How does the Fermi-Löwdin Orbital Self-interaction Correction work? The view from 10^-10 feet

The Fermi-Löwdin Orbital Self-interaction Correction (FLOSIC) is a unitarily invariant version of the Perdew-Zunger SIC that removes self-interaction errors (SIE) from density functional theory (DFT) calculations. Over the past several years, FLOSIC has been tested in a wide array of settings. We will review several of these applications and comment on FLOSIC's successes and limitations. Recently, we have given attention to the well-known problem that DFT methods systematically underestimate chemical reaction barrier heights. Through orbital-by-orbital analysis, we identify stretched bond orbitals as the main source of SIE in barrier height predictions. We introduce X/C, the ratio of the self-exchange energy to the self-Coulomb energy, as a metric to help understand how SIC improves the predictions. X/C = 1.0 for all orbitals for the exact (and self-interaction free) density functional, but differs from 1.0 by various amounts when using practical density functional approximations. Monitoring changes in X/C for corresponding orbitals is a convenient way to pinpoint how SIC contributes to total energy differences. We demonstrate this for the case of barrier heights and select transition metal systems. This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, as a part of the Computational Chemical Sciences Program under Award No. DE-SC0018331.