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

Ullrich, Carsten A.

doi:10.1103/PhysRevA.100.012516

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:

Ullrich, Carsten A. ^[1]

Univ. of Missouri, Columbia, MO (United States)

Publication Date:: 2019-07-25

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.  doi:10.1103/PhysRevA.100.012516.

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                    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

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                    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.

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@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}

}

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https://doi.org/10.1103/PhysRevA.100.012516

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Figures / Tables:

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.

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Works referenced in this record:

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

Barth, U. von; Hedin, L.
Journal of Physics C: Solid State Physics, Vol. 5, Issue 13
DOI: 10.1088/0022-3719/5/13/012

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

Gunnarsson, O.; Lundqvist, B. I.
Physical Review B, Vol. 13, Issue 10
DOI: 10.1103/PhysRevB.13.4274

Potential in spin-density-functional theory of noncollinear magnetism determined by the many-electron ground state
journal, April 2007

Gidopoulos, Nikitas I.
Physical Review B, Vol. 75, Issue 13
DOI: 10.1103/PhysRevB.75.134408

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

Hohenberg, P.; Kohn, W.
Physical Review, Vol. 136, Issue 3B, p. B864-B871
DOI: 10.1103/PhysRev.136.B864

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

Kohn, W.; Sham, L. J.
Physical Review, Vol. 140, Issue 4A, p. A1133-A1138
DOI: 10.1103/PhysRev.140.A1133

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

Spin-current density-functional theory for a correct treatment of spin-orbit interactions and its application to topological phase transitions
journal, November 2018

Trushin, Egor; Görling, Andreas
Physical Review B, Vol. 98, Issue 20
DOI: 10.1103/PhysRevB.98.205137

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

Capelle, Klaus; Campo, Vivaldo L.
Physics Reports, Vol. 528, Issue 3
DOI: 10.1016/j.physrep.2013.03.002

Density-functional theory for systems with noncollinear spin: Orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer
journal, July 2018

Ullrich, Carsten A.
Physical Review B, Vol. 98, Issue 3
DOI: 10.1103/PhysRevB.98.035140

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

Lima, N. A.; Oliveira, L. N.; Capelle, K.
Europhysics Letters (EPL), Vol. 60, Issue 4
DOI: 10.1209/epl/i2002-00261-y

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

Lima, N. A.; Silva, M. F.; Oliveira, L. N.
Physical Review Letters, Vol. 90, Issue 14
DOI: 10.1103/PhysRevLett.90.146402

Simple parameterization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity
journal, July 2012

França, Vivian V.; Vieira, Daniel; Capelle, Klaus
New Journal of Physics, Vol. 14, Issue 7
DOI: 10.1088/1367-2630/14/7/073021

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

Carrascal, D. J.; Ferrer, J.; Smith, J. C.
Journal of Physics: Condensed Matter, Vol. 27, Issue 39
DOI: 10.1088/0953-8984/27/39/393001

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

Carrascal, D. J.; Ferrer, J.; Smith, J. C.
Journal of Physics: Condensed Matter, Vol. 29, Issue 1
DOI: 10.1088/0953-8984/29/1/019501

Landscape of an exact energy functional
journal, April 2016

Cohen, Aron J.; Mori-Sánchez, Paula
Physical Review A, Vol. 93, Issue 4
DOI: 10.1103/PhysRevA.93.042511

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

França, Vivian V.; Coe, Jeremy P.; D’Amico, Irene
Scientific Reports, Vol. 8, Issue 1
DOI: 10.1038/s41598-017-19018-x

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

Shiba, H.; Pincus, P. A.
Physical Review B, Vol. 5, Issue 5
DOI: 10.1103/PhysRevB.5.1966

Spin electric effects in molecular antiferromagnets
journal, July 2010

Trif, Mircea; Troiani, Filippo; Stepanenko, Dimitrije
Physical Review B, Vol. 82, Issue 4
DOI: 10.1103/PhysRevB.82.045429

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

Nossa, J. F.; Islam, M. F.; Canali, C. M.
Physical Review B, Vol. 85, Issue 8
DOI: 10.1103/PhysRevB.85.085427

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

Kim, Min-Cheol; Sim, Eunji; Burke, Kieron
Physical Review Letters, Vol. 111, Issue 7
DOI: 10.1103/PhysRevLett.111.073003

Quantifying Density Errors in DFT
journal, October 2018

Sim, Eunji; Song, Suhwan; Burke, Kieron
The Journal of Physical Chemistry Letters, Vol. 9, Issue 22
DOI: 10.1021/acs.jpclett.8b02855

Finding Density Functionals with Machine Learning
journal, June 2012

Snyder, John C.; Rupp, Matthias; Hansen, Katja
Physical Review Letters, Vol. 108, Issue 25
DOI: 10.1103/PhysRevLett.108.253002

Inhomogeneous Electron Gas
journal, March 1973

Rajagopal, A. K.; Callaway, J.
Physical Review B, Vol. 7, Issue 5
DOI: 10.1103/physrevb.7.1912

Understanding and reducing errors in density functional calculations
text, January 2012

Kim, Min-Cheol; Sim, Eunji; Burke, Kieron
arXiv
DOI: 10.48550/arxiv.1212.3054

The Hubbard Dimer: A density functional case study of a many-body problem
text, January 2015

Carrascal, Diego; Ferrer, Jaime; Smith, Justin C.
arXiv
DOI: 10.48550/arxiv.1502.02194

Landscape of an exact energy functional
text, January 2015

Cohen, Aron J.; Mori-Sánchez, Paula
arXiv
DOI: 10.48550/arxiv.1506.02230

Density-functional theory for systems with noncollinear spin: orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer
text, January 2018

Ullrich, Carsten A.
arXiv
DOI: 10.48550/arxiv.1805.06417

Quantifying Density Errors in DFT
text, January 2018

Sim, Eunji; Song, Suhwan; Burke, Kieron
arXiv
DOI: 10.48550/arxiv.1809.10347

Works referencing / citing this record:

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

Pluhar, Edward A.; Ullrich, Carsten A.
Physical Review B, Vol. 100, Issue 12
DOI: 10.1103/physrevb.100.125135

Exchange-correlation magnetic fields in spin-density-functional theory
text, January 2019

Pluhar, Edward A.; Ullrich, Carsten A.
arXiv
DOI: 10.48550/arxiv.1907.08724

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

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Similar Records

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

Abstract

Citation Formats

Figures / Tables:

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

Potential in spin-density-functional theory of noncollinear magnetism determined by the many-electron ground state journal, April 2007

Spin in density-functional theory journal, August 2012

Challenges for Density Functional Theory journal, December 2011

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

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

Spin-current density-functional theory for a correct treatment of spin-orbit interactions and its application to topological phase transitions journal, November 2018

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

Density-functional theory for systems with noncollinear spin: Orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer journal, July 2018

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

Simple parameterization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity journal, July 2012

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

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

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

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

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

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

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

Understanding and reducing errors in density functional calculations text, January 2012

The Hubbard Dimer: A density functional case study of a many-body problem text, January 2015

Landscape of an exact energy functional text, January 2015

Density-functional theory for systems with noncollinear spin: orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer text, January 2018

Quantifying Density Errors in DFT text, January 2018

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

Exchange-correlation magnetic fields in spin-density-functional theory text, January 2019

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

Potential in spin-density-functional theory of noncollinear magnetism determined by the many-electron ground state
journal, April 2007

Spin in density-functional theory
journal, August 2012

Challenges for Density Functional Theory
journal, December 2011

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

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

Spin-current density-functional theory for a correct treatment of spin-orbit interactions and its application to topological phase transitions
journal, November 2018

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

Density-functional theory for systems with noncollinear spin: Orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer
journal, July 2018

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

Simple parameterization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity
journal, July 2012

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

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

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

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

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

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

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

Understanding and reducing errors in density functional calculations
text, January 2012

The Hubbard Dimer: A density functional case study of a many-body problem
text, January 2015

Landscape of an exact energy functional
text, January 2015

Density-functional theory for systems with noncollinear spin: orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer
text, January 2018

Quantifying Density Errors in DFT
text, January 2018

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

Exchange-correlation magnetic fields in spin-density-functional theory
text, January 2019