The dependence of exchange energy on orbital overlap

Several methods of estimating exchange energies have been tested for the interaction of two hydrogen atoms in 2s, 2p or hybrid valence states. The simplest relationship previously used, X = KS 2/R, does not give an accurate picture of the dependence on internuclear distance. A two-term expression X = S 2(AR -1 + BR -2) is considerably better but fails for the case of exchange between orthogonal orbitals (S = 0). An alternative expression in which C 0 - C is the penetration part of the two-electron coulomb integral, is just as accurate, contains no more constants and holds equally well for orthogonal and non-orthogonal orbitals. C 0 - C is a better measure of the net overlap of two orbitals than is the overlap integral S, because the latter is zero for orbitals which are orthogonal but nevertheless overlap. We have found no method of deducing the constants K, A or B other than by calculating the exchange energy exactly at one or two values of R.