Hydration energetics is analyzed for a set of ions. The analysis is conducted on the basis of a spatial-decomposition formula for the excess partial molar energy of the solute that expresses the thermodynamic quantity as an integral over the whole space of the solute-solvent and solvent-solvent interactions conditioned by the solute-solvent distance. It is observed for all the ionic solutes treated in the present work that the ion-water interaction is favorable at the expense of the water-water interaction and that the variations of the ion-water and water-water interactions with the ion-water distance compensate against each other beyond the contact distance. The extent of spatial localization of the excess partial molar energy is then assessed by introducing a cutoff into the integral expression and examining the convergence with respect to the change in the cutoff. It is found that the excess energy is not quantitatively localized within the first and second hydration layers, while its correlations over the variation of ions are good against the first-layer contribution.
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