6759
J. Phys. Chem. 1991,95,6759-6762
Relaxation of Molecules wlth Chemically Significant Amounts of Energy: Vibrational, Rotatlonal, and Translational Energy Recoil of an N,O Bath Due to Collisions with NO2 ( E = 63.5 kcai/moi) Liedong Z h g , James Z. Cbou, and George W . Flynn* Department of Chemistry and Columbia Radiation Laboratory, Columbia University, New York, New York 10027 (Received: June 24, 1991; In Final Form: July 22, 1991)
Singledision quenching of highly vibrationallyexcited NO2by N20 molecules has been studied. The ground state, N20(OOOO), first (u,) asymmetric stretch, N20(W1),and first ( u l ) symmetric stretch, N20(10%),vibrational levels of NzO were probed by using infrared diode laser techniques following pulsed dye laser excitation of NOz to an energy E = 63.5 kcal/mol (22 200 cm-I). Excitation of both the N20 ~ ~ ( 1 0 % and ) ~ ~ ( states ~ 1by )collisions with high-energy NO2 is accompanied by only a small rotational and translational energy increase. In marked contrast, rotational excitation of N20(00%) ground-state molecules due to collisions with high-energy NO2 is accompanied by a large increase in translational energy.
introduction The simplest model for unimolecular decomposition is the Lindemann mechanism1I2in which a substrate S is excited by collisions to a level S* with energy sufficient to cause break up of the substrate. For large molecules the time scale for decomposition of S* is sufficiently long that further collisions with the bath molecules can cause deactivation of the excited substrate, thus quenching the reaction prows. While many studies of the quenching of such highly excited substrate molecules have been performed?-20 until recently there was no technique that could
( I ) Lindemann, F. A. Trans. Faraday Soc. 1922,17, 598. (2) Oref, 1.; T a d , D. C. Chem. Rco. 1990, 90, 1407. Tardy, D.C.; Rabindtch, B. S. Clem. Rcv. 1977, 77,369. (3) Hippler, H.; Tm,J.; Wmdelken, H. J. J. Chem. fhys. 1983,78,6709. Abel, 6.; Hcmg, 6.; Hlppler, H.; Tra, J. J. Chem. fhys. 1989, 91, 900. Heymann, M.;Hippler, H.; Nahr, D.; Plach, H. J.; Troc, J. J. fhys. Chem. 1988,92,5507. Dove, J. E.;Hi ler, H.; Tra, J. J. Chem. fhys. 1985,82, 1907. Hcymann, M.;Hippler, ZPlach, H. J.; T m , J. Ibfd. 1987,87,3867. (4) Barker, J. R.; Roui, M.J.; Pladzicwicz, J. R. Chem. fhys. b t t . 1982, 90, 99. Barker, J. R. J . fhys. Chem. 1984. 88, 11. Shi, J.; Bernfeld, D.; Bark, J. R. 1.Chum. fhys. 19811,88,6211. Shi, J.; Barker, J. R. Ibid, 1988, 88,6219. Zellweger, J. M.;Brown, T. C.; Barker, J. R. J. Chem. fhys. 1985, 83, 6261. (5) Yerram. M. L.; Brenner, J. D.; King, K.D.; Barker, J. R. J. fhys. Chem., submitted for publication. (6) Jalcnak, W.; Waton, Jr., R. E.; Sears, T. J.; Flynn, G. W. J. Chem. fhy8. 1988,89,2015. Jalenak, W.; Waton, Jr., R. E.; Sears, T. J.; Flynn. G. W. J. Chem. fhys. 1985,83,6049. (7) Wkcek, A. J.: Weston, Jr., R. E.; Flynn, G. W. J. Chem. fhys. 1991, 94, 6483. (8) Cafraquillo, E. M.;Utz, A. L.; Crim, F. F. J. Chem. fhys. 1988,88, 5976. (9) Tamp, F.; Halle, S.; Vaccaro, P. H.; Field, R. W.; Kinscy, J. L. J . Chem. fhys. 1987,87, 1895. (10) &wick, C. P.;Orr, B. J. J. Chem. fhys. 1990,93,8634. Bewick, P.; MaftiM, J. F.; Orr, B. J. J. Chem. fhys. 1990, 93, 8643. (11) Tang, K. Y.; Parmenter, C. S. J . Chrm. fhys. 1983, 78, 3922. Krajnavich, D.J.; Pannenter, C. S.; Catlctt, D. L. Chem. Rco. 1987,87,237. Tang, K. Y.;Pannenter, C. S. J. Chem. fhys. 1983,78,3922. Thoman, Jr., J. W.; Kable, S. H.; Rock,A. 6.;Knight, A. E. W. J . Chem. fhys. 1986,85, 6234. (12) Weuman, R. Bruce; Rice, Stuart. Chem. fhys. Lett. 1978,61, 15. Chernoff, Donald A.; Rice, Stuart A. J. Chem. fhys. 1979,70,2511,2521. Sulka Mark:Tw. James: Rice. Stuart A. J. Chem. fhvs. 1980.72.5733. (13) B o v i l & ~ a , ~ T J.;. Andrew,, B. K.;Stout, J. E.; Weisman, R. B. J . Chem. Phys. 1990,92,4627. (14) Donmlly, V. M.;Keil, D. 0.;Kaufman, F. J. Chem. fhys. 197!9,71, 659. (IS) Keyrcr, L. F.;Levine, S. 2.;Kaufman, F. J . Chem. fhys. 1971,51, 355. K-, L.F.; Kaufman, F.; Zipf, E. C. Chem. fhys. b t r . 1968.2.523. (16) Schwartz, S. E,;Johnston, H. S. J. Chem. fhys. 1969, SI, 1268. (171 thou, J. 2.;H h t t , S. A.; Hcnhbqer, J. F.; Brady, 6.;Spector, 0. 6.; Chla, L.; Flynn. 0. W. J . Chem. Phys. 1989, 91, 5392.
OO22-3654/91/2095-6759S02.50/O
be used to follow these processes with quantum state nsolved detail on a single-collision time scale.18 The high density of quantum states of the substrate S*made such studies difficult to perform experimentally. Recently, we reported the deactivation of highly vibrationally excited NOz* by C02 bath molecules on a singlecollision time scale using infrared diode laser probe techniques to resolve the excitation of the COz(OOol) asymmetric stretch vibrational level.I8 We were able to completely resolve not only the vibrational excitation of this asymmetric stretch mode but also, due to the extraordinary resolution of the diode probe method,"-21 the rotational excitation and translational recoil of these same vibrationally excited molecules. To fully analyze the deactivation process for such highly vibrationally excited molecules as NO2*, however, the level of excitation, rotational profiles, and translational recoils of different vibrational modes,as well as the amount of energy transferred to the rotational and translational degrees of freedom of the ground (vibrationless) state of the bath molecules, are required. We report here for the first time the single-collisionenergy-transfer process between highly vibrationally excited NO2*molecules and N20 molecules, in which the level of excitation of the two different bath stretching modes (N20(10%) and N20(0@1)),their rotational populations, and their translational energy recoil profiles have been probed. In addition, the translational recoil energy of several rotational levels of the vibrationless ground-state N20(ooo0,J),arising from N02*/N20 collisions, has been determined and found to be dramatically different than that of the vibrationally excited states, indicating quite different mechanisms for the excitation of bath states with and without vibrational excitation. Experimental Section
The diode laser probe technique used in our laboratory has been described in detail In brief, excited NO2molecules (NOJq) are produced at energy E = 22 200 cm-' by an excimer pumped dye laser (-20 ns pulse width) working at 450.5 nm,
NOz
+ hv(450.5 nm)
-
NO2(@
The N02(mmolecules are in states which are a mixture of -80% highly vibrationally excited electronic ground state and 20% electronically excited states." Collisions of NOJa with N20caw translational, rotational and vibrational excitation of the first v1 (18) Chou, Jama 2.; Flynn, George W. J . Chem. fhys. 1990,93,6099. (19) Chou, Jama 2.; Hewitt, Scott A,; Hcrshberger, John F.; Flynn, George W. 1.Chem. fhys. 1990, 93, 8474. (20) Brady, B. Ph.D. Thesis, Columbia University, 1986. (21) Hewitt, Scott A,; Hershbcrgcr, John F.; Chou, Jama 2.;Flynn, W. J . Chem. Phys. 1990, 93,4922.
CO 1991 American Chemical Society
6760 The Journal of Physical Chemistry, Vol. 95, No. 18, 1991
Letters a
0 014
0O i l 0 010
2 0 008 0 006
0 004
00’0
R62
0 002
Vibralwnless Ground State 0 010
-0 005
0 000 0 005 Wavenm”rs tiom lhne center
-0 010
b 0 008
0 006 P
E
0 004
00’1
0 002
N,O
First Asymmetric Stretching Stale
0 000
TR-338K
.O 004 0 000 0 004 Wavenumbers trom line center
0 008
L
0 000-
2
0006-
E 0 002-
I
I
I
1
I
200
400
600
800
1000
,/(2J + I)] as a and fits (solid lines) to Boltzmann plots of In [N,,,, function of J(J + 1) observed 1 ps after excitation o?NO$m. (a) Data for wl oo0z obtained from R branch transitions with J = 5, 14,24, 25, 32, and 31. (b) Data for 10% 10°l obtained from R branch transitions with J = 7, 8, 17, 18,28,29, and 30. The data were taken at 295 K,using 25 mTorr of a 1:l mixture of N20/N02. The mean time between N02/N20gas kinetic collisions is 4 f l under these conditions.
-
+
symmetric stretching (1000, 1285 cm-’) and u3 asymmetric stretching (0001,2224 cm-’) vibrational states as well as rotational and translational excitation in the ground vibrationless (oo00)level,
NO+’)
+ N20(0000)
-
+
+
N02(E-M)+ N20(O0°1,J,V)
+ N20(1000,J’,V’) N02(E-M)+ N2O(OOOO,J”,V’9 NOJ’-w
J , J’, J”repre~enfrotational angular momentum quantum numbers and V, V’, V’!,the recoil velocities for the corresponding rovibrational states. A tunable diode laser operating CW a t 4.5 pm is used to probe the P and/or R branch bands of the following transitions,
+ hv(4.5 pm) N20(1000,J’,V9 + hu(4.5 r m ) N20(0O00,J”.V”) + hv(4.5 pm) N,0(0O01,J,V)
--
Ri5
lrst Symmetric Stretching Slate
I
+ N20(OOOO) NO2(a + N20(0000)
10°O
~
Figure 1. Nascent experimental N20 rotational distributions (circles)
NOJ‘)
C
T-295K
0004-
I
0 008
TT:320K
0 oio-
I
R18
Rotational Distribution
10’0
N20(0002,Ji1,V) N,0(1O01,J~f1,V’) N20(0001,J”fl,V’’)
Velocity recoils are measured by probing the nascent Doppler profiles for different spectral lines. The initially excited molecules can produce deexcited species, such as which are also able to excite N20. In the present experiments, however, the N 2 0 concentrations and Doppler velocity profiles are measured at such a short time after the initial dye laser excitation pump pulse and at such low sample pressures that these channels are minimized.’* The excimer pumped dye laser excitation beam and the diode probe beam are passed collinearly through a 2.5-m cell. The gas sample, which is a 1:l mixture of NO2 and N20 at 25 mTorr and 295 K, is premixed and purified by several freeze-pump-thaw cycles. An additional measurement was carried out at a sample temperature of 261 K, conditions which minimize the ambient
oooo
-
W a w n ~ m b e r stiom line center
-
state 00“l R(62), (b) the asymmetric stretching state w l 0002 R(18), and (c) the symmetric stretching state 10% ¶ e l R(15) spectral lines after collisions of N20with highly excited NO$R at E = 22 200 cm-I. The circles are data points. The solid curvcs are the best
+
fits to a Gaussian function. The dotted lines are room temperature w l Doppler profiles. The measured nascent line width of the R(62) transition is 0.0070 cm-I, for wl 0002 R(18) it is 0.0041 cm-I and for 10% 1001 R( 15) it is 0.0041 cm-I. For comparison the room temperature line width is 0.004077 cm-l.
-
-
oooo
+
population of the 10°O N 2 0 vibrational level. The time-domain absorption of infrared diode laser light is detected by a liquidnitrogen-oooled InSb detector, then amplified and signal averaged on a LeCroy 9400 digital oscilloscope, and finally stored on an IBM PC/AT computer for further analysis. N 2 0 signal amplitudes are measured 1 ps after excitation of NOJa, a time scale on which an average molecule in the sample has suffered only 0.25 collisions.
Results The interaction between excited NOi‘) and N 2 0 leads to the excitation of translational, rotational, and vibrational degrees of freedom of the N 2 0 molecules. The N 2 0 signal amplitudes measured at a time 1 ps after NOJq excitation for a number of rotational states of the different vibrational levels were normalized by diode and dye laser intensity. The nascent rotational distributions for the 10% symmetric stretching state and Oool asymmetric stretching state are shown in Figure 1. The rotational distribution can be approximated by a Boltzmann distribution. Measurements were repeated several times to obtain the best average rotational distributions. For the vibrationally excited states between the nascent the increase in rotational temperature (AP) rotational temperature and ambient temperature was A P l m = 40 f 23 K, and AP,,,p, = 37 f 18 K. In the case of 10%. the rotational temperature measurement was repeated a t a reduced ambient temperature (261 K) where the ambient population of the 10°O state of N 0 is lowered by more than a factor of 2. A similar value for A$,& was found, indicating that pure rotational scattering by collisions of N O J a with ambient N 2 0 (IOOO) molecules is not a significant process compared to vibrational excitation of N 2 0 to the 10% level.
1rhe Journal of Physical Chemistry, Vol. 95, No. 18. 1991 6761
Letters
TABLE I: Lim Width Maaurement R d t s revibrational transition P: K 875 i110 OOol: R(62) 1090 t 150 oo00 W1: R(50) 350 & 45 lo%-- 1001: R(15) 372 & 50 Wl -W2 R(24) #The average translational temperature derived from the measured line width Av via (Av/0.004077)2(300)= fl, where 0.004077 cm-' is the N20line width at T = 300 K.
-.
oooo-
corresponding to the vibrational energy loss AE,. The probability for a transition from state i to statej is give? in this semiclassical picture by
where V,l(r) is the matrix element for the potential of interaction, and Au,, = AE+Jh is the change in vibration frequency during the vibration to translation energy-transfer process. This transition probability is optimized when V,,(t) changes on a time scale f < l/Av,,, since the term in exp[2riAu,,t] oscillates between +1 and The translational excitation of N 2 0 molecules scattered into -1 on a time scale t l/Au,,. The rate of change of V,,(t) is in the 10% and OOOl states, as well as the recoil velocity of N 2 0 turn controlled by the relative collision velocity and the steepness, (o0oO.J") rotationally excited ground-state molecules produced or rate of change with distance, of the intermolecular potential. by collisions with NOJO, were measured by determining the size The most rapidly changing part of the intarmolecular potential, of the absorption signal at a number of frequencies surrounding the short-range repulsive region, gives rise to the highest frequency the absorption line center 1 ps after dye laser excitation of NOz. Fourier components for Vu('). For heavy molecules such as NO2 The nascent absorption line shapes can be well fit to a Gaussian and N 2 0 studied here at room temperature, the relatively low function as shown in Figure 2, reflecting a Doppler-broadened average collision velocities preclude large energy loss to the distribution of excited N 2 0 molecules. The full width halftranslational degrees of freedom, even for collisions which sample maximum (fwhm) line widths were averaged over a number of the steep repulsive potential wall of the intermolecular potential. experimental runs for each vibrational mode. The width of the The line widths observed in the present experiments for the vifitted Doppler profile provides a measure of the translational brationless N20(ooo0) level correspond to mean vibrational energy temperature of the nascent N20molecules. The average increases loss to translation of 1600 cm-' per collision. This is just the in translational temperature for the individual revibrational states magnitude of vibration-translation (V-T) energy transfer prederived from these line broadening measurements are shown in dicted by the above simple impulsive force/Fourier transform Table I. The line width of the ground vibrationless state, as shown argument for heavy molecules at room temperature whose in Figure 2, is significantly broader than the room temperature short-rangeinteraction potential can be described as exponentially ambient value, and substantially broader than the m i l line widths repulsive with a characteristic range of -0.2 A, typicfl of many for the two excited vibrational levels N20(10%)and N20(OO01). small polyatomic molecules.23 Note that sufficient energy is In these experiments, the signal amplitudes were measured in both contained in the NOJO molecule to transfer much more energy the time-domain and frequency-domain simultaneously. By than observed, but the dynamics of the collision process limit the measuring the signal amplitude at times later than 1 ps, the magnitude of the energy transfer. collisional relaxation of the transient line width back to the ambient In contrast to the ground vibrationless state, energy transfer Doppler width can be observed. from which produces vibrational excitation in the N 2 0 The total rate coefficients (k;) for the energy-transferprocess bath occurs by a mechanism in which almost no energy is are given in Table I1 for the two vibrational states studied. Z/ki transfered to the translational degrees of freedom as reflected by is the average number of collisions required to excite a particular the narrow line widths observed for recoiling N20(0001,J) and vibrational state.'* The overall energy-transfer efficiency to the N20(1000,J). By use of the same Fourier transform argument excited vibrational states is relatively small, but comparable to that observed for NOJQ/C02collisions producing COz(OOOl).l* as given above, these results suggest a resonant vibrational energy-transfer mechanism in which vibrational energy in the NO2 Although the amount of energy transferred from N02(O to N 2 0 is exchanged for vibrational energy in N 2 0 with Auu = [ 1/h]AEw3 is large when the N 2 0 vibrational states are excited, such events 0. Such a transfer can be brought about by the long-range are so rare (-1% gas kinetic) that the average energy transferred attractive part of the intermolecular p ~ t e n t i a l ,which ~ ~ , ~changes ~ per collision in these processes remains small. [The average only slowly with distance, yielding Fourier components of the amount of energy transferred to the uI and u3 first excited states interaction force which are near zero frequency. Indeed the weak per collision is (1285 cm-'/92) = 14 f 4 cm-', and (2224 recoil for the vibrationally excited species also suggests energy cm-'/106) = 20 6 cm-', respectively.] The vibrational energy transfer at a distance, indicating a long-range force mechanism transfer per collision is accompanied by only small rotational and for the excitation of the bath vibrational modes. translational excitation, less than 1 cm-I per collision. On the other The rotational profiles observed for the excited states of the hand, there is a much larger amount of energy going into the bath, N20(O001)and N20(1000), which show only small changes translational degrees of freedom for the vibrationless ground state. in J upon vibrational excitation, are also consistent with a long The translational energy increase observed for the J = 62, OOOO range force mediated energy-transfer process.z4~z5 Such a longlevel is 575 110 cm-I while that for the J = 50, OOOO level is range potential of interaction, which can be represented to first 790 f 150 cm-I. This is much larger than the translational energy order by a dipoldipole term,24would have "collisional selection increase for the 10% and @I vibrationally excited states described rules" with AJ f l , completely consistent with the present exabove. perimental data. Finally, changes in the rotational energy for the ground vibrationless state of N20(0000) are comparable to the Discussion changes in translational energy for this same state implying AJ The data presented here gives clear evidence for the existence >> 1. This observation is again completely consistent with a of two quite distinct mechanisms for energy loss by highly vishort-range force mechanism for the translational-rotational brationally excited molecules. Both mechanisms can be understood (V-T/R)excitation of the ground level. The short-range repulsive in the context of a simple time-dependent perturbation theory, part of the potential can only be described reasonably well by a semiclassical picture,22 in which the probability of vibrational multipole expansion which includes rather high order terms. These energy loss to the translational degrees of freedom is optimized higher order multipole terms, of course, can give rise to changes when the Fourier transform of the force acting during the collision has significant amplitude at the frequency 2rAu = [2r/h]AEvib (23) Yardley, J. T.; Moore, C. B. J. Chem. Phys. 1967, 16,4491. Grabiner, F. R.; Flynn, G. W.; Ronn, A. M. J. Chem. Phys. 1973, 59, 2330. (22) See for example: Cottnll, T. L.; McCoubrey, J. C. Mo/ecu/aren erg^ Schwartz, R. N.;Slawsky, Z. I.; Herzfeld. K. F. J. Chem. Phys. 1952, 20, 1591. Tramfer in Gases, Buttemorth London, 1961 Moon, C. B. Aec. Chem. Res. .-.- . 1969, 2,.103. Hardley, J. T. Introduction to Molecular Energy Transfer, (24) Sharma, R. D.;Brau, C. A. J. Chem. Phys. 1969,50,924;Phys. Rev. Academic Pren: New York, 1980. Rapp, D.;Kassal, T. Chem. Rea 1969, Lett. 1967, 19, 1273. 69, 61. (25) Stephenson, J. C.; Moore, C. 8. J. Chem. Phys. 1972, 56, 1295.
-
-
*
*
6762 The Journal of Physical Chemistry, Vol. 95, No. 18, 1991
Letters
TABLE II: Expcriaeabl R d b for Cdlidolls of N@(O) with N# final k 5,. vibrational state molecule-' s-' cm3 Z/k't OOOl (2.74 0.8) X IO-'* 106 30 IO00 (3.11 0.8) X 93 28
**
AF,'cm-l
AER: cm-l 0.3 0.09 0.3 0.09
*
* *
0.7 f 0.2 0.8 0.2
cm-' 20 f 6 14*5
#bp
k$ is the rate constant for transfer of ener y from NO+" to the indicated vibrational state. bZis the gas kinetic collision number for N02/N20 collisions, 2 = 2.90 X molecule-' s-I cm , using uN@ = 3.73 A (ref 18) and uN@ = 4.59 A (ref 28). CAverageenergy transferred per collision to the rotational (AER), translational (AL?), and vibrational degrees of frcedom of N 2 0 for the indicated vibrational states.
P
(eb)
in AI which are sisnificantlylarger than 1. From a simple classical point of view, the rotational angular momentum of the recoiling bath molecules is expected to scale with the translationa! recoil velocity. The rotational angular momentum transferred to the recoiling NzO will be J = pub, where cc is the reduced mass of the NOZ/N20pair, u the recoil velocity, and b the impact parameter (essentially the distance from the NzO center of mass to the point of push off between the two molecules). Thus, the angular momentum imparted to the NzO bath molecules is expected to scale roughly with u. This agrees with the present observations in which the NzO ground state exhibits wide line widths and large AJ while the vibrationally excited states have narrow line widths and small AJ. A long-range attractive force mechanism for collisional excitation of the vibrational states NzO(lO%) and NzO(W1) would predict an excitation probability that scales like"
Icc,,(Noz)~looo(Nz~~lz~,
4,
pf& I C ( f k ( N O Z ) ~ 1 ( N 2 0 ) l z g & where i is the initial state of NOJQ and j and k are the final states of NOz accompanying the respective changes NOz'n + N20(0OOO) NO4 + N2O( 10'0) ly
NO+')
+ NZO(OO%)
-
+
N0Zk
+ NzO(OP1)
-
is expected to be substantially larger than lp,&I2. This is because the NOz transition i j can be achieved by a one quantum vibrational energy change of order 1285 cm-l, while the NO transition i k corresponding to an energy change of 2224 cm-f cannot be brought about by less than a two quantum change in the vibrational modes of NO2. This simply reflects the fact that the v3 (2224 cm-') mode of NzO is substantially higher in frequercy than any of the NO2 modes. While the highly excited vibrational levels of NOz are certain to be strongly mixed harmonic oscillator states, the general result that the NOz transition moment for i - j will be significantly larger than for i k is expected to hold. We find experimentally that the probabilities P,,and Pfk are approximately the same (see Table II), suggesting that the density of states and transition moment factors for NOz in these two processes approximately offset the changes in the NzO transition moment factors. Clearly the excitation of bath vibrational modes occurs by a different mechanism than the rotational-translational excitation of the ground vibrationlcss state. The situation for NzO quenching of NOJn can be described as "vibrationally crisp". The energy of the bath vibrational modes (here 1285 and 2224 cm-') is large compared to the mean bath translational energy (kT 200 cm-I), which controls the NzO/NO,(a collision velocity. In such a case excitation of the high-frequency bath modes by a short-range repulsive force mechanism is essentially ruled out due to the low velocity and the high mode f r e q u e n c i e ~ .Nevertheless, ~~~~ as the bath mode frequencies drop, or the bath translational energy increases, such that hv kT, vibrational excitation could occur by more than one mechanism. A number of experiments are under way to test these ideas which are qualitatively in agreement with the present data for NZO(OO%), NzO(lO%), and N Z 0 ( W 1 ) excitation by collisions with NOz(Q.
-
-
-
-
The final state densities g, and are totally determined by the NO2 since the NzO 10% and &levels are nondegenerate. The ccv. Plk, %lo& and Iare the respective transition dipole moments for the indicated NO2 and NzO transitions. Because the energy of the 10% state is approximately 1285 cm-'while that of W l is about 2224 cm-', the density of states gdis larger by about 10% than gk (Whitten-Rabinowitch approximationz6for the density of states of NOz). The NzO dipole transition moment Acknowledgment. We thank Drs. Ralph E. Weston, Jr., Greg contribution l p w l I Zis about 5 times larger than \wl,y,,lz Hall, and Arthur Sedlacek for many stimulating discussions and (ref 27). However, the NOz dipole moment contribution Ik,,12 helpful suggestions. This work was performed at Columbia University and was supported by the National Science Foundation (Grant No. CHE-88-16581) and the Joint Services Electronics (26) Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions, Wiley: London, 1972. We arc indebted to Dr. Ralph Warton for the ullc of his density Program (US.Army, U.S.Navy, and U.S.Air Force; Contract of statar computer program. No. DAAL03-91-C-0016). Equipment support was provided by (27) Pugh, L. A.; Rao, K. N. In Molecular Spectroscopy: Modern Rethe IBM Materials Research Program, the Office of Naval Research; Rao. K. N., Ed.; Academic: New York, 1976; p 159. search, and the Department of Energy (Grant No. DE-FGOZ(28) Hirschfelder, J. 0.;Curtius, C. F.; Bird, R. B. Molecular Theory of 88-ER13937). Gases and Liquids; Wiley: New York, 19S4; p 11 11.
