  The long-ranged nature of the Coulomb potential requires a proper accounting
for the influence of even distant electrostatic boundaries in the determination
of the solvation free energy of a charged solute. We introduce an exact
rewriting of the free energy change upon charging a solute that explicitly
isolates the contribution from these boundaries and quantifies the impact of
the different boundaries on the free energy. We demonstrate the importance and
advantages of appropriately referencing the electrostatic potential to that of
the vacuum through the study of several simple model charge distributions, for
which we can isolate an analytic contribution from the boundaries that can be
readily evaluated in computer simulations of molecular systems. Finally, we
highlight that the constant potential of the bulk dielectric phase - the Bethe
potential - cannot contribute to the solvation thermodynamics of a single
charged solute when the charge distributions of the solvent and solute do not
overlap in relevant configurations. But when the charge distribution of a
single solute can overlap with the intramolecular charge distribution of
solvent molecules, as is the case in electron holography, for example, the
Bethe potential is needed when comparing to experiment. Our work may also
provide insight into the validity of "extra thermodynamic assumptions"
traditionally made during the experimental determination of single ion
solvation free energies.
