Chemical Potential Calculations in Non-Homogeneous Liquids

TL;DR

This paper extends a novel enhanced sampling technique using Well-Tempered Metadynamics to accurately compute chemical potentials in dense, non-homogeneous fluids, overcoming limitations of traditional methods like Widom insertion.

Contribution

The paper introduces an extension of a recent homogeneous fluid method to non-homogeneous fluids, improving accuracy and efficiency in chemical potential calculations at high densities.

Findings

The method accurately estimates chemical potentials in confined Lennard-Jones fluids.

It overcomes the sampling inefficiency of Widom's method in dense, non-homogeneous systems.

The technique shows no systematic error, providing reliable results at large densities.

Abstract

The numerical computation of chemical potential in dense, non-homogeneous fluids is a key problem in the study of confined fluids thermodynamics. To this day several methods have been proposed, however there is still need for a robust technique, capable of obtaining accurate estimates at large average densities. A widely established technique is the Widom insertion method, that computes the chemical potential by sampling the energy of insertion of a test particle. Non-homogeneity is accounted for by assigning a density dependent weight to the insertion points. However, in dense systems, the poor sampling of the insertion energy is a source of inefficiency, hampering a reliable convergence. We have recently presented a new technique for the chemical potential calculation in homogeneous fluids. This novel method enhances the sampling of the insertion energy via Well-Tempered Metadynamics, reaching accurate estimates at very large densities. In this paper we extend the technique to the case of non-homogeneous fluids. The method is successfully tested on a confined Lennard-Jones fluid. In particular we show that, thanks to the improved sampling, our technique does not suffer from a systematic error that affects the classic Widom method for non-homogeneous fluids, providing a precise and accurate result.