A theoretical approach to the calculation of time-correlation functions of several variables

Abstract

A rigorous expression is obtained which relates time-correlation function of an arbitrary number of coordinates to the correlation of the time derivatives of the original function. It is argued that the formal result can be approximated in several ways: by assuming that the time-decay of the molecular velocities is fast compared to coordinate changes; by assuming that velocities of different degrees of freedom are uncorrelated; and by viewing the approximate expressions as leading terms in a series which can be closed using a cumulant formalism. The general arguments are applied to some specific cases including: the anisotropic rotation of a symmetric top molecule; the intermediate scattering factor for an atom in a molecule; and the combined translation-rotation correlation function that appears in the theory for quadrupole-induced infrared absorption spectrum.