Note: A pairwise form of the Ewald sum for non-neutral systems

Abstract: Using an example of a mixed discrete-continuum representation of charges under the periodic boundary condition, we show that the exact pairwise form of the Ewald sum, which is well-defined even if the system is non-neutral, provides a natural starting point for deriving unambiguous Coulomb energies that must remove all spurious dependence on the choice of the Ewald screening factor.