Reference interaction site model with hydrophobicity induced density inhomogeneity: An analytical theory to compute solvation properties of large hydrophobic solutes in the mixture of polyatomic solvent molecules

Reference interaction site model (RISM) has recently become a popular approach in the study of thermodynamical and structural properties of the solvent around macromolecules. On the other hand, it was widely suggested that there exists water density depletion around large hydrophobic solutes (>1 nm), and this may pose a great challenge to the RISM theory. In this paper, we develop a new analytical theory, the Reference Interaction Site Model with Hydrophobicity induced density Inhomogeneity (RISM-HI), to compute solvent radial distribution function (RDF) around large hydrophobic solute in water as well as its mixture with other polyatomic organic solvents. To achieve this, we have explicitly considered the density inhomogeneity at the solute-solvent interface using the framework of the Yvon-Born-Green hierarchy, and the RISM theory is used to obtain the solute-solvent pair correlation. In order to efficiently solve the relevant equations while maintaining reasonable accuracy, we have also developed a new closure called the D2 closure. With this new theory, the solvent RDFs around a large hydrophobic particle in water and different water-acetonitrile mixtures could be computed, which agree well with the results of the molecular dynamics simulations. Furthermore, we show that our RISM-HI theory can also efficiently compute the solvation free energy of solute with a wide range of hydrophobicity in various water-acetonitrile solvent mixtures with a reasonable accuracy. We anticipate that our theory could be widely applied to compute the thermodynamic and structural properties for the solvation of hydrophobic solute. (C) 2015 AIP Publishing LLC.