Molecular simulation in a pseudo grand canonical ensemble

Abstract

A molecular simulation method is proposed for the evaluation of the equilibrium density of a pure fluid given the temperature, volume, and chemical potential. In this sense, the technique is formulated in the grand canonical ensemble. However, it does not employ true particle insertion and deletion steps as part of the simulation algorithm; instead, the volume fluctuates in a fashion that brings the density to the appropriate value. The chemical potential must be evaluated by some means to guide convergence of the density, but there is little restriction on the manner in which this is done. The technique is demonstrated through application to the hard sphere model. Simple Widom insertion is used to evaluate the chemical potential, yet the proposed technique converges significantly more quickly than the usual grand canonical Monte Carlo when applied at high density. The method is perhaps most appropriately viewed not as pure molecular simulation, but as a hybrid of a simulation and a numerical technique. It may be extended readily for use with the Gibbs ensemble for evaluation of phase equilibria.