Additional Insights between Fermi-Löwdin Orbital SIC and the Localization Equation Constraints in SIC-DFT.

This letter highlights additional mathematical relationships between the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) formalism and the localization equation constraints in SIC-DFT. We demonstrate this relationship analytically by highlighting symmetries in the mathematical expression for the gradient of EPZ-SIC, which has not been previously shown in the scientific literature. To complement our analytical derivation, we also present additional numerical tests that allow us to investigate a possible accelerated-convergence technique that could be used when solving the iterative FLO-SIC equations. Taken together, our results highlight the importance of satisfying the localization equation constraints for obtaining accurate DFT energies, which we demonstrate are nearly satisfied in the FLO-SIC formalism.