Evaluation of Osmotic Virial Coefficients via Restricted Gibbs Ensemble Simulations, with Support from Gas-Phase Mixture Coefficients

We present a method for computing osmotic virial coefficients in explicit solvent via simulation in a restricted Gibbs ensemble. Two equivalent phases are simulated at once, each in a separate box at constant volume and temperature and each in equilibrium with a solvent reservoir. For osmotic coefficient BN, a total of N solutes are individually exchanged back and forth between the boxes, and the average distribution of solute numbers between the boxes provides the key information needed to compute BN. Separately, expressions are developed for BN as a series in solvent reservoir density ρ1, with the coefficients of the series expressed in terms of the usual gas-phase mixture coefficients Bij. Normally, the Bij are defined for an infinite volume, but we suggest that the observed dependence of Bij on system size L can be used to estimate L dependence of the BN, allowing them to be computed accurately at L → ∞ while simulating much smaller system sizes than otherwise possible. The methods for N = 2 and 3 are demonstrated for two-component mixtures of size-asymmetric additive hard spheres. The proposed methods are demonstrated to have greater precision than established techniques, for a given amount of computational effort. The ρ1 series for BN when applied by itself is (for this noncondensing model) found to be the most efficient in computing accurate osmotic coefficients for the solvent densities considered here.