J . Phys. Chem. 1986, 90, 4559-4562
4559
Relaxation in Molecular Infrared Absorption. 3. CHCI,F at Several Wavenumbers. Effect of Rotational EnergyiaPb 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 four different wavenumbers, distributed over the v7 C-F stretching band so as to vary the average rotational energy of the absorbing molecules between 2.4 and 7.8 kJ/mol. Pressure of CHC1,F ranged from 1.5-47 Torr. Mean vibrational energy ranged from 3.37 to 20 kJ/mol. The relaxation mechanism is collisional and, as in the case of CHClF2, consists of parallel R-R’ and resonant V-V exchange. The rate constants are practically independent of the rotational energy.
In part 2,2 relaxation to photophysical steady state during infrared absorption (”hole-filling”) was studied for CHC1F2 only in the low-frequency wing of the absorption band, due to the limited range of the C02 laser.3 There are experimental and theoretical reasons, however, why one would like to vary the laser frequency so as to span the full width of an absorption band. We now report results for a structurally similar Freon, CHClzF, which come close to doing this. The notation will be the same as in part 2. Equations, tables, and figures in parts 1 and 2 will be cited with I: and 11: prefixes. Relevant proper tie^^-^ of CHC12F(g) are listed in Table I. On the experimental side, one would like to measure relaxation over a wide range of absorptivity. We used the C-F stretching band (v,) centered at 1079 cm-I. Measurements were made at 1057, 1068, 1080, and 1090 cm-l. This varies the absolute absorptivity of the m = 0 subspecies, as well as the relative absorptivity of subspecies with m > 0. Based on an anharmonic frequency shift (6) of -8 cm-I, Figure 1 shows a progression of arrows beginning at the laser frequency (solid arrow, m = 0) and moving toward higher wavenumbers at 8-cm-’ intervals ( m = 1, 2, ...). The arrows show that absorptivity increases with C-F stretching excitation at 1057 cm-’ and that it decreases at 1090 cm-I. For a harmonic oscillator (6 = 0), absorptivity on a similar diagram would be constant. Mean excitation numbers ( m ) in the present experiments ranged up to 0.12. On the theoretical side, by changing the frequency at which excitation takes place inside an absorption band, one changes the mean rotational energy (E,,,) of the absorbing molecules.6 In the present experiments, E,,, varied over a threefold range, from 2.4 to 7.8 kJ/mol. This may affect the rate constants (7)for both of the dominant relaxation mechanisms found in part 2-(R-R’) rotational exchange and (V-V) resonant vibrational exchange. For (R-R’) exchange, the effect of rotational energy is likely to be small. Published state-testate dynamical experiments7 indicate
(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. Absfr. Int., E 1983, 44, 1138. (c) Gillette Fellow, 1979-82. (2) (a) Grunwald, E.; Liu, S.-H. J. Phys. Chem., this issue, part 1. (b) Liu. S.-H.: Grunwald. E. Ibid.. this issue. Dart 2. (3) CRC Handbook of Lasers; Pressley,’R. D., Ed.; Chemical Rubber Co.: Cleveland, OH, 1971; Table 8-3. (4) (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. (c) JANAF Thermochemical Tables, 2nd ed.: Natl. Stand. Ref. Data Ser. NSRDS-NBS 37, 1971. ( 5 ) (a) Ultrasonic kV,TjRfor CHCIF2 and CHC12F Rowing, T. D.; Legvold, S. J . Chem. Phys. 1955, 23, 1118. (b) kv,T,Runder IR laser conditions: Grunwald, E.; Lonzetta, C. M.; Popk, S.J . Am. Chem. SOC.1979, 101, 5062. ( 6 ) Herzberg, G. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand: New York, 1945.
0022-3654/86/2090-4559$01.50/0
TABLE I: Some Properties of CHCltF (1) mol symmetry: C, (2) normal-mode wavenumbers: 270 (A’), 368 (A”), 455 (A’), 741 (A’), 806 (A”), 1079 (v,, A’), 1242 (A”), 1313 (A’), 3023 (A’) (3) 1079-cm-’ band (v7): r = 1.488 X lo4 cm2/mol; 6 = -8 cm-I (4) rotational const” (cm-I): A = 0.2323; B = 0.1090; C = 0.0777; no. of rotational fine-structure branches: s = 9 (5) mean rotational energy (kJ/mol) of absorbing subspeciesbat 298 K: 1057 cm-l, 7.8; 1068 cm-l, 3.9; 1080 cm-I, 3.6; 1090 cm-I, 2.4 (6) M, V and V, T/R rate const in eq I:23, I:24: kM,v = 2.8 X 10” s-lM-1 (gas-kinetic collision controlled); kV,T~R = 4 X IO9 s-l M-’ (7) temp, E M (kJ/mol), Ev (kJ/mol): 298 K, 0.071, 3.30; 381 K, 0.223, 5.77; 458 K, 0.451, 8.53; 527 K, 0.716, 11.25 (8) laser properties: wavenumber (C02 transition) pulse length: 1057 (P8) 0.59 ps; 1068 (R4) 0.41 ps; 1080 (R22) 0.59 ps; 1090 (R40) 0.49 ps ‘ A , B, and C are about 30% smaller than the corresponding constants for CHC1F2. *Based on d In a,/dT, eq 11:3, and data in Table 11.
that over a narrow range of rotational quantum numbers, 7 R , R t for polyatomic molecules is nearly independent of the rotational energy.” The present experiments allow E,,, to vary over a considerably wider range. For yv,v of polyatomic molecules, dependence on rotational energy apparently has not been measured. The phenomenon is of interest because, in theory, (V-V) exchange is likely to occur with coupled rotational exchange.* It turns out that the rate law and relaxation mechanisms for CHC12F are, at all experimental wavenumbers, analogous to those ~ both for CHCIFz.2bAs shown in Figures 2 and 3, 1 / increases with the pressure P of CHC12F, and with the mean vibrational energy (EM Ev).At constant P the dependence on ( E M+ E,) is approximately linear and can be rationalized in terms of eq II:13. The parameters b and bslopeagain2bare practically equal. ( E M + Ev)againzb is nearly proportional to C n i ( l + ni), where n, denotes the mean excitation number of the ith mode and the summation extends over all nine vibrational modes of CHC12F. Accordingly, the rate law for 1 / is~ represented by
+
l / =~ [ Y R , R ~+ ~ Y M , M+ 2Cni(1
+ ni)~v,vlP/(1 + bP)
(1)
(7) (a) Mader, H.; Lalowski, W.; Schwarz, R. 2. Naturforsch., A 1979, 34, 1181. (b) Orr, B. J.; Haub, J. G.; Nutt, G. F.; Steward, J. L.; Vozzo, 0. Chem. Phys. Lett. 1981, 78, 621. (c) Rordorf, B. F.; Knight, A. E. W.; Parmenter, C. S.Chem. Phys. 1978, 27, 11. (d) Schrepp, W.; Bestmann, G.; Dreizler, H. Z . Naturforsch., A 1979, 34, 1467. (e) Bomsdorf, H.; Dreizler, H. 2. Naturforsch., A 1981, 36, 473. (f) Casleton, K. H.; Chien, K.-R.; Foreman, P. B.; Kukolich, S. G. Chem. Phys. Lett. 1975, 36, 308. (g) Williams, J. R.; Kukolich, S.G. Chem. Phys. 1979, 36, 201. (h) Tanaka, K.; Hirota, E. J . Mol. Spectrosc. 1976, 59, 286. (i) Roodhart, L. P.; Wegdam, G. H. Chem. Phys. Lett. 1979, 61, 449. (8) Mkrtchyan, M. M.; Platonenko, V. T. Sou. J . Quantum Electron. (Engl. Trans!.) 1978, 8, 1187.
0 1986 American Chemical Society
4560
The Journal of Physical Chemistry, Vol. 90, No. 19, 1986
Liu and Grunwald
1
I/
7.41 torr
1
I
0 1090
1057
- .
Wavenumber
3.97torr
Figure 1. Absorption in the 1079-cm-I u7 C-F stretching band of CHC12F. The laser wavenumbers of 1057, 1068, 1080, and 1090 cm-I are shown by the solid arrows. The dashed lines are spaced at the anharmonic frequency shift.
44 1080 cm-'
0
0
e
4
E, +E, Figure 3. Plots of 10-'/~* vs. EM
12
16
20
(kJ/mol)
+ Ev at several pressures for cL = 1080
cm-I.
TABLE II: Molar Absorptivities of CHC12F, in cmz/mol ( 1 ) Results at 298 K 10-5~~
-
t
(IR spec)O
(laser,
1057
1.27
1.28
1068
4.40
4.46
1080
3.20
3.17
1057 cm-'
0
0
4
E,
+
8
E, (kJ/mol)
Figure 2. Plots of 1 0 - 8 / ~ *vs. EM + Ev at several pressures for uL = 1057 cm-I. Experimental Part Dichlorofluoromethane was obtained from Matheson in better than 99%purity, confirmed by the absence of impurities detectable by GC/MS. The gas was transferred on a standard vacuum line and was degassed before experiments by repeated freeze-pump thaw operations. Procedures for measuring P, Eab,and 1 / r have been described in parts 1 and 2.2 Shortly before the start of the present experiments, the C 0 2 laser was equipped with new optics and new gas-flow controls. The laser gas used in the present experiments was richer in N2 than in part 2. Square-pulse equivalent pulse lengths were 0.4-0.6 ps. Precise values are given in Table I. Relaxation times 7 were short enough to permit use of the same energy-flow pattern (Figure I: 1 ) and computational methods (numerical integration of eq I:17) as in part 2. The anharmonic frequency shift (6 = -0.08 cm-') was obtained from the fundamental and first overtone ( v ~ ,of~ the ) u7 C-F stretching mode. s = uo.2 - 2VO.l. Molar Absorptivity. Table I1 lists low-intensity absorptivities (aA) measured at room temperaure by two independent method^:^ (1) by spectrophotometry, with an accuracy of 4-7% depending on accuracy of wavelength calibration and steepness of the absorption band; (2) by laser beam photometry, with an accuracy
--
10-5Eab/F
wavenumber
-
(9) Duignan, M. T.: Garcia, D.; Grunwald, E. J . Am. Chem. S O ~1981, . 103, 7281.
1090
3.33
3.71
12) Effect of TemDerature exp(-625/T) ex;-1580/T) T i / * [(l + 0.OOlSr) (1 0.00035T)]'uA = 2.072 X 1 0 9 F i25 exp(-394/T), 1068 cm-I aA = 4.662 X 1 0 7 p 7 5exp(-214/T), 1080 cm-I aA = 1.817 X 1 0 8 T i exp(-148/T), 1090 cm-' 2.473 X lo7
+
+
mS)/aA(u)c
M
ratio
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
2.6 4.0 3.3 3.0 0.93 1.33 0.58 0.17 1.32 0.45
0.10 0.006 0.28 0.04 0.004
cm-'
a Measured by conventional spectrophotometry. *Results at constant [CHCI2F]were plotted vs. F and extrapolated to F = 0. P = 130-350 Torr. '6 = -8 cm-l.
of 5%, of the low-fluence, high-pressure (>250 Torr) limit of E,,IF, as described in part 2. The two sets of values are in good agreement, thereby confirming the accuracy and consistency of the measurements. Table I1 also lists U, as a function of temperature for each laser wavenumber. Measurements were made as described in part 2. Pressures of CHC12F were above 100 Torr, to make optical saturation small enough to permit accurate extrapolation to 1/P = 0. Numerical integration according to (II:2) utilized empirical equations of the form (1I:l) to represent a,(?-). With the equations listed in Table 11, the experimental results for Eabwere reproduced at each wavenumber up to about 600 K with a mean deviation of 12%. Mean rotational energies of the absorbing subspecies at each wavenumber were calculated from d In a,/dT on the basis of eq II:3.
The Journal of Physical Chemistry, Vol. 90, No. 19, 1986 4561
Relaxation in Molecular Infrared Absorption TABLE III: Results for CHCllF at 1068 cm-' av value during IR pulse"
0
1.55 0.0014 0.0077 0.0300 0.104 0.339 0.599
44.6 23.8 12.2 6.98 4.35 2.38 2.33
3.04 0.0022 0.0126 0.0374 0.108 0.279 0.545
25.1 13.6 8.13 5.78 3.94 2.71
4.85 0.0018 0.0068 0.0155 0.0322 0.0698 0.191 0.475
29.9 21.0 15.9 11.7 9.23 6.16 4.68
0.0056 0.0301 0.0675 0.183 0.403
34.8 21.8 17.6 13.5 10.2
23.8 0.0079 0.0253 0.0465 0.0933 0.201 0.325
33.7 26.4 23.0 19.4 15.6 13.0
15.5
3.5 f 0.2 298.6 3.2 f 0.2 300.0 3.3 f 0.2 302.9 3.8 f 0.2 308.7 3.7 f 0.3 317.2 4.9 f 0.6 330.8 2.7 f 0.3c 4.8 f 0.3 299.7 4.7 f 0.3 304.1 4.4 f 0.3 309.4 5.2 f 0.3 321.4 5.7 f 0.5 339.1 5.5 f 0.8 352.6 3.7 f 0.4c 6.2f 0.3 300.1 6.3 f 0.3 304.2 6.4 f 0.3 309.2 6.2 f 0.4 315.7 7.0 f 0.4 328.4 7.6 f 0.5 352.9 9.5 f 1.0 397.2 5.0 f 0.Y 16.0f 1.3 309.9 14.4 f 0.8 340.2 16.1 f 0.8 373.0 20.7 f 1.1 445.3 24.7 f 1.3 528.5 10.9 f l . l c 17.3 f 0.9 316.2 18.5 f 0.9 344.0 20.2 f 1.0 370.3 23.4 f 1.2 416.5 28.4 f 1.4 492.2 31.1 f 1.6 550.7 13.8 f 1.3c
0.094 0.126 0.190 0.331 0.546 0.936
3.43 3.66 4.11 5.03 6.36 8.60
0.097 0.142 0.193 0.331 0.557 0.748
3.51 3.93 4.42 5.57 7.29 8.64
0.092 0.121 0.154 0.196 0.293 0.505 0.993
3.50 3.81 4.17 4.62 5.54 7.36 1 1.03
0.118 0.234 0.391 0.858 1.55
3.93 5.36 7.02 11.17 16.59
0.127 0.223 0.332 0.570 1.06 1.51
4.12 5.34 6.56 8.88 13.14 16.69
"See part 2, Table I, footnote b. *For E ( T ) data, see Table I. CIntercepteq 2a.
Kinetic Analysis Definition of T * . In the replacement of unknown parameters by measurable quantities in part 1, the average branch-band area Ab (eq I:7) of the laser-active subspecies was equated to r/s,where r is the measured molar absorption cross section for the vibrational transition (eq. I:l3) and s is the number of rotational fine-structure branches. In principle A b / r is not constant at its mean value of 1/s, however, but varies with wavenumber in the absorption band.''J' The relationship can be predicted theoretically for a symmetric top, for which the variation of fR(Y) is fairly small.'' In the present case of an asymmetric top" and an absorption band with unresolved rotational fine structure, accurate prediction of fR(v) may not be feasible, but the following qualitative remarks can reasonably be made. First, because fR is an ensemble average which includes a diversity of rotational quantum states, one may assume that state-wise differences in branch-band area Abk1are largely averaged out in fR. Second, one may assume that the mean of fR(v) for any representative set of wavenumbers (such as the four used in the present work) is equal to l/s. Let A b / r = fR and let fR be an unknown parameter of magnitude l/s. In eq I:14 and I:17 the unknown parameter then becomes fRT2 instead of T ~ In . a kinetic analysis at fixed wavenumber this introduces a constant factor of error into each measurement, but does not affect the mathematical form of the rate law. When kinetic data at different wavenumbers are compared, however, the unknown factor must be expected to vary with wavenumber, and that will complicate the comparisons. (10)Rademacher, H.;Reiche, F. Z . Phys. 1927, 42, 453. (1 1) (a) Crawford, B. L.; Dinsmore, H. L. J. Chem. Phys. 1950,18, 1682. (b) Fox, K.; Person, W. B. J . Chem. Phys. 1976, 64, 5218. (c) Cross, P. C.; Hainer, R. M.; King, G.W. J . Chem. Phys. 1944, 22, 210.
TABLE I V Results of Kinetic Analvsis r (eq 2b) vs. P (YRR + Erot w avenumber av Scatter' Uexp: ~ Y M , M ) / ~ RkJ/mol '/~~ 0.35 0.20 0.20 1.5 f 0.3d 7.8 1057 1068 0.218 0.021 0.06 1.6 f 0.3 3.9 1080 0.236 0.056 0.07 1.8 f 0.6 3.6 1090 0.278 0.053 0.11 1.2 f 0.2 2.4 av 0.228 0.02 1.5 f 0.2
" Standard deviation of fitted parameters obtained at different pressures. bStandard error in r based on experimental error in P and I / T * . c ~ - ' Torr-' X In the following we shall let T * = TfR1/' and rewrite eq 1 in the cognizant form (2). For CHC12F, in first approximation, T* = 7/3.
Results. Photometric data a t 1068 cm-I, computed values of 1 / T * , and computed average energies and temperatures during the IR pulses are listed in Table 111. Similar results a t 1057, 1080,and 1090 cm-' are given in supplementary Tables SI-SIII. Each result is the average of three or more measurements. Results obtained at 1057 and 1080 cm-' are plotted in Figures 2 and 3. As shown by these typical plots, l / s * increases nearly linearly with the vibrational energy (EM Ev). By calculations similar to those reported in part 2 one finds (supplementary Table SIV)that (EM+ E,) is nearly proportional to Eni(1 + ni) in the following cases: (1)when yi,i is equal for all modes; (2) when yi,i = yssH/vi2; (3) whenever both Cni(l+ ni) and + ni) are dominated by the one or two lowest frequency modes. The equation, EM + Ev = 3.44Cni(l + ni) kJ/mol fits all our ex-
+
perimental conditions with a standard deviation of 3%. Thus, the linear energy dependence shown in Figures 2 and 3 is consistent with that implied by eq 2. According to eq 2, the rate-constant ratio r is independent of P and fR. To test for pressure independence, we fitted our results at constant P and uL (Tables 111, SI-SIII) to eq 2, using the least-squares algorism of Wentworth.I2 Results of these calculations are summarized in Table IV. In order for r to be independent of P, the scatter of the least-squares slopes must be consistent with the experimental error. Comparison of columns 3 and 4 shows that this is indeed the case. More important, r is independent of vL (and hence of the rotational energy E,,,), at least within uncertainty levels defined by the experimental error. The relatively high r value found at 1057 cm-l, where E,,, is relatively high, is physically remarkable but statistically not significant. The parameter b in (2) was calculated by least-squares adjustment to fit all four wavenumbers, using a constant value of 0.228 for r. The result is b = 0.075 f 0.025 Torr-', practically the same value as that found for CHClF2 in part 2. Least-squares results for the intercept parameter in (2), (7R.R' + 2yMM.M)/fR'/', are listed in column 5 of Table IV. Statistically this parameter is likewise independent of uL and E,,,, with an uncertainty comparable to that of r. In summary, although the results obtained for r, (7R.R' + 2yM,M), and fR are inaccurate enough to leave some room for physical variation with uL and E,,,, it is clear that any such variation is relatively small. Rate Constants. Averages obtained for the kinetic parameters are r = 0.228 A 0.02 and (7R.R' 2yM,M)/fR'/* = (1.5 0.2) X lo8 s-I Torr-'. On using the theoretical average, l/s = 1/9, for fR, one obtains the following rate constants: YR,R, + 2yM = (5.0 f 0.7) X lo7 s-l Torr-' and yv,v = (1.1 0.2) X lo7 s-' Torr-'. Both rate constants are nearly independent of the average rotational energy E,,, of the relaxing molecular ensembles. Both
*
+
*
(12)Wentworth, W.E.J . Chem. Educ. 1965, 42, 96.
4562
J . Phys. Chem. 1986, 90, 4562-4568
are also substantially smaller than the corresponding rate constants for CHClF, reported in part 2. Statistically the difference from CHCIF, is highly significant, but a theoretical discussion is beyond the scope of this work. Concluding Remarks. The results of this and the two preceding papers show that relaxation during IR absorption can be measured by relatively simple and inexpensive means. The relaxation times are physically well defined and accurate enough to justify traditional kinetic analysis. In the presence of even mild vibrational excitation, the kinetics of relaxation becomes dominated by resonant v-V exchange. Although resonant v-v exchange is ~ e l l - k n o w n , 'its ~ importance as an autocatalytic collisional
mechanism for overcoming optical saturation has not been adequately appreciated in recent computer modeling of IR absorption. Under the relatively mild conditions of the present experiments, the molecular vibrations remain within the familiar domain of low-energy vibrational spectroscopy.6 In principle there is no reason why, under more drastic conditions, the method should not be extendible above the low-energy domain. However, the validity of the assumptions made in part 1 must then be reexamined carefully. Registry No. CHC12F, 75-43-4.
Supplementary Material Available: Tables SI-SIV of results for CHC1,F at 1057, 1080, and 1090 cm-' and vibrational excitation at statistical equilibrium (4 pages). Ordering information is given on any current masthead page.
(13) Schwartz, R. N.;Slavsky, 2. I.; Herzfeld, K. F. J . Chem. Phys. 1952, 20, 1591.
Modeling the Pressure Effect on the Multiphoton Absorption and Dissociation of CDF,. Collisional Energy Transfer B. Toselli, J. C. Ferrero,* and E. H. Staricco Instituto de Investigaciones en Fisicoquimica de C6rdoba (INFIQC), Departamento de Fisico Quimica, Facultad de Ciencias Quimicas, Universidad Nacional de CGrdoba, Sucursal 16, C. C. 61, 5016 C6rdoba. Argentina (Received: January 30, 1986)
A simple model based on the solution of the master equation, but including rotational effects in the first discrete levels, has been used to model the uL(@) and reaction probability results for CDF3 in a wide range of experimental conditions. We investigated the role played by collisions in order to overcome restrictions to the absorption processes, which is a striking feature of small molecules. By solving the rate equations we have been able to obtain information about the rotational relaxation rate of CDF, by collisions with CDF3,CHF3,and Ar as well as information about the average energy transferred by collisions between the different buffer gases and the vibrationally excited CDF,. For CDF, (CHF3) as collider the values determined are k,,(CDF,-CDF,) = k,,,(CDF3-CHFJ = (3.0-6.0) X ns-' Torr-' and ( A E ) d= 3 kcal mol-', and for Ar as bath ns-' Torr-' and ( A E ) , < 0.7 kcal mol-'. gas, k,,,(CDF,-Ar) = 6.7 X
Introduction The transference of vibrational energy from highly excited molecules to a bath gas has been studied mainly by chemical activation' and more recently by direct t e c h n i q ~ e s . ~Also ~ ~ some attempts were made to obtain information on energy transfer from the multiphoton decomposition of molecules in the presence of a bath gas by modeling the experimental results with a master equation form~lation,"~ as well as in nonreactive condition^.^' Probably one of the most comprehensive studies in this direction was made by Gilbert et al. on ethyl acetate.' As this is a large molecule, the high density of vibrational states assures the resonant condition and thus all of the irradiated molecules absorb the laser radiation and can be excited to energies above the reaction threshold, while competing with collisional deactivation during the pulse. Whereas this is true for large molecules, in the case of small molecules only a fraction of the total population is in ( 1 ) Tardy, D. C.; Rabinovitch, B. S . Chem. Rec,. 1977, 77, 369. (2) Barker, J. R. J . Phys. Chem. 1984, 88, 1 1 . (3) Hippler, H.; Troe, J.; Wendelken, H. J. Chem. Phys. Letr. 1981, 84, 257; J . Chem. Phys. 1983, 78, 6709, 6718. (4) (a) Stone, J.; Thiele, E.; Goodman, M. F.; Stephenson, J. C.; King, D. S. J . Chem. Phys. 1980, 73, 2259. (b) Stephenson, J. C.; King, D. S . ; Goodman, M. F.; Stone, J. J . Chem. Phys. 1979, 70, 4496. (5) Baldwin, A. C.; van den Bergh, H. J . Chem. Phys. 1981, 74, 1012. ( 6 ) Jalenak, W. A,; Nogar, N. S. J . Chem. Phys. 1983, 79, 816. (7) (a) Eberhardt, J. E.; Knott, R. B.; Pryor, A. W.; Gilbert, R. G. Chem. Phys. 1982,69,45. (b) Brown, T. C.; Taylor, J. A.; King, K. D.; Gilbert, R. G. J . Phys. Chem. 1983,87, 5214. (c) Zellweger, J. M.; Brown, T.C.; Barker, J. R. J . Chem. P h p . , in press.
0022-3654/86/2090-4562$01.50/0
resonance with the laser field and the extraction of the amount of energy transferred per collision requires either a knowledge of the fraction of excited molecules or experimental data in conditions where this rotational fractionation could be neglected. So far the results obtained for small molecules were not in all of the cases coincident. The reason can be attributed to the fact that the information was obtained by fitting only the reaction probabilities data, while it is at present well established that a reliable use of the master equation requires a fit to both the reaction probabilities and the absorption cross sections as functions of the incident Also, the convergence of the solution with decreasing grain size was not confirmed and when fractionation was included it was introduced as an adjustable parameter and without considering its intensity dependence during the pulse. Clearly, the wider the range of experimental conditions the master equation results fit, the more confidence can be assigned to the calculations. In this sense, one of the small molecules that received more attention is CDF,, mainly because the selective absorption of COz laser radiation relative to the normal species, CHF,, makes this molecule a candidate for laser enrichment of deuterium.I0 We have recently reported a modeling study which satisfactorily (8) Toselli, B.; Ferrero, J. C.; Staricco, E. H. J . Phys. Chem. 1985, 89, 1492. (9) Jang, J. C.; Setser, D. W.; Ferrero, J. C. J. Phys. Chem. 198!5,89, 414. (IO) (a) Herman, I. P.; Marling, J. B. Chem. Phys. Lett. 1979,64,75. (b) Tuccio, S . A.; Hartford, Jr., A. Chem. Phys. Lett. 1979,65, 234. (c) Marling, J. B.; Herman, I. P.; Thomas, S. J. J . Chem. Phys. 1980, 72, 5603. (d) Evans, D. K.; McAlpine, R. D.; Adams, H. M. J. Chem. Phys. 1982, 77, 3 5 5 1 .
0 1986 American Chemical Society
