On the radial distribution function of a hard-sphere fluid

TL;DR

This paper compares two analytical methods for deriving the radial distribution function of a hard-sphere fluid, finding that the older, simpler approach offers better overall accuracy and broader applicability.

Contribution

The study evaluates and compares two existing analytical approaches, highlighting the superior accuracy and versatility of the older method for hard-sphere fluids.

Findings

The second approach has better global accuracy.

It can be generalized to mixtures of hard spheres.

It is simpler and more effective overall.

Abstract

Two related approaches, one fairly recent [A. Trokhymchuk et al., J. Chem. Phys. 123, 024501 (2005)] and the other one introduced fifteen years ago [S. B. Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)], for the derivation of analytical forms of the radial distribution function of a fluid of hard spheres are compared. While they share similar starting philosophy, the first one involves the determination of eleven parameters while the second is a simple extension of the solution of the Percus-Yevick equation. It is found that the {second} approach has a better global accuracy and the further asset of counting already with a successful generalization to mixtures of hard spheres and other related systems.