A recent work (arXiv:2401.04685) has merged N‐centered ensembles of neutral and charged electronic ground states with ensembles of neutral ground and excited states, thus providing a general and in‐principle exact (so‐called extended N‐centered) ensemble density functional theory of neutral and charged electronic excitations. This formalism made it possible to revisit the concept of density‐functional derivative discontinuity, in the particular case of single excitations from the highest occupied Kohn–Sham (KS) molecular orbital, without invoking the usual “asymptotic behavior of the density” argument. In this work, we address a broader class of excitations, with a particular focus on double excitations. An exact implementation of the theory is presented for the two‐electron Hubbard dimer model. A thorough comparison of the true physical ground‐ and excited‐state electronic structures with that of the fictitious ensemble density‐functional KS system is also presented. Depending on the choice of the density‐functional ensemble as well as the asymmetry of the dimer and the correlation strength, an inversion of states can be observed. In some other cases, the strong mixture of KS states within the true physical system makes the assignment “single excitation” or “double excitation” irrelevant.

中文翻译：

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双电子激发的扩展N中心系综密度泛函理论

最近的作品 (arXiv:2401.04685) 已合并氮‐中性和带电电子基态的中心系综，以及中性基态和激发态的系综，从而提供了一般和原则上的精确（所谓的扩展氮‐中心）中性和带电电子激发的系综密度泛函理论。这种形式主义使得重新审视密度泛函导数不连续性的概念成为可能，在来自最高占据科恩-沙姆（KS）分子轨道的单次激发的特殊情况下，无需援引通常的“密度渐近行为”论证。在这项工作中，我们解决了更广泛的激励类别，特别关注双激励。针对双电子哈伯德二聚体模型提出了该理论的精确实现。还对真实的物理基态和激发态电子结构与虚构的系综密度泛函 KS 系统进行了彻底的比较。根据密度泛函系综的选择以及二聚体的不对称性和相关强度，可以观察到状态的反转。在其他一些情况下，真实物理系统中 KS 态的强烈混合使得分配“单激发”或“双激发”变得无关紧要。