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The Perdew-Zunger (PZ) method provides a way to remove the self-interaction(SI) error from density functional approximations on an orbital by orbitalbasis. The PZ method provides significant improvements for the properties suchas barrier heights or dissociation energies but results in over-correcting theproperties well described by SI-uncorrected semi-local functional. One cure torectify the over-correcting tendency is to scale down the magnitude ofSI-correction of each orbital in the many electron region. We have implementedthe orbitalwise scaled down SI-correction (OSIC) scheme of Vydrov et al. [J.Chem. Phys. 124, 094108 (2006)] using the Fermi-L\"owdin SI-correction method.After validating the OSIC implementation with previously reported OSIC-LSDAresults, we examine its performance with the most successful non-empirical SCANmeta-GGA functional. Using different forms of scaling factors to identifyone-electron regions, we assess the performance of OSIC-SCAN for a wide rangeof properties: total energies, ionization potentials and electron affinitiesfor atoms, atomization energies, dissociation and reaction energies, andreaction barrier heights of molecules. Our results show that OSIC-SCAN providessuperior results than the previously reported OSIC-LSDA, -PBE, and -TPSSresults. Furthermore, we propose selective scaling of OSIC (SOSIC) to removeits major shortcoming that destroys the $-1/r$ asymptotic behavior of thepotentials. The SOSIC method gives the highest occupied orbital eigenvaluespractically identical to those in PZSIC and unlike OSIC provides bound atomicanions even with larger powers of scaling factors. SOSIC compared to PZSIC orOSIC provides more balanced description of total energies and barrier heights.

Improvements in the orbitalwise scaling down of Perdew-Zunger self-interaction correction in many-electron regions