On the use of Bennett's acceptance ratio method in multi-canonical-type simulations

A common strategy for mapping coexistence curves is to employ multi-canonical (MUCA) sampling to simulate along a macrostate path connecting two phases. Central to this approach is the task of accurately calculating the importance weights used in the MUCA procedure, which are needed for both effective sampling and accurate determination of phase boundaries. The purpose of this study is to develop a strategy for determining the importance weights that is built upon Bennett's optimized acceptance ratio method. This approach is shown to be closely related to transition matrix schemes, and is used to compute the vapor-liquid equilibrium of a Lennard-Jones fluid and the liquid-liquid equilibrium of a n-hexane/n-perfluorohexane mixture. For the Lennard-Jones system, the importance weights as a function of the number of particles "N" (at fixed temperature and volume) are obtained by using Bennett's method to estimate free energy differences between N and N+1 particle systems over the desired range of N values. In this application, the method is found to perform slightly better than a related transition matrix scheme. For the n-hexane/n-perfluorohexane liquid mixture, the method is designed to obtain weights as a function of composition (for fixed temperature, pressure, and total number of particles); in this case, the method is found to outperform the Gibbs ensemble approach.