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Linear response time-dependent density functional theory of the Hubbard dimer

  • Diego J. Carrascal
  • Jaime Ferrer
  • Neepa Maitra
  • Kieron Burke
Regular Article
Part of the following topical collections:
  1. Topical issue: Special issue in honor of Hardy Gross

Abstract

The asymmetric Hubbard dimer is used to study the density-dependence of the exact frequency-dependent kernel of linear-response time-dependent density functional theory. The exact form of the kernel is given, and the limitations of the adiabatic approximation utilizing the exact ground-state functional are shown. The oscillator strength sum rule is proven for lattice Hamiltonians, and relative oscillator strengths are defined appropriately. The method of Casida for extracting oscillator strengths from a frequency-dependent kernel is demonstrated to yield the exact result with this kernel. An unambiguous way of labelling the nature of excitations is given. The fluctuation-dissipation theorem is proven for the ground-state exchange-correlation energy. The distinction between weak and strong correlation is shown to depend on the ratio of interaction to asymmetry. A simple interpolation between carefully defined weak-correlation and strong-correlation regimes yields a density-functional approximation for the kernel that gives accurate transition frequencies for both the single and double excitations, including charge-transfer excitations. Many exact results, limits, and expansions about those limits are given in the Appendices.

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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Diego J. Carrascal
    • 1
    • 2
  • Jaime Ferrer
    • 1
    • 2
  • Neepa Maitra
    • 3
  • Kieron Burke
    • 4
  1. 1.Department of PhysicsUniversidad de OviedoOviedoSpain
  2. 2.Nanomaterials and Nanotechnology Research Center, CSIC/Universidad de OviedoOviedoSpain
  3. 3.Department of PhysicsHunter College, City University of New YorkNew YorkUSA
  4. 4.Department of Chemistry and of PhysicsUniversity of CaliforniaIrvineUSA

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