Linear response time-dependent density functional theory of the Hubbard dimer
Linear response time-dependent density functional theory of the Hubbard dimer
复制标题
DOI：
10.1140/epjb/e2018-90114-9
复制
发表时间：
2018-07-02
影响因子：
1.6
通讯作者：
Burke, Kieron
中科院分区：
文献类型：
--
作者：
Carrascal, Diego J.;Ferrer, Jaime;Burke, Kieron
利用不对称Hubbard二聚体研究了线性响应含时密度泛函理论的精确含频核的密度依赖性。给出了核的精确形式，并指出了利用精确基态泛函的绝热近似的局限性。证明了格点哈密顿的振子强度求和规则，并给出了相应的振子强度定义。Casida方法提取振子强度的频率依赖的核被证明产生的准确结果与此内核。一个明确的方式标签的性质的激发。证明了基态交换关联能的涨落耗散定理。弱相关和强相关之间的区别取决于相互作用与不对称性的比率。仔细定义的弱相关和强相关区域之间的简单插值产生了内核的密度函数近似，为单激发和双激发（包括电荷转移激发）提供了准确的跃迁频率。附录中给出了许多精确的结果、极限和关于这些极限的展开式。
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.