Infrared multiphoton dissociation of anisole - American Chemical Society

0.0016 and p4p. = 0.56. These values can be compared with values of 0.002 and 0.60 for Ga[C2H4] in argon13 and are quite consistent with structure 1...
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J. Phys. Chem. 1992,96, 12361240

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the empirical coupling constants by these parameters gives p4* = 0.0016 and pop= 0.56. These values can be compared with values of 0.002and 0.60 for Ga[C2q] in argon” and are quite consistent with structure 1. Jones and Kasai also calculated a small 3d unpaired spin population of 0.02. This contribution must be small because the energy gap between the Ga d, orbital and the ligand r* orbital is large. Overlap is further reduced by the contracted nature of the Ga d orbitals. Species B. This species has a large and almost isotropic Ga Mi and g values less than the free spin value. Substitution of the hfi into equations all = ah + 4/5P (7) aI = aim- 2/5P gives ah = 1650 MHz and P = -40 MHz, if al,and aL are both positive, and aim= -575.7 MHz and P = 4488 MHz, if a,, is positive and aI is negative. Neither of these analyses gives a reasonable unpaired p spin population because P cannot be negative for a p orbital or more than twice as large as the one electron parameter, Po. If we assume that the spectrum was isotropic, then ah = 1650 MHz and p4 = 0.13. The most likely candidate for I B is gallacyclopentane, GaCH2CH2CH2CH2,which is the conI -I gener of A1CH2CHzCH2CH2.3This latter species has pk = 0.18 and p3p = 0.65 and hydrogen hfi associated with the ml = 1/2 line that enabled the stoichiometry to be determined. Unfortunately, we did not observe any H hfi with the gallium species. i

(22) Morton, J. R.; Prcston, K. F. J . Mugn. Reson. 1978, 30, 577.

However, in light of the similarities in values of pm, we tentatively suggest that B is gallacyclopentane. We do not know the exact mechanism for the formation of AlCH2CH2CH2CH2, and therefore it is not appropriate at this point to suggest a mechanism , 4 for the formation of GaCH2CH2CHzCH2. Species C and D. The spectra of C and D were only observed on warming the samples and only gallium isotropic Mi and g values were obtained. Dividing the Mi by 4gave pc = 0.036 and 0.028 for C and D, respectively. Unpaired spin populations in this range suggest a 6 gallium substituted alkyl which is also consistent with the g value of 2.0030. The absence of a H hfi and the absence of sharpening when CzD2Hzwas used instead of C2H4 suggests that GaCH2CH2’ was not the carrier of either of these spectra. It is therefore impossible at this time to assign structures to C and D. It is interesting to note the reaction of Ga atoms with C6H6 in adamantane at 77 K gives a well-resolved spectrum of cyclohexadienyl,2’ which must be produced by addition of adventitious hydrogen atoms to benzene, whereas ethyl has not been detected in the present system. There is no logical reason for this dif€erence if adventitious H 2 0 is the source of the H atoms.21 Annealing experiments revealed that Ga[CzH4] disappears below 205 K whereas Al[C2H4] is stable to 350 K. From this we conclude that Ga[C2H,] is significantly less stable than Al[C2H4],which is consistent with estimates of gas-phase bond strength^.^,'^ b

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Acknowledgment. We thank Drs. J. R. Morton and K. F. Reaton for many helpful discussions. J.A.H. and B.M. also thank NATO for a collaborative research grant (442/82).

Infrared Multiphoton Dissoclation of Anisole: Production and Dissociation of Phenoxy Radical Anne-Marie Schmoltner, Deon S.Anex, and Yuan T.Lee* Chemical Sciences Division, Lawrence Berkeley Laboratory and Department of Chemistry, University of California, Berkeley, California 94720 (Received: May 29, 1991; In Final Form: September 25, 1991)

The infrared multiphoton dissociation of anisole in a molecular beam was studied using pulsed COz laser radiation, with the product recoil energy distributions measured using the time-of-flight technique. The only primary process identified was the dissociation into phenoxy and methyl radicals, with the shape of the translationalenergy distribution of the products revealing a small exit barrier. Under conditions of higher laser fluence, secondary dissociation of the phenoxy radical into carbon monoxide and CSHSwas observed.

Introduction The infrared multiphoton dissociation (IRMPD) of polyatomic molecules has been established as an excellent experimental technique for studying dissociation mechanisms under isolated conditions. IRMPD of medium or large sized molecules is characterized by fast intramolecular energy distribution after absorption of many IR photons, making it possible to use intense IR radiation to prepare hot ground-state molecules similar tothose prepared by thermal excitation.’-’ Subsequent dissociation processcf takeplace acoording to the same mechanisms as thermal decompositi~n.~ Since IR multiphoton absorption can take place under collision-free conditions, detailed information about unimolecular decomposition processes of molecules in their electronic ~

(1) Schulz, P. A.; Sudbo, Aa. S.;Krajnovich, D. J.; Kwok, H. S.; Shen, Y. R.; Lee, Y. T.Annu. Rev.Phys. Chem. 1976,30, 319. (2) Ashfold, M. N. R.; Hancock, G. Gus Kiner. Energy Transfer 1980,4, 73. (3) Oref, I.; Rabinovitch, B. S.Acc. Chem. Res. 1979, 12, 166.

ground state can be obtained in experiments using a molecular beam. The technique used in our laboratory, photofragmentation translational spectroscopy, is particularly well suited for the unambiguous identification of primary diaPociation products and for the derivation of detailed information on the dimciation dynamia from the measurement of product angular and velocity distributions. Mass spectroscopic detection makes the method applicable to a vast range of systems. The thermal decomposition of anisole has been studied rep e a t e d l ~ , ~and ’ the only primary dissociation channel identified (4) Harrison, A. G.; Honnen, L. R.; Dauben, H. J.; W i n g , F. P.J . Am. Chem. Soc. 1960,82, 5593. ( 5 ) Lin, C.-Y.; Lin, M. C. Int. J. Chem. Klncr. 1985,17, 1025. Lin, C.-Y.; Lin, M. C. J . Phys. Chem. 1986, 90,425. (6) Mackie, J. C.; Doolan, K. R.;Nelson, P. F. J. Phys. Chem. 1989,93, 664. (7) Suryan, M. M.; Kafafi, S. A.; Stein, S.E. J . Am. Chem. Soc. 1989, 111, 1423.

0022-3654/92/2096-1236303.00/0 @ 1992 American Chemical Society

The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1237

IR Multiphoton Dissociation of Anisole O-CH3 bond to form the methyl was cleavage of the radical and the phenoxy radical: CsHs-O-CH3 C6H5-0' 'CH3 (1) At temperatures above lo00 K the unimolecular decomposition of the phenoxy radical into carbon monoxide and the cyclopentadienyl radical was 0bserved!9~*~~Colussi et al.l0 suggested a mechanism for phenoxy radical decomposition involving a bridged C&O species (Scheme I). This mechanism is compatible with the low A factor and low activation energy for the process obtained by Lin and Line5

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The phenoxy radical is an important intermedizte in the combustion of aromatic hydrocarbons." The reaction of oxygen atoms with benzene leads to the production of the phenoxy radical and phenol,1z and the decomposition of phenol in turn produces phenoxy radicals. The reaction of molecular oxygen with the phenyl radical was postulated as an additional pathway for the production of the phenoxy radi~a1.I~ One of the goals of our recent investigations has been to find efficient and clean ways of producing phenoxy radicals and to study the dynamics of their decomposition. In our IRMPD experiments, we did find that production of the phenoxy radical was the only primary channel of anisole decomposition at moderate fluence. However, at high laser fluence, the secondary decomposition of some of the phenoxy radicals was observed.

Experimental Section The apparatus used in this experiment has been described in detail previ~usly.'~Briefly, a supersonic molecular beam was crossed at 90" with the output of a pulsed COz laser. Time-offlight (TOF) spectra of the photodissociation products were recorded using a mass spectrometer detector consisting of an electron-impact ionizer, quadrupole mass filter, and Daly ion counter. Rotation of the differentially pumped molecular beam source around the axis defmed by the laser beam allowed the angle between molecular beam and detector to be varied. A continuous supersonic beam of anisole was formed by b u b bling helium or nitrogen through anisole held at 20 OC. The gas mixture at a total pressure of 1W150 Torr was passed through heated lines into the beam source. The nozzle had an aperture of 125-pm diameter and was held at 150 or 200 OC in order to prevent the formation of molecular clusters in the expansion. Typical beam velocities for He-seeded beams were (1.45-1 -65) X lo5 cm/s, with speed ratios of about 8-10. The beam velocity distributions were measured using the time-of-flight method. Two different pulsed COz lasers were used. The earlier experiments were performed using a Gentec DD-250-BTEA COz laser, and the later ones using a Lumonics TEA-820 COz laser. The laser radiation was focused using a 25 cm focal length ZnSe lens. The spot sizes were estimated from burning patterns on tape and paper. With the Gentec laser, fluences were estimated to be 8-17 J/cm2 with laser spot sizes of approximately 1 mm2; with (8) Paul, S.; Back, M. H. Can. J. Chem. 1975, 53, 3330. (9) McMillen, D. F.; Golden, D. M. Annu. Reu. Phys. Chem. 1982, 33, 493. (10) Colussi, A. J.; Zabel, F.; Benson, S. W. Int. 1. Chem. Kinet. 1977, 9, 161. (11) Brezinsky, K. Prog. Energy Combust. Sci. 1986, 12, 1. (12) Sibener, S. J.; Buss, R. J.; Casavecchia, P.; Hirooka, T.; Lee, Y. T. J. Chem. Phys. 1980, 72, 4341. (13) Venkat, C.; Brezinsky, K.; Glassman, I. Nineteenth Symposium (Internutionaf) on Combustion;Combustion Institute: Pittsburgh, 1982; p 143. (14) Wodtke, A. M.; Lee, Y. T. J . Phys. Chem. 1985,89,4744.

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Flight Time (ps) Figure 1. TOF spectra of mle = 93 and mle = 65 at 8' and mJe = 15 at 15' obtained at low laser fluence.

the Lumonics laser fluences of up to 27 J/cm2 over about 4 mm2 were estimated. The best yield was observed at the P(26) line of the 001-020 band at 1041 cm-l. The fundamental frequency of the 0 - C H 3 stretch was determinedI5to lie at 1039 cm-' and is most likely responsible for the initial absorption at this wavelength. For a given laboratory angle, TOF spectra were recorded for each laser shot. The signal was accumulated in a multichannel scaler triggered by the laser pulse. Dwell times of 1-5 @/ChaMel were used. The data acquisition and storage was handled by an LSI-11 laboratory computer. Anisole was obtained from Matheson and was degassed in several freeze-pump-thaw cycles. A GC-MS analysis revealed a minor impurity of benzoic acid (about 0.3%). This impurity was found not to interfere in our experiments, as its vapor pressure is considerably lower than that of anisole.

Results and Analysis Even though the product molecules or radicals fragment extensively upon ionization in the mass spectrometer, parentdaughter ion relationships can be established by identifying common features in the TOF spectra for different mass-to-charge ratios (mle). Corresponding fragment pairs can be idenMied using the condition of momentum conservation in the center-of-mass coordinate system. TOF spectra were measured at laboratory angles between 6" and 50° at m / e = 15,28,29, 30, 31,39,65,75,76,77, and 93, corresponding to the ions CH3+,CO+, CHO+, CHzO+,CH30+, C3H3+,CsH5+,CsH3+,CsH4+,C6H5+,and C6H50+. The parent ion of the expected product of anisole decomposition, phenoxy radical, has a mass of 93 amu; however, major fragments were found at m / e = 39 and 65, with m / e = 39 showing the highest count rate. TOF spectra are shown in Figures 1-5. Figures 1 and 2 show data taken in the fmt set of experiments using the Gentec laser at low fluence (about 15 J/cm2), while Figures 3-5 represent data taken at higher laser fluence (27 J/cm2) using the Lumonics COz laser. The spectra of m / e = 39,65, and 93 at 8" (Figures 1 and 2) show only one feature which is the same for all three masses except for a small shift due to the flight (15) Balfour, W. J. Spectrochim. Acta 1983, 9, 795.

Schmoltner et al.

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Flight Time (ps) Figure 3. TOF spectra of m/e = 93,65, and 28 at 10' obtained at high laser fluence. time of the ions through the quadrupole mass spectrometer, which is a function of the ion m/e. This feature in the TOF spectra can be identified as the phenoxy radical. The corresponding second fragment, methyl radical, was detected at m / e = 15, and the TOF distribution is shown in Figure 1. TOF spectra of m / e = 39 at three different laboratory angles are shown in Figure 2. In contrast to these results, the TOF spectra obtained in the second set of experiments (at higher laser fluence) show an additional feature. The comparison of the spectra at m/e = 39,65, and 93 (Figures 3 and 4) reveals the occurrence of two different

Flight Time (pus) Figure 5. TOF spectra of m / e = 15 at lo', 30°,and SOo obtained at high laser fluence.

reaction channels: The slower feature in all three spectra again corresponds to the phenoxy radical, while the faster feature can be identified with the decomposition product of the phenoxy radical, the cyclopentadienyl radical. Methyl radical was again detected at m / e = 15, and the TOF spectra at three different laboratory angles are shown in F p e 5. Despite the high detector background at m/e = 28, we were able to obtain a TOF spectrum at m / e = 28 as well (Figure 3). The detection of very fast CO at m / e = 28 corroborates the identification of the fast feature in the m / e = 39 and 65 spectra with the secondary dissociation products of phenoxy radical. Figure 4 shows TOF spectra of m / e = 39 at six different laboratory angles, illustrating the relative

IR Multiphoton Dissociation of Anisole

The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1239

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Roduct Translational Energy (kcal/mole) Figure 7. Translational energy distributions, P(ET), for the primary dissociation channel of anisole for low laser fluence (solid curve) and high laser fluence (dashed curve). 0.061

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Figure 6. Newton or velocity diagram illustrating primary and secondary

dissociation channels. The shorter vectors originating at the tip of the beam velocity vector correspond to the primary dissociation product, the phenoxy radical. The longer vectors originating at the tip of a phenoxy radical velocity vector correspond to the secondary dissociation product, the cyclopentadienyl radical. The underlined species indicate which is the detected fragment for each channel. At angles of 20° and larger only secondary products appear.

contributions of the two channels at different angles. At angles of 20° and larger, only secondary products can be observed. The appearance of the photodissociation products in the laboratory frame is illustrated in the Newton diagram shown in Figure 6. Short velocity vectors originatingat the tip of the beam velocity vector represent the centersf-mass velocity of the phenoxy radical recoiling from the methyl radical. The kinetic energy corresponding to this velocity is the maximum energy for this channel as determined by the analysis below. The smaller circle in Figure 6 reprents the possible resultant vectors arising from the addition of the molecular beam velocity to the center-of-mass velocities. The larger arrows and circle represent the velocity of the cyclopentadienyl radical recoiling from carbon monoxide in the secondary decomposition of the phenoxy radical. Again, the maximum kinetic energy from the data analysis which is discussed below was used to determine the velocity shown. In the complete Newton diagram for the sequential decomposition process, a collection of secondary circles would appear, each corresponding to particular primary velocity. Also shown in this diagram are several s o u r d e t e c t o r angles. If a resultant velocity vector falls on one of these lines, then that fragment will be detected at this angle. As can be seen from Figure 6 the primary phenoxy radical will not be seen at laboratory angles of 20' and larger, whereas the secondary cyclopentadienyl radical may be detected beyond 40'.

The data of m/e = 65 and 93 in Figure 3 show slow components (arriving later than approximately 400 ps) that were not accounted for in the data analysis. These slow features did rot originate from the photodissociation of anisole in the beam. They were identified as resulting from time-dependent desorption of anisole molecules from laser heating of a cold surface in the vacuum chamber and did not interface with the analysis of the IRMPD signal. A forward convolution method was used in the analysis of the data in order to determine the translational energy distribution of the reaction products, P(ET).16 From a trial input translational energy distribution, the TOF distributions were calculated and averaged over beam velocities, the finite dimensions of the ine of the ionizer and then compared teraction zone, and the f ~ t size with the experimental data. The trial P(ET) was then adjusted and the process repeated until the best fit was obtained. The angular distributions of the products in the center-of-mass frame (16) Zhao,

X. Ph.D. Thesis, University of California, Berkeley, 1988.

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Product Translational Energy (kcal/mole) Figure 8. Translational energy distribution, P(ET), for the secondary dissociation channel of anisole. were found to be isotropic as expected. The solid lines in Figures 1-5 represent the fits to the data. The P(ET)distributions for the primary channel under the two different experimental conditions are shown in Figure 7, and the P(ET) for the secondary dissociation is shown in Figure 8. The translational energy distributions for the primary product phenoxy radical generated at two different laser fluences (Figure 7) are almost identical. Both distributions peak at 3 kcal/mol and extend to about the same maximum value, 17 and 18 kcal/mol. The differences are small but real. For the conditions of lower laser fluence, the P(ET) is slightly narrower and the average m i l energy is 4.4 kcal/mol, while for higher laser fluence the distribution is somewhat wider and the average recoil energy is about 5.0 kcal/mol. The recoil energy distributions in both cases are fairly well characterized since different TOF spectra are sensitive to different parts of the P(ET). The data for the phenoxy radical at larger angles (12-15O) represent the high-energy tail of the distribution. The fits of the m/e a 15 distributions at small angles, on the other hand, are particularly sensitive to the low-energy part of the P(ET). It has to be emphasized that in all cases the spectra stemming from methyl radical and those stemming from phenoxy radical could be fit with the same recoil energy distributions. However, the minimum recoil energy required for phenoxy to reach the detector at ' 6 is 2.2 kcal/mol (for a typical beam velocity), whereas the minimum recoil energy required for methyl to reach the detector at loo is only 0.2kcal/mol. Thus, it is possible that the P(ET) distributions for the two fragments deviate at very small recoil energies because of the secondary decomposition of some highly vibrationally excited (and thus slow) phenoxy radicals. The P(ET) for the secondary reaction (Figure 8) shows a threshold value of 8 kcal/mol and a maximum energy release of 48 kcal/mol. These values probably have uncertainties of about 2 kcal/mol.

Discussion Several conclusions can be drawn from the recoil energy distributions obtained from this experiment. The only primary process, dissociation into phenoxy radical and methyl radical, shows the same characteristics for both conditions studied. The fact that the translational energy released in the formation of phenoxy and methyl radicals does not change substantially when the laser fluence is increased by 80% indicates that the high rate

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Figure 9. Energy diagram for the primary and secondary dissociation process in the IRMPD of anisole.

of dissociation of vibrationally excited anisole is limiting the further absorption of IR photons or a large fraction of the translational energy released is not simply related to the total internal energy of the excited anisole. The fact that the translational energy distributions peak at a small but finite value indeed suggests the existence of a barrier in the C,H50-CH3 dissociation. Since there is no low-lying electronically excited state in anisole, IRMPD results in dissociation from vibrationally excited molecules in the ground electronic state. Therefore, the peaking of the translational energy distribution away from zero cannot be explained by invoking a dissociation from an excited electronic state. The observation of a barrier is in contrast to most simple bond rupture procases which have been demonstrated by previous investigations of IRMPD'7-20 to result in translational energy distributions that peak at zero energy in accordance with the predictions of statistical theory.2' Examples of this were found in the dissociation of the carbonhalogen bonds in halogenated alkanes," the decomposition of diethyl ether,I8 methyl acetate, and ethyl acetate,Ig and the breaking of carbon-nitrogen bonds in nitroalkanes.20 The fact that h e reactions proceeded without an exit barrier (as evidenced by their translational energy distributions peaking at zero kinetic energy) implies that the reverse reaction, radical recombination, proceeds with no activation energy. An exception to the expectation that the breaking of a single bond via IRMPD to form two radicals should proceed without an exit barrier was demonstrated in the study of the d a m p i t i o n of ethyl vinyl ether.22 In this case, the translational energy distribution measured for dissociation of the carbon-oxygen bond in CH3CH2-OCHCH2to form the two radicals CH3CH2and OCHCH, peaked at 2.7 kcal/mol and extended to near 22 kcal/mol. The origin of the small exit barrier was explained by the electronic rearrangement of the OCHCHz radical, in which the C-O bond has considerable double-bond character. That a barrier is reasonable for this reaction can be seen by considering the reverse radical recombination reaction which resembles, to an extent, a radical addition to a double bond, for which a small barrier would be expected.23

Schmoltner et al. The situation for the dissociation of the C-O bond in anisole via IRMPD is expected to be analogous to that in ethyl vinyl ether due to the electronic rearrangement of the phenoxy radical. As in the OCHCH2 radical, the C-O bond in the phenoxy radical has considerable double-bond character. This view of the electronic structure of the phenoxy radical is supported by theoretical studies that show the structure to lie between the 'phenol" and "diene" structures." The barrier for the bond rupture process in anisole is expected to result from the electronic rearrangement associated with the partial C-O double-bond character in the phenoxy radical. The electronic rearrangement responsible for the partial double-bond character also redistributes the odd electron density on the ring. These rearrangements manifest themselves in the reverse reaction, recombination of methyl and phenoxy radicals, in which the methyl prefers to attach to the ortho and para positions of the benzene ring rather than the oxygen atom.25 The phenoxy radicals which were produced in the earlier part of the laser pulse continue to absorb IR photons and dissociate into cyclopentadienyl radicals and carbon monoxide. This secondary process has a large barrier. Lin and Lin5determined that this step has an activation energy of 44.0 f 0.9 kcal/mol. The large energy release (up to 48 kcal/mol) and the peaking of the translational energy distribution at 14 kcal/mol in the secondary process are indicative of the substantial barrier for this reaction. The dissociation of phenoxy radical to cyclopentadienyl and carbon monoxide is 20 kcal/mol endothermic?.% Consequently, some of the phenoxy radicals must have been excited beyond 68 kcal/mol internal energy. The known thermochemistry of the present system is summarized in Figure 9. Our results therefore indicate that the IRMPD of anisole is a possible and convenient way of producing phenoxy radicals. No other primary products were observed, and with suffcient control of the laser fluence, secondary products could be prevented. Ultraviolet photodissociation of anisole at 248 or 193 nm, on the other hand, which has been used as a source of phenoxy radica15,2' was studied in our laboratory as well, and a number of different primary reaction channels were identified?* indicating possible difficulties in the application of this method in the investigation of the kinetics of phenoxy radical reactions.

Conclusions In the IRMPD of anisole the only primary decomposition channel occurring is rupture of the weakSv9M H 3 bond forming phenoxy and methyl radicals. The recoil energy distribution suggests the existence of an exit barrier for this dissociation channel. Under higher laser fluence conditions, the secondary dissociation of the phenoxy radical was observed. The large recoil energy release is in accordance with the existence of a sizable exit barrier for this process as determined by Lin and Lin.s Acknowledgment. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division, under Contract DE-AC0376SFOOO98. RegistrY NO. C6H5OCH3, 100-66-3; 'CH3, 2229-07-4; C,H5O', 2122-46-5; C5H5, 2143-53-5; CO, 630-08-0. ~~

(17) Sudbo, Aa. S.; Schulz, P. A.; Grant, E. R.; Shen, Y. R.; Lee,Y. T. J. Chem. Phys. 1979, 70,912. (18) Butler, L. J.; Buss, R. J.; Brudzynski, R. J.; Lee,Y. T. J. Phys. Chem. 1983,87,5106. (19) Hintsa, E. J.; Wodtke, A. M.; Lee, Y. T. J . Phys. Chem. 1988,92, 5379. (20) Wodtke, A. M.; Hintsa, E. J.; Lee, Y. T. J . Phys. Chem. 1986, 90, 3549. (21) Robinson. P. J.: Holbrook, K. A. Unimolecular Reactions; Wiler: London, 1972. (22) Huisken, F.; Krajnovich, D.; Zhang, Z.; Shen, Y. R.; Lee, Y . T. J . Chem. Phys. 1983, 78, 3806. '

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(23) Kerr, J. A., Moss,S. J., Eds. Handbook of Bimolecular and Termolecular Gas Reactions; CRC Press: Boca Raton, FL, 1981; Vol. 11. (24) Luzhkov, V. B.; Zyubin, A. S. J. Mol. Struct. (THEOCHEM)1988, 170, 33. (25) Lin, C Y . ; Lin, M.C. Aust. J . Chem. 1986, 39, 723. (26) Chase, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A.; Syverud,A. N . J. Phys. Chem. Ref. Data 1985.14 (Suppl. No. 1); JANAF Thermochemical Tables, 3rd ed.

(27) Kajii, Y.; Obi, K.; Nakashima, N.; Yoshihara, K. J . Chem. Phys. 1987, 87, 5059. (28) Schmoltner,A. M. Ph.D. Thesis, University of California, Berkeley, 1989.