Study of the thermodynamic inconsistency of the potential of mean force calculated using the integral equation theory of molecular liquids

In this study, we investigated thermodynamic inconsistency in the potential of mean force (PMF) calculated using the Ornstein-Zernike (OZ), one-dimensional reference interaction site model (1D-RISM), and three-dimensional OZ (3D-OZ) theories. Two methods were used to obtain the PMF: converting the radial distribution function (RDF) into the PMF, and utilizing the solvation free energy (SFE) of the diatomic solute molecule with an added direct interaction between the two solute atoms. Both for the Lennard-Jones (LJ) and Coulomb systems, the hypernetted chain (HNC) closure showed the best performance among the closure relationships tested in this study. However, the performance of the HNC was not perfect and exhibited significant inconsistency in the PMF. The Kovalenko–Hirata and Kobryn–Gusarov–Kovalenko closures were also tested, with fair results when combined with the 1D-RISM equation but poor results when combined with the 3D-OZ equation. The Verlet-modified (VM) closure was found to be inapplicable to Coulomb systems. In contrast, the modified HNC (MHNC) closure showed relatively good results at high temperatures. Furthermore, we modified the Martynov–Sarkisov (MS) closure for Coulomb systems, resulting in a modified MS closure that yields relatively accurate PMF results. We also discuss the behavior of the SFE for Coulomb systems obtained from the 1D-RISM theory, a thorough analysis of both the RDF and the integrand in the Kirkwood charging formula.