Local Spin Density Approximation Strongly Improved by a Better-Informed Local Scaling of Its Self-Interaction...

The Perdew-Zunger self-interaction correction (PZSIC) makes density functional approximations (DFAs) exact for all one-electron densities. However, it overcorrects in many-electron regions, introducing errors for the uniform-density limit, where uncorrected DFAs are exact. The locally scaled PZSIC (LSIC), based on the iso-orbital indicator z_σ [which distinguishes single-orbital and slowly varying density regions and is used with the local spin density approximation (LSDA)], restores the uniform-density limit and significantly improves results for many properties, including chemical reaction barrier heights, atomization energies, and ionization potentials. Yet, LSIC performs poorly for weakly bonded systems, leaving many unbound, due to limitations of its iso-orbital indicator. To correct this, in this work we propose a new local scaling, LSIC-α, based on the iso-orbital indicator α_σ (which additionally identifies regions of overlapping density tails). A two-parameter scaling function of α_σ is fitted to a subset of the nonbonded appropriate norms for the SCAN and r²SCAN meta-GGAs, and tested on many properties of main-group atoms, molecules, and molecular complexes. LSIC-α greatly improves the interaction energies of weakly bonded systems in the S22 data set while retaining LSIC's accuracy for other properties. This work shows that the errors of LSDA (and presumably of higher-level DFAs) can be largely but not entirely repaired by a proper "do no harm" self-interaction correction.