Determination of second virial coefficients by grand canonical Monte Carlo simulations

In this communication, we investigate the use of grand canonical Monte Carlo simulations to estimate the second virial coefficient. Histogram reweighting calculations were performed to collect two-dimensional histogram for the number of particles and the energy to evaluate the density and pressure at low density. The histogram collected is reweighted for a series of chemical potentials to accumulate pressure, density, and temperature data along the isotherm to obtain the second virial coefficient. While exact calculation of second virial coefficients for arbitrary systems (e.g. mixtures and polyatomic molecules) involves multidimensional integrals, grand canonical simulations can, in principle, provide equation of state information from simulations at appropriately low densities. Our results indicate that the methodology yields reasonable estimates of the second virial coefficient. Agreement to analytical and experimental values is within a few percent for a variety of model and real fluids. There are however practical accuracy issues associated with this method. We discuss why this approach fails to find more precise values of the second virial coefficient even when long runs are used.