CALCULATION OF THE AQUEOUS SOLVATION FREE-ENERGY OF THE PROTON

The value of the proton hydration free energy, Delta G(hyd)(H+) has be en quoted in the literature to be from -252.6 to -262.5 kcal/mol. In t his article, we present a theoretical model for calculating the hydrat ion free energy of ions in aqueous solvent and use this model to calcu late 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 prot onated n-water cluster also in the continuum. All solvated species are treated as quantum mechanical solutes coupled to a dielectric continu um using a self consistent reaction field cycle. We investigated the b ehavior of Delta G(hyd)(H+) as the number of explicit waters of hydrat ion 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 val ue of the hydration free energy for n greater than or equal to 4 stron gly 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.