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

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.