Enhancing the accuracy of interior-scaled Perdew-Zunger self-interaction correction

The Perdew Zunger self-interaction correction (PZ-SIC)¹ 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. This overcorrection is often reduced by LSIC², local scaling of the PZ-SIC to 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 Z in the asymptotic expansion of the exchange-correlation (xc) energy for atoms of atomic number Z, which is neglected by LSIC. LSIC+ applied to LSDA works better for many properties than LSDA-LSIC and the PBE GGA and gives comparable results to the SCAN meta-GGA. Unlike LSIC and LSIC+, SCAN-sdSIC³, seems to describe weak bonds correctly. However, sdSIC spoils the correct asymptotic behavior of the xc potential. Interior-scaled PZ-SIC with improved iso-orbital indicators might be developed to work more widely than the methods considered here.

1. J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981)
2. Zope et al., The Journal of Chemical Physics 151, 214108 (2019)
3. Bhattarai et al., The Journal of Chemical Physics 152, 214109 (2020)