18944
J. Phys. Chem. 1996, 100, 18944-18949
Unusual Insertion Mechanism in the Reaction C(3P) + H2 f CH + H Renee Guadagnini and George C. Schatz* Department of Chemistry, Northwestern UniVersity, EVanston, Illinois 60208-3113 ReceiVed: April 18, 1996X
We use quasiclassical trajectories to study the reaction C(3P) + H2 f CH + H using an accurate ab initio potential surface, making comparisons with recent product distribution measurements. An analysis of the reactive trajectories indicates that the formation of CH + H is completely dominated by insertion to form a 3 CH2 intermediate. However, this C insertion is initiated from nearly linear C-H-H geometries rather than by perpendicular attack as has been found for other insertion reactions (like O(1D) + H2). Perpendicular insertion collisions do occur, but they are almost always nonreactive due to poor coupling between modes initially excited in 3CH2 and the product reaction coordinate (C-H stretch). The calculated product rovibrational distributions are in excellent agreement with experiment, but we find that they are not sensitive to the presence of this modified insertion mechanism. Reactions like O(1D) + H2 may also show the modified insertion mechanism at high energies. Results from C + HD and C + HCl are also examined.
I. Introduction Insertion reactions are well-known in chemistry, with numerous studies of reactions involving species like O(1D)1 and C(1D).2 Typical insertion reactions involve perpendicular approach of the attacking radical to the bond that is to be ruptured. Other approach directions are possible, but a competing reaction mechanism for many reactions for approach angles away from perpendicular is atom abstraction. Recently, Scholefield et al.3 presented reaction dynamics measurements for reactions involving a potentially new candidate for insertion dynamics, namely C(3P). They studied product rovibrational distributions for the reactions of hyperthermal C(3P) with H2, HCl, HBr, and CH3OH. They found CH product distributions for these reactions that were generally similar to each other and also similar to those from the corresponding C(1D) reaction. In addition, they obtained CH λ-doublet and spin-orbit distributions that were essentially statistical, suggesting the formation of a 3CH2 complex during reaction, as might be expected for an insertion mechanism. In this paper we present a theoretical study of the C(3P) + H2 reaction dynamics, with an emphasis on understanding the reaction mechanism and on interpreting the Scholefield et al. experiment. The theoretical results are based on quasiclassical trajectory calculations using a global potential surface (denoted HSG)4 derived from extensive ab initio calculations. This surface was employed in an earlier study4 of the CH + H reaction and of C + H2 f CH2 at energies below those needed for CH + H formation. Agreement with experiment in this earlier study (including a shock tube study5 of C(3P) + H2 f CH + H) was excellent; however, no comparisons involving product distributions were possible at the time. The reaction C(3P) + H2 is electronically complex, and it has only been recently4,6,7 that the topology of the global potential surfaces for the ground and lowest excited state has been fully characterized. Details of this surface will be presented later, but for now we note that C + H2 is an endoergic reaction (by 1.16 eV) that may proceed by either insertion or abstraction pathways. Insertion may occur with essentially no barrier for approach geometries close to perpendicular to produce 3CH2, which is stable by 3.39 eV. 3CH2 may then X
Abstract published in AdVance ACS Abstracts, November 1, 1996.
S0022-3654(96)01164-1 CCC: $12.00
Figure 1. Schematic of potential energy surfaces that correlate to C(3P) + H2, showing C2V geometries except for the dissociation of CH2 to CH + H.
dissociate to give CH + H without an exit channel barrier. Abstraction occurs for linear C-H-H geometries over a barrier of 1.28 eV relative to C + H or 0.12 eV above CH + H. The fact that C + H2 is endoergic makes it qualitatively different from many other insertion reactions such as O(1D) + H2 which are exoergic, but it is not obvious that this should change the insertion mechanism. To study this point, we present results for C + H2 where we have substituted the O(1D) + H2 potential surface of Schinke and Lester (SL) (their surface 1).8 With both the HGS and SL surfaces we have studied reactivity as a function of initial orientation angle, determining the fraction of trajectories which insert, the fraction which react, and the fraction which react via insertion. In addition, we also study the reactions C + HD and C + HCl using the HGS surface to see how the dynamics is perturbed by mass asymmetry. A more thorough description of the potential surface and of the trajectory calculations is given in section II. Section III presents rovibrational distributions and cross sections for C + H2 and C + HX (X ) D, Cl), along with comparisons with experiment. Section IV analyzes the reaction mechanism, including comparisons between C + H2 and O(1D) + H2. Section V summarizes our conclusions. II. Theory A. Potential Energy Surface Properties. Figure 1 presents a schematic of the three electronic states which correlate to C(3P) + H2, showing correlations appropriate for C2V symmetry except © 1996 American Chemical Society
The Reaction C(3P) + H2 f CH + H
J. Phys. Chem., Vol. 100, No. 49, 1996 18945
TABLE 1: Properties of 3CH2 Ground Adiabatic Potential Surface stationary point
energy RCH (eV) (A0)
RHH (a0)
θ (deg)
C + H2 (asymptote) 0 ∞ 1.40 CH2 (C2V 3A2 minimum) -0.20 2.47 1.71 40.4 CH2 (C2V conical intersection) 0.02 2.28 2.22 58.2 CH2 (C2V 3B1 minimum) -3.39 2.04 3.75 133.5 HCH (linear inversion stationary point) -3.13 2.02 4.04 180.0 HHC (linear abstraction point) 1.28 2.23 2.49 0.0 CH + H (asymptote) 1.16 2.12 ∞
for the step in which CH2 dissociates to CH + H. Table 1 summarizes the energies and geometries of the stationary points in Figure 1 along with two linear stationary points. Of the three surfaces that correlate to C(3P) + H2, only the 3A2 state is attractive at long range, forming a shallow (-0.2 eV) minimum. This state exhibits a conical intersection with the 3B2 state, at an energy that is 0.02 eV above the asymptote. However, the zero-point corrected energy of the conical intersection is downhill from C + H2, and even the Born-Oppenheimer surface is purely attractive if one bends a few degrees away from the C2V approach. Since the ground adiabatic surface has no barrier to insertion, it is likely that nonadiabatic effects associated with the conical intersection are unimportant in the reaction dynamics, so we have restricted our calculations to the ground adiabatic surface. Even for the ground surface, geometric phase effects associated with the conical intersection should exist;7 but their importance for C + H2 collisions is unknown, and it is not possible to include them in a trajectory study. Once the deep 3B2 minimum (-3.39 eV) is formed, it is relatively facile to invert CH2 through a linear geometry transition state, requiring only 0.26 eV. Dissociation of CH2 to CH + H is uphill by 4.55 eV and occurs without any exit channel barrier. Another reaction pathway involves collinear abstraction. This pathway takes place without an intermediate well on a surface of 3Π symmetry. There is a small (0.12 eV) barrier in the exit channel for this path, but note that this stationary point has two imaginary frequencies,4 one for atom transfer and the other for bending. The absence of a real bend frequency means that the reaction path for abstraction is not cleanly separated from that for insertion. Because of this, we will not use geometrical criteria to determine whether reaction involves abstraction or insertion. Another linear reaction pathway exists on a 3Σ surface that would lead to the formation of CH(4Σ) + H. CH(4Σ) is 0.74 eV above CH(2Π), so it should have a significantly smaller population under the conditions of the Scholefield et al. experiment. B. Trajectory Calculations. The trajectory calculations were done using a standard quasiclassical method similar to that used in ref 4 and using the HGS surface. The main complication associated with the present application was in sampling the reagent translational energy distribution. According to Scholefield et al.,3 the distribution of carbon lab velocities is given by a shifted Maxwell-Boltzmann distribution as follows:
P(V) ) AV2e-(V-Vs) /R 2
TABLE 2: Reactive Cross Sections and Product Attributes for C + HX (X ) H, D, Cl)
2
where the shift velocity Vs is 8000 ms-1 for ablation of a graphite source, and the width parameter R is chosen to make the translational temperature be 21 000 ( 4000 K. A velocity of 8000 ms-1 corresponds to a translational energy of 4 eV; but transformation to the center of mass converts this to a relative translational energy of 0.57 eV (neglecting the H2 energy), and the temperature associated with the distribution is 3000 K. This
Etrans/eV 1.25 (a) C + H2 f CH + H Qreact (a02) react Qinsert Qinsert 〈V〉 〈N〉 (b) C + HD f CH + D Qreact react Qinsert Qinsert 〈V〉 〈N〉 (c) C + HD f CD + H Qreact react Qinsert Qinsert 〈V〉 〈N〉 (d) C + HCl f CH + Cl Qreact react Qinsert Qinsert 〈V〉 〈N〉 (a) C + HCl f CCl + H Qreact react Qinsert Qinsert 〈V〉 〈N〉
1.50
1.75
2.00
2.50
3.00
0.5 1.3 2.1 2.6 3.9 5.2 0.5 1.3 1.6 1.8 1.9 1.8 13.0 12.4 11.3 9.8 6.9 5.2 0.03 0.07 0.14 0.43 0.84 1.3 6.8 8.2 9.7 10.7 13.6 16.0 0.4 0.9 1.4 1.9 2.7 3.2 0.4 0.9 1.2 1.7 2.2 2.4 12.8a 12.4 11.5 10.6 8.3 6.3 0.03 0.01 0.15 0.36 0.82 1.3 6.2 8.1 10.2 12.0 15.4 18.7 0.4 1.3 1.8 2.5 3.2 0.4 1.3 1.8 2.4 2.8 12.8a 12.4 11.5 10.6 8.3 0.02 0.07 0.34 0.62 1.2 8.8 10.7 13.4 15.0 18.2
3.8 2.9 6.3 2.0 21.6
0.6 1.7 2.4 3.2 4.8 6.3 0.6 1.7 2.4 3.0 3.9 4.5 15.1a 14.8 14.1 13.3 11.6 10.3 0.03 0.01 0.12 0.34 0.64 0.66 6.2 8.6 11.1 12.7 16.1 19.0 0.8 1.8 2.2 2.4 0.8 1.7 2.1 2.3 15.1a 14.8 14.1 13.3 0.08 0.58 1.22 1.8 19.4 27.4 34.3 40.9
2.2 1.8 11.6 3.1 50.4
1.8 1.2 10.3 4.9 52.7
a Note that the insertion cross section does not distinguish between product channels for C + HX.
puts much of the distribution at energies below the reactive threshold (1.16 eV, or 1.06 eV with zero-point correction). However, the width of the distribution is sufficiently broad that energies up to 3.0 eV need to be considered in performing the average over the distribution. Overall, the ensemble average was performed by determining cross sections at 1.0, 1.25, 1.50, 1.75, 2.00, 2.50, and 3.00 eV and then averaging using a simple trapezoidal rule integration. Zero-point energy was not constrained in the product CH’s as this was found to have a minor influence on the results. The most important contribution to the Boltzmann average was found to be at 1.25 eV (0.19 eV above the energetic threshold). To compare with experiment, the cross sections that we present should be multiplied by a factor of approximately 1/3 to describe the fraction of trajectories that sample the reactive potential surface. Initial ground vibrational and rotational states were assumed for most calculations, as the H2 is initially very cold (20 K) in the experiments. Some calculations with initial H2 vibrational state V ) 1 were considered, but aside from a small increase in the amount of product vibrational excitation, the product energy partitioning was not changed significantly. The maximum impact parameter for all cross section calculations was chosen to be 6 a0. The final vibrational and rotational quantum numbers, V and N, were calculated using the standard histogram method. Electronic angular momentum was not included in the definition of N. This should be of minor consequence, as the most probable states have N . 1. III. Cross Sections and Product State Distributions Table 2 presents the integral reactive cross sections Qreact for C + H2, C + HD and C + HCl for energies ranging from 1.25 to 3.00 eV, along with two types of insertion cross sections,
18946 J. Phys. Chem., Vol. 100, No. 49, 1996
Guadagnini and Schatz
Figure 2. Rotational distributions for C + H2 f CH + H based on HGS surface. Included are plots of the cross section versus CH rotational quantum number N for V ) 0 and Etrans ) 1.25, 2.0, and 3.0 eV and the average over the experimental distribution. Also shown are measurements from ref 3, including data from two different spectral transitions.
and the average vibrational and rotational quantum numbers 〈V〉 and 〈N〉. Note that the two equivalent CH products have been summed over for C + H2. All calculations refer to the HGS surface, even those for C + HCl, so the C + HCl results are not intended to provide a quantitative description of that reaction. The insertion cross section Qinsert is defined using all trajectories, whether reactive or not, for which the potential energy drops below -2.4 eV during the collision (taking zero to be separated C + H2 at equilibrium). This corresponds to 70% of the well react is defined using only trajectories which insert depth. Qinsert and react. There are several important trends in Table 2 which we summarize as follows: (1) All the reactive cross sections except those for C + HCl f CCl + H increase rapidly with reagent translational energy. The CCl + H cross section should be limited by a significant exit channel centrifugal barrier at higher energies because of the light mass of the product H atom. react is very close to Qreact in all cases at low energy, (2) Qinsert react . C + H2 is an endotherbut Qinsert is much greater than Qinsert react compared to Qinsert mic reaction, so the smallness of Qinsert close to the reactive threshold can be rationalized based on simple statistical considerations. However, we show in section IV that some features of the trajectories that contribute to react are very much nonstatistical. Qinsert (3) For C + HD, the CD + H product is favored over CH + D except at 1.25 eV. This is the same type of isotope effect as seen for O(1D) + HD,1b and it has been interpreted in terms of a dynamical model in which the light H atom is preferentially ejected from the complex. (4) For C + HCl, the CH + Cl product is favored, except at very low energy. The behavior at high energy arises from the dropping off of the CCl + H cross section mentioned above. Preferential ejection of the H atom only occurs at low energies where the centrifugal barrier is less important. (5) Qreact is smaller for C + H2 than the sum of the two Qreact’s for C + HD or for C + HCl. This difference is related to
symmetry of the intermediate complex in CH2, and the asymmetry in CHD and CHCl, as will further be discussed in section IV. (6) Vibrational excitation is small for all reactions near threshold, then rises with increasing translational energy. The CH(V)1) cross section calculated for the experimental conditions is only a few percent of CH(V)0). This result is consistent with experimental observations. CH vibrational excitation is about the same for C + H2, HD, and HCl, while the CD and CCl products have larger 〈V〉’s. (7) Average product rotational excitation increases with increasing reagent translational energy. 〈N〉 for CH is about the same for C + H2, HD, and HCl, while it is larger for CD and CCl. Figure 2 presents the V ) 0 rotational distribution for C + H2, showing results at 1.25, 2.00, and 3.00 eV, and the average over the experimental translational distribution. This figure shows the increase in average rotational excitation with translational energy that we noted earlier. The width of the distribution, which is quite substantial, also increases. The average over the experimental velocity distribution is dominated by the 1.25 eV result and corresponds to a rotational temperature of 1845 K. The comparison with experiment is essentially perfect, with any differences being within the scatter of the results derived from different spectral transitions. The quoted experimental rotational temperature is 1500 ( 100 K. Figure 3 presents CH rotational distributions for C + HX (X ) H, D, Cl), all for the experimental velocity distribution. This figure shows similar distributions for all three reactions, with an average 〈N〉 of about 7, and a width ∆N ) 6. This lack of dependence of rotational distribution on the reaction being considered is the same as was observed by Scholefield et al. in their studies of C + HX with X ) H, Cl, Br and CH3O/CH2OH. Another possible comparison with experiment that can be made is for the λ-doublet distributions. CH is an example of strong Hund’s case (b) coupling such that the relative population
The Reaction C(3P) + H2 f CH + H
J. Phys. Chem., Vol. 100, No. 49, 1996 18947
Figure 3. Rotational distributions analogous to the experimental average in Figure 2 but for C + HX (X ) H, D, Cl).
of the π(A′) and π(A′′) states is strongly correlated with the direction of the rotational angular momentum vector relative to the plane containing the singly occupied π orbital. The experimental measurements show that the two λ-doublet states have equal population, which means that the angular momentum vector is not correlated with this plane. Our trajectory calculations only refer to the ground adiabatic electronic state so a rigorous determination of the λ-doublet populations is not possible. What we can do as an approximation is to examine the correlation between the direction of the product CH rotational angular momentum vector and the normal to the plane of the three-atoms at a point just before the CH2 intermediate breaks apart (defined as the first time that the H-H distance becomes greater than 3.5a0). This plane will contain the newly formed CH π orbitals, so the correlation tells us whether the π(A′) or π(A′′) state is more important. We have examined this correlation for the experimentally defined reagent velocity distribution, and we find that there is no correlation at all (within statistical uncertainty) between these quantities. This is consistent with the observations, and it means that the repulsion between the H and CH as the complex decays does not play an important role in determining product CH rotational excitation. IV. Analysis of Reaction Mechanism The results in Table 2 indicate that although insertion plays a dominant role in producing reactive collisions, a large fraction of collisions in which insertion occurs are nonreactive. To develop a more detailed understanding as to what this means, in Figure 4 we plot the fractional contribution to the reaction probability for zero impact parameter collisions as a function of cos γ, where γ is the Jacobi angle between the H2 diatomic axis and the C to H2 center-of-mass vector R, when |R| decreases to 3a0 for the first time. Included in the figure are results for C + H2 at 1.25 and 3.00 eV on the HGS surface and for C + H2 at the same energy for the SL surface (the surface for O(1D) + H2). Each plot includes the fraction of insertion, reaction, and insertion followed by reaction (insert/react). Note that on the SL surface, where the well bottom is at -7.3 eV, we have defined insertion as occurring when the potential drops
below -5.4 eV, corresponding to 74% of the well depth. Here is a summary of the results: (1) The HGS results at 1.25 eV indicate a significantly higher probability for insertion than reaction. The cross sections in Table 2 show similar behavior. The reactive and insert/react fractions are the same and are nonzero only for nearly linear collisions (cos γ ) -1 or +1). This dependence on γ is not what would be expected by statistical theory (which would predict a flat distribution). (2) At 3.0 eV the HGS insertion fraction is only about double the reactive fraction on average. The reactive and insert/react fractions are the same for -0.5 e cos y e 0.5 and show a minimum at γ ) 90°. The reactive fraction is significantly larger than insert/react for nearly collinear collisions, indicating that direct collisions can contribute to the reaction at this high energy. (3) For the SL surface at 1.25 eV, the insertion and insert/ react fractions are nearly the same, indicating that insertion almost always leads to reaction. The reactive fraction is nearly the same as insert/react for angles near 90° but is considerably higher for angles close to collinear. This means that direct reaction contributes to the reaction at 1.25 eV. (4) The SL results at 3.00 eV are similar to SL at 1.25 eV except that (a) the fraction of direct reaction is higher and (b) there is a minimum in the reactive and insert/react fractions near γ ) 90°. Note that the HGS and SL results at 3.0 eV are somewhat similar while the corresponding results at 1.25 eV are not. A key question that emerges from the analysis of Figure 4 is why are insertion collisions so inefficient in causing reaction to occur on the HGS surface for γ close to 90°, especially at low energy. On the SL surface, this same inefficiency shows up only at 3.00 eV near γ ) 90°. We have animated numerous trajectories to study this point, and we find that on the HGS surface, insertion from essentially any approach angle leads to the formation of a CH2 complex in which the H-H bond distance has increased from its isolated molecule value (1.4 a0) to a value appropriate for CH2 at equilibrium (3.75 a0). However, there is a significant probability for the CH2 to decay back to C + H2 during the first or second vibrational periods
18948 J. Phys. Chem., Vol. 100, No. 49, 1996
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Figure 4. Fraction of reaction, insertion and insert/react vs cos γ for C + H2. Results for HGS surface are in the left panels; those for SL are in the right. Top panels show 1.25 eV results; bottom are 3.00 eV.
Figure 5. Schematic of a ballistic inversion trajectory. The large sphere is the carbon atom, which has been defined to be at the origin for all times. The two hydrogen atoms are initially the two rightmost spheres, with the C-H2 configuration having C2V symmetry. Successive frames are in intervals of 4 fs, and show the H’s continuously moving to the left, with the H-H bond first breaking, the re-forming. The overall trajectory is nearly symmetric about the origin.
of CH2 due to the inefficient exchange of energy between the vibrational modes of the nascent CH2. This recrossing of the entrance channel bottleneck is especially significant for nearly perpendicular collisions, as in this case the initially excited CH2 has all of its vibrational excitation in the totally symmetric modes (symmetric stretch, bend). Transfer of this excitation to the asymmetric stretch is essential for formation of CH + H products. This causes the dips near γ ) 90° seen in Figure 4. This slow exchange between symmetric and asymmetric modes is less apparent in CHD and CHCl, due to the mass asymmetry. Another important result from our trajectory simulations is that the nascent CH2 often undergoes inversion during the initial encounter so that the C atom appears to go “through” the H2, as pictured in Figure 5. Inversion is facile for CH2 because the inversion barrier (Table 1) is very low compared to the energy available. Inversion is less facile on the SL surface, as the inversion barrier in H2O is 1.5 eV. This means that trajectories like that in Figure 5 are unlikely unless the energy is very high (as in the 3.0 eV result in Figure 4). No correlation between angle of approach and rotational distribution is observed on the HGS surface. This behavior is
what would be expected from statistical considerations. This suggests that although the first couple of vibrational periods of the CH2 complex is very decidely nonstatistical, complexes which last longer than that (which are responsible for most of the reactive trajectories), exhibit dynamics which are closer to statistical. To test the hypothesis of statistical behavior for complexes that react, we have calculated microcanonical statistical distributions for all the entries listed in Table 2. We find that the statistical 〈N〉 values match trajectories fairly closely, with 〈N〉 predicted to vary as (Eavail)3/2, and 〈N〉 being roughly independent of reaction for the CH products, and increased by factors of approximately x2 and 3 for CD and CCl. The comparison of 〈V〉 values is less precise. Statistical theory predicts that 〈V〉 should increase linearly with Eavail and should be independent of reaction for CH products and should be increased by factors of approximately x2 and 3 for CD and CCl, respectively. The dependence on Eavail is in poor agreement with trajectories. Given that reactive CH2 complexes typically have lifetimes of a few vibrational periods, it is probably not surprising that statistical theory is not quantitative. V. Conclusion The most important conclusion from this study is that the C + H2 f CH + H reaction is dominated by a modified insertion mechanism in which the initial approach is close to collinear, but a CH2 complex is formed that decays to CH + H. The more traditional perpendicular insertion occurs readily but is ineffective in causing reaction due to inefficient energy flow between the symmetric and asymmetric stretch modes of the nascent CH2. In addition, the low inversion barrier in CH2 allows for ballistic trajectories in which the C goes right between the two H atoms. This modified insertion mechanism is also found for C + HX (X ) D, Cl) using the HGS potential surface, but not for the O(1D) + H2 reaction (SL surface) except at high energy.
The Reaction C(3P) + H2 f CH + H The comparisons of our C + H2 results with experiment are essentially perfect. This confirms our earlier work4 that suggested that the HGS surface is excellent for dynamics studies. Previously, it had been conjectured3 that significant coupling between the 3CH2 and 1CH2 surfaces might be involved in the reaction mechanism. Our results suggest that this is not needed to explain the data. However, the C(1D) + H2 and C(3P) + H2 product distributions are probably very similar when compared at the same available product energies. Other features of the reaction dynamics that have proven interesting include (1) the product branching in C + HX, which reflects competition between factors which favor and inhibit H atom emission from the complex, (2) product rotational distributions in C + HX which show variation with energy and isotope that are similar to statistical results, (3) product λ-doublet distributions, which are statistical, and (4) the lack of dependence of the rotational distributions on initial approach direction. Points 2 and 4 suggest statistical decay of CH2 complexes after the first couple vibrational periods; however, a more detailed analysis of the results indicates that the results are not completely statistical. Finally, we note that C + H2 provides an excellent example of a reaction where phase space structure of the intermediate complex is divided between direct and chaotic parts.9 Such reactions are usually associated with poor coupling
J. Phys. Chem., Vol. 100, No. 49, 1996 18949 between different degrees of freedom, and often statistical theories make important errors in the description of the unimolecular decay dynamics. Acknowledgment. We thank NSF Grant NSF-9527677 for support of this work and Larry Harding, Toshiyuki Takayanagi, and Hanna Reisler for useful discussions. References and Notes (1) (a) Whitlock, P. A.; Muckerman, J. T.; Fisher, E. R. J. Chem. Phys. 1982, 76, 4468. (b) Fitzcharles, M. S.; Schatz, G. C. J. Phys. Chem. 1986, 90, 3634. (c) Goldfield, E. M.; Wiesenfeld, J. R. J. Chem. Phys. 1990, 93, 1030. (2) Scott, D. C.; de Juan, J.; Robie, D. C.; Schwartz-Lavi, D.; Reisler, H. J. Phys. Chem. 1992, 96, 2509. (3) Scholefield, M. R.; Goyal, S.; Choi, J.-H.; Reisler, H. J. Phys. Chem. 1995, 99, 14605. (4) Harding, L. B.; Guadagnini, R.; Schatz, G. C. J. Phys. Chem. 1993, 97, 5472. (5) Dean, A. J.; Davidson, D. F.; Hanson, R. K. J. Phys. Chem. 1991, 95, 183. Dean, A. J.; Hanson, R. F. Int. J. Chem. Kinet. 1992, 24, 517. (6) Bea¨rda, R. A.; van Hemert, M. C.; van Dishoeck, E. F. J. Chem. Phys. 1995, 102, 8930. (7) Yarkony, D. R. J. Chem. Phys. 1996, 104, 2932. (8) Schinke, R.; Lester, W. A. J. Chem. Phys. 1980, 72, 3754. (9) Davis, M. J.; Gray, S. K. J. Chem. Phys. 1986, 84, 5389.
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