Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

A step in the direction of resolving the paradox of Perdew–Zunger self-interaction correction. II. Gauge consistency of the energy density at three levels of approximation

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/5.0010375· OSTI ID:1781834
 [1];  [2];  [3];  [4];  [4];  [2];  [4];  [5];  [5];  [2]
  1. Temple Univ., Philadelphia, PA (United States); Central Michigan University
  2. Temple Univ., Philadelphia, PA (United States)
  3. Temple Univ., Philadelphia, PA (United States); Central Michigan Univ., Mount Pleasant, MI (United States)
  4. Univ. of Texas at El Paso, TX (United States)
  5. Central Michigan Univ., Mount Pleasant, MI (United States)
+ Show Author Affiliations
The Perdew-Zunger(PZ) self-interaction correction (SIC) was designed to correct the one-electron limit of any approximate density functional for the exchange-correlation (xc) energy, while yielding no correction to the exact functional. Unfortunately, it spoils the slowly-varying-in-space limits of the uncorrected approximate functionals, where those functionals are right by construction. The right limits can be restored by locally scaling down the energy density of the PZ SIC in many-electron regions, but then a spurious correction to the exact functional would be found unless the self-Hartree and exact self-xc terms of the PZ SIC energy density were expressed in the same gauge. Only the local density approximation satisfies the same-gauge condition for the energy density, which explains why the recent local-scaling SIC (LSIC) is found here to work excellently for atoms and molecules only with this basic approximation, and not with the more advanced generalized gradient approximations (GGAs) and meta-GGAs, which lose the Hartree gauge via simplifying integrations by parts. The transformation of energy density that achieves the Hartree gauge for the exact xc functional can also be applied to approximate functionals. Doing so leads to a simple scaled-down self-interaction (sdSIC) correction that is typically much more accurate than PZ SIC in tests for many molecular properties (including equilibrium bond lengths). The present work shows unambiguously that the largest errors of PZ SIC applied to standard functionals at three levels of approximation can be removed by restoring their correct slowlyvarying- density limits. Here, it also confirms the relevance of these limits to atoms and molecules.
Research Organization:
Central Michigan Univ., Mount Pleasant, MI (United States)
Sponsoring Organization:
US Army Research Laboratory (USARL); US National Science Foundation; USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division
Grant/Contract Number:
SC0018331
OSTI ID:
1781834
Alternate ID(s):
OSTI ID: 1631878
Journal Information:
Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 21 Vol. 152; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (45)

Shrinking Self-Interaction Errors with the Fermi–Löwdin Orbital Self-Interaction-Corrected Density Functional Approximation journal November 2018
A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions journal January 2017
Improving “difficult” reaction barriers with self-interaction corrected density functional theory journal May 2002
Scaling down the Perdew-Zunger self-interaction correction in many-electron regions journal March 2006
Communication: Self-interaction correction with unitary invariance in density functional theory journal March 2014
The effect of self-interaction error on electrostatic dipoles calculated using density functional theory journal November 2019
Optimization of Gaussian basis sets for density-functional calculations journal October 1999
Strongly Constrained and Appropriately Normed Semilocal Density Functional journal July 2015
Ab initio theory and modeling of water text January 2017
A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction text January 2019
Relevance of the slowly-varying electron gas to atoms, molecules, and solids text January 2006
Regional self-interaction correction of density functional theory journal August 2003
Local hybrid functionals: Theory, implementation, and performance of an emerging new tool in quantum chemistry and beyond
  • Maier, Toni M.; Arbuznikov, Alexei V.; Kaupp, Martin
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 9, Issue 1 https://doi.org/10.1002/wcms.1378
journal July 2018
Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties: IV. Third-row atoms: Ge through Br journal January 1991
A General Database for Main Group Thermochemistry, Kinetics, and Noncovalent Interactions − Assessment of Common and Reparameterized ( meta -)GGA Density Functionals journal November 2009
Small Representative Benchmarks for Thermochemical Calculations journal October 2003
Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional journal June 2016
Properties of the exchange hole under an appropriate coordinate transformation journal October 2003
Meta-generalized gradient approximation: Explanation of a realistic nonempirical density functional journal April 2004
Effect of the Perdew–Zunger self-interaction correction on the thermochemical performance of approximate density functionals journal January 2004
A simple method to selectively scale down the self-interaction correction journal May 2006
Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds journal June 1991
The effect of the Perdew-Zunger self-interaction correction to density functionals on the energetics of small molecules journal September 2012
Fermi orbital derivatives in self-interaction corrected density functional theory: Applications to closed shell atoms journal February 2015
Stretched or noded orbital densities and self-interaction correction in density functional theory journal May 2019
Perdew-Zunger self-interaction correction: How wrong for uniform densities and large- Z atoms? journal May 2019
Fermi-Löwdin orbital self-interaction correction using the strongly constrained and appropriately normed meta-GGA functional journal October 2019
A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction journal December 2019
Improvements in the orbitalwise scaling down of Perdew–Zunger self-interaction correction in many-electron regions journal May 2020
Ab initio theory and modeling of water journal September 2017
Competing stripe and magnetic phases in the cuprates from first principles journal December 2019
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
Self-interaction-free electric dipole polarizabilities for atoms and their ions using the Fermi-Löwdin self-interaction correction journal July 2019
Ground-state correlation energies for atomic ions with 3 to 18 electrons journal May 1993
Exact-exchange energy density in the gauge of a semilocal density-functional approximation journal January 2008
Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction journal November 2008
Importance of complex orbitals in calculating the self-interaction-corrected ground state of atoms journal November 2011
Full self-consistency in the Fermi-orbital self-interaction correction journal May 2017
Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism journal May 1976
Self-interaction correction to density-functional approximations for many-electron systems journal May 1981
Variational mesh for quantum-mechanical simulations journal April 1990
Accurate and simple analytic representation of the electron-gas correlation energy journal June 1992
Generalized Gradient Approximation Made Simple journal October 1996
Relevance of the Slowly Varying Electron Gas to Atoms, Molecules, and Solids journal November 2006
Density functional theory: Its origins, rise to prominence, and future journal August 2015

Cited By (2)

Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories text January 2020
Accurate and numerically efficient r$^2$SCAN meta-generalized gradient approximation preprint January 2020

Similar Records

Exploring and enhancing the accuracy of interior-scaled Perdew–Zunger self-interaction correction
Journal Article · Sun Feb 28 19:00:00 EST 2021 · Journal of Chemical Physics · OSTI ID:1770567

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Atomic properties
Correlation energy
Density functional theory
Generalized gradient approximations
Local density approximations
Molecular properties