Fock-Matrix Corrections in Density Functional Theory and Use in Embedded Mean-Field Theory

We introduce Fock-corrected density
functional theory (FCDFT),
a semiempirical minimal-basis method part way between density-functional
tight binding (DFTB) and DFT. FCDFT contains DFTB-like Fock-matrix
contributions calculated using simple pairwise formulas and Slater–Koster
transformations, but it also contains the full Kohn–Sham treatment
of Coulombic electrostatics. The resulting method is better suited
than either minimal-basis DFT or DFTB for modeling the low-level subsystem
in embedded mean-field theory (EMFT), improving upon the former by
correcting for basis-set incompleteness and upon the latter by properly
accounting for electrostatics. EMFT calculations using DFT-in-FCDFT
have much smaller errors in orbital energies, dipole moments, and
reaction energies than our previous DFT-in-DFT calculations.