Determination of Free Energy from Chemical Potentials: Application of the Expanded Ensemble Method

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Abstract
The expanded ensemble method, previously developed for free energy calculation [J. Chem. Phys., 96, 1776 (1992)] is applied to calculate chemical potentials. The expanded ensemble is composed as a sum of canonical ensembles with gradually inserting the (N, + 1):th particle. The probability distribution over the subsensembles is directly related to the ratio of the partition functions and, hence, to the free energy difference. The gradual insertion eliminates the difficulties arising in using the standard particle insertion method at high densities. The problem of an optimal choice of subsensembles is studied in detail. Since the chemical potential is defined as the Gibbs free energy per particle for macroscopic systems, the present method allows calculation of free energies in a convenient way. The method is applied to calculate chemical potentials and free energies for a Lennard-Jones system and for the flexible SPC water model. The results are compared with corresponding direct free energy calculations using the temperature expanded ensemble and the efficiency vs precision of the two approaches are evaluated.