Extended molecular Ornstein-Zernike integral equation for fully anisotropic solute molecules: Formulation in a rectangular coordinate system

Abstract

An extended molecular Ornstein-Zernike (XMOZ) integral equation is formulated to calculate the spatial distribution of solvent around a solute of arbitrary shape and solid surfaces. The conventional MOZ theory employs spherical harmonic expansion technique to treat the molecular orientation of components of solution. Although the MOZ formalism is fully exact analytically, the truncation of the spherical harmonic expansion requires at a finite order for numerical calculation and causes the significant error for complex molecules. The XMOZ integral equation is the natural extension of the conventional MOZ theory to a rectangular coordinate system, which is free from the truncation of spherical harmonic expansion with respect to solute orientation. In order to show its applicability, we applied the XMOZ theory to several systems using the hypernetted-chain (HNC) and Kovalenko-Hirata approximations. The quality of results obtained within our theory is discussed by comparison with values from the conventional MOZ theory, molecular dynamics simulation, and three-dimensional reference interaction site model theory. The spatial distributions of water around the complex of non-charged sphere and dumbbell were calculated. Using this system, the approximation level of the XMOZ and other methods are discussed. To assess our theory, we also computed the excess chemical potentials for three realistic molecules (water, methane, and alanine dipeptide). We obtained the qualitatively reasonable results by using the XMOZ/HNC theory. The XMOZ theory covers a wide variety of applications in solution chemistry as a useful tool to calculate solvation thermodynamics. © 2013 AIP Publishing LLC.