Theory of Ionic Hydration: Insights from Molecular Dynamics Simulations and Experiment

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The Born model of ionic solvation prescribes the solvation free energy of ions in a dielectric continuum and is widely used. Despite the fact that the solvent molecules around the ions are highly structured giving rise to molecular phenomena such as dielectric saturation and electrostriction, the Born model yields accurate results compared to experimental data if a proper radius for the ion, the effective Born radius, Reff, is chosen. On the basis of molecular dynamics simulations of ions of varying charge and size in TIP3P water, Reff is identified as the mean of the ionic radius (Rion) and the first peak position in the ion−water pair distribution function (Rgmax). This relationship was verified using experimentally available Rgmax for ions of varying size (0.4−3.0 Å) and charge (−3e to +4e). The new interpretation of Reff implies that the correct expression for the solvation free energy is a combination of two Born free energies, which incorporate the effects of dielectric saturation and electrostriction implicitly. The new solvation free energy formula was used to derive unknown Rgmax for a number of ions whose free energy data are available as well as new expressions for the solvation entropies and enthalpies. An empirical relationship between Rgmax and Rion is established. Potential applications of the findings of this work to free energy simulations, solvation in different solvents, solvation of molecular systems, and biomolecules are discussed.