Absolute hydration free energy of the proton from first-principles electronic structure calculations

The absolute hydration free energy of the proton, ΔG_hyd²⁹⁸(H⁺), is one of the fundamental quantities for the thermodynamics of aqueous systems. Its exact value remains unknown despite extensive experimental and computational efforts. We report a first-principles determination of ΔG_hyd²⁹⁸(H⁺) by using the latest developments in electronic structure theory including solvation effects. High level ab initio calculations have been performed with a supermolecule-continuum approach based on a recently developed self-consistent reaction field model known as surface and volume polarization for electrostatic interaction (SVPE) or fully polarizable continuum model (FPCM). In the supermolecule-continuum approach, part of the solvent surrounding the solute is treated quantum mechanically and the remaining bulk solvent is approximated by a dielectric continuum medium. With this approach, the calculated results can systematically be improved by increasing the number of quantum mechanically treated solvent molecules. ΔG_hyd²⁹⁸(H⁺) is accurately predicted to be -262.4 kcal/mol based on high-level, first-principles solvation-included electronic structure calculations. The absolute hydration free energies of other ions can be obtained by using appropriate available thermodynamic data in combination with this value. The high accuracy of the predicted absolute hydration free energy of proton is confirmed by applying the same protocol to predict ΔG_hyd²⁹⁸(Li⁺).