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.     

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.     

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.     

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     

Lemniscular hexaphyrins as examples of aromatic and antiaromatic double-twist Möbius molecules

Two reported [26] and [28]hexaphyrins are analyzed via measured and computed geometries and NMR-shieldings as examples of respectively 4n + 2 pi-electron aromatic and 4n pi-electron antiaromatic double-twist M?bius ring systems, adopting a lemniscular/figure-eight topology with linking number LK = 2pi. Values of local twist (TW) and nonlocal writhe (WR) derived from the relation Lk = Tw + WR appear relatively insensitive to the aromatic/antiaromatic character. The [26]hexaphyrin may adopt differing solution and solid-state conformations.     

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     

Möbius and twisted graphene nanoribbons: stability, geometry, and electronic properties

Results of classical force field geometry optimizations for twisted graphene nanoribbons with a number of twists N(t) varying from 0 to 7 (the case N(t)=1 corresponds to a half-twist M?bius nanoribbon) are presented in this work. Their structural stability was investigated using the Brenner reactive force field. The best classical molecular geometries were used as input for semiempirical calculations, from which the electronic properties (energy levels, HOMO, LUMO orbitals) were computed for each structure. CI wavefunctions were also calculated in the complete active space framework taking into account eigenstates from HOMO-4 to LUMO+4, as well as the oscillator strengths corresponding to the first optical transitions in the UV-VIS range. The lowest energy molecules were found less symmetric than initial configurations, and the HOMO-LUMO energy gaps are larger than the value found for the nanographene used to build them due to electronic localization effects created by the twisting. A high number of twists leads to a sharp increase of the HOMO-->LUMO transition energy. We suggest that some twisted nanoribbons could form crystals stabilized by dipolar interactions.     

Toward Möbius and Tubular Cyclopolyarene Nanorings via Arylbutadiyne Macrocycles

By harnessing a highly efficient metal-catalyzed tandem cycloaddition reaction as the key benzannulation step, a series of cyclopolyarene nanorings of varied sizes are obtained from poly(arylene-butadiynylene) macrocyclic precursors, which can be synthesized relatively conveniently. Interestingly, due to the nonparallel bond connectivity of the repeat unit, unique Möbius topology is manifested by the cyclopolyarene nanorings composed of an odd number of repeat units, whereas cylindrical tubular structures with radial conjugation are formed with those consisting of an even number of repeat units.     

Graphene Nanobelts,Möbius and Higher Order Möbius Strips Formed from Graphene. A Combined CASSCF/DFT Study

Russian Journal of Physical Chemistry A - Twisted graphene nanoribbons with linking numbers (Lk) of 2 and 3 have been studied at hybrid DFT and CASSCF levels. CASSCF calculations demonstrated...     

Assembly and autochirogenesis of a chiral inorganic polythioanion Möbius strip via symmetry breaking

Using [Mo(2)S(2)O(2)(H(2)O)(6)](2+) and squarate dianion, we synthesized the thiometalate ring compounds [(Mo(2)S(2)O(2))(x)(OH)(y)(C(4)O(4))(z)(Mo(2)O(8))(o)(H(2)O)(p)](n-), where [x,y,z,o,p,n] = [7,14,2,0,2,4] for 1, [6,8,2,2,4,8] for 2, and [4,6,1,1,0,4] for both 3a and 3b, which are chiral and nonchiral isomers, respectively. Not only do the four thiometalate clusters show decreasing symmetry at the molecular level across the series, but the incorporation of the "addendum" {Mo(2)O(8)}(o) unit also allows the thiometalate ring to twist. The reaction initially yields the chiral molecule 3a with a twisted ring, which undergoes spontaneous resolution upon crystallization; the reaction mixture later yields the intrinsically nonchiral isomer 3b with a nontwisted ring. In addition, the compounds are able to promote the electrocatalytic evolution of hydrogen.     

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 strip versus linear and cyclic polyacenes: a Hückel and semiempirical investigation

The electronic structure of finite and infinite linear, cyclic and M?bius strip polyacenes has been investigated by adopting Hückel and semiempirical schemes. Using the Hückel approach, it turns out that the M?bius belting process modifies the highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap in such a way its evolution with chain length is similar to the linear polyacenes rather than their cyclic analogs. These results are corroborated at the Austin model 1 (AM1) level, where the geometry relaxation effects are taken into account. The optimized AM1 structures show that the M?bius defect is localized and extends over a third of the ring. With respect to the Hückel approach, accounting for geometry distortion at the AM1 levels results in an increase in the HOMO–LUMO gap of the M?bius strip relative to the linear and cyclic finite-size structures. On the other hand, when including electron-hole correlation at the configuration interaction singles/Zerner's intermediate neglect of differential overlap level the behavior with system size of the first excitation energy of cyclic and M?bius polyacenes differs from their linear analogs and leads to smaller singlet excitation energies. Received: 20 September 2000 / Accepted: 21 September 2000 / Published online: 28 February 2001     

Hückel and Möbius Aromaticity in Charged Sigma Complexes

In sigma complexes, intermediates in nucleophilic and electrophilic aromatic substitution and other reactions, delocalization in the aromatic ring is formally disrupted. Unexpectedly, computational evidence is presented that favorable processes contain aromatic sigma complexes. Tetracoordinated carbon therein surprisingly employs orbitals that are more similar to sp² than to sp³ hybrids in sigma bonds with adjacent ring atoms. Both leaving groups and nucleo- or electrophiles may donate electrons to the π-system depending on the availability of p-type orbitals to fulfill Hückel (4N+ 2) or Möbius (4N) rules of aromaticity in analogy to conjugated transition-metal metallacycles.     

Phosphorus-fluorine chemistry—XXXVI: Preparation and chemistry of thienyldifluorophosphine

2-Thienyldifluorophosphine has been prepared by chlorine-fluorine exchange in the corresponding dichlorophosphine; the difluorophosphine has been found to undergo redox disproportionation with formation of 2-thienyltetrafluorophosphorane and pentathienylcyclopentaphosphine. Upon reaction with nickel carbonyl, 2-thienyldifluorophosphine forms a tetrasubstituted derivative which may be oxidized by iodine to give tris(thienyldifluorophosphine)nickel(II)iodide. Di- and tri-substituted derivatives of molybdenum carbonyl have been obtained through displacement of the coordinated cycloolefin by the fluorophosphine in bicycloheptadienetetracarbonyl molybdenum and cycloheptatrient-tricarbonyl molybdenum. All compounds were characterized by i.r., n.m.r., and mass spectrometry. A comparison of δ_P values for thienyl-phosphorus compounds with data for the analogous phenyl-phosphorus compounds has shown a high-field shift for the thiophene derivatives in every case. A comparison of δ_F values has shown the opposite effect.     

Optical Physical Mechanisms of Helicene Carbon Nanohoop with Möbius Topology

Optical and spectral properties of carbon nanohoop with Möbius topology is of great interest in nano-science and nano-technology. And it can be imagined that it has a lot of unexpected potential application prospects. However, theoretical calculations based on some figure-of-eight helicene carbon nanohoop with Möbius topology are still insufficient. Therefore, in this paper, we theoretically study the optical and spectral properties of figure-of-eight helicene carbon nanohoop with Möbius topology. Optical and spectral properties are analyzed with visualization method of transition density matrix and charge density difference, which reveal the unique characterization of carbon nanohoop with Möbius topology. Our results can not only deepen the understanding of the optical physical mechanisms of the nanorings with mobius carbons, but also provide deeper insight on optical properties and potential design on optical nanodevices.     

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.