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

Title: Self-consistent implementation of locally scaled self-interaction-correction method

Journal Article · · Journal of Chemical Physics
DOI: https://doi.org/10.1063/5.0130436 · OSTI ID:1925201
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2]; ORCiD logo [2]; ORCiD logo [2]
  1. Univ. of Texas at El Paso, TX (United States); Central Michigan University
  2. Univ. of Texas at El Paso, TX (United States)
+ Show Author Affiliations

Recently proposed local self-interaction correction (LSIC) method is a one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange–correlation and Coulomb energy densities. The LSIC method is exact for the one-electron densities, also recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to the well-known Perdew–Zunger SIC (PZSIC) method as a special case. This article presents the self-consistent implementation of the LSIC method using the ratio of Weizsäcker and Kohn–Sham kinetic energy densities as an iso-orbital indicator. The atomic forces as well as the forces on the Fermi-Löwdin orbitals are also implemented for the LSIC energy functional. Results show that LSIC with the simplest local spin density functional predicts atomization energies of the AE6 dataset better than some of the most widely used generalized-gradient-approximation (GGA) functional and barrier heights of the BH6 database better than some of the most widely used hybrid functionals. The LSIC method [a mean absolute error (MAE) of 0.008 Å] predicts bond lengths of a small set of molecules better than the PZSIC-LSDA (MAE 0.042 Å) and LSDA (0.011 Å). Furthermore, this work shows that accurate results can be obtained from the simplest density functional by removing the self-interaction-errors using an appropriately designed SIC method.

Research Organization:
Central Michigan University, Mount Pleasant, MI (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division
Grant/Contract Number:
SC0018331
OSTI ID:
1925201
Alternate ID(s):
OSTI ID: 1924359
Journal Information:
Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 6 Vol. 158; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (153)

Self-interaction correction to density-functional approximations for many-electron systems journal May 1981
Enhancing the efficiency of density functionals with an improved iso-orbital indicator journal January 2019
Shrinking Self-Interaction Errors with the Fermi–Löwdin Orbital Self-Interaction-Corrected Density Functional Approximation journal November 2018
Self-interaction corrections in semiconductors journal December 1995
A statistical exchange approximation for localized electrons journal January 1971
Accurate and Numerically Efficient r 2 SCAN Meta-Generalized Gradient Approximation journal September 2020
Two avenues to self-interaction correction within Kohn—Sham theory: unitary invariance is the shortcut journal May 2003
Kohn-Sham Self-Interaction Correction in Real Time journal April 2012
Self-interaction-corrected density-functional formalism journal January 1994
Electron correlation and the self-interaction error of density functional theory journal June 2002
Tables of molecular vibrational frequencies. Consolidated volume II journal July 1977
Quadratures on a sphere journal January 1976
Complex Orbitals, Multiple Local Minima, and Symmetry Breaking in Perdew–Zunger Self-Interaction Corrected Density Functional Theory Calculations journal June 2016
A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction journal December 2019
Towards improved local hybrid functionals by calibration of exchange-energy densities journal November 2014
Localized orbitals based on the fermi hole journal January 1984
Experimental Vibrational Zero-Point Energies: Diatomic Molecules journal June 2007
A multicenter numerical integration scheme for polyatomic molecules journal February 1988
Ab initio molecular simulations with numeric atom-centered orbitals journal November 2009
Effect of Complex-Valued Optimal Orbitals on Atomization Energies with the Perdew–Zunger Self-Interaction Correction to Density Functional Theory journal August 2016
Hartree–Fock orbitals significantly improve the reaction barrier heights predicted by semilocal density functionals journal June 2008
Fractional occupation numbers and self‐interaction correction‐scaling methods with the Fermi‐Löwdin orbital self‐interaction correction approach journal May 2020
Stretched or noded orbital densities and self-interaction correction in density functional theory journal May 2019
Self-interaction-free electric dipole polarizabilities for atoms and their ions using the Fermi-Löwdin self-interaction correction journal July 2019
Analytic atomic gradients in the fermi-löwdin orbital self-interaction correction: Analytic Atomic Gradients in the Fermi-Löwdin Orbital Self-Interaction Correction journal December 2018
Inclusion of exact exchange for self-interaction corrected H 3 density functional potential energy surface
  • Csonka, Gabor I.; Johnson, Benny G.
  • Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 99, Issue 3 https://doi.org/10.1007/s002140050318
journal May 1998
Fermi orbital derivatives in self-interaction corrected density functional theory: Applications to closed shell atoms journal February 2015
The Becke Fuzzy Cells Integration Scheme in the Amsterdam Density Functional Program Suite journal May 2013
An improved self‐interaction‐corrected local spin density functional for atoms journal April 1983
A self-interaction-free local hybrid functional: Accurate binding energies vis-à-vis accurate ionization potentials from Kohn-Sham eigenvalues journal May 2014
Piecewise Linearity and Spectroscopic Properties from Koopmans-Compliant Functionals book January 2014
Regional self-interaction correction of density functional theory journal August 2003
Interpretation and Automatic Generation of Fermi‐Orbital Descriptors journal September 2019
Generalized Gradient Approximation Made Simple journal October 1996
Obtaining localized orbitals and band structure in self-interaction-corrected density-functional theory journal September 1999
Self-interaction correction to the local-density approximation in the calculation of the energy band gaps of semiconductors based on the full-potential linearized augmented-plane-wave method journal December 1986
Comment on “Significance of the highest occupied Kohn-Sham eigenvalue” journal December 1997
Atomic Energy Levels for the Thomas-Fermi and Thomas-Fermi-Dirac Potential journal July 1955
Paradox of Self-Interaction Correction book September 2015
Variational, Self-Consistent Implementation of the Perdew–Zunger Self-Interaction Correction with Complex Optimal Orbitals journal November 2014
Zur Theorie der Kernmassen journal July 1935
Electronic structure of cerium in the self-interaction-corrected local-spin-density approximation journal February 1996
Delocalization error: The greatest outstanding challenge in density‐functional theory journal July 2022
Fermi-Löwdin-orbital self-interaction correction using the optimized-effective-potential method within the Krieger-Li-Iafrate approximation journal April 2021
An alternative self-interaction correction in the generalized exchange local-density functional theory journal September 1991
Importance of complex orbitals in calculating the self-interaction-corrected ground state of atoms journal November 2011
Regularized SCAN functional journal April 2019
Complex Fermi–Löwdin orbital self-interaction correction journal June 2022
Localized orbitals and the Fermi hole journal January 1982
Improvements in the orbitalwise scaling down of Perdew–Zunger self-interaction correction in many-electron regions journal May 2020
Self-interaction error overbinds water clusters but cancels in structural energy differences journal May 2020
Systematically Improvable Generalization of Self-Interaction Corrected Density Functional Theory journal June 2022
Improved radial grids for quadrature in molecular density‐functional calculations journal June 1996
Local self-interaction correction method with a simple scaling factor journal January 2021
Communication: Self-interaction correction with unitary invariance in density functional theory journal March 2014
Towards efficient density functional theory calculations without self-interaction: The Fermi-Löwdin orbital self-interaction correction journal October 2019
New development of self-interaction corrected DFT for extended systems applied to the calculation of native defects in 3C–SiC journal April 2006
Application of Self-Interaction Corrected Density Functional Theory to Early, Middle, and Late Transition States journal September 2020
How well do self-interaction corrections repair the overestimation of static polarizabilities in density functional calculations? journal January 2021
Electronic structure of mononuclear Cu-based molecule from density-functional theory with self-interaction correction journal July 2021
Novel method of self-interaction corrections in density functional calculations journal January 2001
Calculations of Al dopant in α -quartz using a variational implementation of the Perdew–Zunger self-interaction correction journal August 2015
Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules II: Non-Empirically Tuned Long-Range Corrected Hybrid Functionals journal January 2016
Fermi-Löwdin orbital self-interaction correction using the strongly constrained and appropriately normed meta-GGA functional journal October 2019
Exact-exchange energy density in the gauge of a semilocal density-functional approximation journal January 2008
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
A self-interaction corrected approach to many-electron systems: Beyond the local spin density approximation journal June 1980
Full self-consistency in the Fermi-orbital self-interaction correction journal May 2017
Koopmans-compliant functionals and their performance against reference molecular data journal August 2014
Fitting the Coulomb potential variationally in Xα molecular calculations journal March 1983
Density-related properties from self-interaction corrected density functional theory calculations journal January 2021
Self-interaction correction for density-functional theory of electronic energy bands of solids journal November 1983
New Basis Set Exchange: An Open, Up-to-Date Resource for the Molecular Sciences Community journal October 2019
Exact differential equation for the density and ionization energy of a many-particle system journal November 1984
Self-interaction corrections in the density functional formalism journal January 1981
Small Representative Benchmarks for Thermochemical Calculations journal October 2003
Assessing the effect of regularization on the molecular properties predicted by SCAN and self-interaction corrected SCAN meta-GGA journal January 2020
An all‐electron numerical method for solving the local density functional for polyatomic molecules journal January 1990
Critical assessment of the self-interaction-corrected–local-density-functional method and its algorithmic implementation journal March 1997
Self-Interaction Corrections Within the Fermi-Orbital-Based Formalism book July 2015
Strongly Constrained and Appropriately Normed Semilocal Density Functional journal July 2015
Replacing hybrid density functional theory: motivation and recent advances journal January 2021
Ground-state correlation energies for atomic ions with 3 to 18 electrons journal May 1993
Achieving linear scaling in exchange-correlation density functional quadratures journal July 1996
Positron binding: A positron-density viewpoint journal September 1994
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
Self-interaction correction and the optimized effective potential journal July 2008
First Principles Approaches to Spectroscopic Properties of Complex Materials book September 2014
On the Question of the Total Energy in the Fermi–Löwdin Orbital Self-Interaction Correction Method journal June 2018
Tests of second-generation and third-generation density functionals for thermochemical kineticsElectronic supplementary information (ESI) available: Mean errors for pure and hybrid DFT methods. See http://www.rsc.org/suppdata/cp/b3/b316260e/ journal January 2004
Chemical bonding theories as guides for self-interaction corrected solutions: Multiple local minima and symmetry breaking journal December 2021
Self-interaction-corrected Kohn–Sham effective potentials using the density-consistent effective potential method journal August 2021
Variational mesh for quantum-mechanical simulations journal April 1990
Band theory and Mott insulators: Hubbard U instead of Stoner I journal July 1991
Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)] journal February 1997
The effect of self-interaction error on electrostatic dipoles calculated using density functional theory journal November 2019
A long-range correction scheme for generalized-gradient-approximation exchange functionals journal August 2001
Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem journal December 1979
The effect of the Perdew-Zunger self-interaction correction to density functionals on the energetics of small molecules journal September 2012
Perdew-Zunger self-interaction correction: How wrong for uniform densities and large- Z atoms? journal May 2019
Atomic Compton profiles within different exchange-only theories journal September 1999
Proof that ∂ E ∂ n i = ε in density-functional theory journal December 1978
Relationship between the highest occupied Kohn-Sham orbital eigenvalue and ionization energy journal August 1999
Accurate forces in a local-orbital approach to the local-density approximation journal August 1990
Fermi-Löwdin orbital self-interaction corrected density functional theory: Ionization potentials and enthalpies of formation: Fermi-Löwdin Orbital Self-interaction Corrected Density Functional Theory: Ionization Potentials and Enthalpies of Formation journal October 2018
Improving “difficult” reaction barriers with self-interaction corrected density functional theory journal May 2002
Study of self-interaction-errors in barrier heights using locally scaled and Perdew–Zunger self-interaction methods journal January 2022
A new mixing of Hartree–Fock and local density‐functional theories journal January 1993
Effect of the Perdew–Zunger self-interaction correction on the thermochemical performance of approximate density functionals journal January 2004
Numerical solution of Poisson’s equation in polyatomic molecules journal September 1988
Using complex degrees of freedom in the Kohn-Sham self-interaction correction journal June 2012
Static dipole polarizabilities of polyacenes using self-interaction-corrected density functional approximations journal March 2021
Multiconfiguration Pair-Density Functional Theory journal August 2014
Local hybrid functionals: An assessment for thermochemical kinetics journal November 2007
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 June 2020
Exchange holes in inhomogeneous systems: A coordinate-space model journal April 1989
PyFLOSIC: Python-based Fermi–Löwdin orbital self-interaction correction journal August 2020
Self-interaction correction with Wannier functions journal April 2008
Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation journal September 1992
Scaling down the Perdew-Zunger self-interaction correction in many-electron regions journal March 2006
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
A simple method to selectively scale down the self-interaction correction journal May 2006
Self-interaction correction in water–ion clusters journal March 2021
Orbital functional for exchange and correlation: self-interaction correction to the local density approximation journal June 1979
Generalized-exchange local-spin-density-functional theory: Self-interaction correction journal July 1988
Functional derivatives of meta-generalized gradient approximation (meta-GGA) type exchange-correlation density functionals journal June 2013
Electronic energy-band structure of the calcium fluoride crystal journal October 1980
Self-interaction correction to the local density Hartree-Fock atomic calculations of excited and ground states journal June 1983
Towards an Optimal Gradient-dependent Energy Functional of the PZ-SIC Form journal January 2015
Ionization potentials and electron affinities in the Perdew–Zunger self-interaction corrected density-functional theory journal May 2005
Implementation of Perdew–Zunger self-interaction correction in real space using Fermi–Löwdin orbitals journal February 2021
Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators journal August 1995
Fermi-Löwdin orbital self-interaction correction to magnetic exchange couplings journal October 2018
Application of an on-site self-interaction-corrected method to Ce and the α-Ce surface journal October 1999
Electronic structures of transition-metal mono-oxides in the self-interaction-corrected local-spin-density approximation journal January 1995
Local hybrid functionals journal January 2003
New approaches for the calibration of exchange-energy densities in local hybrid functionals journal January 2016
Self-interaction-correction theory for density functional calculations of electronic energy bands for the lithium chloride crystal journal April 1984
Atomic-orbital-based approximate self-interaction correction scheme for molecules and solids journal January 2007
Self-interaction corrections in density functional theory journal May 2014
Importance of self-interaction-error removal in density functional calculations on water cluster anions journal January 2020
Study of Self-Interaction Errors in Density Functional Calculations of Magnetic Exchange Coupling Constants Using Three Self-Interaction Correction Methods journal March 2022
Optimization of Gaussian basis sets for density-functional calculations journal October 1999
Study of self-interaction errors in density functional predictions of dipole polarizabilities and ionization energies of water clusters using Perdew–Zunger and locally scaled self-interaction corrected methods journal October 2020
Exploring and enhancing the accuracy of interior-scaled Perdew–Zunger self-interaction correction journal March 2021
Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals journal November 2006
Self-interaction-corrected local-spin-density calculations for rare earth materials journal January 2000
Strategies for Massively Parallel Local-Orbital-Based Electronic Structure Methods journal January 2000
Improved approximate representation of the Hartree-Fock potential in atoms journal June 1977
Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy journal December 1982
Hartree-Fock exchange energy of an inhomogeneous electron gas journal June 1983
Initial Fermi orbital descriptors for FLOSIC calculations: The quick-FOD method journal October 2021
Density Functional Theory with Correct Long-Range Asymptotic Behavior journal February 2005

Similar Records

Local self-interaction correction method with a simple scaling factor
Journal Article · 2020 · Physical Chemistry Chemical Physics. PCCP · OSTI ID:1852598
+1 more
How Do Self-Interaction Errors Associated with Stretched Bonds Affect Barrier Height Predictions?
Journal Article · 2023 · Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory · OSTI ID:1958936
+3 more
Exploring and enhancing the accuracy of interior-scaled Perdew–Zunger self-interaction correction
Journal Article · 2021 · Journal of Chemical Physics · OSTI ID:1770567
+5 more

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Self consistent field methods
Exchange correlation functionals
Local density approximations
Electronic structure
Kohn-Sham density functional theory
Molecular properties
Correlation energy
Atomic energy
Electron density
Density functional theory