Optimized expanded ensembles for simulations involving molecular insertions and deletions. I. Closed systems.

Monte Carlo simulation methods that involve the insertion-deletion of molecules are of wide spread use for the study of thermophysical behavior of complex systems; e.g., for the estimation of chemical potentials in closed-system ensembles. In this work, efficient expanded ensemble methods are described to overcome the lack of ergodicity that often plagues such molecular moves, wherein an arbitrary physical parameter Lambda is used to gradually couple and decouple a partial molecule to and from the system. In particular, we describe the use of (1) acceptance ratio methods for the robust estimation of free-energy changes associated with transitions between Lambda states of the partial molecule, (2) non-Boltzmann sampling of the probability density of Lambda states so that one can achieve either a flat histogram or an optimized histogram based on the maximization of round trips between the Lambda bounds, and (3) an approach to select suitable intermediate stages of the Lambda parameter that maximizes such round trips. The validity of the advocated methods is demonstrated by their application to two model systems, namely, the solvation of large hard spheres into a fluid of small spheres, and the mesophase formation of a block copolymer-homopolymer mixture.