Exploring and enhancing the accuracy of interior-scaled Perdew–Zunger self-interaction correction

Abstract

The Perdew-Zunger self-interaction correction (PZ-SIC) improves the performance of density functional approximations (DFAs) for the properties that involve significant self-interaction error (SIE), as in stretched bond situations, but overcorrects for equilibrium properties where SIE is insignificant. This overcorrection is often reduced by LSIC, local scaling of the PZ-SIC to the local spin density approximation (LSDA). Here we propose a new scaling factor to use in an LSIC-like approach that satisfies an additional important constraint: the correct coefficient of atomic number Z in the asymptotic expansion of the exchange-correlation (xc) energy for atoms. LSIC and LSIC+ are scaled by functions of the iso-orbital indicator z σ , which distinguishes one-electron regions from many-electron regions. LSIC+ applied to LSDA works better for many equilibrium properties than LSDA-LSIC and the Perdew, Burke, and Ernzerhof (PBE) generalized gradient approximation (GGA), and almost as well as the strongly constrained and appropriately normed (SCAN) meta-GGA. LSDA-LSIC and LSDA-LSIC+, however, both fail to predict interaction energies involving weaker bonds, in sharp contrast to their earlier successes. It is found that more than one set of localized SIC orbitals can yield a nearly degenerate energetic description of the same multiple covalent bond, suggesting that a consistent chemical interpretation of the localized orbitals requires a new way to choose their Fermi orbital descriptors. To make a locally scaled-down SIC to functionals beyond LSDA requires a gauge transformation of the functional's energy density. The resulting SCAN-sdSIC, evaluated on SCAN-SIC total and localized orbital densities, leads to an acceptable description of many equilibrium properties including the dissociation energies of weak bonds.

Self-Interaction Correction in Water-Ion Clusters

“…When implemented on FLOSIC-LSDA FLO densities, the methods of Refs. 90 and 93 improve many calculated properties over PZ SIC, including the energies of the stronger bonds 47,[90][91][92][93] , but seriously underbind 93 typical hydrogenand van der Waals-bonded complexes. Our current study with self-consistent FLOSIC implementations of unscaled PZ SIC shows the importance of mitigating the self-interaction error from the electron density and the corresponding energetics in water-ion interactions.…”

“…A scaling method that would enhance the SIC contribution to the binding of OH -(H 2 O) and H 3 O + (H 2 O) clusters and simultaneously reduce the SIC contribution to the binding of water-alkali clusters is highly sought after. A few approaches that locally scale down the PZ SIC have been introduced re-cently [90][91][92][93] , but more development is needed. The scaled methods have not yet been implemented self-consistently.…”

The Fermi-Löwdin self-interaction correction for ionization energies of organic molecules

“…beyond LSIC, here we use two new scaling schemes namely LDA-LSIC+ 68 and its revised version, LDA-rLSIC+, using the scaling functions as shown in Eqs. ( 9) and ( 10) respectively.…”

“…Both these methods assign z σ -dependent corrections to the corresponding energy densities and are devised only for LDA to avoid gauge inconsistency. 67 LDA-LSIC+ 68 is specifically designed to reduce the significant error of LDA-SIC for neutral atoms in the limit of large atomic numbers. 66 Compared to LDA-LSIC, LDA-LSIC+ is more correcting towards the z σ → 0 region, while less towards the z σ → 1.…”

“…Importantly, the second coefficient in the large-Z asymptotic expansion is improved towards the exact value of -0.187 69,70 in both LDA-LSIC+ (-0.183) and LDA-rLSIC+ (-0.196), as opposed to LDA-LSIC (-0.085) and LDA-SIC (-0.724). 68 Nevertheless, all these scaled-down methods guarantee no correction for a uniform electron density (z σ =0) and full corrections for a single electron density (z σ =1). Figure 2 displays a plot of the scaling function f (z σ ) as a function of z σ .…”