On the question of the total energy in FLO-SIC calculations*

The Fermi-Löwdin orbital self-interaction correction (FLO-SIC) formalism is a promising approach for treating the self-interaction error in density functional theory (DFT)^1,2,3,4. Minimizing the total energy in FLO-SIC requires finding optimal positions for the Fermi orbital descriptors. Hence only 3N parameters are involved. Previous SIC calculations satisfied constraints known as the localization equations (LEs), involving the variation of N(N-1)/2 parameters. This raises the question of whether FLO-SIC reaches the same total energy as obtained in SIC-LE calculations. To address this, we implemented a method to perform SIC-LE calculations within the same NRLMOL code that is used for FLO-SIC calculations. Here we compare total energies of a diverse set of atoms and molecules, as well as the molecular atomization energies from fully self-consistent FLO-SIC and SIC-LE calculations.

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