Variation of aromaticity by twisting or expanding the ring content

Generalization of the Huckel rule predicts that the (anti)aromaticity of a neutral ring is qualitatively reverted upon a single twist of the pi-orbital array (Mobius interconversion), and is preserved upon expansion of all the bonds by single C-2 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 Mobius ring is not the opposite of that of the Huckel 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 Huckel and Mobius rings within the Huckel molecular orbital (HMO) framework. Whereas the topological influence of triple bonds is currently neglected in the first-level HMO treatment of pi-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 C-18 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.