The use of a non-spherical reference potential in statistical mechanical perturbation theory

Abstract

The statistical perturbation theory for the pair correlation function using a non-spherical reference potential proposed earlier is studied further and evaluated here. First, we show that for even such a strongly quadrupolar fluid as liquid bromine, relatively few terms of the multiply-infinite set in the first order perturbation theory make a significant contribution. This greatly simplifies the calculations. Next, by comparing the results of the first order perturbation theory with our own Monte Carlo simulation studies for both reference and perturbed systems, we conclude that the first order perturbation theory using a non-spherical reference potential is rapidly convergent for the centre of mass (or orientation averaged) pair correlation function even for liquid bromine. However, the theory appears to converge less rapidly for the higher order spherical harmonic expansion coefficients of the angle dependent pair correlation function.