Increasing the efficiency of Monte Carlo simulation with sampling from an approximate potential

Nested Markov Chain Monte Carlo (MCMC) simulation using two potential functions, where the move for MCMC with one potential function (primary chain) is given by a short MCMC run with the other potential function (auxiliary chain) is well known. However, generally the acceptance of these moves is low. In this work, a scheme has been developed to increase the acceptance rate and applied to (H2O)20 and (H2O)25, where the primary and auxiliary chains are represented by a quantum mechanical (QM) and a classical potential respectively. A comparison between standard and nested MC simulation for (H2O)4 showed impressive results.