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

Journal Article · · European Physical Journal. B, Condensed Matter and Complex Systems
 [1];  [1];  [2];  [3]
  1. Univ. de Oviedo, Oviedo (Spain); Consejo Superior de Investigaciones Cientificas (CSIC), Madrid (Spain). Nanomaterials and Nanotechnology Research Center
  2. City Univ. of New York (CUNY), NY (United States)
  3. Univ. of California, Irvine, CA (United States)

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. In conclusion, many exact results, limits, and expansions about those limits are given in the Appendices.

Research Organization:
Univ. of California, Irvine, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)
Grant/Contract Number:
FG02-08ER46496; FIS2012-34858
OSTI ID:
1595120
Alternate ID(s):
OSTI ID: 1866807
Journal Information:
European Physical Journal. B, Condensed Matter and Complex Systems, Vol. 91, Issue 7; ISSN 1434-6028
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 28 works
Citation information provided by
Web of Science

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Cited By (4)

Accurate double excitations from ensemble density functional calculations journal October 2018
Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation journal March 2019
Special issue in honor of Eberhard K.U. Gross for his 65th birthday journal November 2018
Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation text January 2018

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