Statistical Mechanics of Nonspherical Molecules

Abstract

A general approach to the calculation of the properties of classical fluids made up of nonspherical molecules is discussed. It is assumed that the total interaction energy is a sum of pairwise interactions which are arbitrary functions of the molecular separations and orientations. The pairwise interaction energy, and the two-molecule correlation functions are written as series in the complete set of orthonormal functions of the molecular orientation angles, with coefficients which are functions of the distance of separation. Explicit expressions are given for the thermodynamic properties of these systems, and for the dielectric constant and rotational friction constant. Equations for the coefficients in the series for the pair correlation function are obtained by using a coupling parameter which determines the magnitude of the nonspherical part of the potential. Finally, it is shown that the number and kind of terms which appear in the series for the interaction energy and the pair correlation function are determined by the symmetry of the molecules. In this way, one can bring about a considerable reduction in the complexity inherent in the calculation of the ensemble average properties of molecules having arbitrary shapes.