Structure of uniform hard-sphere fluid: A density functional approach

Abstract

A simple weighted-density approximation (SWDA) based on both local average and bulk densities is used to investigate the equilibrium structure of a uniform hard-sphere fluid. The main advantage of SWDA is computationally much simpler than the WDA of Tarazona based on the local density. The scheme which was pointed out by Percus has been used to interconnect between the structure of a uniform fluid and that of its nonuniform counterpart. The weighting function of the uniform hard-sphere fluid which is the requirement input is taken from the free energy functional approximation based on the truncated density expansion. The calculated results for structure-related functions such as the radial distribution function, cavity function, and cavity function are found to be in good agreement with the computer simulations. Comparisons with other approximations show that the SWDA results are a significant improvement upon those of the Percus–Yevick approximation and of the WDA of Denton–Ashcroft [A. R. Denton and N. W. Ashcroft, Phys. Rev. A 44, 1219 (1991)] based on the higher-order weighted-density approximation, and comparable to those of the WDA of Tarazona [G. P. Brenan and R. Evans, Mol. Phys. 73, 789 (1991)]. These results also provide that the SWDA provides an accurate description of inhomogeneous hard-sphere fluids.