Calculation of the aqueous solvation free energy of the proton

The value of the proton hydration free energy, Delta G(hyd)(H+) has been quoted in the literature to be from -252.6 to -262.5 kcal/mol. In this article, we present a theoretical model for calculating the hydration free energy of ions in aqueous solvent and use this model to calculate the proton hydration free energy, Delta G(hyd)(H+), in an effort to resolve the uncertainty concerning its exact value. In the model we define Delta G(hyd)(H+) as the free energy change associated with the following process: Delta G[H+(gas)+ H2nOn(aq)-->H+(H2nOn)(aq)], where the solvent is represented by a neutral n-water cluster embedded in a dielectric continuum and the solvated proton is represented by a protonated n-water cluster also in the continuum. All solvated species are treated as quantum mechanical solutes coupled to a dielectric continuum using a self consistent reaction field cycle. We investigated the behavior of Delta G(hyd)(H+) as the number of explicit waters of hydration is increased from n = 1 to n = 6. As n increases from 1 to 3, the hydration foe energy decreases dramatically. However, for n = 4-6 the hydration foe energy maintains a relatively constant value of -262.23 kcal/mol. These results indicate that the first hydration shell of the proton is composed of at least four water molecules, The constant value of the hydration free energy for n greater than or equal to 4 strongly suggests that the proton hydration free energy is at the far lower end of the range of values that have been proposed in the literature. (C) 1998 American Institute of Physics.