Semiclassical calculation of cumulative reaction probabilities

Abstract

Calculation of chemical reaction rates lies at the very core of theoretical chemistry. The essential dynamical quantity which determines the reaction rate is the energy-dependent cumulative reaction probability, N(E), whose Boltzmann average gives the thermal rate constant, k(T). Converged quantum mechanical calculations of N(E) remain a challenge even for three- and four-atom systems, and a longstanding goal of theoreticians has been to calculate N(E) accurately and efficiently using semiclassical methods. In this article we present a variety of methods for achieving this goal, by combining semiclassical initial value propagation methods with a reactant–product wavepacket correlation function approach to reactive scattering. The correlation function approach, originally developed for transitions between asymptotic internal states of reactants and products, is here reformulated using wavepackets in an arbitrary basis, so that N(E) can be calculated entirely from trajectory dynamics in the vicinity of the transition state. This is analogous to the approaches pioneered by Miller for the quantum calculation of N(E), and leads to a reduction in the number of trajectories and the propagation time. Numerical examples are presented for both one-dimensional test problems and for the collinear hydrogen exchange reaction.