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Title: 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 generally, this improvement is limited. Here we introduce 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 themore » local scaling factor and the particular density functional approximation.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [3]
  1. Univ. of Texas at El Paso, TX (United States)
  2. Central Michigan Univ., Mount Pleasant, MI (United States)
  3. Temple Univ., Philadelphia, PA (United States)
Publication Date:
Research Org.:
Central Michigan Univ., Mount Pleasant, MI (United States); Univ. of Texas at El Paso, TX (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Chemical Sciences, Geosciences & Biosciences Division; National Science Foundation (NSF)
Contributing Org.:
Texas Advanced Computing Center
OSTI Identifier:
1601995
Alternate Identifier(s):
OSTI ID: 1577220
Grant/Contract Number:  
SC0018331; SC0006818; DMR-090071
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 151; 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

Citation Formats

Zope, Rajendra R., Yamamoto, Yoh, Diaz, Carlos M., Baruah, Tunna, Peralta, Juan E., Jackson, Koblar A., Santra, Biswajit, and Perdew, John P. A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction. United States: N. p., 2019. Web. doi:10.1063/1.5129533.
Zope, Rajendra R., Yamamoto, Yoh, Diaz, Carlos M., Baruah, Tunna, Peralta, Juan E., Jackson, Koblar A., Santra, Biswajit, & Perdew, John P. A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction. United States. doi:10.1063/1.5129533.
Zope, Rajendra R., Yamamoto, Yoh, Diaz, Carlos M., Baruah, Tunna, Peralta, Juan E., Jackson, Koblar A., Santra, Biswajit, and Perdew, John P. Thu . "A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction". United States. doi:10.1063/1.5129533.
@article{osti_1601995,
title = {A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction},
author = {Zope, Rajendra R. and Yamamoto, Yoh and Diaz, Carlos M. and Baruah, Tunna and Peralta, Juan E. and Jackson, Koblar A. and Santra, Biswajit and Perdew, John P.},
abstractNote = {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 generally, this improvement is limited. Here we introduce 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.},
doi = {10.1063/1.5129533},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 21,
volume = 151,
place = {United States},
year = {2019},
month = {12}
}

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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

Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation
journal, September 1992


Improved Slater approximation to SIC–OEP
journal, August 2008


Strategies for Massively Parallel Local-Orbital-Based Electronic Structure Methods
journal, January 2000


Variational mesh for quantum-mechanical simulations
journal, April 1990


Theoretical investigation of the polarizability of small metal clusters
journal, May 1996


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

Self-interaction corrections in the density functional formalism
journal, January 1981


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

Jacob’s ladder of density functional approximations for the exchange-correlation energy
conference, January 2001

  • Perdew, John P.
  • Density functional theory and its application to materials, AIP Conference Proceedings
  • DOI: 10.1063/1.1390175

Beyond the local-density approximation in calculations of ground-state electronic properties
journal, August 1983


Local‐density Hartree–Fock theory of electronic states of molecules with self‐interaction correction
journal, March 1984

  • Pederson, Mark R.; Heaton, Richard A.; Lin, Chun C.
  • The Journal of Chemical Physics, Vol. 80, Issue 5
  • DOI: 10.1063/1.446959

The optimized effective potential and the self-interaction correction in density functional theory: Application to molecules
journal, May 2000

  • Garza, Jorge; Nichols, Jeffrey A.; Dixon, David A.
  • The Journal of Chemical Physics, Vol. 112, Issue 18
  • DOI: 10.1063/1.481421

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

A new mixing of Hartree–Fock and local density‐functional theories
journal, January 1993

  • Becke, Axel D.
  • The Journal of Chemical Physics, Vol. 98, Issue 2
  • DOI: 10.1063/1.464304

Adiabatic-connection approach to Kohn-Sham theory
journal, April 1984


Generalized gradient approximation for the exchange-correlation hole of a many-electron system
journal, December 1996


Optimization of Gaussian basis sets for density-functional calculations
journal, October 1999


Self-consistent calculations of atomic properties using self-interaction-free exchange-only Kohn-Sham potentials
journal, January 1993


Accurate Density Functional with Correct Formal Properties: A Step Beyond the Generalized Gradient Approximation
journal, March 1999


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

Recent developments in libxc — A comprehensive library of functionals for density functional theory
journal, January 2018


Electrical Response of Molecular Systems: The Power of Self-Interaction Corrected Kohn-Sham Theory
journal, April 2008


Positron binding: A positron-density viewpoint
journal, September 1994

  • Baruah, Tunna; Zope, Rajendra R.; Kshirsagar, Anjali
  • Physical Review A, Vol. 50, Issue 3
  • DOI: 10.1103/PhysRevA.50.2191

Climbing the Density Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed for Molecules and Solids
journal, September 2003


A self-interaction-free local hybrid functional: Accurate binding energies vis-à-vis accurate ionization potentials from Kohn-Sham eigenvalues
journal, May 2014

  • Schmidt, Tobias; Kraisler, Eli; Makmal, Adi
  • The Journal of Chemical Physics, Vol. 140, Issue 18
  • DOI: 10.1063/1.4865942

Representative Benchmark Suites for Barrier Heights of Diverse Reaction Types and Assessment of Electronic Structure Methods for Thermochemical Kinetics
journal, December 2006

  • Zheng, Jingjing; Zhao, Yan; Truhlar, Donald G.
  • Journal of Chemical Theory and Computation, Vol. 3, Issue 2
  • DOI: 10.1021/ct600281g

Fermi-Löwdin orbital self-interaction correction to magnetic exchange couplings
journal, October 2018

  • Joshi, Rajendra P.; Trepte, Kai; Withanage, Kushantha P. K.
  • The Journal of Chemical Physics, Vol. 149, Issue 16
  • DOI: 10.1063/1.5050809

A long-range correction scheme for generalized-gradient-approximation exchange functionals
journal, August 2001

  • Iikura, Hisayoshi; Tsuneda, Takao; Yanai, Takeshi
  • The Journal of Chemical Physics, Vol. 115, Issue 8
  • DOI: 10.1063/1.1383587

Complex Orbitals, Multiple Local Minima, and Symmetry Breaking in Perdew–Zunger Self-Interaction Corrected Density Functional Theory Calculations
journal, June 2016

  • Lehtola, Susi; Head-Gordon, Martin; Jónsson, Hannes
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 7
  • DOI: 10.1021/acs.jctc.6b00347

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


Density functional theory: Its origins, rise to prominence, and future
journal, August 2015


Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/physrevlett.77.3865

Quantifying the effects of the self-interaction error in DFT: When do the delocalized states appear?
journal, June 2005

  • Lundberg, Marcus; Siegbahn, Per E. M.
  • The Journal of Chemical Physics, Vol. 122, Issue 22
  • DOI: 10.1063/1.1926277

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

Ionization potentials and electron affinities in the Perdew–Zunger self-interaction corrected density-functional theory
journal, May 2005

  • Vydrov, Oleg A.; Scuseria, Gustavo E.
  • The Journal of Chemical Physics, Vol. 122, Issue 18
  • DOI: 10.1063/1.1897378

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

Time-Dependent Density-Functional Theory with a Self-Interaction Correction
journal, August 2008


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

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

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

Orbital-dependent density functionals: Theory and applications
journal, January 2008


One-electron self-interaction and the asymptotics of the Kohn–Sham potential: an impaired relation
journal, January 2014

  • Schmidt, Tobias; Kraisler, Eli; Kronik, Leeor
  • Phys. Chem. Chem. Phys., Vol. 16, Issue 28
  • DOI: 10.1039/c3cp55433c

Delocalization Errors in Density Functional Theory Are Essentially Quadratic in Fractional Occupation Number
journal, October 2018


Curing difficult cases in magnetic properties prediction with self-interaction corrected density functional theory
journal, July 2001

  • Patchkovskii, S.; Autschbach, J.; Ziegler, T.
  • The Journal of Chemical Physics, Vol. 115, Issue 1
  • DOI: 10.1063/1.1370527

Density Functionals with Broad Applicability in Chemistry
journal, February 2008

  • Zhao, Yan; Truhlar, Donald G.
  • Accounts of Chemical Research, Vol. 41, Issue 2
  • DOI: 10.1021/ar700111a

A statistical exchange approximation for localized electrons
journal, January 1971

  • Lindgren, Ingvar
  • International Journal of Quantum Chemistry, Vol. 5, Issue S5
  • DOI: 10.1002/qua.560050849

Self-interaction correction of localized bands within the LMTO-ASA band structure method
journal, June 1991


A self-interaction corrected approach to many-electron systems: Beyond the local spin density approximation
journal, June 1980


Improved approximate representation of the Hartree-Fock potential in atoms
journal, June 1977


Novel method of self-interaction corrections in density functional calculations
journal, January 2001


Density-functional exchange-energy approximation with correct asymptotic behavior
journal, September 1988


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

The exchange-correlation energy of a metallic surface
journal, December 1975


Variational, Self-Consistent Implementation of the Perdew–Zunger Self-Interaction Correction with Complex Optimal Orbitals
journal, November 2014

  • Lehtola, Susi; Jónsson, Hannes
  • Journal of Chemical Theory and Computation, Vol. 10, Issue 12
  • DOI: 10.1021/ct500637x

Density‐functional theory with self‐interaction correction: Application to the lithium molecule a)
journal, March 1985

  • Pederson, Mark R.; Heaton, Richard A.; Lin, Chun C.
  • The Journal of Chemical Physics, Vol. 82, Issue 6
  • DOI: 10.1063/1.448266

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


Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H2+, He2+, LiH+, and Ne2+
journal, March 2007

  • Ruzsinszky, Adrienn; Perdew, John P.; Csonka, Gábor I.
  • The Journal of Chemical Physics, Vol. 126, Issue 10
  • DOI: 10.1063/1.2566637

The impact of the self-interaction error on the density functional theory description of dissociating radical cations: Ionic and covalent dissociation limits
journal, January 2004

  • Gräfenstein, Jürgen; Kraka, Elfi; Cremer, Dieter
  • The Journal of Chemical Physics, Vol. 120, Issue 2
  • DOI: 10.1063/1.1630017

Atomic Compton profiles within different exchange-only theories
journal, September 1999

  • Zope, Rajendra R.; Harbola, Manoj K.; Pathak, Rajeev K.
  • The European Physical Journal D - Atomic, Molecular and Optical Physics, Vol. 7, Issue 2
  • DOI: 10.1007/s100530050360

Towards an Optimal Gradient-dependent Energy Functional of the PZ-SIC Form
journal, January 2015


Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
journal, May 1976


Construction and application of an accurate local spin-polarized Kohn-Sham potential with integer discontinuity: Exchange-only theory
journal, January 1992


Erratum: Beyond the local-density approximation in calculations of ground-state electronic properties
journal, February 1984


Self-interaction corrections in semiconductors
journal, December 1995


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

  • Goerigk, Lars; Hansen, Andreas; Bauer, Christoph
  • Physical Chemistry Chemical Physics, Vol. 19, Issue 48
  • DOI: 10.1039/c7cp04913g

Accurate forces in a local-orbital approach to the local-density approximation
journal, August 1990


Self-consistent self-interaction corrected density functional theory calculations for atoms using Fermi-Löwdin orbitals: Optimized Fermi-orbital descriptors for Li–Kr
journal, October 2017

  • Kao, Der-you; Withanage, Kushantha; Hahn, Torsten
  • The Journal of Chemical Physics, Vol. 147, Issue 16
  • DOI: 10.1063/1.4996498

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

Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits
journal, August 2005

  • Perdew, John P.; Ruzsinszky, Adrienn; Tao, Jianmin
  • The Journal of Chemical Physics, Vol. 123, Issue 6
  • DOI: 10.1063/1.1904565

Self-interaction correction and the optimized effective potential
journal, July 2008

  • Körzdörfer, T.; Kümmel, S.; Mundt, M.
  • The Journal of Chemical Physics, Vol. 129, Issue 1
  • DOI: 10.1063/1.2944272

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

Ground-state correlation energies for atomic ions with 3 to 18 electrons
journal, May 1993

  • Chakravorty, Subhas J.; Gwaltney, Steven R.; Davidson, Ernest R.
  • Physical Review A, Vol. 47, Issue 5
  • DOI: 10.1103/physreva.47.3649

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


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

Inclusion of exact exchange for self-interaction corrected H 3 density functional potential energy surface
journal, May 1998

  • Csonka, Gabor I.; Johnson, Benny G.
  • Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 99, Issue 3
  • DOI: 10.1007/s002140050318

Phase transitions in rare earth tellurides under pressure
journal, June 2014


Local hybrid functionals
journal, January 2003

  • Jaramillo, Juanita; Scuseria, Gustavo E.; Ernzerhof, Matthias
  • The Journal of Chemical Physics, Vol. 118, Issue 3
  • DOI: 10.1063/1.1528936

Long-range and short-range Coulomb correlation effects as simulated by Hartree-Fock, local density approximation, and generalized gradient approximation exchange functionals
journal, February 2003

  • Polo, Victor; Gräfenstein, Jürgen; Kraka, Elfi
  • Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 109, Issue 1
  • DOI: 10.1007/s00214-002-0398-y

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

Systematic approximations to the optimized effective potential: Application to orbital-density-functional theory
journal, November 1992


Phosphorus NMR Chemical Shifts with Self-Interaction Free, Gradient-Corrected DFT
journal, February 2002

  • Patchkovskii, Serguei; Ziegler, Tom
  • The Journal of Physical Chemistry A, Vol. 106, Issue 6
  • DOI: 10.1021/jp014184v

Electron correlation and the self-interaction error of density functional theory
journal, June 2002


Orbital energy analysis with respect to LDA and self-interaction corrected exchange-only potentials
journal, January 2001

  • Garza, Jorge; Vargas, Rubicelia; Nichols, Jeffrey A.
  • The Journal of Chemical Physics, Vol. 114, Issue 2
  • DOI: 10.1063/1.1327269

Effect of the self-interaction error for three-electron bonds: On the development of new exchange-correlation functionals
journal, January 2004

  • Gräfenstein, Jürgen; Kraka, Elfi; Cremer, Dieter
  • Phys. Chem. Chem. Phys., Vol. 6, Issue 6
  • DOI: 10.1039/b311840a

Self-interaction error in density functional theory: a mean-field correction for molecules and large systems
journal, February 2005


The density functional formalism, its applications and prospects
journal, July 1989


The Role of Self-Interaction Corrections, Vibrations, and Spin-Orbit in Determining the Ground Spin State in a Simple Heme
journal, October 2017


Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965


Self-interaction correction in multiple scattering theory: application to transition metal oxides
journal, January 2009