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

Unusually large energy errors of semi-local density functional approximations (DFAs) for molecules are often strongly reduced by using the Hartree-Fock (HF) electron density instead of the self-consistent DFA density. For reaction barriers and water clusters, some of us earlier found that HF-density functional theory (DFT) succeeds not because the HF density is accurate but due to the cancellation of negative functional-driven error (FE) by positive density-driven error (DE). Since DE, as defined here, is biased toward the self-consistent DFA density and against the HF density, the DE of the HF density is referred to as non-variational density over-localization (NVDO). In this work, we show that interaction energy errors in halogen- and chalcogen-bonded complexes in the B30 dataset are not dominated by density-driven error. Instead, HF-DFT again succeeds through FE-NVDO cancellation. Benchmark Kohn-Sham inversions of coupled-cluster densities for NH3⋯ClF, Cl-⋯ClF, Cl-⋯SF2, Cl-⋯SCF2, and Cl-⋯PF3 provide strong evidence for this cancellation. For additional complexes, we employ the long-range-corrected hybrid LCωPBE as a proxy for electron-transfer errors in the exact density. We also examine several self-interaction correction (SIC) methods and find significant improvement from FLOSIC. We point out common features of the density errors in the NH3⋯ClF and Cl-⋯ClF complexes and three transition states, arguing that significant density-driven errors of energy arise only from electron-transfer errors. We also highlight a 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.