Vibration-Vibration Energy Transfer in Gaseous Collisions By J. D. Lambert P H Y S I C A L CHEMISTRY L A B O R A T O R Y U N I V E R S I T Y OF O X F O R D 1 Introduction Most chemical reactions only occur when sufficient vibrational energy is acquired in a particular interatomic bond of the molecule concerned. The rate at which this energy is taken up or lost and the ease with which it can flow between the different molecular vibrational modes are thus of fundamental importance in chemical kinetics. In particular the various theories of unimolecular gas reac- tions are based on detailed assumptions about rates of energy transfer.l The conversion of translational into vibrational energy in molecular collisions has been extensively investigated by measurements on ultrasonic disperson and absorption.The velocity of propagation of an adiabatic sound wave in a perfect gas is given by and for a monatomic gas where molecular translational energy is freely inter- changed at every collision is independent of the sound oscillation frequency. This is no longer so for polyatomic gases where the quantised internal degrees of freedom do not freely interchange with translation. Supposing Plo is the probability per collision for a change in vibrational quantum number from 1 - 0 (and is less than unity) the average number of collisions required for a molecule to lose one quantum will be Zlo - l/Plo. If 2 is the total number of collisions one molecule suffers per second a vibrational relaxation time p may be defined by the equation Since Zl0 the collision number is a constant and Z is proportional to the gas pressure fi will be inversely proportional to pressure.For convenience relaxa- tion times p are always referred to a pressure of 1 atm. Equation (2) is an approximation as the gas kinetic collision number 2 requires modifying by a factor taking into account the Boltmann distribution of molecules between quantum states. For a simple harmonic oscillator of fundamental frequency v the correct equation is; Z, - Z/3 [I - exp(- hv/kT)] (3) H. M. Frey Ann. Reports 1960 57 28. 67 Quarterly Reviews which approximates closely to (2) for high values of v. At sound frequencies where the period of the adiabatic oscillation becomes comparable with the vibrational relaxation time the vibrational temperature of the gas lags behind the translational temperature throughout the compression-rarefaction cycle and the effective values of C and V2 in eqn.(1) become frequency-dependent. This phenomenon occurs at ultrasonic frequencies and is known as ultrasonic dispersion; it is accompanied by a non-classical absorption of sound. Measure- ment of either may be used to obtain relaxation times. The measurement of vibrational relaxation times by ultrasonic and other (e.g. shock tube) methods has been fully discussed in an earlier Quarterly Review by McCoubrey and McGrath,2 and in other subsequent articles and books.3 Values of Z, are observed varying from a few collisions to several hundred thousand and showing an exponential dependence on the frequency of the relaxing vibrational mode. In addition for heteromolecular collisions the values are highly specific for the nature of the collision partner; for example C0,-H20 collisions are some lo3 times more efficient than C0,-CO collisions.Such in- efficient transfer and such a high degree of specificity are not in accord with observations on the kinetics of unimolecular gas reactions, and it was pointed out thirty years ago by Patat and Bartholom ‘ that vibration-vibration energy transfer between molecules is likely to be at least as important from the point of view of chemical kinetics as vibration-translation transfer.* Conventional ultra- sonic methods give no direct information about vibration-vibration transfer since the energy transferred remains internal and there is no effect on the adiabatic compressibility of the gas. But indirect information has recently been obtained from experiments on ultrasonic dispersion in polyatomic gases possess- ing several active vibrational modes and in their mixtures.This work forms the main subject of the present Review together with discussion of spectroscopic and theoretical sources of information about vibration-vibration transfer. 2 Intramolecular Transfer of Vibrational Energy. Ultrasonic Dispersion in Polyatomic Gases. Intramolecular transfer of energy between different vibrational modes of a polyatomic molecule can only occur in collision. The energy in the different modes is quantised and except in rare cases where there is exact resonance between harmonics the energy discrepancy must be made up by translational energy. For a molecule with two active vibrational modes of frequency v1 and v2 there are three possible vibrational transitions which are illustrated on the energy level diagram in Figure 1 (a) Transfer of translational energy to 0 - 1 excitation of the mode vl with relaxation time &.(b) Transfer of translational energy to 0 - 1 excitation of the mode v2 with relaxation time p2. (c) The a J. C. McCoubrey and W. D. McGrath Quart. Rev. 1957 11 87. K. F. Herzfeld and T. A. Litovitz ‘Absorption and Dispersion of Ultrasonic Waves’ Academic Press New York 1959; T. L. Cottrell and J. C. McCoubrey ‘Molecular Energy Transfer in Gases’ Butterworths London 1961 ; J. D. Lambert ‘Atomic and Molecular Processes’ ed. Bates Academic Press New York 1962 ch. 20. F. Patat and E. BartholomB 2. phys. Chem. 1936 B,32 396. 68 Lambert complex transfer of quantum of vibrational energy from mode vl plus the necessary increment of translational energy to give 0 3 1 excitation of the mode v2 with relaxation time P12.FIG. 1. Energy-level diagram showing possible transitions for a molecule with two active Vibrational modes. For the majority of polyatomic molecules which have been investigated experimentally a single relaxation time is observed corresponding to relaxation of the whole of the molecular vibrational energy. This means that P2 9 PI & Pl2. Vibrational energy thus enters the molecule via process (a) which is rate-control- ling and rapidly flows in complex collisions via process (c) to the second mode (and any other higher modes). Process (b) is too slow to play any r81e. This mechanism is characterised by a single overall relaxation time 18 which can be shown to be related to 18 by the equation 18 = (C,/C,)/!? where C1 is the specific- heat contribution due to mode vl alone and C the total vibrational specific heat.The general picture is that rapid vibration-vibration transfer maintains con- tinuous equilibrium of vibrational energy between the various fundamental modes of the molecule and that the whole of this energy relaxes in a single vibration-translation transfer process via the lowest mode.5 For a few molecules in all of which there is a large difference between v2 and vl the rate of the complex process (c) is much slower and the condition P2 9 P12 > applies. Process (b) is again too slow to play any rsle but process (a) is now faster than process (c). A double relaxation phenomenon results. The vibrational energy of v2 (and any upper modes) relaxes via complex process (c) followed by the faster process (a).Process (c) is thus the rate-determining step and the vibrational energy of the upper modes is transferred with a relaxation time PI2. The vibrational energy of the lowest mode vl relaxes independently by process (a) with the shorter relaxation time PI. This behaviour has been observed for only three gases SO2 CH2C12,' and C2H6.5 The experimental data J. D. Lambert and R. Salter Proc. Roy. SOC. 1959 A 253,277. J. D. Lambert and R. Salter Proc. Roy. SOC. 1957 A 243 78; P. G. Dickens and J. W. D. Sette A. Busala and J. C. Hubbard J. Chem. Phys. 1955,23,787. Linnett ibid. 1957 A 243 84. 69 3 Quarterly Reviews are summarised in Table 1. Two relaxation times are observed p1 and Isl enabling calculation of the collision numbers Z, and ZI2 corresponding to processes (a) and (c) respectively.For all these molecules v > 215 and theore- tical considerations show that the complex step (c) is a transfer of energy between one quantum of mode v2 and two or three quanta of mode ul. (The frequency gap between v and the remaining upper modes is small in all cases and transfer between these is rapid.) Table 1 Experimental collision numbers for intramolecular vibrational energy transfer at 300°K Substance v Va i Au zia 210 (cm.-l) (cm.-l) (cm.-l) so2 519 1151 2 110 2390 390 CHZCl 283 704 2 140 460 30 C2H6 290 820 3 50 74 20 Z, is the collision number for vibration-vibration transfer between i quanta of mode Y and one quantum of mode v,. The general conclusion may be drawn that intramolecular vibration-vibration energy transfer between modes is usually faster than vibration-translation transfer from the lowest mode.In a few cases where there is a large frequency discrepancy between modes so that multiple quantum transfers are involved vibration-vibration transfer is slower. 3 Intermolecular Transfer of Vibrational Energy A. Ultrasonic Dispersion in Mixtures.-Much more information about vibra- tion-vibration transfer can be derived from ultrasonic measurements on binary mixtures. If a relaxing gas A is mixed with a non-relaxing gas B such as helium there are two collision processes by which vibration-translation energy transfer can occur (1) A* + A --t A + A (2) A* + B 3 A + B (vib. + trans.) (vib. -+ trans.). Since (1) and (2) will have different collision efficiencies the result will be a composite relaxation time for A given by 1 1-x x E=7zF4G where x is the mole fraction of B in the mixture &u is characteristic of process (l) and /IAB of process (2)? This can be represented graphically by a linear plot of reciprocal relaxation time PA against mole fraction x.If both A and B are polyatomic relaxing gases there will also be two collision processes corresponding to (1) and (2) for vibration-translation energy transfer from B* in homomolecular and heteromolecular collisions. In addition there 70 Lambert can be a vibration-vibration transfer between A* and B* making five transfer processes in all (1) A* + A -f A + A (2) A* + B - A -I- B (3) A* + B - A + B* (4) B* + B -+ B + B (5) B* + A - B + A (vib. - trans.) (vib. -+ trans.) (vib.- vib. &- trans.) (vib. +trans.) (vib. -+ trans.). If process (3) vibration-vibration transfer does not occur the mixture will show a double relaxation process characterised by two relaxation times PA and @B which will both be related to molar composition by equations of type (4) each giving a linear plot of 1/p against composition. If vibration-vibration transfer does occur the picture is completely altered. Suppose for convenience that pure A relaxes slowly and pure B rapidly so that processes (4) and (5) are both much faster than processes (1) and (2); there are now two alternative possibilities for the overall relaxation process. If vibration-vibration transfer is much faster than all the other processes (3) will maintain the vibrational energy of the whole system (A* + B*) in continuous equilibrium and the total vibrational heat content of both components will relax via the faster of processes (4) or (5).There will thus be a single relaxation time involving the total vibrational energy. The rate-controlling process will be either (4) or (5). If (4) plays the predominant rele as is likely this will give rise to a near quadvotic dependence of overall reciprocal relaxation time on mole fraction of B since the rate of process (4) is proportional to x2 and eqn. (4) no longer applies. This mechanism is closely analogous to the relaxation behaviour shown by pure polyatomic gases giving single dispersion discussed in Section 2. The near-resonant collision process involving transfer of vibrational energy from mode va of molecule A to mode Y of molecule B plays exactly the same r6le as the complex collision process involving transfer of vibrational energy from mode Y to mode v of a single molecular species.Alternatively if process (3) is slower than (4) or (9 but faster than (1) or (2) A will again relax by the route (3) followed by (4) or (3 but now (3) will be rate-determining. This will give a linear dependence of 1 / p ~ on x. B will relax independently and more rapidly via (4) and (9 with linear dependence of l / p ~ on x. There will thus be a double relaxation process with two relaxation times @A involving only the vibrational heat capacity of A and /?B only that of B; both showing linear concentration-dependence. This mechanism is analogous to the relaxation behaviour of those polyatomic gases discussed in Section 2 which show double dispersion because vibration-vibration transfer between modes is slower than vibration-translation transfer from the lowest mode.The nature of the overall relaxation process for mixtures (whether single or double) and the concentration-dependence of the relaxation times are thus determined by the relative rates of processes (1)-(5). Observations of ultrasonic dispersion in the two pure gases A and B and in a series of mixtures extending over the whole concentration range enable a diagnosis to be made of which 71 Quarterly Reviews type of mechanism is followed. The rates of processes (1) and (4) are obtained from the measurements on the pure components and the rates of processes (3) and (5) which give the best fit to the experimental observations can be estimated by trial and error.The results for a series of mixtures are given in Table 2.8 Table 2 Experimental collision numbers for intermolecular vibrational energy transfer at 300"~ A B VA VB i Av ZAB Z u ZBB (cm.-l) (cm.-l) (cm.-l) Singly dispersing mixtures c2H4 C2H6 810 SF CHClF 344 Doubly dispersing mixtures CC12F2 CH3*OCH3 260 CH3Cl CH3.0CH3 732 CHF c2F4 507 SF CH,.O*CHS 344 SFt? C,F* 344 CF4 c2F4 435 Spectroscopic data NO(A2C+) N 2341 NO(X%) CO 1876 NO(X%) N 1876 co CH4 2143 369 1 25 50 1005 122 821.5 1 11.5 40 970 74 250 1 10 5 73 (3 250 3 18 70 421 <3 164 2 16 80 1005 <3 507 1 0 50 1500 5-5 190 2 36 70 1005 5.5 220 2 5 110 2330 5-5 2330 1 11 790 - - 2143 1 267 10,000 - - 2330 1 454 500,000 - - 1534 1 609 33,000 - - ZAB is the collision number for vibration-vibration transfer between one quantum of mode VA of molecule A and i quanta of mode YB of molecule B.(Frequencies VA and VB are for 0-1 vibrational transition.) Mixtures were chosen for which near-resonant vibration frequencies in the two components would be expected to give rise to rapid vibration-vibration transfer (small value of ZAB). It will be seen that whereZABlies below thecollision numbers for vibrational relaxation of the pure components ZAA and ZBB single dispersion is observed; where ZAB lies between 2' and ZBB double dispersion is observed. The actual experimental results for one singly dispersing mixture SF + CHClF, are shown in Figure 2. The lowest vibrational modes of the two molecules lie close enough for rapid vibration-vibration transfer and single dispersion is observed with near-quadratic concentration-dependence of 1 //!I.This indicates that the homomolecular relaxation of CHClF (B) [process (4)] is the rate-controlling step and is faster than the heteromolecular relaxation [process (5)]. The curve calculated for concentration-dependence of 1 /p was obtained by setting up the detailed energy and temperature-relaxation equations developed by Tanczo~,~ and solving over the whole concentration range on an * J. D. Lambert D. G. Parks-Smith and J. L. Stretton Proc. Roy. SOC. 1964 A 282 380. F. I. Tanczos J. G e m . Phys. 1956 25 439. 72 Lambert 1200 800 - -... - -1 I.... I - t u 0 -0 0.5 S c CHUF mole fraction of CHCLF FIG. 2. Reciprocal relaxation times and energy level diagram for SF6 + CHCIF mixtures. 0 observed points; (Reproduced by permission from Proc.Roy. Soc. 1964 A 282,380) curve calculated from theory. electronic computer. The value of ZAB in Table 2 was estimated to give the best fit and may be taken as 50 -& 15. Similar behaviour is shown by the mixture C2H4 + C2H6 investigated experimentally by Valley and Legvold.lo This case is complicated by the double dispersion shown by pure ethane (Section 2) but the torsional (290 crn.-l) mode of ethane relaxes independently of the upper modes in both pure gas and mixtures. A preliminary report has recently been made of a third mixture CO + C,H,O showing single dispersion.ll The mixtures of the second section in Table 2 which were investigated earlier (when erroneous conclusions were drawn),12 all show double dispersion. The details for one mixture SF + C2F4 are shown in Figure 3.There is near- resonance between the lowest (344 cm.?) mode of SF and the first harmonic of the lowest (190 cm.-l) mode of C2F,. Perfluoroethylene shows very efficient homomolecular vibration-translation transfer (ZBB = 5 3 and the estimated vibration-vibration transfer rate (2- = 70) falls between this and the slower vibration-translation transfer rate of sulphur hexafluoride (ZAA = 1005). Double dispersion is observed with the predicted linear concentration-depend- ence of the two relaxation times. The remaining mixtures in this section all of which involve B components whose homomolecular relaxation is very rapid behave similarly. B. Spectroscopic Evidence.-Information about vibration-vibration transfer involving diatomic molecules with comparatively high vibrational frequencies lo L.M. Valley and S. Legvold J. Chem. Phys. 1962 36,481. l1 T. Seshagiri Rao and E. Srinivasachari Nature 1965 206 926. l2 J. D. Lambert A. J. Edwards D. Pemberton and J. L. Stretton Discuss. Faraday Soc. 1962 33 61. 73 Quarterly Reviews "i mole fraction of C,F 1200 800 n - ' E W 400 3 FIG. 3. Reciprocal relaxation times and energy level diagram for SFs 4- C,F4 mixtures. 0 observed points. (Reproduced by permission from Discuss. Faraday Soc. 1962 33 61) has been obtained by flash-photolytic and spectroscopic techniques. Callear showed that vibrationally excited NO in the ground electronic state NO(X2.rr) can be produced by flashing NO mixtures with ultraviolet light and the rate of relaxation in collision with N or CO followed spectro~copically.~~ He also observed the more rapid rate of vibration-vibration transfer between electronic- ally excited NO(A2C+) and N by observing the quenching of resonance fluores- cence.14 The quenching of infrared resonance fluorescence of CO in the presence of CH has been used by Millikan to measure the rate of vibration-vibration transfer for this mixture.16 The values of 2' obtained for all these mixtures are included in Table 2.In the fluorescence quenching experiments on mixtures of NO(A2C+) + N, the former was produced in vibrational levels v = 3 2 and 1 vibration transfers involving all three levels were followed.13 More than 85 % of the transfers involved exchange of a single quantum e.g. which gives a collision number designated by Zti and the values obtained for the three possible transfer were Zi! = 790; 20; = 440; 2:; = 200 which are in the approximate ratio 3 2 1.Thus vibration-vibration transfer usually involves a single quantum but the efficiency of transfer increases almost propor- tionately with increase in vibrational quantum number.'g l3 A. B. Callear Discuss. Faraday SOC. 1962 33 28. l4 A. B. Callear and I. W. M. Smith Trans. Faraday SOC. 1963 59 1735. l5 R. C. Millikan J. Chem. Phys. 1965 42 1439. l6 A. B. Callear J . Appl. Optics Supplement on Chemical Lasers 1964. 74 Lambert 4 Factors Determining the Ef€iciency of Energy Transfer The general significance of the collision numbers recorded in Tables 1 and 2 can be discussed in terms of quantum mechanical theory. For all mixtures listed in Table 2 except the last three the exchanging vibrational frequencies lie close to exact resonance 36 cm.-l being the largest energy discrepancy.An equation derived by Tanczos for resonant-energy exchange should be appli~able.~ This is based on the quantum mechanical theory of Schwartz Slawsky and Herzfeld (S.S.H.)17 and gives the probability P(a b) for resonant energy exchange in a collision between two molecules a and b as Po(a) and Po@) are geometrical orientation factors. m a ) and P(b) are 'vibra- tion factors' for the quantum jumps involved in each molecule; they depend on the detailed physical nature of the process and the intramolecular force constants and contain terms in the intermolecular repulsion parameter and the inverse of v the vibrational frequency of the mode involved. They result in the probability's being enhanced by a steep intermolecular repulsion potential and decreased for modes of high frequency.The vibration factors are also smaller for multiple quantum jumps and this lowers the probability of transfers involving harmonics of fundamental modes. 01 is an intermolecular force constant p is the reduced mass of the collision pair,+o is the minimum value of the intermolecular potential function used. Insufficient data are available on intramolecular force constants and inter- molecular potentials for most of these polyatomic molecules to make quanti- tative a priuri calculations of P(a b) possible. But the general trends produced by various factors are well illustrated in Tables 1 and 2. The first striking con- clusion is that resonant vibration-vibration exchanges do not have unit efficiency as has often been assumed.This is illustrated experimentally by the mixture CHF + C,F, where both components have vibrational modes of identical frequency 507 cm.-l and the estimated value for Z m is 50. The efficiency of near-resonant collisions decreases with rising frequency of the exchanging modes. Were all other factors equal 2' should be proportional to the square of v. This is illustrated by the increase in ZAB from 5 for interchange between CCI,F (VA = 260 cm.-l) + CH,.OCH (vg = 250 cm.-l) to 790 for the mixture NO(A2C) (VA = 2341 cm.?) + N2 (vg = 2330 cm.?) where the vibration frequencies increase by a factor of approximately 10 and Z m by a factor of rather more than 100. 2' values for the other single quantum near-resonant exchanges CHF (507 cm.-l) + C,F (507 cm.-l) SF (344 cm.-') + CHCI,F (369 cm.-l) GH (810 cm.-l) + C2H (821.5 cm-l) l7 R.N. Schwartz Z. Slawsky and K. F. Herzfeld J. Chem. Phys. 1952,20 1591. 75 Quarterly Reviews which have intermediate frequencies all lie in the neighbourhood of 50. The other factor which is important is the relative inefficiency of multiple quantum transfers. This is illustrated by the remaining near-resonant mixtures in Table 2 all of which involve 2- or 3-quantum transitions and show values of Z- ranging from 70 to 110. The intramolecular 3-quantum transfer between the 290 cm.-l and 820 cm.-l modes of ethane (Table l) with a value of Z, = 74 also falls into this class. For all the mixtures of this group there is no apparent correlation between the size of the energy discrepancy dv and 20 which justifies the approximation of treating all these energy exchanges as resonant.The remaining vibration-vibration transfers recorded in Tables 1 and 2 show energy discrepancies ranging from 110 to 609 cm.-l and can no longer be regarded as approximately resonant. They shouId follow a more complicated expression than eqn. (3 involving an exponential term in the energy discrepancy dv.17918 Callear has shown that for the transfers between NO N, and COY recorded in Table 2 where all three components are diatomic molecules with similar molecular weights and would be expected to show similar gas-kinetic collision parameters the value of log ZAB shows a linear plot against dv as predicted.13 The higher transfer efficiency of CH as a collision partner for CO in spite of the large energy discrepancy (dv = 609 cm.-l) is due to its lower molecular weight and to the fact that vibrations which involve hydrugen atoms show a large amplitude owing to the small mass of the hydrogen atom.lg This results in a substantial increase in the vibration factors (cf.eqn. 5) and is the likely explanation for the comparatively high transfer efficiencies shown by hydrogen-containing molecules in vibration-translation,5 as well as in vibration- vibration transfers. Finally the relatively inefficient intramolecular transfers given in Table 1 for SOz and CH,CI, involve both sizeable energy discrepancies and double quantum jumps. For simple polyatomic molecules where reliable molecular parameters are available a priuri quantum mechanical calculations by the S.S.H. method have shown reasonable success with homomolecular relaxation processes.18 Similar calculations have recently been carried out on a number of 0 mixtures for which some experimenial results are available for comparison.20 The calculated ZAP values are shown in Table 3; they must be regarded as only approximate but are in qualitative agreement with the experimental findings.The latter have all been made with very low concentrations of additive (< 2%) and are in- sufficient for exact interpretation. It is clear that vibration-vibration transfer can give a satisfactory explanation for the striking ‘catalytic’ effect on the vibrational relaxation of 0 shown by many polyatomic additives. The trends shown in the values of ZAB in Table 3 are of the same kind as those discussed above for Tables 1 and 2. The striking efficiency of H,O is an example of the ‘hydrogen effect’ combined with a near-resonant collision.[The even more striking value of ZBB for H,O is due to the strong dipole-dipole interaction l* J. L. Stretton Trans. Faraday SOC. 1965 61 1053. l9 D. G. Jones J. D. Lambert and J. L. Stretton J . Chem. Phys. 1965 43,4541. D. G. Jones J. D. Lambert and J. L. Stretton Proc. Phys. SOC. 1965.86. 857. 76 Lambert Table 3 Calculated collision numbers for intermolecular vibrational energy transfer in oxygen mixtures at 3 0 0 " ~ Additive (€3) vg 1534 1092 1444 729 1596 1178 1402 (cm.-l) i Av (cm.-l) 20 462 110 96 42 376 152 170 16,000 490 1800 80 1160 140 ZBB 1 1,600 4960 4050 490 ca. 1 ca. 1 ca. 1 ZAB is the collision number for vibration-vibration transfer between one quantum of the fundamental mode of O e ( v ~ = 1554 an.-') and i quanta of mode YB of molecule B.For pure oxygen ZAA = 8.31 x lo7 (calc.). between molecules which leads to a very deep minimum in the intermolecular potential so that the+o term (cf. eqn. 5 ) takes control. Theoretical calculations giving such high transfer efficiencies are unreliable.] 5 The Rsle of Vibration-Vibration Transfers in Chemical Kinetics Two factors of fundamental importance in unimolecular reaction kinetics are the efficiency of collisional activation and deactivation of molecules and the efficiency of energy transfer between different vibrational modes in the molecule. The various conclusions about efficiency of vibration-vibration transfer which have been discussed above apply equally to homomolecular and heteromolecular collisions.The vibrational deactivation of molecules in homomolecular collisions can occur either by vibration-translation transfer or by resonant vibration- vibration transfer. The efficiencies of both processes depend critically on the frequency of the lowest vibrational mode; the collision number for vibration- translation transfer varies exponentially with frequency; the collision number for resonant vibration-vibration transfer is roughly proportional to the square of the frequency. Comparison of the values for vibration-vibration transfer given above with those for vibration-translation transfer given by Lambert and Salter5 shows that for hydrogen-containing molecules with frequencies below about 500 cm.-l both processes have collision efficiencies ( ~/ZAB) varying between 1/5 and 1/50 and there is little significant difference between them.For molecules containing no hydrogen atom vibration-translation transfer will be substantially less efficient even in this frequency range. As frequency rises above 500 cm.? both efficiencies decrease but vibration-vibration transfer quickly becomes much more efficient than vibration-translation. Thus for 0 (v = 1554 cm.-l) resonant vibration-vibration transfer (ZAB = ca. lo2) is several powers of ten more efficient than vibration-translation (Zlo = ca. lo7) and even a non- resonant collision with an energy discrepancy dv = 462 cm.-l (ZAB = ca. 104) is much more efficient. The temperature-dependence of resonant vibration- vibration transfer is much weaker than that of vibration-translation transfer 77 Quarterly Reviews so that the difference in efficiency will become less marked at higher temperatures.The chemical implication of this is that for moderately complex organic molecules which have torsional frequencies around 250 cm.-l homomolecular vibrational deactivation may be expected to occur by either process and to have a collision efficiency of 1/3 to 1/5 (allowing for the slightly higher efficiency of transfer from upper vibrational levels). Heteromolecular deactivation by an additive with a suitable range of low vibrational frequencies for easy vibration- vibration transfer may well be somewhat more efficient than homomolecular deactivation. This is in accord with recent observations on the kinetics of thermal isomerisation of cyclobutenes.21 Recent ultrasonic work has shown that for the straight-chain hydrocarbons n-pentane and n-hexane which have even lower torsional frequencies (v < 100 cm.-l) vibration-translation transfer occurs at approximately every collision,22 and other flexible organic molecules may be expected to show the same high efficiency.In contrast for all molecules contain- ing no hydrogen atom and for hydrogen-containing molecules with lowest vibrational frequencies above 500 cm.-l deactivation will occur mainly by vibration-vibration transfer with collision efficiencies varying between roughly 1/50 and 1/500. For this group collisions with monatomic additives which can only deactivate by vibration-translation transfer will be much less efficient than self-collisions. Collisions with polyatomic additives can have slightly higher efficiency than self-collisions but only where suitable vibrational frequencies for near-resonant transfer are present ; complex organic molecules possessing a wide spectrum of frequencies are most likely to fulfil this criterion.Otherwise additive efficiencies will be lower. Relative collision efficiencies for deactivation derived from unimolecular reaction kinetics are in accord with these views.2 The different active vibrational modes of polyatomic molecules are usually fairly closely spaced so that vibration-vibration transfer between modes will be near-resonant and will show an efficiency of thesame order as that of vibrational activation and deactivation. Transfer between modes which are widely spaced may be considerably less efficient. 21 H. M. Frey and D. C. Marshall Trans. Faraday SOC. 1965,61,1715; C . S. Elliott and H. M Frey ibid. 1966 62 895. *a R. Holmes G. R. Jones and R. Lawrence Trans. Faraday SOC. 1966 62,46. 78