  The crucial step in density-corrected Hartree-Fock density functional theory
(DC(HF)-DFT) is to decide whether the density produced by the density
functional for a specific calculation is erroneous and hence should be replaced
by, in this case, the HF density. We introduce an indicator, based on the
difference in non-interacting kinetic energies between DFT and HF calculations,
to determine when the HF density is the better option. Our kinetic energy
indicator directly compares the self-consistent density of the analysed
functional with the HF density, is size-intensive, reliable, and most
importantly highly efficient. Moreover, we present a procedure that makes best
use of the computed quantities necessary for DC(HF)-DFT by additionally
evaluating a related hybrid functional and, in that way, not only "corrects"
the density but also the functional itself; we call that procedure corrected
Hartree-Fock density functional theory (C(HF)-DFT).
