Semiclassical calculation of cumulative reaction probabilities

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 B oltzmann average gives the thermal rate constant, k(T). Converged quantum m echanical calculations of N(E) remain a challenge even for three- and four- atom systems, and a longstanding goal of theoreticians has been to calculat e NO accurately and efficiently using semiclassical methods. In this articl e we present a variety of methods for achieving this goal, by combining sem iclassical initial value propagation methods with a reactant-product wavepa cket 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 wavep ackets in an arbitrary basis, so that N(E) can be calculated entirely from trajectory dynamics in the vicinity of the transition state. This is analog ous 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 propagat ion time. Numerical examples are presented for both one-dimensional test pr oblems and for the collinear hydrogen exchange reaction.