where the tilde indicates that Ẽ[ρ] inherits its approximate nature from the approximate nature of Ẽxc [ρ]. Functional forms for the noninteracting kinetic energy (T s ), the Hartree potential (v H ), and the external potential (v ext ) are known. Error in Ẽ may be considered to arise from two contributions: The DC-DFT energy expression, E DC-DFT = Ẽ[ρ HF ], is not variational and therefore its analytic gradient requires solution of coupled-perturbed equations.