Thermodynamic consistency between the energy and virial routes in the mean spherical approximation for soft potentials

A study was conducted to analyze the thermodynamic consistency between the energy and virial routes in the mean spherical approximation (MSA)for soft potentials. The study proved the thermodynamic consistency between the virial and energy routes for any soft potential and within a class of approximations that included the MSA as a particular case. The soft potentials that were considered in the study included the Gaussian core model and logarithmically diverging potentials. The theory of thermodynamic consistency was based on the zero-separation theorems, the generalized mean spherical approximation, and the rational-function approximation. It was also demonstrated that MSA is solvable for the Gaussian core model. It was observed that the viral and energy routes thermodynamics were equivalent for the model.