The escaped charge problem in solvation continuum models

In the present article, we provide an analytical proof of the accuracy shown by integral equation formalism (IEF) continuum solvation method in dealing with the solute electronic charge that quantum mechanically penetrates outside the cavity embedding it. In particular we show that the approximation of the solute–solvent interaction energy obtained by this method is always an upper bound of the exact electrostatic interaction energy and that a lower bound of the exact energy can also be defined. A numerical example for which both approximated bounds and exact energies can be computed is presented.