In this study, we theoretically examined the mechanism of aromaticity induced in closely stacked cofacial π-dimers of 4nπ antiaromatic molecules, which is called stacked-ring aromaticity, in terms of the effective number of π-electrons (N_π) and Baird’s rule. High-precision quantum chemical calculations combined with a multi-configurational wavefunction analysis revealed that double-triplet [¹(T₁T₁)] and intermolecular charge-transfer (CT) electron configurations mix substantially in the ground state wavefunctions of cyclobutadiene and Ni(II) norcorrole dimer models at small stacking distance (d). Since the T₁ configuration gives rise to two unpaired electrons, the remaining 4n-2 π electrons still participate in the intramolecular conjugation, which can be interpreted as the origin of the aromaticity of each monomer. Consequently, the aromaticity of each T₁-like monomer was associated with Baird’s rule. On the other hand, the increased weight of the CT configuration indicated the intermolecular delocalization of the formally unpaired four electrons derived from the ¹(T₁T₁) configuration, resulting in the intermolecular bonding interaction. This interaction contributed to the energy stabilization of the closely stacked π-dimers, even though the degree of the energy gain is considered insufficient for achieving self-aggregation of the π-dimers at d ~3 Å. Our calculations have demonstrated that we should discuss the energy stabilization mechanism separately from the tropicity and structural changes within each monomer, although they are mutually linked through the appearance of ¹(T₁T₁) configuration.

中文翻译：

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从π电子的有效数角度看 stacked-ring aromaticity


在这项研究中，我们从理论上研究了 4nπ 反芳香族分子紧密堆叠的共面 π-二聚体诱导芳香性的机制，这称为堆叠环芳香性，根据 π 电子的有效数 （N_π） 和 Baird 规则。高精度量子化学计算与多构型波函数分析相结合，表明双三重态 [¹（T₁， T₁）] 和分子间电荷转移 （CT） 电子构型在小堆叠距离 （d） 下在环丁二烯和 Ni（II） 去甲酰二聚体模型的基态波函数中基本混合。由于 T₁ 构型产生两个不成对的电子，剩余的 4个 n-2 π电子仍然参与分子内共轭，这可以解释为每个单体芳香性的来源。因此，每个 T₁ 样单体的芳香性与 Baird 规则相关。另一方面，CT 构型的重量增加表明源自 ¹（T₁T₁） 构型的正式不成对的四个电子的分子间离域，导致分子间键合相互作用。这种相互作用有助于紧密堆叠的 π-二聚体的能量稳定，即使能量增益的程度被认为不足以实现 π-二聚体在 d ~3 Å 处的自聚集。 我们的计算表明，我们应该将能量稳定机制与每个单体内的倾向性和结构变化分开讨论，尽管它们通过 ¹（T₁T₁） 构型的出现相互联系。