The calculation of time-correlation functions for molecular collisions

Abstract

A general formalism relating cross sections to collisional time-correlation functions is applied to the calculation of energy transfer in molecular collisions. Basic aspects of the formalism are reviewed, followed by a detailed description of methods suitable for the calculation of quantal state-to-state cross sections. These methods are particularly useful in the description of scattering by large systems, or of systems with high total energies where expansions in target basis sets are unsuitable. We review applications of quantal time-correlation functions (TCFs) to vibrational-rotational energy transfer in molecular collisions. Doubly differential cross sections (in scattering angles and transferred energy) are obtained from Fourier transforms of TCFs of the transition operator by means of two complementary treatments: multiple-scattering expansions for impulsive energy transfer, and a semiclassical limit for short translational wavelengths. The TCFs are evaluated by operator algebra, yielding efficient computational procedures that incorporate large numbers of vibrational-rotational transitions. The treatments are thus well suited to scattering by complex polyatomic targets. Examples are given for inelastic scattering of atoms from diatomic and linear triatomic molecules at hyperthermal collision energies, and the calculated results are compared with experimental measurements. These methods are also applicable to scattering by solid surfaces and by adsorbates, and can include temperature effects. The review lists 140 references to related work on the formalism, methods of calculation and applications.