Determining chemical potentials within the small system grand ensemble

We present a new method for the determination of the excess chemical potential, μex, of a model fluid based on the small system grand ensemble (SSGE). The SSGE method uses a cavity of predetermined radius that is randomly placed within the fluid. A “test particle” is then inserted into the cavity and integrated over the cavity volume. The ensemble average of the Boltzmann factor of the test particle is used to calculate μex. The SSGE method is an extension of the Widom’s test particle method; the two methods become equivalent when the cavity approaches zero volume. The SSGE algorithm is more accurate and efficient than Widom’s method, especially at high fluid densities where the cavity serves to locate regions of low potential energy. We present results for the pure-component Lennard–Jones and hard particle fluids. Additionally, the SSGE allows for the direct calculation of the pressure of the hard particle fluid during a Monte Carlo simulation. The SSGE is also applicable to multi-component systems and can be extended to the isothermal–isobaric ensemble in a straightforward manner. Accordingly, we include some results for μex of various binary Lennard–Jones and hard sphere mixtures in both the canonical and isothermal–isobaric ensembles.