An assessment of the sigma enlarging bridge function for a Lennard-Jones solution using a solvent-solvent correlation function obtained from molecular dynamics simulation

Abstract

We have examined a possibility of using canonical ensemble molecular dynamics (NVT-MD) simulation to prepare the solvent-solvent correlation function (VVCF), which is further utilized in the calculation of solute-solvent correlation function for the solvation free energy (SFE) of the Lennard-Jones (LJ) solution at the infinite dilution. We have employed a combined closure equation where the radial distribution function (RDF) of NVT-MD simulation is used for the short range and the hypernetted chain (HNC) closure for the long range. An appropriate separation for the boundary to switch the RDF of the MD simulation and the HNC closure is determined from the balance between the accuracy of the compressibility equation and the numerical stability. The appropriate separation is found to be from 2.0 to 3.0 in the unit of the LJ particle size. Furthermore, the isothermal compressibility evaluated from the combined NVT-MD closure agrees with those evaluated from the volume fluctuation in the isobaric isothermal ensemble MD simulation. The VVCF obtained from the combined NVT-MD closure is further used in the assessment of the sigma enlarging bridge (SEB) function that was proposed in our earlier works, e.g. [T. Miyata, Bull. Chem. Soc. Japan, 90 (2017) 1095], with which the first rising region of the RDF obtained from an approximate Ornstein-Zernike theory can be corrected by apparently adjusting (typically enlarging) the sigma parameters in the LJ potential. The following two points of view are considered in the assessment of the SEB function. One is the isothermal compressibility of the solvent, and the other is the SFE. It is found that the Kovalenko-Hirata closure with the SEB correction provides rather accurate VVCF, which leads to an accurate isothermal compressibility. The SFE is also improved when we apply the SEB correction to the solute-solvent calculation. While the SEB function includes one parameter, the numerical values of it are parameterized over a wide range of conditions in this study under the usage of the combined NVT-MD closure for the solvent-solvent calculation.