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We derive an alternate expression for the Fermi-Lowdin Orbital Self-Interaction Correction (FLO-SIC) energy gradient and re-visit how the FLO-SIC methodology can be seen as a constrained unitary transformation acting on canonical Kohn-Sham orbitals. We present a new performance and accuracy analysis of the FLO-SIC approach, which we have recently implemented in the massively-parallelized NWChem quantum chemistry software package. Our FLO-SIC implementation has been tested for the prediction of total energies, atomization energies, and ionization potentials of small molecules and relatively large aromatic systems. The ionization potentials of multi-electron systems are calculated with the adaptation of fractional occupation numbers within FLO-SIC. We also carefully examine the possible improvements of these predictions with various SIC scaling methods based on kinetic energy densities and gradients of electronic densities.