Coulomb energies via Stewart densities

We show that the long-range part of the Coulomb self-energy of an electron density ρ(r) is almost identical to that of its associated Stewart density ρ̃(r). Since the latter is obtained by fitting ρ(r) within an auxiliary basis of only s functions, our proposal can be viewed as a hybrid of the RI (resolution of the identity) and KWIK methods.