An approach to the solvation free energy in terms of the distribution functions of the solute–solvent interaction energy

Abstract

The energy representation of the molecular configuration in a dilute solution is introduced to express the solvent distribution around the solute over a one-dimensional coordinate specifying the solute–solvent interaction energy. On the basis of the energy representation, an approximate functional for the solvation free energy of a solute in solution is constructed by adopting the Percus-Yevick-type approximation in the unfavorable region of the solute–solvent interaction and the hypernetted-chain-type approximation in the favorable region. The solvation free energy is then given exactly to second order with respect to the solvent density and to the solute–solvent interaction. It is demonstrated that the solvation free energies of nonpolar, polar, and ionic solutes in water are evaluated accurately and efficiently from the single functional over a wide range of thermodynamic conditions. The extension to a flexible solute molecule is straightforward. The applicability of the method is illustrated for solute molecules with a stretching or torsional degree of freedom.