An efficient implementation of microcanonical, classical variational transition-state theory based on the use of the efficient microcanonical sampling (EMS) procedure is applied to simple bond fissions in SiH2 and Si2H6 using recently constructed global potential-energy surfaces. Comparison is made with results of trajectory calculations performed on the same potential-energy surfaces. The predictions of the statistical theory agree well with and provide an upper bound to the trajectory derived rate constants for SiH2→SiH+H. In the case of Si2H6, agreement between the statistical theory and trajectory results for Si–Si and Si–H bond fission is poor with differences as large as a factor of 72. Moreover, at the lower energies studied, the statistical calculations predict considerably slower rates of bond fission than those calculated from trajectories. These results indicate that the statistical assumptions inherent in the transition-state theory method are not valid for disilane in spite of the fact that many of the mode-to-mode rate constants for intramolecular energy transfer in this molecule are large relative to the Si–Si and Si–H bond fission rates. There are indications that such behavior may be widespread among large, polyatomic molecules.

A general and efficient microcanonical sampling (EMS) procedure based on that of Severin et al. [Chem. Phys. Lett. 57, 117 (1978)] is outlined. The relevant statistical weights are derived. The EMS method can be used for the generation of initial microcanonical states for trajectories or directly in the efficient calculation of microcanonical statistical averages and rate constants. The validity and usefulness of the EMS method is demonstrated in applications to 1D linear chains and 3D molecules such as H2O, SiH2, and Si2H6.

Expressions for the molecular momentum density of states as a function of spatial configuration in an angular momentum resolved microcanonical ensemble are derived. These expressions are then used to formulate an efficient sampling scheme for the generation of spatial configurations or full phase space vectors in an ensemble where both energy and angular momentum are predetermined. Applications to simple diatomic (OH) and triatomic (H 2 0) molecular models are presented.

No abstract

6158 15 0 J. Phys. Chem. 1986, 90, 6158-6167 x 1 0.08 torr N, x 2 0.04 torr N x 5 0.01 torr N, I I I I 20 40 60 80 Time (nsec) Figure 6. Fitting of Monte-Carlo results for 20 Torr of He and three nitrogen pressures, with the N2()CIIU) decay rate set equal to zero, to a first-order formation mechanism. The units of the ordinate are the same as for Figure 4 and give the N2(C311u) concentration in arbitrary units; vertical amplification factors for each curve are indicated on the drawing. The curve for 0.04 Torr of N2 has been displaced upward 2.5 units; the curve for 0.08 Torr of N2 has been displaced 5 units. The squares are the Monte-Carlo points. The solid curves are least-squares best fits to a simple exponential formation. of N, pressure. (The resulting best-fit curves are those shown in Figure 4.)Also shown in Figure 5 are the values of kf obtained from the Monte-Carlo results by analysis of the formation curves which result if k6 is set equal to zero in the calculation. It is simpler to visualize the degree to which the Monte-Carlo results can be fit to a first-order kinetic scheme from such plots. SuchMonte-Carlo curves for 20 Torr of H e are shown in Figure 6 for N2 pressures of 0.01, 0.04, and 0.08 Torr, with the least-squares "best fit" curves drawn through the Monte-Carlo points. These results confirm that a first-order formation provides a reasonable approximation to the production of N2(C3n,). The situation is similar for Ne. The formation constants given in Figure 5 may be compared with the experimental values reported by Cooper et aL2 In contrast to the qualitative agreement noted in Figure 4 between experiment and Monte-Carlo calculations, the results in Figure 5 seem to disagree with experiment. The slopes of kf vs. PN2 yield values of k, = 1.9 X lOI3 dm3 mol-' s-l for He and 2.0 X lOI3 dm3 mol-' s-' for Ne. These are about four times greater than the experimentally reported values obtained from similar plots. In an effort to explain this, the experimental data have been reexamined, and we have found that the uncertainty in the analysis of the experimental data is large and that experimental values of kf more in line with the Monte-Carlo results are reasonable. Also, the much smaller intercept at PN2 = 0 for Ne, in comparison with that for He, predicted by the calculation, is not evident in the original experimental plots. This may be due to deterioration of the signal quality in the experimental data at the lowest N z pressures. Further experiments are needed to determine whether this difference in intercepts is realized. The difference is expected because the loss of energy by qE-by elastic collisions is much more efficient for He than for Ne, owing to the smaller mass of the H e atom. Impurity problems could be especially troublesome at low PK2 and could mask the intercept differences.Finally, Dillong has recently carried out an analytic treatment of the same problem and has obtained results close to those of the Monte-Carlo simulation. A full account of his work is being prepared for publicati...