Comparison of integral equation theories of the liquid state

TL;DR

This paper compares various integral equation closures for liquid state theory, evaluating their predictive accuracy across different systems, and provides tools to facilitate the adoption of modern closures.

Contribution

It systematically assesses the predictive power of multiple closures for the Ornstein-Zernike equation on benchmark systems and offers accessible code for solving these equations.

Findings

Percus-Yevick closure performs worse than some lesser-known closures.

Trends observed can guide better closure selection for specific systems.

The provided code aids in adopting modern closure theories.

Abstract

The Ornstein-Zernike equation is a powerful tool in liquid state theory for predicting structural and thermodynamic properties of fluids. Combined with a suitable closure, it has been shown to reproduce e.g. the static structure factor, pressure, and compressibility of liquids to a great degree of accuracy. However, out of the multitude of closures that exist for the Ornstein-Zernike equation, it is hard to predict a priori which closure will give the most accurate predictions for the system at hand. To alleviate this problem, we compare the predictive power of many closures on a curated set of representative benchmark systems, including those with hard-sphere, inverse power-law, Gaussian core, and Lennard-Jones particles, in three and two dimensions. For example, we find that the well-known and highly used Percus-Yevick closure gives significantly worse predictions than lesser-known closures of equal complexity in all cases studied. We anticipate that the trends observed in our results will aid in making more informed decisions regarding closure choices. To facilitate the adoption of more modern closure theories, we also have packaged, documented, and distributed the code necessary to numerically solve the equations for a given closure and pair interaction potential.