Self-consistent implementation of locally scaled self-interaction-correction method

Abstract: Recently proposed local self-interaction correction (LSIC) method [Zope, R. R. et al., J. Chem. Phys. 151, 214108 (2019)] is a one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities. The LSIC method is exact for the one-electron densities, also recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to the well-known Perdew-Zunger SIC (PZSIC) method as a special case. This article presents the self-consistent implementation of the LSIC method using the ratio of Weizs\"acker and Kohn-Sham kinetic energy densities as an iso-orbital indicator. The atomic forces as well as the forces on the Fermi-L\"owdin orbitals are also implemented for the LSIC energy functional. Results show that LSIC with the simplest local spin density functional predicts atomization energies of AE6 dataset better than some of the most widely used GGA functional (e.g. PBE) and barrier heights of BH6 database better than some of the most widely used hybrid functionals (e.g. PBE0 and B3LYP). The LSIC method [mean absolute error (MAE) of 0.008 \r{A}] predicts bond lengths of a small set of molecules better than the PZSIC-LSDA (MAE 0.042 \r{A}) and LSDA (0.011 \r{A}). This work shows that accurate results can be obtained from the simplest density functional by removing the self-interaction-errors using an appropriately designed SIC method.