LSIC Alpha: An Improved Local Scaling of the Perdew-Zunger Self-Interaction Correction

The Perdew-Zunger self-interaction correction¹ (PZ-SIC) makes density functional approximations (DFAs) exact for all one-electron densities. However, it overcorrects in many-electron regions, introducing errors for the uniform electron densities where uncorrected DFAs are exact. The local scaling of PZ-SIC using the iso-orbital indicator z_σ (called LSIC²) applied to the local spin density approximation (LSDA) restores the uniform density limit and significantly improves results for a wide range of properties such as chemical reaction barrier heights, atomization energies, and ionization potentials. However, LSIC performs poorly for weakly bonded systems due to its choice of iso-orbital indicator. In this work, we propose a new local scaling (LSIC Alpha) based on another iso-orbital indicator α which can recognize not only regions of slowly-varying and one-electron density but also regions where density tails are overlapped. LSIC Alpha greatly improves the interaction energies of weakly bonded systems in the S22 dataset while preserving the remarkable performance of LSIC. Generalizations to higher-level DFAs are being explored.

1] J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981)

2] R. R. Zope et al., J. Chem. Phys. 151, 214108 (2019)