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

Carrascal, Diego J.; Ferrer, Jaime; Maitra, Neepa; Burke, Kieron

doi:10.1140/epjb/e2018-90114-9

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

Journal Article · 02 July 2018 · European Physical Journal. B, Condensed Matter and Complex Systems

DOI: https://doi.org/10.1140/epjb/e2018-90114-9 · OSTI ID:1595120

Carrascal, Diego J. ^[1]; Ferrer, Jaime ^[2]; Maitra, Neepa ^[3]; Burke, Kieron ^[4]

Univ. de Oviedo, Oviedo (Spain); Consejo Superior de Investigaciones Cientificas (CSIC), Madrid (Spain). Nanomaterials and Nanotechnology Research Center; University of California Irvine
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)

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

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

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF)

Grant/Contract Number:: FG02-08ER46496

OSTI ID:: 1595120

Journal Information:: European Physical Journal. B, Condensed Matter and Complex Systems, Journal Name: European Physical Journal. B, Condensed Matter and Complex Systems Journal Issue: 7 Vol. 91; ISSN 1434-6028

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (89)

Application of the dressed time-dependent density functional theory for the excited states of linear polyenes Mazur, Grzegorz; Włodarczyk, Radosław Journal of Computational Chemistry, Vol. 30, Issue 5 https://doi.org/10.1002/jcc.21102	journal	April 2009
Real-time, real-space implementation of the linear response time-dependent density-functional theory Yabana, K.; Nakatsukasa, T.; Iwata, J. -I. physica status solidi (b), Vol. 243, Issue 5 https://doi.org/10.1002/pssb.200642005	journal	April 2006
Dressed TDDFT study of low-lying electronic excited states in selected linear polyenes and diphenylopolyenes Mazur, Grzegorz; Makowski, Marcin; Włodarczyk, Radosław International Journal of Quantum Chemistry, Vol. 111, Issue 4 https://doi.org/10.1002/qua.22876	journal	September 2010
Many-Particle Physics Mahan, Gerald D. Physics of Solids and Liquids (PSLI) https://doi.org/10.1007/978-1-4757-5714-9	book	January 2000
Fundamentals of Time-Dependent Density Functional Theory Marques, Miguel A. L.; Maitra, Neepa T.; Nogueira, Fernando M. S. Lecture Notes in Physics https://doi.org/10.1007/978-3-642-23518-4	book	January 2012
�ber die Gesamtst�rke der von einem Zustande ausgehenden Absorptionslinien Kuhn, W. Zeitschrift f�r Physik, Vol. 33, Issue 1 https://doi.org/10.1007/BF01328322	journal	December 1925
�ber die Zahl der Dispersionselektronen, die einem station�ren Zustand zugeordnet sind Reiche, F.; Thomas, W. Zeitschrift f�r Physik, Vol. 34, Issue 1 https://doi.org/10.1007/BF01328494	journal	December 1925
Über die Zahl der Dispersionselektronen, die einem stationären Zustande zugeordnet sind. (Vorläufige Mitteilung) Thomas, W. Die Naturwissenschaften, Vol. 13, Issue 28 https://doi.org/10.1007/BF01558908	journal	July 1925
Treatment of electronic excitations within the adiabatic approximation of time dependent density functional theory Bauernschmitt, Rüdiger; Ahlrichs, Reinhart Chemical Physics Letters, Vol. 256, Issue 4-5 https://doi.org/10.1016/0009-2614(96)00440-X	journal	July 1996
The exchange-correlation energy of a metallic surface Langreth, D. C.; Perdew, J. P. Solid State Communications, Vol. 17, Issue 11 https://doi.org/10.1016/0038-1098(75)90618-3	journal	December 1975
Molecular excitation energies from time-dependent density functional theory Grabo, T.; Petersilka, M.; Gross, E. K. U. Journal of Molecular Structure: THEOCHEM, Vol. 501-502 https://doi.org/10.1016/S0166-1280(99)00445-5	journal	April 2000
Time-Dependent Density Functional Response Theory of Molecular Systems: Theory, Computational Methods, and Functionals Casida, Mark E. Theoretical and Computational Chemistry https://doi.org/10.1016/S1380-7323(96)80093-8	book	January 1996
Assessment of dressed time-dependent density-functional theory for the low-lying valence states of 28 organic chromophores Huix-Rotllant, Miquel; Ipatov, Andrei; Rubio, Angel Chemical Physics, Vol. 391, Issue 1 https://doi.org/10.1016/j.chemphys.2011.03.019	journal	November 2011
Perspectives on double-excitations in TDDFT Elliott, Peter; Goldson, Sharma; Canahui, Chris Chemical Physics, Vol. 391, Issue 1 https://doi.org/10.1016/j.chemphys.2011.03.020	journal	November 2011
A dressed TDDFT treatment of the 21Ag states of butadiene and hexatriene Cave, Robert J.; Zhang, Fan; Maitra, Neepa T. Chemical Physics Letters, Vol. 389, Issue 1-3 https://doi.org/10.1016/j.cplett.2004.03.051	journal	May 2004
Density functionals and model Hamiltonians: Pillars of many-particle physics Capelle, Klaus; Campo, Vivaldo L. Physics Reports, Vol. 528, Issue 3 https://doi.org/10.1016/j.physrep.2013.03.002	journal	July 2013
Organic Electronic Materials: Recent Advances in the DFT Description of the Ground and Excited States Using Tuned Range-Separated Hybrid Functionals Körzdörfer, Thomas; Brédas, Jean-Luc Accounts of Chemical Research, Vol. 47, Issue 11 https://doi.org/10.1021/ar500021t	journal	April 2014
Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals Kronik, Leeor; Stein, Tamar; Refaely-Abramson, Sivan Journal of Chemical Theory and Computation, Vol. 8, Issue 5 https://doi.org/10.1021/ct2009363	journal	April 2012
Extensive TD-DFT Benchmark: Singlet-Excited States of Organic Molecules Jacquemin, Denis; Wathelet, Valérie; Perpète, Eric A. Journal of Chemical Theory and Computation, Vol. 5, Issue 9 https://doi.org/10.1021/ct900298e	journal	August 2009
Reliable Prediction of Charge Transfer Excitations in Molecular Complexes Using Time-Dependent Density Functional Theory Stein, Tamar; Kronik, Leeor; Baer, Roi Journal of the American Chemical Society, Vol. 131, Issue 8 https://doi.org/10.1021/ja8087482	journal	March 2009
Three-dimensional dynamics of a fermionic Mott wedding-cake in clean and disordered optical lattices Kartsev, A.; Karlsson, D.; Privitera, A. Scientific Reports, Vol. 3, Issue 1 https://doi.org/10.1038/srep02570	journal	September 2013
The calculations of excited-state properties with Time-Dependent Density Functional Theory Adamo, Carlo; Jacquemin, Denis Chem. Soc. Rev., Vol. 42, Issue 3 https://doi.org/10.1039/C2CS35394F	journal	January 2013
Challenging adiabatic time-dependent density functional theory with a Hubbard dimer: the case of time-resolved long-range charge transfer Fuks, Johanna I.; Maitra, Neepa T. Phys. Chem. Chem. Phys., Vol. 16, Issue 28 https://doi.org/10.1039/C4CP00118D	journal	January 2014
On the determination of excitation energies using density functional theory Tozer, David J.; Handy, Nicholas C. Physical Chemistry Chemical Physics, Vol. 2, Issue 10 https://doi.org/10.1039/a910321j	journal	January 2000
Exact time-dependent density functional theory for impurity models Schmitteckert, Peter; Dzierzawa, Michael; Schwab, Peter Physical Chemistry Chemical Physics, Vol. 15, Issue 15 https://doi.org/10.1039/c3cp44639e	journal	January 2013
Excitation energies of dissociating H2: A problematic case for the adiabatic approximation of time-dependent density functional theory Gritsenko, O. V.; van Gisbergen, S. J. A.; Görling, A. The Journal of Chemical Physics, Vol. 113, Issue 19 https://doi.org/10.1063/1.1318750	journal	November 2000
Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange Dreuw, Andreas; Weisman, Jennifer L.; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 119, Issue 6 https://doi.org/10.1063/1.1590951	journal	August 2003
Resonant nonlinear polarizabilities in the time-dependent density functional theory Tretiak, S.; Chernyak, V. The Journal of Chemical Physics, Vol. 119, Issue 17 https://doi.org/10.1063/1.1614240	journal	November 2003
Relationship between long-range charge-transfer excitation energy error and integer discontinuity in Kohn–Sham theory Tozer, David J. The Journal of Chemical Physics, Vol. 119, Issue 24 https://doi.org/10.1063/1.1633756	journal	December 2003
Double excitations within time-dependent density functional theory linear response Maitra, Neepa T.; Zhang, Fan; Cave, Robert J. The Journal of Chemical Physics, Vol. 120, Issue 13 https://doi.org/10.1063/1.1651060	journal	April 2004
A long-range-corrected time-dependent density functional theory Tawada, Yoshihiro; Tsuneda, Takao; Yanagisawa, Susumu The Journal of Chemical Physics, Vol. 120, Issue 18 https://doi.org/10.1063/1.1688752	journal	May 2004
Asymptotic correction of the exchange–correlation kernel of time-dependent density functional theory for long-range charge-transfer excitations Gritsenko, Oleg; Baerends, Evert Jan The Journal of Chemical Physics, Vol. 121, Issue 2 https://doi.org/10.1063/1.1759320	journal	July 2004
Undoing static correlation: Long-range charge transfer in time-dependent density-functional theory Maitra, Neepa T. The Journal of Chemical Physics, Vol. 122, Issue 23 https://doi.org/10.1063/1.1924599	journal	June 2005
On the mapping of time-dependent densities onto potentials in quantum mechanics Baer, Roi The Journal of Chemical Physics, Vol. 128, Issue 4 https://doi.org/10.1063/1.2822124	journal	January 2008
Time-dependent V-representability on lattice systems Li, Yonghui; Ullrich, C. A. The Journal of Chemical Physics, Vol. 129, Issue 4 https://doi.org/10.1063/1.2955733	journal	July 2008
Dynamic polarizabilities and excitation spectra from a molecular implementation of time‐dependent density‐functional response theory: N ₂ as a case study Jamorski, Christine; Casida, Mark E.; Salahub, Dennis R. The Journal of Chemical Physics, Vol. 104, Issue 13 https://doi.org/10.1063/1.471140	journal	April 1996
Perspective: Fundamental aspects of time-dependent density functional theory Maitra, Neepa T. The Journal of Chemical Physics, Vol. 144, Issue 22 https://doi.org/10.1063/1.4953039	journal	June 2016
Density functional theory of electron transfer beyond the Born-Oppenheimer approximation: Case study of LiF Li, Chen; Requist, Ryan; Gross, E. K. U. The Journal of Chemical Physics, Vol. 148, Issue 8 https://doi.org/10.1063/1.5011663	journal	February 2018
Does density functional theory contribute to the understanding of excited states of unsaturated organic compounds? Tozer, David J.; Amos, Roger D.; Handy, Nicholas C. Molecular Physics, Vol. 97, Issue 7 https://doi.org/10.1080/00268979909482888	journal	October 1999
Many-Particle Physics Dowker, J. S. Physics Bulletin, Vol. 33, Issue 3 https://doi.org/10.1088/0031-9112/33/3/038	journal	March 1982
Twenty-five Years of High-Temperature Superconductivity – A Personal Review Anderson, Philip W. Journal of Physics: Conference Series, Vol. 449 https://doi.org/10.1088/1742-6596/449/1/012001	journal	July 2013
Time-Dependent Density-Functional Theory Ullrich, Carsten A. https://doi.org/10.1093/acprof:oso/9780199563029.001.0001	book	December 2011
Theory of the Insulating State Kohn, Walter Physical Review, Vol. 133, Issue 1A https://doi.org/10.1103/PhysRev.133.A171	journal	January 1964
Inhomogeneous Electron Gas Hohenberg, P.; Kohn, W. Physical Review, Vol. 136, Issue 3B, p. B864-B871 https://doi.org/10.1103/PhysRev.136.B864	journal	November 1964
Adiabatic approximation in time-dependent reduced-density-matrix functional theory Requist, Ryan; Pankratov, Oleg Physical Review A, Vol. 81, Issue 4 https://doi.org/10.1103/PhysRevA.81.042519	journal	April 2010
Analytic density functionals with initial-state dependence and memory Ruggenthaler, M.; Nielsen, S. E. B.; van Leeuwen, R. Physical Review A, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevA.88.022512	journal	August 2013
Time-dependent exchange-correlation functional for a Hubbard dimer: Quantifying nonadiabatic effects Fuks, Johanna I.; Farzanehpour, Mehdi; Tokatly, Ilya V. Physical Review A, Vol. 88, Issue 6 https://doi.org/10.1103/PhysRevA.88.062512	journal	December 2013
Charge transfer in time-dependent density-functional theory: Insights from the asymmetric Hubbard dimer Fuks, J. I.; Maitra, N. T. Physical Review A, Vol. 89, Issue 6 https://doi.org/10.1103/PhysRevA.89.062502	journal	June 2014
Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism Gunnarsson, O.; Lundqvist, B. I. Physical Review B, Vol. 13, Issue 10 https://doi.org/10.1103/PhysRevB.13.4274	journal	May 1976
Optical spectrum of a Hubbard chain Maldague, Pierre F. Physical Review B, Vol. 16, Issue 6 https://doi.org/10.1103/PhysRevB.16.2437	journal	September 1977
Landau parameters of almost-localized Fermi liquids Baeriswyl, D.; Gros, C.; Rice, T. M. Physical Review B, Vol. 35, Issue 16 https://doi.org/10.1103/PhysRevB.35.8391	journal	June 1987
Exchange-correlation kernel in time-dependent density functional theory Aryasetiawan, F.; Gunnarsson, O. Physical Review B, Vol. 66, Issue 16 https://doi.org/10.1103/PhysRevB.66.165119	journal	October 2002
Generalized Kohn-Sham system in one-matrix functional theory Requist, Ryan; Pankratov, Oleg Physical Review B, Vol. 77, Issue 23 https://doi.org/10.1103/PhysRevB.77.235121	journal	June 2008
Time-dependent current density functional theory on a lattice Tokatly, I. V. Physical Review B, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevB.83.035127	journal	January 2011
Exact Kohn-Sham eigenstates versus quasiparticles in simple models of strongly correlated electrons Carrascal, D. J.; Ferrer, J. Physical Review B, Vol. 85, Issue 4 https://doi.org/10.1103/PhysRevB.85.045110	journal	January 2012
Time-dependent density functional theory on a lattice Farzanehpour, M.; Tokatly, I. V. Physical Review B, Vol. 86, Issue 12 https://doi.org/10.1103/PhysRevB.86.125130	journal	September 2012
Adiabatic and local approximations for the Kohn-Sham potential in time-dependent Hubbard chains Mancini, L.; Ramsden, J. D.; Hodgson, M. J. P. Physical Review B, Vol. 89, Issue 19 https://doi.org/10.1103/PhysRevB.89.195114	journal	May 2014
Time-Dependent Density-Functional Theory and Strongly Correlated Systems: Insight from Numerical Studies Verdozzi, Claudio Physical Review Letters, Vol. 101, Issue 16 https://doi.org/10.1103/PhysRevLett.101.166401	journal	October 2008
Dynamical Coulomb Blockade and the Derivative Discontinuity of Time-Dependent Density Functional Theory Kurth, S.; Stefanucci, G.; Khosravi, E. Physical Review Letters, Vol. 104, Issue 23 https://doi.org/10.1103/PhysRevLett.104.236801	journal	June 2010
Towards a Description of the Kondo Effect Using Time-Dependent Density-Functional Theory Stefanucci, G.; Kurth, S. Physical Review Letters, Vol. 107, Issue 21 https://doi.org/10.1103/PhysRevLett.107.216401	journal	November 2011
Bethe Ansatz Approach to the Kondo Effect within Density-Functional Theory Bergfield, Justin P.; Liu, Zhen-Fei; Burke, Kieron Physical Review Letters, Vol. 108, Issue 6 https://doi.org/10.1103/PhysRevLett.108.066801	journal	February 2012
Frequency Dependence of the Exact Exchange-Correlation Kernel of Time-Dependent Density-Functional Theory Thiele, M.; Kümmel, S. Physical Review Letters, Vol. 112, Issue 8 https://doi.org/10.1103/PhysRevLett.112.083001	journal	February 2014
Nonadiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density-Functional Theory Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole Physical Review Letters, Vol. 120, Issue 15 https://doi.org/10.1103/PhysRevLett.120.157701	journal	April 2018
Density-Functional Theory for Time-Dependent Systems Runge, Erich; Gross, E. K. U. Physical Review Letters, Vol. 52, Issue 12 https://doi.org/10.1103/PhysRevLett.52.997	journal	March 1984
Local density-functional theory of frequency-dependent linear response Gross, E. K. U.; Kohn, Walter Physical Review Letters, Vol. 55, Issue 26 https://doi.org/10.1103/PhysRevLett.55.2850	journal	December 1985
Correlated electrons in high-temperature superconductors Dagotto, Elbio Reviews of Modern Physics, Vol. 66, Issue 3 https://doi.org/10.1103/RevModPhys.66.763	journal	July 1994
Doping a Mott insulator: Physics of high-temperature superconductivity Lee, Patrick A.; Nagaosa, Naoto; Wen, Xiao-Gang Reviews of Modern Physics, Vol. 78, Issue 1 https://doi.org/10.1103/RevModPhys.78.17	journal	January 2006
Density-functional theory for time-dependent systems Dhara, Asish K.; Ghosh, Swapan K. Physical Review A, Vol. 35, Issue 1 https://doi.org/10.1103/physreva.35.442	journal	January 1987
Inhomogeneous Electron Gas Rajagopal, A. K.; Callaway, J. Physical Review B, Vol. 7, Issue 5 https://doi.org/10.1103/physrevb.7.1912	journal	March 1973
Local Density-Functional Theory of Frequency-Dependent Linear Response Gross, E. K. U.; Kohn, Walter Physical Review Letters, Vol. 57, Issue 7 https://doi.org/10.1103/physrevlett.57.923.2	journal	August 1986
Progress in Time-Dependent Density-Functional Theory Casida, M. E.; Huix-Rotllant, M. Annual Review of Physical Chemistry, Vol. 63, Issue 1 https://doi.org/10.1146/annurev-physchem-032511-143803	journal	May 2012
Tuned Range-Separated Hybrids in Density Functional Theory Baer, Roi; Livshits, Ester; Salzner, Ulrike Annual Review of Physical Chemistry, Vol. 61, Issue 1 https://doi.org/10.1146/annurev.physchem.012809.103321	journal	March 2010
Dynamical self-stabilization of the Mott insulator: Time evolution of the density and entanglement entropy of out-of-equilibrium cold fermion gases Karlsson, D.; Verdozzi, C.; Odashima, M. M. EPL (Europhysics Letters), Vol. 93, Issue 2 https://doi.org/10.1209/0295-5075/93/23003	journal	January 2011
On the Mapping of Time-Dependent Densities onto Potentials in Quantum Mechanics Baer, Roi arXiv https://doi.org/10.48550/arxiv.0704.1787	text	January 2007
Dynamical self-stabilization of the Mott insulator: Time evolution of the density and entanglement entropy of out-of-equilibrium cold fermion gases Karlsson, Daniel; Verdozzi, Claudio; Odashima, Mariana M. arXiv https://doi.org/10.48550/arxiv.0905.1398	text	January 2009
Adiabatic approximation in time-dependent reduced-density-matrix functional theory Requist, Ryan; Pankratov, Oleg arXiv https://doi.org/10.48550/arxiv.0911.0945	text	January 2009
Dynamical Coulomb Blockade and the Derivative Discontinuity of Time-Dependent Density Functional Theory Kurth, S.; Stefanucci, G.; Khosravi, E. arXiv https://doi.org/10.48550/arxiv.0911.3870	text	January 2009
Time-dependent current density functional theory on a lattice Tokatly, I. V. arXiv https://doi.org/10.48550/arxiv.1011.2715	text	January 2010
Assessment of Dressed Time-Dependent Density-Functional Theory for the Low-Lying Valence States of 28 Organic Chromophores Huix-Rotllant, Miquel; Ipatov, Andrei; Rubio, Angel arXiv https://doi.org/10.48550/arxiv.1101.0291	text	January 2011
Perspectives on double-excitations in TDDFT Elliott, Peter; Goldson, Sharma; Canahui, Chris arXiv https://doi.org/10.48550/arxiv.1101.3379	text	January 2011
Towards a description of the Kondo effect using time-dependent density functional theory Stefanucci, G.; Kurth, S. arXiv https://doi.org/10.48550/arxiv.1106.3728	text	January 2011
Progress in Time-Dependent Density-Functional Theory Casida, M. E.; Huix-Rotllant, M. arXiv https://doi.org/10.48550/arxiv.1108.0611	text	January 2011
Time-dependent density functional theory on a lattice Farzanehpour, Mehdi; Tokatly, I. V. arXiv https://doi.org/10.48550/arxiv.1206.6267	text	January 2012
Exact Density-Functionals with Initial-State Dependence and Memory Ruggenthaler, M.; Nielsen, S. E. B.; van Leeuwen, R. arXiv https://doi.org/10.48550/arxiv.1209.2949	text	January 2012
Three-dimensional dynamics of a fermionic Mott wedding-cake in clean and disordered optical lattices Kartsev, A.; Karlsson, D.; Privitera, A. arXiv https://doi.org/10.48550/arxiv.1308.4382	preprint	January 2013
The time-dependent exchange-correlation functional for a Hubbard dimer: quantifying non-adiabatic effect Fuks, Johanna I.; Farzanehpour, Mehdi; Tokatly, Ilya V. arXiv https://doi.org/10.48550/arxiv.1312.1667	text	January 2013
Charge-Transfer in Time-Dependent Density Functional Theory: Insights from the Asymmetric Hubbard Dimer Fuks, J. I.; Maitra, N. T. arXiv https://doi.org/10.48550/arxiv.1312.6880	text	January 2013
Correlated Electrons in High Temperature Superconductors Dagotto, Elbio arXiv https://doi.org/10.48550/arxiv.cond-mat/9311013	text	January 1993
Undoing static correlation: Long-range charge transfer in time-dependent density functional theory Maitra, Neepa T. arXiv https://doi.org/10.48550/arxiv.physics/0502147	text	January 2005

Cited By (7)

Accurate double excitations from ensemble density functional calculations Sagredo, Francisca; Burke, Kieron The Journal of Chemical Physics, Vol. 149, Issue 13 https://doi.org/10.1063/1.5043411	journal	October 2018
Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation Deur, Killian; Fromager, Emmanuel The Journal of Chemical Physics, Vol. 150, Issue 9 https://doi.org/10.1063/1.5084312	journal	March 2019
(Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer Ullrich, Carsten A. Physical Review A, Vol. 100, Issue 1 https://doi.org/10.1103/physreva.100.012516	journal	July 2019
Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles Senjean, Bruno; Fromager, Emmanuel Physical Review A, Vol. 98, Issue 2 https://doi.org/10.1103/physreva.98.022513	journal	August 2018
Projected site-occupation embedding theory Senjean, Bruno Physical Review B, Vol. 100, Issue 3 https://doi.org/10.1103/physrevb.100.035136	journal	July 2019
Special issue in honor of Eberhard K.U. Gross for his 65th birthday Marques, Miguel A. L.; Nogueira, Fernando; Rubio, Angel The European Physical Journal B, Vol. 91, Issue 11 https://doi.org/10.1140/epjb/e2018-90506-9	journal	November 2018
Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation Deur, Killian; Fromager, Emmanuel arXiv https://doi.org/10.48550/arxiv.1812.02461	text	January 2018

Similar Records

The Hubbard dimer: a density functional case study of a many-body problem

Journal Article · 2015 · Journal of Physics. Condensed Matter · OSTI ID:1595136

Carrascal, D. J.; Ferrer, J.; Smith, J. C.; +1 more

Accurate double excitations from ensemble density functional calculations

Journal Article · 2018 · Journal of Chemical Physics · OSTI ID:1595108

Sagredo, Francisca; Burke, Kieron

Charge-transfer excitation energies with a time-dependent density-functional method suitable for orbital-dependent exchange-correlation kernels

Journal Article · 2009 · Physical Review. A · OSTI ID:21313249

Hesselmann, Andreas; Ipatov, Andrey; Goerling, Andreas

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY

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

Citation Formats

References (89)

Cited By (7)

Similar Records

Related Subjects