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 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 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 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-C 18 Ph 4 bridge between donor anisyl substituents plays a crucial role in determining the intriguing chemical/spectroscopical/optical properties of these carbo-chromophores. theme of aromaticity. ‡ Corresponding author netic,…) are not uniquely determined [4], the rule remains qualitative in nature. Before addressing the problem of its quantitative transcription, it is noted that the rule is reversed by applying elementary molecular transformations altering not only the electronic configuration (one-electron spin inversion or two-electron ionization), but also the atomic configuration: one-bond 180°-twisting or one-bond C 2 -expansion, corresponding to Möbius conversion [5] and local carbo-merization, respectively [6]. The quantitative variation of aromaticity upon both latter types of transformations is hereafter addressed from both the theoretical and experimental standpoints. TWISTING THE RING CONTENT: THE MÖBIUS KEY TO AROMATICITYAfter a critical survey of various energetic measures of aromaticity proposed in the literature [7], the relative aromaticity of Hückel and Möbius rings will be scrutinized. Their complementary roles for the quantification of topological aromaticity is then investigated not only for cyclenes, but also for conjugated alkynes and cyclynes, and in particular for ring carbo-mers. Critical survey of HMO energetic a...

Graph Theory of Ring-Current Diamagnetism

“…As pointed out by Chauvin et al, 97 a reference acyclic structural analog, which has always been necessary to estimate the enhanced thermodynamic stability due to cyclic conjugation, must be as identical as possible to the actual cyclic π-system. Unlike actual π-systems, acyclic references so far employed cannot be described by classical resonance structures.…”

“…Unlike actual π-systems, acyclic references so far employed cannot be described by classical resonance structures. 97 The Figure 12. Superposed Clar formula for anthanthrene (27d), together with individual Clar structures (27a27c).…”

“…main conceptual criticism of TRE hence concerns its lack of direct chemical interpretation; the reference structure on which TRE replies represents a hypothetical acyclic reference. 97 The reference energy hence is virtual in nature. MRE is the first aromatic stabilization energy (ASE) calculated without any hypothetical polyene reference.…”

“…30 Chauvin et al, on the basis of the B3PW9/6-31G** geometry, 120,121 combined with the empirical bond-order bond-length relation, 122 proposed a more realistic degree of bond-length alternation (k shot = 1.1878 and k long = 0.7941) for cyclobutadiene (4). 97 If these bond parameters are employed, the TRE and MRE for 4 will increase to ¹0.6055 and ¹0.9600 «¢«, respectively, resulting in a further reduced MRE-to-TRE ratio of 1.585.…”

“…Ring-current patterns of sapphyrin (95) and orangarin (97), obtained by superposing all circuit currents on the molecular plane, are shown in Figure 25. Essentially the same current density maps have been obtained by higher-level calculations, too.…”