where R and I are regular and irregular spherical harmonics, respectively. The regular spherical harmonic a) Electronic mail: andrew.simmonett@nih.gov terms define multipole moments of the density, which can then interact classically through the irregular harmonic form of the Coulomb kernel. This expression is only convergent for well-separated (non overlapping) densities, so the short-ranged interactions are evaluated using the standard Coulomb operator in a pairwise manner.