Variation of aromaticity by twisting or expanding the ring content

Abstract

Generalization of the Hückel rule predicts that the (anti)aromaticity of a neutral ring is qualitatively reverted upon a single twist of the π-orbital array (Möbius interconversion), and is preserved upon expansion of all the bonds by single C2 units (ring carbo-merization). These opposite effects are addressed from quantitative theoretical and experimental standpoints, respectively. (i) According to most resonance energy (RE) schemes, the RE value of a Möbius ring is not the opposite of that of the Hückel version. This also applies to the Aihara’s and Trinajstic’s topological resonance energy (TRE), where a non-aromatic reference in the topological limit is defined as being “as identical as possible” to the parent ring but just “acyclic”. In spite of its conceptual merits, the computing complexity and fictitious character of the TRE acyclic reference resulted in a disuse of TRE as a current energetic aromaticity index. Both the calculation and interpretation of TRE have been revisited in light of a cross-reference between the Hückel and Möbius rings within the Hückel molecular orbital (HMO) framework. Whereas the topological influence of triple bonds is currently neglected in the first-level HMO treatment of π-conjugated systems, a graph-theoretical analysis allows one to differentiate the TRE value of a [3n]annulene from those of the corresponding carbo-[n]annulene. The C18 ring of carbo-benzene is thus predicted to be slightly more topologically aromatic than that of [18]annulene. (ii) Recent experimental and density functional theory (DFT) theoretical studies of quadrupolar carbo-benzene derivatives are presented. The results show that the “flexible aromaticity” of the p-C18Ph4 bridge between donor anisyl substituents plays a crucial role in determining the intriguing chemical/spectroscopical/optical properties of these carbo-chromophores.