[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.     

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.     

Hückel and möbius boundary conditions for solids and orbital symmmetry correlation in the rotational phase transition of molecular crystals

A new cyclic boundary condition which corresponds to a Möbius strip representation of a one-dimensional crystal is introduced. It is compared with the usual Bloch and Born—von Karman boundary condition which is shown to be a Hückel condition in the sense of LCAO MO treatment of a ring structure. The potential relevance of this Möbius condition to one-dimensional molecular and liquid crystals in which the relative molecular orientation changes during phase transition is alluded to. A comparison of the energies for the twisted and non-twisted form of the linear crystal is derived in the LCAO approximation. The orbital symmetry correlation in the concerted twist of the atomic or molecular orbitals atom! the linear backbone during a rotational polymorphic structural transition is also derived.     

Probing the relationship between spin contamination and first hyperpolarizability: Open‐shell Möbius anion

Möbius strip has attracted extensive interest due to its one‐side structure, special physical and chemical properties. A new extended porphyrin with Möbius structure has been synthesized (St?pień et al., Angew. Chem. Int. Ed. 2007, 46, 7869). In this work, an electron is injected into Möbius to form Möbius anion. For Möbius, four methods (B3LYP, BHandHLYP, CAM‐B3LYP, and LC‐BLYP) obtain the similar first hyperpolarizability (β₀). However, for Möbius anion, four methods obtain very different β₀ values (ranging from 9.85 × 10³ to 8.33 × 10⁵ au). Moreover, the β₀ values of Möbius anion are larger than those of Möbius. Why? The considerable variation (ranging from 0.8162 to 1.7630) of spin contamination (S²) of open‐shell Möbius anion captures our attention. To probe the relationship between S² and β₀, the β₀ values of Möbius anion were calculated using 23 methods. Interestingly, the Hartree‐Fock (HF) composition increases from 0 to 50, the S² value ranges from 0.7522 to 1.3372, and the β₀ value increases from 4.3 × 10³ to 7.36 × 10⁴ au. Further, methods are “dissected” to investigate the effect of HF composition on the S². © 2014 Wiley Periodicals, Inc.     

meso‐Aryl [20]π Homoporphyrin: The Simplest Expanded Porphyrin with the Smallest Möbius Topology

An unstable conjugated homoporphyrin was successfully stabilized by introducing meso ‐aryl substitutents. It was evident from the moderate diatropic ring current found by NMR analysis that the newly formed 20π conjugated free base and its protonated form exhibited Möbius aromatic character. Furthermore, complexation as a ligand with an Rh^I ion afforded a unique binding mode and retained the Möbius aromaticity. Overall, these compounds are the smallest Möbius aromatic molecules, as confirmed by spectral and crystal‐structure analysis and supported by theoretical studies.     

Aggregation‐Induced‐Emission‐Active Macrocycle Exhibiting Analogous Triply and Singly Twisted Möbius Topologies

Molecules with Möbius topology have drawn increasing attention from scientists in a variety of fields, such as organic chemistry, inorganic chemistry, and material science. However, synthetic difficulties and the lack of functionality impede their fundamental understanding and practical applications. Here, we report the facile synthesis of an aggregation‐induced‐emission (AIE)‐active macrocycle (TPE‐ET) and investigate its analogous triply and singly twisted Möbius topologies. Because of the twisted and flexible nature of the tetraphenylethene units, the macrocycle adjusts its conformations so as to accommodate different guest molecules in its crystals. Moreover, theoretical studies including topological and electronic calculations reveal the energetically favorable interconversion process between triply and singly twisted topologies.     

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 Reversal in the Lowest Excited Triplet State of Archetypical Möbius Heteroannulenic Systems

The aromaticity reversal in the lowest triplet state (T₁) of a comparable set of Hückel/Möbius aromatic metalated expanded porphyrins was explored by optical spectroscopy and quantum calculations. In the absorption spectra, the T₁ states of the Möbius aromatic species showed broad, weak, and ill‐defined spectral features with small extinction coefficients, which is in line with typical antiaromatic expanded porphyrins. In combination with quantum calculations, these results indicate that the Möbius aromatic nature of the S₀ state is reversed to Möbius antiaromaticity in the T₁ state. This is the first experimental observation of aromaticity reversal in the T₁ state of Möbius aromatic molecules.     

ESI‐MS/MS of expanded porphyrins: a look into their structure and aromaticity

Electrospray mass spectrometry/mass spectrometry was used to investigate the gas‐phase properties of protonated expanded porphyrins, in order to correlate those with their structure and conformation. We have selected five expanded meso‐pentafluorophenyl porphyrins, respectively, a pair of oxidized/reduced fused pentaphyrins (22 and 24 π electrons), a pair of oxidized/reduced regular hexaphyrins (26 and 28 π electrons) and a regular doubly N‐fused hexaphyrin (28 π electrons). The gas‐phase behavior of the protonated species of oxidized and reduced expanded porphyrins is different. The oxidized species (aromatic Hückel systems) fragment more extensively, mainly by the loss of two HF molecules. The reduced species (Möbius aromatic or Möbius‐like aromatic systems) fragment less than their oxidized counterparts because of their increased flexibility. The protonated regular doubly fused hexaphyrin (non‐aromatic Hückel system) shows the least fragmentation even at higher collision energies. In general, cyclization through losses of HF molecules decreases from the aromatic Hückel systems to Möbius aromatic or Möbius‐like aromatic systems to non‐aromatic Hückel systems and is related to an increase in conformational distortion. Copyright © 2016 John Wiley & Sons, Ltd.     

Interplay of Hückel and Möbius Aromaticity in Metal-Metal Quintuple Bonded Complexes of Cr,Mo, and W with Amidinate Ligand: Ab initio DFT and Multireference Analysis**

The aromaticity of metal-metal quintuple bonded complexes of the type M₂L₂ (M=Cr, Mo, and W; L=amidinate) are studied employing gauge including magnetically induced ring current (GIMIC) analysis and electron density of delocalized bonds (EDDB). It is found that the complexes possess two types of aromaticity: i) Hückel aromaticity through delocalization of ligand π electrons with metal-metal δ-bond-forming 6 conjugated electrons (4π and 2δ) ring; ii) Craig-Möbius aromaticity through delocalization of π electrons of both the ligands with metal d-orbitals in Craig type orientation forming 10π electrons ring with a double twist. Extended transition state natural orbital chemical valence (ETS-NOCV) and canonical molecular orbital natural chemical shielding (CMO-NCS) analysis confirm the Craig-Möbius type arrangement of the orbitals. Furthermore, the unprecedented Hückel and Möbius type aromaticity is confirmed from the plot of the current pathways using 3D line integral convolution (3D-LIC) plots. The metal-metal bond order also increases down the group as justified from the complete active space self-consistent field (CASSCF) analysis. Due to an increase in the π and δ electron conjugation, both the Hückel and Möbius aromaticity increase down the group.     

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.     

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.     

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).     

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.     

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.     

Möbius and hückel systems in the SCF and CI approximations

Over the last 15 years since the introduction of Möbius-Hückel theory, a number of varied questions has accumulated. The most interesting of these deals with the question of whether or not the Möbius-Hückel theory is valid in the SCF and SCF-CI approximation. This paper presents a treatmet which shows that the repulsion and exchange contributions are independent of the Möbius vs Hückel nature of the orbital array. Also it is shown that the one-electron terms are symmetry determined and derive from SCF coefficients. An analytical SCF-CI treatment if given. Several further unanswered questions are also considered.     

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.     

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.