New approach to Monte Carlo calculation of the free energy: Method of expanded ensembles

Abstract

We propose a new effective Monte Carlo (MC) procedure for direct calculation of the free energy in a single MC run. The partition function of the expanded ensemble is introduced including a sum of canonical partition functions with a set of temperatures and additive factors (modification). Random walk in the space of both particle coordinates and temperatures provides calculation of free energy in a wide range of T. The method was applied to a primitive model of electrolyte including the region of low temperatures. In similar way other variants of expanded ensembles are constructed (e.g., over the number of particles N or volume V). Its facilities in quantum statistics (path integral Monte Carlo) and some other applications are also discussed.