On the semiclassical description of quantum coherence in thermal rate constants

Abstract

An earlier paper of ours [J. Chem. Phys. 108, 9726 (1998)] used an approximate (linearized) version of the semiclassical initial value representation (SC-IVR) to calculate reactive flux correlation functions for a model of unimolecular isomerization, namely a 1-d double well potential coupled to an infinite set of harmonic oscillators, obtaining excellent agreement with accurate quantum results for this system. Here we analyze this linearized approximation (LA) further, however, and show that it is not capable of describing quantum interference/coherence effects in the longer time recrossing behavior of the isomerization dynamics. (The recrossing effects seen in our earlier work were due to classical mechanics.) To accentuate quantum effects in the recrossing dynamics, the present article considers the double well potential without the harmonic bath, using both the LA and the full SC-IVR. The results of the calculations show that the flux correlation functions given by the LA agrees well with the exact quantum correlation function for times up to ≈ℏβ, meaning that it describes quantum effects in the direct or transition state theory like dynamics accurately. For the longer time recrossing dynamics, however, it agrees with the classical rather than the quantum correlation function, i.e., it does not describe quantum coherence effects on this time scale. The full SC-IVR calculations, however, are in reasonably good agreement with the quantum correlation function for these longer times.