On the hydration of monoatomic ions

Abstract

It is shown that an understanding of some key biological processes such as the thermodynamics of enzyme-ligand binding or the selectivity of ion-channels is ultimately dependent on an understanding of the details of ion hydration. Therefore, a model for calculating the hydration free energy of ions in aqueous solvent is presented. The model is used to first 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)+[H2O]n(aq)→H+[H2O]n)(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 (B3LYP, MP2, MP4, CCSD(T)) coupled to a dielectric continuum using a self consistent reaction field (SCRF) cycle. An investigation of the behavior of ΔGhyd(H+) as the number of explicit waters of hydration is increased reveals convergence by n=4. The converged value is −262.23 kcal/mol and is independent of the ab initio method used. These results indicate that the first hydration shell of the proton is composed of at least 4 water molecules. The result strongly suggests that the proton hydration free energy is at the far lower end of the range of values obtained from the literature. The methodology is then used to calculate the hydration free energies of other ions relative to that of the proton. These include cationic forms of the alkali earth elements Li, Na, and K, and anionic forms of the halogens F, Cl, and Br. 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 (SCRF) 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 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 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.