2024-03-29T23:07:36Zhttp://digital.csic.es/dspace-oai/requestoai:digital.csic.es:10261/1736242020-12-13T09:02:22Zcom_10261_28457com_10261_3col_10261_28462
Linear response time-dependent density functional theory of the Hubbard dimer
Carrascal, Diego
Ferrer, Jaime
Maitra, Neepa
Burke, Kieron
Ministerio de Economía y Competitividad (España)
National Science Foundation (US)
Department of Energy (US)
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.
DC and JF wish to thank funding support from the Spanish Ministerio de Economía y Competitividad via grant FIS2012-34858. NTM thanks the US National Science Foundation CHE-1566197 for support. KB acknowledges DOE grant number DE-FG02-08ER46496.
Peer Reviewed
2018-12-26T10:58:18Z
2018-12-26T10:58:18Z
2018
2018-12-26T10:58:18Z
artículo
http://purl.org/coar/resource_type/c_6501
doi: 10.1140/epjb/e2018-90114-9
e-issn: 1434-6036
issn: 1436-6028
European Physical Journal B 91: 142 (2018)
arXiv:1802.09988v2
http://hdl.handle.net/10261/173624
10.1140/epjb/e2018-90114-9
http://dx.doi.org/10.13039/501100003329
http://dx.doi.org/10.13039/100000001
http://dx.doi.org/10.13039/100000015
Preprint
https://doi.org/10.1140/epjb/e2018-90114-9
Sí
open
Springer Nature