Overlap population and the homopolar dipole

The expression {[^S_AB/(1 + S_AB)]R/2} 2e is shown to be an upper limit approximation to the homopolar dipole. It results from adding the overlap population 4C₁C₂S_AB to the atom with the smaller orbital radius. Dipole moments calculated from this partitioning are closer to the experimental values than those computed with equally sophisticated techniques from the standard gross atomic populations. Atomic charges are identical to Löwdin's in the limiting case when S_ABR/2 = $\text{x}$_AB, but the calculations are over non-orthogonalized AO's.