The DC-DFT procedure sacrifices self-consistency, which implies that the functional defined in Eqs. (4) and ( ) is not variational. This necessitates modification to the analytic gradient. Lack of self-consistency also means that DC-DFT is not beneficial in all cases, but rather only cases that are dominated by densitydriven error. Delocalization driven by SIE tends to fall into the category of density-driven error, as evident from the fact that DC-DFT based on GGA functionals significantly improves results for radicals and barrier heights. (Transition states are usually characterized by partially-broken bonds and thus fractional charges on different chemical moieties, a classic SIE problem. A "density sensitivity" metric (S) has been suggested to determine whether a given problem is dominated by ∆E F or ∆E D . This metric is defined as