How Good is the Density-Corrected SCAN Functional for Neutral and Ionic Aqueous Systems, and What is so Right about the Hartree-Fock Density?

Abstract

Density functional theory (DFT) is the most widely used electronic structure method, due to its simplicity and cost effectiveness. The accuracy of a DFT calculation de- pends not only on the choice of the density functional approximation (DFA) adopted but also on the electron density produced by the DFA. SCAN is a modern functional that satisfies all known constraints for meta-GGA functionals. The density-driven errors, defined as energy errors arising from errors of the self-consistent DFA electron density, can hinder SCAN from achieving chemical accuracy in some systems, including water. Density-corrected DFT (DC-DFT) can alleviate this shortcoming by adopting a more accurate electron density which, in most applications, is the electron density obtained at the Hartree-Fock level of theory due to its relatively low computational cost. In this work, we present extensive calculations aimed at determining the accuracy of the DC-SCAN functional for various aqueous systems. DC-SCAN (SCAN@HF) shows remarkable consistency in reproducing reference data obtained at the coupled cluster level of theory, with minimal loss of accuracy. Density-driven errors in the description of ionic aqueous clusters are thoroughly investigated. By comparison with the orbital-optimized CCSD density in the water dimer, we find that the self-consistent SCAN density transfers a spurious fraction of an electron across the hydrogen bond to the hydrogen atom (H⋆, covalently bound to the donor oxygen atom) from the acceptor (OA) and donor (OD) oxygen atoms, while HF makes a much smaller spurious transfer in the opposite direction, consistent with DC-SCAN (SCAN@HF) reduction of SCAN over-binding due to delocalization error. While LDA seems to be the conventional extreme of density delocalization error, and HF the conventional extreme of (usually much smaller) density localization error, these two densities do not quite yield the conventional range of density-driven error in energy differences. Finally, comparisons of the DC-SCAN results with those obtained with the Fermi-Lowdin orbital self-interaction correction (FLOSIC) method show that DC-SCAN represents a more accurate approach to reducing density-driven errors in SCAN calculations of ionic aqueous clusters.

Workhorse minimally-empirical dispersion-corrected density functional, with tests for weakly-bound systems: r$^{2}$SCAN+rVV10

“…This is rationalized as a density-driven error, rather than an error inherent to rVV10. For example, the hydrogen-bonded water dimer is over-bound by 0.44 kcal/mol or 9% in SCAN, and this error is reduced to 0.13 kcal/mol when SCAN is applied to the more accurate Hartree-Fock electron density, and not to its own self-consistent density 73 . That fact speaks for fitting the b parameter of rVV10 to the binding energy curve of the Ar dimer (as done here) or to the eight dispersion-bound complexes in S22, and not to the whole S22 set.…”

Detection and Correction of Delocalization Errors for Electron and Hole Polarons Using Density-Corrected DFT

“…The same is true for the hybrid SCAN0 functional . The DC-SCAN procedure has been recommended in some recent work, − but in this particular application the quality of SCAN energetics is somewhat degraded by density correction.…”

“…DC-DFT is a simple procedure whereby a self-consistent Hartree–Fock (HF) density, ρ HF , is used to evaluate the XC energy. This procedure incorporates electron correlation effects but avoids self-consistent iterations at the DFT level, which would introduce SIE into the density, and has been shown to afford reasonable reaction barrier heights even when GGA functionals are used. , Although this basic idea is an old one, − it has been revived and championed by Burke and Sim and their co-workers, ,− and more recently by others, − as an ad hoc correction for problems where DFT errors are “density-driven” rather than “functional-driven”. − In such cases, errors may be ameliorated through the use of an SIE-free density, namely, ρ HF . The usefulness of DC-DFT therefore hinges on identifying cases where the error is density-driven because otherwise it is probably not advantageous to sacrifice self-consistency. , Delocalization error in systems with one or more unpaired electrons represents a clear case where the error is density-driven, thus we expect such problems to benefit from DC-DFT.…”

Detection and correction of delocalization errors for electron- and hole-polarons using density-corrected DFT

“…coworkers, 14,[34][35][36][37][38][39] and more recently by others, [40][41][42][43] as an ad hoc correction for problems where delocalization error is "density-driven" rather than "functional-driven". [34][35][36][37][38] In such cases, errors are often ameliorated through the use of a SIE-free density, ρ HF .…”

“…S11), but that means that DC-SCAN up-shifts the energies relative to MP2, as does the hybrid SCAN0 functional. The DC-SCAN procedure has been recommended in some recent work, [40][41][42][43] but in this particular application the quality of SCAN energetics is somewhat degraded by density correction.…”