Simple and Efficient Route toward Improved Energetics within the Framework of Density-Corrected Density Functional Theory

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).