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

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 $$, a total of N solutes are individually exchanged back and forth between the boxes, and the average distribution of solute numbers between the boxes provides the key information needed to compute $$. Separately, expressions are developed for $$ as a series in solvent reservoir density ρ₁, with the coefficients of the series expressed in terms of the usual gas-phase mixture coefficients B. Normally, the B are defined for an infinite volume, but we suggest that the observed dependence of B on system size L can be used to estimate L dependence of the $$, 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 $$ 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.