Calculation of excess free energy in monte carlo simulation for model fluids

Abstract

A method for calculating the entropy and the chemical potential of fluids and solids from the radial free space distribution function (RFSDF) is proposed. The excess entropy is calculated from the RFSDF by elimination the arbitrary definition of a cell to evaluate the free volume. The RFSDF has a constant value at sufficiently long distances, so the long distance RFSDF is calculated by averaging the RFSDF``s at long distances. The chemical potential is calculated by using the long distance RFSDF. This method overcomes the usual difficulties appearing in the calculation of the free energy and leads to results that are comparable to those obtained by other methods. A practial method is proposed to evaluate the excess free energy of model potential systems in the monte Carlo simulation. The excess entropy is calculated from the average of effective acceptance ratio of random configuation in the cell with fixed volume through separate Monte Carlo procedure. No reference system is needed in this method. This method is applied to the Lennard-Jones system as model system of argon and the two-center-Lennard-Jones system as model of liquid nitrogen. Also, this method is applied to the TIP4P and ST2 models of liquid water. The results of this method give good agreement with previous results by other methods. This method saves considerably the computing time compared with other methods. The methods to calculate the excess free energy from the RFSDF in the Monte Carlo simulation for the hard sphere system is modified and extended to the hard dumbbell system. The excess chemical potential is calculated from the average of acceptance ratio at long distances. Also, the excess entropy is calculated from the average of acceptance ratio in the cell with fixed volum. Calulations are performed for hard spheres and hard dumbbells with elongations from 0.2 to 1.0. The calculated results give good agreement with those of the thermodynamic integration from the analytical equations of ...