J. Phys. Chem. 1986,90, 4555-4558
4555
Relaxation in Molecular Infrared Absorption. 2. Results for CHCIF2. Kinetics of Resonant Vibrational Energy Exchange’aib Shu-Huei Lidc and Ernest Grunwald* Department of Chemistry, Brandeis University, Waltham, Massachusetts 02254 (Received: August 21, 1985; In Final Form: March 26, 1986)
Relaxation to photophysical steady state during infrared absorption was measured at 1088 cm-’. Pressures of CHCIF, ranged from 1.55 to 52 Torr and average vibrational energies (above the zero-point energy) from 3 to 20 kJ mol-’. The rate law for relaxation consists of two terms: a simple collisional term, which includes the effect of (R-R’) rotational exchange, and an additional collisional term whose rate is proportional to the vibrational energy. The latter can be attributed, by kinetic analysis, to (V-V) and (V-V,R) resonant vibrational energy exchange, in which a quantum is transferred from any mode of one molecule to the same mode of another molecule. Rate constants are given. Specific rates for relaxation are greater than gas-kinetic collision frequencies.
The rate law for IR absorption in the gas phase, developed in part 1,2 will now be applied to kinetic analysis of relaxation to photophysical steady state. The same notation will be used, and equations, figures, and tables given in part 1 will be cited with an I: prefix. CHClF2 (Freon 22) is a good substrate because under conditions of relatively low fluence (where chemical reaction is negligible), Eab,/Fis a phenomenally complicated function of pressure and fluence, implying an intricate interplay of optical saturation and relaxation. Experimental results obtained in this worklb are summarized in Table I. At 51.7 Torr, E,,/F is nearly equal to the spectrophotometric molar absorptivity uA,showing that relaxation here is fast enough to prevent optical saturation. As the pressure is lowered, however, E,,/F becomes progressively smaller than aA, and at the two lowest pressures Eab,/Fpasses through a minimum as F increases. We shall find, however, that this complex function unfolds into a relatively simple function for 1lr-a function that is well suited to kinetic analysis. Relevant properties of CHClF, are listed in Table IL3” The IR laser operated a t 1088 cm-’, which overlaps the absorption band due to the CF2asymmetric stretch (VJ. When recorded at room temperature with a resolution of 0.2 cm-’, this band is practically a continuum. Figure 1 shows the v9 band as recorded and indicates anharmonic frequency shifts resulting from v9 vibrational excitation.
Experimental Part Chlorodifluoromethane (Freon 22) was obtained from Matheson in better than 99% purity. It was analyzed by GC/MS and found to be free of detectable impurities. The gas was handled on a vacuum line by standard techniques and degassed before experiments by repeated freeze-pumpthaw cycles. The measurement of Ea&,F, and profile(t) has been described in the Test section of part 1, and in references cited therein. The IR pulse profile is that given in Table 1:I. All IR absorption results are ‘thin-cell” results. Gas pressures were measured with a capacitance manometer whose voltage readings had been calibrated with a mercury manometer. Gas leaks from the atmosphere into the sample cell were found to be negligible within the time period of the experiments. The method of calculation of 7 by successive approximations has been given in the Test section of part 1. The calculation of (1) (a) Work supported in part by grants from the National Science Foundation and the Edith C. Blum Foundation. (b) Abstracted from the Ph.D. Thesis of Shu-Huei Liu, Brandeis University, 1983; Diss. Abstr. Int., E 1983, 44, 1138. (c) Gillette Fellow, 1979-82. (2) Grunwald, E.; Liu, S.-H. J. Phys. Chem., preceding paper in this issue. (3) (a) Plyler, E. K.; Benedict, W. S . J. Res. Natl. Bur. Stand. (US.) 1951, 47, 202. (b) Plyler, E. K.; Acquista, N. Ibid. 1952, 48, 92. (4) (a) JANAF Thermochemical Tables, 2nd ed.; Natl. Stand. ReJ Data NSRDS-NBS37, 1971. (b) Milligan, D. E.; Jacox, M.E.; McAuley, J. H. J. Mol. Spectrosc. 1973, 45, 377. (5) (a) Rossing, T. D.; Legvold, S. J. Chem. Phys. 1955, 23, 1118. (b) Grunwald, E.; Lonzetta, C. M.; Popok, S. J. Am. Chem. SOC.1979,101, 5062.
TABLE I: Results for CHCIFl at 1088 cm-l av value during IR pulseb p,
F,‘
Torr J/cm2 aAe
1O4Eab/F,
“/mol
10-’/7, s-l
0.0000 16.1
EM, Ev, K kJ/mol kJ/mol 298.0 0.061 2.39 TTp,
1.55 0.0115 0.0458 0.228 0.582 0.822
6.58 4.24 2.87 3.46 4.00
5.6 f 0.3 5.9 f 0.4 7.3 f 0.6 11.4 f 1.0 13.7 f 1.2
298.2 298.7 300.5 306.0 311.6
0.157 0.272 0.725 2.08 3.23
2.66 3.13 4.93 10.24 15.25
2.47 0.0071 0.0329 0.0728 0.129 0.268 0.474 0.677
9.01 5.73 4.26 3.86 3.24 3.75 4.90
7.4 f 0.3 7.5 f 0.4 7.3 f 0.6 8.2 f 0.5 8.9 f 0.7 12.0 f 0.9 15.8 f 1 . 1
298.3 299.0 299.8 301.0 303.4 309.6 320.5
0.133 0.234 0.322 0.473 0.761 1.51 2.71
2.63 3.13 3.63 4.39 5.88 9.54 15.75
5.17 0.0095 11.25 0.0448 7.87 0.122 7.17
12.9 f 1 . 1 298.8 13.6 f 1 . 1 301.4 16.8 f 1 . 3 307.6
0.145 0.299 0.631
2.82 3.82 5.95
15.51 0.0130 13.70 0.0372 13.11 0.0855 12.62
24.0 f 3.1 301.2 30.2 f 2.6 308.0 32.5 f 2.7 324.5
0.143 0.287 0.559
3.11 4.34 6.61
25.85 0.0107 15.35 0.0360 14.84
34.2 f 6.6 302.0 39.2 f 4.0 313.2
0.123 0.269
3.04 4.46
51.7
0.0218 16.3 f 0.8
”The square-pulseequivalent pulse length in this series is 151 ns. I,, X 106F W/cmZ. bThe pulse-average value of a property Y denotes the average value of Y at which radiant energy is absorbed. YaV = J Y ( t ) w(total,t) dt/Jw(total,t) dt, integrated over the IR pulse. Measured by conventional low-intensity spectrophotometry. = 6.6
TABLE 11: Some Properties of CHCIF? (1) mol symmetry: C, (2) normal-mode wavenumbers: 365 (A”), 422 (A’), 595 (A’), 809 (A’), 1116 ( ~ 9A”), , 1178 (A’), 1 3 1 1 (A’), 1347 (A”), 3023 (A’) (3) 1116-cm? band ( Y ~ ) : r = 3.76 X lo4 cm2/mol; 8 = -10 cm-’ (4) wavenumber (cm-I), uA (cm2/mol) at 298 K: 1088, 1.61; 1098, 5.5; 1108, 7.5; 1118, 14.7; 1128, 3.66 (5) temp depeddence at 1088 cm-l; uA = 6.576T1.*exp(-0.00057‘); 298-600 K (6) mean rotational energy of absorbing subspecies at 1088 cm-‘ and 298 K: 7.8 kJ/mol (7) rotational const (cm-I): A = 0.3412; B = 0.1608; C = 0.1 163; no. of “branch bands” s = 9. (8) M,V and V,T/R rate const in eq I:23, I:24: kM,v = 2.8 X 10” s-lM-l (gas-kinetic collision-controlled); kV,TiR= (1 .O f 0.3) X 109 s - ~M-I ,
w(tota1) was based on eq I:17. It was sufficient to take the summation in (I:17) up to m = 4 only. When it became clear that l / r is in fact a linear function of the vibrational energy [E,(t)
0022-3654/86/2090-4555$01 .50/0 0 1986 American Chemical Society
4556
The Journal of Physical Chemistry, Vol. 90, No. 19, 1986
1116
Liu and Grunwald
I088 cm-’
Wovenumber Figure 1. Absorption from a 1088-cm-I laser in the y9 absorption band of CHCIF, centered at 11 16 cm-I. Solid arrow: absorption by subspecies with m = 0 at 1088 cm-l. Dashed lines spaced at -6 = 10 cm-’ intervals: absorption by subspecies with m = 1, 2, 3, 4.
+
Ev(t)], a more elaborate calculation was tried in which such a linear relationship was assumed. It was found, however, that this elaboration had little effect on the pulse-average result obtained for I/. and, in the end, the elaboration was dropped. For purposes of computing energy balance and temperatures during IR absorption, the absorbing gas was treated as a constant-volume closed system. Molar Absorptiuity. In eq I:14 and I: 17, aA is the Beer’s law molar absorptivity due to the m = 0 subspecies. When the substrate exists at statistical equilibrium, vibrational excitation of the absorbing mode may be neglected for present purposes up to T N 500 K. Statistical equilibrium exists and optical saturation is avoided during IR absorption if the gas pressure (and 117) is high enough so that the denominator in I:14 is nearly unity. Under such conditions Eab = SaAIdt, integrated over the laser pulse. At low intensities where T and aAare nearly constant, this reduces simply to Eab/F= uA. Accordingly, our data in Table I show that for CHCIFz, when P > 50 Torr, optical saturation is nearly avoided. To eliminate its effect more rigorously, we actually plotted Eab vs. 1 / P at constant F and extrapolated to 1 / P = 0. At higher intensities aAis a function of T(t) and therefore varies during the IR pulse. Model calculations for symmetric tops suggestedIb that the temperature dependence may be represented empirically by an equation of the form a,4(T) = A7-n exp[Y(T)I
(1)
where Y(T ) = B / T or B’T. Of the three parameters A , n, and ) known. To B or B’, only two are free since ~ ~ ( 2 9 is8 already evaluate the parameters, we measured Eab under avoidance of saturation over a wide fluence range and numerically integrated eq 2, trying various parameter sets until a set was found that dE,,(t)
= Cv[T(t)] d T = U,[T(t)] Z(t) dt
(2)
reproduced Ea, with a mean deviation of 0, the (TT/R) temperature dependence of uA(vL - ma) is assumed to be the same as that of aA( T). Rotational Energy of Laser-Actiue Subspecies. According to eq I:12 QA(VL,n
= VLx’(VL~T)P(VL)(r/s) ( l - gT)
where X’denotes the ensemble-average mole fraction of the laser-active rotational subspecies. The temperature dependence of aA is essentially that of X’, especially near room temperature. This allows one to estimate the average rotational energy of the laser-active ensemble, as follows. Let [S’] denote the ensembleaverage concentration of the laser-active subspecies at vL. In the absence of IR saturation, [Sf] exists in statistical equilibrium with
I 4 8 12 16 20
OO
E,
E,(kJ/mol) Figure 2. Plot of 1 0 - 8 / ~(s-l) vs. E M + Ev (kJ/mol) for 1.55 Torr of CHCIF,. Irradiation at 1088 cm-I. +
the total absorbing species [A]; that is, K = [S’]/[A] = X’; hence eq 3. By introducing the experimental temperature dependence
RF d In K / d T
= R F d In a A / d T
= Erot(Sf)- ErOt(A)= ErOt(S’) - 1.5RT
(3)
of uA (Table 11), we find that for CHCIFz at 1088 cm-’ and 298 K, E,,(S’) N 7.8 kJ/mol.
Kinetic Analysis Results. A summary is given in Table I. Each entry is an average based on three or more experiments. The pulse-average values listed in Table I are the average values at which radiant energy is absorbed, as defined in footnote b. Because the V-T/R rate of CHCIFz is relatively slow,5 the values of TT/R, and hence of ETIR, are fairly constant, while those of EM and Ev vary substantially. Thus, in first approximation, the measurements probe the dependence of 117 on vibrational excitation. Two facts stand out. First, the values of 1/r are substantially greater than the corresponding gas-kinetic collision frequencies. Second, at constant pressure the values increase systematically with fluence and Eab, and hence with the average vibrational energy during the absorption process. In fact, kinetic plots of I/. vs. the pulse-average vibrational energy EM Ev are essentially linear, as shown in Figures 2 and 3. The slopes and intercepts in these figures increase with pressure, indicating that the relaxation is at least partly collisional. Probable Mechanisms. First, a review of the relation of 7 to k’and k “ is in order. As defined in part 1, k’and k ” are ensemble-average rate constants for relaxation of the laser-active subspecies {S’,Sff}to photophysical steady state (“hole-filling”, in current jargon). In the present experiments, according to the mechanism to be developed, k’and k” are of similar magnitude. ~ be written in acceptable Thus, as indicated in (1:9), 1 / may approximation either as the algebraic or as the harmonic mean of k’and k”. For purposes of kinetic analysis the former is more convenient. We shall therefore adopt eq 4.
+
1 / = ~ (1/2)(k’+ k”)
(4)
Next, an identification of relaxation mechanisms is in order whose relaxation times are known to be longer than T by at least an order of magnitude. Such mechanisms make only minor ~ for present purposes, may be neglected. contributions to 1 / and, The following experimental and theoretical evidence suggests that intramolecular, kinetically first-order relaxation mechanisms may
The Journal of Physical Chemistry, Val. 90, No. 19, 1986 4557
Relaxation in Molecular Infrared Absorption
TABLE 111: Vibrational Excitation of CHClFl at Statistical Equilibrium
i X (EM f Ev)/ (EM + Ey)/ EM t Ev, D kJ/mol (1 t n,) xn,(l + ni) Cn,(l + n,)/u? 4.73 0.97” 298 2.45 0.518 4.71 0.98 321 2.99 0.635 4.66 1.01 422 5.99 1.286 1.02 4.56 503 8.98 1.969 1.01 4.46 574 11.97 2.683 1 .oo 4.36 639 14.96 3.428 700 4.27 0.99 17.96 4.206 T, K
state density 0.00313b 0.00362 0.00728
0.0131 0.0221 0.0353
0.0544
Values are relative. bPer wavenumber. Calculated by Haarhoff algorism. Haarhoff, P. C. Mol. Phys. 1963-4, 7, 101.
,
OO
4
8
12
16
E, + Ev(kJ/mol) Figure 3. Plot of 10-*/r (s-I) vs. EM + EV(kJ/mol) for 2.47, 5.17, and 15.51 Torr of CHC1F2. Irradiation at 1088 cm-’.
A Figure 4. An example of resonant exchange of vibrational energy. In this case u,’ goes up and vi goes down.
all be neglected. First, extensive measurements of V-V’ relaxation for halomethanes6 show no evidence for kinetically first-order processes on microsecond or even millisecond time scales. Second, Doppler-corrected microwave emission spectra due to molecules of similar atomic complexity at extremely low pressures in interstellar space show sharp lines,7 indicating intramolecular relaxation times of microseconds and longer. Finally, EM Ev and vibrational-state densities (Table 111) are well below levels at which high-energy intramolecular relaxation phenomena, currently described by such names as IVR, mode-mixing, quantum ergodicity, and chaos, are kinetically competitive.* Accordingly, possible rate laws for relaxation are kinetically of second order or higher. However, even in this category certain collisional processes are known to be too slow. In particular, rates of V-V’ and V-V‘,TJR relaxation have been measured by IR luminescence and thermal lensing.6 The processes that can be “seen” by these methods have relaxation times which are significantly longer than T. In our view, the only processes that remain eligible are those which conserve vibrational energy in the absorbing mode. This view is inherent in the energy flow pattern shown in Figure I:l. However, that flow pattern was adopted only after model calculations had shownlb that similarly large 1 / r values are obtained
+
(6) (a) Weitz, E.; Flynn, G. W. Annu. Reu. Phys. Chem. 1974, 25, 275. (b) Earl, B. L.; Gamss, L. A.; Ronn, A. M. Acc. Chem. Res. 1978.11, 183. (c) Flynn, G. W. Acc. Chem. Res. 1981, 14, 334. (7) (a) Kroto, H.W. Int. Reu. Phys. Chem. 1981, I , 309. (b) Johnson, D. R.; Lovas, F. J.; Gottlieb, C. A.; Gottlieb, E. W.; Litvak, M. M.; Guelin, M.; Thaddeus, P. Astrophys. J . 1977, 218, 370. (8) (a) McDonald, J. D. Annu. Reo. Phys. Chem. 1979,30, 29. (b) Oref, 1.; Rabinovitch, B. S . Acc. Chem. Res. 1979, 12, 166, Figure 3. (c) Part I, ref 8.
if the M and V modes are treated as existing in statistical equilibrium during the absorption process. In particular, we recognize two processes: intermolecular rotational relaxation (R-R’),9 and resonant vibrational energy exchange (V-V)-normally accompanied by rotational exchange.Ihl2 (R-R’) contributes to the intercepts in Figures 2 and 3, while (V-V), which speeds up on vibrational excitationlo but also contributes to the intercepts, accounts for the nearly linear increase in 117 with EM Ev. By comparing the absorption half-width A u ] / (eq ~ I:19) with typical changes in the branch-band frequency vb (Figure I:2c), one may conclude that, when a laser-active S’ or S” molecule undergoes R-R’ or V-V relaxation, it nearly always transfers into the “A” reservoir (Figure 1:l). For the experiments listed in Table I, the mean value of AvIlzis 0.03 cm-’ and the maximum is 0.08 cm-’. Changes in vb in R-R’ relaxation, by comparison, are likely to be at least as great as the smallest rotational constant, and in most events several times greater. For CHCIFz (Table 11), even the smallest rotational constant is greater than Aul12. Resonant V-V exchange causes relaxation because the center of the absorption band (uo), and hence ub, undergoes anharmonic frequency shifts. The V-V exchange may take place in any mode. Let u, and m denote the quantum number of the ith vibrational mode and of the absorbing mode, respectively. On writing Dunham equationsI3 to represent vibrational-state energies, and using the notation of Herzberg,13 one obtains eq 5 , in which the
+
x’s are the anharmonic interaction constants; 2XM,M = 6. The x’s are typically 1-10 cm-’. Hence nearly any change in any ui, with or without accompanying rotational change, will transfer a laser-active S’ or S” molecule into the A reservoir. Rate Law. We now wish to show that a rate law derived for parallel processes of rotational and resonant vibrational exchange is consistent with the linear plots of 1 / r vs. ( E M E,) shown in Figures 2 and 3. R-R’ exchange is usually treated successfully as a simple second-order p r o c e ~ s .Accordingly ~ we shall adopt eq 6.
+
The rate of V-V exchange, on the other hand, depends on vibrational excitation. For definiteness, consider a resonant collision between A and S’ in which the vibrational quantum numbers change in the ith mode (Figure 4). Let a(ui) and ( ~ ( 0 ; ) (9) (a) McGurk, J. C.; Schmalz, T. G.; Flygare, W. H. Adu. Chem. Phys. 1974,25, 1. (b) Schwendeman, R. H.Annu. Reu. Phys. Chem. 1978,29, 537. (c) Part I, ref 10. (10) Schwartz, R. N.; Slavsky, Z. I.; Herzfeld, K. F. J. Chem. Phys. 1952, 20, 1591; especially eq 19, p 1595.
(1 1) Mkrtchyan, M. M.; Platonenko, V. T. Sou. J . Quantum Elecrron. (Engl. Transl.) 1978, 8, 1187. (12) (a) Treanor, C. E.; Rich, J. W.; Rehm, R. G. J . Chem. Phys. 1968, 48, 1798, 1806. (b) Teare, J. D.; Taylor, R. L.; von Rosenberg, C. W. Nature (London) 1970, 225, 240. (1 3) Herzberg, G. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand: New York, 1945; eq 11.266, 11.271.
4558 The Journal of Physical Chemistry, Vol. 90, No. 19, I986
denote the mole fractions of A(ui) and S’(ui/), irrespective of excitation in other modes. For the two possible directions of resonant exchange, the intrinsic rates are then given by eq 7. The A(uj)
+ S’(V/)
k:(uii,u:t)
-+
A(ui - 1)
+ S’(U; + 1)
= yi,; a(ui)a(u:) ui(ui/
(7a)
+ 1) + S‘(U; - 1) k ; ( u i t , u / l ) = yi,;a(vi) a ( u / ) (vi + l)u/[A] (7b) factors vi(u; + 1) and (vi + l)u:, which cause the basic rate A(uj)
+ S’(U/)
+ 1)[A]
-+
A(ui
constant yi,, to increase with vibrational excitation, come from the theory of Schwartz, Slavsky, and Herzfeld (SSH).IO Let n, = x[uia(vi)] denote the mean excitation number of the ith mode. By summing over viand u: in both directions of resonant exchange, one obtains eq 8. The total k’v,v for all nine modes is given by eq 9. The rate law for S” is analogous. By hypothesis k’j,v-v = 2n;( 1 k’v,v = 2 C [n;( 1
+ nj’)yj,,’[A]
(8)
+ ni’)yi,;]
(9)
[AI
of the model, the mean excitation numbers n; and n/ are equal except in the absorbing mode, where ( m ” ) = ( m ’ ) 1. Consistently with this model, y,,; = y i , F for all i ; hence eq 10. On
+
k“v,v = k’v,v
~YM,M ( m( ) + 1)[AI
(10)
+
substituting in (4b), letting (1 ( m ) ) N 1, and defining yR,R, = (1/2)(7’R,R’ 7”R,R,), one obtains eq 11. The first term on
+
1 / 7 = (7R.R’ + 2YM,M)[Al + 2C[nd1 + ni)ri,il[Al
(11)
the right in (1 I ) is identified with the intercepts in Figures 2 and 3. It remains to show that the second term is proportional to E M Ev. We shall consider two cases: (1) yiqi= yo, a constant inde= y s s H / v t ,as predicted by SSH theory.I0 pendent of i; (2) y,,, In practice there is not much difference between cases 1 and 2 because, in both cases, relaxation is dominated by the two lowest frequency modes (Table 11). This is obvious in case 2; but even in case 1, throughout the temperature range, the two lowest frequency modes account for 70-8 1% of Eni(1 + n,) and hence of the total V-V exchange. In case 1, EM Ev must be proportional to x n i ( l + n,). Table 111 shows that this is nearly true at statistical equilibrium. In that case, (EM + Ev)/[Cni(l + ai)] is nearly constant at 4530 J/mol f 3% in the experimental range. After we allow for differences between T Mand Tv, using the data in Table I, this ratio changes slightly, to 4770 J/mol f 3%. In case 2, the expected proportionality between (EM + Ev)and ni(l + n,)/v? is satisfied in the experimental range with 2% accuracy, as shown by the final column of Table 111. The preceding cases may be regarded as plausible limits for the actual dependence of yi,i on vi. If the actual dependence fits either case or falls in between, the second term on the right in (1 1) will be nearly proportional to E M + Ev. In the following we shall therefore use a formal rate constant yv,v, which is a weighted average according to eq 12. Because of the weighting
+
+
YV,V
= Cni(1 + ni)yi,i/Cni(1
+ ni)
(12)
Liu and Grunwald TABLE I V Test of Rate Law for CHCIFl p,
Torr 1.55 2.47 5.17 15.51 25.85
intercept x obsd 4.2 f 0.4 5.8 f 0.6 9.4 f 1.1 19.7 i 2.4 24.2 f 4
slope x lo-* caicd 3.95 5.9 10.3 19.2 23.2
obsd 2.5 f 0.3 2.4 f 0.3 5.3 f 0.7 8.8 f 1.2 15 f 3
calcd 1.9 2.9 5.1 9.5 11.6
factor ni(1 + n,), yv,vis essentially yl,l for the two lowest frequency modes, which account for 70-81% of C n , ( l + ~ 2 , ) ~ ’ ~ At each pressure, I/. was plotted vs. Cn,(l + n,) and slopes and intercepts calculated by weighted least squares. These parameters are listed in Table IV. According to ( I l), both should be simply proportional to [A], Le., to the pressure of CHC1F2. In fact, the relationships show negative curvature. Experience with very high relaxation rates,I6 above the gas-kinetic collision frequency, suggests that negative deviations from simple proportionality to pressure (which might be due to termolecular and higher order encountersl’) already become significant at fairly low pressures. We shall therefore represent the slopes and intercepts by (13), where b and bslopeare parameters. Using the intercept = (yR,R, + 2yM,M)P/(1 + bP) (13a) slope = 27v,vP/(1 + b s l o , ~ ~ (1 3b) data in Table IV, we calculated the following kinetic constants by weighted least squares: yR,R, + 2yM,M = (2.9 f 0.3) x IO8 s-I Torr-’; b = 0.086 f 0.023 Torr-’; ofit/oexptl = 0.64; ~ Y V , V= (1.4 f 0.2) X lo8s-’ Torr-’; bsloF = 0.081 f 0.027 Torr-’; ofit/oexpt1 = 1.62. The magnitudes of the rate constants are acceptable. Rate constants for rotational exchange tend to be in the range 107-109 s-’ Rate constants for resonant V-V exchange of polyatomic molecules are expected to be high,12,’5relative to gas-kinetic collision frequencies, but facts are hard to find. As far as we know, this is the first report of a measurement of such a rate constant for like polyatmoic molecules.’* In conclusion, in spite of the complexity of the input data (Table I), the rate law obtained for relaxation during IR absorption is a simple algebraic function consistent with precepts of chemical kinetics. It leads to plausible mechanisms and rate constants. Moreover, regardless of mechanism, the bimolecular rate law shows that relaxation accelerates with increasing vibrational energy, which implies that IR absorption under the present collisional conditions is autocatalytic. Registry No. CHCIF,, 75-45-6. (14) Another reasonable model assumes the existence of vibrational steady ~ t a t e s . ’ ~This . ’ ~ model shifts vibrational energy into low-frequency modes and thus further accentuates the already dominant contribution of the two lowest frequency modes to yv,v. We expect, therefore, that the assumption of vibrational steady states will make little practical difference. ( 1 5 ) (a) Shamah, 1.; Flynn, G . J . Chem. Phys. 1978,69, 2474; Ibid. 1979, 70, 4928. (b) McNair, R. E.; Fulghum, S. F.; Flynn, G. W.; Feld, M. S. Chem. Phys. Lett. 1977,48, 241. (c) Grunwald, E.; Liu, S.-H.;Lonzetta, C. M. J . Am. Chem. SOC.1982, 104, 3014. (d) Rothman, N. C.; Dever, D. F.; Garcia, D.; Grunwald, E. J . Phys. Chem., in press. (16) Rogers, T. F. Factors Affecting the Width and Shape of Atmospheric Absorption Lines; Air Force Cambridge Research Center: Cambridge, MA, 1951. (1 7) Tolman, R. C . Principles ofSrntisfical Mechanics; Oxford University Press: Oxford, U.K., 1938; pp 67-71, 76-78, 245-250. (18) For V-V exchange of hydrogen halides, see: Leone, S. R. J . Phys. Chem. Re$ Data 1982, 11, 953.
