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 noninteracting
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 analyzed 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).