Here, ρ indicates the density obtained by variational minimization of Ẽ, as in an ordinary self-consistent DFT calculation, whereas ρ 0 indicates the exact ground-state density obtained upon minimization of the exact functional E[ρ]. For cases where |∆E D | ≫ |∆E F |, the overall error may be reduced by evaluating the approximate functional using a SIE-free density (such as ρ HF ) rather than a self-consistent one. With this idea in mind, the DC-DFT energy functional in Eq. ( ) can be written more explicitly as