The Chemical Potential of Dense Liquids by the Coupled Test Particle Method

A new method for chemical potential estimation is proposed which is based on the coupled particle approach. The coupled particle method defines an attractive solution to the weighting function problem in umbrella sampling, bridging the gap between f and g distributions at high density. A way of eliminating the origin singularity is suggested, which is similar in spirit to the restricted umbrella sampling of Shing and Gubbins, but which is based on geometric rather than energetic criteria. The method is illustrated on the Lennard-Jones system up to a reduced density ρ∗ = 1.1 along the isotherm T∗ = 1.2 and results are compared with the test particle insertion method and empirical equations of state. The new method is particularly useful at high liquid densities where it is superior to the other methods relying on the degree of overlap of f and g distributions. It gives reliable estimates of the chemical potential in the whole range of liquid densities.