Radial Distribution Function in a Two Dimensional Core-Shoulder Particle System

TL;DR

This study compares two methods for calculating the radial distribution function in a 2D core-shoulder particle system, revealing that the simpler test-particle approach is not always more accurate than the Ornstein-Zernike route.

Contribution

It challenges the common assumption that the test-particle route is more accurate than the Ornstein-Zernike method in certain systems.

Findings

Test-particle results are not always superior to Ornstein-Zernike results in this system.

The study provides evidence that the accuracy of density functional theory methods can vary.

Results suggest reconsidering the preference for the test-particle route in similar systems.

Abstract

An important quantity in liquid state theory is the radial distribution function $g(r)$. It can be calculated within the framework of classical density functional theory in two very distinct ways. In the test-particle route, one fixes a single fluid particle, turning it into an external potential in which the inhomogeneous structure of the fluid is calculated by minimising the functional. The second route to $g(r)$ in density functional theory employs the Ornstein-Zernike equation and the pair direct correlation function, that can be obtained from the second functional derivatives of the excess free energy functional. Since typically an approximate excess free energy functional is employed, one generally expects that the test-particle route, which requires only one functional derivative, to be more accurate than the Ornstein-Zernike route. Here we study a two dimensional core-shoulder particle system and present results that challenge this expectation. Our results show that in this system test-particle results for $g(r)$ are not always better than results obtained via the Ornstein-Zernike route.