skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: (Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer

Abstract

Based on the Hohenberg-Kohn theorem of density-functional theory (DFT), all observable quantities of systems of interacting electrons can be expressed as functionals of the ground-state density. This includes, in principle, the spin polarization (magnetization) of open-shell systems; the explicit form of the magnetization as a functional of the total density is, yet, unknown. In practice, open-shell systems are always treated with spin-DFT, where the basic variables are the spin densities. In this work, the relation between DFT and spin-DFT for open-shell systems is illustrated and the exact magnetization density functional is obtained for the half-filled Hubbard trimer. Errors arising from spin-restricted and -unrestricted exact-exchange Kohn-Sham calculations are analyzed and partially cured via the exact magnetization functional.

Authors:
 [1]
  1. Univ. of Missouri, Columbia, MO (United States)
Publication Date:
Research Org.:
Univ. of Missouri, Columbia, MO (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1545508
Alternate Identifier(s):
OSTI ID: 1545424
Grant/Contract Number:  
SC0019109
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 100; Journal Issue: 1; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; Density-functional theory; noncollinear magnetism; Hubbard model

Citation Formats

Ullrich, Carsten A. (Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer. United States: N. p., 2019. Web. https://doi.org/10.1103/PhysRevA.100.012516.
Ullrich, Carsten A. (Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer. United States. https://doi.org/10.1103/PhysRevA.100.012516
Ullrich, Carsten A. Thu . "(Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer". United States. https://doi.org/10.1103/PhysRevA.100.012516. https://www.osti.gov/servlets/purl/1545508.
@article{osti_1545508,
title = {(Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer},
author = {Ullrich, Carsten A.},
abstractNote = {Based on the Hohenberg-Kohn theorem of density-functional theory (DFT), all observable quantities of systems of interacting electrons can be expressed as functionals of the ground-state density. This includes, in principle, the spin polarization (magnetization) of open-shell systems; the explicit form of the magnetization as a functional of the total density is, yet, unknown. In practice, open-shell systems are always treated with spin-DFT, where the basic variables are the spin densities. In this work, the relation between DFT and spin-DFT for open-shell systems is illustrated and the exact magnetization density functional is obtained for the half-filled Hubbard trimer. Errors arising from spin-restricted and -unrestricted exact-exchange Kohn-Sham calculations are analyzed and partially cured via the exact magnetization functional.},
doi = {10.1103/PhysRevA.100.012516},
journal = {Physical Review A},
number = 1,
volume = 100,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: Total ground-state energies of the linear and triangular asymmetric half-filled Hubbard trimer with V1 = 1, V2 = 0, and V3 = 2, comparing exact results with XX and XXr Kohn-Sham calculations.

Save / Share:

Works referenced in this record:

A local exchange-correlation potential for the spin polarized case. i
journal, July 1972


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


Spin in density-functional theory
journal, August 2012

  • Jacob, Christoph R.; Reiher, Markus
  • International Journal of Quantum Chemistry, Vol. 112, Issue 23
  • DOI: 10.1002/qua.24309

Challenges for Density Functional Theory
journal, December 2011

  • Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr200107z

Perspective: Fifty years of density-functional theory in chemical physics
journal, May 2014

  • Becke, Axel D.
  • The Journal of Chemical Physics, Vol. 140, Issue 18
  • DOI: 10.1063/1.4869598

Inhomogeneous Electron Gas
journal, November 1964


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


Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed
journal, March 2009

  • Perdew, John P.; Ruzsinszky, Adrienn; Constantin, Lucian A.
  • Journal of Chemical Theory and Computation, Vol. 5, Issue 4
  • DOI: 10.1021/ct800531s

Density functionals and model Hamiltonians: Pillars of many-particle physics
journal, July 2013


Density-functional study of the Mott gap in the Hubbard model
journal, November 2002


Density Functionals Not Based on the Electron Gas: Local-Density Approximation for a Luttinger Liquid
journal, April 2003


The Hubbard dimer: a density functional case study of a many-body problem
journal, September 2015


Corrigendum: The Hubbard dimer: a density functional case study of a many-body problem (2015 J. Phys.: Condens. Matter 27 393001)
journal, November 2016


Landscape of an exact energy functional
journal, April 2016


Linear response time-dependent density functional theory of the Hubbard dimer
journal, July 2018

  • Carrascal, Diego J.; Ferrer, Jaime; Maitra, Neepa
  • The European Physical Journal B, Vol. 91, Issue 7
  • DOI: 10.1140/epjb/e2018-90114-9

Testing density-functional approximations on a lattice and the applicability of the related Hohenberg-Kohn-like theorem
journal, January 2018


Melting a Hubbard dimer: benchmarks of ‘ALDA’ for quantum thermodynamics
journal, October 2018

  • Herrera, Marcela; Zawadzki, Krissia; D’Amico, Irene
  • The European Physical Journal B, Vol. 91, Issue 10
  • DOI: 10.1140/epjb/e2018-90186-5

Thermodynamic Properties of the One-Dimensional Half-Filled-Band Hubbard Model
journal, March 1972


Spin electric effects in molecular antiferromagnets
journal, July 2010


First-principles studies of spin-orbit and Dzyaloshinskii-Moriya interactions in the {Cu 3 } single-molecule magnet
journal, February 2012


Hubbard Trimer with Spin–Orbit Coupling: Hartree–Fock Solutions, (Non)Collinearity, and Anisotropic Spin Hamiltonian
journal, February 2019

  • Ghassemi Tabrizi, Shadan; Arbuznikov, Alexei V.; Kaupp, Martin
  • The Journal of Physical Chemistry A, Vol. 123, Issue 12
  • DOI: 10.1021/acs.jpca.8b11959

DFT Calculations on the Spin-Crossover Complex Fe(salen)(NO):  A Quest for the Best Functional
journal, November 2007

  • Conradie, Jeanet; Ghosh, Abhik
  • The Journal of Physical Chemistry B, Vol. 111, Issue 44
  • DOI: 10.1021/jp074480t

Can DFT Accurately Predict Spin Densities? Analysis of Discrepancies in Iron Nitrosyl Complexes
journal, August 2011

  • Boguslawski, Katharina; Jacob, Christoph R.; Reiher, Markus
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 9
  • DOI: 10.1021/ct1006218

Benchmarks and Reliable DFT Results for Spin Gaps of Small Ligand Fe(II) Complexes
journal, March 2018

  • Song, Suhwan; Kim, Min-Cheol; Sim, Eunji
  • Journal of Chemical Theory and Computation, Vol. 14, Issue 5
  • DOI: 10.1021/acs.jctc.7b01196

Understanding and Reducing Errors in Density Functional Calculations
journal, August 2013


Quantifying Density Errors in DFT
journal, October 2018


Finding Density Functionals with Machine Learning
journal, June 2012


Inhomogeneous Electron Gas
journal, March 1973


    Works referencing / citing this record:

    Exchange-correlation magnetic fields in spin-density-functional theory
    journal, September 2019


      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.