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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]
  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); Army Research Lab.; 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:
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.
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. doi:https://doi.org/10.1063/5.0010375
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. doi:https://doi.org/10.1063/5.0010375.
@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 = {2020},
month = {6}
}

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