Calculation of surface tension via area sampling

TL;DR

This paper compares molecular simulation techniques for calculating surface tension, finding Bennett and expanded ensemble methods most accurate, while highlighting limitations of free-energy perturbation approaches.

Contribution

It systematically evaluates and compares different thermodynamic methods for surface tension calculation, identifying the most reliable approaches and explaining the failure modes of others.

Findings

Bennett and expanded ensemble methods yield the best accuracy and precision.

Single-stage free-energy perturbation methods can be inaccurate with large area changes.

The test-area method's errors can cancel out, giving misleadingly good results in some cases.

Abstract

We examine the performance of several molecular simulation techniques aimed at evaluation of the surface tension through its thermodynamic definition. For all methods explored, the surface tension is calculated by approximating the change in Helmholtz free energy associated with a change in interfacial area through simulation of a liquid slab at constant particle number, volume, and temperature. The methods explored fall within three general classes: free-energy perturbation, the Bennett acceptance-ratio scheme, and the expanded ensemble technique. Calculations are performed for both the truncated Lennard-Jones and square-well fluids at select temperatures spaced along their respective liquid-vapor saturation lines. Overall, we find that Bennett and expanded ensemble approaches provide the best combination of accuracy and precision. All of the methods, when applied using sufficiently small area perturbation, generate equivalent results for the Lennard-Jones fluid. However, single-stage free-energy-perturbation methods and the closely related test-area technique recently introduced by Gloor et al. [J. Chem. Phys. 123, 134703 (2005)], generate surface tension values for the square-well fluid that are not consistent with those obtained from the more robust expanded ensemble and Bennett approaches, regardless of the size of the area perturbation. Single-stage perturbation methods fail also for the Lennard-Jones system when applied using large area perturbations. Here an analysis of phase-space overlap produces a quantitative explanation of the observed inaccuracy, and shows that the satisfactory results obtained in these cases from the test-area method arise from a cancellation of errors that cannot be expected in general.