Simplification of the Fermi-L\"owdin Self-Interaction Correction Method for Efficient Self-Interaction-Free Density Functional Calculations

Fermi-L\"owdin orbital self-interaction-correction (FLOSIC) method uses symmetric orthogonalized Fermi orbitals as localized orbitals in one-electron SIC schemes. In FLOSIC, a set of Fermi orbital descriptors (FOD) that define the FLOs is obtained by energy minimization. Determination of optimal FODs is a computationally very demanding task. Here, we propose to simplify the FLOSIC calculations by removing self-interaction error (SIE) from a set of selected orbitals of interest (SOSIC). We illustrate the approach by choosing a set of valence orbitals as active orbitals in SOSIC. The results of a wide range of properties obtained using the valence SOSIC (vSOSIC) scheme are compared with those obtained with the Perdew-Zunger SIC. The two methods agree within a few percent for the majority of the properties. The mean absolute error in the vertical detachment energy of water cluster anions with vSOSIC-PBE against benchmark CCSD(T) results is only 15 meV making vSOSIC-PBE an excellent alternative to the CCSD(T) for the case. The calculation on the [Cu$_2$Cl$_6$]$^{2-}$ complex demonstrates that the FOD optimization in vSOSIC is substantially smoother and faster. Assessment of the performance of SIC-r$^2$SCAN shows that it performs similarly to the SIC-SCAN for most properties, but for atomization energies, SIC-r$^2$SCAN outperforms SIC-SCAN.