Bridge function and cavity correlation function for the soft sphere fluid from simulation: Implications on closure relations

Abstract

The soft sphere fluid is of interest as a possible reference fluid since, like the hard sphere fluid, the configurational properties and distribution functions scale with a single parameter. In this paper we present the results of a Monte Carlo simulation study of the cavity correlation function y(r) for the soft sphere fluid. Using the Ornstein–Zernike relationship, the direct correlation function c(r) is determined from simulations of the total correlation function h(r). The bridge function B(r) is calculated by difference. We provide a correlation of the bridge function and demonstrate the usefulness of this reference fluid by calculating some properties of the Lennard-Jones fluid using reference hypernetted chain (HNC) and Rosenfeld and Blum’s prescription for the bridge function state point. The soft sphere bridge function is also compared with the bridge functions for the hard sphere and Lennard-Jones fluids. Finally, it is demonstrated that closures similar to the Percus–Yevick (PY) closure are poor at short range and should only be valid for repulsive fluids; observations are made concerning modifications of the PY closure for repulsive and attractive fluids.