Comparison of absolute free energy calculation methods for fluids and solids

• Published in: Molecular physics Vol. 113; no. 9-10; pp. 1206 - 1216
• Main Author: Sweatman, Martin B.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 19-05-2015; Taylor & Francis Ltd
• Subjects: Computer simulation; Crystal structure; Fluid dynamics; Fluid flow; Fluids; Free energy; Mathematical analysis; Methods; Monte Carlo simulation; phase switch; Sampling; thermodynamic integration
• ISSN: 0026-8976; 1362-3028
• DOI: 10.1080/00268976.2015.1005704

Several established and very general methods for calculating the absolute Helmholtz free energy from Monte Carlo simulations are compared, namely the method of Schilling and Schmid, Speedy's method and the self-referential method of Sweatman et al., and an approach inspired by the phase-switch method of Wilding et al.. It is shown how they are all closely related, in that they all calculate the free energy difference between a pinned configuration, for which the free energy can be calculated analytically, and the state of interest. A novel scheme is devised based on analysis of the advantages and problems with each method. Performance tests with hard sphere fluid and face-centred-cubic crystalline states demonstrate that the novel scheme described here is the most straightforward, efficient and robust method of those tested. The method of Schilling and Schmid requires sampling of rare events and cannot be recommended for high density states. Speedy's method is less efficient than the novel scheme proposed here, while a path sampling approach inspired by the phase-switch method is more complex and less efficient in general. However, for free energy difference calculations involving states that are structurally very similar, a phase-switch method might still be the most efficient method of those tested.