Length scales and interfacial potentials in ion hydration

The Quasichemical Theory (QCT) involves a length-scale organization of solvation thermodynamics. The QCT has been employed in studies of solutes ranging in size from small molecules and ions to proteins. There are three contributions to the QCT free energy: (1) an inner-shell term that includes the direct solute-solvent chemical interactions, (2) an outer-shell packing term that is the free energy to dig out a cavity in the solvent, and (3) an outer-shell long-ranged term that includes all interactions of the solute with the solvent conditional on an empty inner shell. The present study utilizes a regularizing generalization of the QCT and classical simulations to compute these three contributions to the ion hydration free energy out to large cavity radii for eight ions in the alkali halide series. The accuracy of simple approximations for the long-ranged term is also examined. The inner-shell contribution exhibits ion specificity for cavity sizes less than 4-5 Å, followed by a common length scale of 6.15 Å at which its value equals the bulk hydration free energy for all eight of the ions. The 6.15 Å length scale is closely approximated by the distance at which the revised scaled-particle theory packing contribution matches the magnitude of a simple Born estimate for the long-ranged term.