Understanding density driven errors via reaction barrier heights

Density functional approximations can be computationally effective and otherwise correct, but they are plagued with delocalization errors. It is often suggested that a semi-local DFA be evaluated non-self-consistently on the Hartree-Fock (HF) density as a computationally simple fix for delocalization problems. This method can reach remarkable accuracy for complex meta-GGAs like SCAN. This HF-DFT is often presumed to work because the HF density is more accurate than the self-consistent DFA density. We demonstrate that the HF-DFT works for barrier heights by making a localizing charge transfer error or density over-correction, which results in a somewhat reliable cancellation of density- and functional-driven errors. This pattern is supported by a quantitative investigation of the charge transfer error in a reaction transition state. For the huge BH76 database of barrier heights, we lack the exact functional and exact electron densities that would be required to assess the precise density- and functional-driven inaccuracies. Instead, we have found and used three totally non-local functionals (the SCAN 50% global hybrid, the range-separated hybrid LC-PBE, and SCAN-FLOSIC) and their self-consistent densities as proxies. These functionals were chosen because they produce self-consistent barrier heights that are quite precise and because their self-consistent total energies are nearly piecewise linear in fractional electron number - two important similarities to the exact functional.