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

被引:34
作者
Carrascal, Diego J. [1 ,2 ]
Ferrer, Jaime [1 ,2 ]
Maitra, Neepa [3 ]
Burke, Kieron [4 ]
机构
[1] Univ Oviedo, Dept Phys, Oviedo 33007, Spain
[2] Univ Oviedo, CSIC, Nanomat & Nanotechnol Res Ctr, Oviedo, Spain
[3] CUNY Hunter Coll, Dept Phys, New York, NY 10021 USA
[4] Univ Calif Irvine, Dept Chem & Phys, Irvine, CA 92697 USA
基金
美国国家科学基金会;
关键词
CHARGE-TRANSFER EXCITATIONS; EXCITED-STATES; DRESSED TDDFT; EXCHANGE; ELECTRONS; ENERGIES; POLYENES; PHYSICS;
D O I
10.1140/epjb/e2018-90114-9
中图分类号
O469 [凝聚态物理学];
学科分类号
070205 ;
摘要
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.
引用
收藏
页数:21
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