Comparing the use of Gibbs ensemble and grand-canonical transition-matrix Monte Carlo methods to determine phase equilibria

We present results from a computational study investigating the use of Gibbs ensemble and grand-canonical transition-matrix Monte Carlo (GC-TMMC) methods to determine the liquid-vapor phase coexistence properties of pure molecular fluids of varying degrees of complexity. The molecules used in this study were ethane, n-octane, cyclohexane, 2,5-dimethylhexane, I-propanol, and water. We first show that the GC-TMMC method can reproduce Gibbs ensemble results found in the literature. Given the excellent agreement for each molecule, we then compare directly the performance of Gibbs ensemble and GC-TMMC simulations at both low and high reduced temperatures by monitoring the relative uncertainties in the saturation properties as a function of computational time. In general, we found that the GC-TMMC method yielded limiting uncertainties in the saturated vapor density and pressure that were significantly smaller, by an order of magnitude in some instances, than those of the Gibbs ensemble method. Limiting Gibbs ensemble uncertainties for these properties were generally in the 0.8-5.0% range. However, both methods yielded comparable limiting uncertainties in the saturated liquid density, which fell within the range of 0.1-1.0%. In the case of water at 300 K, we found that the Gibbs ensemble outperformed GC-TMMC. The relatively poor performance of the GC-TMMC method in this situation was tied to the slow convergence of the density probability distribution at this low temperature. We also discuss strategies for improving the convergence rate under these conditions.