Hartree-Fock density functional theory works through error cancellation for the interaction energies of halogen and chalcogen bonded complexes

Semi-local functionals are often more accurate for energies when evaluated on the Hartree-Fock (HF) density than on their own self-consistent densities. HF densities are known to greatly reduce or overcorrect the charge-delocalization error associated with semi-local functionals. Over the last decade, this Hartree-Fock density functional theory (HF-DFT) has been systematized as density corrected DFT (DC-DFT), demonstrating remarkable success: improved chemical barrier heights, near chemical accuracy in water cluster binding energies, highly accurate interaction energies for halogenand chalcogen bonded systems, and more. For reaction barriers and water clusters, some of us found earlier that HFDFT works, not because the HF density is accurate but because of cancellation of negative functional-driven error (FE) by positive density-driven error (DE). In this work, we present evidence that interaction energy errors in halogen and chalcogen bonded molecular complexes in the B30 data set are not primarily driven by density errors, and that the success of HF-DFT for these weakly bonded molecular complexes results from a similar cancellation of FE by DE. Our benchmark Kohn-Sham inversion of the coupled cluster densities for NH3 · · ·ClF, Cl− · · ·SF2 and Cl− · · ·SCF2 presents strong evidence for this error cancellation. For most of the complexes, we employ proxies for the electron transfer in the exact density: the LCωPBE long-range-corrected hybrid and the r2SCAN50 global hybrid. We further investigate several self-interaction correction (SIC) methods for these weakly bonded systems, finding significant improvement from FLOSIC. In the conclusions section, we point out the common feature in our present and previous work: Long bonds can lead to non-negligible functional-driven self-interaction error of the energy from otherwise-accurate semi-local functionals in transition states, water clusters, and halogen or chalcogen bonds.