Herschbach, J. Chem.Phys., 1975,62,404. 7 2 L. C.-H. Loh and R. R. Herm, Chem. Phys. Letters, 1976,38,263. 73 D. R. Preuss and J. L. Gole, J. Chem. Phys., 1977,66,2994. 70

71

Chemiluminescence in the Gas Phase

57

heat of vapourization of the metal (AH,) together with a weighted function of the activation energy (En) for the reaction, allowing access to apparent values of both. In the case of La0 (C2n)emission from La + 02/N02,Gole and Preuss 5 2 found agreement between the indicated AH, and the accepted thermochemical value and N20, the same emission also small values of En(5-20 kJ rnol-’). However for LA yielded an apparent AH, significantly lower than the thermochemical value. The explanation was that spin selection rules only allow La(’F) N2O(’Z) to form N,O can form the emitting doublet states in quartet states so that only La(’0) a single collision process. Correction for the changing proportions of La(2D) and (‘F) atoms in the beam as a function of source temperature raised the apparent AH, near to the other values and indicated that E, was of the same magnitude as the other reactions. Jones and Gole 53 have applied similar argumentsto the generation of LaS(C2n) in the reaction La OCS; the singlet state of the latter meant that only La(,D) could be an effective reactant. An inverse case to the above has been found by Dubois and Gole 50 in the TiO(C3A)o’ = 0 emission from the reaction Ti O,, with Ti drawn from a source ranging from 2200 to 2650 K. The apparent AH, was over 80 kJ mol-’ greater than the thermochemical value. This was interpreted as the excited Ti(5F) atom being the effective reactant rather than the ground state Ti(jF), since only an insignificant proportion of the latter could have possessed sufficient thermal energy to overcome an activation energy barrier of 80 kJ mol-’, the alternative possibility. The further postulate that an electron jump mechanism was rate determining supported this interpretation, since the Ti(’$“) has an effective ionization potential of 6.00 eV, 0.83 eV lower than that of Ti(3F) thus enhancing the reaction cross-section of the excited state. In contrast, only the reaction of Ti(3F> with N 2 0 can yield triplet states of Ti0 for spin conservation; these reactants would therefore be expected to preserve a covalent interaction to significantly shorter separations on approach than Ti(5F) + 0,; the lower reaction cross-section for the N 2 0 reaction supports this interpretation.” For heavy atoms such as Pb, spin-orbit splitting in the ground ( 3 P ) state can be significant,just as for Hg(’PO,,) above, and the different multiplets have been found to generate different chemiluminescences. The reaction Pb + O3 to give PbO chemiluminescences showed this effect in a BG study 36 and in a high pressure while the latter also indicated the opening of a new reaction channel when O3 was vibrationally excited using a laser beam. In the case of PbO(a3Z+[1],b3Z’[O-]) bands the intensities varied with the Pb oven temperature in accord with AH, for Pb,36 so that the lowest multiplet (’Po) is the reactant. But the shorter wavelength emission from PbO(B[l]) not only showed bands up to v’ = 4,37 whereas the exoergicity of the Pb(’PO) reaction could only have produced v’ = 0, but also the intensity increased relative to PbO(a,b) intensities as the Pb oven temperature was raised; the difference expressed as an activation energy was -42 kl mol-I, suggesting the latter as the approximately equal to the splitting of Pb(3P0)and (’PI), reactant producing PbO(B). Yet a further emission, tentatively identified as from PbO(A[O+]), appeared when O3 was vibrationally excited and the other emissions were also enhan~ed.~’The underlying reaction dynamics are unclear; since the reactant states correlate adiabatically with PbO(X), the formation of the emitting states must result from minor nonadiabatic processes involving curve crossings in view of c 0 . 0 1 . ~ ~

+

+

+

+

+

Gas Kinetics and Energy Transfer

58

Radiative Lifetimes (zd.--In the simplest way, the spatial distributions of emissions in BG experiments can indicate the order of magnitude of zR. Under single collision conditions, if the product state has short rR (< 100 ns), then the corresponding emission will appear in the narrow and sharply-defined shape of the beam. On the other hand, if zR > 10 ps, the product state molecules will be able to travel outside the beam and the flame will be diffuse. Such observations have proved useful for new states. For example, Oldenborg, Dickson, and a r e 36 were able to deduce zR > 10 p s for PbO(a31:+[1])from the diffuse shape of its emission from Pb + 03. Conversely Yokozeki and Menzinger l4 observed sharply-defined flames, whitish-red for Sm + O,/N,O and whitish-green for Yb + 03,which remained uniform and unchanged in colour at pressures up to 0.7 Pa, giving upper limits of zR < 3 ps for the emitters. More than one type of emitter was formed in Yb + Fa;at very low pressures only a sharply-defined whitish-green flame was observed, but above 0.1 Pa a sharp green cone was surrounded by a blue fringe and a red diffuse cloud, indicating zR -c 3 ps for two emitters (A211) (B'C') and one metastable 0ne.14 Lee and Zare 74 have shown that this red emission disappeared entirely in the presence of 0.4 kPa of Ar, confirming a long zR and consequent susceptibility to quenching. Yokozeki and Menzinger l 4 observed completely diffuse emissions for Sm/Yb + Cl, reactions and the flames showed pronounced colour changes with increasing pressure, accountable to vibrational relaxation, and clearly zR is greater than lops here. The more sophisticated procedures for discerning metastable states in BG systems devised by Gole and co-workers have been mentioned (see p. 50). In low-pressure work, reaction rate limitation cannot be responsible for the diffuse nature of a flame, but in high pressure experiments this is a possible cause. For example, West and Poland " produced a bright orange flame from Ba + CO,/CO which was spherically diffuse in a HPOR. The presence of an unstructured spectrum suggested a polyatomic emitter but little else could be deduced. Direct measurements of zR for states emitting to the ground state have been made using pulsed tunable lasers, by monitoring the photoluminescence decay rate. In one instance, West and Broida 43 used Fe NO, in inert carrier as a source of FeO(X) to obtain zR of 450 & 100ns for FeO(B511) and 550 f 100ns for FeO(A5C+); these states were the upper levels of the orange chemiluminescence band systems observed in Fe + N,0/03 reactions. These short zR were consistent with the lack of rotational relaxation displayed in these bands excited in oxyacetylene flames seeded with Fe(CO), at atmospheric pressure. In a CMB study of Ba Cl,, Mims and Brophy 76 have used a detector which was movable (30 mm) along the direction of the product angular distribution peak, to show that the intensity fall-off of BaCl; continuum emission was indicative of s for this emitter. zR >

+

+

Bond Strength Limits.-If a reaction occurs under single collision conditions, it is likely that a few of the species with the new bond will possess internal energy equivalent to almost the entire exothermicity of the reaction. From the corresponding wavelength of emission a lower limit to the bond strength of the product species can be established. The validity of this depends on recation dynamics; the expectation 74

'Is 76

H. U. Lee and R. N. Zare, J . Mol. Spectroscopy,1977, 64,233. J. B.West and H. M. Poland, J . Chem. Phys., 1977, 66,2139. C. A. Mims and J. H. Brophy, J. Chem. Phys., 1977,66,1378.

Chemiluminescence in the Gas Phase

59

will be most nearly fulfilled for strongly inverted, non-statistical product state distributions but will never be strictly true since the products always separate with finite kinetic energy. Two situations can arise. Where a transition assignment can be made, the highest energy emitting level can be identified with certainty. However, in the case of unresolvable emissions, an assumption that the short wavelength threshold corresponds to a transition from the highest energy state to the ground state is the only recourse; this can only be regarded as an approximation since Franck-Condon factors rarely favour such transitions. In the case of PbO(a3X+[1]+ X)emission, from Pb + O3 in a BG e ~ p e r i m e n t , ~ ~ the banded spectrum was analysed to show that the highest populated level was v' = 14; this defined Ein,(PbO), the total internal energy of this level with respect to the ground state. Much smaller terms, Eint(Pb)and Eint(Os)were calculated for the presumed thermally equilibrated reactants and conservation of energy yielded

Et represents the calculable initial relative translational energy of Pb and 03.Here Dg(Pb0) 2 360.9 & 3.1 kJ mol-' was obtained, in good agreement with the thermodynamic D: = 369.6 4.8 kJ mol-'. Gole and co-workers 77 have shown that such lower limits can be made more certain if the dependence of the intensity on temperature parameters in BG experiments can also be established, principally by varying the beam source temperature. This procedure allows activation energy barriers in the reaction path to be taken into account and a test of the nature of the metal reactant against the possibility of roles of excited states or dimers through comparison of the apparent AH, with established values. Activation energy barriers can be substantial on occasions; e.g. one of 16 to 21 kJ mol-' exists for population of SrF(C,D) states in Sr + F2,52 whereas one of 59.2 f 10.2 kJ mol-I occurs Others can be quite small, such as 5 kJ mol-' between Sc + N 2 0and SCO(A~I'I).~~ for YO(A2n) formation in Y + 02.52 The lower limit for 0: will be too high in the absence of correction for activation energy. At present evidence for the significance of dimers appears to be restricted to alkali metal^.^' Effectively continuous SmO emission arises from Sm + N20 so that D:(SmO) has been estimated from the short wavelength limit at 425 nm.12 This case represents something of a triumph for the chemiluminescent method since the result DE(Sm0) 2 566.9 2.9 kJ mol-' disagreed with thermodynamic results, but more recent thermodynamic work 7 8 has given 569 & 8 kJ mol-' in accord. For deduction of D: limits, the chemiluminescentreaction must be truly elementary. This is not the case for Ca + Br,64 and it is noteworthy that the original erroneous conclusion 7 9 that CaBr(A2n) was formed in a single exchange reaction led to 100 kJ mol" higher than the recent thermodynamic value." D:(CaBr) Engelke and Zare have inverted the above procedure to deduce 0 8 >, 185kJ molfor S-Cl in S2C1, reacting with Ba/Sr; DE values were available for the BaCl and SrCl emitters. Similarly Black, Slanger, and Sharpless have deduced 2 260 & 5 kJ mol- from vacuum-u.v. photodissociation-induced D:(OC-Se)

-

-

'

'

77 78

79

8o 81

D. R. Reuss and J. L. Gole, J. Chem. Phys., 1977,645,880. D. L. Hildenbrand, Chem. Phys. Letters, 1977,48,340. M. Menzinger, Canad.J. Chem., 1974,52,1688. D. L. Hildenbrand, J. Chem. Phys., 1977,66, 3526. G. Black, R. L. Sharpless, and T. G. Slanger, J. Chem. Phys., 1976, 64, 3985, 3993.

Gas Kinetics and Energy Transfer

60

pseudo-continuous Se2(B3X:;;+ X) emission with a short wavelength threshold at 380 & 5 nm. The mechanism was considered to be

+ hv * CO + Se(4'S0) Se(4lSO)+ OCSe + CO + S ~ , ( B ~ ~ C , ) OCSe

(13)

(14) It is perhaps surprising that a large rate constant was found for the second step which violates spin conservation. Table 2 summarizes the lower limits determined for D: parameters during the period under review.

Table 2 D : Lower limits determinedfrom chemiluminescence Species BaO EuF EuO La0

sco

Reactants Ba C102 EU Fz EU NO2 La 0 2 La ocs Pb 0 3 sc 0 2

SiF SmCl SmF

Sm

LaS PbO

SmO Ti0 YO Ybcl YbF YbO

+ + + + + + + SiH4 + F2 Sm + C12

+ F2

+ + + +

NO2 Ti O2 Y +02 Yb ClOz Yb Fz

Sm

Yb

+

0 3

Dg/kJ mo1-I 559.0f 14.6 (a) 542.2f 8.8 (u) 549.8f 2.9 (u) 790.lf 4.2 (a) 569.7f 1.8 (a) 360.9f 3.1 (a) 688.7 (a) 510 (a) 418f 13 (u) 517.lf 8.8 (u) 507.5f 10.0 (u) 566.9f 2.9 (u) 668.6f 12.5 (a) 729.3 (a) 309 (a) 517.6f 9.6 (u) 482 (a) 394.1f 6.3 (u)

Ref.

54 12 12 55 53 36 41 82 14 12 14 12 50

41 74 14 74 14

(a), analysed spectrum; (u), unanalysed spectrum.

+

Miscellaneous Systems.-Three-body Combination Reactions. (i) 0 NO. In a CMB study Ibaraki, Kodera, and Kusonoki 83 have excluded three-body collisions and observed no emission when the NO source was at room temperature. But with the NO source cooled to 100 K they detected an air afterglow with less intensity at shorter wavelengths than normal, but with the same limiting wavelength. This was interpreted as originating from a reaction of O('P) with (NO), dimers and the temperature dependence of intensity indicated a dimer binding energy of 4 to 7 kJ mol'' in close agreement with accepted values. A large reaction cross-section of 1 to 3.4 nm2was indicated for 0 + (NO),, which is difficult to interpret since that for H + (NO), was only 0.035 to 0.09 nm2, as also determined in this study. Golomb and Brown 84 have remeasured the absolute intensity in a conventional flow system from 188 to 363 K, observing only a slight shift to longer wavelengths with rising temperature. A least squares fit of all existing data gave Io(T) (400-800 nm) = (6.9 & 0.4) x 103(300/T)0.9 exp(350/T) Einsteins dmq3s-', applicable to M = 02,Nzfrom 170 to 1250 K ; at 300 K, comparison with the estimate of 82

83 84

C. P. Comer, G. W. Stewart, D. M. Lindsay, and J. L. Gole, J. Amer. Chem. SOC.,1977,99,2540. T. Ibaraki, K. Kodera, and 1. Kusonoki, J. Phys. Chem., 1975,79,95. D. Golomb and 1. H. Brown, J. Chem. Phys., 1975,63,5246.

Chemiluminescence in the Gas Phase

61

Golde, Roche, and Kaufman of the component above 800 nm, suggests a factor of -3 to convert the above into a total emission Io(T). (ii) H + NO. Oka, Singleton, and CvetanovicS6 have observed HNO emission from Hg-photosensitized decomposition of H, in the presence of NO using a modulation technique. Distinctly different zR (two to three orders of magnitude) were found for the HNO(’A”) in the peaks at 690 and 760 nm (shorter lived). Decay kinetics indicated production of the 690nm emitter by H + NO + M while the 760 nm emitter originated from the exchange reaction HgH

+ NO

3

Hg

+ HNO(’A”)

Freedman has observed perturbation broadening of lines in the HNO(’A’’ + XIA‘) absorption spectrum at high resolution. The results indicated that HNO(lA”) is predissociated via accidental predissociation to the HNO(X ) manifold: it follows that HNO(’A”) must be populated in H NO M by this route in reverse and not through HNq3A”) as previously accepted. (iii) N + 0. Two observations of preassociative behaviour have been made with N(4S) and O(3P)atoms in flow systems. Dingle et a1.” have made a high resolution study of NO(C2n + A%+) (0,O) band emission and the rotational structure showed that N, carrier quenched NO(C) more rapidly than it caused rotational relaxation: consequently rotational levels below J = 4 were not detected since they are not preassociatively populated and DZ(N0) must be located at about this energy (626.88 & 0.12 kJ mol-’). Calculations on the mixing between states showed that NO(a4n) was the predissociating state. Campbell and Mason8’ have examined the quenching of Ogawa NO(b4Z- -+ a4n) band emission by CO,,N,O, and H20, finding that v’ = 4 was much less susceptible than v’ = 3,2, with the intensity from the first having a distinctly smaller temperature dependence. Preassociative population of v’ = 4 was invoked as explanation, which located this level 5 to 10 kJ mol-’ below @(NO). Black, Sharpless, and Slanger have shown that vacuum-u.v. photodissociation of N,O generates N(2D), which reacts with N,O to yield NO@%), an alternative source to the usual N + 0 M in discharge flow systems. (iv) N + N. Repetition of experiments yielding apparently spectacular results is always justified. A nice illustration is the attempt by Brennen and Shuman to of Nz(l +) bands from N2(B311J v‘ = 14-26 reproduce Ung’s observation purportedly in the Lewis-Rayleigh afterglow. The failure must be considered to indicate inadvertent production of such as ‘pink afterglow’ conditions in Ung’s system. More details of the Lewis-Rayleigh afterglow mechanism have emerged. Gartner and Thrush ” have measured the kinetic behaviour of N#Y3Z; -+ B311$ bands from v’ = 0 - 8 in the near i.r. and the similarity of bands from v’ and

+

+

+

’’

w 86

87

88

M.F. Golde, A. E. Roche, and F. Kaufman,J. Chem. Phys., 1973,59,3953. K.Oka, D. L. Singleton, and R. J. Cvetanovic, J. Chem. Phys., 1977,66,713. P. A.Freedman, Chem. Phys. Letters, 1976,44,605. T.W.Dingle, P. A. Freedman, B. Gelernt, J. W. Jones, and I. W. M. Smith, Chem. Phys., 1975,

8,171. I. M.Campbell and R. S. Mason, J. Photochem., 1976,5,383. G. Black, R.L. Sharpless, and T. G. Slanger, J. Photochem., 1976,5,435. 9 1 W. Brennen and M.E. Shuman, J. Chem.Phys., 1977,66,4248. 92 A. Y-M. Ung, J. Chem. Phys., 1976,65,2987. 93 E.M.Gartner and B. A. Thrush, Proc. Roy. Soc., 1975,A346,103.

89

’’

Gas Kinetics and Energy Transfer

62

v’ + 4 indicated that the latter populated the former by collision-induced crossing to produce a Boltzmann equilibrium between these levels. Gartner and Thrush 94 also examined the kinetics of N2(1+) emission from lower v‘ levels of N,(B). They confirmed that a large fraction of N + N recombinations (<45%) populate N,(B) and that near-isoenergetic levels of N2(A3Zi)are the overwhelming precursors with a rate constant of lo8 dm3 mol-’ s - l for N2- and Ar-induced crossing from A v’ = 7 to B v‘ = 0. By examining populations of emitting levels, they showed that N, quenching of N,(B) populates essentially the same levels of N,(A) as does radiative-cascading, a further indication of the applicability of the Franck-Condon principle in quenching processes. Heidner, Sutton, and Suchard 9 5 have used Ar(3P) + N, energy exchange to generate N,(A), which was laser-pumped to N,(B) and the decay rate of N2(l +) emission was measured. N,(B) v‘ = 0 showed two decay times superimposed, suggesting coupling of this level to the near-isoenergetic N2(W3A1) v‘ = 0 level. That SF, had no effect on the decay rate was taken to eliminate coupling to also near-isoenergetic N,(A) v’ = 7, since SF, should have vibrationally relaxed this efficiently. Rate constants of 4.2 x lo8 and 5.4 x lo9 dm3 mol-’ s-l were extracted for N,-induced B + W crossing and its reverse, respectively; an upper limit of 1.8 x lo9 dm3 mol-’ s-’ for N,(A) v‘ = 7 crossing to N,(B) v’ = 0 induced by N, was derived from laser sequencing e~perirnents,’~in accord with Gartner and Thrush’s estimate 94 of 1.2 x lo8 dm3 mo1-ls-l. A noteworthy first is the detection of N2(1+) and (2+) emissions in a conventional flame system (NH, + F,) by Cashin et al.” (v) C + N. Washida et al.” have added small flowrates of C,N, to active nitrogen to generate a near-stoicheiometric flow of C atoms and downstream CN emission resulting from three-body C N combination. The CN(B2Z+)(violet) emitter did not correlate with C(,P) + N(4S) and it was considered that CN(C4C-) (with v = 0 near isoenergetic with CN(B) v’ = 5) served as precursor for both CN(B) and CN(A211) (red) emitters, even though CN(A) correlates with the ground state atoms. Three main points favour this argument: (i) no CN(B,D,E,F) emissions from levels close to the dissociation limit were observed, which were highly likely to be populated from CN(A) but not from CN(C) owing to the relative positions of potential energy curves: (ii) the lower-emitting levels were populated with high efficiency, which would have been inconsistent with radiative losses during the vibrational relaxation in CN(A) removing 263 kJ mol-’ to reach the CN(A,B) curve intersection. It was also improbable that crossings could have occurred between the widely separated A and B curves above the intersection at CN(B) v’ = 7, whereas v‘ < 15 was observed: (iii) the apposition of minima and maxima in A and B state populations in the vicinity of the intersection indicated collision-inducedequilibration, consistent with spectroscopically-observed perturbations. Subsequently vibrational relaxation in CN(A) populated lower levels. Another type of CN chemiluminescence was observed by Brunetti and Liuti 99 in

V” =

-

+

94

95 96

97

98 99

E. M. Gartner and B. A. Thrush, Proc. Roy. SOC.,1975, A346,121. R. F. Heidner, D. G. Sutton, and S. N. Suchard, Chem. Phys. Letters, 1976, 37,243. S. N. Suchard, D. G. Sutton, and R. F. Heidner, IEEEJ. Quantum Electronics, 1975, QE11,908. K. D. Cashin, P. S. R. K. Chintapalli, M. Vanpee, and P. Vidand, Combustion and Flame, 1974, 22, 337. N. Washida, D. Kley, K. H. Becker, and W. Groth, J. Chem. Phys., 1975, 63,4230. B. G . Brunetti and G. Liuti, Z.phys. Chem., 1975,94,19.

Chemiluminescence in the Gas Phase

63

reactions of C302 and C2N2 with N and 0 atoms respectively. The reactions of fragments considered to generate the emitting species were :

+ C20 0 + C2N

N

--*

CN + CO

(16)

+ CO

(17)

-+

CN

with the possibility that similar OCCN intermediates could be involved. The populations in CN(B) levels (mainly v’ = 0, 5, 6, or 7) were very different from those produced by C + N + M above suggesting direct formation or crossing from directly-formed CN(A). Brunetti, Liuti, and Schippa loo have added very pure CO to active nitrogen and detected CN violet emission: N2 metastables must play a role here since direct reaction of N(4S) + CO is heavily endothermic.

IF Chemiluminescence. Birks, Gabelnick, and Johnston 44 observed IF(B3r10+) and (A311,) emissions from I, + F2 reaction, with relative intensities varying with total pressure (20.5Pa) in argon diluent. When [I,] was high, B -+ X emission intensity increased with pressure to a plateau at -40Pa. When [I2] was low, moderate increase of pressure enhanced both 4 + X and B -+ X intensities, while larger increases ( > 3 Pa) produced a sharp decrease in A + X intensity. This was consistent with IF(B) having zR 1 ms, with I, mainly responsible for quenching, which never overwhelmed radiative depopulation. IF@) was indicated to have a much longer zR and quenching was the dominant removalroute. The short wavelength threshold of emission (472 & 5 nm) corresponded closely to the exothermicity of the four-centre reaction:

-

I2

+ F2

-+

IF + IF

(18)

However, Valentini, Coggiola, and Lee lo’ have detected a stable species, I,F, produced by I2 + F2 in CMB experiments; hence the reaction

F

+ 12F

3

IF

+ IF,

(19)

exoergic by 268 kJ mol-’ ( ~ 4 4 nm), 7 could account for the above emission. Estler, Lubman, and Zare lo2 have observed similar IF emission from F2 + CH,I/CF,I/ CH212/HI; on the basis of 12F intermediates similar spectra would have been expected but this was not the case and four-centre reactions are even less likely. Accordingly these reactions cannot be regarded as well-understood at present. Engelke, Whitehead, and Zare lo’ have observed IF(A,B) emission in a CMB study of I, + F,, but only when a laser beam was directed into the reaction zone to excite I2 to (B311[Ot]), with IF@) w’ < 10 generated. Photon yield measurements suggested that most reactive collisions of I#) with F2 yielded at least one excited IF molecule. Under these single collision conditions, this must proceed as a fourcentre reaction for the exothermicity to be sufficient to generate IF(@ w’ > 7. An electron jump mechanism could be operative since the ionization potential of the I,@) v’ = 43 concerned is -6.9 eV, not much different from the me& atoms in the Section on Reaction Dynamics, p. 50. The passage via an 1; F, surface would be excluded for the analogous 12(X)reaction.

+

B. G. Brunetti, G. Liuti, and B. Schippa, Guzzettu, 1975, 105, 521. J, J. Valentini, M. J. Coggiola, and Y. T. Lee, Furaday Discuss. Chem. SOC.,1977, 62,232. l o 2 R.C. Estler, D. Lubman, and R. N. Zare, Furaday Discuss. Chem.SOC.,1977,62,317. l o 3 E. Engelke, J. C , Whitehead, and R. N. Zare, Furaday Discuss. Chem. SOC.,1977, 62,222. loo

lo*

Gas Kinetics and Energy Transfer

64

Phosphorus Chemiluminescence. Van Zee and Khan ' 0 4 - ' 0 7 have studied the chemiluminescence produced by the reaction of white phosphorus vapour (P4) with moist air in N, carrier. At atmospheric pressure, the main emission was a continuum, ascribed to an excimer species (PO); considered to be formed in the equilibria:

(PO);

+ P O ( ~ ~+I IPO(X) ) + PO(BZII) + PO(X)

(20) The strongest evidence for this was the marked increase in intensity of the comparatively weak-banded emission from PO(B211) as the temperature was increased; also the similar effect caused by increasing N2 dilution. At the same time, the threshold of the continuum at 335 nm was slightly red-shifted compared with PO(B + X ) emission, just as expected for an excimer of low stabilization energy. Other emissions observed originated from HPO(A'A"), PO(A2Z+) v' < 7, PO(C2Z-) v' < 9, PO(C' 'A) v' < 6, PO(F2Z') v' < 3 and PO(G2ZC+)v' < 2. At low pressure (13.3 Pa) the emission was rather different,'" with P2(c1Zi) 4 < v' < I1 and P2(A111g)0 < v' < 3 bands and a visible continuum with a threshold at 375 nm considered to originate from a (P2:P0)* exciplex formed by the metastable Pz(b3ZC,)state. This is evidently a complex system which offers considerable scope for further study. O('S) Atom Emission. O('S) has a zR of 7 s but shows collision-induced radiation which can be many orders of magnitude faster, marked spectroscopically by pseudomolecular band structure above the O('S + ' D ) line at 557.7 nm. Xe is the most efficient partner and zR for the O('S) : Xe excimer has been determined as 290 f 30ns lo' and 200 ns.'" Formation is a three-body process but, since the reverse dissociation approaches collision frequency, O('S) : M excimers achieve a steady-state concentration in times short compared with the total lifetime. The activation energy for formation of O('S) : Xe has been found log to be -3.0 f 0.8 kJ mol-', which is consistent with the spectroscopically-determined DE of 6.0 kJ mol-', the difference being of the order of RT expected for a thermally equilibrated species. Binding energies and rate coefficients for collision-induced s while for emission increase with the mass of M;zR for O('S) : He is > 5 x Ar, Kr, and Xe the relative enhancements at 300 K are as 1 : 5 : 740.'" In contrast, there was no emission from O('S) : C02 complexes and only C 0 2 quenching of O('S) was ob~erved:"~also for M = H2 the total deactivation rate was about two orders of magnitude larger than the collision-induced emission rate. lo' Similar but weaker collision-induced emission of S('S) has been observed.'"

C2 Chemiluminescence. Arnold, Kimbell, and Snelling have observed C2 Swan (d311g+ a31Xu),Phillips (AIIIu + X'Z:), and Ballik-Ramsay (b3Z; + a31Tu)bands when halomethanes CH2,,X2+11(X = Cl, Br, or I) are treated with flowing H atoms. The Swan band emission (v' < 4) was different from that observed by Luria et aL6 in Na/CC14 systems (v' < lo), although in both cases stripping mechanisms were R. J. Van Zee and A. U. Khan, J. Chem.Phys., 1976,65,1764. R. J. Van Zee and A. U. Khan, J. Phys. Chem., 1976,80,2240. Io6 R.1. Van Zee and A. U. Khan, Chem. Phys. Letters, 1976,41,180. R. J. Van Zee and A. U. Khan, Chem. Phys. Letters, 1975, 36, 123. lo* G. Black, R. L. Sharpless, and T. G. Slanger, J. Chem. Phys., 1975, 63,4546. l o g K. H. Welge and R. Atkinson, J. Chem. Phys., 1976,64, 531. 1 1 0 G. Black, R. L. Sharpless, and T. G. Slanger, J. Chem. Phys., 1975, 63,4551. S. J. Arnold, G. H. Kimbell, and D. R. Snelling, Canad. J. Chem., 1975, 53,2419.

lo4

lo5

Cherniluminescence in the Gas Phase

65

proposed with reaction between species such as C,CX considered to be responsible for the formation of emitters. In such complex systems mechanistic conclusions are based upon identification of reactions of sufficient exothermicity to produce the emitting species in one step. Emissions from both C, and C3 are observed from many hydrocarbon flames particularly under fuel-rich conditions. Although the intensity of C, emission can be accounted for by thermal excitation, the intensity of the Swan bands is substantially greater, suggesting chemical origins. One suggested source is the recombination of electrons and hydrocarbon ions. However the presence of an electric field strong enough to drastically affect electron-ion recombination rates has no effect on Swan band emission nor on CH bands.”, Mann has suggested that the reaction

c3+ o2 c2(d3n) + CO, --*

is responsible, since he found that when an equilibrium mixture of carbon vapour at 2470 K was exposed to 0,in a flow system there was a 50% decrease in C3 emission intensity and a 300-fold increase in C2 emission, particularly from the w’ = 1 level of the d3rZ state.’13 Ozone Reactions. The reaction between 0,and NO is known to occur by two channels, one leading to NO,(X) and the other to electronically excited NO2. The two paths have similar pre-exponential factors and differ only in the higher activation energy of the path leading to electronically excited NO2. In a BG study, in which the NO translational energy was varied, Redpath and Menzinger ‘14 were able to show an enhancement of the chemiluminescent channel with increase in the NO nozzle temperature at the same collision energy. Thus the enhancement was not due to an increase in the internal energy of the NO and was ascribed to the change in the fine structure population of the state. NO(’n3 ,’) yields mainly electronically excited NO2, whereas ground state N0(211,,,) yields NO,(X). Lee and Zare ‘15 have shown that reaction of diethylzinc with 0,in a flow system at pressures 133 Pa gives surprisingly ZnH (’I3 + ,C) emission, with strong Zn(,P, + ‘So) emission. The presence of H atoms was evidenced by the characteristic vibrational bands of OH associated with the reaction H + 0,above 560nm. In view of the energetic proximity of Zn(,P,) and ZnH(,II), together with the high concentrations of the former indicated by emission, there were two possible mechanisms for the formation of ZnH(,lI):

-

(0

Zn(’P) + H, 4 ZnH(’Z) ZnH(’C) + Zn(,P) + ZnH(’n) Zn(,P) + H(,S) + M + ZnH(’n)

+ H(,S) + Zn( ‘So) +M

(ii) In contrast the reaction of dimethylzinc with 0,showed no emission from Zn, ZnH, or OH, but only from formaldehyde. This demonstrates the different chemical fates of the two alkyl groups. The chemiluminesence from 0,+ ethylene mixtures was first observed by Nederbragt et al.’ l6 One component, the Meinel bands of OH(X), was identified and V. 1. Tverdokhebov and N. N. Chirkin, Combust. Expl. and Shock Waves. English Trans., 1970, 6,492. 113

11* 115 116

D. M. Mann, Chem. Phys. Letters, 1977,47, 106. A. E. Redpath and M. Menzinger, J. Chem. Phys., 1975,62,1987. H. U. Lee and R. N. Zare, Combustion and Flame, 1975,2427, C . W. Nederbragt, A. van der Horst, and T. van Duijn, Nature, 1%5,206,87.

Gas Kinetics and Energy Transfer

66

another component was tentatively ascribed to formaldehyde ('A, + 'Al). More recent work 117 has confirmed the identification of the formaldehyde emission and shown that OH(A2X+) emission is also common to all olefin/03 reactions. For olefins higher than ethylene, a-dicarbonyl emissions are observed. Alkylsubstituted olefins produce a band at -520 nm which has been identified as glyoxal (3A,) in the case of propene, but-l-ene, cis- and trans-but-Zene and cyclohexene. Where there are two methyl groups on a carbon atom of the double bond, e.g. for isobutene, trimethylethylene and tetramethylethylene, a rather broader band is observed at about the same wavelength identified as due to triplet methyl glyoxal. Pitts et al.' l7 suggested that the presence of 0,was necessary for its formation, but experiments by Becker et aZ.'" with deoxygenated ozone have shown this not to be the case. The Meinel bands are due to the reaction of H atoms with O3: it is suggested that the OH(A21:+) may be formed by 0 atom reaction with H or HCO. The carbonyl compound emissions probably all arise from a similar type of precursor, possibly akin to that which leads to chemiluminescence in oxetane formation and decomposition (see p. 67). However, the olefin/O, mechanism is complex and not well understood, particularly at the low pressures used in many of the studies, and assignment of reaction paths for these emissions can only be tentative. For the reactions of 0,with allene, emissions from CH,('A), OH (A2Zc') and OH(X) v" 4 9, as well as the previously observed HCHO('A,), have been reported.'lg In the same work, spectra were observed from electronically excited HCO, OH(X) 0'' < 9 and possibly C2(e31T, v' = 0 + a3n, v" = 6) produced in the reaction of 0,with acetylene. In previous work on the latter reaction My et detected OH(A2X+), CH('2- and ,A), and C2(d311g). Sheinson et QZ.,'~' in a study of reactions of O3 with a series of fluorinated olefins in a low pressure (- 130 Pa) flow system, observed chemiluminescence in all cases but that from O3 + C2F, was unlike the others in having a band system extending from 245 to 400 nm, which was efficiently quenched by 0,.By comparison with the spectrum from other sources, it was assigned to CF,. This appears to be the first time that electronically excited CF, has been detected in a reaction system. The previously suggested mechanism of CF, formation in this reaction is not sufficiently exothermic (300 kJ mol-') to generate the CF, emissions observed (requiring 487 kJ mol- '), implying that there must be an alternative path to CF, production. With 0, + C2HCN 122 the main emissions are CN red and violet bands and CH(A2A -,X'n) at 432 nm. 0,readily quenches the CN red bands, possibly by reaction with their precursor, but hardly affects the others. The only emission seen from O3 CS2122is a featureless band with a maximum at -365 nm and a short wavelength cut-off at -280 nm; this is due to S02(A1B,) produced by reaction of the O3 with SO,123an emission common to many reactions of O3 with sulphur compounds. In contrast, the emission bands between 500 and

+

11'

119

lZ0 121 lZ2 lZ3

B. J. Finlayson, J. N. Pitts jun., and R. Atkinson, J . Amer. Chem. Soc.,1974,%, 5356, and refs. therein. V. Schurath, H. Giisten, and R. Penzhorn, J. Photochem., 1976,5,33. D. A. Hansen and J. N. Pittsjun., Chem.Phys. Letters, 1975,35,569. L. T. My, M. Peyron, J. Samanos, and A. Vuillermoz, Compt. rend., 1971,272, C, 1079. R. S. Sheinson, F. S. Toby, and S.Toby, J. Amer. Chem. SOC.,1975,97,6593. S. Toby, F. S. Toby, and B. A. Kaduk, J. Photochem., 1976/7,6,297. H. Akimoto, B. J. Finlayson, and J. N. Pittsjun., Chem. Phys. Letters, 1971, 12, 199.

Chemiluminescence in the Gas Phase

67

825nm, due to excited HSO, are observed when O3 reacts with H2S 124 and thiophene ' 2 2 but not with MeSH and MeS.124 The HSO is produced in the reaction SH

+ O3 + HSO + O2

(22) The chemiluminescencefrom O3 reactions has been applied as a detection method for hydrocarbons in gas chromatography.' 26

Dioxetane Decomposition. 1,Zdioxetanes readily undergo chemiluminescent photolytic or thermal decomposition to carbonyl compounds. The total and relative yields of excited-state products depend on the nature of the substituent in the oxetane ring, but they may be produced in yields of up to 50% and appear to be wholly in their lowest triplet state.' 279 12' A number of theoretical analyses, mostly MO calculations, have attempted to identify the nature of this excitation The decomposition is assumed to be either a concerted process'36 or to involve a 1,4-OCCO b i r a d i ~ a l , ' but ~ ~ there is no clear agreement on the basis of these calculations as to which is operative. A number of these calculations refer specifically to the simplest dioxetane, C2H202,which until recently was not known to exist. have observed HCHO('A2 --* XIA1) emission from the However Bogan et addition of 02('A8) to C2H4 in a heated flow reactor. The emission was first order in each reactant and was attributed to the formation of the unsubstituted 1,2-dioxetaneY which has transient existence before decomposing to formaldehyde. The temperature variation of the intensity indicated an activation energy of 88 kJ mol-'. In a similar experiment with 02('A8) and ethyl vinyl ether,'38 HCHO('A2 -+ X ) emission was observed, the intensity of which was first order in both reactants. This was interpreted as indicating formation of a chemically activated oxetane which underwent rapid decomposition to formaldehyde and ethyl formate. Experiments involving addition of a quenching gas established that the formation of the adduct rather than its decomposition was rate determining. The adduct lifetime was estimated to be < lo-' s and the activation energy for chemiluminescence production to be 42 W mol-'. An interesting feature of this work was that emission was observed only from the formaldehyde and not from ethyl formate: if the exoergicity were statistically distributed, both might be expected to be excited. This could be due to 124

K. H. Becker, M. A. Inocencio, and U. S. Schurath, Internat. J. Chem. Kinetics, Symp. 1, 1975, 205.

M. Weber, U. Schurath, and K. H. Becker, Ber. Bunsengesellschaft Phys. Chem., 1976,80,1244. W. Bruening and F. J. M. Concha, J . Chromatography, 1975,112,253. 127 N. J. Turro,P. Lechtken, N. E. Schore, G. Schusten, H. C. Steinmetzer, and A. Yekts, Accounts Chem. Res., 1974,7,97. lZs C. S. Foote and J. R. Darling, J . Amer. Chem. Soc.,1974, %, 1625. lZ9 E. M. Eveleth and G. Feler, Chem. Phys. Letters, 1973,22,499. lJo M. J. S. Dewar and S. Kirschner, J. Amer. Chem. Soc.,1974,%, 7578. lJ1 D. R. Roberts, J.C.S. Chem. C o r n . , 1974,683. lJ2 W. H. Richardson, F. C. Montgomery, M. B. Yelvington, and H. E. @Neal, J. Amer. Chem. 125

126

SOC.,1974,96,7525. C. W. Eaker and J. H i m , Theor. Chim. Actu, 1975,40,113. lJ4 T.Aoyama, H. Yamakawa, K. Akika, and N. Inamoto, Chem. Phys. Letters, 1976,42, 347. IJ5 L. R. Harding and W. A. Goddard, J. A m r . Chem. Soc.,1977,99,4520. 136 G. B. Schuster, N. J. Turro, H. Steinmetzer, A. P. Schaap, G. Faler, W. Adam, and J. C. Liu, J. Amer. Chem. Soc.,1975,97,7110. 13' D. J. Bogan,R. S. Sheinson, and F. W. Williams, J. Amer. Chem. SOC.,1976,98,1034. 13* D. J. Bogan, R. S. Sheinson, R. G. Gann, and F. W. Williams, J. Amer. Chem. SOC.,1975, 97, 2560. lJ3

Gas Kinetics and Energy Transfer

68

the nature of the mechanism leading to only one excited product, but the evidence is not conclusive since radiationless paths for removal of the ethyl formate exist e.g. decomposition, and the apparatus was not capable of detecting phosphorescence from triplet products. It has been suggested, on the basis of MO calculation^,'^^ that the addition of Oz('Ae) to ethylene would lead initially to a peroxirane intermediate which subsequently rearranges to the oxetane, but another recent theoretical study is in disagreement with this con~lusion.'~~

3 Infrared Chemilumhescence Chemiluminescence in the i.r. is usually associated with formation of reaction products which are in their ground electronic state, but vibrationally excited. In favourable cases its study directly yields detailed vibrational and rotational state distributions of the reaction products. Such knowledge is important for testing reaction rate theories, increasing our understanding of the reactivity of molecules in specific quantum states and identifying reactions capable of sustaining laser action in this region of the spectrum. Recent reviews of this field are those of Carrington and Polanyi and Smith.3 The techniques which are most commonly used are arrested relaxation, fast flow systems, and measurement of chemical laser characteristics. In arrested relaxation two uncollimated beams of reactants meet in a vessel rapidly pumped and maintained at a pressure of to Pa. The vessel walls, cooled to liquid nitrogen temperature or lower, act as a 'sink' for any excited molecules produced in the reaction. Under these conditions, there is little opportunity for secondary collisions to induce relaxation before molecules reach the walls so that the observed chemiluminescence can give both the initial rotational and vibrational distributions, with only small corrections required for rotational relaxation. This information may be combined with knowledge of the total energy released to yield, by difference, the translational energy distribution. Arrested relaxation is the only method based on chemiluminescence capable of producing reliable data for all forms of product energy. Other methods are usually limited to vibrational distributions. In the flow method, a fast-flowing gas stream at pressures of < lo3 Pa is used in which the reactants are mixed and chemiluminescence observed at windows placed downstream from the mixing point. If vibrational relaxation is negligible, or can be measured at successive observation points, it is possible to obtain the initial distribution in vibrational levels. Vibrational distributions are also obtained using chemical laser gain measurements, but the method is less direct than the other two and is less used. The techniques as so far described cannot be applied to endothermic reactions, but the arrested relaxation technique has recently been adapted to that end. The method, termed Chemiluminescence Depletion, applied to the endoergic reaction between a molecule XY and an atom Z, makes use of a rapid exothermic reaction first to prepare the XY in a range of excited vibrational states. The XY is prepared in a flow system leading into the usual cryo-pumped vessel wherein it meets the beam of Z atoms. 1.r. emission is recorded with (i) a continuous flow of the emitting species XY and (ii) an additional pulsed flow of the reactant Z. In the latter case,

'

M.J. S. Dewar and W.Thiel, J . Amer. Chem. SOC.,1975,97,3978.

IJ9

Chemiluminescence in the Gas Phase

69

the XY emissions from the various vibrational levels are seen to be depleted to a degree which is a measure of the extent of the reaction of the emitting state with Z and collisional relaxation. An alternative way of obtaining such information is to produce the vibrationally excited diatomic reactant by direct excitation through absorption of laser radiation.14' This is a very specific and efficient process and is probably preferable; but with the energies currently available from such lasers it cannot produce as wide a range of excited states as chemical excitation. Chemiluminescence is not the only technique capable of giving product state distributions; others are molecular beam methods and flash photolysis/absorption spectroscopy. The former is potentially extremely powerful, offering not only resolution of the various forms of energy involved in the reaction but also the spatial distribution following reactive scattering of the products. The recent advent of tunable dye lasers for laser resonance fluorescence detection of product states should widen its scope considerably. The flash photolysis method is more limited in application and has provided fewer results. Three-atom Systems.-Chemiluminescence and other studies of simple transfer reactions have revealed striking differences between reactions proceeding on potential energy hypersurfaces having an 'early' barrier and those having a 'late' barrier crossing. It has been suggested that the former, having a barrier lying along the co-ordinate of approach of the reacting species, may be identified with exothermic reactions, while the latter, with a barrier lying in the exit valley, are typical of endothermic processes. The investigation of these generalizations continues to be one of the principal applications of i.r. chemiluminescence. Systems most widely studied are reactions between atoms and diatomic molecules, particularly those involving hydrogen/halogen species and producing a diatomic hydride: these offer the advantages that (i) the product is heteronuclear and hence emits, (ii) the small reduced masses of such product molecules give widely spaced energy levels, and (iii) the relative simplicity of these systems, particularly those of low mass, make them more amenable to rigorous theoretical analysis. They are also of great practical interest because many of them can sustain laser action, as detailed in recent reviews.1D3i 14' Polanyi and his co-workers have continued their series of studies on the effects of reactant energy distribution on reaction d y n a m i c ~ . ' ~ ~ 'Earlier ' ~ ~ work has suggested that the reaction rate of a substantially exothermic reaction will be enhanced by a high degree of translational energy in the reactants whereas vibrational excitation of the reactants will enhance endothermic reaction rates. Using arrested relaxation, the effect on the rate of the reaction

H

+ F,

--*

HF

+F

(23)

of increasing the relative translational energy of the H atoms, produced in an oven with temperatures up to 2800K,was compared with enhancement of the internal D. Amoldi, K. Kaufmann, and J. Wolfrum, Phys. Rev. Letters, 1975,34, 1975. J. C. Polanyi and J. C. Schreiker, 'Physical Chemistry An Advanced Treatise, Kinetics of Gas Reactions', ed. H. Eyring, W. Jost, and D. Henderson, Academic Press, New York, 1974, Vol. VIA, Ch. 6. 142 L. T. Cowley, D. S. Home, and J. C. Polanyi, Chem. Phys. Letters, 1971,12, 144. 143 L. J. Kirsch and J. C. Polanyi, J. Chem. Phys., 1972,57,4498. A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi, and J. L. Schreiber, Furaduy Discuss. Chem. Soc., 1973,55,252. 145 D. 1. Douglas, J. C. Polanyi, and J. J. Sloan, J. Chem. Phys., 1973,59,6679. 14*

141

Gas Kinetics and Energy Transfer

70

energy of the F, by production in an oven operating up to 900 K.146 Since this reaction involves attack of a light atom on a diatomic consisting of two heavier atoms, the centre of mass lies effectively at the position of the diatomic and thermal excitation of F, produces little enhancement of its translational energy in the centre of mass frame, but its internal excitation is retained. No effect due to increase of the internal energy of F, (3.3 kJ mol-‘) was observed. In contrast, increase of the relative translational energy of the H atom in the range 3 3 - 4 6 kJ mol-’ increased the thermal average cross-section by a factor of 2.3. Although the energy ranges studied are very different in absolute terms, if the reaction cross-section were to increase as rapidly with vibrational excitation as it does with translation, an increase of a factor of -1.8 would have been expected for the internally excited F,. None was found, in accord with the expectations for such an exothermic (410 kJ mol-’) reaction. The effects of reactant energy distribution on rates of endothermic reactions can be predicted by application of the principle of microscopic reversibility to data on the reverse exothermic reaction. 14’ Use of ‘chemiluminescence depletion’ has provided direct evidence. Reaction (24) was the first to be studied by this technique

+ Br -+

HCl(v” = 1 4 )

Cl

+ HBr

(24)

and has received more attention, by a variety of methods, than any other.‘40*14’* 148 Douglas et produced the vibrationally excited HCl in a variety of prior reactions and observed the depletion of these states in the presence of Br atoms. The depletion rate increased rapidly with increasing v” above v“ = 2, corresponding to excitation above the endothermic barrier of 69 kJ mol-’ which falls between vat = 1 and v” = 2. There was little observable increase in the d 1= 1,2 states accompanying depletion of the higher states, indicating that collisional relaxation was much less important than reaction. This conclusion was supported by classical trajectory calculations by Douglas et aZ.‘48 and by Smith.’49 The latter also drew attention to the importance of electronically non-adiabatic relaxation, particularly for the lower levels, which is possible in this system. (For a more detailed discussion see Chapter 1 of Volume 2 of this series.) Similar results were obtained for the endothermic reactions.148 HF (v” = 1-6) HF (v“ = 1-6)

+ C1 -+ F + HCl + Br + F + HBr

(26)

Under the conditions used in these experiments approximately 96 % of the reactant energy was present as vibration for the highest levels studied. The estimated reaction cross-sections were found to exceed 10- nm’, corresponding to collision efficiencies for reaction approaching 0.1 and hence to very efficient use of vibrational energy in bringing about reaction, as anticipated for endothermic processes. The extent to which the various forms of reactant energy are channelled into similar forms in the products depends upon features of the potential energy surface and the mass combinations of species involved in the reaction (see ref. 1). It appears that in general reactant translational energy in excess of energy required to cross the

’

J. C . Polanyi, J. J. Sloan, and J. Wanner, Chem. Phys., 1976, 13, 1. K. G. Anlauf, D. H. Maylotte, J. C. Polanyi, and R. B. Bernstein, J. Chem. Phys., 1969,51,5716. 14* D. J. Douglas, J. C. Polanyi, and J. J. Sloan, Chem. Phys., 1976, 13, 15. 149 I. W. M. Smith, Chem. Phys., 1977,20,437. 146

14’

Chemiluminescence in the Gas Phase

71

barrier, is channelled predominantly into translation and rotation of the products, and excess vibrational energy appears as product vibration. A number of recent studies by Polanyi’s group are in accord with The effects of excess reactant translational energy in reactions (26) and (27) and the isotope variants (F HD, F + D,) were in agreement with this generaliza-

+

F + H2 + HF

+H

(27) t i ~ n . ’ ~ ~ *By’ ~comparing ’ results for reaction (27) using H2, HD, and D, at 77 and 290 K, it was possible to derive data for the effects of changing the rotational energy of H2 in the range J” = 0-2. The fraction of the total energy going into vibration changed only from 0.70 to 0.67 in going from J = 0 to J” = 1 and rose to 0.69 for J” = 2. No effect on the product rotational distribution could be seen. Existing theoretical calculations are not sufficiently accurate to account confidently for such small changes but there is some qualitative agreement.’” In this work there is an interesting finding for the reactions between F and HD, (28) and (29)

F + HD + HF

+D F + HD + DF + H

(28)

(29) An anomalously low rate of population of HF (w” = 3) was found for reaction (28) compared with (27) and, contrary to expectations, the fraction of the vibrational energy going into the HF cf, = 0.59) from (28) was less than that appearing in DF cf, = 0.63) from (29). The reverse is predicted by trajectory calculations and comparison with F + H, and F + D,. It is suggested that the explanation lies in the fact that for reaction (28) the energy release only exceeds the energy of HF (v” = 3) by -0.8 kJ mol-’, but the energy excess is significantly larger for the other reactions, and that classical mechanics is not suited to handle such systems so close to an energy threshold. The behaviour of the detailed rate constant k, (w” = 3) as a function of reactant energy also differs from the usual behaviour for highly vibrationally excited products: instead of being largely independent of energy, it is only so at high energies, declining markedly at low energies. The temperature dependences of the vibrational distributions found in the above work for F + H2 and F + D, are generally in poor agreement with those found by Coombe and Pimentel 1 5 2 * 1 5 3 using the laser gain technique. An exception is the behaviour of F

+ H2 + HF (v”

= 1)

+H

where agreement is excellent. It is likely that the fault lies with the particular laser method used which Coombe and Pimentel admit is subject to some uncertainties. Reaction pairs such as (28) and (29) offer an opportunity to test recent theoretical work on branching ratios. Development of an information theoretic approach to reaction product energy state distributions has provided a framework in which such results can be classified conveniently, compared and predictions made of reaction properties. Such theories express the observed state distribution in the products in terms of the departure from a statistically expected distribution. These deviations lS0 ls1 lS2 53

D. J. Douglas and 1. C. Polanyi, Chem.Phys., 1976,16, 1. D. S. Perry and J. C. Polanyi, Chem. Phys., 1976, 12,419. R. D. Coombe and G. C. Pimentel, J. Chem. Phys., 1973,59,1535. M. J. Berry, J. Chem. Phys., 1973,59,6229.

Gas Kinetics and Energy Transfer

72

may in turn be expressed as ‘entropy deficiencies’ and related to the branching ratios. Refs. 154 and 155 give a detailed account of the theory; refs. 156-159 give recent advances relevant to branching ratios. For reactions (28) and (29) the experimental results indicate that the vibrational contribution to the entropy deficiency is virtually identical for both reaction paths and hence the observed branching ratio r H F / D F arises almost entirely from the differences in the rotational energy distributions.160 The distributions treated by information theory yield a value of rHF/DF = 1.41 in excellent agreement with existing experimental values which range from 1.40-1.45. The branching ratio is known to vary strongly with the rotational level of the reactant and Perry and Polanyi ‘‘I suggest that this agreement would not be as good if selected reactant rotational states were considered. Kaplan and Levine take up this point and show that it is possible to obtain good agreement between values of r obtained from information theoretic treatment of the experimental distributions and values obtained by trajectory calculations. Information theory seems less successful in handling branching in reactions (30) and (31).

+ BrCl+ HBr + C1 H + BrCl -+ HCI + Br H

(30) (31)

Summation of the experimental detailed rate constants for these reactions gives = 0.40 compared with the value of 3.2 obtained by application of information theory to the product energy di~tributi0ns.l~~ In this study Polanyi and Skrlac also confirmed the previously observed ‘microscopic branching’ 164 for the reaction

rHCI/HBr

H

+ ICI + HCI + I

(32) i.e. the product energy states show two distinguishable distributions. Bimodal product vibrational distributions have been suggested for reaction (33) and bimodal rotational distributions for the hot atom reactions 144 (34) and (35) and the thermal reaction 165 (36). But in the case of reaction (32) the detailed rate constant, H

+ C12 (v” > 0) + HCI + C1 C1 + HI + HCI + I H + C1, HCI + Cl H + SCI, + HCl + SCl -+

(33) (34)

(35) (36)

R. D. Levine and R. B. Bernstein, Accounts Chem. Res., 1974, 7, 12. R. B. Bernstein and R. D. Levine in ‘Advances in Atomic and Molecular Physics’, eds. D. R. Bates and B. Bederson, Academic Press, New York, 1975, vol. 11, p. 215. 156 R. D. Levine and R. Kosloff, Chem. Phys. Letters, 1974,243,300. lS’ U . Dinur, R. D. Levine, and M. J. Berry, Chem. Phys. Letters, 1975, 34, 199. 158 U.Dinur and R. D. Levine, Chem. Phys. Letters, 1975, 31,410. 159 R. D. Levine and R. B. Bernstein, Chem. Phys. Letters, 1974, 29, 1. 160 R. B. Bernstein and R. D. Levine, J. Chem. Phys., 1974,61,4926. 1 6 1 D. S. Perry and J. C. Polanyi, Chem. Phys., 1976,12,37. 162 H. Kaplan and R. D. Levine, Chem. Phys., 1976,13, 161. 163 J. C. Polanyi and W. J. Skrlac, Chem. Phys., 1977, 23, 167. 164 M. A. Nazar, J. C. Polanyi, and W. J. Skrlac, Chem. Phys. Letters, 1974, 29,473, 165 H. Heydtmann and J. C. Polanyi, J. Applied Optics, 1971, 10, 1738. lS4

155

Chemiluminescence in the Gas Phase

73

k(u,J,T), distribution is bimodal with respect to all three variables. The fractions of the reaction exothermicity entering the various parts of the ‘high J’ component (i.e. that with high internal energy) were& = 0.65,f, = 0.24,f~ = 0.11. For the ‘low J’ component the figures were f, = 0.36,f, = 0.04 and fT = 0.60.’63 There was also evidence of microscopic branching in reaction (31) but the energy distributions overlapped sufficiently to complicate the issue. On the other hand, reaction (30) showed no sign of such branching. Such behaviour has been interpreted as being due to the existence of two favoured paths across the potential energy hypersurface leading to the same products. In the case of reaction (32) the two paths are identified as approach of the H atom to the two different ends of the molecule. If the approach of the H atom to the Cl end of the molecule has a high energy barrier, then it is energetically favourable to approach the I end, followed by migration to the C1 end to form HCl in ‘high J’ states. The ‘low J’ branch is attributed to direct attack on the C1 end. The same mechanism applies to reaction (31), but in the case of reaction (30), if the low barrier of approach is at the Br end and HBr is being formed, there is no energetic advantage in an approach from the C1 end and so no branching is seen. I and Br atoms can be formed in the ,P3/2 and ,Pll, states in these reactions. It was found that the yield of the excited species (2P1/2)was orders of magnitude less than the microscopic vibration-rotation branching ratio, thus eliminating the possibility that branching was associated with paths to these two products. Sung and Setser 166 have undertaken a similar study of the reactions

3

HF

+ X*(2P112)

for both HBr and HI. Both paths have been suggested to occur with high probability for HI, on the basis of an analysis by information theory 15’ of the product energy distributions found by Jonathan et al.167 Energy transfer from vibrationally excited HF to produce electronically excited I and Br atoms has also been observed and therefore it is important in any investigation to separate the two sources of excited atoms, Using a fast flow apparatus and an interferometric detection system, Sung and Setser 166 were able to monitor both the very weak ,PI/, + ,P3/2 atomic emissions and those from vibrationally excited HF. They found Br* to be formed both directly from the reaction (10.4 % of the HF, formation rate) and by V + E energy transfer. I* was also formed by energy transfer but the direct formation was negligible (t0.5%). Moreover the energy distributions were significantly different from those of Jonathan et aZ.167 The present distributions appear to be less relaxed and hence likely to be more indicative of the initial distribution. The discrepancy between the product energy distributions found for the F + H, has already been reaction by Coombe and Pimentel 1 5 2 * 16* and Polanyi mentioned. There is also disagreement with the results of Berry on the same system. The importance of these data for modelling the F, + H, chemical laser, as a test of the laser gain method and for comparison with theoretical calculations has 166

16’

T. P. Sung and D. W. Setser, Chem. Phys. Letters, 1977, 48,413. N. Jonathan, C. W. MeIliar-Smith, S. Okuda, D. H. Slater, and D. Tidin, Mol. Phys., 1971, 22, 561.

M. J. Berry, J . Chem. Phys., 1973, 59,2229.

Gas Kinetics and Energy Transfer

74

prompted Krogh et ~ ~ 1to. investigate l ~ ~ the discrepancies in product vibrational state population values to see whether they can be explained by the different extents to which energy transfer has relaxed the initial distribution during the period of measurement. Two of the studies are by flash photolysis-induced laser action and involve times of 12 ps and 5 p. The other results come from arrested relaxation measurements which should not involve any significant relaxation. There is agreement on the ratio (NJN,) of population of d‘ = 2 and d’= 1 states and its temperature dependence. However there is disagreement on N3/N2 and its temperature dependence. Modelling the system using recently obtained data for V-Y energy exchange, Krogh et al. showed that the discrepancy could not be due to vibrational deactivation. The calculations indicated very little effect of energy exchange on the laser measurements and hence still leave a 30% discrepancy between the results of the two laser-based measurements for N3/N2; the arrested relaxation value falls mid-way between the other two. Further the laser results still indicate that N,/N2 decreases with increase in temperature while the arrested relaxation values show the opposite trend. It is suggested that this difference may be due to the different extent to which rotational equilibration has been achieved in the d’ = 2 state (J” < 14) and the zl” = 3 state (J” < 7) at the time of measurement, but on this reasoning the good agreement for N2/N1would require compensating lack of rotational equilibration for the v” = 1 and v” = 2 populations.

-

-

Reactions of Atoms with Polyatomic Molecules.-HF Chemihminescence. Hydrogenabstraction reactions of F atoms with organic compounds and inorganic hydrides produce vibrationally and rotationally excited HF, emissions from which can be characterized in an arrested relaxation experiment or, as recently shown, in a fast flow system (linear flowrates up to 85 m s-l).17* To a limited degree the energy content and distribution in the HF is indicative of the role played by the other part of the polyatomic molecule in the reaction. Results, mainly from Setser and his group, have been reported for alkanes, aldehydes, ketones, ethers, alcohols, nitriles, nitro compounds, aromatics, cycloalkanes, halogen-substituted alkanes, SiH,, GeH,, PH,, NH,, NzH4,H2S, H,02, Si(Me),, and other corn pound^.'^^-^^^ The greater complexity of the species involved and the limitation that only one product of the reaction is being studied makes interpretation much less clear than for three atom systems. Furthermore, although trajectory calculations using an LEPS surface have been made, they require the system to be reduced effectively to a three atom reaction RH + F. Such calculations have clarified some features of the reactions, indicating the extent of mixed energy release for this type of mass combination, the s for transfer of the H atom from R to F and the very short period of occurrence of multiple encounters in many of the trajectories, but they are necessarily of limited value.’ 78

-

0. D. Krogh, D. K. Stone, and G. C. Pimentel, J . Chem. Phys., 1977, 66,368. D. J. Smith, D. W. Setser, K. C. Kim, and D. J. Bogan, J. Phys. Chem., 1977,81,898. 171 D. J. Bogan, D. W. Setser, and J. P. Sung, J. Phys. Chem., 1977, 81,888. 172 W. H. Duewer and D. W. Setser, J. Chem. Phys., 1973,58,2310. 173 H. W. Chang and D. W.Setser, J. Chem. Phys., 1973,58,2298. 174 D. J. Bogan and D. W. Setser, J. Chem. Phys., 1976, 64, 586. 17s J. H. Parker, Internat. J . Chem. Kinetics, 1975, 7,433. 176 K. C. Kim and D. W. Setser, J. Phys. Chem., 1973, 77,2493. 177 K. C. Kim, D. W. Setser, and C. M. Bogan, J. Chem. Phys., 1974,60, 1837. 17* R. L. Johnson, K. C. Kim, and D. W. Setser, J, Phys. Chem., 1973, 77,2499. 169

Chemiluminescence in the Gas Phase

75

A simple and significant comparison which can be made is between the energy of the maximum observed HF (d’,J’’) level and an estimate of the total energy available based on the thermochemistry of the reaction. Since one of the products is a radical, the availability of accurate thermodynamic data often limits the precision of the comparison, but nevertheless it is clear that in many cases the maximum energy of excitation of the HF is significantly less than the total available energy. The difference is believed to be related mainly to the radical reorganization energy. When initially formed the polyatomic radical has a geometry characteristic of its structure in the parent Compound, which may be significantly different from its equilibrium configuration. If the time required for the radical to reorganize to its equilibrium configuration is long on the time scale of the reaction, then this energy is not available to the HF. In cases where the odd electron in the radical can become delocalized, the reorganization energy may include this resonance stabilization energy. Differences in the time taken for the radicals to reach their stable configurations are demonstrated in a study of F atom reactions with a series of aldehydes, RCHO, where R = H, CH,, CD,, and C6H5.172 Only for HCHO does the maximum energy of the HF (d’,J”) correspond closely to the thermochemical limit. For the other three compounds there is a discrepancy of 25 to 35 kJ mol’ : the larger RCO radicals apparently take longer to relax to their equilibrium geometries. Where it can be assumed that the maximum energy has been taken up by the HF, this limit provides thermochemical information about the reaction. This has been used as the basis for the determination of an upper limit to a number of bond dissociation energies which are not well established, e.g. D(GeH,-H), D(SiH,-H), D(PH,-H), D(NH,-H), and D(N2H,-H). The availability or otherwise of the radical stabilization energy can also affect the fraction of energy entering the various energy levels of the HF and generally the thermochemistry is the major influence on the results. However, it is not the only influence. Thus for the compounds CH4, SiH,, and GeH, the total fraction of energy in the HF entering vibration (6) is similar (60%), as are the energy distributions, but on going to substituted methanes, as the size of the attached group increases, deviations from this pattern are seen.173s174For C2H6 = 62%) there is little deviation but for CMe4,f, has decreased to 56%. More striking is the change in the population of the highest vibrational level produced: for C2H6,v” = 3, it is 0.36 and drops to 0.15 for CMe,. The population of this level is sensitive to the thermochemistry, since there is usually just enough energy to populate it, but in these cases the thermochemistry is similar. It is suggested that this effect is caused by the bulkier radicals such as neopentyl impeding the departure of the HF from the reaction site, with subsequent ‘encounters’ between the two leading to sharing of the HF vibrational energy. In general, the vibrational energy disposal is similar to that observed in the three-atom F HX reaction, but the rotational energy disposal differs both generally and in features particular to a given reaction. Overall the amount of rotational energy taken up by the HF is less for the organic reactants than for a diatomic molecule, which may imply that the other product, the polyatomic radical, is taking away some of the rotational energy, which cannot occur in the three-atom case. The rotational distributions are much less well characterized than those for vibration, but some interesting differences for several compounds have been discovered. For example, a large degree of rotational energy disposal in the HF formed

uo

+

Gas Kinetics and Energy Transfer

76

from SiH4 and GeH, relative to MeX has been found and is parallelled by a much larger reaction cross-section for the first two compounds. It is suggested that the two observations are connected; the large cross-sections for reaction lead directly to highly rotationally excited products. However, the problems of such simple interpretations are seen in the same studies where it is shown that despite the very similar reaction rates of C2Hs and Me20, they lead to very different rotational distributions in HF formed from them."'' Chemiluminescencefrom Polyatomics and Related Systems. Until 1974 the applications of the arrested relaxation technique had been limited to the observation of emissions from diatomic products. In that year, J. D. McDonald and his co-workers published a paper in which they analysed in some detail the problems associated with detection and analysis of i.r. emissions from polyatomics under arrested relaxation conditions, and described the construction of an apparatus, shown in Figure 3, to perform such experiments. The major features of the equipment, essential to overcome the problem of low signal-to-noise ratio expected, were the use of a Michelson interferometer in the detection system, with Fourier transform of the interferograms and the immersion of the whole apparatus, including the interferometer, in a liquid nitrogen jacket. The equipment has been used to study the reactions of F atoms with olefins and aromatics and their halogen-substitutedderivatives,"' reactions of C1 atoms with some halogenated olefins and ally1 bromide,182 and reactions of 0 atoms with 3-chlorocyclohexene and 5-chloro-1-pentene.lE3 Reactions of F atoms (and C1 atoms) with olefins proceed by two paths, abstraction and substitution, viz.

F

+ C2H3X

+ C2H2X + X + C2H3F 4

HF

(39)

From classical kinetics and molecular beam studies it is known that abstraction occurs by direct encounter and gives little internal energy to the organic fragment while the substitution reaction involves formation of an intermediate complex. Two notable features of the i.r. chemiluminescence results for the abstraction reactions are (i) in some cases emissions are observed from the radical as well as the HF, (ii) the HF vibrational energy distribution is dramatically different from that which is observed for F atom abstraction from saturated molecules. Typically the population ratio of the d' = 1 and v" = 2 levels, N,/N,, is 0.2 to 0.5 for saturated substrates such as H2 and CH,, but rises to 1.2 to 1.5 for the unsaturated compounds. It is believed that this is not due to the thermochemistry of the reaction, as might be the explanation for saturated compounds (see HF chemiluminescence), but rather that the electronic structure of the unsaturated radical enhances the HF-radical long range interactions, so that some of the reaction exoergicity can be removed by the radical fragment as the products separate. Supporting evidence for this is (i) the observation of bands attributed to the C2H, radical in the F + C2H4 reaction and 179

lSo lS1 lE3

J. G. Moehlmann, J. T. Gleaves, J. W. Hudgens, and J. D. McDonald, J. Chem. Phys., 1974, 60,4790. J. G. Moehlmann and J. D. McDonald, J. Chem. Phys., 1975,62, 3052. J. G. Moehlmann and J. D. McDonald, J. Chem. Phys., 1975, 62,3061. J. F. Durand and J. D. McDonald, J . Chem. Phys., 1976,64,2518. J. T. Gleaves and J. D. McDonald, J . Chem. Phys., 1975, 62,1582.

,

SHIELD

L-----(

1 0 CM

Figure 3 Arrested relaxation apparatus, Key to lettering: ( A ) gas bearing; (B) scanning drive magnet: ( C ) scanning drive electromagnet: ( D )flexible bellows tube; ( E ) beam splitter, (FJfixed mirror for signul interferometer: (C) scanning mirror: ( H )germanium lenses: ( J ) reference interferometer. Dotted lines indicate light paths for signal, He-Ne laser reference, and white light reference sources (Reproduced by permission from J. Chem.Phys., 1974,60,4792)

FEED TUBE

F@AM INSULATION

--CONE

ADIATION SHIELD

-4 -4

B

P

2

E

GI

3

3

RJ

4

0

2:

%'

3

2

R 3

0

Gas Kinetics and Energy Transfer

78

analogous radicals in the benzene and substituted benzene cases, (ii) despite the higher population of the lower vibrational levels in the HF, the highest observed HF (v”,J”) level corresponds closely to the value expected if the full exoergicity of the reaction were available. There are exceptions to this last observation; reaction (41)

F

+ C3H,

--+

HF

+ C,H,

(41)

produces HF with a high energy cut-off well below the exoergicity, suggesting that the ally1 radical reorganization time is long compared with the time for HF to separate from it. A similar result was obtained for toluene. For the substitution reactions lS2 the results were interpreted by comparison of the observed vibrational energy distribution with the distribution to be expected if the reaction exoergicity were distributed statistically among the various vibrational modes of the product. It was found that for all aromatics, and for those reactions with substituted olefins in which F was substituted for C1 or Br, the product vibrational energy was partitioned statistically. For olefins in which the F was substituted for H or Me, the distribution was non-statistical. It is known from other studies that the intermediate formed by addition of the F atom to the olefin has -400 kJ mol-’ excess energy and survives at least several rotational periods before ejecting an atom or radical. This is long enough for its energy to become statistically distributed before the atom or radical is ejected. It is argued therefore that any non-statistical distribution in the products must arise from effects which occur in the exit channel of the reaction. In the ejection of H or Me from the intermediate there is known to be an energy barrier to surmount, but for C1 and Br removal the barrier is negligible. The non-statistical distribution in the products thus reflects distortions of the energy distribution in the molecule occurring in passing across the exit barrier. However the occurrence of such effects is not sufficient to yield an observable non-statistical distribution. The molecular distributions are being observed at times of the order of milliseconds after the reactive collision, which is sufficient time, in many cases, for intramolecular relaxation of the original vibrational distribution. Durana and McDonald,’ 8 2 on reviewing their results for both F atom and C1 atom substitution reactions, suggest that the density of states in the excited molecule may be used as an indicator for the rate of intramolecular relaxation. On the time scale operative in this work it seems that product molecules with vibrational state densities > lo4 cm- are likely to relax to a statistical energy distribution before observation even if they have a non-statistical distribution immediately after reaction. In a similar study of the reaction of 0 atoms with 5-chloropent-1-ene and 3-chlorohexene, vibrationally excited HCI was observed in both cases,183 This must arise from rearrangement of the initial 0 atom adduct to the double bond to give a carbonyl compound since HCl elimination is only energetically possible if such compounds are formed. The vibrational energy distribution in the HCl is remarkable for two reasons, (i) it is virtually identical for the two compounds and hence independent of the site at which the molecule was originally energized, (ii) it is markedly non-statistical with the d’= 2 state being the most highly populated. These findings indicate that the energy in the adduct must have become completely randomized before the elimination step and the non-statistical energy distribution in the product must indicate effects arising in the exit channel of the reaction as in some of the substitution reactions.

’

Chemiluminescence in the Gas Phase

79

+

Miscellaneous Rovibrationally Excited Systems.-0 CS,. Reaction of O(3P)with CS2 is capable of producing laser emission via the principal pumping reaction

0 + cs -+

co + so

(42)

which is 357 kJ mol-’ exothermic; Smith has reviewed earlier work on this system. The characteristics of reaction (42) are reasonably well known, but details of the 0 + CS2 reaction are less well understood, particularly the relative importance of the three possible channels (CS

o+cs,+

+ so

{ ocs+ s

CS, SO, and OCS have been detected previously and recently S2 has also been found, so that positive evidence exists for all channels. Using crossed molecular beams, Hudgens et have observed the i.r. emissions from the reactions 0 + CS and 0 + CS,. From the latter, emissions from CS,SO, and CO were observed but not OCS: here the CO vibrational spectrum had two maxima, one at very low vibrational energies, the other at v” x 7. In contrast, that from 0 + CS had one maximum at v’’ w 12, in agreement with other recent work.lE5 The difference between the two spectra was taken as evidence that the CO did in fact originate from a path of 0 + CS2 rather than from secondary reactions in the system: the fraction going by this path was estimated to be 10%. Using molecular beamlmass spectrometry, Slagle et ~ 1 2 . lestimate ~~ that the OCS-producing path constitutes -9% of the reaction. It is difficult to reconcile this value with the fact that no OCS i.r. emissions were observed by Hudgens et al., unless it is assumed that negligible amounts of the reaction exoergicity are entering OCS vibrations. Data on collisional quenching of vibrational states of CO are essential for modelling the 0/CS2 laser and there have been a number of recent i.r. emission studies using fast-flow discharge systems to this end for 3 < w’’ < 18 with a number of quenching ga~es.l~’*’~~

F2 + H2. Visible emissions from H2 + F2 flames are due to transitions from vibrationally excited (d’ = 4-9) HF molecules with Ad’ = 4-6. Much of this emission is due to the H + F, reaction which can populate HF (d’< lo), but in a recent study Ganguli et have shown that other reactions may also contribute. They caused H, to react with partially dissociated F2 in a flow system and, under the conditions used, the F + H2 and H + F2 reactions were over and most of the HF had radiated after -50 ms, but weak emissions from HF d’ < 9 could be observed at much later times. The intensity was a maximum when the H2 flowrate was 5 % less than the F, flowrate. It is suggested that the excited HF arises either from three-body combination of H + F atoms or from H atom recombination followed by energy transfer to HF.

-

J. W. Hudgens, J. T. Gleaves, and J. D. McDonald, J. Chem. Phys., 1976,64,2528. N. Djeu, J. Chem. Phys., 1974,60,4109. lE6 I. R. Slagle, J. R. Gilbert, and D. Gutman, J. Chem. Phys., 1974, 61, 704. M. Braithwaite and I. W.M. Smith, J.C.S. Faraday ZZ, 1976, 72,288, 299. lE8 Y.S. Lieu, R. A. McFarlane, and G. J. Wolga, J. Chem. Phys., 1975, 63,228, 235. lE9 P. S. Ganguli, B. L. Hertzler, and M. Kaufman,Chem. Phys. Letters, 1976, 37, 310. lE4 IE5

Gas Kinetics and Energy Transfer

80

O(3P)+ Hydrocarbons, Becker et a1.190have studied emission from vibrationally excited OH produced from reactions of 0 atoms with C2H4, C3Hs, and HCHO. Overtone bands Av" = 7-4 were observed possibly up to v" = 11 and certainly d' < 10 with considerable intensity: the source reaction was considered to be O+CHO+OH+CO

(43)

which is sufficiently exoergic to produce v" = 11. Analysis of the rotational distribution in w" = 10 enabled deduction of the thermochemistry and hence Ag(298 K) = 44.8 f 4 kJ mol" for the CHO radical. (HI), + F,. Dimeric HI is found in concentrations as high as 5% in supersonic beams of HI. Durana and McDonald 19' have produced such a beam and allowed it to intersect an effusive beam of F2 at total pressures <7 x Pa. The i.r. emissions were observed and simultaneously the (HI), concentration was monitored mass spectrometrically. Emission was observed from HF (v" = 1,2,3): emissions, if any, from IF could not be monitored because they were outside the frequency range of the detector. When dimers were removed from the beam by heating the HI beam or reversing the reactant sources, the HF emissions disappeared. Furthermore care was taken to remove any H2 impurity to eliminate the possibility of reactions between it and F or F, generating the HF. It is suggested that the source of HF is one or both of the reactions F, F,

+ (HI), --+ HF + HI + IF, + (HI), -+ HF + HI + I + F,

AH = -389 kJ mol-'

(44)

- 109 kJ mol"

(45)

AH=

Reaction (44) might be expected to yield HFv" < 10, and (45) v'' < 3, which is the observed limit. The possibility of contributions from (HI)n,n >, 3 cannot be entirely excluded. Formation of Gaseous HNC. Although emissions from interstellar space have been assigned to HNC, the molecule has never before been observed terrestrially in the gas phase. Arrington and Ogryzlo l g 2report its formation in a flow system, treating active nitrogen with HCN, C2H2, C2H4, MeCN, MeBr, MeI, and a mixture of CNBr and H, and also in the reaction of H atoms with CNBr. 1.r. emission was observed and the main features were intense bands at 3.02pm (HCN) and at 2.74 pm assigned to the N-H stretch in HNC. A sufficiently intense spectrum was obtained from the reaction of active nitrogen with MeBr to allow the resolution of the rotational structure. O('D) + H,. Flash photolysis of H 2 / 0 3 mixtures decomposes the O3 to yield O(lD) which reacts rapidly with H2 to produce OH v" < 4. Downey et ~ 1 . ' ~ ' found that with sufficient dilution with a rare gas the vibrational excitation of the OH could be converted into rotational excitation at a rate which exceeded the rate of R -+ T transfer. In this way a rotational population inversion was produced lgo

191

lg2 lg3

K.H. Becker, H. Lippman, and U. Schurath, Ber. BunsetzgesellschaftPhys. Chem.,1977,81,567. J. F. Durana and J. D. McDonald, J. Amer. Chem. SOC.,1976,98,1289. C. A. Arrington and E. A. Ogryzlo, J. Chem. Phys., 1975,63, 3670. G. D. Downey, D. W. Robinson, and 1. HSmith, J. Chem. Phys., 1977, 66,1685.

Chemiluminescence in the Gas Phase

81

which could sustain laser action. The production of a pure-rotational collisionally pumped laser was quite unexpected. Optimum experimental conditions were H2: O3 : M (where M is a rare gas) in the ratio 3 : 1 : 86 at a total pressure of 1.9 kPa. Lasing was observed for a number of rotational transitions in the v" = 0 and 1 levels of OH.

3 An Overview of Molecular Energy Transfer in Gases ~~

~

BY A. B. CALLEAR

1 Introduction In gases, energy-transferring collisions are continuously changing the quantum states of individual molecules. The transitions involve translational, rotational, vibrational, and electronic energy. A full description of the behaviour of a gas would require a great many kinetic steps. By selecting particular states for study in laboratory experiments, considerable progress has been made in the identification of these elementary steps, and in the measurement of their rates. For example, we know that in our atmosphere, when a nitrogen molecule occupies the first vibrational level, the rate of direct conversion of the vibrational energy into translation is very slow, requiring some lo9 or so gas kinetic collisions. This extreme metastability of the vibrational energy of small molecules is a remarkable feature of the subject. An exchange of vibrational quanta between N, molecules, however, is comparatively fast, requiring about lo3 collisions. N2(u = 2) + N2(u = 0) Ft 2N2(w = 1) The V-V transfer to O2 would be slower because energy would have to be converted into translation. In air, the CO, would have a dominant role in securing vibrational transitions of the N2 because the step N~(w = 1) + C02(000)+ N,(v = 0) + C02(001)

exciting the antisymmetric mode v 3 of the CO,, is very fast. Vibration-translation relaxation of C02(001) is rapid because it may occur in small steps, down the v 3 + v1 --+ v2 ladder. It is a common aspect of several types of molecular energy transfer that the greater the energy to be converted into translation the less probable the process becomes. Thus transfer between the closely spaced rotational states of N, occurs at practically every collision. Through such selective studies our knowledge has advanced sufficiently to permit a description of some of the main processes which are occurring in our environment. Amongst the earliest of experiments pertaining to molecular energy transfer, in the 1920's, was the observation that the velocity of sound in COz is a function of the gas pressure and the frequency of the sound waves. At low frequencies the velocity depends on the internal specific heat of the molecules. At sufficiently high frequencies and low pressures, excited vibrational and rotational states cannot interchange with translation rapidly enough to participate in the compressional heating and cooling cycle associated with sound propagation, and the velocity increases. Studies of this dispersion of the sound velocity became the principal technique for studying rotational and vibrational relaxation. 82

An Overview of Molecular Energy Transfer in Gases

83

However, more common nowadays are relaxation methods in which a system is disturbed from equilibrium, and thereafter the time behaviour of a particular quantum state, or group of states, is monitored spectroscopically. Usually the relaxing species is in great excess so that the decay behaviour is pseudo first order. The bimolecular rate coefficient is then found by division of the pseudo first-order coefficient by the concentration of relaxing gas. During the last decade there has been a great advance in laser techniques. In this essay a few topics have been selected, to sketch an overview of the subject. 2 Vibrational-tolTranslational Energy Transfer The vibration-to-translation relaxation of CO(v = l), with various collision partners, was investigated some years ago by Millikan.' In a flow system at ambient temperature, CO was excited with intense i.r. radiation, and resonance fluorescence was observed downstream. From the increase in the decay rate due to added gases, rate coefficients were measured. In Table 1 these have been converted into P I * , the probability of deactivation per collision, by dividing the bimolecular rate coefficient by the collision frequency. These vintage results illustrate very well the reduced mass effect, i.e. that the probability increases with decreasing mass of the deactivating atom.

Table 1 Probabilities per collision of V-T relaxation of CO(u = 1) with collision partners of diflerent mas's Relaxing gas PlO (expt.1 PI0

Hz HD D, He 5 x 10-7 2.9 x 10-7 2.6 x 10-8 3.1 x 10-8

Ne

co

4.3 x 10-9

40-9

2.4 x 10-4 8.3 x 10-5

3.3 x 10-8

0.9 x 10-9

10-3

10-4

(CalC.1

The relaxation probabilities are low because the intermolecular repulsive forces between CO and the collision partner are soft, the potential energy changing only slowly with separation. During collision the forces therefore tend to act on the centre of mass of the diatom, there being insufficient impact on the particular atom that is struck to excite the vibration. The lighter the deactivator the greater is its velocity and the more effective it becomes because the duration of the collision is shorter. In the limit of an infinitesimal collision duration, the energy would be preferentially transferred to the atom that is struck. Rapp and Kassal have given a full discussion of classical theories, and comparison with quantum mechanical models. These aspects are illustrated in Figure 1 for a collinear collision between CO and an atom. The potential energy is conveniently approximated as Cexp[ - ( x X)/Z], where x is the distance between the centre of mass of the CO and the colliding atom, Xis the internal vibrational co-ordinate of the CO, and C is a constant. The quantity 1 is sometimescalled the characteristiclength. The potential energy curves of Figure 1 correspond to the function Cexp( - x/Z), representing the intermolecular potential energy with X constant. The upper curve relates to CO(v = l), being continuously equidistant from the lower CO(u = 0)curveby hv, where v is the vibrational frequency. For a collision of CO(u = I), with a relative translational energy k T at ambient temperature, the classical turning-point is at B. Region A is the turning-point for

-

R.C. Millikan, J. C k m . Phys., 1963,38,2855. D. Rapp and T.Kassal, C k m . Rev., 1%9,69,61.

Gas Kinetics and Energy Transfer

84

Distance between C O and He atom, marked at intervals of 0.lA Figure 1 Variation of potential energy with distance for collision of CO with He

the relaxed molecule. If the transition occurred at this energy it would be associated with a jump of nearly 0.5 A in the x co-ordinate and this has a very small probability. The classical amplitude of the CO(v = 1) vibration is about 0.093 A, being the full swing of one of the atoms from its inner to its outer turning-point. So that at B the change of intermolecular potential energy with the oscillation of the vibrator is small compared with hv, and the coupling of vibration and translation is weak. It is difficult for the system to achieve the required momentum change, on the gently repulsive potential energy snrface. If the relative kinetic energy is increased to hv for CO(v = l), turning-points C and D arise, which are now separated by only 0.1 A. The potential energy curves are much steeper at the turning-points, and a relatively strong coupling of vibration and translation results. Therefore the vibration translation relaxation of small molecules in a gas must occur in the high energy tail of the kinetic energy distribution. This simple, one-dimensional representation of the problem has been treated quantum mechanically and detailed equations for application to gases were worked out by Schwartz, Slawsky, and Herzfeld (SSH theory). This first order perturbation theory provides a useful guide to the order of magnitude of the relaxation probability, P l 0 , which takes the form

p is the reduced mass of the collision pair, thep, are the relative momenta in vibrational state i with x = 00, and Vlo is a vibrational matrix element.4 T,,is the dominant

quantity and has been called the translational overlap T I 0

=

I+

mU(x)~o(x)~l(~)~

-00

R. N. Schwartz, Z. I. Slawsky, and K. F. Herzfeld, J. Chem. Phys., 1952,20, 1591. A. B. Callear and J. D. Lambert, Comprehensive Chemical Kinetics, 1969, 3, 182.

An Overview of Molecular Energy Transfer in Gases

85

U(x) is the intermolecular potential energy, and F,(x) and F,(x) are standing waves of unit amplitude corresponding to the translational motions associated respectively with the 'u = 0 and 'u = 1 states of the system. Approximate F,(x) for the C, D trajectories are included in Figure 1. The main contribution to T I , is in the region of the turning-point D. At larger values of x, where the waves execute regular oscillations, the positive and negative parts of the overlap interfere and cancel out. For systems of larger reduced mass, e.g. CO + Ar, F,(x) executes regular oscillation at smaller x which greatly reduces the magnitude of the translational term, so that the reduced mass effect reflects the dependence of wavelength on mass. For the exponential potential energy function, the translational term is given by

-T?O POP1

- 4n4v214exp[ - 2n1(pO - p l ) / f i ] .

With harmonic oscillator wave functions for the vibrational terms, some P,, relevant to this discussion, using the potential energy curves of Figure 1, have been calculated and are listed in Table 2.

Table 2 SSH probabilities for V-T relaxation of CO(u = I) Relative translational energy

He Ar

0.1 hv 1.6 x 10-7 3.6 x lo-'*

hv 1.1 x lo-' 5 x 10-

Included in Table 1 are Millikan's calculations based on SSH theory, which requires averaging T i over the velocity distribution. It is notable that the theory greatly exaggerates the reduced mass effect, which is commonly found. Nevertheless, it does provide a simple model which accounts for several aspects of vibrational energy transfer and has had a valuable role in the evolution of the subject. The main handicap in trying to test theories is usually ignorance of the form of the interaction potential. The rates are extremely sensitive to the steepness of the potential near the turning points. Secrest and Johnson have obtained exact solutions for a harmonic oscillator undergoing a collinear collision on an exponential, repulsive potential. If the relative kinetic energy is less than Utv, adequate for most thermal systems, the discrepancies with SSH theory are quite small for all mass parameters. Obviously any collinear model is deficient because the real problem is three-dimensional, with rotational transitions accompanying vibrational relaxation. The rates of vibration-translation relaxation of I: ground states of diatomic molecules increase with decreasing vibrational freq~ency.~ For example, for 0,-02 collisions at ambient temperature Pl0 = 5 x lo-', and for C1,-Cl, collisions at ambient temperature P,, = 3 x lo-'; the frequencies of the first fundamentals are 1556 cm-' and 557 cm-', respectively. This aspect can be understood with reference to Figure 1. For a fixed relative translational energy of say kT, the distance between the A,B turning-points increases with increasing vibrational frequency which decreases the rate; for the exponential potential energy function, xB xA= I ln[l + hv/kT].

-

-

D. Secrest and B. R. Johnson, J. Chem. Phys., 1966,45,4556.

Gas Kinetics and Energy Transfer

86

In the translational overlap, this decreasing rate with increasing energy to be converted into translation is manifest as the change of momentum which appears in the exponent. The energy conversion to translation in an inelastic collision is -AE, minus the isothermal change of internal energy. Vibration-translation relaxation of polyatomic molecules was first investigated with the ultrasonic methods. A remarkably simple relationship, discovered by Lambert and SalterY6is that the logarithm of the number of gas kinetic collisions for V-T relaxation is roughly proportional to vmin, the lowest fundamental frequency of the molecule. Their diagram is reproduced in Figure 2, and shows that hydrides belong to a separate class, undergoing significantly faster relaxation than nonhydrides

30

v / cm-’ Figure 2 The Lambert-Salter plot: 0, molecules containing no H atoms; 8 , molecules containing one H atom; @, molecules containing two or more H atoms (Reproduced by permission from Proc. Roy. SOC.,1959, A253,277)

Lambert and Salter interpreted their empirical correlation as follows. In most polyatomic molecules the energy levels are such that the energy corresponding to the lowest vibrational frequency is much larger than the energy difference between the lowest and the next highest frequency. The rate-determining step for population of all the modes is therefore relaxation of the first vibrational level, because excitation of this level demands the greatest vibration-to-translation energy conversion. This interpretation has been largely confirmed and extended by subsequent laser experiments. Even when the lowest and next highest frequencies differ by a factor of two or so, a substantial interconversion of vibrational and translational energy can be circumvented by pooling; e.g. if v1 is approximately twice v2 then J. D. Lambert and R.Salter, Proc. Roy. Soc., 1959, A253,277.

An Overview of Molecular Energy Transfer in Gases

2 ABC(010) e ABC(100)

87

+ ABC(000).

For a given vibrational frequency, diatomic hydrides would be expected to undergo faster V-T relaxation than non-hydrides because the H atom has a large amplitude of vibration. The significance of the vibrational amplitude has been discussed earlier in relation to Figure 1. In the limit of zero amplitude the coupling of vibration and translation would vanish. In polyatomic 'molecules containing hydrogen, vminmay or may not be associated with a large displacement of a H atom, depending on the form of the normal co-ordinate of that particular vibrational mode. However, Stretton found satisfactory agreement between the experimental results of Figure 2 and SSH calculations, which establishes that the faster hydride relaxation is a result of their greater vibrational amplitude. Stretton discovered that a universal choice of I = 0.18 A gave a reasonably good match of SSH theory with experiment. It may be concluded, therefore, that the V-T relaxation of polyatomic molecules is understood in good outline. The more recent laser techniques have revealed some of the details of the energy equilibration between the modes of vibration. For example, Siebert and Flynn * excited OCS to 2v2 with radiation from a Q-switched C 0 2 laser, and were able to detect i.r. fluorescence from each of the vl, v2, and v3

'

O C S energy levels Figure 3 Vibrational levels of OCS. Heavy arrow indicates laser pumping frequency (After Siebert and Flynn *)

fundamentals, following the pulsed excitation. The energy levels are indicated in Figure 3. Only a tiny fraction of the molecules undergo radiative decay and detection of the extremely weak emission was facilitated by using signal averaging over a great many pulses. The rise of the v2 emission was too fast to measure, presumably because of the occurrence of the resonant step OCS(020)

+ ocs(o0o) e 20cs(010).

' J. L. Stretton, nuns. Faraday SOC.,1965, 61, 1053. *

D. R. Siebert and G. W. Flynn, J. Chem. Phys., 1976,64,4973.

Gas Kinetics and Energy Transfer

88

The measured rise time of the v3 emission corresponded to 145 collisions of the OCS(020) generated initially, and the mechanism is discussed in detail. The v1 rise was found to be slower than the v3 rise by about six fold. Following this initial period of rapid energy partitioning amongst the modes of vibration, the collisionally coupled system decayed comparatively slowly with a single relaxation time, corresponding in pure OCS to 7800 collisions, which agrees well with ultrasonic measurements. Of course there remain a number of uncertainties and complications in this experiment which require clarification. But this application of laser techniques, along with others of a similar kind, have now validated the Lambert-Salter interpretation of the simple dependence of the V-T relaxation rate of polyatomic molecules on vmln. One further aspect of V-T relaxation which merits brief comment is the vibrational selection rules. In thermal systems the great majority of simple molecules in low quantum states are expected to undergo V-T relaxation predominantly by unit changes of the vibrational quantum number. A A v = 2 change obviously incurs a doubling of the energy to be interchanged with translation; also, for such a change the vibrational matrix element is usually much smaller than for Av = 1. :Pu,u-2 for V-T However, there are precious few measurements of relaxation at ambient thermal energies. A common difficulty with such an experiment is that V-V exchanges have a vastly greater probability and tend to establish a statistical distribution in the excited vibrational levels. Brown and Klemperer = 15 and 25), finding that A v = 2 investigated the V-T relaxation of 12(B3rIo;)(v transitions are as probable as A v = 1. The vibrational spacing is only 100 cm-', which may account for the high Av = 2 probability in this system. If the relative kinetic energy is large compared with hv, the vibrational quantum number may change by several units. Schinke ei al.,'' for example, studied the excitation of HZ in collision with H', in crossed beams. With a relative kinetic energy of 20eV, transitions with A v G 5 were detected, Av = 1 having the highest probability. The SSH theory also predicts that Pa,a-l = vP1,', i.e. that the rate of V-T relaxation should be proportional to the vibrational quantum number for the harmonic oscillator model. No experimental test of this rule has been reported. It requires measurement of the V-T rates of the low vibrational states of a diatomic molecule.

-

-+

3 Vibrational-to-VibrationalEnergy Transfer Although the relaxation of CO(v = 1) is slow in the inert gases, as described in the previous section, addition of a polyatomic species, with a vibrational frequency close to that of CO, induces a fast decay of the excitation. The catalysis of the relaxation is due to intermolecular exchange of vibrational energy, or V-V transfer. The first convincing observation of fast V-V transfer with detection of the excited acceptor was a study of the relaxation of 12C1602(001),in which excitation of the antisymmetric stretching mode was achieved with Q-switched C 0 2 laser radiation." Addition of a triatomic gas, X, increased the initial decay rate of '2C1602(001),and R. L. Brown and W. Klemperer, J. Chem. Phys., 1964,41,3072. lo 11

R.Schinke, H. auger, V. Herman, H. Schmidt, and F. Linder, J. Chem. Phys., 1977, 67, 1187. J. C. Stephenson, R. E. Wood, and C. B. Moore, J. Chem. Phys., 1968,48,4790.

An Overview of Molecular Energy Transfer in Gases

89

a corresponding initial rise of X(OO1) was observed. The excited molecules were detected by monitoring their i.r. emission.

+

12c1602(001) X(o00)# 12c'602(000)

+ X(oo1)

Such processes are reversible and may proceed to 'equilibrium' when

AE is the difference between the X vibrational quantum and that of C02.Such V-V transfer was demonstrated for X = 12C160180 , 13C160214N2160, , and 15N,160. A different approach to observation of excitation in the acceptor was the detection of OCS(OOl), produced l 2 in the reaction N,(v = 1)

+ OCS(OO0) Ft N ~ ( v= 0) + OCS(OOl),

via its microwave spectrum. The rate of exchange of vibrational quanta between molecules decreases with increasing energy discrepancy, IAEI. Results for diatomic non-hydrides are shown in Figure

r

.-0

\ N2 ,NO ( A )

.-ln

5c) - 3 9

k

\ \ \

NO,CO

o

\@ \ \

b -4-

Y-

ln

C

e

N2,CO

-e

> 7 -5-

\

rc 0

$NO

\

CI -6-

\

B0

\

co,o*@,

L

Q

9

-7-

(5,

0 1

0

100

200

-A

I 300 /cm

LOO

500

6 I0

-l

Figure 4 Gross dependence of V- V exchange probability on energy discrepancyfor non-hydride diatomic molecules (295 K)

The point N2,NO(A), close to exact resonance (AE = 0), corresponds to transfer between NO(A2C+)(v = 0) and N2(X'C~)(w= l),and was measured by observing the effect of N2 on the U.V. fluorescence of NO. The remaining points relate to M. Bogey, A. Bauer, and S. hhes, Chem. Phys. Letters, 1974, 24,516.

90

Gas Kinetics and Energy Transfer

experiments in which both molecules are in their ground electronic states.13 The scatter about the broken line drawn through the points reflects differences in the nature of the interactions which cause the transitions to occur, for example differences in the intermolecular potentials. For these systems, energy transfer is induced by the short range repulsive forces, as for V-T relaxation. The probabilities vary from loe3 with AE = 0 to lo-’ for AE = -600 cm-I. The decrease of probability with increasing IAEI can be understood from a consideration of Figure 1. With AE = 0, the potential energy curves, and hence the pairs of turning-points, come into coincidence; there is no momentum restriction. With increasing IAEl, the distance between the turning-points increases. From SSH theory, the probability of the V-V exchange, AB(v = 1)

+ CD(w = 0)

4

AB(v = 0) + CD(V= l),

takes the form 16V& V&T2p2 PI0 = 01

fi2PoP1

The translational overlap term, T, is similar to that for V-T relaxation, with the v2 in the pre-exponential factor replaced by (vAB - v , - ~ ) . ~The exponential term, which is dominant, is still controlled by the change of linear momentum. The probability contains the product of the squares of the vibrational matrix elements of each molecule. (A modified equation for T is required to treat the case of close or exact resonance.) The SSH calculation agrees reasonably well with the broken line of Figure 4. The slope of the broken line of Figure 4 is approximately the same as that of the non-hydride Lambert-Salter correlation, Figure 2, corresponding to a drop of lo4 in the transfer probability for conversion of 600cm-’ of energy into translation. This approximate equality of the slopes was first noted by Lambert.14 In the framework of the SSH model, the common rate of variation of the probability with the magnitude of the energy converted into translation arises because the translational overlap term is the same. Figure 5 is a plot of log probability versus AE, for a set of V-V experiments conducted with 12C1602(001)described earlier in this section.” For small lAEl, the exchange rates are much faster than found for the exchange between the diatomic molecules shown in Figure 4. Indeed the transfer of vibrational quanta between COz molecules of different isotopic composition can occur at the gas kinetic collision rate. It was suggested by Mahan I5 that long-range, polar interactions are responsible for these fast rates close to resonance. The v3 vibration of COz is associated with an oscillating electric dipole, and such an oscillating dipole exerts a force on a neighbouring C 0 2 molecule to induce a change of its v3 normal co-ordinate. This long-range coupling, through the dipole field, can cause V-V transfer to occur, provided the energy discrepancy IAEI is small. l3

l4

A. B. Callear in ‘Relaxation Methods in Gases, Physical Chemistry’, ed. Eyring, Henderson, and Jost, Academic Press, London, 1975, vol. VIB,p. 719. J. D. Lambert, ‘Vibrationaland Rotational Relaxation in Gases’, Clarendon Press, Oxford, 1977. B. H. Mahan, J . Chem. Phys., 1967,46,98.

An Overview of Molecular Energy TranNer in Gases

0

20 0

91

LOO

-A E /cm-' Figure 5 l%e V-V exchange probabilities from 12C1600,(OOl) to various collision partners a function of AE (298 K ) (After Stephenson et al.")

CIS

In a quantitative theoretical treatment, Sharma l 6 calculated the rates of dipole4ipole induced V-V transfer between 12C1602(OOl)and some of the acceptor molecules in Figure 5. Good agreement with experiment was achieved for transfer to 12C'60'80, with AE = - 18 cm-l. However, to match the experimental rate coefficient for transfer to 13C1602,AE = -66cm-', it was necessary to include a contribution due to the dipole-octupole interaction. The dipole-octupole coupling allows a simultaneous change AJ = + 3 of the rotational quantum number of the acceptor, which on average lowers the energy to be converted into translation by ~ 4 cm-'. 5 Reduction of IAEI by multiple changes of J, which can be induced by polar interactions of high order, has subsequently been exploited by many authors to interpret their experimental data, The credibility gaps need detailed investigation and in principle it is possible to examine simultaneous rotational changes with molecular beam techniques. Sharma and Brau considered the near resonant energy transfer between C02(O01)and N2, and matched the experimental results fairly convincingly with a model in which the dominant interaction is between the C02(001) dipole and the N2 quadrupole. Energy transfer from the diatomic molecules CO, HCl, HF, and DF in high vibrational levels has been investigated by Smith and his collaborators. For example, in the work of Hancock and Smith," gas streams containing CS2 and atomic oxygen were allowed to mix in a spherical vessel to generate CO(14 > z1 > 3) by the reactions 0 cs2 -+ cs so

+ + 0 + cs cot + s. -+

The excited molecules were monitored from their i.r. fluorescence. From an analysis of processes populating and depopulating particular quantum l6

R. D. Sharma, Phys. Rev., 1969, 177, 102. R. D. Sharma and C. A. Brau, Phys. Rev. Letters, 1967, 19, 1273. G. Hancock and I. W. M. Smith, Appl. Opr., 1971, 10,1827.

92

Gas Kinetics and Energy Transfer

states in the presence of relaxing gases, probabilities of V-V transfer to 02,N,, CO, NO, and OCS were measured. Results are included in Figure 6, where the logarithm of the exchange probability divided by the vibrational quantum number is plotted versus AE. Theory requires that the probability depends on vibrational matrix elements which in these systems introduces a factor which is proportional to the vibrational quantum number of the CO'. This factor is divided out so that the effect of changing AE (due to the anharmonicity of the CO vibration) can be isolated and examined.

100

200

300

400

-A E / cm-' Reduced probabilities of V-V transfer from CO' to various acceptors (295 K) (Reproduced by permission from Appl. Opt., 1971,10, 1827)

Figure 6

With IAEI c 100cm", the probabilities agree well with Sharma's theory, assuming dipole-dipole interaction, but not with IAEI > 100 cm" where the theoretical rates, ignoring the dipole-octupole interaction, are too small. Close to exact resonance there is little variation with IAEI, indicating that the discrepancy between the vibrational frequencies may be taken up by means of simultaneous rotational transitions. Transfer to OCS is fast because its dipole derivative is much larger than those of CO and NO. The slowest rates are to the homonuclear O2 and N,. Lines drawn through the data have the same slope as the Lambert-Salter non-hydride plot or

An Overview of Molecular Energy Transfer in Gases

93

the Figure 4 plot; for a given acceptor, the rate of change of log probability with AE is approximately the same. In a more detailed theoretical discussion, Dillon and Stephenson conclude that the cross-sections for exchange of more than one vibrational quantum are substantial in these experiments with excited CO. 4 Electronic-to-Translational Energy Transfer In this section, conversion of electronic-to-translational energy in atom-atom collisions is discussed. Two rather different situations are considered: first, one in which the potential energy curves are continuously separated by approximately the same energy, as in vibrational relaxation; and secondly, the case where the potential energy curves cross. The intramultiplet relaxation of the first 2P states of the alkali metal atoms, in collision with the inert gases, belongs to the first category, at least for the heavier alkalis. If, for example, sodium vapour is irradiated with just one of the D lines, isolated with a monochromator to populate either the J = 1/2 or 3/2 states, in the presence of inert gases both D lines are observed in fluorescence.

Being one of the simplest types of kinetic process, the mechanism is of considerable interest. The spontaneous emission rate of the excited atom is known and therefore, by studying the variation of the intensities of the D components as a function of [MI, .the rate coefficients can be evaluated. In the case of sodium at ambient temperature, IAEI 4 kT so that the ratio of the forward to the backward rate coefficients is 0.5, the ratio of the degeneracies of the 1/2 and 3/2 states. The measurements are not straightforward because the resonance radiation undergoes imprisonment or trapping within the reaction volume and the effective lifetime is longer than the radiative lifetime. According to Dashevskaya et aLY2' there are two somewhat different mechanisms for the intramultiplet relaxation of the alkali 2Pstates in collision with the inert gases.

Region 1

1 Nuclear Separation

Figwe 7 Potential energy diagramfor collision of alkali atom with an inert gas atom l9

2o

T . A. Dillon and J. C. Stephenson, Phys. Rev., 1972, A6,1460. E. I. Dashevskaya, E. E. Nikitin, and A. I. Reznikov, J. C k m . Phys., 1970,53,1175.

Gus Kinetics und Energy Transfer

94

Figure 7 is a schematic potential energy diagram. At long range, region 1, the 2P3/2term splits into 2113/2and '2 molecular states; in the former the excited electron occupies a pn orbital, and in the latter the repulsive pa orbital. At smaller values of the internuclear separation, the 2113/2 and 2111,2states differ in energy by 2/3 AE, where AE is the multiplet splitting. The 211 states become repulsive at short range, region 2, as the inert gas atom, moving in along the nodal plane of the n electron, strikes the core of the alkali. Transitions occur both in regions 1 and 2. If IAEI % kT, relaxation in region 2 predominates because the steep, short range forces are required to induce the large electronic energy change (discussed previously in relation to Figure 1). The operator which causes transitions to occur in region 2 is rotation of the nuclei; the associated, time-dependent magnetic field induces a spin-flip, coupling the 0 = 1/2 and 3/2 states. The nuclear motion is treated classically (time-dependent, semi-classical perturbation theory), with trajectories calculated from the potential energy data of Baylis." But when the velocity is averaged over the initial and final states the derived dependence on the change of internal energy is the same as in the translational term T 2 of SSH theory, except that the momentum change corresponds to 2/3 AE, the energy separation in region 2. In region 1 the operator is just the radial motion of the nuclei, which mixes the = 1/2 components of the ' Z and 21-i1,2molecular states. The difference of energy is the perturbation which causes the transition to occur, and the probability is strongly dependent on the relative velocity. Relaxation by this mechanism is expected to be predominant if IAEI 4 kT.

Table 3 Cross-sections (A2)for the 'P, + 'P+ transition in Rb and Cs vapour 2o Partners

TlK

Rb-He AE = 238 ~ m - '

300 600 900

Rb-Ar

300 600 900

Rb-Xe

300 600 900

Cs-He AE = 554 cm-I

300 600 900

Region 1 1.4 x 0.16 0.52

Region 2 0.93 x lov2 0.047 0.10

Experimental 5.4 x loq2 0.28 0.90

3.2 x 2.3 x 10-4 1.6 x 10-3

2.7 x 10-4 1.3 x 10-3 2.6 x 10-3

4.0 x 10-4 2.3 x 10-3

2.7 x 10-7 3.5 x . 3.2 x 10-4

1.1 x 10-3 1.3 x 10-3 1.7 x 10-3

2.1 x 10-4 3.3 x 10-3 1.7 x

7.0 x 10-7 1.0 x 10-4 8.5 x 10-4

4.6 x 7.6 x 10-4 2.5 x 10-3

4.5 x lo-' 5.8 x 10-4 2.6 x 10-3

8.6 x

lo-)

In Table 3, calculations of Dashevskaya et al. are compared with experimental measurements of Gallagher,22who conducted a detailed investigation over a wide temperature range. Experiment and theory agree fairly well, and it would appear that the mechanisms of relaxation have been correctly identified. For Na(2P), Reid and Dalgarno 23D24 carried out a one-dimensional partial wave

23

W.E. Baylis, J. Chem. Phys., 1969, 51,2665. A. Gallagher, Phys. Rev.,1968, 172, 88. R. H.G.Reid and A. Dalgarno, Chem. Phys. Letters, 1970, 6, 85.

24

R. H. G. Reid, J. Phys. (B), 1973, 6,2018.

21

22

An Overview of Molecular Energy Transfer in Gases

95

I

200

600

400

-A E/cm-' Variation of cross-sectionwith AE for intramultiplet relaxation in Ar or He (300 K):

&He; 0,Ar

calculation and confirmed that in this system relaxation occurs by mechanism 1. Close agreement with experiment was found. In Figure 8 the dependence on AE of the logarithm of the collision cross-section for the intramultiplet relaxation is illustrated for He and Ar at 300 K. With the alkali results is included a measurement of the collisionally induced J = 3 + 4 transition of F~(u'D).~'For these systems in which the potential energy surfaces are approximately equidistant or parallel, energy transfer has a low probability if IAE I > 600 cm- . Chosen next as a complete contrast to the behaviour of the alkali atoms is the relaxation of O('D) to O(3P) by the inert gases. In this system, although AE = - 15 870 cm-', in collision with the heavier inert gases energy transfer occurs with high probability. The rate coefficients of Table 4 are as reported by Heidner

'

Table 4 Deactivation of O('D) at 300 K (from Heidner and Husain 2 6 ) Rate coeficient /an3 s-I He

Ne

Ar Kr

Xe

<7 1.1 7.1 1.5 1.0

x 10-16 x 1044 x 10-13 x lo-" x 10-10

Probability per collision <2 x 10-6 5 x 10-5 3 x 10-3

0.07 0.2

A. B. Callear and R.J. Oldman, Trans. Faruduy SOC.,1967,63,2888.

96

Gas Kinetics and Energy Transfer

and Husain,26 measured by producing O('D) by flash photolysis of 0,, and monitoring its decay by atomic absorption in the vacuum U.V. The cause of the fast relaxation of O('D) in collision with the heavy inert gases may be found by considering the sets of potential energy curves of Figure 9, recently published by Dunning and Hay.27 The 311 and 'Zc-states, correlating with O(3P), cross the 'Z' and 'A states which correlate with O('D). In the interaction with Kr and Xe, the O(lD) exhibits marked chemical affinity, acting as an electron acceptor, and the molecular states have ionic character. The potential energy curve crossing allows the transition to occur and in principle the rate can be evaluated using the Landau-Zener e q ~ a t i o n , ~a~ two-state, -~' time dependent, semi-classical perturbation theory. However, detailed calculations have not yet been reported. For the O('D), Ne interaction, from Figure 9 it appears that the lowest crossing-point lies at an energy of 0.39 eV above that of the separated atoms. The probability of deactivation of O('D) by Ne would be much smaller than that listed in Table 4 if the transition occurred at such a crossing-point.

L

1 1.0

2.0

3.0

4.0 1.0

1 1 2.0

1

3.0

t 4.0

Nuclear Separation / A

Figure 9 Potential energy curves for collision of 0 atoms with inert gas atoms (After Dunning and Hay 2 7 )

The intramultiplet relaxation of Cl('P), with AE = 881 cm-', also appears to have a high probability in collision with the heavy inert gas atoms, and the occurrence of curve crossing has been p o ~ t u l a t e d .In ~ ~collision, C1(2P,,2) splits into a E (ground state) and a I I 3 / 2 state.j' Presumably the transition occurs between the n3/2 state and the ITll2 state, the latter correlating with Cl(2Pl/2). In this section, two rather different types of E-T process have been considered. 26

27 28 29

30 31

R. F. Heidner and D. Husain, Inrernar. J. Chem. Kinetics, 1974, 6, 77. T. H. Dunning and P. J. Hay, J. Chem. Phys., 1977,66,3767. L.Landau, Physik. 2.Sowjetunion, 1932, 2,46. C. Zener, Proc. Roy. SOC.,1933, A M , 660. I. S. Fletcher and D. Husain, J.C.S. Faraday II, 1978,74,203. M. Krauss and P. S. Julienne, J. Chem. Phys., 1977, 67, 669.

An Overview of Molecular Energy Transfer in Gases

97

First, many atomic terms exhibit quite low probabilities of intramultiplet relaxation in collision with inert gases, depending in a similar manner on A E as V-T and V-V energy transfer. It remains to be seen how Cl(,P) can be understood when potential energy curves are available. The second case is one in which the two states belong to different atomic terms. It will then frequently be found that potential curves of pairs of molecular states cross, providing a direct route for relaxation if the crossing point is thermally accessible.

5 Electrdc-to-Vibrational Energy Transfer There are also two extreme cases of electronic-to-vibrationalenergy transfer to consider. One is a 'resonant' process which may occur on a gently repulsive potential energy surface and which usually changes the vibrational quantum numbers in the acceptor molecule by unity. The other type is the 'non-resonant' transfer in which the conversion into vibrational energy has a low efficiency; the non-resonant vibrational excitation may be a consequence of the recoil accompanying kinetic energy release on a very repulsive potential energy surface. Resonant transfer can be discussed in relation to Figure 1. Consider the intramultiplet relaxation Hg(3P1-+o) by collision with N2,in which the change of electronic energy of the Hg atom is - 1767 cmHg(3P1) + N2 W 3 p O )+ N2 The rate coefficient is 4.3 x lo-', cm3 molecule-' s - l at 300 K.32 If the potential energy surface is slightly repulsive as in Figure 1, for an initial relative kinetic energy of kT the classical turning-points for E-T relaxation would be well separated and the process has a low probability. But if the N, is excited to v = 1, the energy conversion into translation, which is the separation between the potential energy surfaces, is reduced to 563 cm- ; the corresponding turning-points are then located within a comparatively small distance of each other. Although the excitation of the N2 vibration limits the rate, the restriction is far outweighed by the reduction in IAE(,just as in a comparison of V-V with V-T energy transfer. The real potential energy surface for this reaction is probably attractive at long range, which steepens the repulsive potential for a given incident energy, bringing the turning-points into closer proximity. Evidence for vibrational excitation of N, in the Hg(3P,-ro) relaxation was reported by Horiguchi and T s ~ c h i y a . At ~ ~ low N, pressures the metastable Hg(3Po) is efficiently removed at the vessel walls, but the N,(w = 1) is not, apparently surviving a great many wall collisions. The N2(w = 1) therefore accumulates in the system and the effect of the reverse J = 0 -, 1 pumping could be detected. In general, for the collisional coupling of two of the spin-orbit states of atoms, the potential energy of the system does not correspond to just two surfaces displaced by AE. For example, with reference to Figure 7 for Na(,P), degeneracies which exist for the free atom are lifted in collision, and the spin-orbit coupling is often weakened. In all the known examples of E-V resonant exchanges, the magnitudes of the AE are such that the processes probably require the short-range repulsive wall, i.e. the Nikitin region 2, though little definitive information is presently available. -+

3Z 33

R. J. CvetanoviC, Progr. Reaction Kinetics, 1964,2, 39; J. R.Barker and R.E. Weston, J. Chem. Phys., 1967, 65,1427. H. Horiguchi and S. Tsuchiya, J.C.S. Faraday IZ, 1975,71, 1164.

GQSKinetics and Energy Transfer

98

Some examples of electronic-to-vibrationalenergy transfer are listed in Table 5. The Hg(3P1.+o)transition is also induced by CO with high efficiency, rate coefficient = 9.3 x cm3 molecule-1 s-l (300 K), and seems to excite CO(v = 1) with approximately unit quantum yield.34 The potential energy surfaces are expected to be strongly attractive for this system (Figure lo), with well depths of the order of 1 eV. The collision complex may consequently be long-lived, and the dynamics complex. An excellent set of E-V transfer systems involving atomic bromine has been studied quantitatively with laser techniques. Some of these results are listed in Table 5. The rate coefficients for relaxation of Br(2P,,2), excitation energy 3685 cm-l, show a systematic decrease with increasing IAEI. The yields of vibrationally excited molecules are >50% in each case, and could all be close to 100%. The vibrational yields are Table 5 Some electronic-to-vibrational energy transfer systems Rate coeflcient Reaction Hg(3P1) Nz(v = 0) 4Hg('P0) N2(v = 1) H&Pl) CO(v = 0) -+ Hg(3Po) CO(v = 1) Br(lP+) HF(v = 0) Br(2P+) HF(v = 1) Br(2P,) HCN(000) 4Br(2P3) HCN(100) Br(ZP+) HCl(v = 0) + Br(2P+) HCI(V = 1) Br(2P,) HBr(v = 0) Br('P+) HBr(v = 1) I('P,) HF(v = 0) I('P3) + HF(v =2) o ( ~ N~ ) -+ o(3~)~ ~ ( v ) HgPPo) CO 4Hg('So) CO(v) Wg(3P1) NO -+Hg('So) NO(v) Na(2P) M + Na(2S)+ M(v) Na(ZP) CO -+ Na(2S)+ CO(v) Na(?P) H2 -+ Na(2S) + H 2 ( 4

+ + + +

+ + + + + + + + +

+

+ + + + +

-+

-+

-+

+

AE/cm-I 563 376 276 -373 -798 - 1126 149

+ +

/an3 molecule-' s4.3 x 10-'2 9.3 x lo-" 3.4 x lo-" 2 x lo-" 8.7 x lo-'" 1.4 x -1.4 x lo-" - 3 x 10-11 1.0 x lo-" 5.5 x lO-'O See text 5.5 x 10-10 2.7 x

Ref. 33 34 36 37 38 38 39 40 41 42 43,44 45 46

obtained by comparing the molecular i.r. emission intensities with the unquenched Br('P,/,) atomic emission, but the computation requires knowledge of several rate coefficients which can lead to wide uncertainties. The HF reaction has been driven in the reverse direction, exciting the HF vibration with an i.r. laser.35 HF(v = 1) + Br(2P,,2) -+ HF(v = 0)

+ Br(2Pl/z)

Lasing action on COz, N,O, HCN, and C2H2 has been observed following collisional relaxation of Br(2~1,2).47 34

3s

36 37

38 39 40 41 4'

43

44

4s *6

47

A. B. Callear and P. M. Wood, Trans. Faraday SOC.,1971, 67, 3399. G. P. Quigley and G. J. Volga, J. Chem. Phys., 1975,62,4560. F. J. Wodarczyk and P. B. Sacket, Chem. Phys., 1976,12,65. A. Hariri, A. B. Petersen, and C. Wittig, J. Chem. Phys., 1976, 65, 1872. S. R. Leone and F. J. Wodarczyk, J. Chem. Phys., 1974, 60, 314. R. D. Coombe.and A. T. Pritt, J. Chem. Phys., 1977,66,5214. J. G. Slanger and G. Black, J. Chem. Phys., 1974, 60,468. G. Karl, P. Kruus, and J. C. Polanyi, J. Chem. Phys., 1967,46,224. G . Karl, P. KTuus, J. C. Polanyi, and I. W. M. Smith, J. Chem. Phys., 1967, 46,244. I. V. Hertel, H. Hofmann, and K. A. Rost, Chem. Phys. Letters, 1977,47, 163. I. V. Hertel, H. Hofmann, and K. A. Rost, Phys. Rev. Letters, 1977, 38, 343. D. S. Y. Hsu and M. C. Lin, Chem. Phys. Letters, 1967, 42, 78. D. A. Jennings, W. Braun, and H. P. Broida, J. Chem. Phys., 1973,59,4305. A. B. Petersen, C. Wittig, and S. R. Leone, Appl. Phys. Letters, 1975, 27, 305; J. Appl. Phys., 1976,47, 1051.

An Overview of Molecular Energy Transfer in Gases

99

\N2

Figure 10 Schematicpotential energy diagramfor collision of H g atoms with Nz,CO, and NHs

There is a recent claim that the deactivation of I(2Pl,2),excitation energy 7603 cm-l, by HF occurs partly by a resonant process generating HF(v = 2).39 There is only a small flux, if any, into the v = 1 level. A Av = 2 transition is rather restrictive for non-hydrides, but not for hydrides because of their large amplitude of vibration. Applying SSH theory with a gently repulsive potential energy surface, V02,2/V& N 0.1 for HF, a restriction which is greatly outweighed by the smallness of IAEI for the double quantum jump. And, incidentally, a quest for the v = 0 + 3 'triple' of HBr (AE = -200 cm-l) in the quenching of I(2P1/2) would not be unreasonable. Summarizing then the status quo for resonant E-V transfer, at least the gross features of the known systems are consistent with the earlier discussion in relation to Figure 1. The exchanges become very fast when exact resonance is approached. Excitation of a vibrational mode which minimizes IAEI is preferred; deactivation of Br('P,/,) by HCN excites the closely resonant CH vibration, and not the off-resonant CN vibration 37 (AE = - 1590 cm-'); carbon dioxide is excited to C02(101),4' with A E = 52 cm-l. The unique observation of the Av = 2 transition in the I('PilZ)/HF exchange is intriguing. In comparison, deactivation of I(2P1/2)by N, via a Av = 3 transition, AE = -697 crn-', is exceedingly slow, the rate coefficient for total removal of I(2P112) by N, at 300 K being only 2 x cm3 molecule-' s - ' . ~ ~The V&/Vtl 48

R.J. Donovan and D. Husain, Trans.Faraday SOC.,1966, 6 2 , l l .

Gas Kinetics and Energy Transfer

100 of

M restricts the multiple vibrational jump in the non-hydride diatomic molecule. Turning now to the sub-class of non-resonant E-V energy transfer, it is convenient first to consider the quenching of O('D) by N, for which at 300 K the rate coefficient is ~3 x lo-'' cm3 molecule-' s - ' . ~ '

O('D)

+ Nz(v = 0)

+

+

O(3P) N,(v)

The states of N, produced in this reaction have been examined by Slanger and Black:' using a stimulated Raman technique. Excitation occurs only into the lowest few vibrational levels with conversion of = 1 / 3 of the 15 870 cm" of electronic energy into vibration. The closest 'resonant' transfer, O('D)

+ N2(v = 0) + q 3 P ) + N,(v

= 7),

with AE = - 156 cm-', seems to have a negligible role. The reaction rate is fast because there is a long-range attractive interaction between O('D) and N,, of the kind seen in Figure 9 for the O('D)/Xe interaction. The attraction gives rise to a crossing of potential energy surfaces, providing a direct route for O(3P)formation. The potential energy surfaces of the initial and final states are not continuously equidistant by M A E in the transition region, so that a resonant process which minimized the overall IAEI of the reaction is irrelevant to this case. It is in distinct contrast to relaxation between low-lying spin-orbit multiplets of the same atomic term, around which the previous discussion of resonant E-V transfer has revolved. The excited atoms Na(,P) (excitation energy 16 965 cm-') and Hg(3P0)(excitation energy 37 645 cm-') are rapidly deactivated to their ground states by most diatomic and polyatomic molecules,32 which must be due to crossing of potential energy curves. In the Hg(3P0) systems it would appear that a long-range, attractive interaction between the excited atom and the quenching molecule is required in order that a free crossing to the ground state may occur, without a potential energy barrier. This statement is based on a comparison of the quenching of H S ( ~ P by ~ ) N2 and CO. The former is very slow, rate coefficient ~ 2 . 5x cm3 molecule-1 s-' at 300 K, whilst the latter is fast, rate coefficient 1.0 x lo-'' cm3 molecule" s-' at 300 K.I3 The Hg(3Po)/C0well depth is probably of the order of 1 eV. A curious intermediate situation is the Hg(3Po)/NH3 case where the well depth is x0.7 eV,50 such that the HgNH3* complex may be collisionally stabilized, but apparently the interaction is not strong enough for the potential energy surface to cross that of the ground state at an energy that is thermally accessible at ambient temperature. These types of potential energy surface are illustrated in Figure 10. The slow quenching rate of Hg(3Po) by N, implies that the interaction is not sufficiently attractive to cause the potential energy surfaces to cross. The energy separation in the region of the turning-points should allow 'internal resonances' to occur, in which only a fraction of the overall internal energy change appears as vibration in the N,. Other molecules which are rather unreactive, such as fluorinated hydrocarbons, also tend to give low rates of deactivation of excited atoms. The vibrational excitation, which ensues in the non-resonant E-V transfer, may result from the recoil forces to which the collision complex is subject as the particles 49

J. A. Davidson, C. M. Sadowski, H. I. Schiff, G. E. Streit, C. J. Howard, D. A. Jennings, and A. L.Schmeltekopf,J. Chem. Phys., 1976,64,57; I. S. Fletcher and D. Husain, Cunad.J. Chem., 1976,54, 1765.

50

A. B. Callear and J. H. Connor, J.C.S. Furuduy ZI, 1974, 70, 1667.

An Overview of Molecular Energy Transfer in Gases

101

separate on the steep potential energy surface. Karl et aL4' carried out one of the earliest experimental studies, by investigating i.r. emission from CO(v) produced in the deactivation of Hg(3Po). The results were later refined by Fushiki and T~uchiya,'~using a modulated light source with phase sensitive detection of the i.r. emission. The population of states up to v = 4 increases approximately linearly with v, with a maximum flux into v = 5; there is negligible production of states with v > 9. Conversion of the entire electronic energy into vibration corresponds to v = 20; the yield of vibrational energy is thus x1/3, the remainder appearing as translation and rotation. Fushiki and Tsuchiya were able to interpret the form of the CO vibrational distribution using the half collision model of Levine and Bern~tein,'~ but with the steepness of the intermolecular potential energy as an adjustable parameter. With reference to Figure 10, following a crossing from the Hg(3P0) - CO to the Hg('So) - CO surface, the system is subject to recoil forces as it would be in the separatory phase of a high energy collision. Such collisions induce multiple vibrational transitions, an example of which is the H+ + H, molecular beam experiment mentioned in the section on V-T relaxation.l o Other examples of non-resonant E-V transfer of Hg('P) and Na(,P) are listed in Table 5. The quenching of Na('P) by CO is typically non-resonant, with maximum rates into v = 2 and 3; individual levels of CO were monitored in absorption using CO laser radiation, exciting the atomic sodium with a dye laser.45 The other studies of Na(,P) quenching were conducted with a crossed molecular beam technique in which the conversion into translational energy was ascertained from a velocity analysis. The sodium was laser excited in the crossing region. Deactivation by each of the gases H,, D,, N,, CO, and C2H4 is shown to be non-resonant, with about half of the energy retained internally as vibration and rotation by the quenching molecule.43 In the quenching by N,, the velocity spectrum is broad and structureless, free from spikes corresponding to particular vibrational levels, indicating a major degree of rotational excitation. Quenching of Na('P) by oxygen seems to produce both 02a'A, and 0,b'Z:. In the quenching by N,O and CO, there is evidence for some degree of resonant transfer, though an unequivocal separation from the elastically scattered component, also contributing at low velocities, is difficult to achieve. A remarkable feature of this interesting research is the discovery of anisotropy in the direction of polarization of the exciting fight.44 With the plane of polarization such that predominantly the Z state is populated in collision, the cross-section for inelastic scattering is greater than if the ll state is predominantly populated (Figure 7). 6 Electronic-to-Electronic Energy Transfer A classical example of electronic energy transfer is the deactivation of Hg(3P1) by Na(3 S )

.

Hg(3P1)

+ Na(3,S)

-+

Hg('S0)

+ Na(n,L)

This system has been re-examined by Czajkowski et aZ.,53exciting a mixture of the dl 52 53

Y.Fushiki and S . Tsuchiya, Chem. Phys. Letters, 1973,22,47. R. D. tevine and R.B. Bernstein, Chem. Phys. Letters, 1972, 15, I . M.Czajkowski, G . Skardis, and L.Krause, Cunud. J. Phys., 1973,51, 334.

Gas Kinetics and Energy Transfer

102

metal vapours with the 2537 A resonance radiation (c.w.) and measuring the intensities of various sodium lines in emission. It is not a trivial problem to derive the cross-sections into particular n,L states from measurement of line intensities, because the complete set of rate coefficients for all processes depopulating each of the upper states has to be known. Many transitions encompass the i.r. regions, including emission from the F and higher L states, and have not been investigated. Another complication results from cascading, secondary processes which populate all states of lower internal energy. Time resolved studies would assist the analysis of these complications.

8P

/

/

0

/ 8

-71-

-6P

-4 -3 -2 -1 0 1 Internal energy change marked at intervals of lo3 cm-'

-5

Figure 11 Cross sections for electronic energy transferfrom Hg* to Na (503 K) (After Czajkowski et ~ 1 . ~ ~ )

Results of Czajkowski et al. are shown in Figure 11, as a plot of reaction crosssection against the change of internal energy. The cross-sections are obtained by dividing the rate coefficients by the mean velocity. A striking feature of Figure 11 is that the cross-sections peak sharply about AE = 0, i.e. resonant transfer predominates. This behaviour is in complete contrast to the E-V relaxation of these excited atoms. If the data points are examined in detail, curiously the two reactions with the highest cross-sections, populating the 9 s and 8 0 states of sodium, have AE = 162 cm-I and 316 cm-', whereas the cross-section of the exothermic process populating the 8P state, AE = - 113 cm-l, is only i) as large. In electronic-toelectronic energy transfer, when the acceptor has a high density of electronic states at the energy of the donor, the gross features of resonant transfer should generally be found. The detailed pattern is controlled by the disposition of the crossings, or near crossings, of the potential energy surfaces. The schematic potential energy diagram of Figure 12 is a hypothesis which illus-

An Overview of Molecular Energy Transfer in Gases

103

--

--Nudea r Separation Figure 12 Long range crossing points for excitation transfer from Hg* to Na (schematic). Full lines Hg* + Na; broken lines Hg + Na*

trates, in the simplest manner, how the behaviour of the Hg/Na system may be understood. The potential energy of the Hg(63P1) + Na(32S) collision complex is represented by just two curves, one repulsive corresponding to states with quartet character, and the other attractive corresponding to the doublet states, in which there is bonding between the 3s sodium electron and the 6s orbital of the excited mercury atom. The broken lines represent Hg('S,) + Na(n,L) final states. The main point that Figure 11 is designed to illustrate is that with lAEl small, crossings occur at long range, which explains why resonant behaviour arises. The atom pair has access to short range crossing-points only if the trajectory has a small impact parameter. Otherwise the centrifugal potential causes the system to turn at larger radial distances. Transitions occur at crossing-points between states that have the samez component of the total electronicangular momentum, i.e. they are homogeneous in the quantum number R. Figure 11 is also designed to illustrate how the longest range crossings may correspond to AE positive. A more realistic example is that of Dashevskaya et al.54 who calculated detailed rates for the Rb*/Cs system. If the rubidium atom is prepared in the Rb(2P3/2) state, three channels are available following inelastic collision.

The calculated rates show fair agreement with experiment, the intramultiplet relaxation of Rb('P) having the largest cross-section, and occurring at the longest range crossing-points. Crossing rates were calculated using the Landau-Zener equation.

7 Rotational-to-TranslationalEnergy Transfer Ultrasonic techniques were the first to be applied to the study of R-T rela~ation.~ The velocity dispersion that is observed usually provides an average relaxation time over many different rotational transitions. Most simple molecules, such as N2, 0,, 54

E. I. Dashevskaya, E. E. Nikitin, A. I. Voronin, and A. A. Zembekov, Cunud.J. Phys., 1970,48, 981.

Gas Kinetics and Energy Transfer

104

HCl, and HzO, have been shown to require less than m10 gas kinetic collisions for rotational relaxation at ambient temperature. The behaviour of H, and Dzis exceptional because the rotational levels are comparatively widely spaced. In p-Hz, two dispersion regions occur, one corresponding to 170 collisions due to the J = 2 + 0 transition, and the other to 300 collisions due to the J = 4 -+ 2 t r a n ~ i t i o n . The ~~ 4 --* 2 is less probable than the 2 -+ 0 because the energy change of the former transition is greater than the latter. It will be adduced later that the magnitude of IAEI, the energy converted into translation, dominates R-T transfer as it does most of the other types of energy conversion discussed in the previous sections. During the last few years the subject has advanced on three fronts, with a common objective, to determine the behaviour of individual quantum states. There has been great progress in the theory of rotational relaxation. Molecular beam techniques have advanced to a stage where R-T relaxation of single levels can be observed, including aspects of the angular dependence. Spectroscopic methods, with single state preparation, have revealed much detail of selection rules and hence of the nature of the interactions which induce the transitions. It is convenient first to mention briefly the theory. An accurate quantum scattering method, close coupling, is now available which is exact for the potential energy function that is used.56 The problem amounts to finding the solutions of a set of simultaneous, second-order differential equations. Listed in Table 6 are calculated cross-sections 5 7 for rotational relaxation of HCl by Ar, with initial relative translational energies of 200 and 500 cm- The initial and final rotational quantum numbers are designated as J and J’ respectively.

’.

Table 6 Cross-sections (A2)for rotational relaxation of HCI by Ar, with relative translational energies of 200 cm- and 500 cmEnergy

J‘ 0 1 2 3 4 5

/cm0 21 64 127 212 318

J=O 200

46 24 1.5

J=O 500 29 14 6.7 0.6

0.4

J=l 200 16

J=l

16 3.4 0.2

18

-

500

10

5.2

1.1 0.4

J-3 200 1 .o 2.9 8.1 5.1 0.2

J=3 500 1.4 2.8 7.7

-

7.3 1.5

The data of Table 6 show that transitions with AJ = 1 have the highest probability, but multiple changes of J are allowed in these single collision events. As yet only a handful of these calculations has been carried out because they require an enormous amount of computer time, especially at high energies when the number of accessible channels is large. Theoreticians are presently searching for methods which require less computation, but retain sufficient precision to be usefully applied to these and other problems, such as the role of simultaneous rotational transitions in V-T relaxation. The exact result obviously provides the yardstick for the assessment of the value of approximate methods. The detection of R-T relaxation with crossed beam techniques requires immense experimental skill because the energy changes are small. Blythe et aL5* described 5 5 K.Geide, Acustica, 1963, 13, 31. 56

57 58

A. M. Arthurs and A. Dalgarno, Proc. Roy. SOC.,1960, A256, 540. S. Chapman and S. Green, J. Chem. Phys., 1977, 67,2317. A. R. Blythe, A. E. Grosser, and R. B. Bernstein, J. Chem. Phys., 1964, 41, 1917.

An Overview of Molecular Energy Transfer in Gases

105

one of the first successful experiments, finding evidence for the J = 0 -,2 transition of 0-D,, in collision with atomic potassium, from the velocity distribution of the inelastically scattered component. The beam techniques for such measurements have been developed and refined by Toennies and his collaborator^.^^ Van den Bergh et aL60 measured the cross-section for inelastic collision of Li' with H2, using time of flight detection. The experiment had to be designed such that the primary Li+ beam had a very small divergence and narrow energy spread in order that the small energy changes could be resolved in the flight time spectrum. The primary beam, 0.6 eV centre of mass energy, was chopped electrostatically and was then crossed with a H2 nozzle beam. Inelastic cross-sections were measured for the J = 0 -+ 2 and J = 1 -+ 3 transitions at various angles. The relative cross-sections show encouraging agreement with theory.61 Another remarkable experiment was described recently by Gentry and Giese,62 in which cross-sections for rotational transitions were measured in the HD-HD diatom-diatom system. The beams were produced with electromechanicallyoperated valves, generating gas pulses of % 15 p s duration, at 0.5 s - l repetition. Thereby vastly greater densities than normally used in crossed molecular beam experiments were achieved: The translational energy spectrum was measured from the flight time to an ionizer and quadrupole detector. The following transitions were quite well resolved 2HD(J = 0) -+ 2HD(J = 0) -+

HD(J = 1) + HD(J = 0)

-+

2HD(J = 1)

+ HD(J =

2)

+ HD(J = 0)

It is the only experiment where the rotational states of both molecules have been identified. In the earliest spectroscopic studies of R-T relaxation, the diatomic molecules I2 and NO were prepared in single rovibronic states with monochromatic light. At low pressures the excited molecules are isolated from collision and each fluorescence band is comprised of just a single line of each branch. Foreign gas collisions induce both rotational and vibrational transitions, the former spreading the rotational structure and the latter giving rise to new bands. With such experiments it has been demonstrated that multiple changes of the angular momentum quantum number of the diatomic molecule can occur in a singIe collision event. Collisions of NO(A2Z')(w = 1) (2144 A Cd line) with Ar or N2 induces transitions in which AJ Q +5.63 Several studies have been conducted with 12(B3110:) excited with various atomic lines. The rotational levels are closely spaced and A J < 40 transitions have been shown to occur with several collision partners. In some systems the initial rotational state shows some persistence even following vibrational r e l a ~ a t i o n .The ~ ~ vibrational levels are also closely spaced and relaxation occurs with a sufficiently high probability that the rotational levels are 59 6o 62

63 64

J. P. Toennies, Chem. SOC.Rev., 1974, 3,407. H. E. Van den Bergh, M. Faubel, and J. P. Toennies, Faraday Discuss. Chem. SOC.,1973,55,203. G. M. Kendall and J. P. Toennies, Faraday Discuss. Chem. SOC.,1973,55,227. W. R. Gentry and C. F. Giese, Phys. Rev. Letters, 1977, 39, 1259. H.P. 9roida and T . Carrington, J. Chem. Phys., 1963, 38, 136. J. I. %dnfeld and W. Klemperer, J. Chem. Phys., 1965, 42, 3475.

106

Gas Kinetics and Energy Transfer

not scrambled by prior collisions. By studying changes of polarization induced by collision, McCaffery 6 5 has shown that the direction of the total angular momentum tends to be conserved following inelastic collision. Energy transfer of rovibronic states of the mixed halogen diatomics is presently under study by Clyne and co-workers,66using dye laser techniques which permit selection over a range of J in a particular vibronic band. In understanding the rotational relaxation of diatomic molecules, considerable advances have been made in the last few years using i.r. lasers as the excitation source. Thus Hinchen and Hobbs 67 were able to excite selectively HF(u = 1;J = 2,3,4, or 9, using a pulsed HF laser tuned to individual lines. Collisional population of J states not initially selected was monitored in absorption with a C.W. HF laser (u = 2 3 1) operating at low power (Lr. double resonance). HF was the sole collision partner. Rate coefficients were measured for transitions with AJ < +3. The logarithm of the rate coefficients is shown to be a linear function of AE, though the interpretation is a little complicated by the Occurrence of vibrational relaxation.68 This experiment differs in three important aspects from the earlier research on rovibronic states of NO or 12. First, the molecule is in its ground electronic state and the system is more amenable to calculation. Secondly, the rotational constant of HF is 21 cm-', so that the levels are well spaced. Thirdly, laser excitation allows the molecular behaviour to be scanned over a range of initial J states. Lang et aL6' recently described a somewhat similar experiment, exciting HF(v = 1; J = 3 or 5) with a multiline C.W. HF laser, with extrinsic line selection. With Ar as collision partner, relaxation was monitored from the i.r. fluorescence. With J = 3 excited initially, the measured, relative rate coefficients for J = 3 + 1 : 3 + 2 : 3 + 4 : 3 -+ 5 are 0.51 : 1.0 : 0.41 : 0.13 at x400 K. The ratios of the cross-sections of Table 6 for 200 cm-' relative energy (Elk = 286 K) are 0.36 : 1.0 : 0.63 : 0.03, a similar pattern but weighted more into the AJ = 1 channels. As yet, there are no reports of close coupling calculations for the HF-Ar experiment. In Figure 13 the logarithm of the relative rates measured by Lang et al. (adjusted to negative AE by detailed balancing) are plotted against AE. The approximately linear behaviour emphasizes the dominance of the magnitude of the energy change on the rates, and an apparently minor restriction if any on the change of angular momentum. In this molecular system, it is the short-range repulsion which causes the transitions to occur. In an extensive series of experiments using microwave double resonance, Oka and his associates 70-73 have made great progress in unravelling microscopic detail of the rotational relaxation of polyatomic molecules in gases. The technique consists of saturating a particular microwave transition with powerful C.W. pumping radiation, 65 66

K. Kata, S. R. Jeyes, A. J. McCaffery, and M. D. Rowe, Chem. Phys. Letters, 1976,39,573. M. A. A. Clyne and A. H. Curran in 'GasKinetics and Energy Transfer', ed. P. G. Ashmore and R. J. Donovan (Specialist Periodical Reports), The Chemical Society, London, 1977, vol. 2, p. 239.

67 68

69 'O

''

72

73

J. J. Hinchen and R. H. Hobbs, J. Chem. Phys., 1976, 65,2732. L. H. Sentman, J. Chem. Phys., 1977, 67,966. N. C. Lang, J. C. Polanyi, and J. Wanner, Chem. Phys., 1977,24,219. T. Oka, J. Chem. Phys., 1966,45,754; 1967,47,13; 1968,48,4913; 1962,49,3135. R. M. Less and T. Oka, J. Chem. Phys., 1968,49,4234; 1969,51,3027. P. W. Daly and T. Oka, J. Chem. Phys., 1970,53,3272. A. R. Fabris and T. Oka, J. Chem. Phys., 1972,56,3168.

An Overview of Molecular Energy Transfer in Gases

107

-A E/cm-’ Figure 13 Viariation with AE of rate coe@cients for R-T relaxation of HF in collision with &(-4OoK): 0 , A . T - -1; O , U = -2; @,,AJ= -3 (After Lang ef ~ 1 . ~ ~ )

and then monitoring the effect of the disturbance on states not initially pumped with a weak microwave probe signal. The initial disturbance is transmitted to other levels via collision^.'^ In the pure vapours of H2C0, DHCO, HCN, H2CC0, and NHJ, Oka demonstrates that electric dipole selection rules are obeyed, i.e. AJ = 0 f 1, AK = 0, + e -. The transitions are induced by dipole-dipole interaction, and occur at long range. The relaxation process may be either R-T,. or else if IAEI is extremely small, R-R resonant rotational transfer. With a symmetric top for example, an R-R transition would be

( K = 4 , J = 5)

+(K=

3 , J = 4) + ( K = 4 , J = 4)

+ (K=3,J=

5)

requiring no change of the total angular momentum and a AE that is finite only because of small changes of centrifugal distortion. Oka conducted detailed studies with NH,. Relaxation in collision with rare gases is shown to be unrestricted by the electric dipole rules; AK # 0 and A J < 5 were observed strongly. The cross-sections for relaxation are an order of magnitude smaller than in pure NH3, and apparently the transitions induced by the rare gases require the short-range repulsion. This view is supported by the hole-transferring experiment of Freund et al.74 A hole is burned in the Doppler profile of an NH, transition using laser excitation. In self collisions, the hole, or translational velocity distribution, is retained following rotational relaxation because it occurs at long range. In He, the hole is smeared out because when the molecules experience the short-range repulsion the velocity distribution is changed. Time resolved experimentshave been developed which permit the rates of relaxation in polyatomic gases to be measured directly. These are microwave-microwave double resonance, i.r. microwave double resonance, and microwave coherence recorded a rate phenomena. Thus, for example, Brown 75 and also McGurk et coefficient of sz 1.5 x cm3 molecule-l s - l for relaxation of OCS(J = 1) in self collisions at ambient temperature. To date, essentially all the time resolved measurements have been restricted to the two states directly pumped. 74 75

76

S. M. Freund, J. W. C . Johns, A. R. W. McKellar, and T. Oka,J. Chem. Phys., 1973,59,3445. S. R.Brown. J. Chem. Phys., 1974,60,1722. J. C. McGurk, R. T. Hofmann, and W.H.Flygare, J. Chem. Phys., 1944,60,2922.

Gas Kinetics and Energy

108

Transfer

Just a single molecule, He,(a3Ct), is known to undergo anomalously slow R-T r e l a ~ a t i o n .In ~ ~collision with He atoms at low temperature, the probability of rotational relaxation of high J levels is B Even the ‘wobbling’ 3He4He(a3C+) shows very weak coupling of rotation and translation. It would appear that in He2(a3E:)-He collisions, the surfaces of equipotential energy are very nearly spherical about the centre of the diatomic molecule. 8 Rotational-to-Electronic Energy Transfer A beautiful experiment, which demonstrates that interconversion of rotational and electronic energy may occur efficiently, has been recently described by Smith et aL7* Metastable Xe(,P,) atoms were generated by electron impact, and then excited to high Rydberg states, 27 -c n < 34 (n is the principal quantum number) with light from a pulsed laser. In the presence of NH, at lo-’ Torr, sets of processes were identified in which rotational energy of the NH, is converted into electronic energy of the Xe atom. For example, with n = 27 initially, the following closely resonant conversions were observed.

+ NH, (J = 4 ) 3 Xe(n Xe(n = 27) + NH, (J = 5) -+ Xe(n Xe(n = 27) + NH, ( J =6)4 Xe(n Xe(n = 27) + NH3 (J = 7 ) + Xe(n Xe(n = 27)

-

+ NH, 45) + NH, 56) + NH, 75) + NH, 39)

(J = 3) (J = 4) (J = 5)

(J = 6 )

The transitions occur at very long range with rate coefficients of about 10-6-10-7 cm3 molecule-1 s-’. The dipole selection rules, AK = 0 and A J = - 1, are obeyed, Each of the final states of the Xe atom was identified by determining the threshold field strength for ionization. 9 Final Comment The subject has advanced greatly during the last decade, both in experiment and theory. No doubt this progress will continue to reveal the much needed, finer details of the various processes listed here, as well as to develop new aspects such as collisional radiative energy transfer. Apologies are extended to those whose works have not been included in this short overview. 77

78

A. B. Callear and R. E. M. Hedges, Trans.Faraday SOC.,1970,66,2921. K.A. Smith, F. G. Kellert, R. D. Rundel, F. B. Dunning, and R. F. Stebbings, Phys. Rev. Letters, 1978,40,1362.

4 Laser Studies of Vibrational, Rotational, and Translational Energy Transfer BY R. T. BAILEY AND F. R. CRUICKSHANK

1 Introduction Energy transfer among translational, rotational, and vibrational degrees of freedom is of fundamental importance. The rates, pathways, and cross-sections for energy transfer beween various modes of polyatomic molecules are of crucial importance for our understanding of chemical reactivity in molecular systems. The rapidly developing interest in this field has arisen in part from the recognition of the importance of experimental information regarding the intermolecular forces and collision mechanisms which govern the interactions between molecules. Without these data, the various theoretical treatments of molecular relaxation and energy transfer cannot be tested in a meaningful fashion. Energy transfer processes, observed as the relaxation of energy from one vibrational mode into all modes of the molecule, are the reverse of activation of a mode for chemical decomposition. These two processes are linked by the ratio of their rates, which is a function of their equilibrium constants calculable from the Boltzmann distribution. The study of energy transfer reveals, therefore, a great deal of information on the process of activation and should lead to useful theories for the prediction of Arrhenius activation energies. The inability to make such predictions presently constitutes the main difficulty in the accurate prediction of reaction rate constants. A knowledge of the efficiency of energy transfer processes is also of fundamental importance in developing new and more efficient molecular laser systems as well as improving existing lasers. It is the detailed changes in the populations of the molecular quantum states, controlled largely by relaxation processes, which determine the overall population inversion, and therefore efficiency, of most laser systems, Molecular relaxation in gases has been studied by a wide variety of techniques. Some of these include ultrasonic, shock-tube, microwave, molecular beam, spectrophone, laser, and chemiluminescence techniques. The dramatic development of molecular energy transfer work in the past few years has benefited particularly from the parallel development of i.r. laser systems, both discrete frequency and tunable, together with advances in instrumentation in the i.r. region. Interest in the theoretical aspects of energy transfer is also increasing rapidly. Calculations of energy transfer cross-sections are, however, still hampered by the complexity of the problem, which makes it difficult to include physically realistic potentials (even when these are known) in the calculations. The problem rapidly becomes intractable for any but the simplest systems and approximations have to be made. More work is needed to verify the validity of many of the approximations in current usage. However, some progress has been made in explaining particular aspects of energy transfer processes (e.g. the 109

110

Gas Kinetics and Energy Transfer

temperature dependence of V-V rates in certain systems) although theories of this type are not generally applicable to other systems. A field intimately connected with energy transfer is that of laser initiated or promoted chemical reactions (i.r. photochemistry) and laser isotope separation. This rapidly growing field has recently been reviewed’ and is not included in this Report. There have been a number of recent reviews dealing with various aspects of laserexcited i.r. fluorescence in molecular g a ~ e s . ~The - ~ present Report is concerned only with laser-excited energy transfer between vibrational, rotational, and translational levels that occurs during molecular collisions, the molecule remaining in the ground electronic state. Energy transfer involving excited electronic states is not considered except in one or two isolated cases where it is relevant to the mechanism of vibrational relaxation. The literature search covers the period up to June 1977 with the exception of a few journals not available in translation. A few articles appearing after this date have been included but no systematic search was made beyond June 1977.

2 Experimental Techniques Energy transfer in molecular systems can be studied in several ways all of which depend on achieving an excess population of an upper quantum level and following the relaxation of this level to lower quantum levels. The excess population can be accomplished by direct absorption of an i.r. laser of suitable wavelength or by stimulated Raman pumping. The i.r. laser pump can be operated CW and the fluorescence spectrum recorded in the usual way. The kinetics of energy transfer are difficult to unravel from this type of data but useful information can nevertheless be obtained. Alternatively, and more commonly, pulsed excitation can be used and the emission monitored by fast response, sensitive, i.r. detectors. The results in this case are more readily interpreted kinetically since the lifetimes of the molecular energy states are obtained directly. Stimulated Raman pumping is again a pulsed technique whereby vibrationally excited states can be produced in molecules which do not have suitable i.r. active modes. In all these experiments the characteristics of the laser pump systems are of vital importance. A large number of laser frequencies are now available spanning almost the entire u.v.-visible to far i.r. spectrum. Many of these lasers are, however, still at the development stage while others are unsuitable (for various reasons) for energy transfer studies. The basic principles of the laser can be found in a number of texts.5 Chemical applications of lasers have also been reviewed.’ Discrete Frequency Lasers.-Helium-Neon. The 3.39 pm transition of the helium-neon laser has been used in some early experiments.6 The relatively low powers obtainable from this system make it generally unsuitable for energy transfer work except where S. Kimel and S . Speiser, Chem. Rev., 1977,77,437. C . B. Moore, Adv. Chem. Phys., 1973,23,41. E. Weitz and G. Flynn, Ann. Rev. Phys. Chem., 1974,25,275. R. T . Bailey and F. R.Cruickshank, in ‘Molecular Spectroscopy’,ed. R.

F.Barrow, D. A. Long, and D. J. Millen (Specialist Periodical Reports), The Chemical Society, London, 1974, vol. 2, p. 262.

D. Ross, ‘Lasers: Light Amplifiers and Oscillators’, Academic Press, New York, 1969; ‘Lasers’, Dekker, New York,ed. A. K. Levine and A. J. DeMaria, 1971, vols. 1, 2, and 3. J. T. Yardley and C. B. Moore, J. Chem. Phys., 1966,45,1066; 1968,49,111.

Laser Studies of Vibrational,Rotational, and Translational Energy Transfer

111

no alternatives exist. The 3.39 pm (2950 cm-') frequency lies in the region where C-H stretching vibrations are found. Carbon Dioxide. Many different versions of this laser are available commerciallyboth CW and pulsed. Continuous powers of over 10 kW and pulsed outputs of many megawatts are currently available. Normal CW operation occurs near 10.6 pm but with a grating in the cavity the laser can be tuned to several hundred discrete vibrationrotation transitions between 886 and 1096 cm". The CW-laser can also be pulsed and Q-switched to provide short high power pulses, typically 10 kW in pulses 300 ns wide for a 2 m cavity. Passive Q-switching using saturable absorbers can also be employed. Shorter pulse widths can be obtained using mode-locking techniques.' By using an intracavity GaAs electro-optic modulator a train of 2011s pulses can be obtained. Using cavity dumping techniques single pulses of about 10 kW peak power and 20 ns duration can be selected from the train.' A significant advance in i.r. laser development was the introduction of the transversely excited atmospheric pressure (TEA) laser. By operating the active medium at atmospheric pressure vacuum problems are eliminated and the output power per unit volume increased. It is difficult to achieve uniform excitation of the gas mixture at atmospheric pressure since the glow discharge tends to constrict to an arc, heating the gas and destroying laser action. To overcome this problem, techniques have been devised to preionize the gas which helps to initiate a uniform glow discharge between the main electrode^.^ A typical pulse from a TEA laser varies from 70 to 250 ns in width with powers of several megawatts readily available. Several commercial systems are available but for energy transfer studies a laser capable of a high repetition rate should be chosen. An alternative to the usual longitudinal or transverse gas discharge is electron beam excitation. High energy electrons produced in a separate chamber enter the lasing medium through a suitable thin metal window. With this system the excitation pulse can be tailored to suit the decay characteristicsof the lasing levels and optimum power output obtained. Higher gas pressures can also be used ( > 50 atm*) and large volumes of gas can be uniformly excited. When shorter pulse widths are required active mode locking techniques can be empl~yed.'~-'~Single pulses can then be selected from the train by use of a suitable switching element. Typically pulses of 1-2 ns duration with an energy in the mJ range are obtained when an intracavity loss modulator is used. Milam et aLi4 have employed several cavity dumping techniques to produce continuously variable and precisely controllable pulses 0.5-2.0 ns wide at powers up to 0.3 kW. Various electro-optic shuttering schemes have also been utilized to produce pulses as short as P. K. Cheo, in ref. 5, vol. 3, p. 111. lo l1 l2 l3

l4

*

T. J. Bridges and P. K. Cheo, Appl. Phys. Letters, 1969, 14,262. H. Foster, Optics andkser Technol., 1972,4, 121. F. Rheault, J. L. Lachambre, J. Gilbert, R. Fortin, and M. Blanchard, Canad. J. Phys., 1972, 50, 1876. D. T. Davis, D. L. Smith, and J. S. Keval, I.E.E.E,-J. Quantum Electron., 1972, QE-8, 846. J. F. Figueira, W. H. Reichelt, G. T. Schappert, T. F. Stratton, and C. H. Fenstermacker, Appf. Phys., Letters, 1973, 22, 216. M. C. Richardson, Optics C o r n . , 1974, 10,302. D. Milam, R. A. Bradbury, A. Hordvik, A, Schlossberg, and A. Szoke, 1.E.E.E.-J. Quantum Electron., 1974, QE10, 20. 1 atm = 101.325 kN m-2.

112

Gas Kinetics and Energy Transfer

1 ns from non-mode-locked TEA lasers. l 5 An electro-optic shutter, activated by a pulse generator and switched by a laser triggered spark gap, has also been used to produce optical pulses as short as 600 ps from a TEA laser. Passive mode-locking with SF, as saturable absorber can also be used to produce pulses in the 1.5 to 10 MW range. Until recently, most laser resonator systems were confocal or hemispherical (using a grating in place of one reflector). These resonator systems are generally stable and enable regeneration to occur without significant loss. With high gain systems the so-called unstable resonator system may be used. In addition to providing convenient output coupling, such a system produces a large and uniformly filled mode volume (in contrast to the stable confocal resonator) and has good transverse mode selection.”-21 Higher output power is also obtainable due to the greater mode volume in the unstable system. For energy transfer measurements it is desirable for the laser to have good pulse-topulse stability and single mode operation. This is difficult to achieve in TEA lasers due to spontaneous mode locking. These problems can be overcome, however, by using a hybrid laser consisting of a low pressure CW C 0 2 laser amplified by a TEA high pressure section. Spontaneous mode locking, which normally occurs in TEA lasers is completely removed and single transverse and longitudinal mode operation o b ~ e r v e d . ~Some ~ - ~ ~control over the pulse shape is also possible using this system. Recently, transversely excited COz waveguide lasers operating at atmospheric pressure have been In these systems the active medium was contained in a waveguide of size comparable with that of the mode distribution. If the mode radius (l/epoint) is approximatelyequalto one half thewaveguide radius, then the loss in the guide is very small. The gain and output power per unit volume of gas is substantially higher for the waveguide laser compared with a conventional TEA system. TEA C02 waveguide lasers have been described by Wood et ~ 1 . and ~ ’ Rickwood and Walker.26 Both were of rectangular cross-sectionformed from a copper or aluminium base plate which served as the anode, glass or quartz side walls, and an alternate metal-insulator segmented cathode. Gibson et aL2’ recently described a device in which the segmented cathode was replaced by a continuous resistive cathode consisting of 100 C?cm silicon, 2 or 3 mm thick, with an electrical contact soldered along most of its length. In a waveguide 30 cm long by 1.5 x 1.5 mm2 cross-section, outputs up to 5 Jdm-3 were obtained at atmospheric pressure. Laser action was obtained at pressures over 4atm without preionization and at pulse rates up to 1 kHz. With longer high power systems the considerable pressure gradient down the tube means that optimum laser conditions cannot be maintained throughout the whole lasing l 2 9

‘

’*

I6

l9 2o 21 22

23 24 25

26 27

D. L. Smith and D. T. Davies, Z.E.E.E.-J. Quantum Electron., 1974,QE-10, 138. R. Fortin, F. Rheault, J. Gilbert, M. Blanchard, and J. L. Lachambre, C’d. J. Phys., 1973 51,414. A. E.Siegman and E. A. Szeklas, Appl. Optics, 1974,13,2775. P. E.Dyer and D. J. James, Optics Comm., 1975,15,20. D. F. Walls and K. J. McNeil, Optics Comm., 1976, 18,471. H.Shih, M. 0.Scully, P. V. Auizonis, and W. H. Louisell, Phys. Rev., 1975,All, 630. N . R.Greiner, Z.E.E.E.-J. Quantum Electron., 1975,QE-11, 844. A. Gondhalekar, E. Holzhauer, and N. R. Heckenberg, Phys. Letters, 1973,46a,229. N. R. Heckenberg and J. Meyer, Optics Comm., 1976,16,54. A. Girard, Optics Comm., 1974, 11, 346. 0. R. Wood, P. W. Smith, C. R. Adams, and P. J. Maloney, Appl. Phys. Letters, 1975,27, 539. A.C.Walker and K. R. Rickwood, J. Phys. (E), 1976,9,432. A. F. Gibson, F. F. Rickwood, and A. C. Walker, Appl. Phys. Letters, 1977,31,176. ,

Laser Studies of Vibrational,Rotational, and Translational Energy Transfer

113

medium. This problem has been overcome by the use of a porous Be0 tube as the waveguide.28 Gas is diffused through the walls and pumped out of the two ends of the guide. Chemical Lasers. Chemical lasers have been used extensively for energy transfer studies. By using the molecule under investigation also as the active lasing medium, frequency matching between the pump and absorber is guaranteed. The chemical reaction which produces the inverted population distribution of products must be rapid enough to maintain an appreciable non-equilibrium distribution in competition with various energy redistribution and deactivation processes. Techniques used for initiating the chemical reaction include flash photolysis, electric discharge or heating. For example, HCI lasers have been made by flash initiation of a H, + Cl, mixture. In the majority of chemical laser systems, the emission occurs in the near to mid4.r. region, arising from transitions between vibrational states. An enormous number of systems have now been studied. Bibliographies of some of the earlier chemical laser systems have been p u b l i ~ h e d . A ~ ~useful * ~ ~technique for energy transfer studies is to initiate reactions in appropriate gas mixtures in a TEA discharge laser. In this way, a large number of i.r. laser frequencies can be obtained with similar characteristics to the C 0 2 laser emission but with generally lower CW laser emission has been observed from CS, (1 1.5 pm), C2H, (8 pm), and N 2 0 (10.6 pm) pumped by energy transfer from vibrationally excited CO produced by a glow discharge.33 Pulsed emission has also been observed when the vibrationally excited CO is produced by a frequency doubled C 0 2 laser.34 Tunable Lasers.-Rapid advances have been made in the technology of tunable i.r. laser sources in recent years. They offer considerable promise and should ultimately supersede conventional fixed frequency sources. Tunable lasers include semiconductor diode lasers, spin-flip Raman lasers, (SFRL), and parametric oscillators. Nonlinear mixing using tunable and quasi-tunable laser sources can also be used to extend the frequency range. Semiconductor Diode Lasers. This type of laser is pumped by means of an electric current which creates population inversion between the conduction and valence bands; electrons falling from the conduction band can generate stimulated radiation close to the frequency corresponding to the energy gap. Semiconductor diode lasers can be fabricated to operate at any desired wavelength in the range from 0.6-32 pm. The wavelength range covered by the various compositions is shown in Figure 1. An individual diode can be tuned by a magnetic field, hydrostatic pressure or by temperature ~ h a n g e5-37 . ~ Hydrostatic pressure can provide a very broad tuning range for a single device. A lead selenide diode laser at 28 29

31 3z 33 34 35

36

37

A. Papayoanou and A. Fujisawa, Appl. Phys. Letters, 1975,26,560. S . J. Arnold and H. Rojiska, Appl. Optics, 1973, 12, 169. C. F. Wiswall, D. P. Ames, and T. J. Menne, I.E.E.E.-J. Quantum Electron., 1973, QE9,181. J, Wilson and T. S. Stevenson, Appl. Phys. Letters, 1972, 20, 64. R. Wood and T. Y . Chang, Appl. Phys. Letters, 1972,20,77. J. A. Stregack, B. L. Wexler, and G. A. Hart, Appl. Phys. Letters, 1976, 28, 137. H. Kildal and T. F. Deutsch, Appl. Phys. Letters, 1975,27, 500. ‘Gallium Arsenide Lasers’, ed. C. H. Gooch, Wiley-Interscience, New York, 1969. H. Kressel in ref. 5, vol. 3, p. 1. I. Melngailis and A. Mooradian, in ‘Laser Applications to Optics and Spectroscopy’, ed. M. Sargent and S. F. Jacobs, Addison-Wesley, Massachusetts, 1975, p. 1.

Gas Kinetics and Energy Transfer

114

,- ,

Pb --+

Sn,Se

Pbl,,Sn,To

,

-+

I

PbS 1- So x

-,Go ,To

Pb

t---.l

Pb1,,Cd,S c-Pb i-,Ge ,S *-4

In Asl-rSb, I---++

GaSb

+

- ,As,

I n,'Ga

-,P,

In As

7

A I ,GO 1

-,AS, GO As

P,

M

1

Inl-,Ga,P

1 ,

,7, 2

05

1

1

I

1

I

5

I

'

l

l

i

1

10

20

I

I

I

50

I 1 1 1

10

WAVELENGTH/ p m

Figure 1 Wavelength ranges covered by various semiconductor diode laser materials: -present situation; - - - - possible range covered in near future (Reproduced by permission from 'Very High Resolution Spectroscopy', ed. R. A. Smith, Academic Press, New York, 1976)

77 K has been tuned from 7.5-22 pm using hydrostatic pressure 38 up to 14 kbar*. The diode laser can be coarsely tuned by hydrostatic pressure, and finely tuned by varying the temperature of the junction. Although of relatively low power at present they offer considerable promise in the energy transfer field particularly for monitoring the population of vibrational states. Very high resolution is possible with these devices. Spin-flip Raman Lasers. Spin-flip Raman lasers have been developed extensively over the past few years and are now useful for energy transfer work. The device consists of a semiconducting crystal (e.g. n-type InSb) mounted in a magnetic field (usually a superconducting magnet) at around 4 K. The crystal is pumped with CW or pulsed h e r radiation which is inelastically scattered from the conduction electrons in the semiconductor. The Raman process is associated with spin-reversal transitions whose energy is proportional to the magnetic field in the crystal. Thus by varying the field of the magnet, the frequency of the scattered radiation can be varied. Molecular gas lasers such as CO, COz, and HF have been used to pump n-type InSb, InAs, and HgCdTe. The output characteristics of these devices are listed in Table 1. The narrow linewidths obtainable are a particular feature of the SFRL. Operating 38

*

J. M. Besson, J. F. Butler, A. R. Calawa, W. Paul, and R. H. Rediker, Appl. Phys. Letters, 1965, 7,206. 1 bar = lo5 N m-'.

Laser Studies of Vibrational,Rotational, and Translational Energy Transfer

115

Table 1 SFRL characteristics Wavelength Pump Laser Pulsed COz, 10.6 pm SH of pulsed COz,5.3 pm

CO, 5.6pm PulsedHF, 2.9 pm Pulsed COz, 9.52 pm

Material

range

M a x i m output 1 kW in 1st Stokes

Ref. 39,40

InSb

9-14.6 pm

InSb

5 . 2 4 . 5 pm

700 W in 1st Stokes

41

Ids

2.98-3.00 pm

45 W in 2nd Stokes 25 W in 1st Anti-Stokes 1 W in 1st Stokes 200 W in 1st Stokes

41 41 42 43

HgCdTe

9.7-10.2pm

InSb

1 W in 1st Stokes

44

CW,linewidths of about 0.1 cm-’ are obtained, while in the quasi-continuous mode linewidths as low as lov6cm-’ are possible. In normal pulsed operation, the pulses are about 30 ns wide but in mode-locked operation 3 ns pulses can be obtained. Recently external cavity operation has allowed generation of second and third antiStokes transitions in InSb at 10.6 pm.45 Non-linear Mixing.4ne method of generating tunable coherent i.r. radiation over a broad frequency range is sum and difference frequency generation in a non-linear material using a fixed and a tunable frequency source.46 For example, a cw dye laser and a cw single frequency argon ion laser have been mixed in LiNbO, to generate cw tunable output from 2 . 2 4 . 2 pm.46*47 Dewey and Hocker 48 produced intense pulses of tunable radiation in the 3 to 4pm range by generating the difference frequencies between a tunable dye laser and a Q-switched ruby laser in a phase-matched LiNbO, crystal. This system is limited to shorter wavelengths than 4.5 pm owing to the transmission characteristicsof LiN b0,. Using i.r. transmitting nonlinear material the tunable range can be extended to longer wavelengths. With proustite, Decker and Tittel 49 demonstrated tunability from 3.20 to 5.65 pm and Hocker and Dewey 5 0 from 11 to 23 pm, with peak powers in the kilowatt range. A cw CO and C02 laser have been mixed in CdGeAs, to generate quasi-tunable radiation in the 2.5-17pm range.” Conversion efficiencies of 25% have been measured for this material for second harmonic generation using a pulsed 10.6 pm C02 laser. Using AgGaSz as the non-linear mixing crystal, i.r. difference frequencies have been generated in the 9.018 pm range.52 Two tunable dye lasers pumped by the same nitrogen laser were used. 39 40 41

42 43 44 45 46 47 48 49 51

52

J. T. Ganley, F. B. Harrison, and W. T. Leland, J. Appl. Phys., 1974,45,4980. B. Walker, G. W. Chantry, D. G. Moss, and C. C. Bradley, J. Phys., (D), 1976,9, 1501. R. A. Wood, A. McNeish, C. R. Pidgeon, and S. D. Smith, J. Phys., (0,1973, 6, L144. T.Scragg, C. N. Ironside, R. B. Dennis, and S. D. Smith, Optics Comm., 1976,18,456. R. S. Eng, A. Mooradian, and H. R. Fetterman, Appl. Phys. Letters, 1974,25,453. J. P. Sattler, B. A. Weber, and J. Nemarich, Appl. Phys. Letters, 1974, 25, 491. B. Walker, D. G.MOSS, and G. W. Chantry, Optics Comm., 1977,22,8. ‘Non-linear infrared generation’, ed. Y. R. Shen, Springer-Verlag (Berlin), 1977. A, S. Pine, J. Opt. SOC.Amer., 1974,64,1683. C. F. Dewey and L. 0. Hocker Appl. Phys. Letters 1971,18,58. C . D. Decker and F. K. Tittel, Appl. Phys. Letters, 1973, 22,411. L. 0. Hocker and C. F. Dewey, Appl, Phyp. Letters, 1976,11, 137. H. Kildal and J. C. Mikkelson, Optics Comm., 1974,10, 306. R. J. Seymour, F. Zemike, and C. L. Sam, Optics Comm., 1976, 18, 49; R. J. Seymour and F. Zernike, Appl. Phys. Letters, 1976, 29,705.

116

Gas Kinetics and Energy Transfer

Optical parametric oscillators have been used not only as a tunable laser source, but to down-convert by difference frequency generation using a non-linear crystal. Such systems have the advantage of room temperature operation and broad-band wavelength coverage. Because of the inherently large gain bandwidth practical devices are generally limited to linewidths greater than 0.1 cm". With a frequency doubled Nd:YAG laser, (YAG = Yttrium aluminium garnet) pumping LiNbO,, peak powers of a few kilowatts and pulse-widths of 130-70011s are typically obtained in the region 0.55-3.65 pm. It is thus suitable for pumping hydrogen stretching fundamentals as well as overtone and combination bands in suitable molecules. An oscillator of this type has been used to investigate V + V transfer in HCLS4 The use of the stimulated Raman effect provides a convenient method of producing tunable i.r. radiation. In favourable cases, an efficient (up to 50%) energy conversion can be obtained by stimulated Raman scattering. Provided the initial exciting laser is tunable, each of the successive Stokes and anti-Stokes shifted bands can be tuned. Frey and Pradere" used a tunable dye laser and Grazuyk and ZubarevS6an Nd:Glass laser, to produce tunable radiation down to 7 pm in CH4 and H,. Hydrogen gives the largest Raman shift (4155 cm- ') and very good energy conversion reaching up to 30% in the near i.r. Recent experiments with a high power ruby laser pumping three dye amplifiers have produced tunability down to 16pmVs7To achieve a wide tuning range using the stimulated Raman effect in H, or CH4 very high pump powers are necessary to excite second and third Stokes scattering. However, stimulated electronic Raman scatteringcan give a very large Stokes shift (e.g. 20 OOO cm- ') and the threshold can be very low (less than 1 kW) for resonance Raman scattering. With tunable dye laser sources, stimulated electronic Raman scattering in barium '* and potassium 5 9 vapour has been used to produce tunable i.r. radiation around 2.7 pm with a tunable range of about lo00 cm-' and powers up to 1 kW. Very recently, tunable i.r. radiation has been generated by coherent Raman mixing in hydrogen.60 This process does not require a resonator, is not limited in tuning range by resonances (cf. stimulated resonance Raman scattering), does not require phase matching, and replaces the high peak power tunable source by a fixed frequency pump source. Frequency conversion by coherent Raman mixing involves four radiation fields, the pump, generated Stokes, tunable input, and generated output frequencies related by op- as= o,- coo where op- as = oRis the Raman mode frequency. The coherent mixing process requires the generation of a Stokes field by stimulated Raman scattering and is therefore different from the parametric four-wave mixing process, or CARS 6 1 process, which does not involve a population change. Brosnan ei aL6' generated tunable output between 35 and 13 pm by coherent Raman mixing in H2 gas at 20atm using an Nd:YAG laser pumped LiNbO, parametric oscillator as the imput source. Typical output powers were 6 kW in a 5 ns pulse with 53

54 Is 56 I7 58 59

6o 61

D. C. Hanna, B. Luther-Davies, R. C. Smith, and R.Wyatt, Appl. Phys. Letters, 1974,25, 142; R. B. Weisman and S. A. Rice,Optics Comm., 1976,19,28. S . R. Leone and C. B. Moore, Chem. Phys. Letters, 1973,19,340. R. Frey and F. Pradere, Optics Comm., 1974, 12,98. A. Z. Grazuyk and I. G. Zubarev, I.E.E.E. Conference Quantum Electron., Amsterdam, 1976. J. Cohen, M. Clerc, and R. Rigny, Optics Comm., 1977, 21, 387. J. L. Carlsten and P. C. Dunn, Optics Comm., 1975, 14, 8 . D. Cotter, D. C. Hanna, P. A. Karkkainen, and R. Wyatt, Optics Comm., 1975, 15, 143. S. J. Brosnan, R.N. Fleming, R. L. Henbest, and R. L. Byer, Appl. Phys. Letters, 1977,30, 330. R.F. Begley, A. B. Harvey, and R.L. Byer, Appl. Phys. Letters, 1974,25, 387.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

’

117

’

a resolution of 4 cm- without, or about 0.1 cm- with, an etalon in the parametric oscillator cavity. The CARS process has been used as a source of tunable i.r. radiation down to 16 pm in H,.62 High h u r e Gas Lasers.-Another approach to the generation of tunable i.r. laser radiation is the use of high pressure tunable molecular gas lasers. At pressures above 10 atm there is significant overlap between the vibration-rotation lines in C 0 2 and continuously tunable operation is possible over a limited range.63 Blanchard et aZ.64 have operated a double discharge CO, laser at pressures up to 6 atm. At pressures above this value rather different pumping techniques are necessary. Chang and Wood 6 5 obtained single nanosecond pulses from an optically pumped (33 atm) C 0 2 laser. The C 0 2 inside the 1 mm resonator was excited with the focused output from a pulsed 4.2 pm HBr laser. Similar optical pumping experiments have been reported on N,O which lases at 10.8 pm.66 Direct optical pumping of pure N,O by the HBr laser is limited to 7.5 atm but by using a combination of optical pumping and resonance energy transfer operation at a total pressure of up to 42 atm has been achieved.67 An optically pumped N,O/CO, laser operating at a pressure of 10-20atm has been continuously tuned over about 7 cm- near 10.5 pm.68

’

‘

Other Laser Systems.-The increased interest in laser separation of uranium isotopes has resulted in considerable effort toward the development of lasers operating in the 8 and 16 pm regions. Only a few examples will be quoted from this rapidly expanding area. Laser emission in the 8 pm band of C2H2has been observed in electron-beam controlled discharges in CO-C2H, mixture^.^' Line tunability within the P- and Q-branches has also been demonstrated. Stimulated emission in the 16 pm region has been obtained by optically pumping CF4 and NOCl with a TEA C 0 2 laser.70 16 pm laser radiation has also been obtained from optically pumped C02.7 7 2 Optical pumping has also been used to indirectly pump OCS, C2H2, CS,, and CO,. A frequency doubled TEA CO, laser is used to pump COYwhich subsequently collisionally transfers its energy to the lasing gases.73 A grating tuned OCS laser operating on over 80 lines between 8.19 and 8.36 pm has been developed.74

’*

Detectors.-Since i.r. fluorescence is generally weak, the ideal detector should be highly sensitive over a wide frequency range, have low noise and a short response time. To obtain these characteristics it is necessary to operate near liquid helium temperatures. Alloy detectors such as Hg,-, Cd, Te and Pbl-, Sn, Te operate at 62

64

65 66

67 68

69

‘I0

71 72

73 74

R. Frey, F. Pradere, and J. Ducuing, Optics Comm., 1976, 18,204. F. O’Neill and W. T. Whitney, Optics Comm., 1976, 18, 126. M. Blanchard, J. Gilbert, F. Rhault, J. L. Lachambre, R. Fortin, and R. Tremblay, J. Appl. Phys., 1974,45, 1311. T. Y. Chang and 0. R. Wood, Appl. Phys. Letters, 1973,23,370. T. Y.Chang and 0. R. Wood, Appl. Phys. Letters, 1973, 22,93. T. Y. Chang and 0. R. Wood, Appl. Phys. Letters, 1974,24,182. T. Y. Chang, J. D. McGee, and 0. R. Wood, Optics Comm., 1976,18,57. L. Y. Nelson, C. H. Fischer, S. J. Hoverson, S.R. Byron, F. O’Neill, and W. T. Whitney, Appl. Phys. Letters, 1977, 30, 192. J. J. T i e and C. Wittig, Appl. Phys. Letters, 1977, 30,420. J. A. Stregack, T. J. Manuocia, N. Harris, and B. Wexler, Optics Comm., 1976, 18, 123. R. M. Osgood, Optics Comm., 1976, 18, 123. H. Kildal and T. F. Deutch, Appl, Phys. Letters, 1975,27, 500. T. F. Deutch and H. Kildal, Optics Comm., 1976, 18, 125.

WAVELENGTH/

fi

Figure 2 Response curves for some commercial i.r. detectors (Reproduced by permission from Santa Barbara Research Centre)

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

119

liquid N2 temperature (77 K) but over a limited frequency range. Indium antimonide cooled to 77 K is a sensitive detector out to about 5.5 pm, beyond this wavelength, gold-doped germanium at 77 K is useful out to 9 pm and can be made with a very short response time ( <2 ns). At longer wavelengths, copper-doped germanium is generally used cooled to at least 14 K. This detector covers the region 2-30 pm with a response time of about 1 ns. Zinc-doped germanium may be used out to 40 pm. The characteristics of some typical i.r. detectors are shown in Figure 2. For monitoring the laser pulse, the photon drag detector is very useful. It has an inherent rise time of less than 250 ps, operates at room temperature, is insensitive to electrical interference, and will withstand massive ~verloading.~’At 10.6 pm the responsivity is typically 0.5 mV kW-’ into 50 SZ, so that the instrument has very low sensitivity. It is mainly used for monitoring the output of pulsed and Q-switched C02 lasers for which purpose it is ideally suited. The laser output can also be monitored continuously by passing it through an optimized photon drag detector which transmits about 75% of the radiation. A new class of thermal detector, the pyroelectric detector,76*77 is sensitive, covers a wide frequency range, operates at room temperature, and can be made with a short response time. The detecting ability of the best pyroelectric detectors approaches, within an order of magnitude, that of the ideal thermal detector at room temperature. Pyroelectric detectors are made from materials which have a permanent temperature dependent electric polarization which changes when i.r. radiation is absorbed. A typical pyroelectric detector based on triglycine sulphate has a detectivity of about 6 x 10’ cm Hz* W“. Detectors with a response time of less than 1 ns have been constructed which are based on materials such as strontium barium niobate and lithium tantalate.7 9 However, considerable sacrifice in detectivity is necessary to obtain such fast rise times and these detectors are of little use in pulsed fluorescence work. They are, however of considerable use for CW work and for monitoring laser pulses where their low detectivity is of less importance. Care must be taken in mounting these detectors since pyroelectrics are also piezoelectrics and are therefore sensitive to acoustic interference and mechanical vibrations.

’’

CW and Low Frequency Studies. Since the fluorescent emission in low frequency or cw studies is much stronger than in the pulsed ( > I MHz) case the detector requirements are not so severe. Modulation up to about 1 KHz is frequently employed so that some slow response detectors are not suitable. Pyroelectric detectors are being used increasingly since they are fairly sensitive and can be made with an adequate response time. Fluorescence Techniques.-Low Frequency Measurements. In a typical arrangement, the output from a stable CW COz laser is split into two beams and the major portion passed through the test gas or vapour in a water cooled stainless steel cell. The energy passing through the cell can be monitored to determine the fraction absorbed by the gas. Both the input and fluorescence signals can be modulated by a coupled stepper-motor chopping system so that the phase relationship between the two ” 76

” 79

A. F. Gibson, M.F. Kimmitt, and A. C. Wqlker, Appl, Phys. Letters, 1970,17, 78. E. H. Putley, Optics a n d b s e r Technol., 1971, 3, 150. H. P. Beerman, Ferroelectrics, 1971, 2, 123. A. M.Glass, Appl. Phys. Letters, 1968, 13, 147. A. M. Glass and R. L. Abrams, J. Appl. Phys., 1970,41,4455.

120

Gas Kinetics and Energy Transfer

choppers can be varied in a controlled manner. The appropriate wavelength region in the emitted radiation is isolated either with a monochromator or with bandpass or semiconductor blocking filters, Often the spectrum is recorded in an analogous way to an i.r. absorption spectrum. The output from the detector is usually ratioed against a reference signal obtained from the split part of the input radiation to correct for fluctuations in the laser output. Pressure sensitive transistors can be used to measure the pressure profile in the test gas up to a frequency of 100 kHz. Self absorption can be a major problem with this type of experiment but with a properly designed fluorescence cell this can be largely overcome, and very high analytical sensitivity achieved. 1.r. fluorescence spectroscopy is a valuable technique for following the course of laser induced chemical reactions. Molecules can be vibrationally excited or dissociated by intense i.r. laser radiation and the kinetics of subsequent reactions monitored by i.r. fluorescence spectroscopy. Laser stimulated chemical reactions is an increasingly active field and there is now ample evidence for non-Boltzmann reactions in certain laser stimulated systems.’ High Frequency Measurements. A schematic diagram of a typical experimental arrangement for short pulse work is illustrated in Figure 3. Narrow pulses from a TEA molecular laser, chemical laser, spin-flip laser, or tunable parametric oscillator are focused into the fluorescence cell. Normally optimum power input is between 1 and 10 kW. High powers can lead to local heating of the gas. Pulse widths varying from a few microseconds to less than a nanosecond are used. Since the fluorescence signal is generally very weak some kind of signal averaging is necessary. The reference signal for the waveform sampling system is provided by splitting-off part of the incident beam with a Ge beam-splitter and focusing onto a photon drag detector (where the power is sufficiently high). Wavelength selection is usually provided, where necessary, by filters. High quality, wide band, low noise, electronics are essential and care must be taken to provide adequate shielding from electrical interference especially where electrical discharge lasers are used. The pulse-to-pulse stability of the laser is also important in order to achieve good signal-to-noise ratios. A moderately high pulse repetition rate is also helpful with some types of signal averaging systems.

I

Boacor

1

I2ZE.l Figure 3 Schematic layout for pulsed energy tramfer work with fluorescence signal averaging

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

121

Pulsed tunable laser systems are beginning to make an impact on the energy transfer field. The relatively high powers and spectral purity of some of these sources mean that in certain cases individual vibrational rotational states can be selectively populated or that the population of these states can be monitored with great precision. The optical parametric oscillator has been used to excite single vibration-rotation lines of the first and second vibrational levels in H C y 4 and to pump ground state CO ( u = 0) directly to the second vibrational level ( 0 = 2).'* Double Resonance Techniques.-Double resonance experiments are complementary to fluorescence methods. They can be used to study the relaxational behaviour of vibrational levels whicheither fluoresce weakly or at a frequencyveryclose to that of the pump radiation (so that the weak fluorescence is obscured by the much more intense scattered pump radiation). Furthermore, the i.r. emission is usually not sufficiently intense to permit resolution by a monochromator so that individual rotational levels cannot be studied by conventional fluorescence methods. In i.r. double resonance, the population of a particular level is probed by monitoring the absorption, as a function of time, of weak, stable CW laser radiation tuned to the molecular transition frequency.8"*82 This technique can be used to study energy transfer between different isotopic species such as "CH3F and I3CH3Fby pumping one species and monitoring population changes in the other.82 Changes in population produced by laser pumping can also be detected using microwave absorption techniques. Several such studies have been carried out using N 2 0 and C 0 2 laser pumping freq~encies.'~-'~ The method has recently been demonstrated to have sufficient sensitivity to observe the weak distortion-induced pure rotational transitions in the ground state of tetrahedral molecules.87 A double resonance experiment has been reported using two i.r. lasers tunable over a narrow range by adding or subtracting photons with two microwave sources. The molecules act as non-linear elements which mix the two fields causing a simultaneous two photon transition analogous to the stimulated Raman effect. The tuning range appears to be about 1-2 GHz. One experiment involved pumping one vibration-rotation transition in NH, with a high power CW source and monitoring the population of a second unconnected vibration-rotation transition with a second low power modulated source." Stark switching to bring molecular energy levels in and out of resonancewith an optical or microwavefield has been used in an i.r.-microwave double resonance experiment.8 9 Recent technical developments include particularly the work of Redon and Fourier '* who constructed a parallel plate cell for homogeneous d.c. Stark fields of up to 50 kV cm-l, A Stark shift of 12.6 GHz was recorded for a field of 28.39 kV cm-' in the J = 9, K = 6 line of NH3. These large fields can be used to tune absorption frequencies to exact laser frequencies for double

82

83 84

86 ST 88

89

P. B. Sackett, A. Hordvick, and H. Schlossberg, Appl. Phys. Letters, 1973, 22, 367. J. I. Steinfeld, J, Burak, D. G. Sutton, and A. V. Nowak, J. Chem. Phys., 1970, 52, 5421. J. M. Preses and G. W. Flynn, J. Chem. Phys., 1977,66,3112 and refs. cited therein. J. Lemaire, J. Houreiz, F. Herlemont, and J. Thibault, Chem. Phys. Letters, 1973, 19, 373. H. Jetter, E. F. Pearson, C. L. Norris, J. C. McGurk, and W. H. Flygare, J. Chem. Phys., 1973, 59, 1796. R. F. Curl, J. Mol. Spectroscopy, 1973,48, 165. W. A. Kreiner and T. Oka, Canad. J. Phys., 1975,53,2000. W. A. Kreiner, U. Andresen, and T. Oka, J. Chem. Phys., 1977, 66,4662. S. Freund and T. Oka, Appl. Phys. Letters, 1972, 21, 60. J. M.Levy, J. H. S. Wang, S. G.Kukolich, and J. I. Steinfeld, Phys. Rev. Letters, 1972, 29, 395. M. Redon and M. Fourier, Rev, Sci. Instr., 1975,46,911.

122

Gas Kinetics and Energy Transfer

resonance experiments, and also to allow the study of forbidden transitions. However, with heavier molecules there is a reasonable chance that the laser frequency will coincide with one of the many possible components of a suitable vibrational transition. This is illustrated by the i.r.-microwave double resonance work on the v1 symmetric stretching mode in CF,I.” Non-linear Raman Techniques.-Conventional fluorescence or double resonance measurements can only be used with molecules which have suitable dipolar transitions or where these can be induced, by electric or magnetic fields. Non-linear Raman pumping techniques can be used to produce a high density of vibrationally excited states for transitions which are not i.r. active. Vibrational excitation has been produced in H, for example, by focusing the output from a ruby laser into the high pressure gas. The non-linear Raman effects useful for rapidly populating vibrational levels are the stimulated Raman effect and coherent Raman amplification. The decay or relaxation of the excited vibrational state is usually followed by a technique based on light scattering. Two popular techniques involve measuring the temporal decay of the spontaneous anti-Stokes Raman scattering arising from the populated level and measuring the change in light scattering associated with refractive index changes resulting from gas heating by V-T energy transfer. Stimulated Raman pumping combined with the use of spontaneous anti-Stokes Raman scattering as probe has been used to study hydrogen.”* ” However, direct population of vibrational levels by nanosecond stimulated Raman scattering has only proved feasible for Ha, D,, and CH,. In other gases, stimulated Brillouin scattering competes with the Raman process and preferential pumping of the Brillouin levels occurs because the acoustic lifetime is of the same order as the duration of the excitation pulse. A more generally applicable process proposed by de Martini 94 is based on coherent Raman amplification. In this method, the sample is simultaneously pumped with coherent radiation at v, and v, - v,, where v, is the vibrational frequency of interest. Non-linear interaction within the sample results in a population of the upper vibrational level greater than that which could be achieved by laser pumping at v, alone, utilizing the stimulated Raman effect. This technique can also be used to populate vibrational levels in cases where the stimulated Raman effect is inapplicable. This would include systems in which the threshold for the stimulated Raman effect is greater than for stimulated Brillouin scattering, vibrational levels which do not have the largest gain factor for stimulated Raman scattering, and low pressure gases. The radiation at frequency vo is usually provided by a Q-switched solid state laser and that at v, - v, by a tunable dye laser.95 Alternatively, v, - v, may be provided by Stokes stimulated Raman scattering from the gas itself, a method widely used for energy transfer work. This method is however limited to gases in which stimulated Raman scattering can be excited and to vibrations (usually only one) of that molecule in which the effect is exhibited. A more general technique is to generate the radiation at v, - v, by stimulated Raman scattering from a second independent gas, chosen so that its stimulated frequency coincides with a Raman active frequency in the pumped system.96 This two stage process 91 92

93 94

95 96

H. Jones and F. Kohler, J. Mol. Spectroscopy, 1975,58,125. F.de Martini and J. Ducuing, Phys. Rev. Letters, 1966,17, 117. J. Ducuing and F. de Martini, J. Chem. Phys., 1967,64,209. F. de Martini, Nuovo Cimento, 1967,51B,16. J. Lukasik and J. Ducuing, J. Chem. Phys., 1974,60,331. J. Ducuing, C. Joffrin, and J. P. Coffinet, Optics Comm., 1970,2,245.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

123

provides more controllable excitation conditions and permits the use of low pressures in the sample cell. An alternative technique for pumping the upper vibrational state of gases, where stimulated Brillouin scattering is a problem, is to use much shorter pulse widths.". 9 8 When picosecond pulses are used stimulated Brillouin scattering cannot occur since the acoustic phonon lifetime is much longer than the pulse duration and stimulated Raman pumping is the dominant process. In most of the non-linear pumping experiments, the Schlieren light scattering technique is used to monitor the population of the excited state. When V-T transfer occurs there is a small temperature rise in the gas (of about 1-5 "C), which causes a decrease in the refractive index An(t) according to equation (l), where N ( t ) is the An(t) = -b(n

- l)hv,cN(t)/pC,

number of vibrational quanta,per unit volume which have relaxed at time t, /3 is the thermal expansion coefficient, p is the density, Cp is the molar heat capacity and v, the vibrational frequency. This expression assumes that the rate of propagation of the density change across the illuminated volume is essentially instantaneous and that heat diffusion is negligible during relaxation. The intensity of scattered light I ( t ) resulting from the variation in refractive index is proportional to [N(t)]2.99If there is an exponential decay of vibrationally excited molecules the time dependence of the intensity of scattered light will be of the form I(t) = I(co)[I-exp(-t/z)12 where z is the relaxation time of the first excited state. The value of z is obtained by fitting the observed intensities to the above expression. Experimentally, I ( t ) is obtained by passing a low power stable helium-neon laser through the excited volume and monitoring the intensity fluctuations with a photomultiplier located behind a Schlieren slit. Typical detection limits are about 2 x excited vibrational quanta in the focal volume.

Matrix Isolation Techniques.-In rare gas matrices, at low temperatures, the normal intermolecular energy transfer processes are minimized and as a consequence the lifetimes of the vibrational states of the isolated molecule can be very long. A vibrational relaxation time of about 1 s, for example, was found for N, in inert gas matrices.' O0 Thus, the matrix isolation technique provides the opportunity, in appropriate cases, for investigating the vibrational states of relatively unperturbed 'isolated' molecules. Since the concentration of active species in the matrix is relatively low, the i.r.4.r. double resonance technique has proved the most suitable for studying matrix isolated species. 1.r. fluorescence has been used, however, to measure the lifetime of CO molecules isolated in neon and argon matrices, at 6 K.'O1 The vibrational lifetime was found to be between 4-8 ms, demonstrating the inefficiency of relaxational processes. These were found to become increasingly more effective at higher matrix temperatures. Generally, there is no molecular rotation in the matrix, 97 98

99

loo lol

M. E. Mack, R. L. Carmen, J. Reintjes, and N. Bloemberger, Appl. Phys. Letters, 1970, 16, 209. M. A, Kovacs and M. E. Mack, Appl. Pkys. Letters, 1972,20,487. M. Kerker, 'The Scattering of Light and other Electromagnetic Radiation', Academic Press, New York, 1969, p. 414. D. S. Tinti and G. W. Robinson, J. Chem. Phys., 1968'49, 3229. H. Dubost, L. Abouaf-Marguin, and F. Legay, Phys. Rev. Letters, 1972, 29, 145.

Gas Kinetics and Energy Transfer

124

so lifetimes of pure vibrational states are obtained. These lifetimes are, of course, directly influenced by intermolecularenergy transfer processes and so provide a means of probing the intermolecular interactions leading to energy transfer. The isolated species whose vibrations are weakly coupled to the solid host matrix may also be used to probe the dynamical processes occurring in the solid.

The Thermal Lens Technique.-The thermal lens technique lo4is complementary to the fluorescence t y p of experiments in that, in principle, it enables the magnitude of the exo- or endo-thermicity of a V-V energy transfer step to be determined. The apparatus consists of a cylindrical i.r. gas cell, 30 cm or more in length, through which a TEMooC02- and TEM,, He/Ne - laser beam pass co-axially with each other and the cell walls. Traditionally an iris is positioned, before the cell, to define the beam diameters, and the He/Ne radiation is collected alone, after projection over 1-2 m, via a 632.8 nm narrow band pass filter, on an axially aligned pinhole masking a photomultiplier tube. The C02 laser is pulsed and when such a pulse is absorbed by the sample in the cell, heat is taken up from (or given out to) the translational degrees of freedom, depending on whether the V-V transfer is endo- or exo-thermic. The resulting refractive index gradient converges or diverges the TEM,, beam profiIe of the Hewe laser and, behind the axially aligned pinhole, an increased or decreased signal amplitude is observed, giving the sign of AH in the V-V transfer. As the slower V-T transfer follows the V-V process, and since it must be by definition exothermic with respect to translation, a slower exponential decay in lens signal results from the associated divergence of the He/Ne beam. Finally the 'pumped' gas at the core of the cell cools and the detected signal rises to its original value again with a lifetime which is a function of the thermal diffusivity, K, of the sample gas [K = K(pC,)-' where K = thermal conductivity coefficient of the gas, p its density and Cp the constant pressure molar heat capacity]. For this last relaxation it has been shown that, contrary to previous interpretation~,"~the lifetime is not in fact exponential, but is quadratic and given by the relation (3) Io5 s-3 =

B(;

+ 1)

(3)

where s is the lens signal measured as the difference between the equilibrium signal amplitude and that at time t ; z is the quarter lifetime of s and B is a constant determined by the iris aperture, length of the cell, and absorption coefficient of the gas. Previous interpretations in terms of the relaxation modes of the cell gave T ~ = ~a2/x2 , CPP ~ where a is the cell radius and x, a dimensionless quantity, is the RTK first root of the appropriate Bessel function. The value of x lies between 2.4 and 3.8 and so t lo2 Io3

Io4 loS

Gy(:)2,

/ ~ =~ ~ ~ ,

where d is the radius of the iris aperture. Thus these

F. R. Grabiner, D. R. Siebert, and G. W. Flynn, Chem. Phys. Letters, 1972, 17, 189. R. D. Bates, G. W. Flynn, J. T. Knudtson, and A. M. Ronn, J. Chem. Phys., 1972,57,4174. 'Chemical and Biochemical Applications of Lasers', ed. C. B. Moore, Academic Press, 1974, Vol. 1, p. 184 etc. R. T . Bailey, F. R. Cruickshank, D. Pugh, and W. Johnstone, in 'Proceedings of the Royal Institution Conference, Lasers in Chemistry', ed. M. West, Elsevier, Amsterdam, 19 77, p. 257.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

125

lifetimes are 50-100 times less than previously predicted, but the derived values of K agree with those for example for C2H, within the +S% present error in determining d. Further work is in progress to reduce this error and increase the accuracy of the model. Detailed analysis of the processes occurring in the cell is essential to the proper understanding of how to extract energy transfer data from the faster V-T and V-V sections of the curve, and more particularly to verify the linearity of the relationship between lens signal and AH of the V-V step. The role of the iris diaphragm is not well understood. There exists an optimum iris aperture for which the divergent effect of the lens is greatly increased. We are currently investigating this effect, and it seems that it may greatly influence the fast sections of the signal and thus the calculations of zv-v and zV-=. The Evaluation of Energy Transfer Probabilities from Fluorescence Data.-An example of the evaluation of a multiple-exponential fluorescence decay curve incorporating all the features of such a process is the treatment of the DCI/CO/N2 system (carried out in the presence of He buffer gas). In this system lo' the CO fluorescence is monitored and the early, fast V-V processes are analysed. These arise from the reaction scheme, shown in equations (4)--(6), the DCI having been excited essentially

+ CO(U= O)&DCl(U = 0) + CO(; = 1) DCl (U= 0) + N2 (U= 1) DCI (U = 1) + N2 (U = O)& (U= 0) + CO(u = 1) N2 (U = 1) + CO(U = O)&N2 DCI(U = 1)

(4)

(5)

(6)

instantaneously by a DCl laser. The object was to measure k,, k,, and k2 having been previously measured in the appropriate binary mixtures by an exactly analogous experiment. For the above system the double exponential, V-V transfer, CO fluorescence decay may be written in the approximate form m1uor

cc (1

- A ) -exP(-~~'exptlt) + Aexp(-~k"e,p,,O

(7)

where klexptl% 25 k'lexptl,the former corresponding mostly to DCI 3 CO transfer and the latter to CO + N2 transfer. (1 - A) is the fraction of energy in CO after vibrational equilibration. P is the total pressure. However, since the gas mixtures 5 :200: 800 this approximation will were chosen such that typically DCI: CO :N, lead to negligible error. Since kttexptl is most sensitive to k - , it was substituted into the kinetic equations for the system

-

[DCl*] [CO*]

=0

.",*I k-l k-, were obtained from k, and k, via the Boltzmann expression k,/k-,, = exp( - AEJRT). Thus k3 was obtained. This is a second-order rate constant and we shall express such data in units of molecule-' cm3 s-', throughout this Io6 P. F. Zittel and C. B. Moore, Appl. Phys. Letters, 1972, 21, 81.

Gas Kinetics and Energy Transfer

126

Report for consistency with the series in which it appears. [The more often quoted p r values are related to such k values as follows, p z / ( p s torr) = (k/(molecule-' cm3 s-'>)-' x 3.104 x lo-", at 300 K.] More usual binary systems are, of course, far simpler. In all such systems minor corrections can be made for the slow section of the exponential (V-T transfer), but frequently negligible error arises if it is ignored, so great is the difference in rates of the two processes. If the laser pulse energy is kept below -1 mJ, no correction is generally required for translational cooling of the system, unless the pulse repetition rate is very high. Rate constants determined as above are then related to a specific energy transfer probability to facilitate comparison with the theoretical models (vide infra) in order to deduce the mechanism of each specific energy transfer process. Clearly, the detailed structure of the i.r. spectra involved in each case strongly influences the validity of the various kinetic assumptions necessary. Generally, however, the population of the upper level 'pumped' by the laser is so great (even population inversion is possible) that the relaxation lifetime (7)of the fluorescence corresponds to the decay of a single state, free from reverse-reaction interference. It is sometimes possible to verify experimentally the lower state to which the 'pumped' state (m) relaxes and then z-l = nk,, m - l for a one component sample at molecular concentration n. Now nk,,,-l = (Pm,m-l)~, where z is the collision frequency and (Pm,m-l)is the probability of a one quantum transfer during a collision. If hv 9 kT, the above analysis holds, but when they become comparable (hv is the quantum transferred in the collision) km,m-lx km-l,mand a simple analysis is possible only if the laser pump can produce considerable population inversion. For mixtures of gases (or if we consider the different vibrational level spacings in a one component, anharmonic oscillator model) the component with the lowest frequency (or the higher vibrational levels in the anharmonic case) will be preferentially populated by transfer at typical laser pulse energies. If K is the equilibrium constant for the process AB(v) CD(V')-+ AB(v 1) C D ( d - 1) AE, (8)

+

+ +

+

in the binary system A B (frequency v ) and CD (frequency v'), then K = exp(AE/kT = exp[h(v' - v)/kT]. AE is positive if v' > v and then K % 1. Thus large concentrations of AB(v + 1) may prevail, i.e. the lower frequency component is preferentially excited in the transfer step. If this population rises sufficiently its V-T transfer may become kinetically limiting, whereas it is usually expected that V-V equilibration is the faster process. Such V-T transfer limiting the rate of rise of population of an upper vibrational level is illustrated in the case of the CO/N2 laser which operates only on high u transitions [wherepopulation inversion is possible as above (CD = N2)], but not on the o = 1 4 transition. Ultra-high resolution i.r. spectroscopy, made possible by the recent introduction of tunable i.r. laser sources, is proving invaluable in unravelling the details of the vibrational/rotational manifolds even for large species lo7 such as UF,. Double resonance experiments with similar tunable lasers lo' permit the identification of the exact upper and lower states involved in each transfer step. These experiments vastly increase confidence in the experimental identification of lo' lo*

C. P. Robinson in ref. 105. R. T. Bailey, F. R. Cruickshank, G. Crowder, D. Pugh,S. D. Smith, C. A. Pidgeon, P. N. D. Maggs, T. Scragg, and C. Ironside, unpublished data.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

127

(Pm,m- 1) values and should totally eliminate confusion over multi-step possibilities in relaxation mechanisms.lo9 The sure identification of the transition together with the accuracy with which (Pm,m-l)can be obtained from the laser experiments will inevitably lead to an awareness of the essential features of the energy transfer mechanism of particular molecular types. 3 Theoretical Prediction of Energy Transfer Probabilities (PmJ The purpose of this section is to briefly review the historical background to current theories (already reviewed up to 1974) 110-120 for the prediction of the probability (Pm,m - that, during a bimolecular collision, vibrational energy will be transferred from the state of vibrational quantum number u = M of one species into the other species. The literature from 1974 to July 1977 is more critically surveyed and the future of such calculations assessed. The accuracy of the various current techniques and the conditions under which they may be invalidated are also examined.

’)

General Techniques.-A fully detailed, accurate description of the state of the excited oscillator and of the intermolecular potential during the collisions, even if it were possible, cannot be used since it would consume excessive amounts of time even on the fastest computers. Accordingly, recourse must be .made to a wide selection of approximation techniques. The foundations of the current approach were laid by Landau and Teller 12’ who approximated the intermolecular potential to a simple exponential function and assumed that the oscillator was simple harmonic. An important result of their theory was the Landau-Teller rule, viz. T,=, = l[n z,,~ for vibration 3 translation energy transfer of an oscillator in state u = n of lifetime T”=,,. This rule must be obeyed if all vibrational levels equilibrate more rapidly than the manifold equilibrates with translation and this is generally the case,122-125particularly in laser fluorescence experiments.’26 More recently the Schwartz-Slavsky-Herzfeld theory 2 7 has been

’

Io9 I1O

H. K . Shin, Chem. Phys. Letters, 1976,40,316. T. L. Cottrell and J. C. McCoubrey, ‘Molecular Energy Transfer in Gases’, Butterworths,

London, 1961. P. Borrell, Adv. Mol. Relaxation Processes, 1967, 1, 69. 112 ‘Transfer and Storage of Energy by Molecules’, ed. G.M. Burnett and A. M. North, WileyInterscience, New York, 1969,2, 58. 1 1 3 C. B. Moore, in ‘Fluorescence’, ed. G. G. Guilbault, Dekker, New York, 1967, p. 133. 114 K . Takayanagi, Progr. Theor. Phys. Suppl. Kyoto, 1963,25, 1. 115 K . Takayanagi, Adv. Atomicand Mol. Phys., 1965,1,149. 116 K . F.Herzfeld, ‘Thermodynamics and Physics of Matter’, Princeton University Press, Princeton, New Jersey, 1965. 11’ D. Rapp and T.Kassal, Chem. Rev., 1969, 69, 61. 11* K. Herzfeld and T. A. Litowitz, ‘Absorption and Dispersion of Ultrasonic Waves’, Academic Press, New York, 1959. 119 D. %crest, Ann. Rev. Phys. Chem., 1973,24,379. l Z o R. T. Bailey and F. R. Cruickshank, Applied Spectroscopy Reviews, 1975, 10, 1. l Z 1 L. Landau and E. Teller, Phys. 2.Sowjetunion, 1936, 10,34. l z 2 R. J. Rubin and K.E. Schuler, J, Chem. Phys., 1956,24, 68. l Z 3 E. W. Montroll and K.E. Schuler, J. Chem. Phys., 1957,26,454. lZ4 K . E. Schuler, J. Chem. Phys., 1960,32, 1692. l z 5 C. C. Rankin and J. C. Light, J. Chem. Phys., 1966,46, 1305. l Z 6 W . D. Breshears, Chem. Phys. Letters, 1973, 20,429. l Z 7 R. N. Schwartz, Z. I. Slawsky, and K.F. Herzfeld, J. Chem. Phys., 1952,20,1591. 111

128

Gas Kinetics and Energy Transfer

extensively used. Like the Landau-Teller theory this also uses a harmonic oscillator and exponential (repulsive term only) potential function. However the system is treated quantum mechanically throughout, using the first order distorted wave approximation (FODWA)."' This latter requires that Pll0(u) be small for all intermolecular velocities, u, considered. Very careful checks must be carried out in order to ensure that this condition is satisfied, since (P,,o> may be << 1 (10-2-10-3) because the number of molecules of velocity u is small and not because P1,o(u) is small. Indeed it is generally true that the high velocity end of the intermolecular velocity distribution is responsible for most of the energy transfer. Several workers have used this or similar treatments.'"* '14* 116*118* 128-132 Anharmonic intermolecular potentials have been introduced. An accurate potential function for the He/H, system has been used to test the assumptions and approximations of the SSH approach.133* It was found that potential functions, constructed by summing exponential functions between each pair of atoms, were totally useless. More careful fitting to Lennard-Jones potentials derived from gas kinetic data also gave poor results where long range forces might be important (e.g. in the near resonant condition, vide infra), since the gas kinetic experiments are not sensitive to these and so characterize them poorly. Calculations discussed so far are in a fixed collinear geometry, the realistic three-dimensional case being attained by multiplying the collinear result by 3. Mies 134 found this a good approximation, but 4 was better for the He/H, system. He also found that head-on collisions were not the most efficient in energy transfer for the He/H2 system, contrary to the usual assumptions. Mies also found that (Pl,o) could be several orders of magnitude in error if oscillator anharmonicity was not included. For He/H, the anharmonicity factor (, Vll0 Vo where ,V, is the potential function for elastic scattering of He by H2 in the state u = n) is 10% greater than the harmonic value of 1 and this results in a reduction of ( P , , o ) by 2-3 orders of magnitude owing to its dependence on the square of the wave function. Rapp has included this correction, together with those for the limitations of the FODWA and its failure at high temperature, in calculations on N, + N,, obtaining ten times less than the experimental result. This modified SSH theory correctly predicts the increase in (P1,o)in the series N,, CO, 02,C12, Br2, 12. Long range interactions were neglected. This precision is typical of current general expectations from a theory of this nature. A further limitation on the original SSH theory was that series convergence in averaging (Pl,o) would only occur if the energy transferred in the collision, AE 4 + p ( ~ , , * ) where ~ q,* is the intermolecular velocity for which energy transfer probability is a maximum and p is the reduced mass of the colliding pair. For a molecular weight of 10 at 300 K and the most probable molecular velocity, AE w 200 cm-'. Thus serious errors arise if the quantum transferred exceeds 200 cm", which it commonly does in the molecules studied by laser techniques. J. M. Jackson and N. F. Mott, Proc. Roy. SOC.,1932,A137,703. K.Takayanagi and T. Kishimoto, Progr. Theor. Phys. Kyoto, 1953,9,578. K.Takayanagi, J. Phys. SOC.Japan, 1959,14,75. 1 3 1 A. F. Devonshire, Proc. Roy. SOC.,1937,A158,269. 132 K.Takayanagi and Y. Mianoto, Sci. Report Saitama University, 1959,Alll, 101. 133 M.Krauss and F. H. Mies, J. Chem. Phys., 1965,42, 2703. lJ4 F.H.Mies, J. Chem. Phys., 1965,42,2709. 128

lZ9 130

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

129

Recentl~,’~’ in the derivation of an ostensibly more accurate approximation than the 3 multiplier for conversion from a collinear result to the three-dimensional result, a somewhat modified SSH theory has been used. A difficulty l J 6 similar to that outlined above was encountered at low temperatures (125 K for He/CO) in integration by the saddle-point method and numerical methods were necessary.13’ Thus an apparently sharp increase in (Pl,o) at temperatures < 125 K was shown to be an artefact of the original calculation. Some degree of anharmonicity has been considered in the SSH oscillator 13* and for high vibrational temperatures coupled with low translational temperatures the populations of the lower vibrational states can be much lower than those predicted by the Landau-Teller model and the overall energy relaxation rate increased. The SSH type of approach has been refined 139s140 by the inclusion of higher orders of approximation than the FODWA. This was important in the consideration of multiquantum transition probabilities. For small amplitude vibrations only, a semi-classical calculation of (Pl ,o) is frequently adequate and simplifies the work in polyatomic systems. In this treatment the intermolecular trajectory is assumed to behave classically and the time dependent perturbation due to the collision is coupled with the time dependent Schrodinger equation of the oscillator to yield transition probabilities. The harmonic oscillator exponential potential approximations have been so used 141-143 although anharmonic intermolecular potentials have also been included.141s3 2 y 144 Semiclassical theories have recently been reviewed in detail 14’ and the reader is referred to this work for further information. The advantage of the semi-classical approach is probably its simpler treatment of three-dimensional effects such as molecular rotation. More recently such calculations have been used to probe the significance of multi-quantum transition^."^-'^^ A totally classical approach or ‘quasi-classicaltrajectory’ (non quantized oscillator) calculation continues to find favour. This calculation is based on a model with anharmonic oscillator and exponential, repulsive,143 intermolecular potential or anharmonic oscillator and anharmonic interaction p~tential.’~’~ 5 0 Recent work has concentrated on introducing more realism into the potential hypersurface and employing quasi-classical trajectories on it. De-excitation probabilities can agree relatively well (within a factor of three) with experimental data.’ 51-’53 299

’

’

W. A. Wassam and R. D. Levine, J. Chem. Phys., 1976,64,3118. J. J. Price and C. J. S. M. Simpson, J. Chem. Phys., 1977, 66, 1385. 13’ W. A. Wassam and R. D. Levine, J. Chem. Phys., 1977,66,1387 (also, erratum therein). 13* C. E. Treanor, J. W. Rich, and R. G. Rehm, J. Chem. Phys.,1%8,48, 1798. 139 G. Jolicard and L. Galatry, J. Chem. Phys., 1975, 63,2787. 140 G. Jolicard, J. Chem. Phys., 1975,63,2798. 141 C. Zener, Proc. Cambridge, Phil. SOC.,1932, 29, 136. 142 C. Zener, Phys. Rev., 1931, 37, 556. 143 D. Rapp, J. Chem. Phys., 1960,32,735. lo4 T.L.Cottrell and N. Ream, 7kms. Faraday SOC.,1955,51, 1453. 145 J. W. Duff and D. G. Truhlar, Chem. Phys., 1975,9,243. lo6 R.L. McKenzie, J , Chem. Phys., 1975,63,1655. 14’ R.L. McKenzie, J. Chem. Phys., 1976,64, 1498. lo*R. L.McKenzie, J. Chem. Phys., 1977, 66, 1457. 149 S. W. Benson and G. C. Berend, J. Chem. Phys., 1964,40, 1289. lS0 E. B. Alterman and D. J. Wilson, J. Chem. Phys., 1965,42,1957. lS1 H.E.Bass and D. L. Thompson, J. Chem. Phys., 1977, 66,2545. N. Sathyamurthy and L. M. Raff, J. Chem. Phys., 1977, 66,2191. lS3 H.K.Shin, J . Chem. Phys., 1977,62,4130. 135 136

Gas Kinetics and Energy Transfer

130

Techniques for Near-resonant Transfer.-As the transfer of vibrational energy between the colliding molecules becomes more resonant (thermoneutral), so the ability of the SSH and allied theories to predict {Pl,o) diminishes. In the case of vibrationvibration (V-V) energy transfer the long range potential terms in the intermolecular potential begin to dominate the rate as the transfer becomes more perfectly resonant. As demonstrated above, such interactions are the most difficult to quantify by experiments independent of energy transfer. Conversely, near-resonant energy transfer provides an excellent measure of these long range interactions if only the mathematical tools for their extraction could be perfected. Near-resonant energy transfer processes are very efficient and feature prominently in laser population ‘pumping’ mechanisms e.g. CO,*(v,)

+ N2+ Cot + N2* + 18 cm-’

(9)

where the very slight energy mis-match of 18 cm-’ is taken up as translational energy. For this process it is now well established that the energy transfer probability passes through a minimum at lo00 K and thus at T < lo00 K the wrong temperature dependence is predicted by the SSH theory, i.e. instead of In {Pr,o(V-V)) decreasing linearly as T-* increases, it begins to curve and increase again (Figure 4) below lo00 K. Such curvature has been predicted 137 for the CO/He system at low temperature and ascribed largely if not entirely to rigorous attention to fulfilment of the requirements of detailed balancing. Attractive forces are, however, generally accepted as important for V-V and V-T rates where the collision partners are p ~ l a r i z a b l e . ’ ~ ~ Sharma et aZ.155-157expanded the N2/C0, intermolecular potential in terms of multipole moments, The first non-vanishing contribution was the interaction of the N, quadrupole transition moment, Q , with the COz transition dipole moment. Rotation effects were excluded by using the spherical potential Y = pQ/2r4 i.e. the r.m.s. average over all molecular orientations. Short range forces were represented by a rigid sphere whose collision diameter was not dependent on the internal states of the molecules. A semi-classical treatment then completed the calculation and the correct temperature dependence of {P1,o(V-V)) was predicted. For the near resonant transfer,

-

CO(u = 2)

+ CO(u = 0) -+2CO(u = l),

(10)

it has been shown that dipole-dipole interactions dominate. The semi-classical treatment leads to 1-10 times the gas kinetic cross-section. Molecules with small transition dipoles, e.g. NO, have no significant long range cross-sections. behaviour of {Pl,o(V-V)) obtained that the T ’ It has recently been suggested by Sharma was due to the impact parameter approximation used and not to the long- or short-range nature of the potential used. This temperature behaviour had been proposed as a means of distinguishing those systems in which long range forces were important.I5’ lS4 ls5 ls6

15’ Is8 ls9

A. Tam, G. Mae, W. Park, and W. Harper,Phys. Rev. Letters, 1975, 35,85. R. D. Sharma and C. A. Brau, Phys. Rev. Letters, 1967,19, 1273. R. D. Sharma, 1969,177, 102. R. D. Sharma and C. A. Brau, J, Chem. Phys., 1969,50,924. J. D. Stettler and N. M. Witriol, Chem. Phys. Letters, 1973, 23, 95. Y . Noter, I. Burak, and A. Szoke, J. Chem. Phys., 1973,59,970.

-

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer 10-2

1

-

' Q'

10-0 ~

I

I

1

I

2000

1000

T/K

131

3000

+

+

Figure 4 V-V energy transfer probability for COz(OOol) N2(v = 0 ) + CO2(OO00) Nz(v = 1) 19 cm-', (d-d = d&ole-diple) (Reproduced by permission from A h . Chem. Phys., 1973,23,41)

+

The validity of the impact parameter approximation (IPA) as used in the above calculation of Stettler and Witriol has been challenged,'" but the difference in results between the IPA and the two-state model proposed as a more consistent approach has been shown to be negligible at least for the processes considered. However, the use of the IPA was not validated totally, insufficientlydetailed calculations having been performed. has obtained good agreement with experiment for the More recently Sharma process in equation (1 1)

'"

"'

CO(u = n

- 1) + CO(v = 1) -,CO(u = n) + CO(u = 0) AH = -[26.9(n - 1) - 0.09(n2 - l)] cm-'

(1 1)

where only dipoledipole interactions seem to be significant. In comparing his straight line path IPA methods with the presumably more exact distorted wave Born approximation (DWBA), Sharma finds the two to be in excellent agreement for the C02/14N2and COz/' 'Nz near-resonant systems. Further tests along similar lines lci4 have confirmed that, for kinetic energies of relative motion equal to or greater than the distorting potential well depth, the DWBA and straight path results agree within 20%. This seems to conflict with the findings of Dillon and Stephenson 6 5 who evaluated dipole-dipole integrals over the intermolecular trajectory during the collision. They considered relative energies of s, 2 ~4s, , 8s and 16s where E is the well depth of the Lennard-Jones (6-12) distorting potential, and used classical mechanics to describe the intermolecular motion. Their l6O 161 162 163 164

16s

P. D. Gait, Chem. Phys. Letters, 1976,41, 236. J. D. Stettier and N. M. Witriol, Chem. Phys. Letters, 1976,41,241. R. D. Sharma, Chem. Phys. Letters, 1975,30,261. R. D. Sharma and R. H. Picard, J. Chem. Phys., 1975, 62,3340. R. D. Sharma and R. R. Hart, J. Chem. Phys., 1975,63,5383. T. A. Dillon and J. C. Stephenson, J. Chem. Phys., 1973,58, 3849.

Gas Kinetics and Energy Transfer

132

conclusion was that the straight path approximation was considerably in error. As yet this discrepancy is unresolved. Andreev 166 has also criticized the Sharma theory principally on two grounds; these are that rotation and vibration should not be separated when the impact parameter is approximately equal to the gas kinetic molecular dimensions (where they are most important for vibrational energy transfer), and that the short interaction hard sphere approximation should make the transfer probability virtually temperature independent. However Andreev’s modified theory and the original Sharma theory give similar results. At n > 7 in the CO scheme above, (Pl,o(V-V)) falls as much as an order of magnitude below the measured rates. Sharma attributed this to the inaccuracies of the Born approximation used and has refined it to the second-order approximation (SODWBA). Dillon and Stephenson 168*169 have also concluded that the Born approximation fails for high u state systems and have used a scattering (S matrix) approach to overcome this. They show that the cross-section for the transfer of (n + 1) quanta in such a collision is less than ten times smaller than the cross-section for an n quantum exchange. This results principally from the relaxation of the Au = & 1, AJ = f1 selection rules on removal of the Born restriction. A total vibrational excitation of 15 quanta yields cross-sections ten orders of magnitude greater than the Born approximation in the non-resonant limit and two orders of magnitude smaller in the resonant limit. In the former case the deviation from the Born result is particularly great at low molecular quantum number, u, of the energy acceptor. For nearly resonant cases the deviation is greatest at high u. It is claimed that neglect of anharmonicity will have no effect on this result (despite what we have said previously!). This latter treatment gives good agreement with HF, DF, HCl, and CO2(vS) systems. Current theories do not seem to give the correct reduced however (tested by isotopic-substitution experiments). mass d Tpendence The Vibrational Quantum Number Dependence of (Pm,n).-Using a semi-classical treatment with anharmonic oscillator and exponential repulsive potential, McKenzie 147 has derived transition probabilities (Pmsn(V-T))for the system

CO(m)

+ He + CO(n) + He

(12)

The results are presented in Figure 5 and their correlation with experiment 17’ in Figure 6. From Figure 5 it is clear that at the ‘normal temperatures of laser work multiquantum transitions are negligible for low u initial states but not if u 20. The Landau-Teller T-* dependence of ln(P,,,(V-T)) also deviates from linearity in the usual way. This happens even if the attractive forces are omitted from the intermolecular interaction potential. It is attributed to accurate averaging integrations McKenzie’s at the low collision energies. This view is supported by treatment suggests that around 300 K multiquantum transfers will be significant,

-

166 167

16* 169

172

E. A. Andreev, Chem. Phys. Letters, 1971, 11,429. R. D. Sharma, R. B. Malt, R. R. Hart, and R. H. Picard, Chem. Phys. Letters, 1975,35,286. T. A. Dillon and J. C. Stephenson, Phys. Rev., 1972, A6, 1460. T. A. Dillon and J. C. Stephenson, J. Chem. Phys., 1973,58,2056. D. J, Seery, J. Chem. Phys., 1973,58, 1796. G . Hancock and I. W. M.Smith, Appl. Optics, 1971, 10, 1827. H. K. Shin, J. Chem. Phys., 1971, 55,5233. H. K, Shin, J. Chem. Phys., 1972,57, 1363.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

133

E fFECTIVE TEMPERATURE, T~ J K 300 1000 3000 5000 I

I

I

I

1-0

rn-n

0

'

= 20-19

2-0

@

2 4 6 8 10 12 RELATIVE .COLLISION SPEED, G/km s-'

Figure 5 Multiquantum transition probabilities for CO(m)/He collision using L (range parameter) = 0.2 nm. Tp locates the most efective collision speed for the transition (Reproduced by permission from J. Chem. Phys., 1976,64, 1504)

/

L = 0.03 nm

0.1I

I

1

I

I

5 10 15 20 INITIAL-STATE VIBRATIONAL QUANTUM NO., m Figure 6 Comparison of experimental rate constants at 300K with those calculated for CO(m)/He collisions using a simple repulsive potential (Reproduced by permission from J. Chem. Phys., 1976, 64, 1504)

0

Gas Kinetics and Energy Transfer

134

(a) (b) Figure 7 Comparison of calculated cross-sections for the single step and sumsf-steps quenching ofC02(OOol)by (a) Ne and (b) C02(OOoO).The points are experimentaldata (Reproduced by permission from Chem. Phys. Letters, 1976,40, 320)

for molecules with low vibration frequencies, at only moderately high values of u (e.g. around D = 10 for Br2). His treatment will not be accurate for 'very heteronuclear' molecules such as the hydrogen halides. These molecules are much more complex to treat, e.g. Shin 174* 17' has considered energy transfer in HF, via dimers, for initial states up to u = 5 at 300K. Good agreement was obtained with the experimental data of Kwok and Wi1ki11s.I~~ The polyatomic situation is, of course, more complex. Shin has examined the relaxation of the (00'1) state of Cot. (This is the very important 'pumped' state of the C02 laser). He finds 177 that the T - %dependence of the energy transfer crosssection of this state observed experimentally is in close agreement with that predicted for the sum of the three processes c02(00°1)

+ c02(00°0)

[

-b 3

Similar results were obtained for CO2(00'1) dependence of the cross-section for the (00'1) 173 176

+ c0,(00"0) c0,(10'0) + c02(00°0) CO2(2O00) + cO,(OOOO) + Ne (see Figure 7). The temperature

C02(11'0)

-b

(10'0) transfer is very strong owing

H. K. Shin, J. Chem. Phys., 1975,63,2901. H.K.Shin, I.E.E.E.-J. Quantum Electron., 1975,QE-11,679. M.A. Kwok and R. L. Wilkins, J. Chem.Phys., 1975,63,2453. H. K. Shin, Chem. Phys. Letters, 1976,40, 316.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

135

to the large energy mis-match which is transferred to the translational motion of the colliding pair. The Effect of Rotatian on (Pm,*).-In small molecules, where the rotational level spacings are within an order of magnitude of kT, rotational effects can strongly influence the value of (Pm,m-l).kT is -208 cm-I at 300 K, so that in the series H,, HF, HCl, HBr the rotational line spacings (2B) are -60, 42, 21, and 17 cm-' respectively and so rotational effects are likely to be significant in these 178-182 at the lower end of the temperature range (as usually studied by laser techniques). Stephens and Cool 83 have shown that the difference between theory and experiment can be as much as lo6 when the energy mis-match in such systems is -500 cm-l. This discrepancy has been reduced dramatically by taking account of large changes in rotational quantum number (i.e. 1AJI @ 1) together with other refinements in a semi-classical calculation. More recent calculations on the system

HX(u = 0) + C02(001)+ HX(U = 1) + C02(000)

(13)

where X = F, Cl, or I indicated lB4 that the curvature of the trajectory ('orbiting collisions') was probably the only refinement necessary to a Sharma type theory in order to calculate probabilities acceptably close to the experimental values. Unless rotational effects are considered, V-T theories predict that (PI,-,) for DCl + DCl % HCl + HCl, since the lowering of molecular velocity due to the heavier isotope is more than compensated for by the lowering of vibration frequency. Experimentally, however, the opposite is true, and inclusion of the rotational effects as above removes the disparity. If the ratio of the fundamental vibration frequency, o,,to the rotation frequency, Be, is large compared with the range of angular momentum transitions having strong coupling (i.e. the closeness of the donor to a near-resonant acceptor state), it has been suggested 14' that, for the anharmonic diatomiclatom system a collinear collision model is quite adequate e.g. for CO and N,, coe/Be% 1 and there are no near-resonant transitions with small AJ. Thus rotation has virtually no effect. However, for H,, @,/Beis not large and near-resonant vibration-rotation transitions with small AJ are accessible (e.g. o = 1, J = 14 and o = 0, J = 16). Here the closeness of initial rotational states to rotational states capable of near-resonant vibration-rotation transitions allows the initial rotational state to influence (PI,-J. Similar arguments apply, but become less significant as we progress along the series; HF, HCl, HBr. These all exhibit deviation from Landau-Teller ( T - + ) temperature dependence, the effect becoming less marked as the molecular weight and oJBeincreases. treatment of vibration-rotation interactions gives good agreement for Moore's HCl IB5 but does not explain the isotope effect for the relaxation of Cl, (o = 1) by 178

180 182

la3 lB5

T. L. Cottrell, R. C. Dobbie, J. McLain, and A. W. Read, 7kuns. Furuchy Soc., 1964, 60,241. T. L. Cottrell and A. J. Matheson, Tkns. Faruchy SOC.,1962,58,2336. T. L. Cottrell and A. J. Matheson. 7kum. Furuchy SOC.,1963,59,824. S . W. F3enson and G. C. Berend, J. Chem. Phys., 1966,44,4247. C. B. Moore, J. Chem. Phys., 1%5,43,2979. R. R. Stephens and T. A. Cool, J. Chem. Phys., 1972,56,5863. P. D. Gait, Chem. Phys. Letters, 1975, 35,72. W. D. Breshears and P. F. Bird, J. Chem. Phys., 1969,50, 333.

136

Gas Kinetics and Energy Transfer

HCI or DCI in which 186 HCI is 2-4 times the more effective. A recent Monte Carlo quasiclassical trajectory study has been shown to reproduce the observed results with acceptable accuracy, but only at the high end of the temperature range studied. Long-lived collisions and dimer formation are unlikely to be significant under these circumstances. A similar type of study l S 2for the system C02(001) H2/D2+ C02/(000) H2/D2 has predicted both the experimental isotope ratios and rates, concluding that the major relaxation mechanism is vibration-rotation for T < 700 K and vibrationtranslation for 700 K < T Q 1500 K.

+

+

The Present Position and Future Trends.-Much more realism in the potential surfaces which are used, particularly in quasiclassical trajectory studies, is a notable feature of recent calculations. It is clear that greater attention to the accuracy of evaluating integrals over the thermal distribution of states is beginning to show that some of the predicted (Pm,m-l)behaviour was an artefact of the less accurate previous methods. Undoubtedly, further increases in accuracy of models may be expected to reveal more such artefacts. The questions of multiple collision effects '13' and the effect of altering molecular parameters during the collision are now being raised.18* So far it has been assumed that the relevant energy level manifold for vibrational energy transfer is a simple set of vibration-rotation levels. However, no molecule of any appreciable size is this simple. Such well-known factors as Coriolis splitting enhance the opportunity for near-resonant matching of levels by removing degeneracies. This effect would be expected to result in an effect of rotation of the molecule on the energy transfer efficiency and thus on (Pm,n-l). The laser beam generates an electric field which may be calculated via Poynting's theorem, e.g. a 100 W (0.1 mJ pulse in I p s ; a minimal requirement for successful i.r. laser induced fluorescence) beam incident on a 5 mm x 5 mm area produces 550 V cm- l . Frequently much higher energies are used, and the resultant electric fields during the pulse cause a dynamic Stark effect producing level splittings of 0.01 cm- l . Such an effect could be important in allowing multiquantum transitions in i.r. photochemistry where laser intensities are often B lo6 W cm"! In a few years we should expect to see the emergence of a set of factors which are 1) prediction, together with the simplest possible acceptably essential to any (Pm,maccurate approximation which may be applied to a given molecular type, H,, HX, C 0 2 etc. It is, however, distressing to see such progress slowed by the almost total lack of uniformity of notation amongst theoreticians in this field, together with jargon-filled descriptions of models of such brevity as to be at times incomprehensible. Perhaps these areas will also receive attention in the future. N

4 Data on Compounds Hydrogen.-V-T Transfer. Vibrational relaxation in hydrogen and its isotopes has received much attention in recent years. This interest partially stems from the existence of reliable potential energy surfaces for the H,-H2, H,-He, and H2-Li systems. Full three-dimensional quantum calculations of vibrational and rotational lS6 la' la*

W. D. Breshears and P. F. Bird, J. Chem. Phys., 1969,51, 3660. H.K.Shin, J. Chem. Phys., 1975, 62,4130. G. Jolicard, Chem. Phys. Letters, 1976, 37, 355.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

137

energy transfer probabilities have been carried out for these systems based upon recent progress in the approximate solution of the close coupled equations.189-'91 It is thus possible to investigate specific features of the interaction potential in detail with the availability of reliable energy transfer data. Most of the reported experimental work has used non-linear Raman techniques to vibrationally excite H, or D, and laser Schlieren methods to monitor the progress of vibrational relaxation. As we have seen, this method does not monitor the vibrational energy directly, but rather the density changes associated with energy transfer to translation during V-T relaxation are observed. The first investigation of vibrational relaxation in H, was made by de Martini and Ducuing in 1966. They studied H2in the pressure range 20-60 atm. using stimulated Raman pumping and spontaneous anti-Stokes Raman scattering to monitor the decay of the excited vibrational states. Vibrational lifetimes between 1O-4Ops were obtained corresponding to a rate constant of (3.85 & 0.38 x 10'" molecule-' cm3 s - l at 300 K in good agreement with the value obtained by extrapolation of acoustical relaxation data to lower temperature^.'^^ In a later study, the coherent Raman amplification technique was used to redetermine the molevibrational lifetime of H, at 300 K.96A rate constant (1.36 & 0.14) x cule-' cm3 s- was obtained considerably different from their previous result. No reason was given for the discrepancy in relaxation times, but the later result was confirmed by Kovacs and Mack using picosecond Raman pumping and a laser Schlieren probing technique. Since the vibrational frequency of hydrogen and its isotopes is very high (4161 cm-' for H,) the relaxation of vibrational excitation is relatively slow. Consequently, the presence of very small amounts of impurities increase the relaxation rate and can lead to considerable error. This is a problem common to all homonuclear diatomic molecules owing to their very slow observed relaxation times. Careful purification is essential if reliable energy transfer results

'

Table 2 V + T / R transfer rate constantsfor hydrogen at room temperature Collision Partners Hz-Hz

H2-Dz

H2-He HI-Ar Hz-Nz I32432

D2-HD

D2-3He D2-'He D2-Ar lgo lgl

Ig2 Ig3 194

Ig5

10'' k/molecule-' cm3 s -' 3.85 f 0.4 13.6 f 1.4 14.1 f 1.4 10.8 f 1.9 22.1 f 3.5 1.81 0.57 14.6 f 0.5 1.42 f 0.1 2.72 f 0.5 10.6 f 1.2 2.82 f 1.1 0.70 f 0.07 0.05 f 0.004

Ref: 93, 192 96 98 193, 194 195 193 193 202 195 98 95 95 95 95

H. Rabitz and G. Zarur, J. Chem. Phys., 1974, 61, 5076. P. McGuire and J. P. Tonnies, J. Chem. Phys., 1975, 62,4623. J. Schaefer and W. A. Lester, jun., J. Chem. Phys., 1975, 62, 1913. J. H. Kiefer and R. W. Lutz, J. Chem. Phys., 1966, 44, 668. M. M. Audibert, C. Joffrin, and J. Ducuing, Chem. Phys. Letters, 1973, 19, 26. M. M. Audibert, C. Joffrin, and J. Ducuing, Chem. Phys. Letters, 1974, 25, 158. J. Lukasik and J. Ducuing, Chem. Phys. Letters, 1974, 27, 203.

138

Gas Kinetics and Energy Transfer

are to be obtained for these systems. Ducuing and co-workers also used the coherent Raman pumping method to study the self relaxation of hydrogen and in the presence of helium and argon. In these experiments a rate constant of 1.07 x molecule-’ cm3 s-’ was found for H,-H2 transfer which is about 25% slower than the value obtained previously. This discrepancy was thought to arise from sample heating in the original work but impurities may also play a part. Addition of helium or argon was found to increase the relaxation time and a value of 1.79 x lo-’’ molecule-’ cm3 s-’ was found for the relaxation rate constant for H,-He and 5.71 x molecule-’ cm3 s-’ for the rate constant for H,-Ar relaxation. Coherent Raman pumping using a tunable dye laser was used to measure the vibrational relaxation in D, both as the pure gas and in mixtures with HD, 3He, 4He, and Ar.95 These results are included in Table 2. Recently Ducuing and co-workers have extended their work to the measurement of vibrational relaxation times of H2,Ig4D2,195and ortho- and para-H2,196as a function of temperature. One object of this work was to determine the validity of the Landau-Teller theory at low temperatures. The development of this theory, the modified SSH theory, takes into account the attractive forces between the molecules during a collision which shOuld become important at low temperatures. The Landau-Teller theory predicts that log ‘t should show a linear dependence on T * whereas , the SSH theory, modified to take account of the attractive part of the intermolecular potential, does not. In the case of H2194and D2I9’ very marked deviations from linearity were observed at low temperatures. This was particularly true for H,, where at the lowest temperatures the relaxation time became essentially independent of temperature, demonstrating the importance of the attractive part of the potential at low temperatures. However, several of the proposed theoretical models give satisfactory agreement with the experimental results and on the existing evidence these cannot be distinguished. There is however, some evidence lg4 that ternary collisions may contribute to deactivation at low temperatures in addition to binary collisions. A similar temperature dependence of the relaxation rate was observed in studies of H, in mixtures with 4He and 3He in the range 450-60K.197 Below 300K marked deviations from linearity of log k versus T-* were observed (Figure 8). The influence of the difference in reduced mass for the two collision pairs H,-3He and H,-4He is clearly seen below 300 K, similar to the results in D,-D2 and D,-H, pairs.19’ However, below 200K the temperature variation with He partners is considerably reduced particularly for 3He. This suggests that changes in rotational quantum number may occur during collision due to the anisotropy of the intermolecular potential. Energy transfer between vibration and rotation can be studied conveniently both experimentally and theoretically in the case of ortho-(u = 0, J = 1) and para-(u = 0, J = 0) hydrogens. Hopkins and Chen have attempted to estimate the importance of V-R transfer in H, by analysing the isotopic variations of the room temperature rate on the basis of Moore’s simplified theory. It seems however that only a more sophisticated quantum treatment can adequately explain the vibrational relaxation of H, at low temperatures. Audibert et ~ 1 . ” reported ~ a study of the vibrational relaxation time lg6 19’ 198

M. M. Audibert, R. Vilaseca, J. Lukasik, and J. Ducuing, Chem. Phys. Lefters, 1975,31,232. M. M. Audibert, C. Joffrin, and J. Ducuing, J. Chem. Phys., 1974, 61,4357. B. M, Hopkins and H. L. Chen, J. Chem. Phys., 1972,57,3161.

Laser Studies of Vibrational,Rotational, and Translational Energy Transfer

I

139

Log ( k / molecule” cm3 s-1)

nH2-‘He

. nH2-’He

Figure 8 Log k/molecule-’ cm3s-’ as a function of T - t : I-shock tube data, II-theory (Reproduced by permission from J. Chem. Phys., 1974,61,4357)

of ortho-para mixtures of H2as a function of temperature (400-50 K) and of the molecule fraction (0-4.75) of ortho-H,. A primary objective of this work was to establish the influence of rotational levels below 250 K and to provide a test of theoretical treatments of rotational energy transfer. Above 250 K, +rwas found to be independent of the mole fraction of ortho-H,, but at lower temperatures (80 K) a linear dependence of z on the mole fraction of the ortho species was observed. Thus, at low temperatures, the rate of vibrational de-excitation is dependent on the population of the initial rotational states. The authors came to the conclusion that a full quantum mechanical treatment was needed to interpret the vibrational relaxation of H2and that classical treatments 99 were inadequate. V-V Transfer. The use of the laser-Schlieren technique for monitoring the decay of vibrationally excited states limits the data to V-T rates. Monitoring the population of vibrational levels of dipolar molecules using the i.r. fluorescence technique Ig9

G. B. Sorensen, Chem. Phys., 1974,5,244.

Gas Kinetics and Energy Transfer

140

however, allows V-V transfer rates to be measured directly. Recently, two studies have been reported 2oop201 which use non-linear Raman pumping and i.r. fluorescence monitoring to study V-V transfer in hydrogen in mixtures with other gases. Matsui et aL2" measured rate constants for V-V and V-T processes in H,-CO and D2-CO mixtures by using stimulated Raman excitation of H2 and measuring the rise and decay of the fluorescence at 4.7 um from the CO. Total pressures of 10 to 25 atm were used with CO compositions ranging from about 1.5 to 13%. The experimental data obtained were consistent with the following processes,

V-T/R

CO(U

1)

+ H2 + CO(U= 0) + H2

H ~ ( u= 1) + H2

+

k , = 4.44 x

If: 5% molecule-' cm3 s-l

H ~ ( v= 0) + H2 k2 = 1.33 x

& 3% molecule-' cm3 s-'

D,(u = 1) + D2 -,D2(u = 0) + D2 k3 = 2.79 x lo-''

v- v H,(u = 1)

+ CO(U= 0) -,H,(v

= 0) k, = 1.40 x

f 30% molecule''

cm3 s-'

+ CO(u = 2,l) f 45% molecule-' cm3 s-'

D2(v = 1) + CO(U= 0) + D,(u = 0) + CO(v = 1) k , = 4.28 x +, 18% molecule''

cm3 s-'

The ratio of k,/k,, the two V-V transfer processes of 0.033, was surprisingly small considering the near resonant condition in the case of Au(H,) = -1 with Au(C0) = +2. This is probably a consequence of the small dipole matrix element associated with the Au = 2 transition in CO and to the neglect of explicit V-R interactions. V-V energy transfer rates in various H,-additive gas mixtures were also measured by Miller and Hancock.201 These authors used a coherent Raman pumping technique to populate the first vibrational ( u = 1) level of hydrogen, and monitored the i.r. fluorescence from a number of additive gases including HCl, DCI, HBr, DBr, C02, N20, l2C0, I3CO, and NO. Two separate cells were used, the first to generate stimulated Raman emission in H, gas at 4 atm and the second containing the H,-additive gas mixtures at pressures between 0.1-1 atm to study the V-V processes. With this arrangement, V-V processes could be measured at relatively low pressures so that the relaxation rates were proportionally slower and easily measurable. Reliable data at pressures as low as 9.3 kNm-2 were obtained. The vibrational energy level diagram for the Raman pumping of H2, V-V transfer to H(D)X and decay of excited H(D)X is shown in Figure 9. The pathways for transfer to both fundamental and overtone levels are shown. The vibrational energy transfer rates are included in Table 3 together with the rates for CO,, N20,CO, and N O collision partners. In the case of H,-HC1 the V-V and V-R, T processes are as follows: 2oo 201

H. Matsui, E. L. Resler, and S. H. Bauer, J. Chem. Phys., 1975, 63,4171. R. G. Miller and J. K. Hancock, J. Chem. Phys., 1977,66, 5150.

Laser Studies of Vibrational, Rotational, and Translational Energy T r m f e r

141

Figure 9 Energy level diagram for V-V transfer from Hz(v = 1) to H(D)X using coherent Raman pumping, ,u = pm (Reproduced by permission from J. Chem. Phys., 1977,66, 5150)

H~(= u I)

+ HCl(U = 0) 3H ~ ( =u 0) + HCl(u = 1) +AE = 1274cm-1

H~(= u 1) H,(o

+ H ~ ( =u 0) 5 H ~ ( =u 0) + H ~ ( =u 0)

+ AE = 4161 cm-' = 1) + HCl(o = 0) 5 H ~ ( u = 0) + HCl(U = 0) +AE = 4161 cm-'

+ H ~ ( =u 0) 2 HCl(U = 0) + H,(u = 0) +AE = 2886 cm-' HCl(o = I) + HCl(o = 0) 3 HCl(U = 0) + HCl(u = 0) HCl(0 = 1)

+AE = 2886 cm-I In these expressions, k l , is the V-V transfer rate from H2(o = 1) to HCl(u = 1). The remaining processes are V - R P deactivations of H2(o = 1) and HCl(u = 1). Since k , % k - l and k4 and k , 9 k , the relaxation rates may be written,

and where rf and z, are due to V-V and V-R/T processes respectively, XHzand A',,, are the mole fractions of H2 and HCI, respectively. At low XH(D)X values, there was a linear relationship between (rS)-' and XH(D)X allowing accurate values of transfer rates to be obtained. In Table 3 values of energy transfer probability and collision cross-section are also tabulated. The probability is seen to drop off rapidly as the energy mis-match (AE) between the u = 1 levels increases. Any quantitative treatment of these energy transfer results however should account for factors such as the large

Gas Kinetics and Energy Transfer

142

Table 3 Vibrational energy transfer rate constants for H,-HX, H2-C02, H2-C0, H,-NO, and H2-N20 (ref. 201) Energy

defectlcm 1274(~= 1) - l 5 0 8 ( ~= 2) 2069(v = 1) DCl 34(v = 2) 1604(v = 1) HBr - 8 6 5 ( ~= 2) 2321(v = 1) DBr 527(~= 2) 181 l(OO1) coz 51 l(021) 444(101) 1936(001) Nz0 795(021) 679(101) l2C0 2017(v = 1) -loo(v = 2) 2069(v = 1) 1 3 c o -6(v = 2) N O ~ I I , ) 228q.u = ij 43qv = 2)

Molecule HCl

Cross-

10'' kl

molecule - cm3 s 4687 f 652

Probability

section/A2

8.62 x 10-5

2.60 x 1 0 - 3

2139 f 93

3.95 x 10-5

1.19 x 10-3

695 f 56

1.26 x 10-5

3.93 x 10-4

658 f 112

1.19 x 10-3

3.72 x 10-4

1543 f 93

2.01 x 10-5

8.63 x 10-4

1434 f 43

1.82 x 1 0 - 5

8.02 x 10-4

38 f 30

6.02 x lo-'

2.06 x 10-5

2.47 x

7.22 x lom5

30 f 0.6 130 f 53

amplitude of vibration, multiquantum transitions, hydrogen bonding, multipole moments (due to large dipole and quadrupole moments of HX), etc. The transfer probabilities in Table 3 for H2-C02 and H,-N,O are an order of magnitude smaller than that for H2-HCl. The H2-C02 transfer laser is thus not expected to be as efficient as the N2-C02 laser where the energy transfer rate is orders of magnitude faster.,', A rather different approach to the study of V-V transfer in H2has been used by Pirkle and These authors utilized the rapid V-V transfer between HF and H, to selectively excite H,. The energy level diagram (Figure 10) shows the lowest vibrational states of HF, H2 and D2 and HCl. The H2-D2 or H,-HCl gas mixtures contained trace amounts of HF which was excited to the u = 1 level by a pulsed HF chemical laser. Fast near-resonant V-V transfer occurred to H2(u = l), and the subsequent deactivation of excited H, by D2 or HCl was monitored by i.r. fluorescence from HF. The energy transfer between H2 and HF is fast compared with the rate of energy transfer to D2 or HCl. The result obtained in the temperature range 220-450K, together with the energy transfer probabilities are given in Table 4. The room temperature value of (5.37+, 0.78) x molecule-' cm3 s-' for the H,-HCl transfer rate constant is in good agreement with the values obtained by molecule-' cm3 s-' and by Millar and Hancock Bott ,04 (3.88 +, 0.47) x (4.67& 0.65) x molecule-' cm3 s-'. The latter authors also used the laser excited HF method (but monitored the HCl fluorescence)in addition to the coherent Raman pumping technique. As shown in Table 4 the measured V-V probabilities exhibit only a slight temperature dependence. Because the energy discrepancies for 202

203 204

R. Frey, L. Lukasik, and J. Ducuing, Chem. Phys. Letters, 1972, 14, 514. R. J. Pirkle and T. A. Cool, Chem. Phys. Letters, 1976,42, 58. J. F. Bott, J. Chem. Phys., 1974, 61, 2530.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

143

4000-

IE

3000-

0

\ * a a z

W

2000--' J

a v) w

4

4

z

0 a a m

t

5

1000-

0-

Figure 10 Lowest vibrational levels in HF, H2, Dz, and HCI (Reproduced by permission from Chem. P h p . Letters, 1976,42, 58)

the V-V processes in Hz-Dz and H,-HCI are similar, the large probabilities for the H,-HCI system must arise from the stronger interactions with the polar HCI molecule. The weak temperature dependencies of the probabilities are in marked contrast to the pronounced inverse temperature dependence associated with the near-resonant V-V transfer between Hz and HF for which AE = 197 cm-'. Also included in Table 4 is the rate constant and probability for energy transfer between H, and HCN. This result was also obtained using trace amounts of HF pumped by a pulsed HF laser.205 Table 4 Rate data for H2-Dz, Hz-HCN, and H2-HCl in the ronge 220-450 K V-V Rate constant x 10l6/

System H2-D2 H2-HCl H2-HCN 205

TemperaturelK 224 299 448 21 5 299 446 298

molecule-' cm3s - I 90f 15 101 f 12 102 f 12 528 f 12 503 f 78 310 f 93 196 f 5

Probability x lo5 1.73 2.24 2.77 8.9 10.0 7.5 38.0

J. A. McGarvey, N. E. Friedman, and T.A. Cool, J. Chem. Phys., 1977, 66, 3189.

Ref. 203 203 203 203 203 203 205

144

Gas Kinetics and Energy Transfer

Hydrogen Fluoride.-V-T,R Transfer. Vibrational energy transfer processes in mixtures of HF with other gases have been studied extensively in conjunction with the development of HF chemical lasers. Hydrogen halides exhibit extremely fast relaxation and the energy transfer probabilities in mixtures with other gases commonly exhibit a strong inverse temperature dependence below about 400 K. These phenomena are associated with the highly anisotropic intermolecular potentials with minimum energy configurations which are favourable for efficient V-V and V-R transfer. These intermolecular interactions are particularly strong for HF. The gas kinetic model for all HX is the simplest possible. Excitation with the appropriate HX chemical laser raises the molecule to the first excited vibrational level from which it subsequently decays by gas phase collisions. Thus, since there is only one vibrational mode, a single exponential curve should be observed and the p r value should be constant. molecule-' cm3 s-' at Airey and Fried 206 obtained a value of 2.9 x 350 K for the self-relaxation rate constant for HF, about three orders of magnitude faster than predicted by the Lambert-Salter correlation. Other values are collected together in Table 5 . These data show that the reproducibility of relaxation measurements in various systems is better than 20%, a remarkable result in view of the extreme sensitivity of the decay rate to minute traces of water. Table 5 Rate data for V-T,R relaxation in HF and DF Species

HF(v

=

1)

HF(v = 2) HF(w = 3) HF(v = 4) HF(w= 5) DF(v = 1)

TemperuturelK 350 294 350 295 295 297 295 298 296 296 296 296 298

10l2k/molecule-' cm3s2.90 2.70 1.63 2.70 1.89 2.61 1.74 1.63 16.4 f 0.5 26.0 f 1.0 27.0 f 1.0 8.6 f 0.5 0.74 0.78

Ref.

206 207 183 208 209 210 211 176 176 176 176 176 209 210

The most searching test of the various energy transfer theories is provided by the prediction of the temperature dependence of the energy transfer rate constant. The temperature dependence of the transfer rate for HF has been measured in the range 460-1030 K using i.r. fluoresence.2 A double exponential curve was observed and attributed to the fast V-V process shown in equation (14) in addition to a

''

2HF(v = 1)

V-T rateconstant of 1.74 x 206 207

2oB =09

210 211

-+

HF(v = 0)

+ HF(u = 2)

(14)

molecule" cm3 s-': In Figure 11 the temperature

J. R. Airey and S. F. Fried, Chem. Phys. Letters, 1971, 8, 23. J. R. Hancock and W. H. Green, J. Clrem. Phys., 1972,56,2474. W . H. Green and J. K. Hancock, 1.E.E.E.-J. Quantum Electron., 1973, QE-9, 50. J. J. Hinchen, J. Chem. Phys., 1973, 59, 233. R. A. Lucht and T. A. Cool, J. Chem. Phys., 1974,60,2554. J. F. Bott, J. Chem. Phys., 1972, 57,96.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

1

0.01

0.04

I

0.06

I 0.08

I

0.10 (TlU)-”3

I

0.12

I

0.14

145

0.16

Figure 11 Temperature dependence of pt for the vibrational relaxation of HF. 0 Shock heated laser-induced fluorescence results; - shock heated measurements; laser-induced fluorescence; - - - - modified shin theory, (T = 2.55 A (Reproduced by permission from J. Chem. Phys., 1972,57, 96)

furnace heated

dependence of p o is compared with the predictions of Shin’s theory 212 and with previously measured values. The theoretical dependence, modified by the inclusion of a 14.6 kJ mol-’ attractive intermolecular potential provides a good fit to the experimental data.2f3 Using the same technique Breshears et aL214 examined the temperature dependence from 600 to 2400 K and found a maximum in p z near 1400 K in agreement with Figure 11. Lucht and Cool 215 examined the temperature dependence of the quenching rates of HF(u = 1) and DF(u = 1) with CO, in the range 295-670 K. The deactivation rates were found to decrease strongly with increasing temperature, which was interpreted in terms of absorption of the large energy defects by rotational motion of the halide. Similarly, Bott and Cohen 216 measured the total rates for V-V and V-T,R quenching of H F by H,, HCl, DF, CO,, D,, N,, O,,CO, HBr, and NO. Near room temperature and for molecules with small energy defects, measured p7 values varied as positive powers of T,whereas for molecules with larger AE, p z varied as negative powers of T. Moreover, plots of transition probability against A E segregated into two distinct lines, one for homonuclear and one for heteronuclear molecules. The positive power T dependence was interpreted by Ah1 and Cool 217 in terms of strong attractive intermolecular forces between HF and the other hydrogen halides. The attractive forces in HF/DF systems were attributed to hydrogen bonding (important below about 500 K).’ 7 5 212 213 214 215 216 217

H. K. Shin, Chem.Phys. Letters, 1970,6,494; J. Phys. Chem., 1971,75,1079; Chem.Phys. Letters, 1971,10, 81. J. F. Bott and N. Cohen, J. Chem. Phys., 1971,55, 3698. L. S. Blair, W. D. Breshears, and G. L. Scott, J. Chern. Phys., 1973,59, 1582. R. A. Lucht and T. A. Cool, J. Chem. Phys., 1974, 60, 1026. J. F. Bott and N. Cohen, J. Chern. Phys., 1973, 58, 4539. J. L. Ah1 and T. A. Cool, J . Chem. Phys., 1973, 58, 5540.

Gas Kinetics and Energy Transfer

146

The main conclusions from the foregoing results may be briefly summarized as follows: (i) HF(u = 1) relaxation is appreciably faster than in any other HX-HX system and in particular (except at very high temperatures) it is faster than DF-DF relaxation; (ii) The Landau-Teller plots of p z are non-linear and display a wide minimum between 600-1000 K. The high relaxation rates and the non-linearity of the Landau-Teller plots at low temperatures are probably due to strong dipole-dipole interactions. The isotopic effect (DF slower than HF) can be explained by strongly preferred V-R over V-T transfer. Finally, the maximum in the Landau-Teller plots can be interpreted as the net result of the short range V-R,T and the long range V-R mechanism governing the relaxation at high and low temperatures, respectively. At very high temperatures the V-T mechanism becomes important and DF relaxes faster than HF. Rotational relaxation rates for single vibration-rotation levels in HF were recently reported by Paterson et aL218 using a time resolved pump-probe technique. Relaxation rate constants for HF self-quenching were (2.4 f 0.1) x lo-' and (1.5 & 0.2) x lo-' molecule cm3 s-' for the rotational relaxation of the P1(5) and Pi(6) transitions. These rate constants were in close agreement with those obtained from collisional linewidth data at higher HF pressure^.^' Preliminary measurements were also reported for the rotational relaxation of HF quenched by H2. A rate constant k of (2.5 f 0.9) x 10"O molecule-' cm3 s-' was obtained for this process.

-'

'

ReZaxation with A tumic Species. The theoretical and experimental interest in the

HF chemical laser have resulted in a number of studies of the deactivation of HF(u = 1) by reactive atomic species such as F, H, and 0.220-230 Classical trajectory calculations 2 3 1 9 2 3 2 for H + HF(u) indicate that H atoms can be the dominant deactivator in HX laser systems. Measurement of H + HF(u = 2 or 3) deactivation by Kwok and Wilkins 233 are in good agreement with trajectory calculations. However, for H + HF(u = 1) these authors found a rate constant slightly slower than predicted while Quigley and Wolga 234 reported an upper limit of 1.5 x molecule-' cm3 s-', more than two orders of magnitude slower. More recently, Heidner and Bott 23 reported vibrational deactivation rates for HF(u = 1) and DF(u = 1) by H and D atoms at 295 K using i.r. fluorescence and 218 219

L. M. Peterson, G. H. Lindquist, and C. B. Amold, J. Chem. Phys., 1974,61,3480. W. F. Herget, W. E. Deeds, N. M. Gailar, R. J. Lovell, and A. H. Nidsen, J. Opt. SOC.Amer., 1962,52, 1113.

220

221

222

223 224

226

227 228 229

230 231

232 233 234 235

N. Jonathan, C. M. Melliar Smith, and D. H. Slater, Mol. Phys., 1971,20,93. H . W. Chang and D. W. Setser, J. Chem. Phys., 1973,58,2298. R. M. Osgood, A. Javan, and P. B. Sackett, Appl. Phys. Letters, 1972,20,469. R. M. Osgood, P. B. Sackett, and A. Javan, Appl. Phys. Letters, 1973,22,254. M. J. Bina and C. R. Jones, Appl. Phys. Letters, 1973,22,44. J. A. McGarvey, N. E. Friedman, and J. A. Cool, J. Chem. Phys., 1977, 66,3189. A. Hariri, A. B. Peterson, and C. Wittig, J. Chem. Phys., 1976, 65, 1872. J. J. Hinchen and R. H. Hobbs, J. Chem. Phys., 1975, 63,353. R. S. Chang, R. A. McFarlane, and G. J. Wolga, J. Chem. Phys., 1972,56, 667. J. F. Bott and N. Cohen, J. Chem. Phys., 1972,59,447. J. R. Airey and I. W. M. Smith, J. Chem. Phys., 1972,57, 1669. D. L. Thompson, J. Chem. Phys., 1972,57,4170. R. L. Wilkins, J. Chem. Phys., 1973,58,3038. M . A. Kwok and R. L. Wilkins, J. Chem. Phys., 1974,60,2189. G. P. Quigley and G. J. Wolga, Chem. Phys. Letters, 1974, 27, 276. R. F. Heidner and J. F. Bott, J. Chem. Phys., 1975, 63, 1810.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

147

Table 6 Rate data for vibrational deactivation of HF(v = l), DF(v = 1) by H and D atoms at 300 K (alZ k in molecule -%m3 s") Species

+ HF H + DF D + HF D + DF

H

a

Classical trajectory Ref. 232 Ref. 232 ka' kNb 2.8 x 8.8 x 7.8 x 10-13 1.5 x 10-12 7.5 x 10-13

Ref. 233 kR -k kN (1.2 kO.7) x 10-12

Experimental Ref. 234 Ref. 235 kR

+

kR

k N

+ kN

(2.3 A 0.9 x 10-13

1.5 x 10-14

(1.1 ~ 0 . 3 )x 10-13 (3.0 k2.7) x lo-'* (-1.7 f 15) x

6.0 x 1 0 4 3 1.7 x 1 0 4 3 8.3 x 10-14

kR denotes vibrational deactivation accompanied by F atom abstraction by the incoming or H kN denotes vibrational deactivation without atom exchange.

D atom;

isothermal calorimetry for the H atom concentration measurements. Again upper limits for the rate constants were defined but the lower rates were imprecise. These results along with earlier work and classical trajectory calculations are included in Table 6. The agreement with the trajectory calculations was poor, suggesting that too small a barrier for fluorine atom exchange was used in the calculation. A more accurate determination of the potential energy surfaces that are required for classical trajectory studies of deactivation rates is needed. The study of the HF(u = 1) + H-atom rates was recently extended by Bott and Heidner 236 to include the H-atom deactivation rates of HF(v = 2) and HF(v = 3). The v = 2 and 3 levels of HF were produced by sequential absorption of photons from the 1-0, 2-1, and 3-2 transitions of a pulsed TEA HF chemical laser. The exponential decay times of HF(v = 3 -,v = 0) fluorescenceand the measured H-atom concentrations were used to calculate a removal rate constant of 1.0 x lo-'' molecule-' cm3 s-l for HF(v = 3). This rate was about 400 times faster than that for the deactivation of HF(u = 1) by H atoms and about 100 times faster than the deactivation rate of Table 7 Deactivation rate data for HF (u) by H atoms at 295 K compared with HF self-relaxation rates HF(v)-H 2,

1 2 3

k/molecule - cm3s (2.3 f 0.7) x (1.1 A0.5) x (1.1 ~ 0 . 3 x) lo-''

HF(+HF Ref. 235 236 236

klmolecule-' cm3s - I 1.8 x 1.0 x lo-" 2.2 x lo-"

Ref. 237 238 239

HF(v = 2). The measured rate constants are given in Table 7 together with selfrelaxation rate constants for HF. Preliminary results for the temperature dependence of H + HF(u = 3) and cl + HF(v = 3) were recently reported.240 Both show an activation energy which is either zero or slightly negative. Deactivation of HF(v = 3) by D atoms was found to be slower (20-30%) than quenching by H atoms in the temperature range 200-300 K. Vibrational relaxation data have also been obtained on HF(v = 1) with F and 0 atoms at room temperature.234 The rate constant for F atoms was found to be 236

237 238 239 240

J. F. Bott and R. F. Heidner, J. Chem. Phys., 1977,66,2878. J. F. Bott, J. Chem. Phys., 1974, 61, 3414. N. Cohen and J. F. Bott, Appl. Optics, 1976, 15,28. M. A. Kwok and N. Cohen, paper presented at 172nd Meeting of American Chemical Society, San Francisco, Aug. 1976. R. F. Heidner and J. F. Bott, Ber. BunseweselIschaftph.vs. Chem., 1977, 81, 128.

148

Gas Kinetics and Energy Transfer

Table 8 Rate constants for the deactivation of HF(u = 1) and DF(v = 1) by 0, F, and C1 atoms (refs. 234, 241) Species

k(HF)/molecule-' cm3s-'

WP) W2P)

Cl(2P)

(3.1 *Oo.6)x (2.8 rtO.6) x (7.4 1.6) x

10-13

k(DF)/molecule cm3s (7.8 f 2.2) x (6.5 A 1.2) x 10-13 (2.0 f 0.3) x 10-l2

molecule-' cm3 s-' and for 0 atoms (3.1 f 0.6) x (2.8 & 0.6) x molecule-' cm3 s-'. In a later publication this work was extended to include the vibrational relaxation of HF and D F by 0, Cl, and F atoms at 300 K.241 The rate constants measured are included in Table 8. These results show that C1 atoms are more effective than F atoms and 0 atoms are the most effective. Also, in all cases, a particular atom relaxes DF(v = 1) more effectively than HF(v = 1). These results provide further evidence for the validity of the vibronic to translation energy transfer model proposed by Nikitin 242 to account for the quenching effects of atoms with ground states which have electronic orbital angular momentum degeneracy. Both the order of magnitude of rates for P-state atoms relative to those for S-state atoms and the molecular isotope effect support this conclusion. It was also shown that for HF and DF atom transfer reactions are not an important channel in the relaxation of HF(u = 1) and DF(u = 1). In similar experiments involving deactivation of HF(u = 1) by bromine atoms, a resonanceeffectwas observed.243The spin-orbit splittingin Br(2P4-2P+= 3685 cm' ') is closely resonant with several possible vibration rotational transitions in HF. The fluorescence decay curves consisted of double exponentials, a fast exponential due to E-V transfer between the vibrational mode of HF and the electronic mode of Br, and a slow time constant arising from V-R,T, and E-T processes. This double exponential behaviour is not found in the relaxation of HF(v = 1) by 0, F, or C1 atoms for which a resonant energy transfer process is not available. It is characteristic of systems (e.g. CO,, N,, HF, H,) when resonant V-V transfer occurs. One possible E-V resonant process is

HF(u = 1, J = 5 )

+ Br('P+)

HF(v = 0, J = 6)

+ Br(2P4)

(15)

A J = I , A E = -9cm-' Assuming k w k' gives

where zfis the time constant for the fast decay, and PB,and PHFare partial pressures. From this analysis a value of k = (3.1 1.5) x lo-" molecule-' cm3 s-' corresponding to about six or seven gas kinetic collisions for the E-V transfer process was obtained. Relaxation with Foreign Molecules. Relaxation of HF(v = 1) and DF(u = 1) by transfer to C 0 2yields rates of 1.15 x lo-'* and 5.45 x lo-'' molecule-' cm3 s-', respe~tively."~For the 0 = 0, levels of HF and DF, the relaxation rate constants and 5.86 x molecule-'cm3 s-'. A rate for CO2(OO01) are 1.11 x 241

242 243

G. P. Quigley and G. J. Wolga, J. Chem. Phys., 1975, 63, 5263. E. E. Nikitin and S. Ya Umanski, Faraday Discuss. Chem. SOC.,1972, 53, 1. G. P. Quigley and G. J. Wolga, J. Chem. Phys., 1975, 62,4560.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

149

constant of 6.21 x molecule-' cm3 s-' was measured for the process in equation (17). The Sharma-Brau theory was applied to the DF(o = 1) case

'''

DF(v = 1)

+ DF(u = 0) + 2DF(v = 0)

(17) with C02 quencher but is probably invalid owing to the strong intermolecular forces which result in a very fast rate where most of the energy defect is taken up by the rotational levels. With Ar, N,, and H2 collision partners rate constants of > 1.02 x >1.02 x and >4.08 x molecule-' cm3 s-' were measured at a temperature of 350K.244 The faster rate in the case of H, was attributed to near-resonant processes such as that equation (18) where AE = 17, 50,

HF(v = 1, J') + H ~ ( v= 0, J) + HF(v = 0, J'

- 1) + H,(v

=

1, J)

(18) or 85 cm-' for J' = 5, 4, or 3, respectively. In a later, room temperature, study 2 0 9 rate constants for HF with Ar (or He) of > 1.86 x lo-'' molecule-' cm3 s-' and 9.41 x molecule-' cm3 s-' for DF with Ar (or He) were obtained. For HF + H,, and DF + H,, the same study gave rate constants of 7.4 x lo-', and 1.4 x lo-', molecule-' cm3 s-I. The decrease in rate from HF to DF was presumed to demonstrate the importance of energy transfer to rotational levels. For the quenching of DF(u = 1) by HF, a rate constant of 1.06 x 10-12molecule-' cm3 s-' was obtained by the same workers '09 in agreement with previous values of 1.27 x lo-'' molecule-' cm3 s-'. The relaxation of DF(v = 1) by N, yielded a slower rate of 6.2 x molecule-' cm3 s-'. Recently, the reactions of F atoms with various hydrogen sources have been studied as a means of producing vibrationally excited HF. This has stimulated relaxation studies with alkanes and other less common quenchers. Thus, we find that quenching of HF(v = 1) by Table 9 Rate constants for the deactivation of HF(v = 1) byfluorine compounds Quencher ClFj CF4 WFJ F2

SFs

klmolecule - em3s 3.53 1.30 9.41 3.10

x x

10-14

x

10-15

x 1045 1.55 x 10-15

Ref. 245 220 220 221 220,221

CH4, C2Hs, C,H,, C4H10, cyclopropane, and C1F3,245has been studied, yielding relaxationrateconstantsof 1.65 x 3.37 x 10"2,4.19 x lo-',, 5.26 x lO"', 9.95 x lo-',, and 3.53 x lo-', molecule-' cm3 s-', respectively. The latter rate with ClF, is much faster than for the other fluorine sources (cf. Table 9) and may be due to a strongly attractive intermolecular potential as evidenced by the formation of a HF-ClF, azeotrope. The n-alkane data are interesting in that the deactivation cross-section varies linearly with the number of carbon atoms and the ratio of the cross-section for F + RH + HF + R to that for HF(v = 1) + RH + HF(v = 0) + RH is constant for all R and equal to 18 k 2. 244

W. H. Green and J. A. Hancock, I.E.E.E.-J. Quantum Electron., 1973,QE-9, 50.

245

J. K. Hancock and W. H. Green, J. Chem. Phys., 1973,59,6350.

Gas Kinetics and Energy Transfer

150

As we have seen, the HF(DF) self-relaxation rates at low temperatures differ greatly from their high temperature values, due probably to strongly attractive intermolecular potentials. Such attractive forces should play a much less important role in the relaxation of HF(DF) by H,(D,) so that the room temperature rates should not differ so greatly from the values extrapolated from high temperatures. Vibrational relaxation rates for HF(v = I) and DF(v = I) with H, and of DF(u = I) with D2 have been measured at temperatures from 440 to 690 K and also at 295 K using a combined shock-tube laser-induced fluorescence techniq~e.~" The room temperature rates are included in Table 10 together with the rates for other hydrogen halides. The relaxation times of DF(v = 1) with H, at different temperatures fall along an extrapolation of the data obtained in shock tube experiments at high temperatures.246 The data above 450 K have a temperature dependence very similar to that of HF self-relaxation at high temperatures but the rates for HF-HF are close to double those for DF-H,. The DF-H, relaxation rate goes through a maximum at 300 K, while the HF and DF self-relaxation rates have maxima near 1200 K. If the rate for DF-H, relaxation can be described by a two term expression similar to the HF-HF case, the attractive term must be about 150 times smaller than the corresponding term for HF-HF relaxation. The more limited data on HF-H2 and DF-D2 relaxations suggest that the relaxation times decrease at higher temperatures in much the same way as DF-H,. From Table 10, it appears that H, deactivates Table 10 Relaxation of hydrogen halides by hydrogen Species HF(v = 1) DF(v = 1)

Collision partner H2 H 2

D2

HCI(U = 1)

DCl(v

= 1)

HBr(v = 1)

H 2

HD D2 n-Hz P-Hz HD D2 H 2

H2 HD D2

Relaxation rate constant 1016k/molecule-1 cm3 s-I 118 f 34 205 f 22 31 f 12 53 f 9 25 f 3 5 f 0.6 214 f 22 186 f 19 84k9 18f2 189 f 68 65 f 3 20 f 1.2 12 f 1.7 .

Probability 2.7 x 10-5 4.7 x 10-5 9.8 x 9.4 x 5.5 x 10-6 1.3 x 3.9 x 10-5 3.4 x 10-5 1.9 x 10-5 4.6 x 3.06 x 10-5 1.2 x 10-5 4.2 x 3.1 x

Ref. 204

204 204 247 248

248 249 249 249 249 250 251 252 253

each of the hydrogen halides at roughly the same rate at room temperature and the effect of isotopic substitution of the halides is to give similar results. This suggests that a similar deactivation mechanism is operating in all the hydrogen halide-H, systems. 246 247

248 249

250 251

252

2s3

J. F. Bott and N. Cohen, J. Chem. Phys., 1973,58,934. H. L. Chen and C. B. Moore, J. Chem. Phys., 1971,54,4072. B. M. Hopkins and H. L. Chen, J. Chem. Phys., 1972,57,3162. P. F. Zittel and C. B. Moore, J. Chem. Phys., 1973,58,2922. R. J. Donovan, D. Husain, and C. D. Stevenson, 7hanr. Faraday Soc., 1970,66,2148. H. L. Chen, J . Chem. Phys., 1971,55, 5551. B. M.Hopkins and H. L. Chen, J. Chem. Phys., 1973,59,1495. M. Margottin-Maclou, L. Doyennette, and L. Henry, Appl. Optics, 1971,10, 1774.

h e r Studies of Vibrational,Rotational, and Translational Energy Transfer

151

V-V Transfer. A room temperature value of 4.03 x lo-'' molecule-' cm3 s-' has been measured by Bott 211 for the V-V process in equation (19) by observed u = 2

2 HF(u = 1) + HF(u = 0) + HF(u = 2)

(19)

fluorescence. The relaxation of the u = 3 and u = 5 levels was also monitored by observing the fluorescence in the near i.r. using appropriate filters and photomultiplier detection. It was found that the Landau-Teller prediction (that vpz be constant)was obeyed,indicating a fast V-V relaxation rate with Boltzmann equilibrium between the vibrational levels. Rate constants have also been determined for the relaxation shown in equation (20) by monitoring fluorescence from the u = 2 and HF(u = 2)

+ HF(v = 0) + 2HF(o = 1)

(20)

u = 1 levels.222A value of 2.07 x lo-'' molecule-' cm3 s-' was obtained for this V-V process. Rotational relaxation was also observed by these authors. The decay of the u = 3 level of HF has also been studied by pumping the u = 1 and u = 2 levels simultaneously and observing the u = 3 fluorescence at 11 100 cm-' with a ph~tomultiplier.~~~ A rate constant of 4.93 x lo-'' molecule-' cm3 s-' was observed so that upz is 1.9 ps Torr for u = 3 and 3 ps Torr for the u = 2 level. The u = 2 level has also been excited directly using a Nd:YAG laser.224 For the u = 1 level, a rate constant of 2.23 x molecule-' cm3 s-' was observed for the V-T processes, but the V-V processes were apparently too fast to be measured with the equipment used. Recently, energy transfer data have been reported for HF-HCN and DF-HCN mixtures in the temperature range 2-50 K.225 The highly polar HCN molecule, if regarded as a quasi-diatomic, should exhibit similar energy transfer characteristics to HX molecules. However, HCN has additional vibrational degrees of freedom making possible additional laser transitions. An HF or D F chemical laser was used to produce HF(u = 1) or DF(u = 1) molecules and vibrational fluorescence from HF, DF, or HCN was monitored. The temperature dependence of the vibrational energy transfer probabilities for HF-HCN and DF-HCN show a pronounced inverse temperature dependence and relatively large probabilities consistent with the known features of the HF-HCN, HF-HF, and HCN-HCN intermolecular potentials. These potentials have large anisotropies and relatively strong attractive minima. There is evidence for a stable linear complex between HF and HCN. Examination of Figure 12 reveals a discrepancy in the values of self-deactivation probabilities for HCN as determined from relaxation measurements with HF-HCN and DF-HCN mixtures. The HCN self-deactivation rate constants measured in HF-HCN mixtures are about 60% higher at all temperatures than the values obtained from the DF-HCN mixtures. At room temperature the two values (1.96 f 0.5) x and molecule-' cm3 s-' bracket the value of (1.74 0.2) x (1.40 f 0.2) x molecule-' cm3 s-' observed by Harira et a1.226in Br2-HCN mixtures. The origin of this discrepancy is unknown. Interest in the operation of the DF-C02 transfer laser has stimulated energy transfer studies on DF-C02 mixtures. Since the chemical reactions producing vibrationally excited DF have sufficient energy to populate DF to levels up to at least u = 4, information on the transfer rates from DF in each of the four vibrational levels, in addition to the transfer rate from excited C02(001) to ground state

Gas Kinetics and Energy Transfer

152 I0 8 6 4

2 HC FJ (r! m 0)

2-

t

T

=!

$ lo2 m

0

CK

a

e 6 4

2

16: I

I

2

2

1

I

4

I

I

I

6

l

8

l

l

lo3

TEMPERATURE

/

I

I

2

3

4

K

Figure 12 Temperature dependence of the probabilities for deactivation of HCN(001) by HCN(000) (Reproduced by permission from J. Chem. Phys., 1977,66, 3189)

DF(u = 0), is required. A study of this type was reported by Hinchen and H o b b ~ , ~ ~ ' who determined the vibrational energy transfer rates between DF(u = 2), DF(u = l), and COz using the fluorescence technique. The DF in the DF-C02 mixtures was excited to both u = 1 and u = 2, by pumping with a pulsed DF laser operating simultaneously on the (1-0) and (2-1) transitions. By monitoring the fluorescence at 1.7, 3.5, and 4.4 pm the temporal behaviour of the DF(u = 2), DF(u = l), and CO2(o01) population was followed. Rate constants of 1.58 x lo-'' molecule-' cm3 s-' for DF(u = 2) + C 0 2 transfer and 4.66 x lo-'' molecule-1 cm3 s-' for COz(OO1) deactivation by DF were obtained. The rate constants for DF-C02 transfer obtained in this study are compared in Table 11

Table 11 Rate constants for DF-C02 vibrational energy transfer at 300 K (molecule-' cm3s-') DF(u = l)-COz DF(v = 2 w 0 2 DF(u = 3)-C02 C02(001)-DF Ref. 6.2 x 10-l2 4.0 x 4.7 x 5.3 x (350K) 7.5 x 10-l2

-

1.6 x lo-'' 6.8 x 10-l2 -

-

-

7.1 x 10-13 5.9 x 10-13

227 230 229 229

-

8.1 x 1 0 - 1 3 5.6 x 10-13

215 228

lo-" -

1.6 x

4.7 x

1043

-

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

153

with those obtained previously by other workers. The rate constant for the DF(u = 1) + C02 transfer compares favourably with values obtained by other workers supporting the validity of the kinetic analysis. The value obtained for C02(001) deactivation by DF, 4.7 x molecule-' cm3 s-', agrees with the value of Chang et aZ.228but is only about half the value quoted by Bott and C ~ h e n . ~ ~ ~ The very fast rates for V-V energy transfer between DF and C 0 2 can in part be attributed to strong interactions between the molecular polar moments. However, the energy transfer requires the absorption of quite large energy discrepancies between the vibrational levels in DF and Cot. In the case of DF(u = 1 + 0) this amounts to 557cm-' and for DF(u = 2 + 1) it is 465 cm-'. Dillon and Stephenson'69 have proposed a theoretical description of energy transfer between DF(u = 1) and C 0 2 which agrees well with experiment at 300 K. The theory is a semiclassical, nchorder, perturbation approach, and the interaction is described as a combination of V-V and R-R transfer where the V-V transfer is described by a dipole-dipole interaction and the R-R by the interaction of the DF dipole with the quadrupole moment of C02. Large V-V transfer rates are predicted since the energy defect is absorbed as rotational excitation in the colliding molecules. This calculation, applied to DFfv = 2) --+ C 0 2 transfer, gave a rate constant of 1.2 x lo-'' molecule-' cm3 s- for single quantum exchange, and a predicted double quantum transfer rate constant of 5.9 x molecule-' cm3 s-', The sum of these two values 1.8 x lo-'' molecule-' cm3 s-' compares well with the experimental result of (1.6 & 0.4) x lo-'' molecule-' cm3 s-'. The unusual temperature dependence and very fast rate for HF/DF transfer has 4

2

Id: c I

v)

%6 E

7i4 V *

-t

2

lo"

Figure 13 Temperature dependence of the rate constant, k, for HF V-V transfer (Reproduced by permission from I.E.E.E.-J. Quantum Electron., 1975, QE-11, 679)

154

Gas Kinetics and Energy Transfer

led to the introduction of a theoretical treatment involving the formation of dimers.' 75 In the presence of strong attractive forces, colliding HF or DF molecules can form a dimer or loosely bound complex which can exist with a long lifetime (much longer than the vibrational period) resulting in efficient energy exchange. As the temperature is raised, the thermal motion tends to destroy the energetically favoured orientation decreasing the probability of energy transfer. This model was invoked to explain the behaviour of the energy transfer processes for T < 500 K; at higher temperatures, the rapid rotational model (VVR) becomes dominant resulting in an increased rate. The sum of these two processes explains the minimum value found near 700 K in both HF-HF and DF-DF collisions. The temperature dependence of the experimental and theoretical rate constants are given for H F in Figure 13 in the temperature range 300-2000 K. Reasonable agreement was found with available experimental results, but insufficient data are presently available to rigorously test this model. Hydrogen Chloride, Bromide, and Iodide.-V-T,R Transfer. The pattern of energy transfer established for HF continues with the other hydrogen halides with rotation appearing to play a vital role owing to the strong dipolar interactions. The selfrelaxation rate constant for HCl was found to be 2.54 x 247 and 2.17 x molecule-' cm3 s'1.253 As in the case of HF, the SSH theory is invalid for HCI at 296 K. The relaxation rate constant for DCI-DCl was found to Table 12 Some recent V-T,R rate constantsfor HCI, HBr, and HI quenching at room temperature Species HCl(V = 1)

Quencher 3He 4He Ne Ar He HCl

c1

HCl(V DCl(V

= 2) = 1)

Br Br

3He 4He Ne

Ar HBr(v

=

1)

DCI CH4 CD4

HzO

2s6 257

zs8

5.6 2.8 3.4 6.2 2.6 8.5 2.8 3.3 2.2

x x x

1047 1047

lo-'*

x 10-17

x

1044

x x 10-13 x 1044 x 5.9 x 1047

1.0 x 10-17 1.9 x 7.8 4.5 1.5 8.7 4.7 2.0

Ref. 254 254 254 254 254 247 258 257 257 254 254 254 254

x x 10-13 x

120 120 120

x x

1044

120 120

x 10-15

120

120 1) 10-13 120 R. V. Steele and C. B. Moore, J. Chem. Phys., 1974,60,2794. B. M.Hopkins, H. L. Chen, and R. D. Sharma, J. Chem. Phys., 1973,59,5758. B. M. Hopkins, A. Baronavski, and H. L. Chen, J . Chem. Phys., 1973, 59,836. S. R. Leone, R. (3. MacDonald, and C. B. Moore, J. Chem. Phys., 1975,63,4735. R. 0.MacDonald, C. B. Moore,I. W. M.Smith, and F. J. Wodarczyk, J. Chem. Phys., 1975,

HI(v

254 255

3He HD HBr HI

Rate constant/ molecule- cm3 s - 1 1.2 x 10-l6

62,2934.

=

1.9 x 1.5 x

1044

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

‘

155

’

be 7.76 x 10- molecule- cm3 s- in agreement with the earlier work of Breshears and Bird.’*’ Clearly, kHcl-Hcl 9 kml-Dcl, so that V-T,R transfer is most likely to be dominant, since V-T transfer would produce the opposite result. Some of the more recent relaxation rates for the hydrogen halides are summarized in Table 12. From the temperature dependence of the rate constants for various inert gases between 800 and 4100 K,17’ and between 295 and 700 K,254it was shown that there was a decreased probability of energy transfer with reduced mass. This effect is stronger than that predicted by any V-T or V-T,R theory. The Landau-Teller is obeyed, which was taken as evidence for the importance relation (log p z cc T*) of hard collisions in these systems. The ratio of the relaxation probabilities PHcI-Ar/PDcI-Ar w 2 is evidence that rotational energy transfer is important with Ar. As the rare gas quencher becomes lighter this ratio decreases, indicating the increased importance of translational motion. At lower temperatures, between 196 and 345 K, HCI self-relaxation shows a decrease in rate with increasing temperature.255 This is opposite to the behaviour of the HCI-He system and is interpreted in terms of an attractive potential between HCI molecules. The HCI-HBr system has been interpreted in a similar fa~hion.’’~ Single temperature studies of HBr + HCl, using isotopic pairs of quenching 2 5 6 have demonstrated the overriding importance of vibrational energy species,252s transfer unlike Moore’s 247 earlier conclusions. Recently, the laser-excited fluorescence method has been used to measure the deactivation rates of HCl(u = 1) and HCI(u = 2) by Br atoms.257 The impetus for this work was provided by the possibility of using the HCI(u = 2)-Br deactivation as a means of separating C1 isotopes. An HCI laser was used to produce HCl(u = 1) and a tunable parametric oscillator to pump HCI directly to = 2 from u = 0. Using direct excitation of HCI(u = 0) the kinetics of deactivation by Br atoms are simple and reliable rates can be extracted. The rate constant for the u = 1 quenching was (2.8 rf: 0.52) x molecule-’ cm3 s - l at 295 K and for 0 = 2 the rate constant was (1.8 & 0.33) x molecule-’ cm3 s-l at 294 K. The deactivation of HCI(u = 1) by Br was shown to occur by V-T,R transfer, while the deactivation of HCI(u = 2) was believed to occur largely by reaction. The rate constant for the deactivation of HCI(u = 1) by Br, is (3.26 k 0.13) x molecule” cm3 s-’ so that the vibrational deactivation of HCI(u = 1) by Br is about 10 times faster than by Br, and about lo5 times faster than by Ar.2s4 Thus, the reactive nature of Br must be important in collisions of HCl and Br. Both the molecule’’ cm3 s-’, and the V-T,R rate V-E rate constant, k = 9.1 x constant are of the same order of magnitude. Thus, in a single collision, between HCI(u = 1) and a bromine atom both V-E and V-T,R channels are important in producing HCl(u = 0). This strongly suggests that the non-adiabatic coupling of the electronic states of BrHCl is sufficiently large to play a role in vibrational deactivation. The deactivation of HCl(u = 2) by Br is dominated 2 5 7 by process (21), HCI(u = 2)

+ Br

3

HBr(u = 0)

+ Cl + 245 cm”

(21)

with processes (22) and (23) playing only a minor role.

+ .Br +‘HCI(u = 0) + Br + 5667 cm-’ HCI(u = 2) + Br + HCl(u = 1) + Br + 2782cm-’

HCI(u = 2)

(22) (23)

Gar Kinetics and Energy Transfer

156

Table 13 Rate constantsfor V-V transfer in HC1 and HBr at room temperature Excited molecule HCI(v = 1)

Quencher D 2

ocs

cm3s - l 2.2 x 10-13 6.3 x 10-13

k/molecule

N2

3.0 x

1044

co

7.3 3.3 5.6 2.9

1044

HCl(v = 2)

HCl

HBr(w = 1) HBr(w = 2)

ocs HBr

x

x lo-” x 10-l2 x 10-l2

Ref.

261 256 261 261 54 256 262

TEMPERATURE/K

Figure 14 Temperature dependence of the rate constants for HCl-CO, V-V transfir (k,) and HCl-CO, V-T vibrational relaxation (k4) (Reproduced by permission from J. Chem. Phys., 1975, 63, 3115)

The relaxation of HCl(v = 1) by Cl atoms has recently been studied by MacDonald et aLZs8 The rate constant obtained, k = (8.5 2.5) x molecule-’ cm3 s-I, was lo6 times faster than the corresponding rate for argon quenching.254 Chemical forces, and atom exchange were thought to be responsible for this increased rate, 259

260

261

G. C. Pimentel and P. N. Noble, J. Chem.Phys., 1968,49, 3165. D. J. Seery, J. Chem. Phys., 1975,63,3115. J. M.Allee, M. Margottin-Maclou, J. Menard, and L. Doyennette, Compt. rend., 1974, 279, B, 305.

262

B.M.Hopkins and H. L. Chen, Chem. Phys. Letters, 1972,17,500.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

I57

+

i.e. C1' + HCI + C1'H C1. The rate constant was found to be independent of pressure over a wide range (a factor of lo2 for Ar and 10 for HCl), indicating a bimolecular and not termolecular process. Evidence for the strong attraction of C1 for the H in HCI has been found from matrix studies of CIHC1.259 Y-Y Transfer. Some recent rate constants for V-V transfer in HCl and HBr mixtures with various quenchers are collected in Table 13. Seery "O has reported shock tube-fluorescence measurements on the V-V and V-T transfer rates in HCl-CO mixtures in the temperature range 700-2000 K. The time resolved fluorescent emission from the shock-heated gas was monitored at 3.5 and 4.7 pm corresponding to emission from HCI and CO respectively. The experimental rate constants are presented as a function of temperature in Figure 14. The rate constants for V-V transfer above 1000 K show good agreement with an extrapolation of the measurements of Allee et aL2" in the temperature range 300-1000K. The room temperature transfer rate constants 7.3 x molecule-' cm3 s-' measured by Allee et aZ.26' is in good agreement with the room temperature value of Chen and Moore.263 The fluorescence data of Allee et al., included V-V measurements on HCl-D2 and HCI-N, in addition to HCI-CO mixtures, in the temperature range 300-1000 K. The plots of rate constant against temperature for all three systems exhibited a broad minimum in the region of 700-900 K for HCI-D,, 500-700 K for HCI-N2, and 400-500 K for HCI-CO. In conclusion, the unusual characteristics of the HX molecules, particularly HF, require theoretical treatments which take account of strong attractive forces, deep potential wells, large dipole moments, large rotational spacing etc. While it is possible to construct models which reproduce certain features of HX molecular behaviour, i.e. the decrease in relaxation rates and the existence of a minimum for HF, no single model adequately describes all the features quantitatively for the HX systems.

Carbon Dioxide.-Because of the importance of the C 0 2 laser, and various CO, transfer lasers, a vast amount of information on the kinetics of energy transfer on C02, in the pure gas and in mixtures with a wide variety of other gases, has been accumulated. Interest in the relaxational processes in this molecule is still very active, stimulated by the continuing development of high power lasers. The energy level diagram for the low-lying states of C 0 2 is shown in Figure 15. The strongest laser transitions near 10.6 pm occur between the vibration-rotation transitions of the asymmetric stretching fundamental at 2349 cm-I (00'1) and the symmetric stretching fundamental at 1388 cm- (10'0). Laser transitions also arise near 9.4pm between the (00'1) and the (02'0) levels. The two lower laser levels (10'0) and (02'0) are strongly coupled by Fermi resonance interactions.

'

Relaxation from the (00'1) Level. Numerous studies on the relaxation rates of CO2(O0'1) with a variety of partners have been made. Accounts of earlier work on this topic can be found in previous review^.^-^ The laser-induced fluorescence technique has been used to measure the rates for the deactivation of C02(00'1) by 263

H. L.Chen and C.B. Moore, J. Chem. Phys., 1971,!%, 4080.

Gas Kinetics and Energy Transfer

158

i i

J

i 31

27

23

\

J

28

24 20 16

I

:

1

1

OZ% RESONANCE

Figure 15 Detailed energy level diagram for COz, (OOol-lOoO) and (OO"142"O) transitions, including rotational levels, p = pm (Reproduced by permission from 'Lasers', ed. A. K.Levine and A. J. Demaria, Dekker, New York, 1971 vol. 3)

a variety of r n ~ l e c u l e s .More ~ ~ ~recently ~ ~ ~ rate constants for the quenching of C02(OOo1)by ONF, COF,, and O3 were reported.279 In each case, rapid near264

L. 0.Hocker, M. A. Kovacs, C. K. Rhodes, G. W. Flynn, and A. Javan, Phys. Rev. Letters, 1966, 17, 233.

265 266 267 z68

z69 270

271

272 273 274

275 276 277

278 279

C. B. Moore, R. E.Wood, B. Hu, and J. T. Yardley, J. Chem. Phys., 1967,46,4222. W. A. Rosser, A. I).Wood, and E. T . Gerry,J. Chem. Phys., 1969,50,4996. W. A. Rosser and E. T. Gerry,J. Chem. Phys., 1969,51,2286. W. A. Rosser, R. D. Sharma, and E. T. Gerry,J . Chem. Phys., 1971,!54,1196. J. C. Stephenson, R. E. Wood, and C. B. Moore, J. Chem. Phys., 1971,54,3097. W. A. Rosser and E. T . Gerry, J. Chem. Phys., 1971,54,4131. M. A. Kovacs and A. Javan, J. Chem. Phys., 1969,50,4111. J. C. Stephenson and C. B. Moore, J, Chem. Phys., 1970,52,2333. J. C. Stephenson, R. E. Wood, and C. B. Moore, J. Chem. Phys., 1971,54, 3097. H. Gueguen, I. Arditi, M. Margottin-Maclou, L. Doyennette, and L. Henry, Compt. rend., 1971,272, B, 1139. R. S.Chang, R. A. McFarlane, and G. J. Wolga, J. Chem. Phys., 1972,56,667. J. C. Stephenson and C. €3. Moore, J. Chem. Phys., 1972,56,1295. J. C. Stephenson, J. Finzi, and C. B. Moore, J. Chem. Phys., 1972,56, 5214. Y.V. C. Rao, J. S. Rao, and D. R. Rao, Cheh. Phys. Letters, 1972,17,531. T. A. Cool and J. R. Airey, Chem. Phys. Letters, 1973, 20,67.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

159

resonant V-V transfer was observed with deactivation rate constants of (1.7 f 0.2) x (9.4 k 1.2) x and (1.19 & 0.2) x lo-', molecule-' cm3 s-' for ONF, COF2, and 0,, respectively. Shock tube measurements were used to provide similar data for CO, and OCS using H2 and its isotopes as collision partners. The results for C 0 2 agreed with the predictions of Sharma's theory but those for OCS did not. Additional results have also been reported for V-V self-quenching in C02.281 Collisional pumping to the (01'1) combination level was measured by monitoring the 4.3 pm fluorescence associated with the (01'1) + (01'0) transition. The rise time of the fluorescence from (01'1) monitors the rate of population of this level from the initially excited (OO"1) level. The rate constant for the process

,*'

C02(01'1)

+ C0,(00"0)

-b

c02(00°1)

+ CO,(Ol'O)

(24)

was found to be (1.6 f. 0.3) x lo-'' molecule-' cm3 s-'. Using Sharma's theory, assuming dipole-dipole and dipole-octupole interactions, a rate constant of 2.2 x lo-'' molecule-' cm3 s-' was obtained in good agreement with the observed value. The temperature variation of the self-quenching rates of C02(00"1) and CO2(OOo1)-C0 V-V transfer rates were measured in the temperature range 180-300K.282 Both V-T self-deactivation and V-V rates showed a minimum at the same group about ambient temperature. In a subsequent, more detailed reported variable temperature studies of self-quenching of 2C02(0001)in the range 300-900K. At room temperature, a V-V transfer rate constant for 12C02 of (1.15 f 0.12) x lo-'' molecule-1 cm3 s - ' was obtained, smaller than the value previously obtained by Burak et al.281 The Sharma and Brau theory overestimated the magnitude of the transfer rate for 12C02+ "CO,(AE = 12 cm-') but gave good agreement with the previous results of Stephenson and Moore 276 for 12C02+ 13C02(A.E= 66 cm-') above 500 K. Rotational relaxation of the (00O1) level has also been studied in both pure C02 and in mixtures with He and N, using the i.r.-i.r. double resonance technique.284 The measured rate constants were and (3.7 f.0.6) x lO-"molecule-' (4.0 f 0.6) x lo-", (1.9 f.0.3) x lo"', cm3 s-' for relaxation with C02, He, and N, respectively, as collision partners.

'

Relaxation from the (10'0) and (02"O) Leveis. The increased interest in the depopulation of the lower lasing levels is a direct consequence of the importance of these levels to the efficiency of CO, lasers. Particularly, the near resonant exchange between the symmetric stretching modes and the bending mode via processes such as 10"O

+ OOO + 01'0 + 01'0

(25)

283

C . J. S. M. Simpson, P. D. Gait, and J. M. Simmie, Chem. Phys. Letters, 1973,22, 144. I. Burak, Y.Noter, and A. Szoke, I.E.E.E.-J. Quantum Electron., 1973, QE-9, 541. A. Chakroun, M. Margottin-Maclou, H. Gueguen, L. Doyennette, and J. Henry, Compt. rend., 1975,281, B, 29. L. Doyennette, M. Margottin-Maclou, A. Chakroun, H. Gueguen, and L. Henry, J. Chem.

284

Phys., 1975, 62,440. R. R. Jacobs, K. J. Pettipiece, and S. J. Thomas, Appl. Phys. Letters, 1974, 24, 375.

280 281 282

Gas Kinetics and Energy Transfer

160

has been discussed e x t e n ~ i v e l y . ~ ~Marriott ~ - ~ ~ ~ 2 8 5 calculated a rate of k = 3.1 x molecule-' cm3 s-' for this process. Rhodes et aZ.293obtained a value of 1.24 x lo-'' molecule-' cm3 s-' for the same process using an i.r. double molecalculated a rate constant of 3.1 x resonance technique. Seeber cule-' cm3 s-' a value which was also obtained by Bulthius and Ponsen 288*289 from experiments involving the decay of the laser emission in the afterglow of a C 0 2 molecule-' cm3 s-') laser discharge. A similarly slow decay rate (k 3 x for the relaxation of the C02(10'1) state was obtained by Rosser et aL2" using an electrical perturbation technique. Recently, De Temple et aZ.'" in another pulsed afterglow experiment, found two decay rates for the (10'0) level, a fast rate, (k = 5.2 x lo-'' molecule-' cm3 s-l) and a slower rate, (k = 5.2 x lo-'' molecule-' cm3 s-') in agreement with the earlier work of Rhodes et aZ.293 The rates were found to be linearly dependent on C 0 2 pressure and were not affected by the pressure of He. They were therefore assigned to V-V equilibration processes within the v1 and v 2 modes of C02. Further work on this system was recently reported by Bulthius and P o n ~ e n , ~ ' ~ molecule-' cm3 s-', rate who presented evidence that the slow, k = 3.1 x was associated with V-V transfer between the (10'0) and (01'0) levels. This implies a much slower exchange rate between these two levels than generally accepted. The k = 1.2 x 10- molecule- cm3 s- relaxation was attributed to the redistribution of populations of levels such as (10'0) and (02'0), and (10'0) and (0220) by molecular collisions. The very fast rate with k = 3.1 x lo-'' molecule-' cm3 s-' was suggested to arise from rotational relaxation. Irradiation of CO, by P(18) 10.6 pm pulses leads to a depletion of the symmetric stretch (10'0) level and to the population of the asymmetric stretch (00'1) level. The 4.3 pm fluorescence which follows the excitation pulse monitors the decay of the (00'1) state. This excitation scheme was employed by Burak and Gamss 294 to study low C 0 2 pressures in the presence of buffer gases. At low pressures, only two rotation-vibration levels are coupled to the radiation field, and the extent of excitation is determined by power broadening of the inhomogeneous Doppler transition. When the pressure of the buffer gas is increased, the non-interacting rotational levels are coupled to the excitation processes via collisions and a marked increase in fluorescence intensity is observed. The effect of various pressures of buffer gas on the fluorescence intensity was considered theoretically with a two level model using a semiclassical treatment of the molecular field interactions. The rotational relaxation rate constant obtained from this treatment, k = 5.9 x lo-'' molecule'' cm3 s-', was high when compared molecule-' cm3 s-' measured directly for the with the value of 2.2 x

"'

-

''

28s 286 287 288

289 290

291 292

293 294 29s 296

'

'

R. Marriott, Proc. Phys. Soc., 1964,84,877. R. D. Sharma, J. Chem. Phys., 1968,49,5195. K . N.Seeber, J. Chem. Phys., 1971,555077. K. Bulthius and G. T. Ponsen, Chem. Phys. Letters, 1972,14,613. K. Bulthius, J. Chem. Phys., 1973, 58, 5786. W. A. Rosser, E. Hoag, and E. T. Gerry, J. Chem. Phys., 1972,57,4153. T. A. De Temple, D. R. Suhre, and P. D, Coleman, Appl. Phys. Letters, 1973, 22, 349. K. Bulthius and G. J. Ponsen, Chem. Phys. Letters, 1973, 21,415. C. K. Rhodes, M.J. Kelley, and A. Javan, J. Chem. Phys., 1968,48, 5730. I. Burak and L. A. Gamss,J. Chem. Phys., 1976,65, 5385. A. Lecuyer, J. Phys. (Paris), 1975, 36, 617. M. Heutz-Aubert and M. P. Chevalier, Compt. rend., 1973, 276, B, 211.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

161

C0,-He system.284* 29J Heutz-Aubert and Chevalier have also studied the V-R,T transfer between CO2(O1'0) and ortho- and ~ a r a - H , . , ~ ~ Relaxation from the (01'0) Level. Relaxation of the bending mode of CO,(Ol'O) below room temperature plays a key role in the 16 pm cooled COP laser. This has stimulated a laser fluorescence study of the deactivation of this mode by CO, and by argon down to a temperature of 150 K.," No convenient laser transition was available for the direct excitation of the (01'0) mode but several indirect pumping schemes were evaluated. Indirect excitation of the bending mode by populating the (11'0,03'0) level at 2076 cm- with a CO chemical laser and subsequent deactivation to the (01'0) level failed to produce significant population of this level. The technique that was successfully used was to pump the (00'1) level of CO,, by V-V exchange from CO, excited by a CO chemical laser. This level was then deactivated by argon and CO, to the (11'0, 03'0) level at a rate which was faster than the collisional deactivation of the (01'0) level producing an excess population. The rate constant measured for the relaxation of the (01'0) level was (6.5 f 0.9) x molecule-' cm3 s-' at room temperature in good agreement with values obtained from other techniques.298 The temperature variation of this rate constant in two mixtures containing 0.3% CO, 1.5% CO,, and 98.2% Ar, and also 2.7% CO, 18.4% CO,, and 78.9% Ar is shown in Table 14. The C0,-CO, and C0,-Ar rate constants are also included. From Table 14 it is apparent that the deactivation rate of CO,(Ol'O) is almost independent of temperature in the range 150-300 K. This contrasts with the V-V self-quenching of the (00'1) mode which increases with falling temperature in this range.

'

Table 14 Vibrational deactivation rate data for CO, (01'0) (ref. 297) T/K Rate constantslmolecule- cm3s Mixture A"/ Mixture Bb/ kc02-co2 x 10-16 296 9.03 285 8.13 250 5.46 215 4.53 181 3.38 156 3.60 0.3% COY1.5% C02, 98.2% Ar;

x 1045

x 10-15

1.79 1.96 1.57 1.63 1.39 1.44

5.64 6.95 6.08 6.83 5.99 6.18

2.7% COY18.4% COZY 78.9%

kcoz

x

8.25 7.14 4.53 3.48 2.45 2.64

Ar.

ReZaxationfrom the (10'1) and (02'1) Levels. Finzi and Moore 299 have carried out measurements of fast V-V energy transfer following direct excitation of COz(10' 1) and (02'1) combination levels with a tunable parametric oscillator

+

+ C02(OOo1)- 22cm-' + CO,(00'1) - 21 cm-'

CO2(1Oo1) CO~(Oo"0)+ CO2(lO0O) C02(0200) CO2(O2'1) + CO,(OO'O)

(26) (27)

The relevant transitions are shown in Figure 16. Resonant V-V processes then populate the (10"0), (02"0), and (00'1) levels. The population of the (10'1) and (02'1) states was monitored by observing fluorescence near 4.3pm with a narrow band filter. The radiation near 4.3pm arising from (00'1) + (00'0) transition was 297

298 299

D. C. Allen, T. J. Price, and C . J. S. M. Simpson, Chem. Phys. Letters, 1977,45, 183. M. Huetz Aubert and F. Le Poutre, Physica, 1974, 78,435. J. Finzi and C. B. Moore, J. Chem. Phys., 1975,63,2285.

Gas Kinetics and Energy Transfer

162 4000

I

SYm Stretch

Bend

Asym. Comb. Stretch Levels

Figure 16 Fluorescent emission from C02pumped by 2.7 pm radiution from a parametric oscillator, p = pm (Reproduced by permission from J. Chem. Phys., 1975, 63, 2285)

Table 15 Measured V-V rate constants and calculated cross-sectionsfor CO, (ref. 299) Species coz ( l 0 O l ) coz (02"l)

k/molecule-' cm3s-' (1.3 f O . l ) x 10-lo (1.2fO.l) x 1 0 - ' O

Cross-section!A' expt. theory

2 4 4 4 21

43

AEIcm-' -22 -21

selectively absorbed using a CO, filter cell in front of the detector. The measured V-V rate constants and calculated 276 cross-sections are shown in Table 15.

Nitric Oxide.-In many respects nitric oxide shows anomalous behaviour similar to that found for HX molecules. The NO(v = 1) self-quenching rate is at least five orders of magnitude faster than the corresponding rates in N,, CO, or O2 at room temperature and increases with decreasing temperat~re.~" The relaxation at T = 298 K has been shown to be due to bimolecular collisions In a later investigation the deactivation rates of NO(v = 1) by He and N2 in the temperature 300

J. C . Stephenson, J. Chem. Phys., 1973,59, 1523.

Laser Studies of Vibrational,Rotational, and Translational Energy Transfer

163

Table 16 Vibrationaltransfer rate datafor NO and CO at T = 298 K (ref.301) k/molecule-' cm3s-I kN0-M

kc0-M

(1.83 f0.22) x (2.02 0.40) x 10-14 (1.89 f 0.15) x (3.69 f 0.28) x (2.02 f 0.19) x 10-13 (2.64 f 0.22) x 10-13 (2.05 h0.16) x (9.00 f 1.86) x

(i.wk0.50) x (1.37 kO.19) x (9.22 k0.62) x (1.18 fO.08) x (9.93 f 0.93) x (1.99 f 0.09) x (4.50 f 0.93) x (1.37 ko.12) x

10-13 10-13 10-14 10-13

1044

range 100-300 K were measured by Stephen~on.~"Room temperature rates for the quenching of NO by H20, D20, NO2, CH,, C2H4, C2H6, and C4HI0, of N2(u = 1) by NO, and of CO(u = 1) by NO2 and N204were also measured. The laser excited fluorescence technique was employed, whereby NO molecules were optically pumped into the u = 1 state by frequency doubled pulses from a TEA CO, laser. The room temperature results for the deactivation of NO by various collision partners are shown in Table 16, which also includes the results for CO. The deactivation probabilities of NO(u = 1) by NO showed a minimum at about 400K,with the probability increasing by a factor of 3 as the temperature was lowered from 300 to 100K. Similar arguments to those used in the case of HX molecules can be used to explain the observed temperature dependence of the rates. Alternatively, the temperature dependence of the NO rate can be explained qualitatively by a modification of V-E resonance theory of Nikitin.242 Glanzer 303 has also recently studied the relaxation of the lower vibrational states of NO(X211) in collisions with NO and Ar. Carbon Monoxide.-V-T Transfer. The CO laser cannot be used to excite directly ground state CO since the laser runs only on transitions originating from CO(u > 1) and these do not overlap the frequency of the fundamental due to anharmonicity. Optical parametric oscillators,304frequency doubled C 0 2 lasers,305-308and energy

Table 17 V-T energy transfer rate constantsfor CO Quencher k/molecule - cm3s He (2.0f 1.0) x 1 0 4 7 Ar ~ ( 3 .f 0 1.0) x H2 D 2

302 303 304 305 306 307

(4.5 f 0.4) 5.0 4.5 (1.4 f 0.5)

x x 10-l6 x x lo-"

Ref. 305 305 305 314 307 305

J. C. Stephenson, J. Chem. Phys., 1974,60,4289. J. Billingsley and A. B. Callear, 7'kuns. Faraduy SOC.,1971,67,257. K. Glanzer, Chem. Phys., 1977,22,367. R. C, Abrams and 0. R. Wood, Appl. Phys. Letters, 1971,19, 518. W. H. Green and J. K. Hancock, J. Chem. Phys., 1973,59,4326. J. C. Stephenson and E. R. Mosburg, J. Chem. Phys., 1974,60,3562. D. F. Starr and J. K. Hancock, J . Chem. Phys., 1975,63,4730. G. Mastrocinque, A. Chakroun, L. Doyennette, H. Gueguen, M. Margottin-Maclou, and L. Henry, Chem. Phys. Letters, 1976, 39, 347.

164

Gas Kinetics and Energy Transfer

transfer systems 3 0 9 have all been used in order to excite CO. Time dependent gain techniques with probe CO lasers have also yielded energy transfer inf~rmation.~ lo* Table 17 summarizes the V-T data. The rate constants given in Table 17 are 30-40% larger than those of Millikan.3'2 The high efficiency of H, in a series of supposedly pure V-T transfer is attributed 312 to a near resonant V-R process. para-H, is about twice as effective as ortho-H2 in deactivating CO(o = 1) and para-H, (J = 2) is thought to quench very efficiently CO by the near-resonant process (28).

''

CO(o = 1)

+ H,(J

= 2) + CO(u =

0) + H,(J = 6) + 88 cm-'

(28)

ortho-H, has no such near resonant option. The mechanism is supported by recent work of Sharma and However, the rotation of D2and its more attractive Lennard-Jones potential do not seem to give it such efficiency in CO(o = 1) quenching. Indeed it is comparable with He. Table 18 V-V energy transfer rate constants for CO (Rt$ 306 unless otherwise indicated) Quencher 1013k/molecule-'cm3s-I N2 0 2 0 3

clz

NO

co

CH4 CFo SFs H2O D2O H2S C2H6 C2H4 C4H10

CHjOH CzHsOH MeCHO HCOOH MeCOOH

0.005 0.00085 f 0.00009305 4.7 f 2 0.00074 0 . 0 0 0 0 6 3 0 5 0.22 f 0.008305 see text p. 457 0.09 f 0.004,305 0.092,3070.099 2.00 f 0.03305 0.011 f 0.0003305 2.0 f 0.5 0.14f 0.02 0.20 f 0.02 0.10 f 0.09 1.20 f 0.08 2.00 f 0.09 1.8 f 0.4 1.8 f 0.2 1.50 f 0.01 3.6 f 0.5 6.2 f 1.1

V-V Transfer. Table 18 lists some of the relevant rate constants. Clearly, for a diatomic such as CO(v = 1) to be quenched by a V-V process, the quencher must take up vibrational energy. 309

310 311

312 313

31* 315

K.-K. Hui and T. A. Cool, J. Chem. Phys., 1976, 65, 3536. H. T.Powell, J. Chem. Phys., 1975,63,2635. M. C. Gower, G. Srinivasan, K. W. Billman, J. Chem. Phys., 1975,63,4206. R. C. Millikan and L. A. Osburg,J. Chem. Phys., 1964,41,2196. R. D. Sharma and C. W. Kern, J. Chem. Phys., 1971,55,1171. D. F. Starr, J. K. Hancock, and W. H. Green, J. Chem. Phys., 1974, 61, 5421. W. Q. Jeffers and J. D. Kelley, J. Chem. Phys., 1971, 55,4433.

165

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

CO Serf Quenching. A CW laser was used 314 to probe the time dependent gain on various CO transitions following a low energy pulse discharge in CO. The processes studied were the series shown in equation (29). CO(u = u)

+ CO(u = 0) + CO(u = v - 1) + CO(V= 1) - A E

(29)

The vibrational anharmonicity energy defect AE, is given by (30). AE, x 26(u

- 1)cm-’

(30)

Rate constants k:,’ -1 were measured at 100, 300, and 500 K. Generally, such rate constants decrease as u increases since the energy defect becomes larger. This difference in decay rate between a pair of levels u and u - 1 provides the mechanism for population inversion during relaxation in CO. Individual k$ : values were deduced by measuring gain behaviour on all bands from v = 2-12 and subjecting the entire matrix of data to kinetic analysis. The transfer rate constants increased up to u = 3, explaining the absence of gain on the 4-3 and lower transitions. This maximum in rate has been prediced 315 on the basis of Sharma-Brau theory and results from the linear increase in k,q;’_, with u (due to the transition dipole moment dependence) countered by the decrease in k:;:- 1, due to increasing AE,. Above u = 4 the rates at 300 K decline by a factor of 0.55 in agreement with earlier data.”’ At 100 K the energy defect might be expected to become more significant and lead to a higher factor for the decline of k:;-l with u. However, this factor has been quoted 316 as -0.45 and thought 317 to be due to the short range forces maintaining the impact energy despite temperature lowering. Gain-time behaviour showed that k:;; was largest at 100 K and that this shifted to k!; at 300 K and k:; at 500 K. This is in keeping with the decreasing significance of AE, as temperature increased. These results are summarized in Table 19. The 100 K value of kg;: agreed closely with the work of Stephenson et aZ. and ;k: agreed ’ 0 6 with the value of Smith et aZ.,316although Powell’s values at 100 K are more strongly dependent on AE, than Smith’s [the decline in k over u = 4 is by a factor of 3 (Table 19) compared with Smith’s 0.451. Powell attributed this difference to excited state-excited state quenching interferences in Smith’s work. Table 19 Vibrational quantum number (u) dependence of the V-V energy transfer rate constant for CO (ref. 314)

316

317

1oi3k::i-l/molecule-l cm3s-1 v value 75 K 100 K 300 K 500 K 71 40 2 19.3 14.5 22.7 18.0 124 34 3 21.8 20.5 37 10 4 15.6 18.7 5 14 3.1 8.7 14.2 6 6.2 0.93 3.9 2.8 0.25 8.8 7 8 1.2 2.0 5.1 1.2 2.8 9 0.75 1.7 10 1.1 0.47 11 0.75 12 G. Hancock and I. W. M. Smith, Appl. Optics, 1971,10, 1827. C. Wittig and I. W. M. Smith, Chem. Phys. Letters, 1972, 16,292.

Gas Kinetics and Energy Transfer

166

The discrepancy between the results of Gower et aL311 and those of Powell et al. is difficultto reconcile. Not only was Gower's maximum k:;t-l value at higher v, although the temperature was lower, but the k:;t-l values declined by a factor rather less than 3 at high v, whereas a greater sensitivity of kf;:-l to AEo would have been expected. Gower et al. rationalize the discrepancy by considering the relaxation of the A J = -fi 1 rule as in the calculations of Wittig.318 Currently, however, it is difficultto assess the importance of multiquantum rotational transitions. values, 1.r.-i.r. double resonance studies 319 have been used to examine k::,"::' i.e. rate constants for process (31). CO(U)+ CO(d) + CO(O- 1)

+ CO(d + 1) + AE

(31)

A Sharma-Brau calculation was stated to predict values close to those needed to explain the state population temporal evolution, but values of experimental k::;2';+ were not given. Consequently it is not possible to assess the significance of their suggested lAvl = 2 transitions. CO quenched by H, and N,. The processes shown in (32) and (33) were studied 307

+ H, kco/H~,CO(v = 0) + H2+ 2143 cm-' CO(v = 1) + N,(v = 0) f CO(u = 0) + N,(u = 1) - 188 cm-' CO(v = 1)

(32) (33)

from 100-650K by fluorescence techniques. The former process may be considered as a V-T transfer, whereas the latter is a V-V transfer step, since transfer to H2(u = 1) is far too endothermic (AE = -2018 cm-I) to be significant. For H, the logarithm of the deactivation probability is a linear function of T-*, for T < 400 K, in accord with Landau-Teller expectations. The discrepancy above 400 K is attributed at least in part to attractive forces. For N, the quenching rate constant (Table 18) was found to level off at about 400 K so that extrapolation to the shock tube results would be impossible. No theoretical treatment accounts satisfactorily for these results. Studies 308 with 14N, and ISN2over the range 100-700 K indicated that for the most resonant system, CO/15N,, (AE = -108.3 cm-'), the transfer rate constant decreased with increasing temperature, levelling off between 600 K and 700 K. This contrasts completely with the CO/14N2 system (AE = - 183.5 cm") where k increased from 100 K to 700 K and at 100 K the transfer constant is 33 times smaller than for the IsN2 system. This difference was correlated with the difference in AE, since the discrepancy decreased with increasing temperature. Again no satisfactory theoretical explanation exists for these results. CO with Miscellaneous Quenchers. Process (34) has been studied 307 from 163 K CO(u = 1)

+ C02(000)

4

CO(u = 0)

+ C02(001) - 206 cm"

(34)

to 406 K and the results agreed very well with those measured for the reverse process when detailed balancing calculations were applied. This observation lends confidence to the quality of laser fluorescence experimental results which have been subjected to criticism recently on the grounds that such measurements are made far from equilibrium. 319

C. Wittig and I. W. M. Smith, J.C.S., F a r A y ZZ, 1973, 69, 939. Ph. Brechignac, G. Taieb, and F. Legay, Chem. Phys. Letters, 1975,36,242.

Laser Studies of Vibrational, Rotational, and TranslationalEnergy Transfer

167

Studies with CH,, CF,, and SF, from 100 K to 350 K on CO(u = 1) fluorescence quenching indicated that the CO/CF, rate constant was twenty times faster than the CO/CH4 value even though the fundamental band centre mis-match was greater in the CF, case (see, however, Table 18). The CF, system followed the inverse temperature dependence characteristic of a near-resonant system and this, together with the faster value led to the postulate that multiquantum processes were important. The CF4 combination bands at 2147,2164, and 2187 cm" would be closely resonant with the CO(2143 cm-') fundamental. This idea is supported by the great strength of C-F transition dipole moments in general, since this would imply overtone moments significantly stronger than might otherwise be expected. Combination bands are probably also responsible for the comparatively high SF, quenching constant, but no details of mechanism have been so far deduced. This is scarcely surprising in view of the complexity of the SF, spectrum. With O3 as quencher, the processes responsible for CO(u = 1) quenching were primarily

CO(u = 1)

+ 0 3 ( 0 ) CO(u = 0) + 03(200) - 63 cm-I CO(u = 0) + 0,(101) + 32cm-' -+ CO(u = 0) + 03(002) + 1oOcm-' 3

3

CO Quenched by Large Organic Molecules. In Table 17 rate constants are listed for CO(u = 1) quenching by various relatively complex organic molecules.306 These constants are about 10-20 times lower than the analogous values for the CO2(0O01) 1e~el.j~'Since CO(u = 1) is 2143 cm-' and C02(o001) is 2350 cm-I above the ground state, it is clear that V-V transfers must play a significant role involving states of COz other than the ground state. Such possibilities do not, of course exist for CO. Sulphur Dioxide.-V-Tand V-V Transfer. Sulphur dioxide is an example of a molecule exhibiting double dispersion in ultrasonic studies. The proposed explanation is that a V-V transfer step is slower than the V-T transfer from the lowest vibrational mode. Laser studies 321 support this view. The relevant energy level diagram is shown in Figure 17. A Q-switched C 0 2 laser (1080cm-') was used as excitation source in an i.r. fluorescence experiment. The model adopted was that, after excitation of v1 by the laser pulse, v1 3 v3 V-V transfer occurred and was responsible for the observed rise in i.r. fluorescence at 1350 cm-'. This was followed by equilibration of the v1 and v 3 modes with the v2 mode which was undergoing rapid V-T transfer (kV-T 7.8 x molecule-' cm3 s - l from ultrasonic work). It is interesting to note that there is some doubt about which SO2 state is directly excited by the laser. 'Hot band' absorptions such as v1 3 2v1 (as well as the more obvious 0 vl) transitions could well contribute. The net effect will still, however, be that the v1 level is populated within the laser pulse width, hot bands equilibratingby fast, near-resonant processes such as (35).

-

S02(2v,)

+ SO2(O) + 2S02(v1)- 6 cm-'

(35)

On the basis of the above model, the slow fluorescence decay rate is not the usual 320 321

J. C, Stephenson, R. E. Wood, and C.B. Moore, J. Chem. Phys., 1972,56,4813. D. R. Siebert and G. W. Flynn, J. Chem. Phys., 1975, 62, 1212.

168

Gas Kinetics and Energy Transfer

3000

t

2v3

--v, + 3v2

2000r4 v2

' > I

r

1500

-

yt

+

+

v3

v2

3 ~ 2

i 9

a iAJ

z

w

7 . 4 ~ FLUORESCENCE TO GROUND STATE

2V2

I000

500

-

v2

COZ LASER ENERGY 1080cm"

=

0

SO;! E N E R G Y LEVELS

Figure 17 The principal energy levels of SOz, p = pm (Reproduced by permission from J. Chem. Phys., 1975,62, 1216)

V-T rate but corresponds to process (36) with possibly some contribution from

+ S02(2v2) + 12Ocm-'

S02(vl) + S02(0) ,S02(0)

process (37). The rate constant for (36) was found to be (1.3 rfi 0.17) x S02(v3)

+ SOz(0)

SO2(O)

(36) mole-

+ SO2(2vZ)+ 330 cm-'

(37) cu1e-l cm3 s-'. The rate constant from the fluorescence rise-time was assigned to process (38) -+

SOz(vl) + SOz(0) -+ SOz(0) + SOZ(v3)- 21Ocm-I and was found to be (5.2 & 1.3) x

(38)

molecule-' cm3 s-'. In support of this

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

169

endothermic mechanism is the observation of a fast transient cooring step in the short-timescale thermal lens experiment.322 The lens experiment heating rate constant also agrees 322 'reasonably' well with the slower ultrasonic relaxation rate (0.78 x molecule-' cm3 s-') and is within a factor of two of the rate of process (36). Our modifications to the theory of the lens experiment may resolve this difference (see experimental section). Similar fluorescence studies on Sl8O2 indicated 323 that the fluorescence decay was due to a combination of processes (39) and (40) with a rate constant of

+ Sl8O2(O) + S ' 8 0 2 ( 0 ) + Sl8O(2v2) + 325cm-' + S1802(2v2) + 105 cm-' Si802(vl) + S1802(0) + S'802(0) S1802(v3)

(39)

(40) molecule-' cm3 s-'. This is close to the value for 'ordinary' (1.1 & 0.06) x SO2 and might be expected since the energy levels for both molecules are very similar. Again, as for SO2, the fast fluorescence rise of S1802 is assigned to process (41) S1802(vl)

+ Sl8O2(O) + Sl8O2(0) + S1802(v3)- 220cm-'

(41) molecule-' cm3 s-'. with a rate constant of 6.1 x In the case of the S1802, the v2 fluorescence rise-time was onlyjust quantifiable and an approximate rate constant of 1.5 x molecule-' cm3 s-' was observed. Flynn et aZ.324improved the accuracy of this measurement by reducing laser scatter and adding buffer gases to reduce the rather large heating effects always present in studies on low-lying levels, However, given that the V-T rate for v2 is fast, the second (fluorescence decay) rate constant of the usual consecutive reaction pair will essentially be due to translational equilibration, i.e. it will be very slow. In this case the agreement between the v2 fluorescence rise-time and the v3 fluorescence decay constant is satisfactory. Further support for the above model came from the study in which MeF was used to excite indirectly SI6O2 and S1802. Here again it was clear that the SO, bending mode (v2) was not directly excited by the MeF, but that the fluorescence decay steps were as in the pure SO2 experiments. This result is surprising in view of the fact that the 2v2 mode of SO2 differs by less than 20 cm-' from the MeF(v3) state. It seems clear, however, that the S02(2v2)state is not closely coupled to S02(vl) or S02(v2) (e.g. the S02(2v2) absorption in the i.r. has never been reported). Thus only processes involving first order harmonic oscillator matrix elements seem to be favoured in energy transfer.

Transfer. The energy level diagram for N 2 0 is shown in Figure 18. Following excitation 3 2 5 * 3 2 6 of the (20'0) level by a DF laser, the (01'0) v2, V-T relaxation was observed and the rate constant was (0.31 & 0.03) x molecule- em3 s- '. Table 20 lists the rate constants for this process with various collision partners. The relaxation of the N20(O01) level has received much more attention than the (010) level despite the importance of the latter in determining DF laser atmospheric

Nitrous Oxide.-V-T

322

323 324

325 326

D. R,Siebert, F. R. Grabiner, and G. W. Flynn, J. Chem. Phys., 1974,60, 1564. B. L. Earl, A. M. Ronn, and G. W. Flynn, Chem. Phys., 1975,9, 307. R. C.Slater and G. W. Flynn, J. Chem. Phys., 1976, 65,425. R. T. V. Kung, J. Chem. Phys., 1975,63,5305. R . T.V. Kung, J. Chem. Phys., 1975,63,5313.

Gas Kinetics and Energy Transfer

170

20°0

12@0

I

1 04'0 - ooo I

I

0 1'0 -

I c

"rTV

f

"'TV2

I7)r

Figure 18 The principal energy levels of N20 (Reproduced by permission fromJ. Chem. Phys., 1975,63,5305)

propagation characteristics. In the case of pure N20, V-V transfer will dominate the quenching of the (001) state, however the value for N20(001) quenching by Ar molecule-' cm3 s-'. has been reported 3 2 7 * 3 2 8 as 0.032 k 0.002 x Table 20 V-T energy transfer rate constantsfor N 2 0 (u2) (refs. 325, 326) 10" klmolecule-' cm3 s-I 0.032 f 0.005 0.23 f 0.03 43.5 f 11 0.31 f0.03 6.6 f 1.3

Quencher

Ar

Nz H20 NzO

NO

-

V-Y Transfer. DF laser experiments 3 2 5 * 3 2 6 yielded the value 6.6 f 1.3 x molecule-' cm3 s-' for v1 v2 V-V transfer in N20. The value (0.2 0.02) x molecule-' cm3 s-' was also obtained for v3 -+ v2, v1 V-V transfer. The effect of rare gases on the former process was also examined and values are listed in Table 21. The relative efficiency of Ar and N2 in quenching N 2 0 v1 fluorescence contrasts with the results for the v3 where N2 was found to be 60 times more efficient than Ar. This was attributed to the near-resonant (AE 100cm-') V-V exchange between N 2 0 (00'1) and N2(u = 1). Long range dipole forces were thought important in this process. The near-resonant processes between N2(u = 1) and N,0(12"0) (AE 132 cm-') or N20(04"0)(AE 10 cm-') seem not to occur. The necessity for multiquantum exchange in these steps no doubt renders them very inefficient (see e.g. SO2).

-

327

32*

-

J. T. Yardley, J. Chem. Phys., 1968,49,2816. J. K. Hancock, D. F. Starr, and W. H. Green, J. Chem. Phys., 1974,61, 3017.

-

Laser Studies of Vibrational,Rotational, and Translational Energy Trmfer

Table 21 V-V energy transfer rate constantsfor N20(u,

-+ u2) (refs. 325,

171 326)

k/molecule-l cm3 s-' 1.1 k0.2 1.6 f 0.3 136 f 68 6.6 f 1.3

Quencher

Ar N2 H20

N20

The effect of temperature on N20(001) fluorescence quenching has been studied by several groups.329-331 The N,0(001) quenching by CO is roughly independent of temperature between 144 and -405 K and the rate constant for this process i.e. (42)

N20(001)+ CO(u = 0) + N20(000) + CO(v = 1) + 81 cm-'

(42)

T/K 104

I00

500

300

200

150

1

I

I

I

I

-

A

-La \A

--11 \A

I

A

L

L

c 0

-

4

I

e u

< 0, 2 I

e

f

s

M 103

a

t 0.12

0.14

0.16

0.18

(TIKS'/3

Figure 19 N20 selfquenching rate constants as a function of T-*: 0 re$ 276 A ref. 331 re$ 329. The broken line summarizes shock tube and acoustic results on V-T transfer of NzO(010) (Reproduced by permission from J. Chem. Phys., 1975,62,3751) 3 2 9 D. F. Starr and J. K. Hancock, J. Chem. Phys., 1975,62,3747. 330 M. Margottin-Maclou, A. Chakroun, H. Gueguen, and L. Henry, Compr. rend., 1975,281, B, 29. 331

L. Doyennette, M. Margottin-Maclou, A. Chakroun, H. Gueguen, and L. Henry, J. Chem. Phys., 1975, 62,440.

Gas Kinetic3 and Energy Transfer

172

molecule-' cm3 s-'. Other processes are much more strongly is 77.7 x temperature dependent and we quote values at 300 K only: N20(001)

+ N20(0)

N 2 0 (m n 0) k = 0.22 x

+ N20(0), molecule''

cm3 s-'

(43)

+

N20(001) + CO(0) + N20(m n 0) CO(0) molecule-' cm3 s-' k = 0.17 x

(44)

+ Ar k = 0.023 x

(45)

N20(001) + Ar

+ N20(mnO)

molecule''

cm3 s-'

The data for N 2 0 self-quenching are displayed in Figure 19. Many relaxation pathways exist for molecules such as N 2 0 e.g. processes (46) (intermolecular energy N20(001)

+ N20(0) -+

N20(0) + N20(12"0)

- 238 cm"

(46)

transfer) and (47) (intramolecular transfer, i.e. all energy remains in the initiallyN20(001)

+ N20(0) + N20(04"0) + N20(0) - 98 cm-'

(47)

excited molecule). The latter step (47) is deduced indirectly to be primarily responsible for N20(001) quenching. Intermediate or energy sharing cases exist such as (48). N,0(001)

+ N20(0) + N,0(100) + N20(01'0) + 350cm-'

(48)

Neither Sharma-Brau nor SSH calculations fit the variable temperature data over the whole range, particularly below 300 K. This may be because the value of the V-V transfer probability for a given velocity and impact parameter is not 4 1 as required for validity of the Sharma-Brau perturbation approach (see theoretical Section). Moore 3 3 2 has used an optical parametric oscillator to excite the R(30) line of N20(1001) with a 70 ns, 10 pJ pulse. No mechanistic details of the relaxation were given, but the quenching constant for the N20(10"1) state was found to be (500 60) x molecule-' cm3 s-'. Ozone.-V-T Transfer. Following rapid V-V thermalization, ozone vibrations relax to translation through the (010) This has been demonstrated by P(30) (9.5 pm) C 0 2 laser excited fluorescence experiments. 03(101) and 03(003) fluorescences were monitored and yielded essentially the same data. The rate constants for V-T relaxation of O3 by various collision partners are listed in Table 22. A careful study, by Rosen and of the 03/CH4 system revealed that at low CH4 pressures a double exponential decay could be discerned, the fast component agreeing within experimental error with the observed rate constant reported by Kurylo et ~ 1 . ~This ~ ' fast process is attributed to V-V coupling as in (49) and (50).

+ CH4(0) + O,(OOO) + CH,(v,) - 126 cm-' 03(020)+ CH4(0) -+ O,(OOO) + CH4(v4) + 94 cm-'

0,(020)

332 333 334

J. Finzi and C. B. Moore, J. Chem. Phys., 1975, 63,2285. D. I. Rosen and T. A. Cool, J. Chern. Phys., 1973,59,6097. D. I. Rosen and T. A. Cool, J, Chem. Phys., 1975, 62,466.

(49) (50)

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

173

Table 22 V-T energy transfer rate constants for O 3 1013k/molecule-' cm3 s - I ref. 334 ref. 335 0.89 f 0.16 0.19f 0.04 0.131 f0.013 0.98 f 0.05 1.06 f 0.08 7.1 f 0.9 11.8 f 0.7 1.54 f 0.14 4.0 f 0.9 4.83 f 0.44 0.2 f 0.03 0.194 f 0.006 0.6 f 0.03 0.65 f 0.08 0.073 f 0.018 0.06 f 0.03 26.7 f 4.7 19.2 f 1.1 4.2 f 0.9 10.9f 2.8 5.6 f 0.6 4.3 f 0.9 35.3 f 2.4 2.35 f 0.12

Similar couplings could also be present in the systems 03(101)/CH3Cl, 03(101)/CH2C12,and 03(101)/SF6.

V-Y Transfer. Preliminary observations suggest a value of (1.74 0.62) x molecule-' cm3 s - l for the v l , v3 relaxation of ozone to the v2 mode. The (V-T) fluorescence decay rate of the v2 mode is characterized by a rate constant around 0.89 x molecule-' cm3 s-'. It should be noted that the effects of sample heating following the laser pulse can obscure the fast fluorescence decay processes. Indeed laser-induced excitation fractions of around 0.005 for the (001) (pumped) level are typically used. Because the ( v l , ~ 3 ) - ~ V-V 2 coupling rate is not much larger than the apparent V-T quenching rate of v2, the usually clear cut separation of the V-V and V-T processes is not possible in ozone. Clearly, at high pressures of quencher, the rate of decay of the monitored 03(101) or 03(003) state populations should become limited by the (vl, ~ 3 ) - ~ V-V 2 transfer step. Rosen et al. use data from the 03/CC14,/C,H2 and /C02 systems to support the view that this indeed occurs, i.e. the 'V-T' rate constants for these systems [which should be efficient quenchers of the 03(010) state because of the near resonant nature of the processes involved] approach that for the pure O3 case. For processes (51) and (52) the observed 3 0 9 Os(OO1) O,(lOO)

+ OCS(OOO)

+ OCS(O2O) + OCS(OO0) -,03(000)+ OCS(020) +

O,(OOO)

(51)

(52)

total rate constant was 28 x molecule-' cm3 s-'. These are examples of double quantum exchanges and such systems are discussed in the OCS section. The rate of quenching of the O3 fluorescence by MeF was also examined 3 3 4 because of the possible near-resonant processes such as (53) -(55). The rate constant 335

M. J. Kurylo, W. Braun, and A. Kaldor, Chem. Phys. Letters, 1974, 27,249.

Gas Kinetics and Energy Transfer

174

03(001) + MeF(0) + 03(000)+ MeF(v3) - 6 cm-'

(53)

03(100) + MeF(0) --* O,(OOO)

(54)

03(100) + MeF(0) --*

(55)

+ MeF(v3) + 55 cm-' 02(000)+ MeF(v,) - 79 cm-'

for the ozone quenching by MeF was (4.7 & 1.6) x molecule-' cm3 s-' and a value for 03-03 quenching derived from the same experiment was 0.62 x molecule-' cm3 s-' in reasonable agreement with the value given in Table 22. It is therefore possible that the slow V-V transfer step is being shunted by the direct deactivation of the v1 and/or the v3 states by MeF. This would account for the high value of the rate constant. More recently 3 3 6 03(010) fluorescence has been observed directly (12.8-16.7 pm band pass filters). It was found that the V-T transfer given in equation (56) proceeds O,(OlO)

( (T:;:)

with rate constant 0.88

+ 03(000)-,2O,(OOO) x

molecule-' cm3 s-'.

(56) This is the hypo-

thetical uncoupled process. For the coupled process i.e. (57) the rate constant was 03(v1,v2,v3)+ O3(W)

-+

203(000)

(57)

k 0.06)

x lo-'' stant was 1.74 x

molecule-' cm3 s-' and the intermode coupling rate conmolecule-' cm3 s-'. Clearly the proximity of the values of the V-V and V-T energy transfer rate constants in ozone systems makes the kinetics much more complex than many other systems. For this reason less direct techniques such as the NO2 chemiluminescence techniques are less desirable, since details of the role of NO in the various energy transfer steps have yet to be evaluated, but will play a vital role in the overall kinetics of such systems. Ozone systems are scarcely well enough characterized for the available data to be used in tests of the SSH or any other theory. (0.59

Carbonyl Sulphide.-V-T and V-V Transfer. OCS (OOO1) has been produced by transfer from HBr excited by a HBr laser.337 The OCS(00"l) fluorescence decay was monitored and simple exponential decays observed. The extent to which these represent intramolecular V-V and V-T transfer was not known. Rate constants for such decays in various systems are presented in Table 23. More recent work 322 on a thermal lens, using the 1045 cm-' C 0 2 laser line to 'pump' the 2 v2, OCS band, observed only the V-T effect, probably from steps (58), (59), and (60): OCS(2v2) + OCS(0) -b 2 OCS(v2)

(58)

+ OCS(0) + 2 OCS(0) + 524 cm-' OCS(2v2) + OCS(O) + OCS(O) + OCS(v,) + 199 cm-'

(59)

OCS(v2)

(60) The lens results yield a rate constant, for the sum of all such processes, of molecule-' cm3 s-l in excellent agreement with ultrasonic data, but 0.58 x not with the above laser fluorescence data. Apart from the fact that the two 336 337

K.-K. Hui, D. I. Rosen, and T.A. Cool, Chem. Phys. Letters, 1975, 32, 141. B. M. Hopkins, A. Baronawski, and H. L. Chen, J. Chem. Phys., 1973,59, 836.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

175

Table 23 V-T energy transfer rate constantsfor OCS (ref. 337, but see text) lOI3 klmolecule- cm3s -

Quencher

H2 He Ne

0.056 0.017 0.014 0.022,0.047

Ar HBr

1.03 17.4,1.0 309 0.43

ocs N2

experiments may not be monitoring the same effect, the interpretation of thermal lens data must be regarded as suspect in view of what has already been said in the experimental section. The (001) state of OCS has also been 'pumped' by transfer from laser-excitedC0.328 molecule-' cm3 s-' for This work yields rate constants of (14.6 & 1.9) x OCS(OOl)/OCS quenching, (3.2 0.6) x molecule-' cm3 s-' for quenching molecule-' cm3 s-' for quenching by Ar. Siebert by CO and 0.43 f 0.03) x and Flynn 3 3 8 report (0.31 0.06) x molecule-' cm3 s-' for the pure OCS system, V-T transfer, in poor agreement with the above (but see V-V transfer) and in the OCS/Ar system serious disagreement results. Siebert and Flynn report a value about three times faster than the CO transfer result and the HBr transfer of result is extremely slow. It is even slower than the prelienary report 0.08 & 0.02 x molecule-' cm3 s-' for the presumably discrete V-T process (61). These discrepancies remain to be reconciled. Flynn's results 338 OCS(Ol0) + Ar

+ OCS(0)

+ Ar + 520 cm-'

(61)

interpreted in terms of V-T transfer are listed in Table 24. These data agree very well in p* (reduced mass) dependence with SSH predictions.

Table 24 V-T energy transfer rate constantsfor OCS (ref. 338) Quencher

loz3klmolecule-I cm3 s-'

3He 4He Ne

7.1

3.2 0.2 0.08 0.037 0.019 0.31

Ar Kr Xe

ocs

V-V Transfer. An energy level diagram is shown in Figure 20. Fluorescence rise-time experiments will measure the rate of such processes as (62), whereas the HBr and OCS(4vJ

+ OCS(0)

-+

OCS(v,)

+ OCS(0) + 43 cm-'

(62)

CO transfer pumping experiments described above measure process of type (63)-(65)

+ OCS(O) OCS(4v2) + OCS(0)

OCS(v3)

338

-+

+ OCS(0) - 43 cm-' OCS(3V,) + OCS(V2)

OCS(4v2)

-+

D. R.Siebert and G . W. Flynn, J. Chem. Phys., 1976, 64,4973.

(63) (64)

Gas Kinetics and Energy Transfer

176

3000r

u1+ 4v2 +

Y

t UI + 2u2

ui+

u2

LASER PZ2 ( 9 . 6 ~ 1

4 . 8 FLUORESCENCE ~ TO GROUND STATE

"2

19.I p FLUORESCENCE O C S ENERGY LEVELS

Figure 20 The principal energy levels of OCS, ,u = pm (Reproduced by permission from J. Chem. Phys., 1976,64, 4974)

OCS(3v2) + OCS(0)

--+

OCS(2vJ

+ OCS(v,)

(65)

in which the first is rate determining. Thus, according to Flynn, his direct-pumped experiment's fluorescence rise-time and the HBr or CO transfer fluorescence decay rates are the rate of the same process, i.e. equilibration of v3 state population, and he quotes k = (16.8 & 3) x molecule-' cm3 s-' in good agreement with the above. The slow rate of rise of the v1 mode fluorescence was attributed to process (66)

0CS(2v2) + OCS(0) -+ OCS(0)

+ OCS(vl) + 188 cm-'

(66)

molecule-' cm3 s-'. and gave the rate constant (2.67 k 1.1) x Further work must obviously be done in order to resolve the above anomaly of the OCS/Ar system measurements. Perhaps this will also clarify the exact processes involved in the transfer pumping experiments.

Methyl Fluoride.-V-T Transfer. A detailed energy level diagram for MeF is shown in Figure 21. A considerable volume of work on MeF has appeared principally because its fluorescence decay is long-lived, and, as for C02, it is relatively easy to work with,

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

3200r 2800

t

'E

P

: 1 3

ttry

1

2ooot

177

21-;

Fluorescence to ground state

2'6-

16

-

2 ji-

f

MeF (Reproduced by permission from J. Chern. Phys., 1972,56, 6060)

Figure 21 The principal energy levels of

the fluorescence intensity being high for a polyatomic molecule. MeF also has the attraction that the P(20) (1046.9 cm- ') CO, laser line is absorbed by 12CH3F,while the P(32) (1035.5 cm-') laser line is absorbed by the 13CH3F ~ p e c i e s , ~ ~opening ~-~~' the possibility of isotopic separation studies. Other lines [P(14)-P(34)] fail to produce fluorescence at for example 3000 cm- v1 and v4 (3000 cm- ') fluorescencescombined decay with a rate constant of 0.183 x molecule-1 cm3 s-'. All other observable fundamental frequencies share this decay constant. The fluorescence intensity varies as (laser power)'.' in CW laser experiments, but this is predictable on the basis of sample heating and is not indicative of multiphoton processes. Table 25 lists rate constants for the deactivation of 3000 cm-', MeF fluorescence by various collision partners. The value for O2 was corrected for energy sharing in the 0,vibration. From SSH theory, we should expect that the v3 state would become more important in the energy transfer kinetics as the weight of the collision partner increases (i.e. lower frequencies are more significant when average collision velocities are lower). Indeed 3He, 4He, H,, and D, values of k can be predicted with 'reasonable' range parameters in a simple, exponential, repulsive potential SSH calculation. The 'reasonable' size of the range parameters required does not, however, provide a sensitive test of the theory. For the heavier partners 'reasonable' range parameters cannot be found to fit the data and rotational effects have been included in an effort to improve the fit. In the rare gas series above, the ratio (pr2/I)* > 1 at Ne, where p = the reduced mass of the collision pair, r is the radius

'.

339 340 341

E. Weitz, G. W. Flynn, and A. M. Ronn, J. Chem. Phys., 1972, 56, 6060. E. Weitz and G. W. Flynn, J. Chem. Phys., 1973, 58, 2679. E. Weitz and G. W. Flynn, J. Chem. Phys., 1973,58,2781.

Gas Kinetics and Energy Transfer

178

Table 25 V-T energy transfer rate constants for MeF (refs. 339-341) 1013k/molecule-' cm3s-I 0.575 0.243

Quencher

3He 4He Ne

0.020

Ax

0.012 0.0068 0.0059 4.36 0.617 0.012 0.183 0.013 1.6

Kr Xe H 2

D 2 N2

MeF 0 2

03"

This refers to fluorescence from YJ of MeF and probably involves some degree of V-V transfer, e.g. MeF(v3) MeF(vJ)

+ o~(0)MeF(0) + 03(001) + 6 cm" + OJ(O)+ MeF(0) + 03(loO)- 55 cm--f

of the molecular rotor and I is the molecular moment of inertia. This ratio is the value of (average rotational velocity)/(average relative translational velocity). Thus in the rare gas series, for atomic weights > Ne, rotation might be expected to play a role of increasing significance. Current theories are not, however, particularly successful at predicting the observed values. In view of our assessment of the various theories, we feel it is unlikely that the shortcomings of the SSH predictions for MeF can be definitely attributed to rotational effects, although these may be useful in improving the fit. It seems that more accurate calculations are required for these systems.

+

V-V Transfer. The fluorescence rise-times of v6, v2 vs, and v1 + v4 were observed and the rate constants were 33, 27, and 38 (all x lo-',) molecule" cm3 s-' respectively. Since the experimental error is +20% in each of these, we can assume that they are all equal. Hence all these upper levels seem to be 'pumped' from v3 at the same rate and there is no evidence of any sequential V-V transfer mechanism. Flynn's model for v1 excitation is shown in equation (67). For v4 the energy

-

MeF(3v3) + MeF(v,)

-

-+

MeF(v,)

+ MeF( v3) + 140 cm-'

(67) and the Sharma-Brau (near-resonant) treatment gives a

mismatch is 100 cm'' good fit to the data. The rise-time of the 2v3 fluorescence has been found to be very rapid 342 and is < 1 j.u at 133 Nm-2. The suggested mechanism is (68). A recent isotopic double MeF(v,)

+ MeF(v,)

-+

MeF(2v3)

+ MeF(0) + 18 cm-I

(68)

resonance experiment 343 has shown that V-V equilibrium between the isotopic species in process (69) occurs in approximately six gas kinetic collisions, i.e. k

+

12CH3F(v3) '3CH3F(0) + I2CH3F(O)+ I3CH3F(v3) is 466 x 342

343

molecule-' cm3 s - l . Sharma-Brau theory adequately predicts such a

B. L. Earl, P. C. Isolani, and A. M. Ronn, Chem. Phys. Letters, 1976, 39,95. J. M. Press and G. W. Flynn, J. Chem. Phys., 1977,66,3112.

Laser Studies of Vibrational,Rotational, and Translational Energy Transfer

179

value. Clearly the laser pumped state, v3, and its harmonics up to probably at least 3v3 are populated extremely rapidly, and then all transfer to adjacent vibrational levels. From the above experiment it seems likely that the v6 modes of the isotopes equilibrate slightly more slowly.

Rotational Relaxation. An i.r./mkrowave double resonance experiment has been performed 344 on "CH3F where the v3 band was excited by a C02 laser and the absorption coefficient of the J = 3 --* J = 4; K3 or J = 4 + J = 5; K3 (vibrational ground state), microwave transition was monitored. The relaxation rate constant was 29.0 x lo-'' (f6%) molecule-' cm3 s-', or about every molecular collision! This compares 345 with a photon echo value of 9.6 x lo-'' molecule-' cm3 s-'. Methyl Fluoride as an Energy Transfer Agent. The ~ ~ ( 1 0 cm-'), 50 2v3, and 3v3 levels of MeF are populated rapidly and consequent rapid V-V transfer populates the v1 and v4 (2930cm-', 3006 cm-' respectively) levels as well as v2, v5 (both 1470 cm"), and v6 (1182 cm-'). Since the rate of removal of excited MeF from these levels is so low (V-T transfer), large populations of excited MeF can be established. This has the effect of not only producing strong i.r. fluorescence signals, but also allows the use of MeF to 'pump' molecules which do not directly absorb C 0 2 laser radiation, thus greatly extending the scope of i.r. fluorescence techniques. By a suitable choice of concentrations, several processes of interest can be made rate determining, e.g. NO has its u = 1 level at 1876 cm" and this can therefore be pumped from MeF levels 2v3 or v2, v5. Although the energy mis-match in the latter case (-41 1 cm- ') is rather larger than the former (+224 cm-') the v2, vs levels are triply degenerate and thus present a large dipole moment matrix element which necessitates their inclusion in any analysis.346 The rate constant for the V-V transfer was found to be 1.7 x 10- l 3 molecule- cm3 s- ' and was assigned to mechanism (70)

-

+ NO(0) -+

+ MeF(0) - 411 cm-' (70) showed a trend on the grounds that comparison with the CH4 + NO system MeF(v,, vs)

NO(1)

347s348

-

of increased number of collisions being necessary to overcome the increased energy gap [between CH4(v2) (1526 cm-') and NO, mis-match -350 cm-', molecule-' cm3 s"]. A similar analysis has been applied "'to k = 3.1 x the MeF-CO system and the rate constant for mechanism (71) was found to be MeF(v,, vs)

+ CO(0) + CO(0) + MeF(0) - 678 cm-'

(71) molecule-'

molecule-' cm3 s - l compared with k = 0.102 x 0.076 x cm3 s-' for the CH4-CO system (energy level mis-match = 617 cm-'). In a more complex application of this technique, the NO2-MeF system was studied.349The relevant energy levels of NO2 are: v1 (1320 cm-', symmetric stretch), v2 (620 cm-', bending mode) and v3 (1634 cm-' asymmetric stretch). The fluorescence signals from v1 and v2 were only just detectable, but could not be 344

H. Jetter, E. F. Pearson, G. L. Norris, J. C. McGurk, and W. H. Flygare, J. Chem. Phys., 1973,59, 1796.

345 346 347 348 349

R. G. Brewer and R. L. Shoemaker, Phys. Rev. Letters, 1971, 27,631. S. M. Lee and A. M. Ronn, Chem. Phys. Letters, 1974,26,497. A. B. Callear and G. J. Williams, 7kuns. Furaday Sac., 1966,62,2030. J. T. Yardley and C. B. Moore, J. Chem. Phys., 1967,48, 14. S. M. Lee and A. M. Ronn, Spectroscopy Letters, 1975, 8, 915.

Gas Kinetics and Energy Transfer

180

analysed. This was attributed to their low dipole moment matrix elements. The v3 fluorescence was analysed to yield all the data. N20, was present to no more than a few p.p.m. The rate constant for the rise of the v3 fluorescence was given by molecule'' molecule-' cm3 s-' and that for the fall by 4.7 x 14.3 x cm3 s- These values were also measured in the presence of rare gases as shown in Table 26.

'.

Table 26 Rate constantsfor the rise and fall of NO2 (v3)jIuorescence in the presence of MeF (ref. 349) Quencher

lOI3

k,~../molecule-' cmJs-'

He

2.8 4.2

Ar Xe

l O I 3 k,,,l/molecule-l cm3 s0.53 0.84 3 .O

5.2

The rate constant for MeF + NOz, V-V transfer was given by molecule-' cm3 s-' and that for NO, -+ MeF was given by 28 x molecule-' cm3 s-'. In this system, the v3 populating mechanism is 88 x most probably as shown in equations (72)-(76).

+ MeF(0) MeF(0) + MeF(v2) - 416 cm-I MeF(v3) + MeF(0) -+ MeF(0) + MeF(v,) - 423 cm-' MeF(v2, vs) + NO,(O) MeF(0) + N02(v1) + 145, 152 cm-' MeF(v,) + N02(0) -+ MeF(0) + N02(v1) - 125 cm-' N02(0) + N02(v1) N02(v3) + NO,(O) - 300cm-' MeF(v3)

-+

-+

-+

(72) (73) (74) (75) (76)

The rates of steps (72) and (73) would be independent of NO2 pressure (other than any V-T effect which is negligibly slow on the V-V timescale). These steps will not, therefore, be involved in the N02(v3) fluorescence kinetics. Of steps (74), ( 7 3 , and (76), (76) should be slowest (and thus rate determining), since it has the largest energy mis-match. An interesting rare gas addition technique was used to resolve which of steps (74), ( 7 9 , and (76) was rate determining. Clearly rare gas additive, M, increases the rate of v 3 fluorescence rise steps such as (77) and (78). N02(v1)

+M

N02(vz) + M

N02(v3)

+ M - 300 cm-'

(77)

+ N02(v3)

+ M - 240 cm-I

(78)

-+

Experimentally, it was observed that the rate of rise of v3 fluorescence was increased by rare gas addition up to a point whereafter the NO2 v1 and v2 system equilibrated. On the V-V timescale no such effect could operate on the mixed molecule processes (74) and (75). Thus step (76) was indeed rate determining and molecule-' cm3 s-'. its rate constant was 14.3 x Similarly it was deduced that the fluorescence decay rate was due to processes (79) and (80) as well as the reverse of step (76). Jt should be noted that the decay

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

+ N02(0) + N0,(v2) + N02(0) + 240 cm-l N02(v2) + N02(0) N02(v2) + N02(v2) + 0 cm-' N02(v3)

-+

181

(79) (80)

of the v3 fluorescence does not measure a V-T transfer in this case, but a distinguishable, second V-V stretch -+ bend mode transfer. This is characteristic of several triatomics, double dispersion in SO2 having been known for some time.350*35' Lasers thus provide a means for the production of high, specific vibrational level populations and subsequent state selective reactions. A similar study in the MeF-MeCl system 3 5 2 measured the rate constant for process (81) as 10.9 x molecule-' cm3 s-'. kleF(v,)

+ MeCl(0) -+ MeF(0) + MeCl(v,) + 35 cm-'

(81) CD3F. V-T Transfer. The R(24) (978.5 cm-') C 0 2 laser line was used 3 5 3 to excite the v3 mode of CD3F. Most of the vibrational frequencies of CD3F group at 3000

2 000

FLUORESCENCE

I

E

< 0

a

W

% u2

z

w

1000

"3

CDSF ENERGY LEVELS

Figure 22 The principal energy levels of CDSF (Reproduced by permission from Chem. Phys. Letters, 1976,41,413)

lo00 cm-' and 2000 cm-' (Figure 22). Observations have been carried out on the latter fluorescence. Because of this grouping, and as expected from the MeF N

J. D. Lambert and R. Salter, Proc. Roy. Soc., 1957, A243,78. J. C. McCoubrey, R. C. Milward, and A. R. Ubbelohde, Proc. Roy. SOC.,1961, A264,299. S. M. Lee and A. M. Ronn, Chem. Phys. Letters, 1974,24, 535. j S 3 L. A. Gamss, B. H. Kohn, A. M. Ronn, and G . W. Flynn, Chem. Phys. Letters, 1976, 41,413.

350

351 352

Gas Kinetics and Energy Transfer

182 Table 27 V-T energy transfer rate constants Quencher

3He 4He Ne Ar Kr

Xe CDjF

for CD,F

lOI3k/molecule-' cm3s-I 1 .o 0.49 0.037 0.023 0.008 0.025 0.14

case, rapid equilibration of the vibrational levels is followed by slow V-T transfer. Rate constants for the systems studied are presented in Table 27. As expected from SSH theory, k decreases as the reduced mass of the colliding pair increases. Xe seems to present a rather anomalous result. Y-Y Transfer. Rapid activation of the vl, v4 states occurs by V-V transfer from overtones of v2 and v5 both of which would be rapidly populated from v 3 by virtue of the small energy mis-matches involved, i.e. processes (82) and/or (83). Process (82)

+ + CD,F(v,) + CD,F(O) + 34 cm-' CD,F(2v2) + CD3F(0) + CD3F(v4)+ CD,F(O) + 14 cm"

CD3F(2v5) CD,F(O)

(82) (83)

would be expected to be very fast since there is Fermi resonance between 2vs and v l . Processes such as (84) and (85) although more direct, were thought to be less CD,F(v,) CD,F(v,)

+ CD,F2(v2) + CD,F(v1) + CD,F(O) + I7 cm-' + CD,F(v2) + CD3F(v4)+ CD,F(O) - 50cm-'

(84)

(85)

efficient, since two vibrational quanta must change in one molecule simultaneously with one quantum in another. No assisting factors, such as the Fermi resonance discussed above, will participate in these cases. The rate constant for vl, v4 activation was found to be 1.55 x lo-'' molecule'' cm3 s - ~ . Methyl Chloride.-Y-T Transfer. The energy level diagram is shown in Figure 23. Only the v, (732 em-') fluorescence was monitored 354 initially, the signal/noise of the 3000cm-' fluorescence being too low. However, later work on v2 and v1 gave the same results.355 The V-T transfer rate constants are shown in Table 28, the Table 28 V-T energy transfer rate constantsfor MeCl (ref. 355) Quencher

3He 4He Ne

Ar

Kr

Xe H2 Dz

CHI MeCl

0.96 0.16 0.17 0.17 0.17

14.2 3.4 2.7 2.3

J. T. Knudtson and G. W. Flynn, J. Chem. Phys., 1973,58,2684. F. R. Grabiner and G. W. Flynn, J. Chem. Phys., 1974,60,398.

jS4

355

1013k]molecuIe-' cm3s-I 1.8.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

183

7

29662 cm' I

3041.8 em-

'

FUlORESCENCE TO GROUND STATE

2000 2030.0un-l ENERGY/ cm" 1454.6em' 054.9 em-'

FUNDMENTAL VIBRATIONAL KloES W C%cI

Figure 23 Theprincipal energy levels of MeCl (Reproduced by permission from J. Chem. Phys., 1973,58, 2684)

CH, result was corrected for v, ( u = 1) excitation of the CH,. Theoretical predictions of these rate constants were not very close. These data disagree with ultrasonic results by up to 40%, presumably due to interference by the relatively slow V-V process. V-V Transfer. The rate constants for V-V decay of the v3 (732 cm-') and v2 (1355cm-') levels were found to be (24 & 3) x and (50 & 16) x molecule'' cm3 s-', respectively. These may be assumed equal, but that for v1 (2966 cm-') was quoted as (66 & 22) x molecule" cm3 s-'. Probably this value is also the same as the others. A reduction in the experimental error here could lead to interesting results on the detailed mechanism, but low intensities have so far prevented this.

CD3CI. V-T Transfer. The energy levels 3 5 6 group in a very similar way to those of CD3F, i.e. around 1000 cm" and 2000 cm". The data for various collision partners are presented in Table 29. The P(28) (1039.4 cm-') C o t laser line was used to excite the CD3CI vl, v4 and 356

L. A. Gamss, B. H.Kohn, M. I. Pollack, and A. M. Ronn, Chem. Phys., 1976,18,85.

184

Gas Kinetics and Energy Transfer

Table 29 V-T energy transfer rate constantsfor CD3CI (ref. 356) Quencher

He Ne Ar Kr

Xe CDSCI

1013k/rnolecule-' cm3s-' 2.3 0.15 0.053 0.037 0.040 0.87

v3 fluorescence was observed. A common V-T rate was observed for both frequency regions. As for similar systems, k decreases approximately linearly with p* to p values associated with Ar, thereafter the dependence flattens out. This dependence is interpreted as evidence of rotational participation in the transfer process under the condition that the rotation velocity of the collision pair is greater than the collisional velocity. MeCl V-T quenching rate constants are greater than the corresponding CD3Cl values and this is attributed to the lower rotational velocity of the deuteriated compound providing the fewer vibration-rotation energy transfer channels. V-V Transfer. The activation rate constant (16 x lo-', molecule-' cm3 s-') for the v3 fluorescence is assigned to processes of type (86) and (87).

+ CD,Cl(O) -+ CD,Cl(v3) + CD3CI(0) + 328 cm-' CD3C1(v5)+ CD,Cl(O) -+ CD,CI(v,) + CD,Cl(O) + 359 cm-' CD,CI(v,)

(86)

(87) The faster activation rate of the vl, vq fluoresence is attributed to processes ( 8 8 x 9 0 )

+ CD,CI(v,) CD3C1(v2)+ CD,CI(v,) CD,Cl(v,) + CH,CI(v,)

CD3CI(v,)

+ CD3C1(0) - 40 cm-' + CD3CI(v,) + CD,CI(O) - 102 cm-' + CD,CI(v,) + CD3C1(0) - 71 cm-l

+ CD3C1(vl)

(88) (89)

(90) since they are nearer resonance than the first set and would thus be expected to be the faster. Harmonics could also be involved in these transfers. Double resonance studies would provide useful confirmation of these proposals. Methyl Bromide.-V-T Transfer. The relevant energy level diagram 3 5 7 is shown in Figure 24. The R(14) (971.9 cm-') line of a Q-switched COz laser was used to excite the R(2) line of the v6 (methyl deformation) band. After vibrational equilibration, fluorescence of all modes decays at the same rate. In the case of methyl Table 30 V-T energy transfer rate constants for MeBr (ref. 357) Quencher He

Ne

Ar Kr

Xe MeBr 357

10' k/molecule- cm3s - *

1.3 0.4 0.4 0.3 0.32 6.2

B. L. Earl and A. M. Ronn, Chem. Phys., 1976,12, 113.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

185

C H3 Br ENERGY LEVELS Figure 24 The principal energy levels of MeBr (Reproduced by permission from Chem. Phys., 1976, 12, 113)

bromide the kinetic analysis is rather more complex than for the lighter methyl halides, since the slowest V-V process (v3 activation) is only a factor of two faster than the decay. The V-T energy transfer rate constant is found to be (6.2 0.6) x molecule-' cm3 s-'. Values of such rate constants for various collision partners are listed in Table 30. Apart from He, the rate constant is virtually invariant with p*. This is contrary to V-T theory but can be reconciled with rotational participation. More will be said on this point in a general comparison of the methyl halides at the end of this section. V-V Transfer. The usual, 'up the ladder' sequence of v6 harmonics are populated by rapid (- 10 collisions), near-resonant transfer processes of type (91). The v3 state 2MeBr(v6) --* MeBr(2v6) + MeBr(0)

(91)

is almost certainly populated by process (92), for which the rate constant observed MeBr(v6)

+ MeBr(0) -+ MeBr(v,) + MeBr(0) + 341 cm-'

(92)

molecule-' cm3 s-'. was 12.4 x v2, v5 fluorescence activation was rather more complex. It was possible to say only that these levels and the v1,v4 pair were most probably populated by a series mechanism, but which received the energy first was not clear. The observed rate molecule-' cm3 s-'. It is possible that constant for these levels was 33.5 x studies, on the effect of different fractions of molecules excited, will be able to unravel this type of mechanistic problem. Knowledge of other species in the homologous series may also help.

186

Gas Kinetics and Energy Transfer

Table 31 V-T energy transfer rate constantsfor CD,Br (ref. 358) lot3k/molecule-' cm3 s-'

Quencher He

2.3 f 0.31 0.37 f 0.06 0.34 f 0.06 0.31 f 0.06 0.22 f 0.03 3.7 f 0.61

Ne Ar Kr Xe CD3Br

CD3Br. V-T Transfer. The R(10) (969.1 cm-') line of a @switched C 0 2 laser was used 358 to excite the P(39) line of the v2 (methyl symmetric deformation) band of CD,Br. A single V-T transfer rate constant was observed for all levels and values for various collision partners are listed in Table 31. Clearly SSH p* dependence was not followed and again rotational effects can qualitatively account for the discrepancy. V-Y Transfer. Following v2 'up ladder' population of its harmonics, V-V transfer into v5 most probably occurred via process (93). It was proposed that v2 and v5

+ CD3Br(0)+ CD3Br(v5)+ CD,Br(O) - 68 cm-'

CD,Br(v,)

(93)

are Coriolis-coupled, the transfer being essentially instantaneous. v1 lies within 48 cm-' of 2v, and is in Fermi resonance with it, so that it was expected to be populated on the same time-scale via process (94). The rate constant CD3Br(2v,)

+ CD,Br(O)

+

CD,Br(v,)

+ CD,Br(O)

- 40 cm-'

(94)

for the rise in fluorescence in the 2000cm-' region is most probably due to this molecule-' cm3 s-'. process and was found to be (202 47) x vj, v6 fluorescence rise-times most probably reflect the kinetics of process (95) and/or (96) for which the observed rate constant was (27 4 5) x molecule-1 CD,Br(v,) CD,Br(v,)

+ CD,Br(O) + CB3Br(0)

4

4

+ CD,Br(O) + 277 cm-' CD3Br(v6)+ CD,Br(O) + 345 cm-' CD&r(V6)

(95)

(96)

cm3 s-'. These processes have smaller energy deficits than the corresponding vg mechanism and it was felt that the larger 'breathing sphere' parameter made the v6 processes more likely. v3 Population from v2 and/or v5 into 2v3 has a small energy deficit, but such overtone involvement usually reduces the efficiency of such processes by about an order of magnitude. The smaller energy mis-match would tend to counteract this, but the 'breathing sphere' parameter is also smaller, so that overall the v6 route was thought the most probable. v4 Population may well have been indicated by an initial fast decay process only just visible in the 2000 cm-' fluorescence. The rate constant would have been about molecule-' cm3 s-'. This may be assigned tentatively to process (97). 31 x CD3Br(2v,) 358

+ CD3Br(0) + CF3Br(v4)+ CD,Br(O)

S.T.Lin, B. L. Earl, and A. M.Ronn, Chem. Phys., 1976,16,117.

- 178 cm-'

(97)

Laser Studies of Vibrational,Rotational, and Translational Energy Transfer

187

4000

3000 t

E

-scp 3 2000 z w

1000

0

CH31 ENERGYLEVELS

Figure 25 The principal energy levels of Me1 (Reproduced by.permission from Chem. Phys., 1976, 14,375)

Methyl Iodide.-V-T Transfer. The relevant Me1 energy levels 3s9 are shown in Figure 25. The P(30) (934.9 em-') CO, laser line was used to excite the MeT. A single rate constant characterizes all observed fluorescence (vz, v5¶ 2v5, vl, v4) decays and Table 32 lists the values in the presence of various collision partners.

Table 32 V-T energy transfer rate constantsfor Me1 (re$ 359) Quencher

3He 4He

Ne Ar Kr

Xe Me1

1013k/molecule-' cm3 s-l 2.3 1.7 0.59 0.68 0.50 0.40 6.9

For the rare gases from Ne to Xe k is constant within experimental error. As for the other methyl halides, this is contrary to SSH theory and is attributed to rotational effects becoming of increased influence for large p. The constancy of k sets in at lighter rare gas atomic weights than for previous methyl halides as expected also from this proposal. V-V Transfer. Two fluorescence rise-times were observed. The vl and v4 levels 359

Y. Langsam, S. M. Lee,and A. M. Ronn, Chem. Phys., 1976,14, 375.

188

Gas Kinetics and Energy Transfer

near 3000cm-' are most probably populated from the hot v6 manifold by processes (98) and (gg), i.e. from upper harmonics of v6, (v6 being the laser absorbing

+ MeI(0) - 109 cm-' MeI(v4) + MeI(0) - 440 cm- '

MeI(2v5) + MeI(0) + MeI(v,) MeI(3v6) + MeI(0) 3

(98)

(99) state). The rate constant for this activation is (70 & 14) x molecule-' cm3 s-'. The v6 state can also transfer to the v2 and vs levels, presumed coupled by Coriolis resonance,36ovia steps (100) and (101). MeI(v6) MeI(v,)

+ MeI(0) -+ MeI(v2) + MeI(0) - 371 cm-' + MeI(0) + MeI(v,) + MeI(0) - 189 cm-'

(loo) (101) mole-

The rate constant for such steps is no doubt the observed 31.4 x cule-' cm3 s-'.

CD31. V-T Transfer. The P(l0) (952.9 cm-') C 0 2 laser line was used to excite the v2, CD3 symmetric deformation and the 2v5, vl, v4, and v6 fluorescence was monitored.361 A single V-T rate constant was observed (8.4 x molecule'' cm3 s-') and quenching rate constants are listed in Table 33 for various collision partners. Clearly we have the now expected non-SSH behaviour which can be explained by Moore's rotational V-T theory.362

Table 33 V-T energy transfer rate constantsfor CD31 (ref. 361) I Oi3 klmolecule- cm3s -

Quencher He Ar Kr

3.9 0.5 0.53 0.56

Xe

0.43

CDJ

8.4

Ne

V-V Transfer. The v2 and v5 levels are Coriolis-coupled 360 and 2v5 is in Fermi resonance with the v1 level,363so that the rate-determiningstep for the fast fluorescence . proposed mechanism rise-time is most likely the activation of v4 from 2 ~ 5 , ~ 'The is shown by processes (102)--(105). Thus the observed rate constant of

+

+ CD31(0) - 98 cm-' CD31(2v5)+ CD31(0) + 16 cm-' CD31(vl) + CD31(0) - 48 cm-' CD31(v4) + CD31(0) - 168 cm-'

CD31(v2) CD31(0) -,CD31(v,)

+ CD3I(vS) CD31(2v,) + CD31(0) CD3I(v1) + CD,I(O) CD31(vs)

-+

-+

-+

243 x molecule-' cm3 s-' is assigned to this last step. The slower observed V-V rate constant, for the activation of 360 361

362 363

v69

(102) (103) (104) (105)

described by

A. G. Maki and R. M. Hexter, J. Chem. Phys., 1970.53,453, Y . Langsam, S. M. Lee, and A. M. Ronn, Chem. Phys., 1976,15,43. C . B. Moore, J. Chem. Phys., 1965,442979. T . Shimanouchi, 'Table of Molecular Vibrational Frequencies', NSRDS-NBS, 39.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

189

process (106) is given by 29 x 10‘l3 molecule’’ cm3 s-’. This is as expected for CD,I(v,)

+ CD31(0) -+ CD31(v6)+ CD31(0) + 295 cm‘l

(106)

this greater energy mis-match. Comparison of the Methyl Halides V-T Transfer Rates. Figure 26 shows the effect of rare gases on methyl halide V-T transfer. MeF stands out as quite different from the heavier halides. Table 34 lists values of R, the ratio of rotational velocity to

z 0

j 10-4

4

Q

Q

nD 10-6

0

2

6

4

0

10

P ‘I2

Figure 26 The eflect of rare gases on methyl halide V-T quenching. p = reduced mass of the collisionpair: El MeF; A MeCl; 0 MeBr; @.MeI. (Reproduced by permission from Chem. Phys., 1976, 14, 375)

the relative translational velocity of the collision pair [(pr2/I)* where r = molecular rotor radius and I its moment of inertia, and p in the reduced mass of the collision pair]. When R > 1 rotation effects are postulated to be of increasing significance.359 Clearly MeF seems to be much less influenced by rotation than the heavier halides. Table 34 The values of R for methyl halidelrare gas collision pairs MeF MeCl MeBr Me1

He 0.99

Ne

1.1 1.1 1.1

2.2 2.3 2.4

1.9

Ar 2.2 2.7 3.O 3.2

Kr 2.6 3.2 3.8 4.2

Xe 2.7 3.5 4.3 4.7

943 cm-'

R--T

1

*

4

Figure 27 A simplified three-level energy diagram f o r SF6 (levels 4 and 1 are both the ground state)

'

'.

1.r. fluorescence results yield (2.07-1.94) x 10- l 3 molecule- cm3 sAt pressures > 130 N m-' bulk heating of the SF6 occurs giving long 'fluorescence' (emission) lifetimes and participating in the saturation p r o c e s ~ e s . ~ ~ At~ -pressures ~ ~ ~ in excess of 400 N m-2 in a cylindrical cell 6.8 cm long by 2 cm diameter acoustic shocks have been observed3" superimposed on the fluorescence decay trace at 615 cm'' and 943 cm-', and symptomatic of bulk heating. 364

365 366

367 368

369 370 371

372

I. Burak, P. L. Houston, D. G. Sutton, and J. 1. Steinfeld, Z.E.E.E.-J. Quantum Electron., 1971, QE-7, 73. D. G. Sutton, I. Burak, and J. I. Steinfeld, I.E.E.E.J. Quantum Electron., 1971, QE-7,82. H. Brunet, I.E.E.E.-J. Quantum Electron., 1970, QJ3-6, 678. 1. Burak, A. V. Novak, J. 1. Steinfeld, and D. G. Sutton, J. Chem. Phys., 1969,51,2275. H. Brunet, Compt. rend., 1967,264, B, 1721. 0. R. Wood,P. L. Gordon, and S. E. Schwarz, I.E.E.E.-J. Quantum Electron., 1969, QES, 502. H. Brunet, 1.E.E.E.-J. Quantum Electron., 1968, 4, 335. H. Brunet and M. Perez, Compt. rend., 1968,276, B, 1084. 0. R. Wood and S. E. Schwarz, Appl. Phys. Letters, 1970,16,518.

Laser Studies of Vibrational,Rotational, and Translational Energy Transfer

191

It has been shown 373 that ultrasonic and shock tube (near equilibrium) results for SF6 will never agree with results obtained in systems far from equilibrium (e.g. i.r. fluorescence), the lifetimes, for a given pressure, being a factor of -3.5 times shorter in the case of i.r. fluorescence. The argument presented is correct, but in fact is a demonstration of how, near equilibrium, the reverse rate acts to reduce the observed forward rate from the true value, best measured far from equilibrium. Modificationof ultrasonic results by the relation rtrue= (CJC,) robsis not j~stified."~ (Here C, and C, are the heat capacities of the lowest frequency mode and all vibrational modes respectively). This yields the lifetime rtrucof the lowest frequency mode uncoupled from all other modes which is a state unattainable experimentally and not representative of the laser experiment.

V-Y Transfer. Rise-time measurements 374 on the 615 cm-I fluorescence gave, for molecule'' cm3s-l. the V-V transfer from the 943 cm-' mode, kv-v > 15.5 x A second study 3 7 5 on the initial time development of the laser-induced pressure wave gave kV-V > 621 x molecule-' cm3 s-'. More recently fluorescence rise-times were measured accurately 3 7 6 and the V-V pathways that were considered were : sF6(V3) -k sF6 + SF,(V,) + sF6; AE = 325 Cm-' sF6(V3) -k sF6 + sF6(V4 + v6)

+ SF,; AE = 38 Cm-'

sF6(V3) + sF6 + SF,(V,) sF6(2V3) 4-

+ SF,(v6); AE = 38 Cm-' sF6 + SFe(2~4)+ sF6; AE = 35 Cm-'

the 615 cm-' fluorescence arising from the v4, Au = - 1 transition. SSH theory predicts decreasing probability with increasing reduced mass of the collision pair for the first (least resonant) of the above pathways. In the 0-667 N m-2 rare gas pressure range (+80 N m-2 SF,) it was found that for the collision partners He, Ar, Kr, Xe, SF,; k = 163, 86.2, 78, 94, 282 (all x molecule-' cm3 s-' respectively. This is the opposite of the SSH predictions. SSH theory is inapplicable to the remaining near-resonant pathways, but here the Sharma-Brau theory grossly overestimated the reduced mass dependence, although the trend is correct. Long range interactions were therefore thought insignificant in the case Of sF6. A recent report of a double resonance study on SF6 has revealed the presence of a collisionless V-V energy transfer process which can populate the levels (3) (see Figure 27) from the laser excited state. The levels (3) equilibrated with a rate constant of 9.3 x loW8molecule-' cm3 s-' and were excited by transfer from the laser pumped state with a rate constant in excess of 3.1 x molecule-' cm3 s-'! Clearly these rates are faster than gas kinetic collision processes. Additionally, it was found that double resonance signal amplitudes were strongly dependent on the relative polarizations of exciting and probing laser beams. This would be expected in situations where polarizations could not be randomized by collisions on the timescale of the observations. Such collisionless processes undoubtedly play an important role in i.r. laser selective reactions. 373 374

375 376

W. D. Breshears and L. S. Blair, J. Chem. Phys., 1973, 59, 5824. R. D. Bates, G. W. Flynn, and J. T. Knudtson, J. Chem. Phys., 1970,53,3621. I. Burak, P. Houston, D. G. Sutton, and J. I. Steinfeld, J. Chem. Phys., 1970,53, 3632. J. T. Knudtson and G. W. Flynn, J. Chem. Phys., 1973, 58, 1467.

192

Gas Kinetics and Energy Transfer

Rotational Relaxation. The unusual technique of photon echoes 377-379 has been used and it has been deduced that J = 0 + J = 1 or J = 1 + J = 1 transitions are involved in the relaxation of the vibration-rotation levels of SF, excited by 10.591 pm CO, laser radiation [P(20) 00"1-10"0]. The relaxation measured is that for the de-phasing of the transition dipole by a change of rotational state or translational velocity during a collision. In the pressure range 0.27-2.0 N ma2 SF, and 0.133-2.67 N mW2added gas the rate constants are nearly pressure independent and were found to be 14.0, 9.0, 6.0, 18.0 (all x lo-'') molecule-' cm3 s-' for SF, + SF,, He, Ne, and H2, respectively. Summary. Little has apparently been added to the energy transfer data on SF, since 1973. However, SF, is a good, readily available molecular model for UF, and a great deal of work has in fact been done on SF, recently. A very brief public discussion of the complete spectroscopic assignment of the vast range of lines discussed above is no doubt the prelude to a series of publications on some very detailed work concerning this complex molecule. Miscellaneous Compunds.-CS2. A CO laser was used 328 as exciting source, pumping CO as an energy transfer agent. CO fluorescence was monitored. Although the CS2 fluoresced strongly at 6.4pm, this was not monitored. The V-T energy transfer rate constants are listed in Table 35 for the CS, v3 level. Table 35

V-T energy transfer rate constants for CS2 (ref. 328) Quencher

co cs2

l O I 3 klmolecule-I cm3 s-' 0.23 f 0.05 0.67 f 0.1

V-V Transfer. The processes measured would be the sum of (107) and (108) for

+ CS2(001)+ 608 cm-' CO(v = 1) + CS2(000)+ CO(o = 0) + CS2(101) - 42cm-I

CO(u = 1) + CS2(000)+ CO(o = 0)

which the rate constant was found to be (4.2 f 0.7) x

molecule''

(107) (108) cm3 s-'.

C2N2.V-T Transfer. In experiments identical to those on CS2, it was found that kV-= of the vl, v3 levels was (2.4 f .05) x molecule-1 cm3 s-'. This is about molecule-' cm3 s-') for vs 100 times slower than the rate constant (230 x (measured by ultrasonic technique^).^^' The small room temperature heat capacity of the vl, v g levels precludes the possibility of measuring their relaxation by ultrasonic techniques. Table 36 lists the values for various collision partners with C2N,(00100). Table 36 V-T energy transfer rate constants for C2N2(ref. 328) 1013 k/molecule-' cm3 s-I 1 f0.02 C2Nz 2.4 f 0.05 C.K.N. Patel and R.E. Slusher, Phys. Rev. Letters, 1968, 20, 1087. R. L. Abrams and A. Dienes, Appl. Phys. Letters, 1969, 14,237. W. J. Tomlinson, J. P. Gordon, C. H. Wang, C. K.N. Patel, and R. E. Slusher, Phys. Rev.,

Quencher

co

377

378

379

1969, 179,294.

J. D. Lambert, D. Parks-Smith, and J. L. Stretton, Zkzns. Farahy SOC.,1970, 66,2720.

jao

Laser Studies of Vibrational,Rotational, and Translational Energy Transfer

193

molecule-' cm3 s-l for vz, v4. Together with the ultrasonic result, k = 22 x The above results mean that three relaxation times are now known for C2Nz. It is the first molecule to have three relaxation times so identified. Boron Trichloride. V-T Transfer. An i.r.4.r. double resonance experiment using two C 0 2 lasers 381 was employed to examine individual rotational levels during relaxation. The probe laser was tuned to the P(28) COz line (936.8 cm-') to provide most of the kinetic information. An energy level diagram is shown in Figure 28 and V-T transfer rate constants are listed in Table 37 for various collision partners. In the case of the polyatomic quenchers V-V transfer undoubtedly occurs, but no mechanistic details were given. Rotational level participation is much more likely in the case of the diatomic quenchers which have widely spaced vibrational levels. However, simple V-R transfer theory would predict k,, > k,, and kHDcontrary to the tabulated results. This simple interpretation is probably complicated by near-resonant interactions between rotational levels of H2etc. and vibrational levels of ~c1,.38z

1000

)u,+ v4 "2' v4 9

3 v4

I-

1

Figure 28 The principal energy levels of BCL, p = pm (Reproduced by permission from J. Chem. Phys., 1973, 58, 3373) 381

382

P. L. Houston, A. V. Novak, and J. I. Steinfeld, J. Chem. Phys., 1973, 58, 3373. L. L. Poulsen, P. L. Houston, and J. I. Steinfeld, J. Chem. Phys., 1973,58,3381.

Gas Kinetics and Energy TranJfer

194

Table 37 V-T energy transfer rate constantsfor BCI, (ref. 381) Quencher

He Ne Ar Kr Xe

N2 BC13 MeF CHCli HCl DCl

H2 HD D2

1013k/molecule-l cm3s-I 4.7 2.3

1.4 1.1 0.9 1.9 54 20 21 83 51 28 28 19

Figure 29 The principal energy levels of NOCl (Reproduced by permission from Chem. Phys. Letters, 1977,50, 85)

h e r Studies of Vibrational, Rotational, and Translational Energy Transfer

195

Nitrosyl Chloride. V-T Transfer. An energy level diagram is shown in Figure 29. An attenuated TEAL (5 Hz repetition rate) laser pulse was (7 jd cm', absorbed by the NOCl) operating on the P(34) C 0 2 laser line (931 cm-'). In Sb detection monitored only fluorescence in the 5.1-5.6 pm (vl) range, the upper bound being provided by a filter. Table 38 lists the observed V-T rate constants. Table 38 V-T energy transfer rate constants for NOCl (ref. 383) 1013klmolecule-I cm3s-' 4 f 0.9 56 f 6

Quencher Ar NOCl

V-V Transfer. Only four gas kinetic collisions are required for v1 population from the (v, + v,) laser-pumped state, (k = 432 st 108 x molecule-' em3 s-'). A nearly resonant process is most probably responsible and (109) is suggested, or NOCl(O11)

+ NOCI(O11) + NOCl(100) + NOCl(000) + 47 cm-I

(109)

alternatively (or additionally) it could be (110) or (1 11).

+ NOCl(000) + 4 cm-' (110) NOCl(022) + NOCl(000) + NOCl(000) + NOCl(100) + 43 cm-' (1 11) system (described under Using the chemiluminescenceof NOz in the NO + 03* 2 NOCl(Ol1) + NOCl(022)

SiF,. O3 above) Kaldor et al.384 deduced a value of (6.3 f: 1.4) x lo-', molecule-' cm3 s-l for the V-T transfer of equation (112). SiF,*

+ O2 + SiF4 + O2

Energy levels were not specified, nor can this be expected in an indirect observation of this type. Additionally, as already pointed out, the role of the NO in the various energy transfer steps is not yet fully characterized, so that the above result cannot be assigned to a definite process with any degree of confidence. Ammonia. Very little energy transfer work seems to have been carried out on NH3 in the vapour phase. This is surprising in view of the high efficiency and possible importance of the CO, laser-pumped NH3 far i.r. laser. The P(13) (927.7 cm-') N20 laser line has been used385 to pump l4NH, in the upper inversion level of the J = 8, K = 7 (para) rotational state. The laser was intensity-modulated at 700 Hz and a microwave probe wits used in a double resonance configuration. The microwave intensities were observed to alter in a complex manner explicable in terms of V-V, V-T, and R-R relaxations. However no quantitative data were extracted. The v2 vibrational mode of NH, isolated in a N, matrix at 8 K has been excited 386 by the R(10) (969.1 cm-') and R(12) (970.5cm") CO, laser lines. A CW C02 laser was used in a double resonance configuration which was found to be more sensitive than the straightforward fluorescence technique. Clearly, similar techniques would be successful in the gas phase, but as yet there are no data. 383 384

385 386

A. Hartford, Chem. Phys. Letters, 1977, 50, 85. W. Braun, M. J. Kurylo, and A. Kaldor, Chem. Phys. Letters, 1974,28,440. S . Kano, T. Amano, and T. Shimizu, J. Chem. Phys., 1976, 64,4711. L. Abouaf-Marguin, H. Dubost, and F. Legay, Chem. Phys. Letters, 1973, 22,603.

I96

Gas Kinetics and Energy Transfer

r------

3m0t 3

1 2V

-'E

-2v

z

2

4

7-

4 1

Stretching fluorescence

%

P

v +v

2

2000

1

-I

V

Laser excitation c-

1

B€kI

"4

Bend

( 1.r.-inactive) ( 1. r.- active1

"3

Asymmetric stretch

V

Syrrdetric stretch

Figure 30 The principal energy levels of CH, (Reproduced by permission from J. Chem. Phys., 1968, 49, 111)

Methane. V-T Transfer. A helium neon laser was used 387-389 to populate the v3 band of methane (Figure 30). As for most other polyatomics, V-T theory predicts the wrong trend in rate constant as a function of reduced mass (Table 39). V-R theory

Table 39 V-T energy transfer rate constantsfor CH4 (refs. 387-389) Quencher

3He 'He Ne Ar Kr

Xe H Z

HD D2

co N2 0 2

CH, CzHa HCl DC1

10' klmolecule - cm3 s - l 0.3 0.18 0.04 0.02 0.014 0.013 0.34 0.17 0.45 0.033 0.02 0.051 0.22 64 2 0.4

can account for the observed trend, but this may be only fortuitous. Quantitative agreement with such a theory is poor. V-V Transfer. V-V transfer from v3 to v4 was monitored both as a decay of v 3 fluorescence and as a rise of v4 fluorescence. The observed rate constants molecule-' cm3 s-') agree with each other within the (59 x and 82 x rather large (+ 14%) error, so that to this extent the transfer is probably direct. je7

388

389

J. T. Yardley and C. B. Moore, J. Chem. Phys., 1964,45, 1066. J. T. Yardley, M. N. Fertig, and C. B. Moore, J. Chem. Phys., 1970,52, 1450. J. T. Yardley and C. B. Moore, J. Chem. Phys., 1968, 49, 1111.

Laser Studies of Vibrational,Rotational, and Translationul Energy Transfer

Table 40 V-V energy transfer rate constantsfor CH4 (v3-v4) Quencher Ar Ne CH4

197

(refs. 387-389)

1013k/molecule-' cm3s-I 10.4 12.4 70.0

Rare gases do influence the rate of this process, so that intra- and inter-molecular processes both seem important (Table 40). CD4. V-T and V-V Transfer. An HCl laser has been used 390 with HCl as an energy transfer 'pumping' agent. The values of V-T energy transfer rate constants with various collision partners are listed in Table 41. The v, (1092 cm-') mode of Table 41 V-T energy transfer rate constantsfor CD4 (ref. 390) Quencher 3He 4He Ne Ar H2 HCI DCI CHI CD4

1OI3 k/molecule - cm3s 0.56 0.25 0.02 0.007

7.8 4.2 0.64 0.49 0.09

'

CD, has also been pumped with a COz laser and there is overlap between several of the widely spaced CD, vibration-rotation lines and the C02 laser [vz (996 cm' ') is Raman active and cannot be pumped]. Thermal lensing signals 322 have been obtained from theP(14) (949 cm-'), the R(18) (975 cm-'), and theP(24) (1043 cm-') laser lines. Cooling transients (see experimental section) were observed, indicative of endothermic V-V transfer steps, but no rate constants were calculated. The cooling transient amplitude was greatest for the 949 cm-' laser line. This is less than the v4, u = 1, band centre energy. The participation of rotational levels was thought to be the reason for a decrease in this amplitude as the laser line energy was increased. V-T rate constants calculated from the lensing experiments agreed with those of the earlier work. Ethylene. V-T Transfer. From the decay rate of the 5 pm fluorescence 3919 392 the rate molecule-' cm3 s-' constant for V-T energy transfer was found to be 2.25 x in close agreement with the ultrasonic result of 2.22 x molecule cm3 s-'. The dependence of 5 pm and 3 pm fluorescence intensity on laser power was of the order of 2.2 and 3.1 in laser power. Flynn et al. assert that this order differs from the predicted 1.5 and 2.5 by too much to be due to experimental errors in extinction coefficient measurement. They conclude that some multiphoton absorption must occur. Harmonics of the v 7 absorption could be involvedY4together with near 390

391 392

P. F. Zittel and C. B. Moore, J. Chem. Phys., 1973,58,2004. R. C. L. Yuan and G. W. Flynn, J. Chem. Phys., 1972,57, 1316. R. C. L. Yuan and G. W. Flynn, J. Chem. Phys., 1973,58,649.

Gas Kinetics and Energy Transfer

198 Table 42

V-T energy transfer rate constantsfor C2H4 (refs. 391, 392) Quencher 3He 4He Ne Ar Kr Xe H2 D2 CzH4 CH4 0 2

N2

lOI3k/molecule-' cm3s - ' 3.3 1.69 0.207 0.146 0.124 0.109 21.1 54.5 2.2 5.31 0.443 0.254

resonant collisions of the type in (1 13). Table 42 lists values of k,

for various

collision partners. The temperature dependence ( 2 4 8 4 6 2 K) of k followed the Landau Teller equation, (i.e. k increased with temperature). Rotational effects seem to dominate collisions with the higher reduced masses, although even with inclusion of this mechanism, theoretical predictions are in poor quantitative agreement with the observed values. The potential energy functions used in these calculations, to date, have, however, been particularly poor. V-V Transfer. There still remains only a tentative value: for v 7 + vl0, of -31 x molecule" cm3 s-'. D$uoromethane. V-T Transfer. The C 0 2 R(18) (1077.3 cm-') laser line was used 393 to excite CH2F2. Fluorescence was monitored at 19 pm, 7 pm, 4.5 pm, and 3 pm. (i.e. v4, v8, 2vg, and vl, v4 respectively). Temperature variation (273-358 K) studies showed that a ground state absorption was not involved and the absorbing transition was assigned to v4 + v4 vg. Within the typical 10% experimental error the V-T rate constant was the same for all fluorescence frequencies. Table 43 lists such values for various collision

+

Table 43

V-T energy t r m f e r rate constants for CHzF2 (ref. 393) Quencher jHe *He Ne

Ar Kr Xe CHzF2

1013 klmolecule-I cm3 s-I

8.4 8.4 1.3 0.86 0.63 0.80 13

partners; as for the methyl halides, non-SSH behaviour is observed for collision partners heavier than He and Moore's V-T(R) theory accounts for the discrepancies. The low value of v4 (529 cm-') accounts for the (lo2 times) greater energy transfer 393

L. A. Gamss and A. M. Ronn, Chern. Phys., 1975,9,319.

Laser Studies of Vibrational, Rotational, and Translational Energy Transfer

199

probability of CH,F, when compared with the methyl halides, the smaller 529 cm‘’ vibrational quantum being more readily lost to translation. V-Y Transfer. This was too fast for accurate values to be obtained, but two groups of rates were discussed viz. rise-times <5 p s for vl, Vg, and v g levels and approximately instantaneous (< 1 p s ) for 2vg and v4. Biucetyl. An i.r. TEA laser/u.v. monitored, double resonance study 394 was carried out in the pressure range 67-5300Nm-2 with 20MW in a 100ns wide pulse. Serious sample heating almost certainly resulted, so that analysis of the 10 p s perturbations is pointless. 5 Conclusions The period of rapid growth of data in the early 1970s, following the impact of lasers on energy transfer work, has now ended and a period of more thoughtful retrenchment has begun. Increasingly, attention is now focused on quality in terms of reagent purity (vital in e.g. H2 studies), accuracy of theoretical modelling 395 and integration techniques and a probing of subtle effects in intermolecular potentials by isotopic substitution, homologous series studies, and a careful choice of quenchers. The nature of the interaction potential between species has a large effect on quenching rate constants in energy transfer, and effects such as a strong dipole in the quenching species are important even in quenching homonuclear diatomics such as H,. The role of attractive forces in explaining the temperature behaviour of such rate constants is now seriously questioned with the revelation that more accurate mathematical treatment of models can account for this behaviour without attractive forces. It is now Virtually certain that, since approximations are essential in order to make the problem of prediction tractable, no one type of model is likely to be able to adequately describe H,, HCl, and polyatomic vibrational energy quenching. Fortunately, it seems that multiquantum transfers are not usually favoured where simple quantum routes are possible even at greater energy deficits. Fine series of studies are now appearing such as the definitive series on the methyl halides. Important effects emerge from such studies leading, as we have seen, to a far deeper understanding of energy transfer kinetics in polyatomic species. Coriolis coupling of levels and the importance of the (pr2/r)* ratio in assessing the likely importance of rotational effects are noteworthy in this context. The probing of the Vibrational quantum number dependence of k has been initiated with CO and further such work may be expected in the future. The importance 396 of SF, in i.r. photochemistry is unfortunate in that the basic i.r. photophysics of this very complex molecule are comparatively poorly understood (vide supra) at least in the public literature. Admittedly NH, is also a complex molecule, but given that the CO, laser-pumped NH, laser is of considerable importance as a spin flip ‘pump’ giving tunable laser output in the region 13.5-17 pY3”important in uranium isotope separation, more work on NH, will undoubtedly appear soon.

394 395

396 397

A. Yogev and Y. Haas, Chem. Phys. Letters, 1973,21,544. P. D. Gait, Annual Reports (A), 1976,73, 5. F. Banner, T. P. Cotter, K. L. Kompa, and D. Proch, J. Chem. Phys., 1977,67, 1547. R. Harrison, personal communication.

5 Potential Energy Surfaces for Studying the Reactions and Molecular Dynamics of Small PoIyato mic MoIecu les BY J. N. MURRELL

1 Introduction Our ability to calculate from first principles the rates of chemical reactions in the gas phase or the cross-sections of molecular beam scattering has improved considerably in recent years. Such calculations allow us to interpret such experiments in terms of simple physical concepts (complex formation, stripping reactions, energy transfer, etc.) and in addition they provide a route to quantities which may not easily be directly measured in the laboratory. There are, for example, rate constants for reactions which enter the atmosphere-ozone depletion cycle which have not been measured accurately and the value of these may make the difference between gloom and joy. For such calculations, whether by classical or quantum dynamics, it is necessary to know the potential energy function for any configuration of the atoms which is feasibly found at the total energy considered. This potential is defined by the Born-Oppenheimer approximation to be the energy of the system for stationary nuclei as a function of the internal co-ordinates of the molecule. Motion of the system on such a potential surface is called adiabatic and it implies that there is a smooth and continuous change in the electronic wavefunction during the motion. For dynamical problems in which there is a change in electronic state (non-adiabatic processes) one needs to know in addition to the potential energy function, the matrix elements of certain operators (e.g. spin-orbit coupling or nuclear kinetic energy) between different electronic states. The results of dynamical calculations may, or may not, be sensitive to the form of the potential energy surface. In some cases there is an obvious sensitivity: for a reaction proceeding over a surface with an energy barrier, the height of this is crucial. In other cases, particularly exothermic reactions without barriers, an analysis by information theory shows that experimental results can be explained on the basis of minimal information on the energy density of states of the products. However, it is probably true to say that the finer the resolution of the product internal energy states the more sensitive will be the results to the details of the potential surface. This Report deals only with potential energy surfaces for polyatomic molecules that are of a suitable form for dynamical calculations. Diatomic potentials are on the whole well known either from the analysis of atom-atom collisions or from spectroscopy, or by calculation. Potential energy functions for large molecules have been developed for configurations which are near equilibrium, and are used either R. D. Levine and R. B. Bernstein, in 'Dynamics of Molecular Collisions, Part A', ed. W. H. Miller, Plenum Press, New York, 1976.

200

Potential Energy Surfaces - Small Polyatomic Molecules

201

for spectroscopy or for conformational analysis. They are not, however, generally suitable for the study of bond breaking reactions and, therefore, excluded from this discussion is the important field of molecular mechanics.2 Information about potential energy surfaces can come from computational or experimental studies. For the first one has available a broad range of ab initio or semi-empirical methods for calculating the energy at discrete points on the surface. The computational effort required depends on the accuracy that is desired and on the number of atoms and electrons in the system. At one extreme, many points have been calculated with high accuracy (- + 5 kJ mol-’) on the small light atom system H3, and at the other, approximate reaction paths have been obtained for several organic systems using semi-empirical theories. A further restriction in the scope of this Report is that no discussion on the difficulties of making such calculations is g i ~ e n , ~but - ~ the results are used to develop explicit functional forms for the potential energy surface. On the experimental side information comes primarily from spectroscopy, which can give very detailed information about the regions close to equilibrium points, and from dissociation energies. Thermochemistry also provides information about the dissociation limits and from kinetic measurements we gain some information about barriers on reaction paths. In principle, scattering data will give very detailed information about a surface but in practice no direct inversion technique exists to convert differential cross-sections into potentials for polyatomic systems. The trial and error fitting of computed cross-sections to experimental measurements is generally too time consuming to be useful at present. For most dynamical calculations it is not sufficient to know the potential at discrete points on the surface but a functional form of the potential is required. Both classical and quantum calculations involve a step-by-step integration of differential equations over the surface, in one case to get trajectories and in the other to get wavefunctions, and the integration steps can land you at any point on the surface. Only if it is quick to get the potential and its derivations at an arbitrary point (as it is in some semi-empirical methods of calculation) is it feasible to make calculations only at the integration point^.^ However, if a simple functional form of the potential can be found then this is clearly the first choice.

2 General Principles In the Reporter’s opinion the most important general principle is the concept of smoothness. Reaction profiles do not look like a cross-section through the Alps (Figure 1). Firstly they are analytic at most points (i.e. continuous and differentiable) so that a Taylor expansion of the potential about an arbitrary point converges for

’

See comments by K. Rasmussen, Faraday Discuss. Chem. SOC.,1977, 62, 153. G. A. Balint-Kurti, Adv. Chem. Phys., 1975, 30, 137. J. N. Murrell, Adv. Chem. Phys., 1977, 32,93. R. F. W. Bader and R. A. Gangi, in ‘Theoretical Chemistry’, ed., R. N. Dixon and C. Thomson (Specialist Periodical Reports), The Chemical Society, London, 1975, vol. 2, p. 1. P. J. Kuntz, ‘Dynamics of Molecular Collisions, Part By,ed. W. H. Miller, Plenum Press, New York, 1976. M. Karplus, J. Amer. Chem. SOC.,1973, 95, 8160.

202

Gas Kinetics and Energy Transfer

Figure 1 Potential energy surfaces do not look like this

sufficiently small steps from that point. Cusps, for example, are not analytic and although they certainly occur on surfaces they are relatively rare. A second principle that is adopted is that the number of smooth maxima and minima on a reaction profile* is small. For the ground states of most diatomic molecules there is a single minimum and the potential increasesfrom this monotonically to the dissociation limit. In some cases, more often with excited states, there is a single maximum between the minimum and the dissociation limit. Polyatomic surfaces are inherently more complicated than diatomics as it is the rule rather than the exception to find more than one minimum on the surface and paths between these minima will go through maxima or saddle points. However, the number of such extrema is generally still small. This point is illustrated with the example of ozone (0,) which is discussed in more detail later. The molecule has an equilibrium structure of CZusymmetry (bond angle 117") and hence, by symmetry, there must be three such minima on the surface which are equivalent (any one of the three atoms can be the unique central atom). In addition it is well established by calculation that there is a further metastable minimum of D,,, symmetry with rather short bond lengths.' Reaction paths between these four minima will pass through six saddle points, which are stationary points where the curvature is positive in two dimensions but negative in the third. Kinetic studies show that there is little or no barrier to the reaction 0 + O2 -+ 0, and it is therefore unlikely that there are other stationary points on the surface. The general acceptance by chemists of the Hammond postulate that if two states occur consecutively during a reaction and they have approximately the same energy then their interconversion will involve only a small rearrangement of the molecular structure, is an indication that the smoothness of potential energy surfaces is also generally accepted.

* The reaction profile is defined as the potential energy plotted along a path that goes from reactants to products over a minimum activation energy route; a more precise definition is not required in this review.

R. R. Lucchese and H. F. Schaeffer, in the press. G. S. Hammond, J. Amer. Chem. Soc., 1955, 77, 334.

Potential Energy Surfaces - Small Polyatomic Molecules

203

Suppose, for example, that we have a reaction profile as in Figure 2 joining reactants and products with different energies through a transition state. From Hammond's postulate it is inferred that the transition state lies nearer to the higher in energy of

Figure 2 Reaction profile. By the Hammond postulate the solid line is More probable than the dashed line

the two; reactants or products. In other words, curve A is more likely than curve B. Various models of the chemical bond and of reaction profiles have been used to justify this postulate but none emphasizes its generality to all types of reaction. However, with the assumption of analyticity we can write the potentials at the reactant or product as a Taylor expansion about the transition state, e.g.

V(P) = V(T) + +p2V(2)(T)+ 4p3V(3)(T)+ . . . It is now clear that if only even derivatives of V at T are non-zero the reaction profile must be symmetric on the reactant and product sides to all orders. The odd derivatives of V will destroy this symmetry. Suppose V(3)(T)is positive, then this will raise the product side and lower the reactant side and in addition it will shift the first turning point (minimum) on the product side towards T and the first turning point on the reactant side away from T because p 3 V(3)(T)has a positive slope everywhere except at p = 0. To this order therefore Hammond's postulate holds. In fact one can go further and say it holds up to order V(2")(T)where V(2"+1)(T) is the first odd derivative with sign different from that of 1/(3). If we are seeking explicit functional forms to fit a polyatomic surface we must combine flexibility with smoothness. If we have n known facts regarding a surface then we can either fit these exactly with an n-parameter function or we can carry out a least squares fitting on a function containing fewer than n parameters. However, it must be recognized that all data we have about potential energy surfaces are subject to error, and these errors may be considerable for calculated points. It is therefore not necessarily true that an n-parameter function fitted to n data, which are assumed to be exact, will be a more accurate surface in an absolute sense than a function with fewer parameters fitted by a least squares procedure to these data. Suppose, for example, we have n calculated points on the surface Viand we fit these by a k parameter function f (k < n) and examine the residuals lfi- Vil. If each of these residuals is less than the estimated error in V , we must conclude that we have a perfect fit. The reason for emphasizing the above point is that functions may become less smooth as the number of parameters is increased. An nth order polynomial is a

Gas Kinetics and Energy Trander

204

typical case as it can in one dimension have n- 1 turning points. If, for example, we try to fit a diatomic potential by an extended Rydberg function n

V = - D,(1

+ ar + C bjrj)exp( -ar) j =2

(2)

(the exponential imposes the correct dissociation limit), then for large values of n one can find unphysical turning points. It has, however, been shown that for most diatomics such a potential with n < 3 is acceptable."

3 Methods of Calculating Tri-atomic Potentials Cubic Spline Functions.-It is possible to obtain smoothness with exact fitting of a large number of points by piece-wise fitting of the points in small regions combined with a smooth joining at the boundaries. Cubic spline fitting is the most popular approach. For triatomic molecules with a fixed bond angle the potential surfaces can often be represented quite well by rotated Morse curves (rotated about a point in R,R, space with both R, and R, large) whose parameters are cubic spline This procedure has been extended to three dimensions l 3 (i.e. varying the bond angle) using two dimensional cubic splines and this appears to be more efficient than the direct use of three-dimensional cubic spline^.'^-'^ However, a large number of ab initio points are required to generate a spline fitted potential. Approximately seven points are needed to generate one spline function and about 100 are required for each triatomic surface.13 In addition, the condition that for all angles the potential must have a rotated Morse form is rather severe and it has yet to be shown that the method can be extended to more general triatomic surfaces and to systems of larger dimension.

LEPS Surface.-The

most widely used function for atom-diatom reactive scattering calculations has been that which originated in the work of London who used Heitler-London type wavefunctions for the ground state of a three-electron triatomic molecule and obtained the expression

v = Qab

4-

Qbc

+ eca -

- Jbc)z

f (lbc

- Jca)2 + (Jca - Jab)2])'

(3)

Q and J are the Coulomb and exchange integrals, respectively, which occur in the Heitler-London theory. This expression has been developed through the years and has evolved into the so-called LEPS (London-Eyring-Polanyi-Sato) surface in which equation (3) is multiplied by an empirical factor (1 + k)-', which is supposed to account for overlap effects.'* The Coulomb and exchange integrals are then calculated from the singlet and triplet potential energy curves according to expressions (4) and ( 5 ) using a Morse function for and an anti-Morse function for 3&,. 'Vab

lo

l1

I3 l4

Is l6 l7

= (Qab

+ Jab)(l + k)-' - Jab)(1 - k)-'

3 V a b = (Qab J. N. Murrell and K. S.Sorbie, J.C.S. Furuduy ZZ, 1974, 70, 1552. J. N. L. Connor, W. Jakubetz, and J. Manz, Mol. Phys., 1975, 29, 347. J. M. Bowman and A. Kuppermann, Chem. Phys. Letters, 1975, 34, 523. S.K. Gray, J. S. Wright, and X. Chapuisat, Chem. Phys. Letters, 1977, 48, 155. D. R. McLaughlin and D. L. Thompson, J. Chem. Phys., 1973,59,4393. N. Sathyamurthy and L. M. Raff, J. Chem. Phys., 1975,63,464. N. Sathyamurthy, G. F. Kellerhals, and L. M. Raff, J. Chem. Phys., 1976, 64, 2259. F. London, Z . Electrochem., 1929, 35, 552. S. Sato, J. Chem. Phys., 1955, 23, 592, 2465.

(4) (5)

Potential Energy Sugaces - Small Polyatomic Molecules

205

The parameter k can be chosen to give the surface some desired property (e.g. a specified activation and further empirical parameters can be added to give the function greater flexibility.22 There are two features about the LEPS surface which make it particularly attractive in addition to its simplicity. Firstly it has built in the correct dissociation limits (assuming this to be the singlet ground states of the diatomics) and secondly it contains the non-analytic features associated with the Jahn-Teller intersections of systems such as H,. For A, systems and D,, configurations the square rooted term in equation (3) becomes zero and not differentiable. There are in fact two states degenerate at this point and their surfaces, which have energies Q & F),give rise to a conical intersection. For such a system we cannot strictly speak of one ground state surface because it is possible to go from the ground state to an excited state by taking a route which passes through a D,, configuration. One should really say that a system like H, has a double-valued surface for the ground and first excited state, which in LEPS terms is represented by equation (3) with the & choice for the square root. This question of multiple valued surfaces is discussed later. Notwithstanding its wide use and possibilities for parameterization the LEPS surface does not seem to have sufficient flexibility to fit even the complete surfaces of some systems for which it might seem eminently suitable. For example, if parameters are introduced to give an acceptable barrier for the system 23

'

C1+ H2 + Cl-H-H

+ CIH + H

then it leads to a minimum for the configuration H-CI-H and this is not in accord with the kinetics of the reaction HCl D --+ H + DCl. The extension of the LEPS function to four-atom systems (e.g. H4) has also been di~appointing.~~ It appears, notwithstanding its popularity, that the LEPS function is not going to provide a general framework for polyatomic surfaces.

+

DIM Approach.-Another way to guarantee that a polyatomic surface will have the correct dissociation limit is to adopt the diatomics in molecules (DIM) approach to molecular wave function^.^^ The principle for this is to build up polyatomic wavefunctions by coupling together the wavefunctions of diatomic and atomic fragments. In general, more than one product basis function will contribute to the polyatomic wavefunction and the variation theorem will be applied to find the correct linear combination. For example, for H2Cl the states of HC1 which dissociate to ground state atoms are 'E, 'E, 'n, and 3n and each of these can couple with the other hydrogen atom to give a 'A' function (the ground state of the system). Thus to obtain the required potential one diagonalizes a 4 x 4 matrix, the elements of which can be deduced from the atom energies and the diatomic potentials. In some cases (e.g. H,) the DIM potential is equivalent to the LEPS. l9

2o 21 22

J. C. Polanyi and S. D. Rosner, J. Chem. Phys., 1963,38, 1028. J. T. Muckerman, J , Chem. Phys., 1971,54, 1155. R. L. Wilkins, J. Chem. Phys., 1972,57,912; 1973, 58,2326. P. J. Kuntz, E. M. Nemeth, J. C. Polanyi, S. D. Rosner, and C. E. Young, J. Chem.Phys., 1966, 44, 1168.

23 24

2s

A. Persky and M. Baer, J. Chem. Phys., 1974, 60, 133; also personal communication from the authors. A. J. C. Varandas and J. N. Murrell, Faraday Discuss. Chem. Soc., 1977, 62,92. F. 0 Ellison, J. Amer. Chem. SOC.,1963, 85, 3540.

Gas Kinetics and Energy Transfer

206

The DIM method can be applied to all systems (unlike the LEPS potential) but it does not have the capability of producing exact potentials because it uses only the atom and diatom states which correlate with ground state products. Its lineage can be traced back to the valence-bond method in its empirical modification 'atomsin-molecules' 26 but this, in principle, has a complete set of states and can be exact. For some much studied simple systems (e.g. H,, H i , and HeHl) the DIM method gives rather good potentials ti - and it must be emphasized that as normally used it does not contain adjustable parameters as does the LEPS function. However, it is not accurate for many other systems, triatomic and tetra-atomic, for which it has been examined (Li, and H4 for example), and can at most be said to give a qualitative representation of the surface. Notwithstanding its relative simplicity (within the framework of wavefunction methods) the DIM method as presently formulated cannot be a basis for accurate dynamical calculations. Arbitrary Functions.-What have been called 'arbitrary functions' for describing polyatomic potentials are arbitrary in the sense that they are not derived from Hamiltonian's and wavefunctions but they fall into the same class as Morse functions or Rydberg functions for diatomic potentials. In other words, they are simple functions which aim to reproduce the known properties of the potential combined with the assumption of smoothness. For non-reactive atom-diatom collisions many dynamical calculations have been carried out with a potential V(R,r$) = C V,(R,r)P,(cos e)

(6)

1

where the co-ordinates are defined in Figure 3 and P,(cos 0) is a Legendre polynomial. V,(R,r) could, for example, be a Morse function for variable r whose parameters have an R dependence. For example, by analysis of spectroscopic data on H,-Ar Le Roy and Van Kranendonk deduced a potential 27 V(R,

r, e) = c,,,~-yi +

SJ)

- c6~-6(1 + szt)

+ [a,,,C,,,R-m(l +

sS~)

- a6C6R-6(l + s~~)]P,(cose)

(7)

where = (r - ro)/ro,C,,, = [6/(rn - 6)]em,c 6 = [rn/(rn - 6)]e6 and the parameters have the following values: m = 12, 8 = 60.70 cm-', ro = 0.76662 A, s1 = 1.445 A, s2 = 0.919 I$, s3 = 1.45 A, s4 = 0.92 A, a,,, = 0.2998 A, and a6 = 0.1973 A.

C

Figure 3 Co-ordinates suitable for non-reactive collisions

l7

W. Moffitt, Proc. Roy. SOC.,1951, A210,245. R. L. LeRoy and J. Van Kranendonk, J. Chem. Phys., 1974, 61, 4750.

Potential Energy Surfaces - Small Polyatomic Molecules

207

When choosing arbitrary functions there is clearly merit in first examining the simplest that is consistent with minimal requirements and then modifying this as needs arise - the principle of Occam’s Razor that entities are not multiplied without necessity. This has been the approach which has been followed in recent years in the Reporter’s own group for potentials suitable for reactive collisions. The approach is probably best illustrated by starting with a particular example and. then looking later at general features.

HCN. Figure 4 shows contours of a potential for HCN defined by the function specified in Table 1.28 The contours represent the potential for a hydrogen atom

moving around CN with the CN bond length optimized for each position of H relative to the centre of the CN bond. There have been several theoretical studies of this surface and there is agreement about its general f ~ r m . ~ ’ * There ~’ are two minima on the surface, corresponding to linear HCN and HNC and there is a saddle point at a roughly T-shaped configuration. The co-ordinateschosen to describethe potential are the three internuclear distances. These have the advantage over the more usual two lengths and one angle in that they place each of the three atom-diatom dissociation limits on an equivalent footing. They are therefore more suitable for the dynamics of any reaction in which all reactive channels are open. The correct dissociation limits are imposed by writing 31 ‘HCN

= ‘HdR1)

where lim V , = 0 and V,,(R,) Ri+

+ VCN(R2) + VNdR3) f

vdR,,R2,R3)

(8)

etc. are the appropriate diatomic potentials. V , is a

QO

three-body interaction term whose role is to fill the difference between the exact potential and the sum of the diatomic parts. 28 29

30 31

J. N. Murrell, S. Carter, and A. J. C. Varandas, Mol. Phys., 1978, 35, 1325. D. Booth and J. N. Murrell, Mol. Phys., 1972, 24, 1117. P. K. Pearson, H. F. Schaeffer, and U. Wahlgren, J. Chem. Phys., 1975, 62, 350. K. S. Sorbie and J. N. Murrell, Mol. Phys., 1975, 29, 1387.

208

Gas Kinetic3 and Energ). Transfer

Potential Energy Surfaces - Small Polyatomic Molecules

209

In the case of HCN the diatomic potentials are determined by the spin conserving reactions

In principle another channel HCN

-,N(2D) + CH(2X)

(12) has to be considered as this gives the ground state of CH. However, it can be shown that for all CH bond lengths this has a higher energy than that defined by equation (1 1) and it can therefore be ignored.28 We will return later to an example where we have to include two channels for a dissociation. In Table 1 the diatomic potential for NH(3X-) has been expressed as a Rydberg function based upon the experimental dissociation energy, bond length and harmonic force constant. For CN and CH, cubic and quartic force constants are also known so there are sufficient data to determine the coefficients of the extended Rydberg function l o which is shown in the table. Other diatomic functions could have been found which are equally good. Harmonic force fields have been deduced from the vibrational spectra of HCN and HNC, the latter as a matrix isolated species.2*-3 2 These force constants (f11,f22,fi2, andf,,), plus two equilibrium bond lengths and a dissociation energy make a total of 2 x 7 = 14 pieces of data from which parameters in the three-body term can be determined. It can be seen from Table 1 that V , is written as a 14-term polynomial in the three internuclear distances multiplied by a range factor 3

n(l

i- t

- tanh yipi/2),

pi =

Ri- Ry

For each choice of the parameters y t one can solve 14 simultaneous equations to find the coefficients of the polynomial. The function (1 - tanh yp/2) has the limit at large p of 2e-” and it therefore kills any polynomial in p. Our first investigations with functional forms for VI were based upon the three-dimensional extension of the diatomic Rydberg function using exponential range factors. However, triatomic potentials have to be accurate for large negative displacements from equilibrium (unlike diatomics for which such negative displacements are inaccessible) and the exponential is rather explosive in such regions. Unphysical minima were encountered for such configurations using this type of function, but the use of the function (13), which tends to a constant value for large negative pi, does not give this difficulty. It will be noticed that the polynomial part of Vr is a cubic in three variables but terms such as p:p2 are missing. It would require three more pieces of data to fit these and no doubt those could be found using some of the data from calculations on the surface. However, we have found it more convenient to use data which are not related to the potential minima to determine the best values of the range factors yi. Our practice, in general, has been to start with values of y i equal to the exponents in the diatomic functions and to separately span the three factors to find limits within which the overall potential has no unphysical behaviour. In the case of the HCN 32

J. F. Ogilvie, Canad. J. Spectroscopy., 1973, 19, 171.

Gas Kinetics and Energy Transfer

210

surface a more precise criterion was applied by requiring the position and energy of the saddle point to agree as far as possible with cal~ulations.~~ Although a search over a three parameter (yi) space might appear troublesome it must be emphasized that to obtain the potential for a particular choice of yi requires negligible computing time (essentially the time required to diagonalize a 14 x 14 matrix). The final point about the parameter of Table 1 is the choice of reference point for the three-body term as the p i are defined as displacements from this. If a surface has just one minimum then it is convenient to take this minimum as the reference; this simplifies the algebra by which the coefficients of V, are related to the force constants of the triatomic. However, if there is more than one minimum it seems more sensible to choose a reference which is a compromise structure between the minima. This is in line with the principle that if one is making a Taylor expansion of a function over a bounded area then the reference point should be taken as central in that area. For HCN the reference structure is an equilateral triangle whose perimeter is twice the NH distance in HCN (i.e. the perimeter is equal to the sum of the three interatomic distances for HCN). Table 2 shows the properties of the saddle point for the particular potential defined in Table 1. It is seen to have an energy relative to the HCN minimum which is in agreement with the best available calculation. The bond lengths are however a little too short. Table 2 Properties of the HCN-HNC saddle point Energy relative to

RcHIA From potential of Table 1 Calculation 'O

1.054 1.171

1.118 1.181

RNH/A

HCN/eV

1.388 1.430

2.145 2.146

The position so far is that a potential for HCN has been obtained which is in reasonably good agreement with the known properties of the surface. There is, however, no guarantee that it is accurate over the whole space. Figure 5 shows, for example, contours of the potential for N moving around CH with the CH bond length fuced at its diatomic distance. One feature of this figure is the position of a shallow metastable minimum corresponding to the hydrogen bond structure C-H-N. This feature is physically sensible but the rest of the figure is speculation which can only be confirmed or denied by further ab initio calculations. An important point, however, is that a figure of this type is a very good guide as to which are the points on the surface that would be interesting to calculate. Although the potential that has been obtained for HCN has only quadratic force constants of HCN and HNC as input data, it is an anharmonic potential and can be used either to predict anharmonic force constants or to confirm assignments of overtone and combination bands. Such potentials have been found to be quite accurate for spectroscopic purposes, as shown later, although they were not derived with that aspect in mind. SO2. To emphasize the fact that a procedure such as that adopted for HCN has predictive value we can take the example of SO,.33 A potential was derived for this 33

S. Farantos, E. C. Leisegang, J. N. Murrell, K. Sorbie, J. J. Teixeira-Dias, and A. J. C. Varandas, Mol. Phys., 1977, 34, 947.

I

Figure 5 Contours of the HCN potential (Table 1) plotted for N moving around CH with the CH bond length having its diatomic value. Contour A is - 13.4 eV and the interval is 0.6 eV

Gas Kinetics and Energy Transfer

212

molecule using only the spectroscopic data on SO2 and it was found that the resulting function had further minima corresponding to the metastable species SO0 (by symmetry there are two minima for this as either oxygen can be terminal). Ab initio SCFMO calculations were then carried out on SO0 using as a guide the predicted geometry. The metastable minimum was confirmed by these calculations and found to be 90 kJ mol above the SO2 minimum, although the bond angle was 126’ rather than the predicted 180”. A revised potential was then determined for SO2 by adding the energy and geometry of the metastable minima to the input data for the coefficients of V,. SO2 is one of many examples of surfaces which have minima related by symmetry. It is relatively easy to impose this condition on a function of the type we have been considering. To illustrate this we will take 03,a molecule whose surface has been described earlier in this Report. 0 3 .If the reference structure for O3 is taken as an equilateral triangle, then the polynomial part of V , can be expressed in terms of symmetry adapted displacement co-ordinates si defined by 34

where p i = R, = Rq. Because the surface must be symmetric to permutations of the three atoms only totally symmetric combinations of si are allowed in the polynomial part of V,. These totally symmetric combinations are, to fourth order:34 1, s1, s:, (sf si), s:, s&; si), (si - 3s,2s3), sf,s:(s; s t ) , s,(s,” - 3s$,), (sf s3”)2. The minimum energy configuration of O3 has C2” symmetry and this has a dissociation energy, two independent zero first derivations, and four harmonic force constants; a total of seven pieces of data. If the D,, reference structure is given the same perimeter as the equilibrium configuration then it can be shown that the coefficients of s: and sf cannot be determined from these data; they would require cubic and quartic constants for their determination. A potential for O3 was determined by assuming that two other quartic terms, s:(~,’ + s!) and sl(s,”- 3sis3) could be dropped.34y3s We have found no simple answer to the question of which terms to drop if there are more terms in the polynomial at a given order than there are data to fit them.* One can recognize that s1 governs the relationship between the potential and the size of the triangle whereas s2 and s3 give the relationship to the shape of the triangle, so that if one expects fewer turning points with size variation than with shape, it is safer to drop terms involving sl. In two surfaces that have been studied, HCO and C102, it was found that the matrices relating coefficients to input data were singular, or nearly singular, for some selected polynomials, and no algebraic reason could be found for this. In both examples, other polynomials gave no difficulty and suitable potentials have been found.33.36

+

* The problem

+

+

+

has now been solved and is to be published in a joint paper by J. N. Murrell, S. Carter, and I. M. Mills. 34 J. N. Murrell, K. S. Sorbie, and A. J. C. Varandas, Mul. Phys., 1976, 32, 1359. 3s J. N. Murrell and S. Farantos, Mol. Phys., 1977, 34, 1185, 36 S. Carter, I. M. Mills, and J. N. Murrell, to be published.

Potential Energy Sut$aces

- Small Polyatomic Molecules

213

It was mentioned earlier that calculations indicate that ozone has a metastable D,, structure at short bond lengths.’ For a polynomial of the type described it was not possible to reproduce this feature for any value of the range factor (which was taken to be the totally symmetric(1 - tanh ysJ2) whilst at the same time having a potential that gave no barrier to dissociation. There is kinetic evidence that such a barrier

-0.Ooo

0:m

*.-

xlh”

2 : m

2:m

3:ooo

3

Figure 6 Contours of the ozone potential (Table 3) shown with one atom moving around O2 with optimized bond length. Contour B = -6.3 eV and the interval is 0.2 eV. Contour B surroundr the equilibrium (C2Jconfigurationand contour H the metastable (D3,,)structure

if it exists at all is below w 10 kJ mol-l. Barriers arise for low values of y because the three-body term is repulsive and gives rise to a barrier unless it decays as rapidly as the attractive two-body terms. We found that the simplest way to introduce the D,, minimum was by a Gaussian well of the form A exp[ - a(si + s;)] which was 2dded to the p~lynomial.~’The full potential for ozone is given in Table 3, and :ontours of this are shown in Figure 6.

Gas Kinetics and Energy T r m f e r

214

Table 3 Potential for the ground state surface of 0,34

+

+

+

Voo(R2) Yoo(Ra) J'I(sI,s~,sI) Voo(Rl)/eV = -5.21296(1 + 3.75374r)exp( -3.75374r), r = R, - 1.2074 A V , = (P G)(1 - tanh4.6s1/2) P = 8.7066 + 6.5822s1 13.9106s: - 17.1931(~: s:) - 3.1421si(s; s:) 2.6323~3(~: - 3s:) 13.9659(~: s:)' G = -3.0 exp[ - 7 3 s ; $31 Ro (the bond length of the reference triangle) is 1.5698 A.

Vooo = Voo(R1)

+ +

+

+

+

+

+

+

4 Special Features of Potential Surfaces Cusps.-It is not uncommon to find these at some point or points on a polyatomic surface. Let us take H,O as an example. If we remove oxygen from the molecule there are two channels that have to be considered 31

but for spin conservation this must be The ground state of the oxygen atom is coupled to the triplet state of H2. On the other hand, if one removes H, in its singlet ground state then the oxygen must be in the excited ' D state. The 'D-,P splitting of oxygen is 1.958 eV and from accurate calculations on H, the 'Li--'X; separation is equal to this for a bond length of 1.669 A. In other words, when R,, < 1.669 A channel (i) has the lower energy and when R H H > 1.669 A channel (ii) is the lower. The two-body potential VHH that arises in the H20potential function must therefore be cusped as shown in Figure 7. In the full potential of H,O the cusp will exist only at infinite separations of 0 and H,. At finite distances there will be some rounding off of the potential which

I

1 Figure 7 The H-H two-body potential for the ground state of H 2 0

Potential Energy Surfaces - Small Polyatomic Molecules

215

in wavefunction terms we would associate with the mixing of the two channel wavefunctions. At the equilibrium configuration of H 2 0 the H-H distance is 1.51 A, which is on the channel (i) side of the cusp. A three-body interaction term [Vr(in)Jcan be derived for this using the method already described. This must then be joined to a function V,(out) so that there is no overall cusp. This can be done by choosing the coefficients of V,(out) so that the potential function is continuous and has continuous first derivatives. These are essential requirements if the potential is being used as a basis for classical trajectories. Higher order derivatives can be made continuous but that is not essential for trajectory calculations. Figure 8 shows the potential of H 2 0 appropriate to the insertion reaction along a C2,symmetry reaction path. The cusp at large distances is clearly seen but this is gradually rounded off as one approaches the equilibrium configuration of the molecule. The points in the figure are calculations on this path by Gangi and Bader 37 which agree well with the function that has been deduced from spectroscopic data alone. 4

3

1

2

1

Figure 8 Potential energy surface for the 0

3

+ H2+ H20insertion reaction along a path of

C2"symmetry. Contours are spaced at 1 eV

The H20potential shows another type of cusp which is connected with spatial t :orrelation rules.31 We note that

H 2 0 + OH(211) + H(2S) .s allowed except for linear configurations of H 2 0 . In other words, the potential for xeaking an OH bond is cusped for linear configurations but not for bent, as shown In Figure 9.

''

R. A. Gangi and R.F. W. Bader, J.

Chem. Phys., 1970,55,5369.

Gas Kinetic3 and Energy Transfer

216 \ \

Figure 9 Potential for breaking one OH bond in HzOfor linear and bent configurations

Spatial cusps are not so readily built into the type of function we have been considering because they imply that the diatomic potentials are functions of the shape of the three-atom triangle. They are best considered as properties of a twovalued surface, that is, as a function which has two values for each value of R,,R2, and R3. One can see that this must be so because the products for complete dissociation of H 2 0 depend on the route that is taken [equation (17)]. Hence, from the equiliH,O(bent) H,O(linear)

+ H(2S) O@) + 2H(’S) OH(2Z) + H(2S) + O(’D) + 2H(2S)

+ OH(’H)

.1 -+

--+

(17)

brium configuration of H 2 0 we can go adiabatically (i.e. without surface hopping) to different surfaces at the dissociation limit. A two-valued surface of this type is most simply constructed as the eigenvalues of a 2 x 2 matrix

(5

9

where A, B, and j are functions of the interatomic distances. These eigenvalues are E* = & { A

+ B & [ ( A - B)2 + 4j2]*}

(19)

Potential Energy Surfaces - Small Polyatomic Molecules

217

'

The DIM method which involves matrix diagonalization automatically gives rise to the correct spatial and spin cusp. Unfortunately it is much more difficultin general to parameterize the elements of a matrix (if more than two-dimensional) by a data set than it is to parameterize a single-valued function in the way we have described. Fortunately many surfaces either have no cusps, or (like H,)these are in high energy regions of the surface and can effectively be ignored. Saddle Points.--The examples that have been given for explicit triatomic potentials have all been for systems with stable minima. The reason for this is that the method was formulated with the idea that spectral data on the triatomic would be sufficient to determine the parameters in the three-body term. One can, of course, examine other methods of determining the parameters and in particular the least squares fitting to calculated or experimental points on the surface. This has been done for the triplet ground state of NH; (isoelectronic with CH2) and a function obtained 38 which fitted 300 points on the surface (calculated by an unrestricted Hartree-Fock method) with a standard deviation of 21 kJ mol-'. The system CHf has been treated in a similar way 39 using 1200 points on the surface calculated by the DIM method. The standard deviation was 24 kJ mol-'. If one accepts a least squares fitting procedure of this type then there is no reason to confine the function to surfaces which have a stable minimum but repulsive surfaces can be treated as well. The only system of this type examined so far has been H3,24 although there is no reason to believe that the method would fail for other systems. An 18 parameter three-body term has been obtained for H3 which fits points from the best available calculations, including the slope and energy of the Jahn-Teller cusp for D,,, configurations. The standard deviation for 61 points on the surface was 5 kJ mol-' and typical errors in the energy relative to three atoms as zero was 0.3 % over the low-energy regions of the surface. Contours of this surface for a perimeter of 3.76 A, which includes the calculated collinear saddle point, are shown in Figure 10. The properties of this saddle point are compared with those of the input data in Table 4. The function is more accurate Table 4 Properties of the H, saddle point derivedfrom an explicit algebraic function, and comparison with other work Potential of Rlao AElkJ mol-' Allalau A22'lau

A~J'I~U

ref. 24 1.775 45.62 0.322 0.037 -0.062

Ab initio calculation ref. 41b ref. 40 1.765 1.757 46.03 41.01 0.32 0.320 0.024 -0.061 -0.058

Semi-empirical L EPS surface ref. 42

1.701 38.16 0.364 0.024 -0.124

and antisymmetric stretch (A33). Force constants for symmetric stretch (Axl), bend (Az2), Calculations for collinear configurations only. 38 j9

*O

**

M. A. Gittings and D. M. Hirst, Faraday Discuss. Chem. SOC.,1977, 62, 67. E. Herbst, Chem. Phys. Letters, 1977, 47, 517. I. Shavitt, R. M. Stevens, F. L. Minn, and M. Karplus, J. Chem. Phys., 1968,49, 5163. B. Liu, J. Chem. Phys., 1973,58, 1925. R. N. Porter and M. Karplus, J. Chem. Phys., 1964,40, 1105.

Gas Kinetics and Energy

218

Transfer

0

N

y. r

0 r

In 0

{: =a In

0 I

0 c I

In v-

I 0

N

Figure 10 Contours of the H3potential for a triangle of fixedperimeter 3.76 A plotted in the variables (s2,s3) = [(4)*(R2 - R3), (4)*(2R1 - R , - R3)] where R1,R2, and R3 are the bond lengths. Only the physically accessible space is shown. The three equivalent collinear saddle points are shown X and the points marked H are shallow minima for C2, structures with one atom far away from the other two

overall than others that have been published except perhaps in respect to the height of the saddle point. The calculations on which it was based are probably too high by about 8 kJ mol-' at this point. In contrast, the well known Porter-Karplus potential,42which is a modified LEPS function, was fitted to an experimental barrier height of 38 kJ mol-' but other aspects of the surface do not agree with the best calculations. 5 Systems with more than Three Atoms The question of extending the type of function that has been considered to systems with more than three atoms is now discussed. A few remarks on the four-atom case will indicate the line of attack. Let us assume that the potential for a four-atom molecule, interatomic distances R,-R,, can be written as a many-body expansion

etc. represents the sum over all two-body terms. The four-body term must wx be zero at all dissociation limits and the three-body terms must be zero at atom or diatom limits. The two-body potentials in equation (20) can be determined by considering the

where

Potential Energy Surfaces - Small Polyatomic Molecules

219

diatom plus diatom dissociation limits subject to the requirement of spin conservation, thus

Note that VA? is a function of the AB bond length (R,)but to allow for spin cusps, as in the case of H,O, it must be a parametric function of R4, vice versa Vd",'isa function of R4 but depends parametrically on R,. For example, the dissociation of NH, has two channels NH,(singlet)

+

NH(3Z-)

+ H,(3X:)

(i)

Channel (i) is applicable for small NH and large HH distances and channel (ii) for large NH and small HH distances. The three-body terms can be determined if the triatomic potentials are known, by consideration of limits such as

Finally, the four-body term must be determined from properties of the tetra-atomic molecule. The principle of extension to polyatomics is thus clear and attractive; it is that one builds up the total potential from knowledge of the potential surfaces of the fragments. Of course, the method requires this knowledge to exist - and at present it often does not - and, more important, it rests for its success on the assumption that for configurations of chemical interest the many-body expansion will converge. In other words, it is likely to prove an impractical method for a six-atom molecule, for example, if the six-body term is very important. There is insufficient evidence at the present time to confirm or deny the question of convergence of the many-body expansion for molecular configurations of chemical interest. There are clearly some systems, e.g. inert-gas clusters, where it is known from the heat of vapourization of the crystal that two-body terms dominate the potential: the higher order terms are very small but may have a structural significance (e.g. in the inert-gas case they determine the difference in energy between f.c.c. and h.c.p. packing). On another level one has the chemical experience of transferable bond properties (length, force constant, energy, etc.) which implies the dominance of two-body terms in many cases. However, two-body dominance is clearly not universal and the more important question is whether convergence can be shown after three or four-body terms. The following examples will show the extent of our investigations so far. As a first illustration we consider clusters of Be atoms which have been extensively investigated by ab initio SCFMO methods using a large basis. One of the surprising features of these calculations was that a tetrahedral form of Be4 was found to be stable, whereas Be, and Be3 are At first sight this result implies that the four-body term must be responsible-for the stability but a closer examination of the 43

C. W. Bauschlicher, D. H. Liskow, C. F. Bender, and H. F. Schaeffer, J. Chem. Phys., 1975,62, 4815.

44

45

R. B. Brewington, C. F. Bender, and H. F. Schaeffer, J. Chem. Phys., 1976, 64,905. W. Kolos, F. Nieves, and 0. Novaro, Chem. Phys. Letters, 1976, 41,431.

Gas Kinetics and Energy Transfer

220

energies shows that this is not true.45*46 Consider Be,, an equilateral triangle for Be3, and a tetrahedron for Be, with equal bond lengths. We can write for these structures V(Be,) = V(’) V(Be3) = 3V(’)

(24)

+ V(3)

(25)

The important point to note is that although V ( 2 )is repulsive, attractive three-body or four-body terms can make Be, or Be, stable depending on the balance of attraction and repulsion. Note that on passing from Be3 to Be, the repulsive term doubles but the attractive term V(,)increases four-fold. Analysis of the calculations4 5 shows that this is indeed the case. The relevant quantities in equation (26) are, for a bond length of 4ao, V(’) = 0.035, v3)= -0.071, and V(,) = 0.065 au. Note that the four-body term is in fact repulsive. In total, Be, is stable relative to separate atoms by -0.009 au. Expression (26) emphasizes the fact that the stability of a polyatomic system depends not only on the size of the individual n-body terms but also on the number of such terms. The combinatorial factors act against the rapid convergence of the expression when the number of atoms is large. Nevertheless, in the case of Be, clusters there is a reasonable hope that from a knowledge of the potential energy surfaces of Be, and Be, together with a few points on the Be, surface, analytical functions for the two, three, and four-body terms could be obtained which would allow a good estimate of the surfaces for higher clusters. Explicit functions have been obtained for the two, three, and four-body terms of H, (the H3 potential is referred to earlier, see Figure 9), although the available data on H, give only limited flexibility to the four-body term.24 The total potential reproduces quite well that region of the surface of rectangular configurations, particularly the energy and geometry of the D4,, saddle point. Moreover, a search of the six dimensional space leads to the prediction that the four-centre H,-D, exchange reaction should go through a trapezoidal transition state, and this is in agreement with calculations by Silver and Stevens.,’ However, the activation energy for this route is close to the H, dissociation energy and there is good evidence from calculations that the exchange reaction actually goes through a hexagonal H, structure.48 Using the two, three, and four-body terms deduced from the H4 surface and ignoring higher terms, the optimum bond length for H, is predicted to be 1.850 a,: calculations give 1.87 a,. The two, three, and four-body energies at this geometry are - 1.220, 2.288, and - 1.769 au respectively and agreement with the calculated energy is given by adding a five-body energy of +0.31 au and a zero six-body energy. We therefore see that for this system there is convergence in the many-body expansion although it is not as rapid as one would like. The five-body energy can certainly not be ignored. It must be recognized, however, that the D,, form of H, is likely to be an exceptionally poor case for convergence. In valence structure terms 46 47 48

J. N. Murrell, Chem. Phys. Letters, 1978, 55, 1 . D. M. Silver and R. M. Stevens, J. Chem. Phys., 1973,59, 3378. D. A. Dixon, R. M. Stevens, and D. R. Herschbach, Faraday Discuss. Chern. SOC.,1977,62, 110.

Potential Energy Surfaces - Small Polyatomic Molecules

22 1

there is resonance between two KekulC forms and this is bound to give a large deviation from a pair-additive potential. Another tetra-atomic molecule for which there are data available is C103. This system has been studied in order to tackle the dynamics of the reaction

c1 + 0, -+

c10 +

0 2

(27)

which is important for ozone quenching. The surface shows no complications from spin cusps because all dissociation channels lead to ground state products

03('A') + o ~ ( ~+x0; () 3 ~ )

(30)

There is some uncertainty as to whether the two species ClOO and OClO, which are both known, are minima on the same C102 surface, but a surface for C102 has been obtained on the assumption that they are. 3 3 We have already discussed the potential for 0,.We are therefore in the position of having functional forms for both the two and three-body terms and of seeing whether the surface obtained from these alone is physically sensible. In other words, can one ignore the four-body term? The results are very encouraging. The most stable form of the tetra-atomic molecule is predicted to have a central chlorine atom with three C10 bonds and D3hsymmetry overall.49 E m . experiments on the matrix isolated radical suggest that there is a small deviation from planarity with a bond angle OClO 114°.50s51The predicted energy relative to separated atoms is -797 kJ mol-' and the experimental estimate (one has to guess a zero point energy) is -770 kJ mol-'. The most favourable path for the reaction (27) is along a planar configuration to give a transition state ClOOO with LClOO = 180" and L O O 0 approximately equal to the ozone bond angle. The activation energy is small 20 kJ mol-'. Experiments, however, suggest that there is a barrier for the reaction which is much smaller: 1 - 4 kJ m ~ l " . ~ ~ A four-body term can be derived to give as minimum requirements that the C103 minimum has C,, symmetry and that there is a small barrier for reaction (27). A function which fits these minimal requirements has been found 49 to be

-

-

Y(4)/eV= -1.2945W1(1

- tanh 1.8898WJ2)

where 6

Wl/A = J Q C (Ri - 2.1167A) i= 1

R r ,i = 1, 6 being the interatomic distances. 49

50 51

52

J. N. Murrell and S. Farantos. Unpublished work. J. R. Byberg, Chem. Phys. Letters, 1973, 23,414. K. Shimokoshi and Y . Mori, J. Phys. Chem., 1973,77,3058. M. K. A. Clyne and W. S. Nip, J.C S. Faraaky ZZ, 1976, 72,883.

(31)

222

Gas Kinetics and Energy Transfer

6 Condusion In this Report attention has been concentrated on the functional form of the polyatomic potential developed by the Reporter’s own research group, for which he makes no apologies. In the first place the older forms such as LEPS and DIM have been widely used and reviewed many times and there is little to say on them that is new. Secondly, cubic spline fitting is in its early days and there is as yet no evidence that it is going to be useful beyond the triatomic field and will probably not be efficient for all triatomics. Lastly the Reporter’s own studies, whilst still in their early stage, suggest that, providing one is willing to be reasonably flexible about the type of function used, there is no triatomic whose surface cannot be at least qualitatively represented by an explicit function. At the present time sixteen triatomics have been examined and these include bent and linear forms and surfaces which are attractive or repulsive and which have a single or more than one minimum. In no case has failure to find a satisfactory function for a system of interest occurred. The evidence that the many-body expansion is convergent for larger molecules over configurations of chemical interest, is weaker but not negligible. Again there is no system studied for which some function has not been found, although few have as yet been examined. The building up approach is emphasized. For example, work is at present under way to find an explicit potential function for H2C0 which is valid for all configurations of the atoms. This requires preliminary work on H2C (triplet state), H 2 0 (singlet and triplet), and HCO. This preliminary work has almost been completed and it remains to be seen what type of four-body term is required to reproduce the known properties of H,CO.

Author Index" -

Abouaf-Marguin, L., 123, 195 Abrams, R. C., 163 Abrams, R.L., 119, 192 Abramowitz, S., 50 Adam, W., 67 Adams, C. R.,112 Akika, K., 67 Akimoto, H., 66 Ahl, J. L., 145 Airey, J. R., 144, 146, 158 Allen, D. C., 161 Altee, J. M., 156 Alterman, E. B., 129 Amano, A., 12 Amano, T., 195 Ambartzumian R. V., 13 Ames, D. P., 113 Anastasi, C., 35

Bederson, B., 72 Beerman, H. P., 119 Begley, R.F., 116 Bellus, D., 30 Bemand, P. P., 35 Benard, D. J., 46 Benson, R. C., 46 Benson, S. W., 1, 15, 36, 37, 38, 43, 45, 48, 129, 135

Brophy, J. H., 58 Brosnan, S.J., 116 Brown, J. H., 60 Bruening, W., 67 Brunet, H., 190 Brunetti, B. G., 62, 63 Brunner, F., 199 Brunner, P., 7 Bunker, D. L.,7, 9 Bunker, D., 34 Burke, L. A., 41 Burkhalter, J. F.,9 Bulthius, K., 160 Burak, I., 121, 130, 190, 191 Butler, J. F., 114 Byer, R. L., 116 Byron, S. R., 117

Berend, G. C., 129, 135 Bergmann, R.G., 12,23,38,40 Bernstein, R.B., 70, 72 Berry, M. J., 71, 72, 73 Berson, J. A., 2, 37, 38, 39 Besson, J. M., 114 Beyer, T., 4 Beynon, J. H., 6 Bhattacharjee, R. C., 18 Andreev, E. A., 132 Billingsley, J., 163 Cadman, P., 11 Andresen, U.,121 Cain, E. N., 23 Billman, K. W.,164 Anlauf, K. G.,70 Calawa, A. R., 114 Bina, M. J., 146 Aoyama, T., 67 Callear, A. B., 163, 179 Bird, P. F., 135, 136 Arditi, I., 158 Calvert, J. G., 35 Birks, J. W., 50 Arnold, C. B., 146 Campbell, J. D., 13 Black, C., 35 Arnoldi, D., 69 Campbell, I. M.,61 Black, G., 59, 61, 64 Arnold, S. J., 64, 113 Camurny, A., 38 Black, J. G., 15 Aronowitz, D., 33 CapelIe, G. A., 48,49, 50, 53 Blair, L. S., 145, 191 Arrington, C. A., 80 Cargle, V. H., 37 Blanchard, M., 111, 112, 117 Aten, C. F., 52 Carlsten, J. L., 116 Bloembergen, N., 13, 15, 123 Atkinson, R., 35,64,66 Carmen, R.L.,123 Bogan, D. J., 67, 74 Audibert, M. M., 137, 138 Carpenter, B. K., 37 Borrell, P.,127 Auizonis, P. V., 112 Bott, J. F.,142, 144, 145, 146, Carr, R. W.,jun., 9, 10 Carrington, T., 42 147,150 Back, M. H., 23 Carter, W. P. L., 34, 38 Bowen, R. D., 2 Casas,F., 17 Baer, T.,6 Bowers, M. T., 6 Baghal-Vayjooee, M. H., 17 Case, D. A., 4 Bradbury, R. A., 111 Bailey, I. M., 19 Cashin, K. D., 62 Bradford, R. S., jun., 43,49 Bailey, R. T., 110, 124, 126 Chakroun, A., 159, 171 Bradley, C. C., 115 Chalek, C. L., 50,51 Baldwin, J. E., 22 Bradley, J. N., 33 Balquist, J. A., 38 Chan, W. H., 35 Braithwaite, M., 79 Chang, H. W., 74,146 BardorlT, W., 12 Braslavsky, S.,2 Chang, J. S., 35 Barker, J. R., 5, 15 Brau, C.A., 130 Chang, R. S., 146, 158 Barnard, J. A., 9, 18 Brau, W.,50 Chang, T. Y.,113, 117 Baronavski, A., 154, 174 Brauman, J. I., 2, 15 Chao, K.-J., 5 Bass, H. E.,129 Braun, R.,21,22 Chapuisat, X.,39 Basilevsky, M. V., 41 Braun, W.,15, 173,195 Bates, D. R., 72 Chantry, G. W.,115 Breen, W.,61 Chen, D. R.,37 Bates, R. D., 124, 191 Brechignac, Ph., 166 Batt, L.,32, 33 Chen, H.L., 138, 150, 154,156, Brenner, D. M., 39 157, 174 3auer, S. H., 140 Breshears, W. D., 127, 135, 136, Chen, Y.R.,13 3ayer, K. D., 35 145, 191 Cheng, J.-T., 35 Brewer, R. G., 179 3ayrakqeken, F., 35 Cheo, P. K., 11 Bridges, T. J., 111 3eadle, P. C., 32 Broida, H. P., 43, 45, 49, 50,55 Chesnavich, W. J., 6 kcker, K. H., 62, 67, 80 Brom, J. M., 50 Cheung, J. T., 6 3eckhaus H.-D., 33 'See also Supplementary Author Index, p. 229 223

224

Author Index

Chevalier, M. P., 160 Chintapalli, P.S. R. K.,62 Chirkin, N. N., 65 Choo, K. Y.,32, 35 Clarke, T. C., 40 Clements, A. D., 9, 21 Clerc, M., 116 Cocks, A. T., 9,18 CofJket, 1. P., 122 Coggiola, M. J., 13, 63 Cohen, J., 116 Cohen, N., 145, 146, 147, 150 Coleman, P.D., 160 Collister, J. L.,34 Connon, H. A., 23 Cooks, R. G., 6 Cool, T. A., 135, 142, 143, 144,

Dienes, A., 192 Dill, B., 17 Dillon, T. A., 131 Ding, A. M. G., 69 Dingle, T. W., 61 Dinur, U., 72 Djeu, N., 79 Dobbie, R. C., 135 Doering, W. von E., 21, 38, 39 Dolbier, W. R., jun., 21 Donovan, R. J., 150 Dorko, E., 18 Douglas, D. J., 69, 70, 71 Downey, G. D., 80 Dows, D. A., 13 Doyenette, L., 150, 156, 158,

145, 146,158,164, 172,174 Coombe, R. D., 71 Concha, F. J. M., 67

Druliinger, R. E.,43 Dubois, L. H., 50 Dubost, H., 123, 195 Ducuing, J., 117, 122, 137, 138

Conner, C. P., 60 Cotter, D., 116 Cotter, T. P.,199 Cottrell, T. L.,127, 129, 135 Coder, J. A., 35 Cowley, L, T., 69 Cram, D. J., 38 Crawford, R.J., 38 Crim, F. F., 10 Crowder, G., 126 Cruickshank, F. R., 110, 124, 126 Csizmadia, I. G., 40 Curl, R. F., 121 Current, S., 39 Curry, R., 11 Cvetanovic, R. J., 10, 19, 61 Daly, M., 33 Damon, R., 18 Danby, C. J., 7 Darling, J. R., 67 Darnell, K. R.,34 Davies, J. H., 23 Davidovits, P., 56 Davis, D. T., 111, 112 Dean, A. M., 18 Decker, C. D., 115 Deeds, W.E., 146 DeMaria, A. J., 110 de Martini, F., 122 De Meijere, A., 23 Denes, A. S.,40 Dennis, R.B.,115 Derrick, P. J., 2 Dervan, P. B., 39 DeTemple, T. A., 160 Deutsch, T. F., 113, 117 Dever, D. F., 14 Devonshire, A. F., 128 Dewar, M. J. S., 30, 41, 67, 68 Dewey, C. F., 115 Dickson, C. R., 45, 50 Diebold, G. J., 52

159, 171

142

Duewer, W.H., 74 Duff, J. W., 7, 129 Dunn, P.C., 116 Dunbar, R. C., 13 Durana, J. F., 5, 76, 80 Dyer, P.E., 112 Eaker, C. W.,67 Earl, B. L.,169, 178, 184, 186 Eckstrom, D. J., 43,45,48 Edelstein, S. A., 45, 48 Eisenhuth, L.,23 Eland, J. H. D., 7 Ellison, G. B., 11 Engelke, F., 51, 52, 63 Enoch, H. O., 21 Erler, K., 35 E r s t , J., 18 Estler, R. C., 63 Evans, K., 6 Evans,P.J., 18 Eng, R. S.,115 Eveleth, E. M.,67 Eversole, J. D., 43 Eyring, H., 69

I?aler, G., 67 I%rrer, J. M.,5 46,55 I?elder, W., I?eler, G., 67 ITeinstein, S. A., 9 I?enstermacker,C.H., 111 1'errero, J. C., 21 I'ertig, M. N., 196 I?etterman, H. R., 115 1?ield, D., 35 1'ield, R. W., 45, 49, 53 1'igueira, J. F., 111 1?inlayson, B. J., 66 1'inzi, J., 158, 161, 172 1'ischer, C. H., 117 1'isk, G. A., 10

Fleming, R.H., 22 Fleming, R.N., 116 Flowers, M. C., 18 Flygare, W. H., 121, 179 Flynn,G. W., 14, 16, 110, 121, 124, 158, 167, 169, 175, 177, 178, 181, 182, 191, 197 Flynn, R. H., 18 Fontijn, A,, 46, 55 Foos, J. S., 23 Foote, C. S., 67 Ford, G. P.,30,41 Forst, W., 3, 9, 17, 18 Fortin, R., 111, 112, 117 Foster, H., 111 Fourier, M., 121 Fujisawa, A., 113

Frank-Neumann, M., 39 Frankel, D. S., 13 Freasier, B. C., 9 Freed, K.F., 7 Freedman, P.A,, 61 Freund, S., 121 Frey, H. M.,1, 9, 11, 21, 39 Frey, R., 116, 117, 142 Fried, S. F., 144 Friedman, N. E., 143, 146 Friichtenicht, J. F., 45 Gabelnick, S.D., 50 Gailar, N. M.,146 Gait, P. D., 131, 135, 159, 199 Gajewski, J. J., 21, 22 Galatry, L., 129 Gamss, L.A., 160,181,183,198 Ganguli, P. S.,79 Ganley, J. T., 115 Gann, R. G., 67 Gartner, E. M., 61, 62 Gelernt, B., 61 Gemmer, R. V., 39 Gerberich, H. R., 23 Gerry, E. T., 158, 160 Gibson, A. F., 119 Gilbert, J., 111, 112, 117 Gilbert, J. R.,79 Gill, E. K.,13 Girard, A., 112 Glanzer, K., 163 Glass, A. M., 119 Glassman, I., 42 Glatt, I., 15 Gleaves, J. T.,76, 79 Goddard, W.A., tert., 11, 67 Golde, M. F., 42,47, 61 Golden, D. M., 15,32,35,36,37 Gole, J. L., 50 51, 56, 59, 60 Golomb, D., 60 Gondhalekar, A,, 112 Goodman, M.F., 13 Gordon, A. S., 33, 34 Gordon, J. P., 192 Gordon, P. L., 190 Gooch, C. H., 113

Author Index Gould, R. K., 46 Gorokhov, A., 13 Gosavi, R.K., 40 Gower, M. C., 164 Grabiner, F. R., 124, 169, 182 Grant, E. R.,7 Grazuyk, A. Z., 116 Green, W. H., 144, 149, 163, 164,170

Greenberg, A,, 2 Greiner, N. R., 112 Griffin, A. C., 41 Griller, D., 36 Grimm, U.,18 Gringolini, P.,4 Groth, W.,62 Grunwald, E., 14, 16 Gueguen, H., 158, 159, 171 Guillory, W.A., 16 Giisten, H., 66 Gutman, D., 79

225 H[erlemont,F.,121 H[erm, R. R.,56 H erman, Z., 6 H.erschbach, D. R., 51, 56 H ertzler, B. L., 79 H erzfeld, K. F., 127 H essel, M. M., 43 H eutz-Aubert, M.,160, 161 H exter, R. M., 188 H eydtmann, H., 12, 17,72 H iatt, R., 36 H ildenbrand, D. L., 59 H ill, G. A., 14 H inchen, J. J., 144, 146 H inze, J., 67 H ippler, H., 6, 35 H oag, E.,160 H obbs, R.H., 146 H ocker, L. O., 115, 158 H offman, R.,22,38 Holbrook, K. A., 1 H olmes, B. E.,11 H olmlid, L., 7 H olzhauer, E., 112 Hooper, D. G., 33 H opf, H., 23 H opkins, B. M., 138, 150, 154,

Haan, N.H., 12 Haas, Y.,199 Hadley, S. G., 49 Hager, G., 49 Hall, L. H., 48 Hancock, G., 13, 132, 165 156, 174 Hancock, J. K., 140, 144, 149, H ordvik, A., 111, 121 163, 164, 170, 171 Horie, O., 12 H anna, D. C., 116 H ome, D. S., 69 H ansen, D. A., 66 H orowitz, G., 21 H amen, H.-J., 30 H orsley, J. A., 37 H arding, L. B., 11 H oureiz, J., 121 H arding, L. R., 67 H ouston, P.,191, 193 H overson, S. J., 117 H ariri, A., 146 H arper, W., 130 H su, C. J., 52 H u, B., 158 €4arrington, R. E., 12 Harris, D. O., 45 H udgens, J. W.,76, 79 H uestis, D. L., 45 Harris, N., 117 H arris, R., 49, 199 H ui, K.-K., 164, 174 H usain, D., 150 Harrison, A. G., 2 Harrison, F.B., 115 H uybrechts, G., 39 H ymen, B., 21, 22 H art, G. A., 113 Hart, R. R., 131 Ibaraki, T., 60 Hartford, A., 195 Ibuki, T., 12 Harvey, A. B., 116 Inamoto, N., 67 Hase, W. L., 6, 7, 36 Ingold, K. U., 36 Hasselmann, D., 39 Inocencio, M. A., 67 3 ayward, R. J., 4 -I eckenberg, N. R.,112 Ireton, R., 33, 34 Ironside, C. N., 115 -echt, I J., 46 Isolani, P. C., 178 iehre, W. J., 41 4eicklen, J., 2 Jackson, G. E., 9 -Ieidner, R. F., 62, 146, 147 Jackson, J. M., 128 deller, D., 6 Jackson, W. M., 34 ienbest, R.L., 116 Jacobs, R. R., 159 ienderson, D., 69 James, D. J., 112 lenry, B. R., 2, 4 lenry, L., 150, 158, 159, 163, Javan, A., 146, 158, 160 Jayich, S. A., 9 171 Jean, Y.,37, 39 Ienry, J., 159 Jeffers, P.M., 9 lerbst, E., 11 Jeffers, W. Q., 164 Ierget, W. F., 146

Jenkins, J. A., 39 Jenson, R.J., 13 Jetter, H., 121, 179 Joffrin, C., 122, 137, 138 Jolicard, G., 129, 136 Jolly, D. L., 9 Johnson, R. L.,74 Johnston, H. S.,50 Jonathan, N., 73,146 Jones, C. R.,43,45,49, 146 Jones, H., 122 Jones, J. W.,61 Jones, R.W.,51 Jortner, J., 13 Jost, W.,69 Jung, J. H., 9 Just, Th., 18 Kaduk, B. A., 66 Kaldor, A., 173, 195 Kano, S., 195 Kaplan, H., 72 Karkkainen, P.A., 116 Karny, Z., 16 Kassal, T., 127 Katz, T. J., 23 Kaufman, F.,35, 61, 69, 79 Kay, K. G., 3 Kaye, R. L., 39 Keehn, P.,14 Keil, D. G., 9, 35 Kelley, J. D., 164 Kelley, M. J., 160 Kennedy, G. J., 11 Keough, T., 6 Kerker, M., 123 Kern, C. W., 164 Kerr, J. A., 17 Keval, J. S.,111 Khan, A. U., 64 Khe, P. V., 35, 36 Kiefer, J. H., 137 Kikuchi, O., 41 Kildal, H., 113, 115, 117 Kim, K. C., 6,74 Kimbell, G. H., 64 Kimel, S., 13, 110 Kimmitt, M. F.,119 King, D. S., 14 Kirk, A. W., 11 Kirmse, W., 21, 38 Kirsch, L. J., 69 Kirschner, S., 41, 67 Kishimoto, T., 128 Klein, I. E., 9 Kleinermanns, C., 15 Kley, D., 62 Klots, C. S., 6 Knishkowy, B., 14 Knudtson, J. T., 124, 182, 191 KO,A. N., 5 Kodera, K., 60 Kohler, F.,122 Kohn, B. H., 181, 183

Author Index

226

Matsui, H., 140 Maya, J., 55 Maylotte, D. H., 70 Meagher, J. F., 5 Melliar-Smith, C. W.,73, 146 Melngailis, I., 113 Menard, J., 156 Menne, T. J., 113 Menzinger, M.,45,51,54,59,65 Meyer, H., 2 Meyer, J., 112 Meyer, L.-U., 23 Mianoto, Y.,128 Michael, J. V.,35 Mia, F. H., 128 Mikkelson, J. C., 115 Milam, D., 111 Miller, R.G., 140 Miller, W. H., 2, 3 Millikan, R.C., 164 Milne, R. T., 32, 33 Mil'vitskaya, E. M., 2 Lachambre, J. L., 111, 112, 117 Maccoll, A., 33 Milward, R. C., 181 McCluskey, R. J., 9, 10 Lahmani, F.,11 Mims, C. A., 58 McCoubrey, J. C., 127, 181 Laidler. K. J., 13 Mintz, K. J., 10 Lambert, J. D., 181, 192 McCullough, R. D., 32, 33 Mishra, A., 38 McDonald, J. D., 5,6,7,76,79, Landau, L., 127 Moehlmann, J. G., 76 80 Langsam, Y.,187, 188 Montgomery, F. C., 67 MacDonald, R. G., 154 Laupert, R., 12 Montroll, E. W., 127 Lechtken, P., 67 McFadden, D. L., 47, 56 McFarlane, R. A., 79, 146, 148 Mooradian, A., 113, 115 Lecuyer, A., 160 Moore, C. B., 110, 116, 125, McGarvey, J. A., 143, 146 Lee, A., 6 127, 135, 150, 154, 157, 158, Lee, E. K. C., 2 McGee, J. D., 117 . Lee, H. U.,52, 54, 58, 65 McGuire, P., 137 161, 167, 172, 179, 188, 196, 197 Lee, P. H., 46 McGurk, J. C., 121, 179 Morgan, R.P., 2 Lee, R. K. Y., 9 McIver, J. W., jun., 41 Mosburg, E. R., 163 Lee, S. M., 179, 181, 187, 188 Mack, M. E., 123 Lee, Y. T., 5, 13, 63 McKay, G., 33 Moser, C., 37 Moss, D. G., 115 Legan, F., 123, 166, 195 McKee, M. L., 30 Mott, N. F., 128 Leland, W. T., 115 McKenzie, R. L., 129 Mueller, G. W., 18 Lemaire, J., 121 McLain, J., 135 Leone, S. R., 116, 154 McNeil, K. J., 112 Mukamel, S.,5, 13, 14 Murawski, H.-R., 21 Le Poutre, F., 161 McNeish, A., 115 McNesby, J. R., 34 Leroy, G., 41 My. L. T., 66 Leroy, R. J., 6 Mae, G., 130 Makarov, G. N., 13 Naegeli D., 33, 42 Lesclaux, R., 35, 36 Maki, A. G., 188 Nazar, M. A., 72 LeSieckl, M. L., 16 Lester, W. A., jun., 137 Malherbe, R., 39 Nederbragt, C. W., 65 Nelson, L. Y., 117 Letokhov, V. S., 13 Maloney, P. J., 112 Nemarich, J., 115 Levine, A. K., 110 Malt, R. B., 132 Nielsen, A. H., 146 Levine, R. D., 72, 129 Manion, M. L., 21,22 Nikitin, E. E., 3, 148 Levy,J. M., 121 Mann, D. M., 65 Noble, P. N., 156 Lewis, D. K., 9, 33 Manos, D. M., 50 Liebman, J. F.,2 Mansell, P. I., 7 Nordholm, S.,4, 9 Manuocia, T. J., 117 Nordine, P. C., 55 Lieu, Y.S., 79 Light, J. C., 3, 127 Marcus, R. A., 3, 7, 36 Norris, G. L.,121, 179 Lin, M. C., 12 Margottin-Maclou, M., 150, Noter, Y., 130, 159 156, 158, 159, 171 Lin, S. T., 186 Novak, A. V., 121, 190,193 Marriott, R., 160 Noyes, R. M., 37 Lindquist, G. H., 146 Marshall, R. M., 32, 33 Lindsay, D. M., 50, 60 Marta, F., 34 Obenauf, R. H., 52 Lineberger, W. C., 11 Martin, G., 33 OgryAo, E. A., 80 Linton, C., 50 Lippman, H., 80 Mason, R. S., 61 Oka, K., 61 Litowitz, T. A., 127 Matheson, A. J., 135 Oka, T., 121 Matten, A., 12 Liu, J. C., 67 Okuda, S., 73 Kominar, R. J., 33 Kompa, K. L., 199 Koski, A. A., 33 Kosloff, R., 72 Koster, D. F., 14 Kovacs, M. A., 123, 158 Krauss, M., 50, 128 Krech, M. J., 33 Kreiner, W. A., 121 Krenos, J. R.,48, 56 Kressel, H., 113 Krogh, 0. D., 74 Krugh, W. D., 52 Kubin, R. F., 12 Kukolich, S. G., 121 Kung, R. T. V., 169 Kurylo, M. J., 50, 173, 195 Kushawaha, V. S., 50 Kusonoki, I., 60 Kwok, M. A., 134, 146, 147

Liuti, G., 62, 63 Lloyd, A. C., 34 Loh, L. C.-H., 56 Loucks, L. F.,33 Louisell, W. H., 112 Love, P. J., 46 Lovell, R. J., 146 Lubman, D., 63 Lucht, R. A., 144,145 Lui, M. T. H., 33 Lukasik, J., 122, 137, 138, 142 Luria, M., 43,48 Luther, K., 6 Luther-Davies, B., 116 Lutz, R. W., 137 Lutzer, H., 33 Luyckx, L., 39 Lyman, J. L., 13, 15 Lynch, K. P., 35 Lynch, T. R., 38

Author Index Oldenborg, R. C., 50 Olmstead, W. N., 2 Olszym, K. J., 14 O’Neal, H. E., 1,38,67 ONeil, S. V.,11 O’Neill, F.,117 Orth, R., 13 Osburg, L. A., 164 Osgood, R. M., 117, 146 Overend, R., 35 Oxtoby, D. W., 7 Palmer, H. B., 52 Papayoanou, A., 113 Paraskevopoulos, G., 35 Park, W.,130 Parker, J. H., 74 Parkes, D. A., 32,35 Parh-Smith, D., 192 Parrott, T. K., 9, 18, Parson, J. M., 5, 50 Patel, C. K.N., 192 Pattengill, M., 35 Paul, W., 114 Payne, W. A., 35 Pearson, E. F., 121, 179 Pederson, L.D., 37 Penner, A. P., 9, 18 Penzhorn, R., 66 Perez, M., 190 Perona, M. J., 35 Perry, B. E., 48 Perry, D. S., 69, 71, 72 Perry, R. A., 35 Petersen, A. B., 146 Peterson, L. M., 146 Pettipiece, K. J., 159 Peyron, M., 66 Picard, R. H., 131, 132 Pidgeon, C. R., 115 Pilling, M. J., 35 Pimentel, G. C., 71, 74,156 Pine, A. S., 115 Pirkle, R. J., 142 Piszkiewicz, L., 32, 35 Pitts, J. N., jun., 34, 35, 66 Plate, A. F.,2 Poland, H. M., 58 Polanyi, J. C., 42, 69, 70, 71,72 Pollack, M. I., 183 Ponsen, G. T., 160 Pottinger, R., 39 Potzinger, P., 12 Poulsen, L.L., 193 Powell, H. T., 164 Pradere, F.,116, 117 Pratt, G., 35, 36 Preses, J. M., 14,121, 178 Preuss, D. R., 50,56, 59 Price, J. J., 129 Price, S. J. W., 33 Price, T. J., 161 Pritchard, H. 0.,4, 11, 17, 34 Proch, D., 199

227 Pruett, J. G., 45 Pugh, D., 124, 126 Purnell, J. H., 32, 33 Putley, E. H., 119

Ross, J., 5, 14 Rosser, W. A,, 158, 160

Quack, M., 1, 36 Quero, E. D., 21 Quigley, G. P., 146, 148 Quinn, C. P., 32,35

Roth, P., 18 Rubin, R. J., 127 Riichardt, C., 33 Rullman, H., 12 Rynbrandt, J. D., 4 Rynefors, K., 7 Rzepa, H. S., 30

Rabinovitch, B. S., 2,4,5, 8, 9, 12,38 Rabitz, H., 137 R a , L. M., 129 Ramunni, G., 41 Rankin, C. C., 127 Rao, D. R., 158 Rao, J. S., 158 Rao, Y.V. C., 158 Rapp, D., 127, 129 Read, A. W., 135 Ream, N., 129 Rediker, R. H., 114 Redon, M., 121 Redpath, A. E.,65 Rehm, R. G., 129 Reichelt, W. H., 111 Reimann, B., 12 Reinhardt, W. P., 11 Reintjes, J., 123 Renner, C.A., 23 Resler, E. L.,140 Revelli, M. A., 45, 53 Rheault, F., 111, 112, 117 Rhodes, C. K., 158, 160 Rice, S. A., 6, 7, 116, Rich, J. W., 129 Richard, C., 23 Richardson, M. C., 111 Richardson, T. H., 10, 15 Richardson, W. H., 67 Richey, H. G., 21 Rickwood, F.F.,112 Riggin, M.,13 Rigny, R., 116 Rink, J., 13 Roberts, D. R., 67 Robertson, J. A., 35 Robinson, C. P., 13, 126 Robinson, D. W., 80 Robinson, G. W., 123 Robinson, P. J., 1 Roche, A. E., 61 Rockwood, S. D., 13 Rogers, G. J., 35 Rojiska, H., 113 Ronn,A. M., 124,169,177,178, 179, 181, -183, 184, 186, 187, 188, 198 Rosen, D. I., 172, 174 Rosenfeld, R. N., 15 Rosenwaks, S., 50, 55 Ross, D., 110

Sachdev, K., 21,38 Sackett, P. B., 121, 146 Sakurai, K., 50 Salem, L.,37,39,41 Salter, R., 181 Sam, C. L., 115 Samanos, J., 66 Sam, M., 41 Sander, R. K., 6, 51 Sathyamurthy, N., 129 Sattler, J. P., 115 Scacchi, G., 23 Scaiano, J. C., 23 Schaap, A. P., 67 Schaefer, J., 137 Schappert, G. T., 111 Scheller, K., 18 Scheps, R., 6 Schippa, B., 63 Schlag, E. W., 38 Schlossberg, A., 111 Schlossberg, H., 121 Schmid, H., 30 Schore, N. E., 67 Schreiber, J. L., 69 Schuler, K.E., 127 Schulz, P. A., 13 Schurath, U. S., 66, 67, 80 Schuster, G. B., 67 Schwartz, R. N., 127 Schwarz, S. E., 190 Scott, G. L., 145 Scragg, T., 115 Scully, M. O., 112 Secrest, D., 127 Seeber, K. N., 160 Seery, D. J., 132, 156 %gal,G., 41 Semmelhack, M. F., 23 Setser, D. W., 11,15,73,74,146 kyrnour, R. J., 115 Shamah, I., 16 Shamov, A. G., 41 Shanker, R., 50 Sharma, R. D., 130, 132, 154, 158, 160,164 Sharpless, R. L.,59, 61, 64 Shaw, J. H., 35 Shea, K. J., 23 Sheinson, R. S., 66, 67 $hen, K. K., 12 Shih, H., 112 Shimanouchi, T., 188 Shimizu, T., 195

Author Index

228 Shin, H. K., 127, 129, 132, 134, 136, 145 Shoemaker, R. L., 179 Shortridge, R. G., 12 Shull, D. W., 21 Shuman, M. E., 61 Siebert,D. R.,124,167,169,175 Siegman, A. E., 112 Simm, I. G., 7 Simmie, J. M., 159 Simons, J. W., 10, 11 Simpson, C. J. S. M., 129, 159, 161 Singleton, D. L., 19, 61 Skinner, G.B., 9 Skrlac, W. J., 72 Slafer, W. D., 46 Slagle, I. R., 79 Slanger, T. G., 59, 61, 64 Slater, D. H., 73, 146 Slater, R. C., 169 Slawsky, 2. I., 127 Sloan, J. J., 69, 70 Sloane, C. S., 6 Slusher, R. E., 192 Small, R. D., jun., 23 Smith, D. J., 74 Smith, D. L., 111, 112 Smith, G. P., 37 Smith, I. W. M., 35, 36, 42, 61, 70,79,132,146,154, 165,166 Smith, J. H., 80 Smith, P. W., 112 Smith, R. A., 9,21 Smith, R. C., 116 Smith, S. D., 115, 126 Snelling, D. R., 64 Soep, B., 6 Solly, R. K., 23 Sorensen, G. B., 139 Soulignac, J. C., 35, 36 Southall, L. A., 49 Spangler, C. W., 2 Speiser, S., 13, 110 S p i d e r , K., 18 Sridharan, U. C., 47, 56 Srinivasan, G., 164 Staricco, E. H., 21 Starr, D. F., 163, 164, 170, 171 Steele, R. E., 50, 55 Steele, R. V., 154 Stein, S. E., 4 Steinberg, M., 46 Steinfeld, J. I., 121,190,191,193 Steinmetzer, H. C., 67 Stephens, R. R., 135 Stephenson, J. C., 14, 131, 158, 162, 163, 167 Stephenson, L. M., 39 Stettler, J. D., 130, 131 Stevens, R. M., 37 Stevenson, C. D., 150 Stevenson, T. S., 113 Stewart, G. W., 60

Stone, D. K., 74 Stone, J., 13 Storey, P. D., 32, 33 Stratton, T. F., 111 Strausz, 0.P., 40 Stregack, J. A., 113, 117 Stretton, J. L., 192 Struve, W. S., 56 Suchard, S. N., 48, 62 Suhre, D. R., 160 Sung, T. P., 73, 74 Sutton, D. G., 62, 121, 190, 191 Swinehart, D. F., 4 Szeklas, E. A., 112 Szirovicza, L., 34 Szoke, A., 111, 130, 159 raieb, G., 166 rakayanagi, K., 127, 128 rakezaki, Y., 12 ram, A., 130 rang, S. P., 45 Tanner, D. D., 33 Tarakanova, A. V.,2 Tardy, D. C., 2, 8, 33, 34 Taylor, R., 31 Teller, E., 127 Thibault, J., 121 Thiel, W., 68 Thomas, S. J., 159 Thompson, D. L., 129, 146 Thorne, M. P., 31 Thrush, B. A., 42, 61, 62 Tiee, J. J., 117 Tikhomirov, V. A., 41 Timlin, D., 73 Tinti, D. S., 123 Tittel, F. K., 115 Toby, F. S., 66 Toby, S., 66 Tomlinson, W. J., 192 Tonnies, J. P., 137 Townshend, R. E., 41 Treanor, C. E.,129 Tremblay, R., 117 Trenwith, A. B., 33 Troe, J., 1,2,4,6,8,9, 17, 35, 36 Trotman-Dickenson, A. F.,11, 17 Trudwell, B. C., 33 Truhlar, D. G., 129 Tsang, W., 10, 15, 33, 36 Tsuikow-Roux, E., 18 Tsuji, A., 12 Tully, J. C., 6,48 Turner, J. M. C., 33 Turro, N. J., 23, 67 Tverdokhebov, V. I., 65 Ubbelohde, A. R., 181 Umanski, Ya. S., 148 Umpstead, M. E., 12 Ung, A. Y.-M., 61 Uselman, W. M., 35

Utterback, N. G., 45 Valentini, J. J., 63 Vandenboom, Th., 39 van den Burgh, H.,17 Van der Horst ,A., 65 Van Duijn, T., 65 van Mele, B., 39 VanPee, M., 62 VanZee, R. J., 64 Veltman, I., 35, 36 Verma, R. D., 50 Vidand, P., 62 Vilaseca, R., 138 Vuillermoz, A., 66 Wade, L. E., jun., 30 Wagner, H. Gg., 15, 18 Walker, A. C., 112, 119 Walker, B., 115 Walls, D. F., 112 Walsh, R., 1, 6, 9, 19, 30 Walters, W. D., 23 Wang, C. H., 192 Wang, F.-M., 5 Wang, J. H. S., 121 Wanner, J., 70 Washida, N., 35, 62 Wassam, W. A,, 129 Weber, B. A., 115 Weber, M., 67 Weber, R. J., 21, 22 Wehrli, R., 30 Weisman, R. B., 116 Weitz, E., 110, 177 Welge, K. H., 13, 64 Weller, H. N., 23 Wendling, L. A., 40 Werner, A. S.,6 West, J. B., 43, 50, 58 West, K. O., 33 Weston, R. E., jun., 14 Wexler, B. L., 113,117 Whitehead, J. C., 52, 63 Whitney, W. T., 117 Whytock, D. A., 35 Wiberg, K. B., 23 Wicke, B. G., 45 Wilkins, R. L., 134, 146 Willcott, M.R., tert., 37 Williams, D. H., 2 Williams, F. W., 67 Williams, G. J., 179 Wilson, J., 113 Wilston, D. J., 129 Winer, A. M., 34 Wiswall, C. F., 113 Witriol, N. M., 130, 131 Wittig, C., 117, 146, 165, 166 Wodarczyk, F. J., 354 Wolfgang, R., 6 Wolfrum, J., 69 Wolga, G. J., 79, 146, 148, 158 Wong, W. A,, 36

229

Author Index

Wood, A. D., 158 Yamakawa, H., 67 Zahniser, M. S.,35 Wood, 0.R., 112, 117, 163, Yardley, J. T., 110, 158, 170, m e , R.N.,6,16,33,45,50,51, 190

179, 196

Wood, R., 113 Wood, R. A., 115 Wood, R. E., 158, 167 Wren, D. J., 51 Wright, R.S.,37 Wrigley, S. P., 33 Wyatt, R.,116

Yau, A. W., 4,17 Yeh, C.-T., 35 Yekts, A., 67 Yelvington, M.B., 67 Yogev, A., 15, 199 Yokozeki, A., 45, 51 Yuan, R.C. L.,197

Yablonovitch, E., 15 Yabuuchi, H., 33

Zabarev, I. G., 116 Zabel, F., 18

52, 54, 58, 63,65

Zarur, G., 137 Zeller, K. P., 2 Zellner, R., 35, 37 Zener, C., 129 Zeppenfeld, M., 21, 38 Zernike, F.,115 Zittel, P. F., 11, 125, 150, 197 Zitter, R. N., 14 Zvijac, D. J., 3, 5 Zwillenberg, M. L., 42

Supplementary Author Index* Arthurs, A. M., 104 Ashmore, P. G., 106 Bader, R. F. W., 201,215 Baer, M., 205 Balint-Kurti, G. A., 201 Barker, J. R., 97 Bauer, A., 89 Bauschlicher, C. W., 219 Baylis, W. E., 94 Bender, C. F., 219 Bernstein, R. B., 101, 104,200 Black, G., 98 Blythe, A. R., 104 Bogey, M., 89 Booth, D., 207 Bowman, J. M., 204 Brau, C. A., 91 Braum, W.,98 Brewington, R. B., 219 Broida, H. P., 98, 105 Brown, R. L.,88 Brown, S. R., 107 Byberg, J. R., 221 Callear, A. B., 84, 90, 95, 98, 100, 108

Carrington, T., 105 Carter, S.,207, 212 Chapman, S., 104 Chapuisat, X.,204 Clyne, M. A. A., 106,221 Connor, J. H., 100 Connor, J. N. L.,204 Coombe, R. D., 98 Curran, A. H., 106 CvetanoviC, R. J., 97 Czajkowski, M., 101

Dalgarno, A., 94, 104 Daly, P. W., 106 Dashevskaya, E. I., 93, 103 Davidson, J. A., 100 Dillon, T. A,, 93 Dixon, D. A., 220 Donovan, R. J., 99, 106 Dunning, F. B., 108 Dunning, T. H., 96 Ellison, F. O., 205 Fabris, A. R., 106 Farantos, S.,210,212, 221 Faubel, M., 105 Fletcher, I. S.,96, 100 Flygare, W. H., 107 Flynn, G. W., 87 Freund, S. M., 107 Fushiki, Y., 101 Gallagher, A., 94 Gangi, R.A., 201,215 Geide, K., 104 Gentry, W. R., 105 Giese, C. F., 105 Gittings, M. A., 217 Gray, S. K., 204 Green, S., 104 Grosser, A. E.,104 Hammond, G. S.,202 Hancock, G., 91 Hariri, A., 98 Hay, P. J., 96 Hedges, R. E. M., 108 Heidner, R. F., 96

[erbst, E., 217 [erman, V.,88 [erschbach, D. R., 220 [ertel, I. V., 98 [erzfeld, K. F., 84 [inchen, J. J., 106 1 [irst, D. M., 217 I [obbs, R. H., 106 I [ofmann, H., 98 I [ofmann, R. T., 107 I ioriguchi, H., 97 I :award, C. J., 100 I [su, D. S. Y., 98 I hsain, D., 96, 99, 100 I I I I I I

Jakubetz, W., 204 Jennings, D. A., 98, 100 Jeyes, S. R., 106 Johns, J. W. C., 107 Johnson, B. R., 85 Julienne, P. S.,96 Karl, G., 98 Karplus, M., 201, 217 Kassal, T., 83 Kate, K., 106 Kellerhals, G. F., 204 Kellert, F. G., 108 Kendall, G. M., 105 Klemperer, W., 88, 105 Kolos, W., 219 Krause, L., 101 Krauss, M., 96 Kriiger, H., 88 Kruus, P., 98 Kuntz, P. J., 201, 205 Kuppermann, A., 204

* Owing to an error in the original compilation of the Author Index names appearing in Chapters 3 and 5 were omitted and are therefore given in this Supplement.

Author Index

230 Lambert, J. D., 84, 86, 90 Landau, L., 96 Lang, N. C., 106 Lees, R. M., 106 Leisegang, E. C., 210 Leone, S. R., 98 Le Roy, R. L., 206 Levine, C., 200 Levine, R. D., 101 Lin, M. C., 98 Linder, F., 88 Liskow, D. H., 219 Liu, B., 217 London, F., 204 Lucchese, R. R., 202

M cCaffery, A. J., 106 M cGurk, J. C., 107 M cKellar, A. R. W., 107

Ogilvie, J. F.,209 Oldman, R. J., 95, 105, 107 Pearson, P. K., 207 Persky, A., 205 Petersen, A. B., 98 Polanyi, J. C., 98, 106, 205 Porter, R. N., 217 Pritt, A. T., 98 Quigley, G. P., 98 Raff, L. M., 204 Rapp, D., 83 Rasmdssen, K., 201 Reid, R. H. G., 94 Reznikov, A. I., 93 Rosner, S. D., 205 Rost, K. A., 98 Rowe, M. D., 106 Rundel, R. D., 108

M claughlin, D. R., 204 M aes, S., 89 Sacket, P. B., 98 M ahan, B. H., 90 Sadowski, C. M., 100 M anz, J., 204 Salter, R., 86 M illikan, R. C., 83 Sathyamurthy, N., 204 M ills, I. M., 212 M inn, F. L.,217 Sato, S., 204 Schaeffer, H. F., 202, 207,219 M offitt, W., 206 Schiff, H.I., 100 M oore, C. B., 88 Schinke, R., 88 M ‘ori, Y.,221 Schmeltekopf, A. L.,100 M iuckerman. J. T.. 205 Murrell, J. N., 201, 204, 205, Schmidt, H., 88 Schwartz, R. N., 84 207, 210,212,220,221 Secrest, D., 85 Sentman, L.H., 106 Sharma, R. D., 91 Nemeth, E. M.,205 Shavitt, I., 217 Nieves, F.,219 Nikitin, E.E., 93, 103 Shimokoshi, K., 221 Siebert, D. R., 87 Nip, W. S., 221 Silver, D. M.,220 Novaro, O., 219

Skardis, G., 101 Slanger, J. G., 98 Slawsky, Z. I., 84 Smith, I. W. M.,91, 98 Smith, K. A., 108 Sorbie, K. S., 204,207,210,212 Stebbings, R. F.,108 Steinfeld, J. I., 105 Stephenson, J. C., 88,93 Stevens, R. M., 217,220 Streit, G. E., 100 Stretton, J. L., 87 Teixeira-Dias, J. J., 210 Thompson, D. L.,204 Toennies, J. P., 105 Tsuchiya, S., 97, 101 Van den Bergh, H. E., 105 Van Kranendonk, J., 206 Varandas, A. J. C., 205, 207, 210,212 Volga, G. J., 98 Voronin, A. I., 103 Wahlgren, U.,207 Wanner, J., 106 Weston, R. E., 97 Wilkins, R. L., 205 Wittig, C., 98 Wodarczyk, F.J., 98 Wood, P. M.,98 Wood, R. E.,88 Wright, J. S., 204 Young, C. E., 205 Zembekov, A. A., 103 Zener, C., 96,