Direct Monte Carlo calculation of anharmonic free energies

Abstract

A Monte Carlo method for calculating the anharmonic free energy of a solid is proposed. Application of the method to a model Lennard-Jones crystal shows good statistical resolution, for a small periodic system, except near the melting curve. The anharmonic free energy Delta F is seen to have the form Delta F/NkT=A₀-3/2AT for temperatures T above about one-half the melting temperature at all densities studied. The values for A are in better agreement with experimental rare-gas data than are previous estimates from conventional anharmonic perturbation theory. The value of Delta F/NkT as a function of the Lindemann ratio (root mean square displacement over nearest-neighbour distance) lie on a universal curve for all densities and temperatures studied.