Improving the efficiency of Monte Carlo simulations of ions using expanded grand canonical ensembles

While ionic liquids have promising applications as industrial solvents, predicting their fluid phase properties and coexistence remains a challenge. Grand canonical Monte Carlo simulation is an effective method for such predictions, but equilibration is hampered by the apparent requirement to insert and delete neutral sets of ions simultaneously in order to maintain charge neutrality. For relatively high densities and low temperatures, previously developed methods have been shown to be essential in improving equilibration by gradual insertion and deletion of these neutral sets of ions. We introduce an expanded ensemble approach which may be used in conjunction with these existing methods to further improve efficiency. Individual ions are inserted or deleted in one Monte Carlo trial rather than simultaneous insertion/deletion of neutral sets. We show how charge neutrality is maintained and show rigorous quantitative agreement between the conventional and the proposed expanded ensemble approaches, but with up to an order of magnitude increase in efficiency at high densities. The expanded ensemble approach is also more straightforward to implement than simultaneous insertion/deletion of neutral sets, and its implementation is demonstrated within open source software.