5624
J. Phys. Chem. 1993,97, 5624-5627
Vibrational Relaxation of Highly Excited CFzClz and CFzHCl by Monatomic Gases: Dependence on Energy and Mass D.C . Tardy Department of Chemistry, The University of Zowa, Zowa City, Zowa 52242 Received: January 4, 1993
The relaxation of vibrationally excited CF2Cl2 and CF2HCl (the average energy, (E), ranged from 2000 to 30 000 cm-l) by rare gases was monitored with time-resolved optoacoustics. Above 8000-10 000 cm-I, the collision efficiency, @, was independent of excitation energy and deactivator: B(CF2C12) = 1.7 X and B(CF2HC1) = 1.5 X The average energy removed per collision, >, is linear with (E). For (E) < 8000-10 000 cm-1, Bdecreases with decreasing energy; the energy dependence was similar for all deactivators. The present experiments suggest that the energy dependence of the observed ICVT is due to an energy dependence on the microscopic rate coefficient for relaxation and not the initial distribution of vibrational energy.
htroduction Vibrational energy transfer (VET) plays an important role in processes which require excitation to sufficient energies for chemical reaction; e.g., pyrolysis and combustion. Of similar importance is the stabilization of high-energy species. Sincethese two processes are the reverse of one another, equivalent information can be obtained by studying either one.' For diatomic molecules at low levels of excitation, the transfer of vibrational to translational energy (VT) upon gas-phase collisions is well characterized,both experimentally and theoretically.2J However, for polyatomic molecules the theory and experiments are not fully developed. In general, for low levels of excitation the probability for energy transfer increases (i) as the lowest vibrational frequency decreases, (ii) as the excitation energy increases, and (iii) as the mass of the collider decreases. For polyatomic molecules at high levels of excitation (comparable to that for chemical reaction), the probabilities are larger than those reported for diat~mics.~ The categorization of large and small molecule, and high and low energy, has been artificially introduced,a unified theory must connect these categories. A qualitative explanation for the different behavior has been presented by Gordon.5 The experiments reported here were undertaken to determine the energy dependence of the relaxationrate coefficient for moderately small molecules (five atoms) by use of a series of monatomic colliders.
Experimental Section The time-resolved optoacoustic (TROA) technique developed by Beck and Gordon6was used. In this method, a pulsed laser excites thesubstrate which isdiluted with thespecifieddeactivator. The excited substrate undergoes VT relaxation, producing an acoustic wave which propagdtes radially from the excitation cylinder. A piezoelectric transducer placed within the excitation cell is used to detect the nascent pressure wave. The ratio of the amplitude of the rarefaction (L) to the amplitude of the condensation (Z+) wave is a known function of system parameters (laser beam radius, sonic velocity)6 and the VT relaxation time, T ~ T .The rate coefficient for relaxation is related to TVT by k V T = 1/7VTN, where N is the number of molecules per cm3. The data were processed as described by Beck and Gordon.6 The sample cell consists of a 5-Lspherical glass bulb fitted with a pair of sodium chloride windows. A microphone (International Transducer, Model PK14-14) was mounted such that it was midway between the windows and approximately 5 cm (adjustable) from the COZlaser beam (Tachisto Model 215G), which entered and excited through the windows. An aperture 0022-365419312097-5624$04.00/0
(0.09-0.1 5 cm) was placed between the laser and glass bulb; the laser beam entering the cell was determined to have a toghat profile. A Gentec (Model 500-D)Joule meter was used to determine the absorbed energy and the average energy absorbed per molecule. A mixture of rare gas (Air Products: argon, 99.995%; helium, 99.995%; neon, 99.99'32, krypton, 99.995%) was made and expanded into the bulb at ambient temperature (23 "C); the laser was tuned to 9.183 Mm (R38 of the 00°1-0200 band) and 9.201 Mm (R34 of the 0001-0200 band) for CFzClz (PCR Inc., 99%) and CFzHCl (PCR Inc., >97%), respectively. The signal was captured and digitized with a Biomation transient recorder (Model 805) and then averaged (-200 shots with a repetition rate of 1 Hz) with an EG&G 4203 signal averager. The resulting signal (comparableto thoseof ref 6) was transferred to a strip chart recorder for analysis. RMlItS
Constant composition mixtures of argon and substrate were irradiated as a function of total pressure for a given photon fluence. The average absorption coefficient, calculated from the amount of energy absorbed, increased with pressure and leveled off at approximately 500 Torr; this is illustrated in Figure 1. This behavior is indicative of a bimodal energy distribution as reported in systems with similar substituted methanes.' The initial energy distribution consists of those molecules in which energy remains in the absorbing mode (-1088 cm-1) and those in which the energyis distributed between all vibrationalmodes. At sufficient excitation energy, the bimodal distribution becomes a canonical distribution; likewise, sufficient pressure provides a mechanism for collisionally assisted relaxation. Relaxation experiments were performed for a variety of substrate/deactivator mixtures as a function of pressure. Above 800Cb-10000 cm-1, TVT was found to be. a linear function of the deactivator pressure when the pressure varied by a factor of 6. At high energies (>10000 cm-I), kVT was also found to be independent of absorbed energy; below 8000 cm-I, ~ V decreases T with a decrease in absorbed energy. A summary of these experiments is presented in Table I.
Discussion A comparison of k v for ~ the different collision partners involves both the encounter rate and the characteristics of VET for the deactivator and substrate. The collision efficiency, @, is defined as the ratio of ~ V to T a reference collision frequency for that pair of colliders. Thus, @ is an intrinsic quantity which relates to the inherent characteristics of energy transfer per encounterand does 0 1993 American Chemical Society
Vibrational Relaxation of CF2C12 and CF2HCl
The Journal of Physical Chemistry, Vol. 97, No. 21, 1993 5625
30f
cd
v
25t 0'
200
400
600
800
I
20
.
'
2
30
(103~m-1)
1000
(torr)
PAr
I
10
Figure 1. Plots of absorption vs argon pressure for CF2C12 (0with a fluence of 1.0J/cm2) and CF2HC1(O with a fluence of 1.1 J/cm2). On the absorption scale, a value of 10 corresponds to an average absorbed energy of 16 000 cm-I. The two vertical lines (terminated with arrowheads) represent the 95% confidencerange at the limiting pressures.
-
Figure 2. Plot of 8 vs (E) for the CF2C12 system with helium (v),neon (D), and argon (0). The symbols at the right are the averages for these deactivators when (E) > 8000 cm-I, while the symbols with vertical bars located at the far right correspond to the 95% confidence range for a single datum.
--O-.*-r
TABLE I: Summary Data for C F 2 Q and CFZHCl Systems with ( E ) > 8000 cm-I svstemg ~
UHS~
kwb
~~
CF2C12 He Ne Ar CF2HC1 Ne Ar Kr
~
V
T
~
Bd
QDB'
Nf
~~
5.17 2.58 2.85 3.46 4.72 2.85 3.46 3.61
6.04 3.06 2.69
10.4 5.15 4.62
1.72 1.68 1.72
0.08 0.05 0.07
11 19 18
2.80 2.51 2.10
4.09 3.59 3.09
1.46 1.42 1.47
0.03 0.02 0.03
14 13 13
Collision diameters in units of 10-8 cm. Hard-sphere collision frequency in units of lO-'O cm3/(molecule s). Rate coefficient of VT relaxation in units of lo-" cm3/(molecule s). d Collision efficiency in units of 10-3. e 95% confidence range for the mean of 8. /Number of determinations with (E) > 8000 cm-I. g Deactivators are He, Ne, Ar, and Kr.
not include encounter frequencies, which are determined by relative velocity (function of mass) and cross section. The reference frequency is often calculated from the hard-sphere(HS) collision diameters, so j3 = kVT/kHS. The Lennard-Jonescollision frequency has also been successfully used.* It has been pointed out that substantial errorsg (-470%) may be introduced when normal Lennard-Jones parameters are used. However, relative efficiencieswithin a series of deactivatorscan be used successfully in determining trends. For example, /3 calculated from LennardJones parameters will be smaller than those calculated from hardsphere cross sectionsbut will exhibit the same trend. Calculated collisionalefficiencies for the collision partners using hard-sphere cross sections are listed in Table I and plotted in Figures 2 and 3 (for (E) > 8000 cm-I). Although kVTfor CF2C12 with the various deactivators changes by more than a factor of 2, the efficiencies are within -2% of one another. External Comparisons. The relaxation of CFzClz by argon, using other techniques, has also been reported. By looking at population depletions produced by reactions of vibrationally excited CF2C12,the Setser'O group observed j3 = (1.2 f 0.1) X 10-3; the present experiments have @ = (1.72 f 0.03) X 10-3 at a comparable energy. Thermal lensing experiments" give j3 = (1 .O f 0.3) X 10-3,while IR emission experiments of Karve and co-workersl2give p = 0.55 X 10-3. The first three techniquesare in satisfactory agreement but give a p 2-3 times larger than the p of the emission experiments;this discrepancy is outside of the reported error range and may be due to differences in average energies. The Setser group also found that helium was approximately twice as efficient as argon, while the thermal lensing results showed a factor of 3. We find that the efficiencies for
o.oo " 10 20 ' * ( 1 0 3 ~ ~ ) Figure 3. Plot of 8 vs (E) for the CF2HCl system with neon (O), argon (0),and krypton (A). The symbols at the right are the averages for these deactivators when (E) > 8000 cm-I, while the symbols with vertical bars located at the far right correspond to the 95% confidence range for a single datum.
helium and argon are comparable. The origin of these differences is also unknown and further supports the idea that internal comparisons are more reliable. Relaxationof various halo-substituted methaneshave also been studied. Using TROA, Beck and Gordon13 have reported the relaxation of CH&l and CH3Br by argon as 1.3 and 3.3 Torr' ms-l, respectively. This corresponds to an efficiency of 2 X 1 V . Using the ultraviolet absorption technique, the Troe group14 reported /(E) = 4 X 10-3 at 10 000 cm-l for CFJ. A strong energy dependence was observed: j3 increased from 2 X 10-3 at 5000 cm-I to 4.6 X at 15 000 m-l. The larger u,in (lowest vibrational frequency) for the hydrogen-containing methanes may account for the order of magnitude decrease in p compared to the j3 of CFzC12. However, u,in for CFJ is 265 cm-l and is comparable to 2 6 1 cm-I for CF2C12; the factor of 2.4 differencemay be due to experimentaldifferencesor to the initial excitation energy distribution function. Efficiencies of SiF4I5 and SF66were determined by TROA to be 5.1 X lV3and 4.8 X 10-4, respectively. The importance of the low-lying vibrational modes in the relaxation of azulene has recently been shown by trajectory calculations.I6 Thus, it appears that these five- and seven-atom molecules have more than one parameter that determines their efficiencies. Internal Comparisons. There are three characteristics that can be gleaned from the data obtained by the current TROA experiments: (i) the efficiency for a givendeactivator is marginally larger in the CF2Cl2 system than it is in the CFzHC1 system, (ii)
5626 The Journal of Physical Chemistry, Vol. 97, No. 21, 19'93 for a given substrate the deactivators have similar efficiencies, and (iii) for a given substrate-deactivator pair j3 increases with increasing energy and levels off in the region 8000-10 000 cm-I. The interpretation of these observations is discussed in the following subsections. Substrate Efficiencies. The efficiency for both neon and argon increases from 1.42 f 0.03 to 1.72f 0.03 (95%confidence range) in going from CFzHCl to CFzC12. Since this difference is significant at the 99.5% level, an explanation is necessary. The replacement of H with a C1 atom reduces Y,,, from 365 to 261 cm-I and the mean frequency from 930 to 567 cm-I; the average thermal energy increases from 210 to 420 cm-I. The effect of umlnat low levels of excitation has been experimentallyobserved;] j3(self-deactivation) increases from 5.2 X l t 3to 15 X l t 3for CFzHCl and CF2C12,respectively. Due to the more rapid deactivation of H-containing substrates, this is approximately a factor of 2 less than what would be predicted by an exponential gap model for non-hydrogen substrates. The increase of j3 as Vmln decreases exhibits a good correlation, as shown by LambertSalter plots.3 The increase in the density of internal eigenstates (for CF2C12 there are -50 states per cm-I at 5000 cm-I, CFzHCl is 1 order of magnitude smaller) created by the reduced vibrational frequencies also affects the average energy in each vibrational mode. Classical equipartition of energy predicts that the internal energy will be partitioned equally between all modes. The dependence of the classicality of vibrational modes on vibrational frequency in calculating sum of states and unimolecular rate constants has been determined for a few model systems.I8 Recently, Toselli and Barkerlg have pointed out how the breakdown of classical equipartition of energy can skew the apparent results from classical trajectory calculations. However, for CF2C12 at 8000 and 20 000cm-I the u,,, modes receive -20% and 10% more than what classical equipartition would predict; for CF2HCl the numbers are 40% and 15%,respectively. For a given total energy, the average energy in the lowest mode of CFzClz is less than that for CF2HCl. Since ~ V increases T with ( AE) and (AE)is found to increase with oscillator energy, it is expected that kvT for a given total energy would be smaller for CF2C12 than it is for CFzHCl. Thus, if the relaxation occurs through the lowest vibrationalmode, a decreasein Y,,, will produce both an increase in j3 because of the reduced energy mismatch and a decrease in j3 due to the smaller amount of energy which is located in this mode. It appears that these opposing effects nearly offset one another for these substrates; the effect of vmln may be larger than the one affecting the average energy in the vmlnoscillator. Deactivator Efficiencies. For a given substrate, the efficiency is found to be independent of deactivator. In the CF2Clz system helium, neon, and argon are similar, while in the CFzHCl system neon, argon, and krypton are similar. Both the mass and interaction potential are changing in these series. At a given temperature, all deactivators will have the same kinetic energy; however, the deactivator with a smaller mass will have a higher relative velocity: u(He)/v(Ar) = 3.2. In the case of diatomic substrates,*Othe higher velocityimplies a shorter interaction time, Le., a more impulsive collision, and a higher collision efficiency. Thus, if collision duration is important for these molecules, then it must be offset equally by another parameter such as the interaction potential. Attractive interactions which generally increase with mass (i.e., the number of electrons) will facilitate VET, e.g., argon will be more effective than helium. For strong interactionsin which a true collision complexis formed, the energy is statistically distributed, and the kinetic energy released would be independent of mass. However, if this were the case, then j3 would be on the order of 0.1, a factor -50 times larger than what is observed. Thus, it does not appear that the observed energy
Tardy transferred results from a statistical distribution of a long-lived collision complex. This is also consistent with other systems.21 Although caution must be observed when comparing results from different techniques, it appears that the dependence of j3 on mass ofdeactivator for a given substratedoes not appear to follow a simple rule. For example, the independence of j3 and mass has been observed in the deactivation of chemically activated l,l,ltrifluoroethane.z2 However, the Setser grouplohas also reported that argon is more efficient than helium in deactivation of chlorofluoroethanes, but the reverse is true for chlorofluoromethanes. Nonetheless, in most systems, it is observed that at moderately high excitation energies j3 increases in going from helium to argon followed by a slight increase, decrease, or leveling off depending upon the system.' At low levels of excitation,the efficiencyin the CFzClz systemz3 decreases in going from helium (14 X l C 3 ) to neon (9 X to argon (3 X 10-3). For the same system at high energy, the Setser group observed a factor of 2 decrease in going from helium (2.1 X lC3)to argon (1.2 X IC3). The thermallensingresultsll showed a larger difference for helium and argon: 3.8 X lC3and 1.OX 10-3, respectively. Various models in which the deactivator collides with pseudodiatomic can be used to mimic the increase ordecrease in j3 with massof thedeactivator. However,a constant j3 of 1.7 X 1 t 3for all monatomic deactivators as observed in the present TROA experiments cannot be simply modeled. Energy Dependence. For energies in excess of 8000-10 000 cm-I, the efficiency and ~ V are T constant for all deactivators; below the 8000-10 000-cm-I threshold, these quantities increase with increasing average energy. An acceptable model must account for this dependence on the average energy. We note that the calculated average energy can be the result of low fluence/ high total pressure or high fluence/low total pressure experiments. For a general energy distribution of the substrate, the observed ~ V is T given by
-
where k v ~ ( Eis) the energy-dependent relaxation rate coefficient when the substrate has internal energy E and F(E) is the fraction of substrates that have E such that JF(E) d E = 1 and ( E ) = JEF(E) dE. Since the absorption experiments are used to calculate the average energy absorbed per molecule in the irradiated volume, it is necessary that ( E ) be calculated over the same set of molecules, i.e., not just those that absorb. Thus, there is some ambiguity in finding the correct population distribution from the measured value of ( E ) : for a given ( E ) ,the average energy for each molecule which absorbs a photon, (e), will be small when the fraction of molecules absorbing is high or ( E ) will be large if the fraction of molecules absorbing photons is low. In general, if q is the fraction of molecules that absorb ( a ) , then (E) = q( e). Fortheexperimentswith ( E )> 8000-10 OOOcm-l,acanonical, not bimodal, energy distribution in which all substrates have absorbed at least one photon is expected.' Under theseconditions, the shape of F(E) is a function of ( E ) and F(E) is normalized, and if kvT(E) is not observed to be energy dependent (kvT(E) = k $ ~ )then , it is seen that ~ V will T not be a function of energy:
This energy independence of kVT has also been observed for the vibrational energy relaxation in a homologous series of fluorinated alkanes.24 Below 10000 cm-l (where a bimodal distribution is postulated'), the energy dependence of ~ V may T be due to that of F(E) and/or k v ~ ( E )First . consider that theenergy dependence results from F(E). For the case that a fraction q of substrates is excited with an average energy ( e ) , and k v ~ ( 0=) 0 for E = 0 and for E # 0 k v ~ ( E=) k $ ~then , kVT = kVT'. Theobserved independence
Vibrational Relaxation of CF2C12 and CF2HCl
The Journal of Physical Chemistry, Vol. 97, NO. 21, 1993 5621
of j3 with pressure for a given ( E )and the observation of an initial bimodal distribution suggest that VV transfer is much faster than the observed VT and that F(E) depends only on ( E ) , i.e., not on the initial excitation function. Now we consider the various models for the case that k v ~ ( E ) is energy dependent. If intramolecularvibrational energy transfer (IVET) in the substrate is rapid compared to other relaxation processes, then at all times the average energy in each oscillator will be determined by the quantum statistics; Le., classical equipartition of energy is not appropriate. Since at these energies the oscillators are not classical, the lower vibrational frequencies will receive an increasingly larger fraction of the total energy as the total energy decreases. If the relaxation occurs predominately through the lowest frequency oscillator, then j3 will increase as the total energy decreases since this oscillator will receive a larger fraction of ( E )as ( E ) decreases. This increase in kVTis opposite to what is experimentally observed. However, if IVET is slow, then energy will be locked into specific modes. The observed relaxation is a sum over all relaxing modes, ~ v T ( E=) CCkvT(i,Ei)fii,Ei), where the sums are over the i vibrational modes such that LEi = E andfii,Ei) is the fraction of the ith oscillators in the ensemble that contain Ei in the ith mode. As the modes with the faster relaxation times are depleted, the remaining energy will relax through the slower (higher vibrational frequency) modes. This effect will be amplified if the initial energy is low and thedistribution is bimodal. Theobserved independence of 0 with pressure for a given average energy suggests that slow IVET is not the cause for the experimental energy dependence of 8. There is other evidence that the IVET is now slow. The average energy in a number of vibrational modes has been observed for C F Z Cand ~ CFJ26 ~ ~ ~ at various levels of excitation with a pulsed C02 laser. It was concluded that the excitation energy is collisionally randomized between all modes with a rate coefficient of 10-11 cm3/molecules, i.e., 1000 times faster than the observed relaxation rate coefficients which we observe. Thus, it appears that IVET is not the bottleneck in the relaxation and the cause for the energy dependence of 0 and kvT. Another model which exhibits energy dependence on k v ~ ( E ) is the deactivation of a simple harmonic oscillator. This model predicts that k v ~ ( Ewill ) scale with the vibrational energy (E) of the o~cillator.~*~ Thus, for kvT(e) = ek”VT then ~ V = T jkvT(e) de) de = k ” v ~ J t f i ede ) = k”vT(e)osc,wherefie) is the fraction of oscillatorsthat have e and the average energy for each oscillator is ( e ) = Jefic) de. If this doorway oscillator is coupled to other substrate oscillators, then its average energy can be related to the average vibrational energy of the substrate. In the high-energy, classical limit, ( e ) = (E)/noscwhere noscis the total number of oscillators in the substrate. Thus, for this model kVT would be linear with ( E ) . If F(E) was bimodal, then k V T would increase more rapidly with ( E ) , Le., -(E)2. Recently, weZ4 have shown that 0 = /(E) where is the average energy removed per collision. Thus, above 8000-1 0 000 cm-1 increases linearly with ( E ) ,and below 8000 cm-1 the experiments show that this quantity has a stronger than linear dependence on energy. Assuming that /(E) is linear with ( E ) (as in the harmonic oscillator model described above), then extrapolation of j3 to ( E ) = 0 gives /(E) = 0.7 X 10-3 and 0.5 X 10-3 for CF2C12 and CF2HC1, respectively. This is -7 times smaller than that reported for the CF2C12 experimentsat low levels of excitation.2) However, this difference may be due to different initial energy distributions and/or an inadequate extrapolation.
-
-
Conclusions Vibrationally excited CF2C12 and CF2HCl were created by multiphoton excitation with a C02 laser; the average energies were in the range 2000-30 000 cm-I. Vibrational to translational rate coefficients ( ~ v Tfor ) the deactivation of the substrates by a rare gas (helium, neon, argon, krypton) bath were determined by monitoring the translational energy uptake via TROA. For energies in excess of 8000-10 000 cm-I, kvT(Ar) was 4.6 X 10-13 and 3.6 X lO-I3 cm3 molecule-l s-I for CFzClz and CF2HC1, respectively. At lower energies ~ V increased T with increasing energy. These results suggest that for energies greater than 8000 cm-l the average amount of energy transferred per collision is linear with the average internal energy. At low energies, the decrease in kVT may be due to the energy distribution and/or an energy dependence for the microscopicrelaxation rate coefficient. The present experiments suggest the second alternative. The relativecollisionefficienciesfor all deactivatorswere similar (- 1.5 X 10-3) and exhibited similar energy dependence; the collisional efficiency in the CF2C12 system was slightly greater than that in the CF2HCl system.
Acknowledgment. Support from this work by the Unitedstates Department Energy, Division of Chemical Sciences, Office of Basic Energy Sciences (Grant DE-FGO2-87ER13700), was greatly appreciated. The work performed by B. H. Song in acquiring the data for these experiments is greatly appreciated. References and Notes (1) Tardy, D. C.; Rabinovitch, B. S. Chem. Rev. 1977, 77, 369. (2) Yardley, J. T. Introduction to Molecular Energy Transfer;Academic Press: New York, 1980. (3) Lambert, J. D. Vibrational and Rotational Relaxation in Gases; Clarendon Press: Oxford, 1977. (4) Oref, I.; Tardy, D. C. Chem. Reu. 1990, 90, 1407. (5) Gordon, R. J. J . Chem. Phys. 1990, 92, 4632. (6) Beck K. M.; Gordon, R. J. J . Chem. Phys. 1987,87,5681; 1988,89, 5560. (7) Letokhof, V. S. Laser Spectroscopy of Highly Vibrationally Excited Molecules; Adam Hilger: New York, 1989. (8) Lawrance, W. D.; Knight, A. E. W. J . Chem. Phys. 1983,79,6030. (9) Lendvay, G.; Schatz, G. C. J . Phys. Chem. 1992, 96, 3752. (10) Sobczynski, R.; Setser, D. W.; Slagle, A. R. J . Chem. Phys. 1990, 92, 1132. (11) Ma, Y.; Xu, Z. Chem. Phys. Lett. 1983, 98, 563. (12) Karve, R. S.; Sarkar, S. K.; Rama Rao, K. V. S.; Mittal, J. P. Spectrochim. Acta 1987, 43A, 165. (13) Beck, K. M.; Gordon, R. J. Laser Chem. 1988, 91, 47. (14) Abel, B.; Herzog, B.; Hippler, H.; Troe, J. J . Chem. Phys. 1989,91, 900. (15) Beck, K. M.; Gordon, R. J. J. Chem. Phys. 1990, 92, 6011. (16) Clarke, D. L.; Gilbert, R. B. J . Phys. Chem. 1992, 96, 8450. (17) Rossing, T. D.; Legvold, S. J . Chem. Phys. 1953, 25, 1116. (18) Tardy, D. C. Ph.D. Dissertation, University of Washington, Seattle, WA, 1967. (19) Toselli, B. M.; Barker, J. R. Chem. Phys. Lett. 1990, 174, 304. (20) Schwartz, R. N . ; Slawsky, Z. I.; Herzfeld, K. F. J . Chem. Phys. 1952, 20, 509 1. (21) Gilbert, R. G. Int. Rev. Phys. Chem. 1991, 10, 319. (22) Marcoux, P. J.; Setser, D. W. J . Phys. Chem. 1978, 82, 97. (23) Olson, J. R.; Legvold, S. J . Chem. Phys. 1963, 39, 2902. (24) Tardy, D. C. Energy Relaxation of Highly Vibrationally Excited Molecules: Homologous series CnF2”+2and C,H2.+1F. J. Phys. Chem.,
following paper in this issue. (25) Dolzhikov, Y. S.; Letokhof, V. S.; Makarov, A. A.; Malinovsky, A. L.; Ryabov, E. A. Sou. Phys. JETP 1986,63, 1161. (26) Bagratashvili, V. N.; Doljikov, V. S.; Letokhof, V. S.; Ryador, E. A. Laser Induced Processes in Molecules; Kompa, K. L., Smith, S. D., Eds.; Springer: Berlin, 1979.
