The Møller-Plesset adiabatic connection (MPAC) provides a rigorous framework for developing approximate functionals for E c from HF-density-based features . MPAC recovers exact E c and its largecoupling limit is a functional of the HF density . The MPAC-based approximate functionals have achieved exceptional accuracy for weak interactions . While the method known as HF-DFT (and its densitycorrected DFT generalization ), also applies ap-proximate functionals to HF densities, fundamental distinctions exist. First, the two use different frameworks, as HF-DFT still approximates quantities within the KS DFT, whereas the MPAC functionals directly target wavefunction-E c . Second, unlike density-corrected DFT, the MPAC functionals make no assumptions about whether the HF density is more accurate than that of DFA . They are instead designed to map the HF densities to wavefunction-based E c , irrespective of the underlying accuracy of the HF densities .