Perdew-Zunger self-interaction correction: How wrong for uniform densities and large-Z atoms?*

Semilocal exchange-correlation (xc) energy of a many-electron system is not exact for all one-electron densities. In 1981, Perdew and Zunger (PZ) subtracted the fully nonlocal self-interaction error orbital-by-orbital, making the corrected functional exact for all one-electron densities. Although the PZ self-interaction correction (SIC) eliminates many errors of semilocal functionals, it is often worse for equilibrium properties of molecules and solids. Nonempirical semilocal functionals are usually designed to be exact for uniform electron gases, but PZ SIC is not so designed. We have extrapolated from the Ne, Ar, Kr, and Xe atoms to estimate the relative errors of the PZ SIC xc energies (with localized SIC orbitals) in the limit of large atomic number: about +5.5% for the LSDA-SIC and about -3.5% for nonempirical generalized gradient (PBE)-SIC and meta-generalized gradient strongly constrained and appropriately normed (SCAN)-SIC approximations [1]. The SIC errors found here are considerably larger than the error previously estimated on the uniform gas using LSDA-SIC localized orbitals. These errors may explain the shortcomings of PZ SIC for equilibrium properties, opening the path to a generalized SIC.
[1] B. Santra and J.P. Perdew J. Chem. Phys. 150, 174106 (2019)