Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: 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

Abstract

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 testsmore » 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.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [3]; ORCiD logo [1]; ORCiD logo [3]; ORCiD logo [4]; ORCiD logo [4]; ORCiD logo [1]
+ Show Author Affiliations
  1. Temple Univ., Philadelphia, PA (United States)
  2. Temple Univ., Philadelphia, PA (United States); Central Michigan Univ., Mount Pleasant, MI (United States)
  3. Univ. of Texas at El Paso, TX (United States)
  4. Central Michigan Univ., Mount Pleasant, MI (United States)
Publication Date:
Research Org.:
Central Michigan Univ., Mount Pleasant, MI (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division; National Science Foundation (NSF); US Army Research Laboratory (USARL); USDOE
OSTI Identifier:
1781834
Alternate Identifier(s):
OSTI ID: 1631878
Grant/Contract Number:  
SC0018331; DMR-1607868; 1625061; W911NF-16-2-0189
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 152; Journal Issue: 21; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Local density approximations; Correlation energy; Generalized gradient approximations; Density functional theory; Atomic properties; Molecular properties

Citation Formats

Bhattarai, Puskar, Wagle, Kamal, Shahi, Chandra, Yamamoto, Yoh, Romero, Selim, Santra, Biswajit, Zope, Rajendra R., Peralta, Juan E., Jackson, Koblar A., and Perdew, John P. 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. United States: N. p., 2020. Web. doi:10.1063/5.0010375.
Copy to clipboard
Bhattarai, Puskar, Wagle, Kamal, Shahi, Chandra, Yamamoto, Yoh, Romero, Selim, Santra, Biswajit, Zope, Rajendra R., Peralta, Juan E., Jackson, Koblar A., & Perdew, John P. 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. United States. https://doi.org/10.1063/5.0010375
Copy to clipboard
Bhattarai, Puskar, Wagle, Kamal, Shahi, Chandra, Yamamoto, Yoh, Romero, Selim, Santra, Biswajit, Zope, Rajendra R., Peralta, Juan E., Jackson, Koblar A., and Perdew, John P. Thu . "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". United States. https://doi.org/10.1063/5.0010375. https://www.osti.gov/servlets/purl/1781834.
Copy to clipboard
@article{osti_1781834,
title = {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},
author = {Bhattarai, Puskar and Wagle, Kamal and Shahi, Chandra and Yamamoto, Yoh and Romero, Selim and Santra, Biswajit and Zope, Rajendra R. and Peralta, Juan E. and Jackson, Koblar A. and Perdew, John P.},
abstractNote = {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.},
doi = {10.1063/5.0010375},
journal = {Journal of Chemical Physics},
number = 21,
volume = 152,
place = {United States},
year = {Thu Jun 04 00:00:00 EDT 2020},
month = {Thu Jun 04 00:00:00 EDT 2020}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/5.0010375
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 22 works
Citation information provided by
Web of Science
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Small Representative Benchmarks for Thermochemical Calculations
journal, October 2003

  • Lynch, Benjamin J.; Truhlar, Donald G.
  • The Journal of Physical Chemistry A, Vol. 107, Issue 42
  • DOI: 10.1021/jp035287b

Ab initio theory and modeling of water
journal, September 2017

  • Chen, Mohan; Ko, Hsin-Yu; Remsing, Richard C.
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 41
  • DOI: 10.1073/pnas.1712499114

Scaling down the Perdew-Zunger self-interaction correction in many-electron regions
journal, March 2006

  • Vydrov, Oleg A.; Scuseria, Gustavo E.; Perdew, John P.
  • The Journal of Chemical Physics, Vol. 124, Issue 9
  • DOI: 10.1063/1.2176608

A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction
journal, December 2019

  • Zope, Rajendra R.; Yamamoto, Yoh; Diaz, Carlos M.
  • The Journal of Chemical Physics, Vol. 151, Issue 21
  • DOI: 10.1063/1.5129533

The effect of the Perdew-Zunger self-interaction correction to density functionals on the energetics of small molecules
journal, September 2012

  • Klüpfel, Simon; Klüpfel, Peter; Jónsson, Hannes
  • The Journal of Chemical Physics, Vol. 137, Issue 12
  • DOI: 10.1063/1.4752229

Exact-exchange energy density in the gauge of a semilocal density-functional approximation
journal, January 2008

Competing stripe and magnetic phases in the cuprates from first principles
journal, December 2019

  • Zhang, Yubo; Lane, Christopher; Furness, James W.
  • Proceedings of the National Academy of Sciences, Vol. 117, Issue 1
  • DOI: 10.1073/pnas.1910411116

Improvements in the orbitalwise scaling down of Perdew–Zunger self-interaction correction in many-electron regions
journal, May 2020

  • Yamamoto, Yoh; Romero, Selim; Baruah, Tunna
  • The Journal of Chemical Physics, Vol. 152, Issue 17
  • DOI: 10.1063/5.0004738

Self-interaction correction to density-functional approximations for many-electron systems
journal, May 1981

Self-interaction-free electric dipole polarizabilities for atoms and their ions using the Fermi-Löwdin self-interaction correction
journal, July 2019

Fermi orbital derivatives in self-interaction corrected density functional theory: Applications to closed shell atoms
journal, February 2015

  • Pederson, Mark R.
  • The Journal of Chemical Physics, Vol. 142, Issue 6
  • DOI: 10.1063/1.4907592

Fermi-Löwdin orbital self-interaction correction using the strongly constrained and appropriately normed meta-GGA functional
journal, October 2019

  • Yamamoto, Yoh; Diaz, Carlos M.; Basurto, Luis
  • The Journal of Chemical Physics, Vol. 151, Issue 15
  • DOI: 10.1063/1.5120532

Full self-consistency in the Fermi-orbital self-interaction correction
journal, May 2017

Regional self-interaction correction of density functional theory
journal, August 2003

  • Tsuneda, Takao; Kamiya, Muneaki; Hirao, Kimihiko
  • Journal of Computational Chemistry, Vol. 24, Issue 13
  • DOI: 10.1002/jcc.10279

Improving “difficult” reaction barriers with self-interaction corrected density functional theory
journal, May 2002

  • Patchkovskii, Serguei; Ziegler, Tom
  • The Journal of Chemical Physics, Vol. 116, Issue 18
  • DOI: 10.1063/1.1468640

Effect of the Perdew–Zunger self-interaction correction on the thermochemical performance of approximate density functionals
journal, January 2004

  • Vydrov, Oleg A.; Scuseria, Gustavo E.
  • The Journal of Chemical Physics, Vol. 121, Issue 17
  • DOI: 10.1063/1.1794633

Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds
journal, June 1991

  • Curtiss, Larry A.; Raghavachari, Krishnan; Trucks, Gary W.
  • The Journal of Chemical Physics, Vol. 94, Issue 11
  • DOI: 10.1063/1.460205

Shrinking Self-Interaction Errors with the Fermi–Löwdin Orbital Self-Interaction-Corrected Density Functional Approximation
journal, November 2018

  • Sharkas, Kamal; Li, Lin; Trepte, Kai
  • The Journal of Physical Chemistry A, Vol. 122, Issue 48
  • DOI: 10.1021/acs.jpca.8b09940

Stretched or noded orbital densities and self-interaction correction in density functional theory
journal, May 2019

  • Shahi, Chandra; Bhattarai, Puskar; Wagle, Kamal
  • The Journal of Chemical Physics, Vol. 150, Issue 17
  • DOI: 10.1063/1.5087065

A simple method to selectively scale down the self-interaction correction
journal, May 2006

  • Vydrov, Oleg A.; Scuseria, Gustavo E.
  • The Journal of Chemical Physics, Vol. 124, Issue 19
  • DOI: 10.1063/1.2204599

Relevance of the Slowly Varying Electron Gas to Atoms, Molecules, and Solids
journal, November 2006

Properties of the exchange hole under an appropriate coordinate transformation
journal, October 2003

  • Tao, Jianmin; Springborg, Michael; Perdew, John P.
  • The Journal of Chemical Physics, Vol. 119, Issue 13
  • DOI: 10.1063/1.1604377

The effect of self-interaction error on electrostatic dipoles calculated using density functional theory
journal, November 2019

  • Johnson, Alexander I.; Withanage, Kushantha P. K.; Sharkas, Kamal
  • The Journal of Chemical Physics, Vol. 151, Issue 17
  • DOI: 10.1063/1.5125205

Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional
journal, June 2016

  • Sun, Jianwei; Remsing, Richard C.; Zhang, Yubo
  • Nature Chemistry, Vol. 8, Issue 9
  • DOI: 10.1038/nchem.2535

Importance of complex orbitals in calculating the self-interaction-corrected ground state of atoms
journal, November 2011

Meta-generalized gradient approximation: Explanation of a realistic nonempirical density functional
journal, April 2004

  • Perdew, John P.; Tao, Jianmin; Staroverov, Viktor N.
  • The Journal of Chemical Physics, Vol. 120, Issue 15
  • DOI: 10.1063/1.1665298

Local hybrid functionals: Theory, implementation, and performance of an emerging new tool in quantum chemistry and beyond
journal, July 2018

  • Maier, Toni M.; Arbuznikov, Alexei V.; Kaupp, Martin
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 9, Issue 1
  • DOI: 10.1002/wcms.1378

Perdew-Zunger self-interaction correction: How wrong for uniform densities and large- Z atoms?
journal, May 2019

  • Santra, Biswajit; Perdew, John P.
  • The Journal of Chemical Physics, Vol. 150, Issue 17
  • DOI: 10.1063/1.5090534

Strongly Constrained and Appropriately Normed Semilocal Density Functional
journal, July 2015

Communication: Self-interaction correction with unitary invariance in density functional theory
journal, March 2014

  • Pederson, Mark R.; Ruzsinszky, Adrienn; Perdew, John P.
  • The Journal of Chemical Physics, Vol. 140, Issue 12
  • DOI: 10.1063/1.4869581

Shrinking Self-Interaction Errors with the Fermi–Löwdin Orbital Self-Interaction-Corrected Density Functional Approximation
journal, November 2018

  • Sharkas, Kamal; Li, Lin; Trepte, Kai
  • The Journal of Physical Chemistry A, Vol. 122, Issue 48
  • DOI: 10.1021/acs.jpca.8b09940

Improving “difficult” reaction barriers with self-interaction corrected density functional theory
journal, May 2002

  • Patchkovskii, Serguei; Ziegler, Tom
  • The Journal of Chemical Physics, Vol. 116, Issue 18
  • DOI: 10.1063/1.1468640

Scaling down the Perdew-Zunger self-interaction correction in many-electron regions
journal, March 2006

  • Vydrov, Oleg A.; Scuseria, Gustavo E.; Perdew, John P.
  • The Journal of Chemical Physics, Vol. 124, Issue 9
  • DOI: 10.1063/1.2176608

Communication: Self-interaction correction with unitary invariance in density functional theory
journal, March 2014

  • Pederson, Mark R.; Ruzsinszky, Adrienn; Perdew, John P.
  • The Journal of Chemical Physics, Vol. 140, Issue 12
  • DOI: 10.1063/1.4869581

The effect of self-interaction error on electrostatic dipoles calculated using density functional theory
journal, November 2019

  • Johnson, Alexander I.; Withanage, Kushantha P. K.; Sharkas, Kamal
  • The Journal of Chemical Physics, Vol. 151, Issue 17
  • DOI: 10.1063/1.5125205

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

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Accurate and numerically efficient r$^2$SCAN meta-generalized gradient approximation
    preprint, January 2020

      Sort by:
      [ × clear filter / sort ]

      Similar Records in DOE PAGES and OSTI.GOV collections: