Physical interpretation and assessment of the Coulomb-hole and screened-exchange approximation for molecules

Hedin's Coulomb-hole and screened-exchange (COHSEX) approximation for the one-electron Green-function self-energy is examined for small molecules through second order in the bare interaction (COHSEX2). Numerical examples suggest that the COHSEX2 approximation works better for ionization potentials and generalized overlaps (Dyson amplitudes) than does either Koopman's theorem or the usual second-order Green-function (GF2) approximation. This result has been traced to the superior quality of Hedin's GW approximation evaluated to second order in the bare interaction (GW2). (The GW self-energy is the simple product of the Green function G and the screened interaction W in the time-and-position space representation.) The COHSEX2 approximation is found to be a rather crude approximation for the GW2 self-energy at the center of the highest occupied molecular orbital--lowest unoccupied molecular orbital energy gap, but is still superior to the GF2 approximation in most of our calculated results and is amenable to limited dynamical corrections. The primary potential advantage of the COHSEX approximation over the GW approximation is that no sums over virtual orbitals need be performed once the static screened interaction or polarization is known. Our results suggest that accurate density-functional approximations for the static screened interaction or polarization can lead to self-energies of accuracies beyond both Koopmans's theorem and the GF2 level.