Understanding density driven errors for reaction barrier heights

Abstract

Delocalization errors, such as charge-transfer and some self-interaction errors, plague computationally-efficient and otherwise-accurate density functional approximations (DFAs). Evaluating a semi-local DFA non-self-consistently on the Hartree-Fock (HF) density is often recommended as a computationally cheap remedy for delocalization errors. For sophisticated meta-GGAs like SCAN, this approach can achieve remarkable accuracy. When this HF-DFT (or DFA@HF) significantly improves over the DFA, it is often presumed that the HF density is more accurate than the self-consistent DFA density. By applying the metrics of density-corrected density functional theory (DFT), we show that HF-DFT works for barrier heights by making a localizing charge transfer error or density over-correction, thereby producing a somewhat-reliable cancellation of density- and functional-driven errors for the energy. A quantitative analysis of the charge transfer errors in a few transition states confirms this trend. We do not have the exact functional and exact densities that are needed to evaluate the exact density- and functional-driven errors for the large BH76 database of barrier heights. Instead, we have identified and used three non-local proxy functionals (the SCAN 50% global hybrid, the range-separated hybrid LC-$\omega$PBE, and SCAN-FLOSIC) and their self-consistent densities. These functionals yield reasonably accurate self-consistent barrier heights, and their self-consistent total energies are nearly piecewise linear in fractional electron number - two important points of similarity to the exact functional. We argue that density-driven errors of the energy in a self-consistent density functional calculation are second-order in the density error, and that large density-driven errors arise primarily from incorrect electron transfers over length scales larger than the diameter of an atom.

v1: Submitted in preparation for the annual FLOSIC all-hands meeting. v2: Significant revisions prior to submission at JCTC. v3: Significant revisions (completely new Supp Info) in response to private discussions with colleagues and peer review (NB: arXiv limit on number of characters in abstract, so it's truncated)

References in corpus (11)

• Fractional charge perspective on the band-gap in density-functional theory
• Fractional spins and static correlation error in density functional theory
• Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations
• The Importance of being consistent
• Exact-exchange energy density in the gauge of a semilocal density functional approximation
• Fermi Orbital Derivatives in Self-Interaction Corrected Density Functional Theory: Applications to Closed Shell Atoms
• A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction
• Stretched or noded orbital densities and self-interaction correction in density functional theory
• A Step in the Direction of Resolving the Paradox of Perdew-Zunger Self-interaction Correction. II. Gauge Consistency of the Energy Density at Three Levels of Approximation
• Study of self-interaction-errors in barrier heights using locally scaled and Perdew-Zunger self-interaction methods
• Extending density functional theory with near chemical accuracy beyond pure water

Cited by in corpus (8)

• Accuracy of Charge Densities in Electronic Structure Calculations
• Seven Useful Questions in Density Functional Theory
• A simple and efficient route towards improved energetics within the framework of density-corrected density functional theory
• Kohn-Sham inversion with mathematical guarantees
• Local Exchange-Correlation Potentials by Density Inversion in Solids
• The rise and fall of stretched bond errors: Extending the analysis of Perdew-Zunger self-interaction corrections of reaction barrier heights beyond the LSDA
• Examining the Impact of Local Condition Violations on Energy Computations in DFT
• Reducing Self-Interaction Error in Transition-Metal Oxides with Different Exact-Exchange Fractions for Energy and Density