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Semilocal density-functional approximations (DFAs), including thestate-of-the-art SCAN functional, are plagued by the self-interaction error(SIE). While this error is explicitly defined only for one-electron systems, ithas inspired the self-interaction correction method proposed by Perdew andZunger (PZ-SIC), which has shown promise in mitigating the many-electron SIE.However, the PZ-SIC method is known for its significant numerical instability.In this study, we introduce a novel constraint that facilitates self-consistentlocalization of the SIC orbitals in the spirit of Edmiston-Ruedenberg orbitals[Rev. Mod. Phys. 35, 457 (1963)]. Our practical implementation within theall-electron numeric atom-centered orbitals code FHI-aims guarantees efficientand stable convergence of the self-consistent PZ-SIC equations for bothmolecules and solids. We further demonstrate that our PZ-SIC approacheffectively mitigates the SIE in the meta-GGA SCAN functional, significantlyimproving the accuracy for ionization potentials, charge-transfer energies, andband gaps for a diverse selection of molecules and solids. However, our PZ-SICmethod does have its limitations. It can not improve the already accurate SCANresults for properties such as cohesive energies, lattice constants, and bulkmodulus in our test sets. This highlights the need for new-generation DFAs withmore comprehensive applicability.

Self-interaction corrected SCAN functional for molecules and solids in the numeric atom-center orbital framework