The correspondence principle and intramolecular dynamics

Abstract

It is the purpose of this paper to describe some recent developments in the semiclassical approximations to quantum vibrational dynamics. In section 1 we describe a new and very simple method for finding uniformized semiclassical wavefunctions. The wavefunctions are given explicity as contractions over Gaussian functions, with the parameters of the Gaussians chosen according to an arbitrary classical trajectory. The semiclassical functions moreover are highly suitable for use as basis functions in ab initio work. In section 2 we present new results for the quantum dynamics of a highly anharmonic classically chaotic system with an infinite number of quantum bound states. The results show the utility of the spectral criterion we have been advocating as a measure of phase-space flow in molecular systems, and they show some interesting quantum effects. Also, we show that the classical and quantum dynamics of a local-mode C—H stretch agree extremely well as to the fraction of available phase space covered in the course of the subsequent dynamics. In quantum-mechanical systems the optical spectrum gives a direct measure of this fraction.