Radial Distribution Function for a Hard Sphere Liquid: A Modified Percus-Yevick and Hypernetted-Chain Closure Relations

Abstract

Establishment of the radial distribution function by solving the Ornstein-Zernike equation is still an important problem, even more than a hundred years after the original paper publication. New strategies and approximations are common in the literature. A crucial step in this process consists in defining a closure relation which retrieves correlation functions in agreement with experiments or molecular simulations. In this paper, the functional Taylor expansion, as proposed by J. K. Percus, is applied to introduce two new closure relations: one that modifies the Percus‑Yevick closure relation and another one modifying the Hypernetted-Chain approximation. These new approximations will be applied to a hard sphere system. An improvement for the radial distribution function is observed in both cases. For some densities a greater accuracy, by a factor of five times compared to the original approximations, was obtained.

Spiers Memorial Lecture: Towards understanding of iontronic systems: electroosmotic flow of monovalent and divalent electrolyte through charged cylindrical nanopores

“…Although the use of the HNC approach requires numerical solutions of the Ornstein-Zernike (OZ) integral equations, these solutions are expected to be considerably more accurate in capturing strong ion correlations than their MSA counterparts. 137,138 In spite of additional computation cost, this gain in accuracy might represent a good compromise whenever ne details of equilibrium distributions close to interfaces are required, as is the case for the calculation of the zeta potential close to a highly charged pore surface.…”