Computer simulation and group theoretical statistical mechanics of liquid water and methyl chloride: Part 1, Neumann's Principle.

Abstract

Neumann's Principle is applied to the molecular dynamics of liquids in the laboratory frame (X, Y, Z) and molecule fixed frame (x, y, z). In the absence of symmetry breaking influences, and in an isotropic medium of diffusing molecules, it states that the totally symmetric irreducible representation is the key to whether a thermodynamic ensemble average exists in either frame. In liquid water, with molecules of C 2ν symmetry, and liquid methyl chloride, with molecules of C 3ν symmetry, the Neumann Principle, evaluated with the help of group theory, is found to be in agreement with computer simulations of components of linear and angular momentum auto correlation functions in both frames.