Dielectric relaxation as a multiplicative stochastic process: I. General theory

A rigorous and general approach is developed to the relaxation of molecular dipoles on the microscopic scale, embodied in the orientational time-autocorrelation function. The usual difficulties of using the stochastic Liouville equation (SLE) are bypassed by replacing the cumulant expansion with a continued fraction. This reduces to that of Sack or Gross in the appropriate limit.The autocorrelation function is formed from approximants of this continued fraction, which is ideally suited for numerical computation, and as a basis for the newly developed technique of semi-stochastic molecular dynamics simulation. The numerical solution automatically produces the spectral moments of interest to order of truncation, so that the number of unknowns is reduced to one at each and every stage of approximation. This concerns the rate of energy dissipation, denoted by β, a scalar, tensor or super-tensor according to the nature of the diffusion process under consideration.The new continued fraction can be used to describe spatial rotational diffusion of the asymmetric top using the appropriate Fokker-Planck diffusion operator. It is a considerable improvement therefore on a model such as the planar itinerant librator, an approximant of the Mori continued fraction.