Aromaticity with a twist: Möbius [4n]annulenes

Aromatic M?bius [4n]annulenes with 4n pi electrons, originally conceived by Heilbronner, are characterized computationally. These (CH)(12), (CH)(16), and (CH)(20) minima have nearly equal C-C bond lengths, small twist angles around the rings, and magnetic properties (NICS, nucleus-independent chemical shifts--see above at various positions in [16]annulene--and magnetic susceptibility exaltations) indicating significantly diatropic ring currents. The M?bius forms are not the most stable isomers but may contribute significantly to the chemistry of these annulenes. [structure: see text]     

Möbius aromaticity in [12]annulene: cis-trans isomerization via twist-coupled bond shifting

Density functional and coupled cluster calculations show that facile thermal configuration change in [12]annulene occurs via a twist-coupled bond-shifting mechanism. The transition state for this process is highly aromatic with M?bius topology. At the CCSD(T)/cc-pVDZ//BH&HLYP/6-311+G** level, the isomerization of tri-trans-[12]annulene 1a (CTCTCT) to its di-trans isomer 2 (CCCTCT) via such a mechanism has a barrier of 18.0 kcal/mol, in good agreement with earlier experiments. Two other aromatic M?bius bond-shifting transition states were located that result in configuration change for other [12]annulene conformers. This mechanism contrasts sharply with diradical configuration change for acyclic polyenes and with planar bond-shifting mechanisms generally assumed for annulenes. This constitutes evidence that neutral M?bius aromatic annulenes play a role in the dynamic processes of neutral [4n]annulenes.     

Figure eights, Möbius bands, and more: conformation and aromaticity of porphyrinoids

The aromatic character of porphyrins, which has significant chemical and biological consequences, can be substantially altered by judicious modifications of the parent ring system. Expansion of the macrocycle, which is achieved by introducing additional subunits, usually increases the so‐called free curvature of the ring, leading to larger angular strain. This strain is reduced by a variety of conformational changes, most notably by subunit inversion and π surface twisting. The latter effect creates a particularly convenient access to Möbius aromatic molecules, whose properties, predicted over 40 years ago, are of considerable theoretical importance. The conformational processes occurring in porphyrin analogues are often coupled to other chemical phenomena, and can thus be exploited as a means of constructing functional molecular devices. In this Review, the structural chemistry of porphyrinoids is discussed in the context of their conformational dynamics and π‐electron conjugation     

Unambiguous identification of Möbius aromaticity for meso-aryl-substituted [28]hexaphyrins(1.1.1.1.1.1)

meso-Aryl-substituted [28]hexaphyrins(1.1.1.1.1.1) have been examined by (1)H, (13)C, and (19)F NMR spectroscopies, UV-vis absorption spectroscopy, magnetic circular dichroism spectroscopy, and single-crystal X-ray diffraction analysis. All of these data consistently indicate that [28]hexaphyrins(1.1.1.1.1.1) in solution at 25 degrees C exist largely as an equilibrium among several rapidly interconverting twisted M?bius conformations with distinct aromaticities, with a small contribution from a planar rectangular conformation with antiaromatic character at slightly higher energy. In the solid state, [28]hexaphyrins(1.1.1.1.1.1) take either planar or M?bius-twisted conformations, depending upon the meso-aryl substituents and crystallization conditions, indicating a small energy difference between the two conformers. Importantly, when the temperature is decreased to -100 degrees C in THF, these rapid interconversions among M?bius conformations are frozen, allowing the detection of a single [28]hexaphyrin(1.1.1.1.1.1) species having a M?bius conformation. Detailed analyses of the solid-state M?bius structures of compounds 2b, 2c, and 2f showed that singly twisted structures are achieved without serious strain and that cyclic pi-conjugation is well-preserved, as needed for exhibiting strong diatropic ring currents. Actually, the harmonic-oscillator model for aromaticity (HOMA) values of these structures are significantly large (0.85, 0.69, and 0.71, respectively), confirming the first demonstration of stable M?bius aromatic systems consisting of free-base expanded porphyrins without the assistance of metal coordination.     

The aromaticity and Möbius characteristics of carbeno[8]heteroannulenes and triplet state annulenes

Two types of annulene which may show significant M?bius aromatic character and bond and twist delocalisation are proposed; triplet states with 4n + 2 occupancy of the p pi array of atomic orbitals and a novel 8-pi carbeno[8]heteroannulene ring system 1 where the Hückel highly antiaromatic nature as a planar system can be attenuated or even reversed by the C2 symmetric M?bius distortion.     

Möbius bis and tris-spiroaromatic systems

We propose that a general class of bis and tris-spiro 7-membered ring systems with a common atom X, of which there are a number of examples characterised crystallographically, can in fact be considered as spiroaromatic molecules in which each ring exhibits some degree of M?bius 4n pi-electron aromaticity. The aromaticity is probed as a function of the spiro-atom using ab initio calculations of the NICS(0) values, which indicate that the M?bius-aromaticity increases as the spiro-atom is changed e.g. from Al to P, and from e.g. P to As.     

Intrinsically chiral aromaticity. Rules incorporating linking number, twist, and writhe for higher-twist Möbius annulenes

The geometries of coiled annulenes belonging to the chiral C2 and D(n) (n = 2,7) point groups are defined by two chiral indices, W(r) and T(w), respectively (writhe and twist), which sum to give an overall integer linking number, L(k) (the C?lug?reanu-White-Fuller theorem). While the value of L(k) can been equated with single-twist (L(k) = 1pi), double-twist (L(k) = 2), and higher-order (L(k) > 2) twisted (M?bius-Listing) annulenes, we suggest that the correct Huckel molecular-orbital treatment is to use T(w) specifically in the 2p(pi)-2p(pi) overlap correction first suggested by Heilbronner, rather than L(k). Quantitatively, because many of these systems project much of the finite value of T(w) into W(r), a simple mechanism exists to increase the pi-electron resonance stabilization beyond what simple Heilbronner theory predicts. Examples of a diverse set of such chiral annulenes are dissected into W(r) and T(w) contributions, which reveals that those with the minimum value of T(w) are associated with the greater delocalized stability.     

Enumeration of Möbius type cyclic polyazulenoids

A Möbius type cyclic polyazulenoid is a kind of nonalternant conjugated hydrocarbon, consisting of a cyclic series of alternatingly fused five membered rings and seven membered rings, which forms a “Möbius belt of rings” or say, “Möbius belt of azulenes”, more precisely. As a sequel of the recent paper (Deng and Zhang in J Math Chem 54(2):416–427, 2016), which counts “belt type” cyclic polyazulenoid, this article studies the enumeration problem of Möbius type cyclic polyazulenoid. We obtain the exact counting formula for the number of Möbius type cyclic polyazulenoids with n azulene units, by a method based on coding technique and a generalization of ‘Burnside’ lemma. And we give the numerical results for n not larger than 20, which may contribute to the fully synthesis of Möbius type cyclic polyazulenoids.     

Disclosure of Ground-State Zimmerman-Möbius Aromaticity in the Radical Anion of [6]Helicene and Evidence for 4π Periodic Aromatic Ring Currents in a Molecular “Metallic” Möbius Strip

In 1966, Zimmerman proposed a type of Möbius aromaticity that involves through-space electron delocalization; it has since been widely applied to explain reactivity in pericyclic reactions, but is considered to be limited to transition-state structures. Although the easily accessible hexahelicene radical anion has been known for more than half a century, it was overlooked that it exhibits a ground-state minimum and robust Zimmerman-Möbius aromaticity in its central noose-like opening, becoming, hence, the oldest existing Möbius aromatic system and with smallest Möbius cycle known. Despite its overall aromatic stabilization energy of 13.6 kcal mol⁻¹ (at B3LYP/6-311+G**), the radical also features a strong, globally induced paramagnetic ring current along its outer edge. Exclusive global paramagnetic currents can also be found in other fully delocalized radical anions of 4N+2 π-electron aromatic polycyclic benzenoid hydrocarbons (PAH), thus questioning the established magnetic criterion of antiaromaticity. As an example of a PAH with nontrivial topology, we studied a novel Möbius[16]cyclacene that has a non-orientable surface manifold and a stable closed-shell singlet ground state at several density functional theory levels. Its metallic monoanion radical (0.0095 eV band gap at HSE06/6-31G* level) is also wave-function stable and displays an unusual 4π-periodic, magnetically induced ring current (reminiscent of the transformation behaviour of spinors under spatial rotation), thus indicating the existence of a new, Hückel-rule-evading type of aromaticity.     

Aromaticity and Möbius antiaromaticity in monocyclic [11]annulenium cations

Monocyclic [11]annulenium cations, which are experimentally unknown, have been studied primarily via DFT methods but also with some CCSD(T) validation. We have located six minima: two doubly trans (26, 27), one triply trans (28), one singly trans (29), one quintuply trans (trannulene-type, 33), and one all-cis (31). The first three are aromatic, 33 is modestly aromatic, 29 is nonaromatic, and the last is a M?bius antiaromatic species. We also investigated the fusion of various numbers of three-membered rings (3MRs) to the central 11-membered ring (11MR). We found several planar, all-cis-[11]annulenium ion derivatives as well as another M?bius antiaromatic species (52b); for comparison, we also found planar, antiaromatic all-cis-[12]annulene (60) and [15]annulenium cation (61) derivatives. The (anti)aromatic characterization of these compounds is based mainly on calculated magnetic data for the ground singlet and vertical triplet states, although aromatic stabilization energies (ASE) are also considered. Data for optimized triplets, several of which are M?bius aromatic systems (31t, 52t, 63t, 64t), are also included. Several of these cations are reasonable synthetic targets.     

Confusion of Möbius aromaticity: disruption of annulenic pathway in singly N-confused [28]hexaphyrin and its mono-Pd(II) complex

Singly N-confused [26] and [28]hexaphyrins (4, 5) with planar and twisted structures, respectively, were prepared via the acid catalyzed [3 + 3] condensation of N-confused and regular tripyrrane precursors. Hückel aromaticity is observed for [26]hexaphyrin, while the [28]hexaphyrin and its mono-Pd(II) complex exhibit "nonaromaticity" in spite of their M?bius-type structures, judging from the spectroscopic features and theoretical calculations.     

Synthesis and properties of the first Möbius annulenes

Heilbronner in 1964 predicted that annulenes with ".. a planar perimeter of N=4r AO's, which would yield an open shell configuration when occupied by 4r electrons, can be twisted into a closed shell M?bius strip perimeter without loss in pi electron energy". We have been able to synthesize the first [4n]annulene with such a M?bius topology and now present further M?bius isomers and the details of their preparation as stable compounds. To address the question whether the twist in the pi system has an effect on the properties we systematically investigate energy, geometry and magnetic parameters of a large number isomers of [16]annulenes. The M?bius twisted annulenes are consistently more aromatic than the non-twisted isomers. This is true for the parent as well as our benzoannelated systems. Our results are in contrast to those published recently by C. Castro, W. L. Karney, P. von R. Schleyer et al.     

Möbius function and characteristic monomials for combinatorial enumeration

After the definitions of amplified representations and number-theoretical vectors, the markaracter table of a cyclic subgroup is converted into the corresponding Q-conjugacy character table. The conversion is shown to necessitate an interconversion matrix that contains M?bius functions as elements. Since the interconversion matrix gives characteristic monomials for cyclic groups, all the powers appearing in each of the characteristic monomials are shown to be integers. Characteristic monomials for finite groups are then built up by starting from those of cyclic groups. This procedure clarifies the fact that all the powers appearing in each characteristic monomial for finite groups are integers. The relationship between characteristic monomial tables and unit-subduced-cycle-index tables is discussed with respect to their application to isomer enumeration. Received: 15 July 1998 / Accepted: 16 December 1998 / Published online: 16 March 1999     

Mössbauer spectroscopy of liquid SnCl4 solutions trapped in a rigid microemulsion

A rigid microemulsion was prepared containing submicroscopic droplets of liquid aqueous tin tetrachloride solution. Recoilless-ray resonance absorption (the Mössbauer effect] was achieved in this system, indicating that the organic dispersion medium of the microemulsion behaved as a carrier, enhancing the Debye-Waller factor for the quasiliquid phase of the system. The Mössbauer spectra reflected the presence of two types of tin(IV) in the cavities of the microemulsion: SnCl₄ species situated in the bulk solution and on the cavity wall, respectively.