Correction of Kovalenko-Hirata closure in Ornstein-Zernike integral equation theory for Lennard-Jones fluids

Abstract

We have studied the accuracy of Ornstein-Zernike (OZ) integral equation theory in terms of the solvation free energy (SFE) for a two-component Lennard-Jones system at the infinite dilution limit. We have employed the hypernetted chain (HNC), Kovalenko-Hirata (KH), Kobryn-Gusarov-Kovalenko (KGK), and Percus-Yevick (PY) closure equations. Further, we have extended the Verlet-modified (VM) closure to the two-component system to examine the accuracy of this method in terms of the SFE. Molecular dynamics simulations were employed to compare the results with the above mentioned OZ theories. The HNC and KH approximations significantly overestimate the SFE, whereas the PY approximation tends to underestimate it. The overestimation of the SFE by the KGK approximation becomes significant when the solvent density is relatively high. In contrast, the VM approximation is found to be rather accurate at all studied conditions. An analysis of the integrand for the SFE reveals that, to improve the SFE, the first rising (FR) region in the radial distribution function (RDF) must be corrected. We have also tested the sigma-enlarging-bridge (SEB) function that we proposed previously [T. Miyata and Y. Ebato, J. Mol. Liq. 217 (2016) 75] for the correction of the FR region of the RDF. In this study, we applied the SEB function to both HNC-type and KH-type closures and found that these combinations (SEB-HNC and SEB-KH) improve the SFE significantly.