A Parameterization of Empirical Sigma Enlarging Bridge Correction of Kovalenko-Hirata Closure in Ornstein-Zernike Theory for Lennard-Jones Fluids

We report the parameter values included in the sigma enlarging bridge (SEB) function for two-component Lennard-Jones fluids within the Ornstein-Zernike (OZ) integral equation framework, which was first proposed in our previous study [T. Miyata, Y. Ebato, J. Molec. Liquids, 217 (2016) 75] to improve the accuracy of the solvation free energy (SFE). In this article, we consider a wide range of thermodynamic states, with varying the solute size and the solute-solvent interaction strength. The SEB parameter was evaluated via the least square fitting of the first rising region of the radial distribution function obtained from OZ theory to that from molecular dynamics simulation. The SEB function was applied to both the hypernetted chain (HNC) and Kovalenko-Hirata (KH) closures. It is found that the SEB parameter increases monotonically with the solute size, whereas it hardly depends on the solute-solvent interaction strength. Also, the performance of bare HNC, bare KH, Percus-Yevick, and Verlet-modified closures are also examined, to report the relationship between the solute volume and the error of the SFE obtained from OZ theory. We found that the SFE errors under both HNC and KH closures are not necessarily proportional to the solute volume.