A computer simulation method for the calculation of chemical potentials of liquids and solids using the bicanonical ensemble

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Abstract
We present a method for the calculation of the chemical potential of a liquid or solid using molecular dynamics or Monte Carlo computer simulations of the material. Like several previously presented methods, it is based on the insertion and deletion of particles from the system. It is based on what we call a ‘‘bicanonical ensemble,’’ which is an equilibrium statistical mechanical ensemble characterized by a temperature T and a volume V and in which all systems have either N or N−1 particles. The chemical potential is simply related to the fraction of the systems of the ensemble that have N particles. It is possible to construct algorithms, combining either molecular dynamics motion or Monte Carlo moves with the insertion and deletion of particles, such that the set of states generated by the algorithm constitute a Markov chain whose stationary distribution is that of the bicanonical ensemble. The key to the success of the method is a feature that leads to a high success rate for the insertion and deletion steps, even at high densities, thus giving good statistics for the chemical potential. The method is applied to a two‐dimensional liquid of particles with a pairwise additive inverse 12th power repulsive potential, for which it gives accurate results for the chemical potential for the entire equilibrium liquid range of densities. The method is applicable and accurate for the two‐dimensional solid of the same particles, and so it can be used in studies of the phase diagram for two‐dimensional materials.