The chemical potential in dense fluids and fluid mixtures via computer simulation

Abstract

We describe a new computer simulation technique to evaluate the chemical potential in dense fluids, where the usual test particle method fails. The method rests on the use of the well known Widom test particle equation in conjunction with another equation which is the inverse of the Widom equation. We show that the distribution functions (f and g, respectively) that describe the distribution of the test particle interaction energy u t for these two equations are exactly related (equation (10) below), and that g can be obtained accurately for the values of u t that are needed to calculate the chemical potential. This equation provides the basis for the method. We also propose a further refinement called ‘restricted umbrella sampling’, which improves the efficiency of placing the test particle in the fluid for a fixed configuration of real molecules. Detailed tests of the method are presented using the Monte Carlo technique, for both pure Lennard-Jones (LJ) fluids and LJ mixtures. We find that the method works for pure LJ fluids up to the triple point density, (at T* = 0·7 and 1·2) and for most mixtures except those involving a very large solute molecule. The method preserves the desirable feature of having a test particle that is not coupled in any way to the solvent. Thus it should be suitable for molecular dynamics calculations, and also for the evaluation of other properties besides the chemical potential.