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 semilocal DFA non-self-consistently on the Hartree–Fock (HF) density is often recommended as a computationally inexpensive remedy for delocalization errors. For sophisticated meta-GGAs like SCAN, this approach can achieve remarkable accuracy. This HF-DFT (also known as DFA@HF) is often presumed to work, when it significantly improves over the DFA, because the HF density is more accurate than the self-consistent DFA density in those cases. 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 overcorrection, 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 randomly selected transition states confirms this trend. We do not have the exact functional and electron densities that would be needed to evaluate the exact density- and functional-driven errors for the large BH76 database of barrier heights. Instead, we have identified and employed three fully nonlocal proxy functionals (SCAN 50% global hybrid, range-separated hybrid LC-ωPBE, and SCAN-FLOSIC) and their self-consistent proxy densities. These functionals are chosen because they yield reasonably accurate self-consistent barrier heights and because 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.

Testing the r2SCAN Density Functional for the Thermodynamic Stability of Solids with and without a van der Waals Correction

“…Typically, semilocal density functional approximations (local spin-density approximations, GGAs, and meta-GGAs) underestimate barrier heights of transition states due to the self-interaction errors. For gas-phase chemical reactions, the barrier heights are more realistic with SCAN-like meta-GGAs than with GGAs due to a reduction of self-interaction errors, and are improved further by existing self-interaction corrections . Barrier heights in condensed phases, including barriers to vacancy mobility, have not yet (to our knowledge) been explored with SCAN-like functionals.…”

How Do Self-Interaction Errors Associated with Stretched Bonds Affect Barrier Height Predictions?

“…Very recently, Kaplan et al 38 compared density-driven and functional-driven errors for the BH76 set of reaction barrier heights for a variety of DFA’s and using different choices of the proxy for n exact , the exact density. For LSDA, the Perdew, Burke, and Ernzerhof generalized gradient approximation (PBE) 39 and the strongly constrained and appropriately normed SCAN meta-GGA, 40 they also obtained density-driven errors using self-consistent densities from the corresponding PZSIC–DFA calculations as the proxy.…”

Simple and Efficient Route toward Improved Energetics within the Framework of Density-Corrected Density Functional Theory

“…There is a further source of error cancellation in the density sensitivity measure: since the density sensitivity is measured using an approximate exchange-correlation functional, errors in that functional can cancel the ones in the density as functional errors and density-driven errors have opposite signs . That such an error cancellation can occur is well-known. ,, …”

“…43 That such an error cancellation can occur is well-known. 29,56,67 In that context, we also mention the work of Kepp, who proposed a recipe to assess the degree of normality that evaluates four distinct functionals on each other's selfconsistent densities. 68 The use of various functionals reduces the probability of error cancellation in measuring the abnormality of the reaction.…”