Stacked-ring aromaticity from the viewpoint of the effective number of π-electrons

In this study, we theoretically examined the mechanism of aromaticity induced in closely stacked cofacial π-dimers of 4<i>n</i>π antiaromatic molecules, which is called stacked-ring aromaticity, in terms of the effective number of π-electrons (<i>N</i> _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 (<i>d</i>). Since the T₁ configuration gives rise to two unpaired electrons, the remaining 4<i>n</i> - 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 <i>d</i> ∼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.