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

Study of Self-Interaction Errors in Density Functional Calculations of Magnetic Exchange Coupling Constants Using Three Self-Interaction Correction Methods

Journal Article · · Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory
We examine the role of self-interaction errors (SIE) removal on the evaluation of magnetic exchange coupling constants. In particular we analyze the effect of scaling down the self-interaction-correction (SIC) for three non-empirical density functional approximations (DFAs) namely, the local spin density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation, and recent SCAN family of meta-GGA functionals. To this end, we employ three one-electron SIC methods: Perdew-Zunger [Perdew, J. P.; Zunger, A. Phys. Rev. B, 1981, 23, 5048] SIC, the orbitalwise scaled SIC method [Vydrov, O. A. et al., J. Chem. Phys. 2006, 124, 094108], and the recent local scaling method [Zope, R. R. et al., J. Chem. Phys. 2019, 151, 214108]. We compute the magnetic exchange coupling constants using the spin projection and non projection approaches for sets of molecules composed of dinuclear and polynuclear H-He models, organic radical molecules, and chlorocuprate, and compare these results against accurate theories and experiment. Our results show that for the systems that mainly consist of single electron regions, PZSIC performs well but for more complex organic systems and the chlorcuprates, an overcorrecting tendency of PZSIC combined with the DFAs utilized in this work is more pronounced, and in such cases LSIC with kinetic energy density ratio performs better than PZSIC. Furthermore, analysis of the results in terms of SIC corrections to the density and to the total energy shows that both density and energy correction are required to obtain an improved prediction of magnetic exchange couplings.
Research Organization:
Central Michigan Univ., Mount Pleasant, MI (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0018331
OSTI ID:
1860638
Alternate ID(s):
OSTI ID: 1866254
Journal Information:
Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory, Journal Name: Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory Journal Issue: 12 Vol. 126; ISSN 1089-5639
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

References (109)

Broken symmetry approach to calculation of exchange coupling constants for homobinuclear and heterobinuclear transition metal complexes journal October 1999
About the calculation of exchange coupling constants in polynuclear transition metal complexes: Calculation of Exchange Coupling Constants journal April 2003
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
Fractional occupation numbers and self‐interaction correction‐scaling methods with the Fermi‐Löwdin orbital self‐interaction correction approach journal May 2020
Density functional studies of molecular magnets journal September 2006
A statistical exchange approximation for localized electrons journal January 1971
Zur Theorie des Ferromagnetismus book January 1985
Localized orbitals and the Fermi hole journal January 1982
Effect of configuration and conformation on the spin multiplicity in xylylene type biradicals journal October 2000
Some thoughts about the stability and reliability of commonly used exchange?correlation functionals ? coverage of dynamic and nondynamic correlation effects journal May 2002
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
Symmetry and broken symmetry in molecular orbital description of unstable molecules IV: comparison between single- and multi-reference computational results for antiaromtic molecules journal June 2011
Variational calculation of small energy differences. The singlet-triplet gap in [Cu2Cl6]2− journal October 1992
Orbital interactions, electron delocalization and spin coupling in iron-sulfur clusters journal October 1995
A self-interaction corrected approach to many-electron systems: Beyond the local spin density approximation journal June 1980
Structural dependence of the singlet-triplet gap in doubly bridged copper dimers: a variational CI calculation journal February 1994
Influence of the self-interaction error on the structure of the DFT exchange hole journal February 2002
Paradox of Self-Interaction Correction book September 2015
Self-Interaction Corrections Within the Fermi-Orbital-Based Formalism book July 2015
Structural dependence of magnetic exchange coupling parameters in transition-metal complexes journal February 2013
Accuracy of density functional theory methods for the calculation of magnetic exchange couplings in binuclear iron(III) complexes journal January 2020
New Basis Set Exchange: An Open, Up-to-Date Resource for the Molecular Sciences Community journal October 2019
A Green’s-Function Approach to Exchange Spin Coupling As a New Tool for Quantum Chemistry journal November 2015
On the Question of the Total Energy in the Fermi–Löwdin Orbital Self-Interaction Correction Method journal June 2018
Post-B3LYP Functionals Do Not Improve the Description of Magnetic Coupling in Cu(II) Dinuclear Complexes journal March 2018
Shrinking Self-Interaction Errors with the Fermi–Löwdin Orbital Self-Interaction-Corrected Density Functional Approximation journal November 2018
Accurate and Numerically Efficient r 2 SCAN Meta-Generalized Gradient Approximation journal September 2020
Ferromagnetic spin alignment in molecular systems: an orbital approach journal May 1993
Magnetic Exchange Couplings with Range-Separated Hybrid Density Functionals journal May 2010
Magnetic Couplings in Spin Frustrated Fe 7 III Disklike Clusters journal November 2013
The Triplet–Singlet Gap in the m -Xylylene Radical: A Not So Simple One journal November 2013
Restricted Ensemble-Referenced Kohn−Sham versus Broken Symmetry Approaches in Density Functional Theory:  Magnetic Coupling in Cu Binuclear Complexes journal March 2007
Ab initio calculation of the magnetic exchange interactions in (.mu.-oxo)diiron(III) systems using a broken symmetry wave function journal December 1992
Anisotropic exchange in transition-metal dinuclear complexes. 6. Bis(-.mu.-chloro)bis(dichlorocuprates(II)) journal February 1985
Density Functional Calculations of Magnetic Exchange Interactions in Polynuclear Transition Metal Complexes journal October 1997
Orbital interactions in metal dimer complexes journal August 1975
Failure of Time-Dependent Density Functional Theory for Long-Range Charge-Transfer Excited States:  The Zincbacteriochlorin−Bacteriochlorin and Bacteriochlorophyll−Spheroidene Complexes journal March 2004
Toward the Prediction of Magnetic Coupling in Molecular Systems:  Hydroxo- and Alkoxo-Bridged Cu(II) Binuclear Complexes journal February 1997
The Controversial Ground State of Tetramethyleneethane. An ab Initio CI Study journal July 2000
Trimethylenemethane. Comparison of Multiconfiguration Self-Consistent Field and Density Functional Methods for a Non-Kekulé Hydrocarbon journal January 1996
Theoretical Approaches to Direct Exchange Couplings between Divalent Chromium Ions in Naked Dimers, Tetramers, and Clusters journal January 1997
Importance of self-interaction-error removal in density functional calculations on water cluster anions journal January 2020
Assessing the effect of regularization on the molecular properties predicted by SCAN and self-interaction corrected SCAN meta-GGA journal January 2020
Local self-interaction correction method with a simple scaling factor journal January 2021
How well do self-interaction corrections repair the overestimation of static polarizabilities in density functional calculations? journal January 2021
Correlation consistent valence basis sets for use with the Stuttgart–Dresden–Bonn relativistic effective core potentials: The atoms Ga–Kr and In–Xe journal February 2001
Jacob’s ladder of density functional approximations for the exchange-correlation energy conference January 2001
Analysis of the magnetic coupling in binuclear complexes. I. Physics of the coupling journal February 2002
Improving “difficult” reaction barriers with self-interaction corrected density functional theory journal May 2002
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
On the Non‐Orthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals journal March 1950
Exchange coupling in transition-metal complexes via density-functional theory: Comparison and reliability of different basis set approaches journal August 2005
About the calculation of exchange coupling constants using density-functional theory: The role of the self-interaction error journal October 2005
Accurate magnetic exchange couplings in transition-metal complexes from constrained density-functional theory journal January 2006
Scaling down the Perdew-Zunger self-interaction correction in many-electron regions journal March 2006
Comment on “About the calculation of exchange coupling constants using density-functional theory: The role of the self-interaction error” [J. Chem. Phys. 123, 164110 (2005)] journal March 2006
Reply to “Comment on ‘About the calculation of exchange coupling constants using density-functional theory: The role of the self-interaction error’” [J. Chem. Phys. 123, 164110 (2005)] journal March 2006
A simple method to selectively scale down the self-interaction correction journal May 2006
Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals journal November 2006
Many-electron self-interaction error in approximate density functionals journal November 2006
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
Performance of the M06 family of exchange-correlation functionals for predicting magnetic coupling in organic and inorganic molecules journal March 2008
The role of range-separated Hartree–Fock exchange in the calculation of magnetic exchange couplings in transition metal complexes journal January 2011
Valence bond description of antiferromagnetic coupling in transition metal dimers journal May 1981
Energy‐adjusted a b i n i t i o pseudopotentials for the first row transition elements journal January 1987
Localized and canonical atomic orbitals in self‐interaction corrected local density functional approximation journal February 1988
Density‐functional thermochemistry. III. The role of exact exchange journal April 1993
Magnetic coupling constants and vibrational frequencies by extended broken symmetry approach with hybrid functionals journal September 2012
A challenge for density functionals: Self-interaction error increases for systems with a noninteger number of electrons journal August 1998
Generalized gradient approximation to the angle- and system-averaged exchange hole journal September 1998
Communication: Self-interaction correction with unitary invariance in density functional theory journal March 2014
Fermi orbital derivatives in self-interaction corrected density functional theory: Applications to closed shell atoms journal February 2015
Self-interaction corrections applied to Mg-porphyrin, C 60 , and pentacene molecules journal April 2016
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
Fermi-Löwdin orbital self-interaction correction to magnetic exchange couplings journal October 2018
Stretched or noded orbital densities and self-interaction correction in density functional theory journal May 2019
Fermi-Löwdin orbital self-interaction correction using the strongly constrained and appropriately normed meta-GGA functional journal October 2019
The effect of self-interaction error on electrostatic dipoles calculated using density functional theory journal November 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
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
PyFLOSIC: Python-based Fermi–Löwdin orbital self-interaction correction journal August 2020
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
Implementation of Perdew–Zunger self-interaction correction in real space using Fermi–Löwdin orbitals journal February 2021
Static dipole polarizabilities of polyacenes using self-interaction-corrected density functional approximations journal March 2021
Exploring and enhancing the accuracy of interior-scaled Perdew–Zunger self-interaction correction journal March 2021
Self-interaction-corrected Kohn–Sham effective potentials using the density-consistent effective potential method journal August 2021
Self-interaction error overbinds water clusters but cancels in structural energy differences journal May 2020
Electron correlation and the self-interaction error of density functional theory journal June 2002
Towards efficient density functional theory calculations without self-interaction: The Fermi-Löwdin orbital self-interaction correction journal October 2019
Inhomogeneous Electron Gas journal November 1964
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
Antiferromagnetism. Theory of Superexchange Interaction journal July 1950
Self-interaction-free electric dipole polarizabilities for atoms and their ions using the Fermi-Löwdin self-interaction correction journal July 2019
Fermi-Löwdin-orbital self-interaction correction using the optimized-effective-potential method within the Krieger-Li-Iafrate approximation journal April 2021
Escaping the symmetry dilemma through a pair-density interpretation of spin-density functional theory journal June 1995
Optimization of Gaussian basis sets for density-functional calculations journal October 1999
Full self-consistency in the Fermi-orbital self-interaction correction journal May 2017
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
Electronic structure and magnetism of Mn 12 O 12 clusters journal January 1999
Extent and limitations of density-functional theory in describing magnetic systems journal October 2004
First-principles study of spin-electric coupling in a { Cu 3 } single molecular magnet journal October 2010
Strongly Constrained and Appropriately Normed Semilocal Density Functional journal July 2015
Generalized Gradient Approximation Made Simple journal October 1996
Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)] journal February 1997
Assessment of Double-Hybrid Density Functional Theory for Magnetic Exchange Coupling in Manganese Complexes journal April 2019
The Role of Self-Interaction Corrections, Vibrations, and Spin-Orbit in Determining the Ground Spin State in a Simple Heme journal October 2017