Calculation of the hard sphere radial distribution function

Abstract

We describe a recursive formula for calculating the hard sphere radial distribution function under the Percus-Yevick approximation. It provides a simple and exact way to evaluate the expressions arising in Wertheim's solution of the hard sphere radial distribution function. The method does not increase in complexity at large distances. It has been used to evaluate the function at distances up to 20 times the hard sphere diameter. The same recursive formula can be applied to calculate derivatives of the distribution function which are useful in the thermodynamic analysis of equations of state obtained from perturbation theories.