Viability of Möbius Topologies in [26]‐ and [28]Hexaphyrins

Recently, hexaphyrins have emerged as a promising class of π‐conjugated molecules that display a range of interesting electronic, optical, and conformational properties, including the formation of stable Möbius aromatic systems. Besides the Möbius topology, hexaphyrins can adopt a variety of conformations with Hückel and twisted Hückel topologies, which can be interconverted under certain conditions. To determine the optimum conditions for viable Möbius topologies, the conformational preferences of [26]‐ and [28]hexaphyrins and the dynamic interconversion between the Möbius and Hückel topologies were investigated by density functional calculations. In the absence of meso substituents, [26]hexaphyrin prefers a planar dumbbell conformation, strongly aromatic and relatively strain free. The Möbius topology is highly improbable: the most stable tautomer is 33 kcal mol^?1 higher in energy than the global minimum. On the other hand, the Möbius conformer of [28]hexaphyrin is only 6.5 kcal mol^?1 higher in energy than the most stable dumbbell conformation. This marked difference is due to aromatic stabilization in the Möbius 4n electron macrocycle as opposed to antiaromatic destabilization in the 4n+2 electron system, as revealed by several energetic, magnetic, structural, and reactivity indices of aromaticity. For [28]hexaphyrins, the computed activation barrier for interconversion between the Möbius aromatic and Hückel antiaromatic conformers ranges from 7.2 to 10.2 kcal mol^?1, in very good agreement with the available experimental data. The conformation of the hexaphyrin macrocycle is strongly dependent on oxidation state and solvent, and this feature creates a promising platform for the development of molecular switches.     

[32]π Fused Core‐Modified Heptaphyrin with Möbius Aromaticity

A new fused core‐modified 32π heptaphyrin with Möbius aromatic character is reported. The ¹H NMR data indicated a weak Möbius aromaticity at 298 K; however, at 213–183 K, the molecule predominates [4n]π Möbius conformation with strong diatropic ring current, which was further confirmed by X‐ray analysis. The protonation experiment led to preservation of the Möbius aromaticity at 298 K. Nevertheless, the experimental results were further supported by theoretical studies. Overall, this study represents the first example of Möbius aromatic fused core‐modified expanded porphyrin.     

Mechanochemically Triggered Topology Changes in Expanded Porphyrins

A hitherto unexplored class of molecules for molecular force probe applications are expanded porphyrins. This work proves that mechanical force is an effective stimulus to trigger the interconversion between Hückel and Möbius topologies in [28]hexaphyrin, making these expanded porphyrins suitable to act as conformational mechanophores operating at mild (sub-1 nN ) force conditions. A straightforward approach based on distance matrices is proposed for the selection of pulling scenarios that promote either the planar Hückel topology or the three lowest lying Möbius topologies. This approach is supported by quantum mechanochemical calculations. Force distribution analyses reveal that [28]hexaphyrin selectively allocates the external mechanical energy to molecular regions that trigger Hückel–Möbius interconversions, explaining why certain pulling scenarios favor the Hückel two-sided topology and others favor Möbius single-sided topologies. The meso-substitution pattern on [28]hexaphyrin determines whether the energy difference between the different topologies can be overcome by mechanical activation.     

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.     

A Möbius Aromatic [28]Hexaphyrin Bearing a Diethylamine Group: A Rigid but Smooth Conjugation Circuit

The reaction of [26]hexaphyrin with triethylamine in the presence of BF₃?OEt₂ and O₂ furnished a diastereomeric mixture of a diethylamine‐bearing [28]hexaphyrin as a rare example of a Möbius aromatic metal‐free expanded porphyrin. The Möbius aromaticity of these molecules is large, as indicated by their large diatropic ring currents, which are even preserved at 100 °C, owing to their internally multiply bridged robust structure with a smooth conjugation network. These molecules were reduced with NaBH₄ to give an antiaromatic [28]hexaphyrin, and were oxidized with MnO₂ to give aromatic [26]hexaphyrins, both through a Möbius‐to‐Hückel topology switch induced by a C? N bond cleavage.     

Topology Switching in [32]Heptaphyrins Controlled by Solvent,Protonation, and meso Substituents

The switching of topology between “figure‐eight”, Möbius, and untwisted conformations in [32]heptaphyrins(1.1.1.1.1.1.1) has been investigated by using density functional theory calculations. Such a change is achieved by variation of one internal dihedral angle and, if properly controlled, can provide access to molecular switches with unique optical and magnetic properties. In this work, we have explored different conformational control methods, such as solvent, protonation and meso substituents. Despite its antiaromatic character, most of the [32]heptaphyrins (R=H, CH₃, CF₃, Ph, C₆F₅) adopt a figure‐eight conformation in the neutral state, owing to their more‐effective hydrogen‐bonding interactions. The aromatic Möbius topology is only preferred with dichlorophenyl groups, which minimize the steric hindrance that arises from the bulky chlorine atoms. The conformational equilibrium is sensitive to the solvent, so polar solvents, such as DMSO, further stabilize the Möbius conformation. Protonation induces a conformational change into the Möbius topology, irrespective of the meso‐aryl groups. In the triprotonated species, the conformational switch is blocked and a non‐twisted conformer becomes much more stable than the figure‐eight conformation. We have shown that the relative energies of the protonated [32]heptaphyrins are dominated by aromaticity. Importantly, this topology switching induces a dramatic change in the magnetic properties and reactivity of the macrocycles, as revealed by several energetic, magnetic, structural, and reactivity indices of aromaticity.     

PdII Complexes of [44]‐ and [46]Decaphyrins: The Largest Hückel Aromatic and Antiaromatic,and Möbius Aromatic Macrocycles

Reductive metalation of [44]decaphyrin with [Pd₂(dba)₃] provided a Hückel aromatic [46]decaphyrin Pd^II complex, which was readily oxidized upon treatment with DDQ to produce a Hückel antiaromatic [44]decaphyrin Pd^II complex. In CH₂Cl₂ solution the latter complex underwent slow tautomerization to a Möbius aromatic [44]decaphyrin Pd^II complex which exists as a mixture of conformers in dynamic equilibrium. To the best of our knowledge, these three Pd^II complexes represent the largest Hückel aromatic, Hückel antiaromatic, and Möbius aromatic complexes to date.     

PdII Complexes of [44]‐ and [46]Decaphyrins: The Largest Hückel Aromatic and Antiaromatic,and Möbius Aromatic Macrocycles

Reductive metalation of [44]decaphyrin with [Pd₂(dba)₃] provided a Hückel aromatic [46]decaphyrin Pd^II complex, which was readily oxidized upon treatment with DDQ to produce a Hückel antiaromatic [44]decaphyrin Pd^II complex. In CH₂Cl₂ solution the latter complex underwent slow tautomerization to a Möbius aromatic [44]decaphyrin Pd^II complex which exists as a mixture of conformers in dynamic equilibrium. To the best of our knowledge, these three Pd^II complexes represent the largest Hückel aromatic, Hückel antiaromatic, and Möbius aromatic complexes to date.     

Hückel theory applied to large linear and cyclic conjugated π-systems

By use of rotational symmetry (C_n-symmetry) a lower limit to the frontier orbital (HOMO-LUMO) gap in large molecules with linear and cyclic conjugated π-systems containing simple repetitive units has been calculated within the Hückel approxmation. The frontier orbitals are shown to be the same in series of cyclic oligomers and liner polymers containing the same repetitive units. The orbital gap is calculated from the repetitive units closed on themselves to give a ring of Hückel or, alternatively, Möbius topology depending on the number of conjugated π-electrons in a liner array between the ends of the repetitive unit. For 4n (4n+2) systems the small ring of Hückel (Möbius) topology will give the frontier orbitals.     

Spiral Intramolecular Charge Transfer and Large First Hyperpolarizability in Möbius Cyclacenes: New Insight into the Localized π Electrons

Much effort has been devoted to investigating the unusual properties of the π electrons in Möbius cyclacenes, which are localized in a special region. However, the localized π electrons are a disadvantage for applications in optoelectronics, because intramolecular charge transfer is limited. This raises the question of how the intramolecular charge transfer of a Möbius cyclacene with clearly localized π electrons can be enhanced. To this end, [8]Möbius cyclacene ([8]MC) is used as a conjugated bridge in a donor–π‐conjugated bridge–acceptor (D–π–A) system, and NH₂‐6‐[8]MC‐10‐NO₂ exhibits a fascinating spiral charge‐transfer transition character that results in a significant difference in dipole moments Δμ between the ground state and the crucial excited state. The Δμ value of 6.832 D for NH₂‐6‐[8]MC‐10‐NO₂ is clearly larger than that of 0.209 D for [8]MC. Correspondingly, the first hyperpolarizability of NH₂‐6‐[8]MC‐10‐NO₂ of 12 467 a.u. is dramatically larger than that of 261 a.u. for [8]MC. Thus, constructing a D–π–A framework is an effective strategy to induce greater spiral intramolecular charge transfer in MC although the π electrons are localized in a special region. This new insight into the properties of π electrons in Möbius cyclacenes may provide valuable information for their applications in optoelectronics.     

Bond-alternating Hückel-Möbius and related,twisted linear,cyclic and helical systems—their molecular orbitals,energies and phase correlation upon dissociation

Cyclic group formalism and screw symmetry operation are used to clarify and generalize the definition of Hückel and Möbius systems. It is shown that the Möbius ring system has half-integral pseudo-angular momentum similar to that of spin space, and that applications of Möbius electronics to chemical reactions have been based on truncated single-circle Möbius rings which have unique beginning and end (Sect. 2). This concept is illustrated by application to the [1, 7] antarafacial hydrogen shift (Appendix A and Figs. A1–A3). Definition of a Hüickel versus Möbius ring system for in-plane and out-of-plane π, δ and φ orbitals as well as the appropriate relative angle of twists are given (Sect. 2 and Table 1). Using the concept of the compatibility of the twist (screw) angle and rotation around a ring, we also derive the proper phase coherence and energy correlation between a parent cyclic (Hückel or Möbius) molecule and its dissociated linear fragments (Sect. 4). The concept of parentage in diabatic fragmentation is discussed. Forfinite, open, helical chain molecules, an exact periodic boundary condition based on the compatibility of twist angle and number of turns in a helical ring parent molecule is applied to derive their analytic wave functions (Sect. 5 and Table 2). Forbond-alternating “linear” and cyclic Hückel and Möbius systems we also derive the explicit LCAO-MO wavefunctions, energies, their degeneracies and their exact corresponding quantum members for even and odd atom systems at highest bonding and lowest antibonding levels (Sect. 3, Figs. 1–3). The corresponding wavefunctions and energies for uniform-bond systems are given for comparison and for completeness (Sect. 3).     

Regioselective Synthesis and Characterization of Multinuclear Convex‐Bound Ruthenium‐[n]Cycloparaphenylene (n=5 and 6) Complexes

Mono‐ and multinuclear complexes of ruthenium and [n]cycloparaphenylene (CPP, n=5 and 6) were synthesized in excellent yields through ligand exchange of the cationic complex [(Cp)Ru(CH₃CN)₃](PF₆) with CPP. In the multinuclear complexes, ruthenium selectively coordinated to alternate paraphenylene units to give bis‐ and tris‐coordinated Ru complexes for [5] and [6]CPPs, respectively. Single‐crystal X‐ray analysis revealed the Ru was coordinated with η⁶‐hapticity on the convex surface of CPP.     

Macrocyclic π-systems with C2-symmetry as the sum of π-systems with hückel and möbius topology

The π-system of a macrocycle with twofold rotation symmetry and 2N conjugated π-electron can conveniently be regarded as the sum of two cyclic N π-electron systems having Hückel and Möbius topology, respectively.     

Hückel and Möbius Expanded para‐Benziporphyrins: Synthesis and Aromaticity Switching

The four expanded p‐benziporphyrins A,C‐di‐p‐benzi[24]pentaphyrin(1.1.1.1.1), N‐fused A‐p‐benzi[24]pentaphyrin, A,D ‐di‐p‐benzi[28]hexaphyrin(1.1.1.1.1.1), and A,C‐di‐p‐benzi[28]hexaphyrin(1.1.1.1.1.1) were obtained in three‐component Lindsey‐type macrocyclizations. These compounds were explored as macrocyclic ligands and as potential aromaticity switches. A BODIPY‐like difluoroboron complex was obtained from the A,C‐di‐p‐benzi[24]pentaphyrin, whereas A,C‐di‐p‐benzi[28]hexaphyrin yielded a Möbius‐aromatic Pd^II complex containing fused pyrrole and phenylene subunits. Conformational behavior, tautomerism, and acid‐base chemistry of the new macrocycles were characterized by means of NMR spectroscopy and DFT calculations. Free base N‐fused A‐p‐benzi[24]pentaphyrin showed temperature‐dependent Hückel–Möbius aromaticity switching, whereas the A,C‐di‐p‐benzi[28]hexaphyrin formed a Möbius‐aromatic dication.     

Syntheses and structures of Cd(II) and Co(II) compounds of 4-[(3-pyridyl)methylamino]benzoate anion

Three coordination polymers containing Cd(II) and Co(II), connected via 4-[(3-pyridyl)methylamino]benzoate (L^?), have been synthesized in hydrothermal conditions. In [Cd(L)Cl] _n (1), adjacent Cd(II) cations are linked by carboxylates to give a dinuclear cluster. Pairs of L^? bridge the dinuclear cluster to form double helical chains, and these chains are further linked by Cl^? to produce a 4-connected net with (4²?·?6³?·?8) topology. [CdL₂] _n (2) contains 1-D ladder-like chains. The packing structure displays a 3-D supramolecular structure, with π?···?π interactions stabilizing the framework. [CoL₂] _n (3) has a 2-D extended supramolecular structure via π?···?π interactions of 1-D coordination polymers of 3. The crystal structures of 1–3 have been determined by single-crystal X-ray diffraction. Luminescent properties for 1 and 2 are discussed.     

A Fully Conjugated Porphyrin-[36]Octaphyrin-Porphyrin Hybrid Tape Exhibiting Möbius Aromaticity

Directly meso-meso linked porphyrin-tetrabromo[36]octaphyrin-porphyrin hybrid trimer 10 was successfully synthesized via acid-catalyzed condensation reaction and subsequent oxidation. Zn^II-metalation of 10 induced transannular meso-meso bond formation to give Möbius aromatic bis-Zn^II octaphyrin 11 , which was oxidized by DDQ/Sc(OTf)₃ to provide fully conjugated porphyrin-[36]octaphyrin-porphyrin hybrid tape 12 as the first example of porphyrin tape exhibiting Möbius aromaticity. Hybrid tape 12 displays significantly red-shifted absorption and small electrochemical HOMO-LUMO gap, indicating the effective conjugation through the whole chromophores.     

SiIV Incorporation into a [28]Hexaphyrin That Triggered Formation of Möbius Aromatic Molecules

Incorporation of Si^IV into an expanded porphyrin has been achieved for the first time. Treatment of [28]hexaphyrin 1 with CH₃SiCl₃ and N,N‐diisopropylethylamine gave Si^IV complex 2 and its N‐fused product 4 that both have Möbius aromatic nature. In both complexes, the coordinated Si atom is satisfied in a typical trigonal bipyramidal coordination. Si^IV incorporation induces conformational rigidification and redshifted absorption profiles due to σ–π conjugation between the Si atom and hexaphyrin macrocycle. Tamao–Fleming oxidation of 2 with H₂O₂ gave β‐hydroxy [28]hexaphyrin 5 , which exists as a ruffled rectangular shape in the solid state, yet it has been revealed to exist predominantly as a twisted Möbius aromatic conformer in CH₂Cl₂.     

Investigation of Cycloparaphenylenes (CPPs) and their Noncovalent Ring-in-Ring and Fullerene-in-Ring Complexes by (Matrix-Assisted) Laser Desorption/Ionization and Density Functional Theory

[n]Cycloparaphenylenes ([n]CPPs) with n=5, 8, 10 and 12 and their noncovalent ring-in-ring and [m]fullerene-in-ring complexes with m=60, 70 and 84 have been studied by direct and matrix-assisted laser desorption ionization ((MA)LDI) and density-functional theory (DFT). LDI is introduced as a straightforward approach for the sensitive analysis of CPPs, free from unwanted decomposition and without the need of a matrix. The ring-in-ring system of [[10]CPP⊃[5]CPP]^+. was studied in positive-ion MALDI. Fragmentation and DFT indicate that the positive charge is exclusively located on the inner ring, while in [[10]CPP⊃C₆₀]^+. it is located solely on the outer nanohoop. Positive-ion MALDI is introduced as a new sensitive method for analysis of CPP⊃fullerene complexes, enabling the detection of novel complexes [[12]CPP⊃C_{60, 70 and 84}]^+. and [[10]CPP⊃C₈₄]^+.. Selective binding can be observed when mixing one fullerene with two CPPs or vice versa, reflecting ideal size requirements for efficient complex formation. Geometries, binding and fragmentation energies of CPP⊃fullerene complexes from DFT calculations explain the observed fragmentation behavior.     

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.