Perturbation theory for liquids with a hard sphere plus square well potential

Abstract

Numerical data have been obtained for a series of perturbation theory in the form of Barker-Henderson discrete representation. A hard sphere liquid (864 particles) was modeled by the Monte Carlo method for 106 values of occupancy from the range η = 0.005–0.530 (step 0.005); the well width was varied from 0 to 1.5 hard sphere diameters. For each occupancy, averaging was done over 60·106 ensembles. Approximating analytical expressions are given as functions of well density and width for the first three terms of the free energy decomposition. For reduced temperature T* = 1.0, the standard error in the free energy calculation (three orders of perturbation theory if the above expressions are used) is of the order of ±0.001. Analysis of four-particle correlations revealed peaks at distances of 1.35 A and 1.65 A (η = 0.53) in the high-density region of hard sphere liquids, which are absent in crystals and dense liquids. It is analyzed whether the results are useful for realization of WCA theory of simple liquids in second order perturbation theory.