Group theory and the diffusion of molecules, dynamics and structure

Abstract

Point group theory is used in the laboratory and molecule fixed frames (X, Y, Z) and (x, y, z) respectively to develop three principles upon which to base the analysis of diffusional processes in N particle atomic and molecular ensembles. The symmetry signatures of ensemble averages at field free equilibrium, and in the steady state under applied external fields are given in the point group Rh (3) and in thirty-six molecular point groups. Physical examples of "group theoretical statistical mechanics" (g.t.s.m.) are given in terms of a new interpretation of the Weissenberg effect and of a theoretical prediction of shear induced depolarized light scattering. New fluctuation-dissipation theorems are developed from the principles and applications of g.t.s.m. for an applied electric field of arbitrary strength, and some corroborative computer simulations reported for liquid water and methyl chloride. Structural applications are discussed finally in the form of angularly resolved pair radial distribution functions.