Collision time-correlation functions in the semiclassical limit. II. Vibrational–rotational energy transfer in molecule–molecule collisions

Abstract

A semiclassical limit of collisional time-correlation functions is applied to energy transfer in collisions between two molecules. The internal degrees of freedom (vibration and rotation) are treated quantum mechanically while the relative motion is described by classical trajectories for fixed molecular orientations. Hence the theory is well-suited to the analysis of energy and angular distributions in collisions governed by general intermolecular potentials, including highly anisotropic short-range forces. Cross sections are given as Fourier transforms of correlation functions of time-evolution operators for the internal degrees of freedom. These operators are determined by action integrals of the intermolecular forces evaluated along the classical trajectories. Correlation functions for coupled harmonic vibrations are obtained using an operator algebra. Rotational correlation functions are calculated by means of an asymptotic expansion appropriate to large transfers of angular momentum. Compact analytical expressions are derived for cross sections in collisions involving symmetric-top, spherically symmetric, and linear molecules. Expressions for average rotational energy transfer, readily obtainable from time-of-flight experiments, are also derived for symmetric top molecules.