Time Correlations and Conditional Distribution Functions for Classical Ensembles of Free Rotors

Abstract

Explicit expressions are obtained for the classical rotational time-correlation functions for free rotation of the following: the linear, spherical-top, and symmetric-top molecule. This is done by deriving the eigenfunctions and eigenvalues of the potential-free rotational Liouville operator for each case. Conditional distribution functions for orientations and angular momenta are then constructed, and correlation functions are computed by evaluating phasespace averages with the distribution functions. The results obtained agree with those of Sears for the linear molecule and Steele for the spherical top, but differ somewhat from the calculation of Agrawal and Yip for the symmetric top molecule. The reason for this discrepancy is discussed briefly.