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.