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

Fermi-Löwdin-orbital self-interaction correction using the optimized-effective-potential method within the Krieger-Li-Iafrate approximation

Journal Article · · Physical Review A
Perdew-Zunger self-interaction correction (PZ-SIC) offers a route to remove self interaction errors on an orbital-by-orbital basis. A recent formulation of PZ-SIC by Pederson, Ruzsinszky and Perdew proposes restricting the unitary transformation to localized orbitals called Fermi-Löwdin orbitals. This formulation, called the FLOSIC method, simplifies PZ-SIC calculations and was implemented self-consistently using a Jacobi-like (FLOSIC-Jacobi) iteration scheme. In this work we implement the FLOSIC approach using the Krieger-Li-Iafrate (KLI) approximation to the optimized effective potential (OEP). We compare the results of present FLOSIC-KLI approach with FLOSIC-Jacobi scheme for atomic energies, atomization energies, ionization energies, barrier heights, polarizability of chains of hydrogen molecules etc. to validate the FLOSIC-KLI approach. The FLOSICKLI approach, which is within the realm of Kohn-Sham theory, predicts smaller energy gaps between frontier orbitals due to the lowering of eigenvalues of the lowest unoccupied orbitals. Results show that atomic energies, atomization energies, ionization energy as an absolute of highest occupied orbital eigenvalue, and polarizability of chains of hydrogen molecules between the two methods agree within 2%. Lastly the FLOSIC-KLI approach is used to determine the vertical ionization energies of water clusters.
Research Organization:
Central Michigan Univ., 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:
1781837
Journal Information:
Physical Review A, Journal Name: Physical Review A Journal Issue: 4 Vol. 103; ISSN 2469-9926
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (114)

Novel method of self-interaction corrections in density functional calculations journal January 2001
Regional self-interaction correction of density functional theory journal August 2003
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
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
Magnetic Signatures of Hydroxyl‐ and Water‐Terminated Neutral and Tetra‐Anionic Mn 12 ‐Acetate journal June 2019
Interpretation and Automatic Generation of Fermi‐Orbital Descriptors journal September 2019
A statistical exchange approximation for localized electrons journal January 1971
Localized orbitals and the Fermi hole journal January 1982
Localized orbitals based on the fermi hole journal January 1984
A comparative analysis of Hartree-Fock and Kohn-Sham orbital energies journal April 1998
Self-Interaction Corrections Within the Fermi-Orbital-Based Formalism book July 2015
Libxc: A library of exchange and correlation functionals for density functional theory journal October 2012
A mean-field self-interaction correction in density functional theory: implementation and validation for molecules journal October 2003
Polarizabilities as a test of localized approximations to the self-interaction correction journal September 2009
On the Question of the Total Energy in the Fermi–Löwdin Orbital Self-Interaction Correction Method journal June 2018
Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials: Simple yet Efficient journal January 2019
Shrinking Self-Interaction Errors with the Fermi–Löwdin Orbital Self-Interaction-Corrected Density Functional Approximation journal November 2018
Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals journal April 2012
Variational, Self-Consistent Implementation of the Perdew–Zunger Self-Interaction Correction with Complex Optimal Orbitals journal November 2014
Physical Meaning of Virtual Kohn–Sham Orbitals and Orbital Energies: An Ideal Basis for the Description of Molecular Excitations journal September 2014
What Do the Kohn−Sham Orbitals and Eigenvalues Mean? journal April 1999
Phosphorus NMR Chemical Shifts with Self-Interaction Free, Gradient-Corrected DFT journal February 2002
Small Representative Benchmarks for Thermochemical Calculations journal October 2003
Importance of self-interaction-error removal in density functional calculations on water cluster anions journal January 2020
Local self-interaction correction method with a simple scaling factor journal January 2021
The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham orbital energies journal January 2013
Curing difficult cases in magnetic properties prediction with self-interaction corrected density functional theory journal July 2001
A long-range correction scheme for generalized-gradient-approximation exchange functionals journal August 2001
Interpretation of the Kohn–Sham orbital energies as approximate vertical ionization potentials journal February 2002
Local hybrid functionals journal January 2003
Accurate polymer polarizabilities with exact exchange density-functional theory journal December 2003
Scaling down the Perdew-Zunger self-interaction correction in many-electron regions journal March 2006
Density functionals from many-body perturbation theory: The band gap for semiconductors and insulators journal April 2006
A simple method to selectively scale down the self-interaction correction journal May 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
Improved exchange-correlation potential for polarizability and dissociation in density functional theory journal May 2007
Calculation of electric dipole (hyper)polarizabilities by long-range-correction scheme in density functional theory: A systematic assessment for polydiacetylene and polybutatriene oligomers journal March 2008
Self-interaction correction and the optimized effective potential journal July 2008
Orbital energies and negative electron affinities from density functional theory: Insight from the integer discontinuity journal July 2008
Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory journal May 2012
Local‐density Hartree–Fock theory of electronic states of molecules with self‐interaction correction journal March 1984
Density‐functional theory with self‐interaction correction: Application to the lithium molecule a) journal March 1985
Localized and canonical atomic orbitals in self‐interaction corrected local density functional approximation journal February 1988
Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds journal June 1991
A new mixing of Hartree–Fock and local density‐functional theories journal January 1993
Constraining density functional approximations to yield self-interaction free potentials journal June 2012
Self-interaction correction in a real-time Kohn-Sham scheme: Access to difficult excitations in time-dependent density functional theory journal August 2012
The optimized effective potential and the self-interaction correction in density functional theory: Application to molecules journal May 2000
Electronic responses of long chains to electrostatic fields: Hartree-Fock vs. density-functional theory: A model study journal February 2014
Self-interaction corrections in density functional theory journal May 2014
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
Density functional approximations for orbital energies and total energies of molecules and solids journal August 2018
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
Atlas of putative minima and low-lying energy networks of water clusters n = 3–25 journal December 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
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
Understanding band gaps of solids in generalized Kohn–Sham theory journal March 2017
Self-interaction error overbinds water clusters but cancels in structural energy differences journal May 2020
Influence of the long-range exchange effect on dynamic polarizability journal August 2005
Use of Löwdin orthogonalised Fermi orbitals for self-interaction corrections in an iron porphyrin journal September 2016
On derivatives of the energy with respect to total electron number and orbital occupation numbers. A critique of Janak's theorem journal May 2019
Comparison of self-interaction-corrections for metal clusters journal February 2002
Towards efficient density functional theory calculations without self-interaction: The Fermi-Löwdin orbital self-interaction correction journal October 2019
A Simplification of the Hartree-Fock Method journal February 1951
A Variational Approach to the Unipotential Many-Electron Problem journal April 1953
Self-interaction-free electric dipole polarizabilities for atoms and their ions using the Fermi-Löwdin self-interaction correction journal July 2019
Optimized effective atomic central potential journal July 1976
Improved approximate representation of the Hartree-Fock potential in atoms journal June 1977
Exact differential equation for the density and ionization energy of a many-particle system journal November 1984
Systematic approximations to the optimized effective potential: Application to orbital-density-functional theory journal November 1992
Ground-state correlation energies for atomic ions with 3 to 18 electrons journal May 1993
Optimization of Gaussian basis sets for density-functional calculations journal October 1999
Origin of the field-counteracting term of the Kohn-Sham exchange-correlation potential of molecular chains in an electric field journal June 2000
Self-interaction-free time-dependent density-functional theory for molecular processes in strong fields:  High-order harmonic generation of H 2 in intense laser fields journal January 2001
Understanding and correcting the self-interaction error in the electrical response of hydrogen chains journal June 2008
Full self-consistency in the Fermi-orbital self-interaction correction journal May 2017
Proof that ∂ E ∂ n i = ε in density-functional theory journal December 1978
Self-interaction correction to density-functional approximations for many-electron systems journal May 1981
Self-interaction correction for density-functional theory of electronic energy bands of solids journal November 1983
Exact results for the charge and spin densities, exchange-correlation potentials, and density-functional eigenvalues journal March 1985
Variational mesh for quantum-mechanical simulations journal April 1990
Accurate forces in a local-orbital approach to the local-density approximation journal August 1990
Accurate and simple analytic representation of the electron-gas correlation energy journal June 1992
Generalized Kohn-Sham schemes and the band-gap problem journal February 1996
Comment on “Significance of the highest occupied Kohn-Sham eigenvalue” journal December 1997
Magnetic anisotropy barrier for spin tunneling in Mn 12 O 12 molecules journal October 1999
Atomic-orbital-based approximate self-interaction correction scheme for molecules and solids journal January 2007
Self-interaction correction in the LDA + U method journal July 2007
Fractional charge perspective on the band gap in density-functional theory journal March 2008
Koopmans-compliant functionals and their performance against reference molecular data journal August 2014
Electrical Response of Molecular Systems: The Power of Self-Interaction Corrected Kohn-Sham Theory journal April 2008
Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction journal April 2008
Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy journal December 1982
Metal-insulator transition in Kohn-Sham theory and quasiparticle theory journal March 1989
Generalized Gradient Approximation Made Simple journal October 1996
Electric Field Dependence of the Exchange-Correlation Potential in Molecular Chains journal July 1999
Electrical Response of Molecular Chains from Density Functional Theory journal November 2004
Density Functional Theory with Correct Long-Range Asymptotic Behavior journal February 2005
Ultranonlocality and accurate band gaps from a meta-generalized gradient approximation journal November 2019
Density functional theory: Its origins, rise to prominence, and future journal August 2015
Density-functional energy gaps of solids demystified journal June 2018
Tuned Range-Separated Hybrids in Density Functional Theory journal March 2010
The Role of Self-Interaction Corrections, Vibrations, and Spin-Orbit in Determining the Ground Spin State in a Simple Heme journal October 2017

Similar Records

Complex Fermi–Löwdin orbital self-interaction correction
Journal Article · Thu Jun 16 20:00:00 EDT 2022 · Journal of Chemical Physics · OSTI ID:1872758

On the Question of the Total Energy in the Fermi–Löwdin Orbital Self-Interaction Correction Method
Journal Article · Sun Jul 08 20:00:00 EDT 2018 · Journal of Chemical Theory and Computation · OSTI ID:1781804

Towards efficient density functional theory calculations without self-interaction: The Fermi-Löwdin orbital self-interaction correction
Journal Article · Tue Oct 29 20:00:00 EDT 2019 · Journal of Physics. Conference Series · OSTI ID:1781833