Complexity reduction in self-interaction-free density functional calculations using the Fermi-Löwdin self-interaction correction method

Abstract: Fermi-L\"owdin (FLO) self-interaction-correction (SIC) (FLOSIC) method uses symmetric orthogonalized Fermi orbitals as localized orbitals in one-electron SIC schemes resulting in a formal reduction in the scaling of SIC methods (e.g. Perdew-Zunger SIC (PZSIC) method) but requires a set of Fermi orbital descriptors used to define the FLOs which can be computationally taxing. Here, we propose to simplify the SIC calculations using a selective orbital scaling self-interaction correction (SOSIC) by removing SIE from a select set of orbitals that are of interest. We illustrate the approach by choosing a valence set of orbitals as active orbitals in the SOSIC approach. The results obtained using the vSOSIC scheme are compared with those obtained with PZSIC which corrects for SIE of all orbitals. The comparison is made for atomization energies, barrier heights, ionization energies (absolute highest occupied orbital [HOO] eigenvalues), exchange coupling constant and spin densities of Cu-containing complexes, and vertical detachment energies (VDE) of water cluster anions. The agreement between the two methods is within a few percent for the majority of the properties. The MAE in the VDE (absolute HOO eigenvalue) of water cluster anions with vSOSIC-PBE with respect to benchmark CCSD(T) results is only 15 meV making vSOSIC-PBE an excellent alternative to the CCSD(T) to obtain the VDE of water cluster anions. The vSOSIC calculation on [Cu$_2$Cl$_6$]$^{2-}$ complex demonstrates that, in addition to the cost savings from using fewer orbitals to account for SIC, the FOD optimization in vSOSIC is also substantially smoother and faster.