A direct derivation of the optimized effective potential using orbital perturbation theory

The Hartree-Fock (HP) orbitals and energies are related to the Kohn-Sham (KS) orbitals and energies through an orbital perturbation theory. While the HF method is proposed as a density functional theory, the equalization of the HF density and the KS density leads to a constraint on the perturbation terms. To first order, this constraint gives the standard optimized effective potential (OEP) equation. Further, it is shown that operating the Laplacian operator on the above constraint will lead naturally to Nagy's local effective exchange potential obtained by summarizing the HF and the KS single particle motion equations. The higher order perturbation terms, the Green's function version of the approach and the inclusion of the correlation in the OEP equation using this method are briefly discussed.