  A fundamental weakness of density functional theory (DFT) is the difficulty
in making systematic improvements to approximations for the exchange and
correlation functionals. In this paper, we follow a wave-function-based
approach [N.I. Gidopoulos, Phys. Rev. A, 83, 040502 (2011)] to develop
perturbative expansions of the Kohn-Sham (KS) potential. Our method is not
impeded by the problem of variational collapse of the second-order correlation
energy functional. Arguing physically that a small magnitude of the correlation
energy implies weak perturbation and hence fast convergence of the perturbative
expansion for the interacting state and for the KS potential, we discuss
several choices for the zeroth-order Hamiltonian in such expansions. Our first
two choices yield KS potentials containing only Hartree and exchange terms: the
exchange-only optimized effective potential (xOEP), also known as the
exact-exchange potential (EXX), and the Local Fock exchange (LFX) potential.
Finally, we choose the zeroth order Hamiltonian that corresponds to minimum
magnitude of the second order correlation energy, aiming to obtain at first
order the most accurate approximation for the KS potential with Hartree,
exchange and correlation character.
