Formal connections between the high-density scaling limit of the correlation energy functional E c ͓n͔ 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 ͑2002͔͒ is equivalent to the high-density limit of the exact correlation potential, and thus provides the first self-consistent finite-basis-set

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... ementation of a Kohn-Sham ͑KS͒ 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 E c ͓n͔.