Hartree-Fock (1s,2s) interorbital pair correlation energies and absolute overlap integrals

Interorbital pair correlation energies between 1s and 2s Hartree-Fock orbitals are shown to be proportional to the square of the absolute overlap integral ℱ‖φ1Sφ2S‖dτ. The proportionality constant is independent of the nuclear charge and the number of 1s and 2s electrons, but shows an exclusion effect of about 10% for each occupied 2p orbital. Using only four parameters (a proportionality constant and a 2p exclusion effect each, for singlet and triplet coupled pairs) we reproduce fifty-six ab initio pair energies (ranging from −0.00047 to −0.00891 hartree) with a root-mean-square deviation of 0.0001 hartree.