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Cited by 20,887Advanced Chemical Physics StudiesPhysics of Superconductivity and MagnetismThermodynamic and Structural Properties of Metals and Alloys

Self-interaction correction to density-functional approximations for many-electron systems

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Perdew, J. P., Zunger, Alex·1981·Physical Review B
DOI 10.1103/physrevb.23.5048
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Abstract

The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

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  • The majority of excited-state calculations are based on many-body perturbation theory (e.g., G0W0, self-consistent GW, BSE, DMFT) and are performed on top of a DFT calculation, which provides the starting point.

    “The majority of excited-states calculations are based on many-body perturbation theory (MBPT), e.g. G 0 W 0 and self-consistent GW [31-33], the Bethe-Salpeter equation (BSE) [34], or dynamical mean field theory (DMFT) [35], and are performed on-top of a DFT calculation, which provides the starting point for both self-consistent and one-shot approaches.”

    From Precision and efficiency in solid-state pseudopotential calculations (2018) · cites this paper as [35]

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Authors
Perdew, J. P., & Zunger, A.
Affiliations
Tulane University (US)
ORCID
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
1981-05-15
Volume
23
Issue
10
Pages
5048-5079
ISSN
0163-1829 (ISSN-L)
DOI
10.1103/physrevb.23.5048
OpenAlex
W2052637367
Cited by
20,887
References
122
Citations by year
2026: 452 · 2025: 624 · 2024: 646 · 2023: 651 · 2022: 680 · 2021: 730 · 2020: 839 · 2019: 790 · 2018: 816 · 2017: 816 · 2016: 835 · 2015: 835 · 2014: 935 · 2013: 835 · 2012: 760
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
Physical review. B, Condensed matter (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
  • Physical Sciences › Engineering › Mechanical Engineering › Thermodynamic and Structural Properties of Metals and Alloys
Keywords
self-interaction correction, density functional theory, local spin density approximation, exchange-correlation hole, Kohn-Sham potential, Hohenberg-Kohn theorem, band gap underestimation, spin splitting, fractional occupation numbers, rare gas solids, CuCl, transition metals

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