Why integer valence point-charge model works so well

Integer valence counting works extremely well in determining stability of chemical compounds. It comes as a surprise that the same integer valence counting also works very well in comparing energies of different lattice structures of the same composition, even though an incomplete (non-integer) charge transfer is expected in realistic systems. Then, why is the point charge model reasonably accurate (even more than employment of real partial charge)? Here, by partitioning the charge density via atom-centered Wannier functions, we justify the integer valence counting approach through a systemic analysis of multi-pole expansion of the Coulomb energy. Our results demonstrate the dominance of the point charge contribution over the finite moment ones, and reveal the important role of local point group symmetry in suppressing first few low-order moments. While the inaccuracy grows expectedly as the system’s covalency increases from LiF, ZnO, GaAs to Si, surprisingly a reasonable accuracy is still achieved by an effective ionic assignment even for Si (as Si⁴⁺Si^4- ). Our formulation also illuminates the removal of the infamous self-interaction in such a simple approach, further explaining its unexpected success in numerous applications.