Unconventional Error Cancellation Explains the Success of Hartree-Fock Density Functional Theory for Barrier Heights

Energy barriers, which control the rates of chemical reactions, are seriously underestimated by computationally-efficient semi-local approximations for the exchange-correlation energy. The accuracy of a semi-local density functional approximation is strongly boosted for reaction barrier heights by evaluating that approximation non-self-consistently on Hartree-Fock electron densities, as known for about 30 years. The conventional explanation is that Hartree-Fock theory yields the more accurate density. This article presents a benchmark Kohn-Sham inversion of accurate coupled-cluster densities for the reaction H$_2$ + F $\rightarrow$ HHF $\rightarrow$ H + HF, and finds a strong, understandable cancellation between positive (excessively over-corrected) density-driven and large negative functional-driven errors (expected from stretched radical bonds in the transition state) within this Hartree-Fock density functional theory. This confirms earlier conclusions [Kaplan et al., J. Chem. Theory Comput. 19, 532--543 (2023)] based on 76 barrier heights and three less reliable, but less expensive, fully-nonlocal density-functional proxies for the exact density.