The Fokker–Planck–Langevin model for rotational Brownian motion. I. General theory

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Abstract
The rotational Langevin and rotational Fokker–Planck equations form the basis for a model of molecular rotation in fluids (the FPL model). In this article, the general series expressions for the angular velocity–orientation conditional probability densities for linear and for spherical molecules are derived. Contained in the general expansions of the conditional probability densities are correlation functions involving various collections of angular velocity and reorientational variables, including all of the reorientational correlation functions for linear and spherical molecules, and the correlation functions which describe motional modulation of anisotropic spin–rotational interactions in spherical molecules. Expressions for all reorientational correlation functions,correlation times and spectral densities for linear and spherical molecules, and for the correlation time for the anisotropic spin–rotational interactions in spherical molecules are given. A strategy for the computation of the reorientational memory functions associated with the reorientational correlation functions is presented.