Linear response time-dependent density functional theory of the Hubbard dimer
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. In conclusion, many exact results, limits, and expansions about those limits are given in the Appendices.
- Authors:
-
- Univ. de Oviedo, Oviedo (Spain); Consejo Superior de Investigaciones Cientificas (CSIC), Madrid (Spain). Nanomaterials and Nanotechnology Research Center
- City Univ. of New York (CUNY), NY (United States)
- Univ. of California, Irvine, CA (United States)
- Publication Date:
- Research Org.:
- Univ. of California, Irvine, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)
- OSTI Identifier:
- 1595120
- Alternate Identifier(s):
- OSTI ID: 1866807
- Grant/Contract Number:
- FG02-08ER46496; FIS2012-34858
- Resource Type:
- Accepted Manuscript
- Journal Name:
- European Physical Journal. B, Condensed Matter and Complex Systems
- Additional Journal Information:
- Journal Volume: 91; Journal Issue: 7; Journal ID: ISSN 1434-6028
- Publisher:
- Springer
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Carrascal, Diego J., Ferrer, Jaime, Maitra, Neepa, and Burke, Kieron. Linear response time-dependent density functional theory of the Hubbard dimer. United States: N. p., 2018.
Web. doi:10.1140/epjb/e2018-90114-9.
Carrascal, Diego J., Ferrer, Jaime, Maitra, Neepa, & Burke, Kieron. Linear response time-dependent density functional theory of the Hubbard dimer. United States. https://doi.org/10.1140/epjb/e2018-90114-9
Carrascal, Diego J., Ferrer, Jaime, Maitra, Neepa, and Burke, Kieron. Mon .
"Linear response time-dependent density functional theory of the Hubbard dimer". United States. https://doi.org/10.1140/epjb/e2018-90114-9. https://www.osti.gov/servlets/purl/1595120.
@article{osti_1595120,
title = {Linear response time-dependent density functional theory of the Hubbard dimer},
author = {Carrascal, Diego J. and Ferrer, Jaime and Maitra, Neepa and Burke, Kieron},
abstractNote = {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.},
doi = {10.1140/epjb/e2018-90114-9},
journal = {European Physical Journal. B, Condensed Matter and Complex Systems},
number = 7,
volume = 91,
place = {United States},
year = {Mon Jul 02 00:00:00 EDT 2018},
month = {Mon Jul 02 00:00:00 EDT 2018}
}
Web of Science
Works referenced in this record:
Molecular excitation energies from time-dependent density functional theory
journal, April 2000
- Grabo, T.; Petersilka, M.; Gross, E. K. U.
- Journal of Molecular Structure: THEOCHEM, Vol. 501-502
Asymptotic correction of the exchange–correlation kernel of time-dependent density functional theory for long-range charge-transfer excitations
journal, July 2004
- Gritsenko, Oleg; Baerends, Evert Jan
- The Journal of Chemical Physics, Vol. 121, Issue 2
Local density-functional theory of frequency-dependent linear response
journal, December 1985
- Gross, E. K. U.; Kohn, Walter
- Physical Review Letters, Vol. 55, Issue 26
Undoing static correlation: Long-range charge transfer in time-dependent density-functional theory
journal, June 2005
- Maitra, Neepa T.
- The Journal of Chemical Physics, Vol. 122, Issue 23
Time-dependent V-representability on lattice systems
journal, July 2008
- Li, Yonghui; Ullrich, C. A.
- The Journal of Chemical Physics, Vol. 129, Issue 4
Treatment of electronic excitations within the adiabatic approximation of time dependent density functional theory
journal, July 1996
- Bauernschmitt, Rüdiger; Ahlrichs, Reinhart
- Chemical Physics Letters, Vol. 256, Issue 4-5
Nonadiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density-Functional Theory
journal, April 2018
- Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole
- Physical Review Letters, Vol. 120, Issue 15
Density functional theory of electron transfer beyond the Born-Oppenheimer approximation: Case study of LiF
journal, February 2018
- Li, Chen; Requist, Ryan; Gross, E. K. U.
- The Journal of Chemical Physics, Vol. 148, Issue 8
Über die Zahl der Dispersionselektronen, die einem stationären Zustande zugeordnet sind. (Vorläufige Mitteilung)
journal, July 1925
- Thomas, W.
- Die Naturwissenschaften, Vol. 13, Issue 28
Fundamentals of Time-Dependent Density Functional Theory
book, January 2012
- Marques, Miguel A. L.; Maitra, Neepa T.; Nogueira, Fernando M. S.
- Lecture Notes in Physics
Three-dimensional dynamics of a fermionic Mott wedding-cake in clean and disordered optical lattices
journal, September 2013
- Kartsev, A.; Karlsson, D.; Privitera, A.
- Scientific Reports, Vol. 3, Issue 1
Progress in Time-Dependent Density-Functional Theory
journal, May 2012
- Casida, M. E.; Huix-Rotllant, M.
- Annual Review of Physical Chemistry, Vol. 63, Issue 1
On the determination of excitation energies using density functional theory
journal, January 2000
- Tozer, David J.; Handy, Nicholas C.
- Physical Chemistry Chemical Physics, Vol. 2, Issue 10
Real-time, real-space implementation of the linear response time-dependent density-functional theory
journal, April 2006
- Yabana, K.; Nakatsukasa, T.; Iwata, J. -I.
- physica status solidi (b), Vol. 243, Issue 5
Density functionals and model Hamiltonians: Pillars of many-particle physics
journal, July 2013
- Capelle, Klaus; Campo, Vivaldo L.
- Physics Reports, Vol. 528, Issue 3
Frequency Dependence of the Exact Exchange-Correlation Kernel of Time-Dependent Density-Functional Theory
journal, February 2014
- Thiele, M.; Kümmel, S.
- Physical Review Letters, Vol. 112, Issue 8
Correlated electrons in high-temperature superconductors
journal, July 1994
- Dagotto, Elbio
- Reviews of Modern Physics, Vol. 66, Issue 3
The calculations of excited-state properties with Time-Dependent Density Functional Theory
journal, January 2013
- Adamo, Carlo; Jacquemin, Denis
- Chem. Soc. Rev., Vol. 42, Issue 3
On the mapping of time-dependent densities onto potentials in quantum mechanics
journal, January 2008
- Baer, Roi
- The Journal of Chemical Physics, Vol. 128, Issue 4
Extensive TD-DFT Benchmark: Singlet-Excited States of Organic Molecules
journal, August 2009
- Jacquemin, Denis; Wathelet, Valérie; Perpète, Eric A.
- Journal of Chemical Theory and Computation, Vol. 5, Issue 9
Application of the dressed time-dependent density functional theory for the excited states of linear polyenes
journal, April 2009
- Mazur, Grzegorz; Włodarczyk, Radosław
- Journal of Computational Chemistry, Vol. 30, Issue 5
Twenty-five Years of High-Temperature Superconductivity – A Personal Review
journal, July 2013
- Anderson, Philip W.
- Journal of Physics: Conference Series, Vol. 449
Does density functional theory contribute to the understanding of excited states of unsaturated organic compounds?
journal, October 1999
- Tozer, David J.; Amos, Roger D.; Handy, Nicholas C.
- Molecular Physics, Vol. 97, Issue 7
Tuned Range-Separated Hybrids in Density Functional Theory
journal, March 2010
- Baer, Roi; Livshits, Ester; Salzner, Ulrike
- Annual Review of Physical Chemistry, Vol. 61, Issue 1
Doping a Mott insulator: Physics of high-temperature superconductivity
journal, January 2006
- Lee, Patrick A.; Nagaosa, Naoto; Wen, Xiao-Gang
- Reviews of Modern Physics, Vol. 78, Issue 1
Challenging adiabatic time-dependent density functional theory with a Hubbard dimer: the case of time-resolved long-range charge transfer
journal, January 2014
- Fuks, Johanna I.; Maitra, Neepa T.
- Phys. Chem. Chem. Phys., Vol. 16, Issue 28
A long-range-corrected time-dependent density functional theory
journal, May 2004
- Tawada, Yoshihiro; Tsuneda, Takao; Yanagisawa, Susumu
- The Journal of Chemical Physics, Vol. 120, Issue 18
Theory of the Insulating State
journal, January 1964
- Kohn, Walter
- Physical Review, Vol. 133, Issue 1A
Landau parameters of almost-localized Fermi liquids
journal, June 1987
- Baeriswyl, D.; Gros, C.; Rice, T. M.
- Physical Review B, Vol. 35, Issue 16
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
Relationship between long-range charge-transfer excitation energy error and integer discontinuity in Kohn–Sham theory
journal, December 2003
- Tozer, David J.
- The Journal of Chemical Physics, Vol. 119, Issue 24
Excitation energies of dissociating H2: A problematic case for the adiabatic approximation of time-dependent density functional theory
journal, November 2000
- Gritsenko, O. V.; van Gisbergen, S. J. A.; Görling, A.
- The Journal of Chemical Physics, Vol. 113, Issue 19
Double excitations within time-dependent density functional theory linear response
journal, April 2004
- Maitra, Neepa T.; Zhang, Fan; Cave, Robert J.
- The Journal of Chemical Physics, Vol. 120, Issue 13
The exchange-correlation energy of a metallic surface
journal, December 1975
- Langreth, D. C.; Perdew, J. P.
- Solid State Communications, Vol. 17, Issue 11
Optical spectrum of a Hubbard chain
journal, September 1977
- Maldague, Pierre F.
- Physical Review B, Vol. 16, Issue 6
Exact time-dependent density functional theory for impurity models
journal, January 2013
- Schmitteckert, Peter; Dzierzawa, Michael; Schwab, Peter
- Physical Chemistry Chemical Physics, Vol. 15, Issue 15
Reliable Prediction of Charge Transfer Excitations in Molecular Complexes Using Time-Dependent Density Functional Theory
journal, March 2009
- Stein, Tamar; Kronik, Leeor; Baer, Roi
- Journal of the American Chemical Society, Vol. 131, Issue 8
Perspective: Fundamental aspects of time-dependent density functional theory
journal, June 2016
- Maitra, Neepa T.
- The Journal of Chemical Physics, Vol. 144, Issue 22
Assessment of dressed time-dependent density-functional theory for the low-lying valence states of 28 organic chromophores
journal, November 2011
- Huix-Rotllant, Miquel; Ipatov, Andrei; Rubio, Angel
- Chemical Physics, Vol. 391, Issue 1
�ber die Zahl der Dispersionselektronen, die einem station�ren Zustand zugeordnet sind
journal, December 1925
- Reiche, F.; Thomas, W.
- Zeitschrift f�r Physik, Vol. 34, Issue 1
Perspectives on double-excitations in TDDFT
journal, November 2011
- Elliott, Peter; Goldson, Sharma; Canahui, Chris
- Chemical Physics, Vol. 391, Issue 1
Dynamical self-stabilization of the Mott insulator: Time evolution of the density and entanglement entropy of out-of-equilibrium cold fermion gases
journal, January 2011
- Karlsson, D.; Verdozzi, C.; Odashima, M. M.
- EPL (Europhysics Letters), Vol. 93, Issue 2
Dynamic polarizabilities and excitation spectra from a molecular implementation of time‐dependent density‐functional response theory: N 2 as a case study
journal, April 1996
- Jamorski, Christine; Casida, Mark E.; Salahub, Dennis R.
- The Journal of Chemical Physics, Vol. 104, Issue 13
Dynamical Coulomb Blockade and the Derivative Discontinuity of Time-Dependent Density Functional Theory
journal, June 2010
- Kurth, S.; Stefanucci, G.; Khosravi, E.
- Physical Review Letters, Vol. 104, Issue 23
Analytic density functionals with initial-state dependence and memory
journal, August 2013
- Ruggenthaler, M.; Nielsen, S. E. B.; van Leeuwen, R.
- Physical Review A, Vol. 88, Issue 2
Adiabatic and local approximations for the Kohn-Sham potential in time-dependent Hubbard chains
journal, May 2014
- Mancini, L.; Ramsden, J. D.; Hodgson, M. J. P.
- Physical Review B, Vol. 89, Issue 19
�ber die Gesamtst�rke der von einem Zustande ausgehenden Absorptionslinien
journal, December 1925
- Kuhn, W.
- Zeitschrift f�r Physik, Vol. 33, Issue 1
A dressed TDDFT treatment of the 21Ag states of butadiene and hexatriene
journal, May 2004
- Cave, Robert J.; Zhang, Fan; Maitra, Neepa T.
- Chemical Physics Letters, Vol. 389, Issue 1-3
Density-Functional Theory for Time-Dependent Systems
journal, March 1984
- Runge, Erich; Gross, E. K. U.
- Physical Review Letters, Vol. 52, Issue 12
Inhomogeneous Electron Gas
journal, November 1964
- Hohenberg, P.; Kohn, W.
- Physical Review, Vol. 136, Issue 3B, p. B864-B871
Charge transfer in time-dependent density-functional theory: Insights from the asymmetric Hubbard dimer
journal, June 2014
- Fuks, J. I.; Maitra, N. T.
- Physical Review A, Vol. 89, Issue 6
Dressed TDDFT study of low-lying electronic excited states in selected linear polyenes and diphenylopolyenes
journal, September 2010
- Mazur, Grzegorz; Makowski, Marcin; Włodarczyk, Radosław
- International Journal of Quantum Chemistry, Vol. 111, Issue 4
Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange
journal, August 2003
- Dreuw, Andreas; Weisman, Jennifer L.; Head-Gordon, Martin
- The Journal of Chemical Physics, Vol. 119, Issue 6
Time-Dependent Density-Functional Theory and Strongly Correlated Systems: Insight from Numerical Studies
journal, October 2008
- Verdozzi, Claudio
- Physical Review Letters, Vol. 101, Issue 16
Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals
journal, April 2012
- Kronik, Leeor; Stein, Tamar; Refaely-Abramson, Sivan
- Journal of Chemical Theory and Computation, Vol. 8, Issue 5
Organic Electronic Materials: Recent Advances in the DFT Description of the Ground and Excited States Using Tuned Range-Separated Hybrid Functionals
journal, April 2014
- Körzdörfer, Thomas; Brédas, Jean-Luc
- Accounts of Chemical Research, Vol. 47, Issue 11
Resonant nonlinear polarizabilities in the time-dependent density functional theory
journal, November 2003
- Tretiak, S.; Chernyak, V.
- The Journal of Chemical Physics, Vol. 119, Issue 17
Inhomogeneous Electron Gas
journal, March 1973
- Rajagopal, A. K.; Callaway, J.
- Physical Review B, Vol. 7, Issue 5
Local Density-Functional Theory of Frequency-Dependent Linear Response
journal, August 1986
- Gross, E. K. U.; Kohn, Walter
- Physical Review Letters, Vol. 57, Issue 7
On the Mapping of Time-Dependent Densities onto Potentials in Quantum Mechanics
text, January 2007
- Baer, Roi
- arXiv
Dynamical self-stabilization of the Mott insulator: Time evolution of the density and entanglement entropy of out-of-equilibrium cold fermion gases
text, January 2009
- Karlsson, Daniel; Verdozzi, Claudio; Odashima, Mariana M.
- arXiv
Adiabatic approximation in time-dependent reduced-density-matrix functional theory
text, January 2009
- Requist, Ryan; Pankratov, Oleg
- arXiv
Dynamical Coulomb Blockade and the Derivative Discontinuity of Time-Dependent Density Functional Theory
text, January 2009
- Kurth, S.; Stefanucci, G.; Khosravi, E.
- arXiv
Time-dependent current density functional theory on a lattice
text, January 2010
- Tokatly, I. V.
- arXiv
Assessment of Dressed Time-Dependent Density-Functional Theory for the Low-Lying Valence States of 28 Organic Chromophores
text, January 2011
- Huix-Rotllant, Miquel; Ipatov, Andrei; Rubio, Angel
- arXiv
Perspectives on double-excitations in TDDFT
text, January 2011
- Elliott, Peter; Goldson, Sharma; Canahui, Chris
- arXiv
Towards a description of the Kondo effect using time-dependent density functional theory
text, January 2011
- Stefanucci, G.; Kurth, S.
- arXiv
Progress in Time-Dependent Density-Functional Theory
text, January 2011
- Casida, M. E.; Huix-Rotllant, M.
- arXiv
Time-dependent density functional theory on a lattice
text, January 2012
- Farzanehpour, Mehdi; Tokatly, I. V.
- arXiv
Exact Density-Functionals with Initial-State Dependence and Memory
text, January 2012
- Ruggenthaler, M.; Nielsen, S. E. B.; van Leeuwen, R.
- arXiv
Three-dimensional dynamics of a fermionic Mott wedding-cake in clean and disordered optical lattices
preprint, January 2013
- Kartsev, A.; Karlsson, D.; Privitera, A.
- arXiv
The time-dependent exchange-correlation functional for a Hubbard dimer: quantifying non-adiabatic effect
text, January 2013
- Fuks, Johanna I.; Farzanehpour, Mehdi; Tokatly, Ilya V.
- arXiv
Charge-Transfer in Time-Dependent Density Functional Theory: Insights from the Asymmetric Hubbard Dimer
text, January 2013
- Fuks, J. I.; Maitra, N. T.
- arXiv
Undoing static correlation: Long-range charge transfer in time-dependent density functional theory
text, January 2005
- Maitra, Neepa T.
- arXiv
Works referencing / citing this record:
Accurate double excitations from ensemble density functional calculations
journal, October 2018
- Sagredo, Francisca; Burke, Kieron
- The Journal of Chemical Physics, Vol. 149, Issue 13
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journal, March 2019
- Deur, Killian; Fromager, Emmanuel
- The Journal of Chemical Physics, Vol. 150, Issue 9
(Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer
journal, July 2019
- Ullrich, Carsten A.
- Physical Review A, Vol. 100, Issue 1
Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles
journal, August 2018
- Senjean, Bruno; Fromager, Emmanuel
- Physical Review A, Vol. 98, Issue 2
Special issue in honor of Eberhard K.U. Gross for his 65th birthday
journal, November 2018
- Marques, Miguel A. L.; Nogueira, Fernando; Rubio, Angel
- The European Physical Journal B, Vol. 91, Issue 11
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