Cumulative reaction probabilities: A comparison between quasiclassical and quantum mechanical results

This article presents a quasiclassical trajectory (QCT) method for determining the cumulative reaction probability (CRP) as a function of the total energy. The method proposed is based on a discrete sampling using integer values of the total and orbital angular momentum quantum numbers for each trajectory and on the development of equations that have a clear counterpart in the quantum mechanical (QM) case. The calculations comprise cumulative reaction probabilities at a given total angular momentum J, as well as those summed over J. The latter are used to compute QCT rate constants. The method is illustrated by comparing QCT and exact QM results for the H+H2, H+D2, D+H2, and H+HD reactions. The agreement between QCT and QM results is very good, with small discrepancies between the two data sets indicating some genuine quantum effects. The most important of these involves the value of the CRP at low energies which, due to the absence of tunneling, is lower in the QCT calculations, causing the corresponding rate constants to be smaller. The second is the steplike structure that is clearly displayed in the QM CRP for J = 0, which is much smoother in the corresponding QCT results. However, when the QCT density of reactive states, i.e., the derivatives of the QCT CRP with respect to the energy, is calculated, a succession of maxima and minima is obtained which roughly resembles those found in the QM calculations, although the latter are considerably sharper. The analysis of the broad peaks in the QCT density of reactive states indicates that the distributions of collision times associated with the maxima are somewhat broader, with a tail extending to larger collision times, than those associated with the minima. In addition, the QM and QCT dynamics of the isotopic variants mentioned above are compared in the light of their CRPs. Issues such as the compliance of the QCT CRP with the law of microscopic reversibility, as well as the similarity between the CRPs for ortho and para species in the QM and QCT cases, are also addressed.