Algebraic perturbation theory for dense liquids with discrete potentials

TL;DR

This paper introduces a simple algebraic theory to accurately predict the first-order correction to the structure of dense liquids with discrete potentials, effectively simplifying complex many-particle correlations.

Contribution

It presents a novel algebraic perturbation approach that simplifies the calculation of structural corrections in dense liquids with discrete interactions, reducing computational complexity.

Findings

Accurately predicts g_1(r) with high-density approximation

Effectively models three-particle correlations using volume exclusion

Reproduces structure of core-softened liquids with anomalous properties

Abstract

A simple theory for the leading-order correction g_1(r) to the structure of a hard-sphere liquid with discrete (e.g. square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively eliminates four-particle correlations from g_1(r) with good accuracy at high densities. For the particular case of discrete perturbations, the remaining three-particle correlations can be modeled with a simple volume-exclusion argument, resulting in an algebraic and surprisingly accurate expression for g_1(r). The structure of a discrete "core-softened" model for liquids with anomalous thermodynamic properties is reproduced as an application.