Solvation free energy of polar and nonpolar molecules in water: An extended interaction site integral equation theory in three dimensions

The solvation free energy of polar and nonpolar molecules in water is examined using the statistical mechanical integral equation theory which was recently introduced by Beglov and Roux (J: Phys. Chem. 1997, 101, 7821). The integral equation is an extension of previous theories based on the reference interaction site model (RISM) and the hypernetted chain equation (HNC) to determine the one-dimensional site-site radial pair correlation functions. Since the integral equation provides the average density of the solvent interaction sites in three-dimensional (3d) space around a complex molecular solute of arbitrary shape, it is thereby referred to as the 3d-RISM-HNC integral equation. In the present paper, the accuracy of the 3d-RISM-HNC integral equation is examined by comparing the calculated excess solvation free energy at infinite dilution with experimental. data for a set of nonpolar (n-alkanes) and polar (n-alcohols, n-carboxylic acids, and simple amides) molecules. Thermodynamic integration is used to calculate the excess solvation free energy on the basis of the average site densities obtained by the 3d-RISM-HNC equation. Two extensions were made to improve the accuracy of the integral equation. First, the susceptibility of pure liquid water (an input for calculating the excess solvation free energy of molecules in the infinite dilution limit) was obtained by combining information from a molecular dynamics simulation with the RISM-HNC integral equation. Second, empirical water hydrogen and water oxygen bridge functions were introduced and optimized for improving the accuracy of the theory. The calculated solvation free energies are in good accord with experimental data, although further work will be required for quantitatively accurate results. These preliminary results indicate that the 3d-RISM-HNC equation with well-calibrated optimized bridge functions is a promising approach for calculating the hydration free energy of complex molecules.