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The Perdew-Zunger(PZ) self-interaction correction (SIC) was designed tocorrect the one-electron limit of any approximate density functional for theexchange-correlation (xc) energy, while yielding no correction to the exactfunctional. Unfortunately, it spoils the slowly-varying-in-space limits of theuncorrected approximate functionals, where those functionals are right byconstruction. The right limits can be restored by locally scaling down theenergy density of the PZ SIC in many-electron regions, but then a spuriouscorrection to the exact functional would be found unless the self-Hartree andexact self-xc terms of the PZ SIC energy density were expressed in the samegauge. Only the local density approximation satisfies the same-gauge conditionfor the energy density, which explains why the recent local-scaling SIC (LSIC)is found here to work excellently for atoms and molecules only with this basicapproximation, and not with the more advanced generalized gradientapproximations (GGAs) and meta-GGAs, which lose the Hartree gauge viasimplifying integrations by parts. The transformation of energy density thatachieves the Hartree gauge for the exact xc functional can also be applied toapproximate functionals. Doing so leads to a simple scaled-downself-interaction (sdSIC) correction that is typically much more accurate thanPZ SIC in tests for many molecular properties (including equilibrium bondlengths). The present work shows unambiguously that the largest errors of PZSIC applied to standard functionals at three levels of approximation can beremoved by restoring their correct slowly-varying-density limits. It alsoconfirms the relevance of these limits to atoms and molecules.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

A Step in the Direction of Resolving the Paradox of Perdew-Zunger  Self-interaction Correction. II. Gauge Consistency of the Energy Density at  Three Levels of Approximation