Connections between second-order Görling–Levy and many-body perturbation approaches in density functional theory

Formal connections between the high-density scaling limit of the correlation energy functional Ec[n] in density functional theory and second-order energy expressions from different perturbation theory formulations are presented. It is demonstrated that the second-order correlation potential considered by Grabowski et al. [J. Chem. Phys. 116, 4415 (2002)] is equivalent to the high-density limit of the exact correlation potential, and thus provides the first self-consistent finite-basis-set implementation of a Kohn–Sham (KS) potential correct through second-order. A different second-order correlation functional based on the exchange-only KS approach is introduced. It is shown that this second-order correlation functional leads to the same self-consistent KS realization as the one derived from the second-order component of Ec[n].