A study on the approximated angular averaging of distribution functions obtained from the Ornstein–Zernike theory for diatomic solutes consisting of fused Lennard-Jones particles immersed in a Lennard–Jones monatomic solvent

Abstract

We propose an approximate method to obtain an angular averaged distribution function around an atom of a diatomic solute molecule consisting of fused Lennard–Jones (LJ) particles solvated in an LJ monatomic solvent. Our method employs the Ornstein–Zernike and closure equations for the correlation function between a single-centered solute and solvent by assuming spherical symmetry for the potential interaction. In setting the potential along the radial direction, the interaction between the solvent and solute atom that is covalently bonded to the atom located at the origin is also considered, as is typical in interaction site models. The proposed method accurately describes the angular averaged distribution function between a solvent and a solute atom that is completely buried inside the other atom in the solute, where the term “buried” indicates that the sum of the radius of one atom and the bond length is less than the radius of the other atom. The obtained angular-dependent one-dimensional distribution function is also reasonable for buried solute atoms. Thus, the proposed method is superior to the reference interaction site model (RISM) theory. However, our method failed to correctly describe the distribution function for an unburied atom of the solute, for which the RISM theory would be better than the proposed method. Furthermore, we demonstrated that sigma enlarging bridge (SEB) correction [T. Miyata, Bull. Chem. Soc. Japan, 90 (2017) 1095] is applicable to the proposed method. The combination of the method proposed in this study and SEB correction improves both the first rising region of the angular averaged distribution function and the solvation free energy.