A key feature of the MPAC of Sec. II A is that the density associated with Ψ λ varies with λ. In contrast, in the density-fixed AC used in KS DFT, the density remains unchanged with respect to λ. This occurs because Ψ DFT λ minimizes ⟨ T +λ Vee ⟩ and integrates to the physical ρ that arises from the physical Ψ 1 = Ψ DFT 1 = Ψ. When λ = 0, Ψ DFT λ reduces to the non-interacting KS wavefunction (the one that solely minimizes kinetic energy and yields true ρ), and when λ = 1 we again have a physical system. Hence, only when λ = 1, Ψ λ and Ψ DFT λ are equal to each other. Within KS DFT, correlation energy is then given by