The value of the proton hydration free energy, ΔGhyd(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, ΔGhyd(H+), in an effort to resolve the uncertainty concerning its exact value. In the model we define ΔGhyd(H+) as the free energy change associated with the following process: ΔG[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 ΔGhyd(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 free energy decreases dramatically. However, for n=4–6 the hydration free 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⩾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.

We calculate free energy changes of ionization reactions in aqueous solvent using a self-consistent reaction field method. In the calculations all species are treated as quantum mechanical solutes coupled to a solvent dielectric continuum. We show for a series of substituted imidazole compounds that both absolute and relative pK a values for the deprotonation of nitrogen on the imidazole ring can be obtained with an average absolute deviation of 0.8 units from experiment. This degree of accuracy is possible only if the solutes are treated at the correlated level using either G2 type or density functional theory. Inconsistencies in published experimental free energies of hydration that might undermine the reliability of the calculated absolute pK a values are discussed.

The hydration free energies relative to that of the proton are calculated for a representative set of monatomic ions Z±. These include cationic forms of the alkali earth elements Li, Na, and K, and anionic forms of the halogens F, Cl, and Br. In the current model the relative ion hydration free energy is defined as Δ[ΔGhyd(Z±)]=G(Z±[H2O]n(aq))−G(H+[H2O]n(aq))−G(Z±(gas))−G(H+(gas)), where the solvated ions are represented by ion–water clusters coupled to a dielectric continuum using a self-consistent reaction field cycle. An investigation of the behavior of Δ[ΔGhyd(Z±)] as the number of explicit waters of hydration is increased reveals convergence by n=4. This convergence indicates that the free energy change for the addition of water to a solvated proton–water complex is the same as the free energy change associated with the addition of water to a solvated Z±–water complex. This is true as long as there are four explicitly solvating waters associated with the ion. This convergence is independent of the type of monatomic ion studied and it occurs before the first hydration shell of the ions (typically ⩾6) is satisfied. Structural analysis of the ion–water clusters reveals that the waters within the cluster are more likely to form hydrogen bonds with themselves when clustering around anions than when clustering around cations. This suggests that for small ion–water clusters, anions are more likely to be externally solvated than cations.

Helices are among the predominant secondary structures in globular proteins. About 90% of the residues in them are found to be in the alpha-helical conformation, and another 10% in the 3(10) conformation. There is a standing controversy between experimental and some theoretical results, and controversy among theoretical results concerning the predominance of each conformation, in particular, helices. We address this controversy by ab initio Hartree-Fock and density functional theory studies of helices with different lengths in a vacuum and in the aqueous phase. Our results show that (1) in a vacuum, all oligo(Ala) helices of 4-10 residues adopt the 3(10) - conformation; (2) in aqueous solution, the 6-10 residue peptides adopt the alpha-helical conformation; (3) there might be two intermediates between these helical conformers allowing for their interconversion. The relevance of these results to the structure and folding of proteins is discussed.

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