J . Phys. Chem. 1988, 92, 3836-3839
3836 CH30z + CH302
+
-+
CH30H
-
-+
2CH30
+ 0,
+ H C H O + 0,
CH,OOCH,
CH3OOH
+ 0,
@a) (8b) (8c)
+ CH202
(8d)
+
with a branching ratio for channel 8a, ksa/(kss k8b + ksc + k M ) , of 0.35.1° Methoxy radicals produced in reaction 8a will react with O,, present in large excess," to produce hydroperoxy radicals. C H 3 0 + 0,
-
CHzO
+ H0,
(9)
These HOz radicals can then react with CH3O2 radicals, leading to an enhanced CH302decay and an overestimation of k8. The relative importance of this secondary removal of CH3Oz was not quantitatively assessed in our earlier study due to the large uncertainties on the recommended Arrhenius parameters a t that timeI5 and our knowledge that the present investigation was in (15) DeMore, W. B.; Margitan, J. J.; Molina, M. J.; Watson, R. T.; Golden, D. M.; Hampson, R. F.; Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R. 'Evaluation No. 7 of the NASA Panel for Data Evaluation", JPL Publication 85-37, 1985.
progress. Modeling calculations were thus performed to quantify the effects of reaction 9 followed by reaction 1 on our previous determination of k8. This simulation was performed using the present value for kl and literature values for k,, k9, and the + kgb+ kgc+ k8d)8916 (assumed to be branching ratio k8a/(k8a temperature independent). The experimental data over the temperature range 228-380 K are best fit by the modeled curves for a k8value 15% lower than that derived from a purely second order analysis. This leads to the revised Arrhenius expression k8 = (1.4 f 0.4)
X
exp[(220 f 7 0 ) / T ] cm3 molecule-' s-l
Acknowledgment. The research described herein was conducted with the partial support of the National Aeronautics and Space Administration (Agreement W-l5,8 16). Registry No. H02, 3170-83-0; CH3O2, 2143-58-0; CH302H,303173-0; 0 2 , 7782-44-7; H2, 1333-74-0; C12, 7782-50-5; CH4, 74-82-8; CH3OH, 67-56-1. (16) Baulch, D. L.; Cox,R. A,; Hampson, R. F.; Kerr, J. A,; Troe, J.; Watson, R. T. J. Phys. Chem. Ref.Data 1984, 13, 1259.
Flash Photolysis Kinetic Absorption Spectroscopy Study of the Gas-Phase Reactlon H02 C2H502over the Temperature Range 228-380 K
+
Philippe Dagaut, Timothy J. Wallington, and Michael J. Kurylo* Chemical Kinetics Division, Center for Chemical Physics, National Bureau of Standards, Gaithersburg, Maryland 20899 (Received: September 28, 1987; In Final Form: January 15, 1988)
-
Flash photolysis kinetic absorption spectroscopy was used to investigate the gas-phase reaction between hydroperoxy and ethylperoxy radicals between 228 and 380 K in the pressure range 25-400 Torr: HOz + C2HS02 products (1). Due to the large difference between the self-reactivities of the two radicals, first- or second-order kinetic conditions could not be maintained for either species. Thus, the rate constant for reaction 1 was determined from computer-modeled fits of the radical absorption decay curves recorded at wavelengths between 230 and 280 nm. This procedure yielded a value for k l at 298 K of (5.3 & 1.0) X lo-'' cm3 molecule-' s-' independent of total pressure (using N2)between 25 and 400 Torr. The Arrhenius expression derived from the present study over the temperature range 248-380 K is k l = (5.6 & 2.4) X exp[(650 1 2 5 ) / q cm3 molecule-' s-', where the quoted errors are 20. from linear least-squares analyses. A reanalysis of our earlier measurements of the CZH5O2 self-reaction, CzH502+ C2H502 products (2), using this expression for kl results in the exp[-(110 f 40)/7'l cm3 molecule-' s-I. revised Arrhenius equation: k2 = (8.5 f 1.1) X
-
Introduction Accurate kinetic data concerning the reactions of alkylperoxy radicals are needed to understand the complex role of these species as intermediates during the oxidation of organic compounds in combustion systems and in the atmosphere. Of the many investigations exploring the gas-phase reactivity of alkylperoxy radicals, only one' concerns the reaction of ethylperoxy radicals with HO,, and that study was limited to room temperature. Under atmospheric conditions where low N O concentrations prevail (such as in pristine marine locations), reaction 1 can compete effectively with reaction 3, which is generally considered to be the dominant loss process for such peroxy radicals. HOz + CZH5O2 products (1) CZH5O2
+ NO
-
CzH5O
+ NO2
C2H5Oz kinetics. Thus, for example, the determination of the rate constant for the self-reaction of ethylperoxy radicals (reaction 2) requires accurate measurements of k , in order to assess the role of secondary chemistry. CZH5O2 + CZH5O2 products (2)
-
This article details the results of our recent flash photolysis UV absorption spectroscopy investigation of the temperature dependence of k l and of the possible effect of total pressure on kl at 298 K. These studies are part of a series of investigations in our laboratories designed to quantify peroxy radical reactivities and their UV absorption cross sections. The results reported herein are also used to reevaluate our recent measurements of the Arrhenius parameters for k,.
(3) In addition, as previously discussed,'V2 reaction l plays an important role in most laboratory experiments designed to study
Experimental Section The apparatus and experimental methodology have been detailed in earlier report^.^,^ HO, and CZH5O2 radicals were
(1) Cattell, F. C.; Cavanagh, J.; Cox, R. A,; Jenkins, M. E. J . Chem. Soc., Faraday Trans. 2 1986, 82, 1999. ( 2 ) Wallington, T. J.; Dagaut, P.; Kurylo, M. J. J . Photochem. 1988, 42, 173.
(3) Kurylo, M. J.; Ouellette, P. A.; Laufer, A. H. J. Phys. Chem. 1986, 90, 437. (4) (a) Kurylo, M. J.; Ouellette, P. A. J . Phys. Chem. 1986, 90, 441. (b) Kurylo, M. J.; Ouellette, P. A. J . Phys. Chem. 1987, 91, 3365.
This article not subject to US.Copyright. Published 1988 by the American Chemical Society
+ CZH5O2 at 228-380
Gas-Phase Reaction H0,
The Journal of Physical Chemistry, VoJ. 92, No. 13, 1988 3837
K
produced by the flash photolysis (A 1 300 nm) Of C12-CzH6-CH30H-02-N2 mixtures via the reaction sequence Clz
+ hv
C1+ C2H6 C1+ CH3OH
CzH5 + 0 CH20H
2
+
+
+ N2
+
0 2
+
2C1
HC1
(4)
+ C2H5
(5)
H C 1 + CHzOH
(6)
C2H5O2 + Nz
(7)
+
+
HOz
+ CH20
(8)
Variation of the C12concentration (together with the flash energy) and of the concentrations of C& and C H 3 0 H permitted control of the total peroxy radical concentration and of the initial peroxy [H02]o. Reagent conradical concentration ratio, [C2H50210/ centrations were chosen on the basis of the known rate constants for reactions 5-8 to ensure that peroxy radical production was complete within 100 ps after the flash. The ranges of reagent concentrations used to achieve this were (in units of molecules/cm3) Cl,, (0.7-3.5) X CH30H, (1.1-5.5) X C2H6, (1.1-5.5) X and 0,, (0.4-5.2) X 10l8 (with Nz added to achieve the desired total pressure between 25 and 400 Torr). Appropriate pairings of these concentrations, coupled with flash energies between 200 and 400 J, resulted in [C2H502]0= (2-9) X l O I 3 molecules/cm3, [HOzlo = (1-9) X 1013molecules/cm3, and [C2H502]0/[H02]0= 0.22-6.0. The reagents had the following purities: Cl,, 99.96% (used after redistillation); C H 3 0 H , spectral grade (used after vacuum drying and redistillation); 02, 99.99%; N,, 99.999%; and C2H6, 99.99%. Photolysis mixtures were prepared by combining calibrated flows of the gases in a mixing chamber immediately upstream of the reaction cell. This flowing procedure allowed for complete sample replacement every four to five flashes, corresponding to a residence time of =30 s. The kinetic analysis of the decay curves is identical with that utilized in our H0, + CH302 investigation^.^-^ Briefly, the kinetic decays of HOz and C2H5O2 following their simultaneous flash photolytic production are described by the reaction sequence (1, 2, and 9).
HOz
+ H02
+
H202,
+0 2
(9 )
Because of the large difference between k2 and k9, the peroxy radical concentration ratio changes from its initial value during the course of reactive decay and neither pseudo-first- nor -second order kinetic conditions with respect to either radical can be maintained. In addition, overlap of the UV absorption spectra of the two radicals results in an absorption decay curve at analysis wavelengths between 215 and 250 nm which has components attributable to both HO, and C2H5O2. Consequently, the kinetic analysis required computer modeling of the experimental data. The simultaneous differential equations describing the temporal history of the radicals as defined by reactions 1, 2, and 9 were numerically to generate concentration versus time data for all reactants and products. The production of C2H5O via reaction 2 and the subsequent generation of HOz via C2H50 0, were included in these modeling calculations. These data were in turn used to calculate transient absorption curves at the analysis wavelengths by using appropriate absorption cross sect i o n ~ . ~ , ~ In . ’ ~this procedure, the cross section of CzHsOzH (assumed to be the major product of reaction 1) was set equal to that of C H 3 0 2 H ,an approximation that seems justified con-
+
(5) Kurylo, M. J.; Dagaut, P.; Wallington, T. J.; Neuman, D. M. Chem. Phys. Lett. 1987, 139, 513. (6) Dagaut, P.; Wallington, T. J.; Kurylo, M. J. J . Phys. Chem., in press. (7) Brown, R. L. HICHEM: A Fortran Code f o r Homogeneous Isothermal Chemical Kinetic Systems; National Bureau of Standards: Gaithersburg, MD, 1981; NBSIR 81-2281. (8) Braun, W.; Herron, J. T.; Kahaner, D. K. Int. J . Chem. Kinet. 1988, 20, 51. (9) Kurylo, M. J.; Wallington, T. J.; Ouellette, P. A. J. Photochem. 1987, 39, 201. (IO) DeMore, W. B.; Sander, S. P.; Molina, M. J.; Golden, D. M.; Hampson, R. F.; Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R. JPL Publ. 1987, 87-41.
189250
0
Tim. ms
20
Figure 1. Experimental absorption decay curve recorded at 250 nm. [C2H502] = 3.97 X lOI3 molecules/cm3; [HO,]= 6.92 X 10” molecules/cm3; p = 100 Torr; T = 298 K; channel width = 50 ps; signal average of 200 flashes. The curves were calculated with the following rate constants (in units of cm3 molecule-I s+): k2 = 5.9 x k9 = 1.8 X (A) k , = 4.5 X 10-l2,(B) k , = 5.0 X and (C) k l = 5.5 x 10-12.
sidering the similarity of ucH,02and uCzHSOz between 21 5 and 300 nm2. The initial radical concentrations used in the calculations were experimentally determined in two ways, as previously de~ c r i b e d . ~In. ~the first procedure, [HO,], and [C2H502]ofor a particular flash energy and Clz concentration were calculated from the initial absorptions measured at two distinct wavelengths assuming Beer’s law. Such a calculation was least prone to systematic error for monitoring wavelengths where there was an appreciable absorption component due to both radicals. The second procedure utilized the measurement of the total initial peroxy radical concentration as calculated from the initial absorption recorded under conditions where CZHSO2 was present alone (Le., in the absence of CH30H). This total concentration, together with the initial absorption in a mixed radical experiment (performed under the same conditions of flash energy and [Cl,]) allowed for the calculation of [HO,], and [C2H5O2J0.This second procedure was most useful for experiments using a monitoring wavelength at which absorption was predominantly due to C2H5O2 radicals. The agreement between the initial radical concentrations determined via both methods provided a verification of the stoichiometric conversion of C1 into peroxy radicals and suggested the absence of secondary reactions during the radical production period. This observation and modeling verification of the lack of secondary removal of H 0 2 or CZHSO2 at the initial concentrations used established the validity of reaction sequence (1, 2, and 9) in curve fitting our experimental data. Transient absorption decay curves were recorded at 230,250, and 280 nm by using a 75-W Xe arc lamp and a multipass optical configuration through the cell (four passes = 225-cm path length). For a fixed set of experimental conditions, the absorption curve was acquired by using a microprocessor-controlled transient digitizer to signal average 80-200 flashes (depending on the radical concentration and analysis wavelength), Typical data acquisition channel widths of 20 and 50 ps were used, and the absorption was recorded with a monochromator dispersion of 2.6 nm, the same as used in most of our recent cross-section measurement experi m e n t ~ The . ~ ~temperature ~ of the mixing chamber and the reaction cell was controlled by the passage of water/ethylene glycol or ethanol (from an external temperature regulator) through jackets surrounding each of these two apparatus sections. ReSults Figure 1 shows a typical experimental absorption decay curve (obtained at an analysis wavelength of 250 nm) together with three modeling simulations differing only in the value chosen for k l . Room temperature experiments were performed at total pressures (N, diluent) of 25, 100, and 400 Torr. At 100 Torr, data were recorded at analysis wavelengths of 230,250, and 280 nm without any statistically significant difference in the calculated rate constants. Thus, experiments at the other pressures were con-
3838 The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 TABLE I: Rate Constants for Reaction 1 kl,” lo-’* cm3 molecule-l temp, K 25b 1OOb 7.3 A 1.0 248 213 6.0 0.5 5.4 f 1.0
298 340 380
* *
5.2 f 1.0 3.4 1.0 3.1 f 0.5
-
IVI
4OOb
5.5 f 1.2
“Each value is an average of 10-20 determinations. bTotal pressure of nitrogen (Torr). ducted with a 250-nm analysis. This wavelength was chosen in order to maximize u ~ ~ H ~ ~ the / uC2H502 H ~ , absorption itself, and the sensitivity of the fit to changes in kl as discussed in ref 5 and 6. The 298 K data summarized in Table I demonstrate the lack of any discernible pressure dependence of k l , and the data are therefore averaged to give k1(298 K) = (5.3 f 1.0) X
cm3 molecule-’ s-]
where the uncertainty is two standard deviations. On the basis of the observed pressure independence, experiments at other temperatures between 248 and 380 K were all performed at 100 Torr. The results obtained are also given in Table I and are fit by the Arrhenius expression:
kl = (5.6 f 2.4)
X
exp[(650 f 1 2 5 ) / q cm3 molecule-’ s-I
where the uncertainties again represent two standard deviations. Given the similarities in magnitude between kl and the rate constant for the reaction of H 0 2 with CH302,the assessment of confidence limits presented in ref 6 applies to the present study as well. Thus, uncertainties in the radical absorption cross sections translate nonlinearly into an additional uncertainty of f20% on the k l values reported here. At temperatures below 248 K, the experimental absorption curves could not be reproduced by our chemical kinetic model due to the presence of a transient residual absorption. We could find no such evidence (absorption 5 0.2%) for a similar absorption tail at T I 248 K. At lower temperatures (228 and 238 K), this absorption was most pronounced at 250 nm as determined from measurements between 230 and 280 nm. These observations are discussed later. The 1 order of magnitude reactivity range covered by reactions 1, 2, and 9 results in mixed-order decay curves whose shapes were found to be very sensitive to secondary production and removal of either peroxy radical to the extent that such production or removal would effect the change in radical concentration ratio with time. Thus, the ability of the computer-generated compite-absorption curves to reproduce the shape of the experimental data under all conditions indicates both the adequacy of the radical decay mechanism assumed and the correct accounting of all absorbing species. In the absence of product analysis, this sensitivity enables us to dismiss any significant contribution from a reaction channel producing C2H50 OH 02.In the presence of C2H6, the OH would lead to secondary generation of C2H5O2. the time profile of which would be [C2H6]dependent. Inclusion of such a channel (with a yield of 0.5) resulted in modeled decay curves that were markedly different in shape from the experimental data and yielded k , values that were [C,H,] dependent in contrast with our observations.
+
Dagaut et al.
+
Discussion In Figure 2, we present an Arrhenius fit of our data together with the room temperature result of Cattell et al.’ at 2.4 Torr. As can be seen, there is excellent agreement between both studies for k1(298 K). This agreement can be used to indicate the pressure independence of k, at room temperature over the more expanded range of 2.4-400 Torr. It can be noted, in addition, that this consensus value for kl(298 K) is considerably larger than previous estimates which were used for a quantitative assessment of the effects of secondary reactions on measurements of k2 (in cm3
Y
2.0
3.0
5.0
4.0
1000/T, K-l Figure 2. Arrhenius plot for k , . This work: 0 , -.
Reference 1:
0.
by Adachi et a].;’’ 1.5 X molecule-I s-’): 1.66 X by by Anastasi et al.I3 Niki et a1.;12 1.53 X It is interesting to compare the temperature dependencies and magnitude of kl and k l o (the rate constant for the reaction of CH3O2 with H 0 2 ) . Similarities in the derived Arrhenius
+ C2H5O2 H 0 2+ C H 3 0 2
HO2
-+
-+
+0 2 C H 3 0 0 H + 0, C2H5OOH
(1)
(10)
“activation energies” would be expected if the two reactions proceed via parallel mechanisms as shown. Our observations of E , / R = -(650 f 125) and E l o / R = -(720 f 100) support this idea. The “inverse” temperature dependence or “negative” activation energy calculated for both reactiQnsfurther suggests that product formation occurs through an adduct intermediate. H02
+ RO2
++
ROOHO2
--+
ROOH
+0 2
This intermediate is expected to be more stable in reaction 1 than in reaction 10, due to the larger inductive effect of the ethyl group compared with that for CH3. Indeed, our measurement of k l / k l o iz 1.8 is in agreement with such an expectation. Finally, our observation of a low-temperature transient residual absorption in studies of reaction 1 but not in those of reaction 10 lends further support for such adduct formation and stability. As discussed earlier,2 reaction 1 is an important secondary reaction in the photochemical system (C2H6-C1 in the presence of excess 0,) typically used for studying reaction 2. In this system, hydroperoxy radicals are produced via reaction 2a (which has a branching ratio, kk/k2, of 0.62 to 0.79 between 228 and 380 K14), followed by reaction 11. Using these values for the branching C2H5O + 0
2
-+
CH3CHO
+ HO2
(11)
ratio, we have modeled the composite transient absorption decay curves obtained in such a photochemical system in order to render an accurate accounting of secondary chemistry in our earlier measurements of k2.2 In this reanalysis, values of k , , k9, and k l l were taken from the present work, ref 8, and ref 15, respectively, with k2 varied to yield a best fit to the experimental data. These calculations yield an Arrhenius expression for reaction 2: k2 = (8.5 f 1.1)
X
exp[-(110 f 40)/T] cm3 molecule-’s-’
where the uncertainties are two standard deviations. The agreement between this expression and our earlier (less rigorous) (11) Adachi, H.; Basco, N.; James, D. G. L. Int. J . Chem. Kinel. 1979, I J , 1211. (12) Nib, H.; Maker, P. D.; Savage, C. M.; Breitenbach, L. P. J . Phys. Chem. 1982, 86, 3825. (13) Anastasi, C.; Waddington, D. J.; Wooley, A. J . Chem. Soc., Faraday Trans. 1 1983, 79, 505. (14) Anastasi, C.; Brown, M. J.; Smith, D. B.; Waddington, D. J . Presented at the Joint Meeting of the French and Italian Sections of the Combustion Institute, Amalfi, Italy, June 1987. (15) Baulch, D. L.; Cox, R. A,; Hampson, R. F., Jr.; Kerr, J. A.; Troe, J.; Watson, R. T. J . Phys. Chem. ReJ Data 1984, J3, 1254.
J . Phys. Chem. 1988, 92, 3839-3842 recommendation,2 based only upon our preliminary room temperature value for k l , is attributable to the fact that k l / k z >> 10 over the complete temperature range. Acknowledgment. This research was performed with the partial
3839
support of the Upper Atmosphere Research Program of the National Aeronautics and Space Administration under Interagency Agreement W 15,8 16. Registry No. HOz, 3 170-83-0; C2H502, 3 170-61-4.
Comparison of the Optoacoustic and Hg Tracer Methods for the Study of Energy-Transfer Processes in Gas Mixtures Timothy J. Wallington, Walter Braun,* Center for Chemical Physics, National Bureau of Standards, Gaithersburg, Maryland 20899
Kenneth M. Beck, and Robert J. Gordon* Department of Chemistry, University of Illinois at Chicago, Chicago, Illinois 60680 (Received: December 8, 1987)
Rates of energy transfer from vibrationally excited SF6 and pentafluorobenzene to argon in the gas phase have been studied by using the Hg tracer technique and time-resolved optoacoustics. These two techniques which rely on fundamentally different physical principles were found to give equivalent results. The implications for the study of energy-transfer processes in gas mixtures are discussed.
I. Introduction The rate a t which energy is transferred between vibrational, rotational, and translational degrees of freedom in gaseous systems is of fundamental importance in understanding the fate of species excited as a result of chemical or physical processes. A variety of different techniques have been applied to the study of energy transfer from vibrationally excited molecules. These include ultraviolet absorption,’q2 infrared a b ~ o r p t i o n infrared ,~ fluores~ e n c eoptoacoustics,5,6 ,~ thermal lensing,’ and most recently the H g tracer technique.8 However, at present it is difficult to compare the results from studies using these different techniques as, in general, these methods have been applied to measure relaxation rates of different gas mixtures, using different excitation methods and excitation energies. Furthermore, the above methods do not all monitor the same specific relaxation processes. For example, the ultraviolet absorption method measures changes in vibrational excitation whereas the Hg tracer and optoacoustic techniques monitor changes in the translational excitation of the mixtures. Recently in our two laboratories we have applied the optoacoustic and Hg tracer methods to the study of the rates of energy transfer in a wide variety of gas mixtures. The former technique measures the development of a pressure wave, propagating from (1) Hippler, H.; Troe, J.; Wendelken, H. J. J . Chem. Phys. 1983,78, 5351. (2) Ichimura, T.; Mori, Y.; Nakashima, N.; Yoshihara, K. J. Chem. Phys. 1985, 83, 117. (3) Jalenak, W.; Weston, Jr., R. E.; Sears, T. J.; Flynn, G. W. J . Chem. Phys. 1985,83, 6049. (4) Rossi, M. J.; Pladzievicz, J. R.; Barker, J. R. J . Chem. Phys. 1983, 78, 6695. (5) Smith, N. J. G.; Davis, C. C.; Smith, I. W. M. J . Chem. Phys. 1984, 80, 6122. (6) Beck, K. M.; Ringwelski, A.; Gordon, R. J. Chem. Phys. Left. 1985, 12, 529. (7) Siebert, 0. R.; Grabiner, F. R.; Flynn, G. W. J . Chem. Phys. 1974, 60, 1504. (8) Braun, W.; Scheer, M. D.; Kaufman, V. J . Res. Nufl. Bur. Sfand. 1986, 91, 313.
0022-365418812092-3839$01SO10
the origin of excitation, at some distant (initially undisturbed) point in the fluid medium. The latter technique measures the temporal change in absorption at 254 nm by a trace of Hg vapor caused by Doppler and Lorentz line broadening due to the heating of a gas mixture. Both techniques measure the rate at which energy is transferred from the initial vibrational excitation to translational excitation of the gas. In order to compare the results obtained from these two different methods we have conducted relaxation experiments in mixtures of SF6 and argon and of pentafluorobenzene (PFB) and argon in our two laboratories. Both methods depend to a greater or lesser degree on various physical processes which occur during relaxation (e.g., the specific relaxation mechanism and occurrence of fluid flow) which will be discussed. 11. Experimental Section
The apparatus and experimental techniques used in the optoacoustic (OA)6 and Hg tracer”’ methods have been described previously and hence only a brief description is given here. In both experimental systems a C 0 2 TEA laser tuned to the P20, 10.6-llm C 0 2 laser line was used to excite the SF6 and PFB mixtures. Excitation energies were in the range 3000-6000 cm-’ in the Hg tracer technique and 3000-20 000 cm-’ in the optoacoustic study. This energy range was dictated by our previous observations that at such energies relaxation rate constants for SF6/Ar and PFB/Ar mixtures are independent of energy,12qi3thus facilitating a direct comparison of the results from the two different methods. II.A. Optoacoustic Method. In the OA experiments, mixtures were irradiated in a large cylindrical static cell (30 cm long, 31 cm id.). A fast piezoelectric transducer placed 8.6 cm normal (9) Braun, W.; Scheer, M. D.; Cvetanovic, R. J. J . Chem. Phys. 1987,88, 3715. (10) Wallington, T. J.; Scheer, M. D.; Braun, W. Chem. Phys. Lett. 1987, 138, 538. (11) Dagaut, P.; Wallington, T. J.; Braun, W. J . Phorochem., in press. (12) Beck, K. M.; Gordon, R. J. J . Chem. Phys. 1987, 87, 5681. (13) Braun, W.; Wallington, T. J. Chem. Phys. Left. 1987, 140, 441.
0 1988 American Chemical Society
