Integral equation theory of the exchange potential, HOMO–LUMO properties, and sum rules for the exchange-correlation force
I. A. Howard, Norman Henry March · World Scientific series in 20th century physics · 2009
Recently, a formally exact integral equation for the exchange potential V x(r) has been presented by the authors. In the admittedly simplistic limit in which Slater–Kohn–Sham and Hartree–Fock determinants become equal, this integral equation reduces to that given by Della Sala and Gorling. Here, a proposal is made to relate, but now approximately, the formally exact equation for V x(r) to HOMO–LUMO properties. The addition of a correlation contribution V c(r) to V x(r), the sum being the exchange-correlation potential V xc(r), is finally considered, some exact properties and especially sum rules for the force −∂V xc/∂r being the focus.