  Determining the solvation free energies of single ions in water is one of the
most fundamental problems in physical chemistry and yet many unresolved
questions remain. In particular, the ability to decompose the solvation free
energy into simple and intuitive contributions will have important implications
for models of electrolyte solution. Here, we provide definitions of the various
types of single ion solvation free energies based on different simulation
protocols. We calculate solvation free energies of charged hard spheres using
density functional theory interaction potentials with molecular dynamics
simulation (DFT-MD) and isolate the effects of charge and cavitation, comparing
to the Born (linear response) model. We show that using uncorrected Ewald
summation leads to unphysical values for the single ion solvation free energy
and that charging free energies for cations are approximately linear as a
function of charge but that there is a small non-linearity for small anions.
The charge hydration asymmetry (CHA) for hard spheres, determined with quantum
mechanics, is much larger than for the analogous real ions. This suggests that
real ions, particularly anions, are significantly more complex than simple
charged hard spheres, a commonly employed representation.
