Umbrella-sampling realization of ‘‘Widom’’ chemical potential estimation

The ‘‘Widom’’ or ‘‘test-particle’’ technique for the computational estimation of excess chemical potentials of model fluids has been very useful at low and moderate densities. However, as usually implemented, it becomes inefficient and eventually unreliable on going to high densities, due to inadequate sampling. This article describes a straightforward solution to this problem by the use of ‘‘umbrella sampling’’ to ensure that all parts of phase space relevant to the estimation are included. The method is illustrated by application to the Lennard-Jones system at kT/ε=1.2 and at various densities up to ρσ3=0.9.