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Additional Insights between Fermi-Löwdin Orbital SIC and the Localization Equation Constraints in SIC-DFT
Fredy W Aquino1, Bryan M Wong1
1Department of Chemical & Environmental Engineering, Materials Science & Engineering Program, and Department of Physics & Astronomy , University of California-Riverside , Riverside , California 92521 , United States.
Abstract:
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.
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