Accurate double excitations from ensemble density functional calculations

Sagredo, Francisca; Burke, Kieron

doi:10.1063/1.5043411

Title: Accurate double excitations from ensemble density functional calculations

Abstract

The recent use of a new ensemble in density functional theory (DFT) to produce direct corrections to the Kohn-Sham transitions yields the elusive double excitations that are missed by time-dependent DFT (TDDFT) with the standard adiabatic approximation. But accuracies are lower than for single excitations, and formal arguments about TDDFT suggest that a correction kernel is needed. In principle, ensemble DFT with direct corrections at the exchange level must yield accurate doubles in the weakly correlated limit. We illustrate with exact calculations and analytic results on the Hubbard dimer. Lastly, we also explain the error in formal arguments in TDDFT.

Authors:

Sagredo, Francisca ^[1];

^[1]

Univ. of California, Irvine, CA (United States)

Publication Date:: Tue Oct 02 00:00:00 EDT 2018

Research Org.:: Univ. of California, Irvine, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1595108

Alternate Identifier(s):: OSTI ID: 1475243

Grant/Contract Number:: FG02-08ER46496

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 149; Journal Issue: 13; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

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                    Sagredo, Francisca, and Burke, Kieron. Accurate double excitations from ensemble density functional calculations.  United States: N. p., 2018. 
Web.  doi:10.1063/1.5043411.

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                    Sagredo, Francisca, & Burke, Kieron. Accurate double excitations from ensemble density functional calculations.  United States.  https://doi.org/10.1063/1.5043411

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                    Sagredo, Francisca, and Burke, Kieron. Tue .  
"Accurate double excitations from ensemble density functional calculations".  United States.  https://doi.org/10.1063/1.5043411.  https://www.osti.gov/servlets/purl/1595108.

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@article{osti_1595108,

  title        = {Accurate double excitations from ensemble density functional calculations},

  author       = {Sagredo, Francisca and Burke, Kieron},

  abstractNote = {The recent use of a new ensemble in density functional theory (DFT) to produce direct corrections to the Kohn-Sham transitions yields the elusive double excitations that are missed by time-dependent DFT (TDDFT) with the standard adiabatic approximation. But accuracies are lower than for single excitations, and formal arguments about TDDFT suggest that a correction kernel is needed. In principle, ensemble DFT with direct corrections at the exchange level must yield accurate doubles in the weakly correlated limit. We illustrate with exact calculations and analytic results on the Hubbard dimer. Lastly, we also explain the error in formal arguments in TDDFT.},

  doi          = {10.1063/1.5043411},

  journal      = {Journal of Chemical Physics},

  number       = 13,

  volume       = 149,

  place        = {United States},

  year         = {Tue Oct 02 00:00:00 EDT 2018},

  month        = {Tue Oct 02 00:00:00 EDT 2018}

}

Copy to clipboard

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Works referenced in this record:

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Works referencing / citing this record:

Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation
text, January 2018

Deur, Killian; Fromager, Emmanuel
arXiv
DOI: 10.48550/arxiv.1812.02461

Complex adiabatic connection: A hidden non-Hermitian path from ground to excited states
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Burton, Hugh G. A.; Thom, Alex J. W.; Loos, Pierre-François
The Journal of Chemical Physics, Vol. 150, Issue 4
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Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation
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Deur, Killian; Fromager, Emmanuel
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Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer
text, January 2020

Baker, Thomas E.; Poulin, David
arXiv
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Title: Accurate double excitations from ensemble density functional calculations

Abstract

Citation Formats

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

Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory journal, May 2018

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Double excitations within time-dependent density functional theory linear response journal, April 2004

Exploring weight-dependent density-functional approximations for ensembles in the Hubbard dimer journal, July 2018

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

Perspective: Fundamental aspects of time-dependent density functional theory journal, June 2016

Assessment of dressed time-dependent density-functional theory for the low-lying valence states of 28 organic chromophores journal, November 2011

Excitation energies from density functional perturbation theory journal, December 1997

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Density-functional theory for ensembles of fractionally occupied states. II. Application to the He atom journal, April 1988

Ghost- and self-interaction-free ensemble calculations with local exchange–correlation potential for atoms journal, October 2003

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

Time-dependent density functional theory: Past, present, and future text, January 2004

A dressed TDDFT treatment of the 21Ag states of butadiene and hexatriene journal, May 2004

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Excited states in density functional theory journal, January 1998

Exact and approximate Kohn-Sham potentials in ensemble density-functional theory text, January 2014

Exact ensemble density functional theory for excited states in a model system: Investigating the weight dependence of the correlation energy journal, January 2017

Electron correlations in narrow energy bands journal, November 1963

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Hardness of molecules and the band gap of solids within the Kohn-Sham formalism: A perturbation-scaling approach journal, December 1995

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

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Coordinate scaling and adiabatic connection formula for ensembles of fractionally occupied excited states journal, November 1995

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Complex adiabatic connection: A hidden non-Hermitian path from ground to excited states journal, January 2019

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Density-functional theory for systems with noncollinear spin: orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer
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Time-dependent density functional theory: Past, present, and future
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The Hubbard Dimer: A density functional case study of a many-body problem
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Assessment of Dressed Time-Dependent Density-Functional Theory for the Low-Lying Valence States of 28 Organic Chromophores
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Excitations and benchmark ensemble density functional theory for two electrons
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Generalised adiabatic connection in ensemble density-functional theory for excited states: example of the H ₂ molecule
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Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles
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Ghost-interaction correction in ensemble density-functional theory for excited states with and without range separation
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Double excitations within time-dependent density functional theory linear response
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Exploring weight-dependent density-functional approximations for ensembles in the Hubbard dimer
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The Hubbard dimer: a density functional case study of a many-body problem
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Perspective: Fundamental aspects of time-dependent density functional theory
journal, June 2016

Assessment of dressed time-dependent density-functional theory for the low-lying valence states of 28 organic chromophores
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Excitation energies from density functional perturbation theory
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Excitations and benchmark ensemble density functional theory for two electrons
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Fundamentals of Time-Dependent Density Functional Theory
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Density-functional theory for ensembles of fractionally occupied states. II. Application to the He atom
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Ghost- and self-interaction-free ensemble calculations with local exchange–correlation potential for atoms
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Density functionals and model Hamiltonians: Pillars of many-particle physics
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A dressed TDDFT treatment of the 21Ag states of butadiene and hexatriene
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Excited states in density functional theory
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Exact and approximate Kohn-Sham potentials in ensemble density-functional theory
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Exact ensemble density functional theory for excited states in a model system: Investigating the weight dependence of the correlation energy
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Electron correlations in narrow energy bands
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Hardness of molecules and the band gap of solids within the Kohn-Sham formalism: A perturbation-scaling approach
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Density-functional theory for systems with noncollinear spin: Orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer
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