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Title: Density Matrix Implementation of the Fermi–Löwdin Orbital Self-Interaction Correction Method

Journal Article · · Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory
ORCiD logo [1];  [2]; ORCiD logo [3]
  1. Univ. de Buenos Aires (Argentina)
  2. Univ. of Texas, El Paso, TX (United States)
  3. Central Michigan Univ., Mount Pleasant, MI (United States)
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The Fermi–Löwdin orbital self-interaction correction (FLOSIC) method effectively provides a transformation from canonical orbitals to localized Fermi–Löwdin orbitals which are used to remove the self-interaction error in the Perdew–Zunger (PZ) framework. This transformation is solely determined by a set of points in space, called Fermi–Löwdin descriptors (FODs), and the occupied canonical orbitals or the density matrix. In this work, we provide a detailed workflow for the implementation of the FLOSIC method for removal of self-interaction error in DFT calculations in an orbital-by-orbital basis that takes advantage of the unitary invariant nature of the FLOSIC method. In this way, it is possible to cast the self-consistent energy minimization at fixed FODs in the same manner than standard Kohn–Sham with one additional term in the Kohn–Sham Hamiltonian that introduces the PZ self-interaction correction. Each energy minimization iteration is divided in two substeps, one for the density matrix and one for the FODs. Expressions for the effective Kohn–Sham matrix and FOD gradients are provided such that its implementation is suitable for most electronic structure codes. Here, we analyze the convergence characteristics of the algorithm and present applications for the evaluation of NMR shielding constants and real-time time-dependent DFT simulations based on the Liouville–von Neumann equation to calculate excitation energies.

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:
1925162
Journal Information:
Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory, Vol. 127, Issue 2; ISSN 1089-5639
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

References (54)

Density functional studies of molecular magnets journal September 2006
A bird's-eye view of density-functional theory journal January 2006
Density functional theory for transition metals and transition metal chemistry journal January 2009
Density functional theory: Its origins, rise to prominence, and future journal August 2015
Localized orbital scaling correction for systematic elimination of delocalization error in density functional approximations journal September 2017
Local Scaling Correction for Reducing Delocalization Error in Density Functional Approximations journal February 2015
Density functional theory and the band gap problem journal March 1985
Core ionization potentials from self-interaction corrected Kohn-Sham orbital energies journal November 2007
Orbital interactions in metal dimer complexes journal August 1975
Localized and canonical atomic orbitals in self‐interaction corrected local density functional approximation journal February 1988
Ionization potentials and electron affinities in the Perdew–Zunger self-interaction corrected density-functional theory journal May 2005
Scaling down the Perdew-Zunger self-interaction correction in many-electron regions journal March 2006
Effect of the Perdew–Zunger self-interaction correction on the thermochemical performance of approximate density functionals journal January 2004
Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals journal November 2006
Paradox of Self-Interaction Correction book September 2015
A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction journal December 2019
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
Fermi orbital derivatives in self-interaction corrected density functional theory: Applications to closed shell atoms journal February 2015
Communication: Self-interaction correction with unitary invariance in density functional theory journal March 2014
On the Non‐Orthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals journal March 1950
Canonical Configurational Interaction Procedure journal April 1960
A fast intrinsic localization procedure applicable for a b i n i t i o and semiempirical linear combination of atomic orbital wave functions journal May 1989
PyFLOSIC: Python-based Fermi–Löwdin orbital self-interaction correction journal August 2020
Additional Insights between Fermi–Löwdin Orbital SIC and the Localization Equation Constraints in SIC-DFT journal October 2018
Improved band gaps and structural properties from Wannier–Fermi–Löwdin self-interaction corrections for periodic systems journal December 2020
Implementation of Perdew–Zunger self-interaction correction in real space using Fermi–Löwdin orbitals journal February 2021
On Löwdin's method of symmetric orthogonalization*: Löwdin's Method of Symmetric Orthogonalization journal January 2002
Self-Interaction Corrections Within the Fermi-Orbital-Based Formalism book July 2015
Variational, Self-Consistent Implementation of the Perdew–Zunger Self-Interaction Correction with Complex Optimal Orbitals journal November 2014
Analytic energy gradients for the spin-free exact two-component theory using an exact block diagonalization for the one-electron Dirac Hamiltonian journal August 2011
Initial Fermi orbital descriptors for FLOSIC calculations: The quick-FOD method journal October 2021
Interpretation and Automatic Generation of Fermi‐Orbital Descriptors journal September 2019
Shrinking Self-Interaction Errors with the Fermi–Löwdin Orbital Self-Interaction-Corrected Density Functional Approximation journal November 2018
The effect of self-interaction error on electrostatic dipoles calculated using density functional theory journal November 2019
Fermi-Löwdin orbital self-interaction correction to magnetic exchange couplings journal October 2018
Self-interaction error overbinds water clusters but cancels in structural energy differences journal May 2020
Fermi–Löwdin orbital self-interaction correction of adsorption energies on transition metal ions journal April 2022
Static dipole polarizabilities of polyacenes using self-interaction-corrected density functional approximations journal March 2021
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
Systematic approximations to the optimized effective potential: Application to orbital-density-functional theory journal November 1992
Curing difficult cases in magnetic properties prediction with self-interaction corrected density functional theory journal July 2001
Ab Initio Methods for the Calculation of NMR Shielding and Indirect Spin−Spin Coupling Constants journal January 1999
On the exponential solution of differential equations for a linear operator journal November 1954
Propagators for the time-dependent Kohn–Sham equations journal August 2004
Simulating molecular conductance using real-time density functional theory journal October 2006
Complex Orbitals, Multiple Local Minima, and Symmetry Breaking in Perdew–Zunger Self-Interaction Corrected Density Functional Theory Calculations journal June 2016
Complex Fermi–Löwdin orbital self-interaction correction journal June 2022
Comparison of DFT Methods for Molecular Orbital Eigenvalue Calculations journal March 2007
Scaling of the self-energy correction to the HOMO-LUMO gap with magnesium cluster size and its potential for extrapolating to larger magnesium clusters journal July 2018
Self-interaction-corrected Kohn–Sham effective potentials using the density-consistent effective potential method journal August 2021
Density‐functional theory with self‐interaction correction: Application to the lithium molecule a) journal March 1985
Comment on “Additional Insights Between Fermi-Löwdin Orbital SIC and the Localization Equation Constraints in SIC-DFT” journal April 2019
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
DFT Calculations on Charge-Transfer States of a Carotenoid-Porphyrin-C 60 Molecular Triad journal March 2009

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Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Algorithms
Chemical calculations
Density functional theory
Energy
Hamiltonians