Dependence of the Time-Correlation Functions of Molecular Random Motions on the Intermolecular Potential

Abstract

A general theory on the time-correlation function and the spectral density for the random motion in molecular system is presented. We study the dependence of these functions on the intermolecular potential and on the rate of fluctuation of the potential. It is shown that the fluctuating intermolecular interactions or potentials not only introduce the randomness to molecular motion but also characterize important details of the randomness. Here we assume that the fluctuation can be regarded as a Gaussian random process contributed from the perturbers around the molecule. Therefore, the theory may be applied to the molecular motions in the liquid state. As an example of application of the present theory we discuss the collapse of multiplet structure in magnetic resonance spectrum of two-spin system; Anderson's results for the exchange narrowing of spectrum is derived as a special case of our formulation. The correlation functions and the spectral densities for the random reorientation of diatomic molecules are studied quantum mechanically as second example of application. Graphical presentations are given for the dependence of these functions on the intermolecular potential. The shape of vibrational spectra of molecules can be thus analyzed quantitatively by using the present theory.