Free energy of ion hydration: Interface susceptibility and scaling with the ion size

Free energy of solvation of a spherical ion in a force-field water is studied by numerical simulations. The focus is on the linear solvation susceptibility connecting the linear response solvation free energy to the squared ion charge. Spherical hard-sphere solutes, hard-sphere ions, and Kihara solutes (Lennard-Jones modified hard-sphere core) are studied here. The scaling of the solvation susceptibility with the solute size significantly deviates from the Born equation. Using empirical offset corrections of the solute size (or the position of the first peak of the solute-solvent distribution function) do not improve the agreement with simulations. We advance a new perspective on the problem by deriving an exact relation for the radial susceptibility function of the interface. This function yields an effective cavity radius in the Born equation calculated from the solute-solvent radial distribution function. We find that the perspective of the local response, assuming significant alteration of the solvent structure by the solute, is preferable compared to the homogeneous approximation assuming intact solvent structure around the solute. The model finds a simple explanation of the asymmetry of hydration between anions and cations in denser water shells around anions and smaller cavity radii arising from the solute-solvent density profiles.