Pressure of Coulomb systems with volume-dependent long-range potentials

TL;DR

This paper investigates the pressure calculation in Coulomb systems with volume-dependent potentials, correcting the virial pressure expression and demonstrating its equivalence to free energy derivatives under certain conditions.

Contribution

It provides a corrected virial pressure formula for Coulomb systems with volume-dependent potentials and clarifies the inaccuracies in recent literature.

Findings

Corrected virial pressure expression for volume-dependent potentials.

Demonstrated equivalence with free energy derivative when potential energy is homogeneous.

Identified errors in a recent publication's pressure formula.

Abstract

In this work, we consider the pressure of Coulomb systems, in which particles interact via a volume-dependent potential (in particular, the Ewald potential). We confirm that the expression for virial pressure should be corrected in this case. We show that the corrected virial pressure coincides with the formula obtained by differentiation of free energy if the potential energy is a homogeneous function of particle coordinates and a cell length. As a consequence, we find out that the expression for pressure in the recent paper by J. Liang \textit{et al.} [\href{https://doi.org/10.1063/5.0107140}{J. Chem. Phys. \textbf{157}, 144102 (2022)}] is incorrect.