A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction

Abstract

Self-interaction (SI) error, which results when exchange-correlation contributions to the total energy are approximated, limits the reliability of many density functional approximations. The Perdew-Zunger SI correction (PZSIC), when applied in conjunction with the local spin density approximation (LSDA), improves the description of many properties, but overall, this improvement is limited. Here we propose a modification to PZSIC that uses an iso-orbital indicator to identify regions where local SI corrections should be applied. Using this local-scaling SIC (LSIC) approach with LSDA, we analyze predictions for a wide range of properties including, for atoms, total energies, ionization potentials, and electron affinities, and for molecules, atomization energies, dissociation energy curves, reaction energies, and reaction barrier heights. LSIC preserves the results of PZSIC-LSDA for properties where it is successful and provides dramatic improvements for many of the other properties studied. Atomization energies calculated using LSIC are better than those of the Perdew, Burke, and Ernzerhof (PBE) generalized gradient approximation (GGA) and close to those obtained with the Strongly Constrained and Appropriately Normed (SCAN) meta-GGA. LSIC also restores the uniform gas limit for the exchange energy that is lost in PZSIC-LSDA. Further performance improvements may be obtained by an appropriate combination or modification of the local scaling factor and the particular density functional approximation.

Self-interaction error overbinds water clusters but cancels in structural energy differences

“…More generally, for nonmetals (including water), any large error of SCAN is dominated by self-interaction. Improvements in the way the SIE is handled are under development (46)(47)(48), but here we will apply only a currently standard way.…”

Simple hydrogenic estimates for the exchange and correlation energies of atoms and atomic ions, with implications for density functional theory

“…Recent work has shown that the Perdew-Zunger selfinteraction correction (PZ SIC), which makes any approximate density functional exact for non-overlapped one-electron densities, introduces errors of as much as 6% in the large-Z or slowly-varying-density limit [20], and that these errors can degrade the predicted equilibrium properties of molecules. Carefully scaling down the PZ SIC correction to zero in slowly-varying regions yields much better results [21,22]. The LYP correlation functional is highly accurate for first and second row molecules, but highly inaccurate for the uniform gas.…”

“…Recent work [20][21][22] has shown that errors of even a few percent in the uniform-density limit can seriously undermine the accuracy of approximate density functionals for the equilibrium properties of atoms and small molecules.…”

Implementation of Perdew–Zunger self-interaction correction in real space using Fermi–Löwdin orbitals

“…A number of approaches have been proposed to remove the SIEs. 7,[9][10][11][12][13][14][15][16] In this work, we focus on the most widely used self-interaction-correction, developed by Perdew and Zunger (PZ-SIC) 7 , which has been used to study atoms, molecules, and solids. 8,13,14, A. Perdew-Zunger Self-interaction-correction (PZ-SIC)…”