Comparison of absolute free energy calculation methods for fluids and solids

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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, and an approach inspired by the phase-switch method of Wilding 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.
Original languageEnglish
Pages (from-to)1206-1216
JournalMolecular Physics
Issue number9-10
Early online date11 Feb 2015
Publication statusPublished - 2015


  • free energy, thermodynamic integration, Monte Carlo simulation, phase switch


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