Deriving analytical expressions for the state dependencies of the effective pair potential parameters using VIM theory

In this work, based on the variational inequality minimizing (VIM) theory of statistical thermodynamics and using the (6,12) Lennard-Jones potential function as an effective pair potential (EPP), analytical expressions for the temperature and density dependencies of the EPP parameters have been obtained. The resulting equation of state can predict thermodynamic properties such as internal energy and Helmholtz free energy for simple dense fluids such as Ar, CO, N2, and CH4 with differences less than 5%.