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

The barrier height controls the rate of a chemical reaction. Barrier heights are seriously underestimated by computationally-efficient semi-local density functional approximations to the exchange-correlation energy. For reaction barrier energies, the accuracy of a semi-local density functional approximation is boosted strongly by evaluating that approximation on Hartree-Fock electron densities, and not self-consistently, as known since 1992. 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 H₂ + F → HHF → H + HF. We find a strong, understandable cancellation between large positive (excessively over-corrected) density-driven and large negative functional-driven errors within this Hartree-Fock density functional theory. This work supports the conclusions reached earlier [1] for 76 barrier heights using three less reliable but useful fully-nonlocal proxies for the exact density.: the SCAN50 global hybrid, the LCωPBE long-range-corrected hybrid, and the FLOSIC self-interaction correction to the SCAN meta-generalized gradient approximation.

[1] A.D. Kaplan, C. Shahi, R.K. Sah, P. Bhetwal, and J.P. Perdew, Understanding Density-Driven Errors for Reaction Barrier Heights, Journal of Chemical Theory and Computation 19, 532 (2023).