The Simple Connectedness of Tame Algebras with Separating Almost Cyclic Coherent Auslander–Reiten Components

We study the simple connectedness of the class of finite-dimensional algebras over an algebraically closed field for which the Auslander–Reiten quiver admits a separating family of almost cyclic coherent components. We show that a tame algebra in this class is simply connected if and only if its first Hochschild cohomology space vanishes.

     

Aromatic and Antiaromatic Pathways in Triphyrin(2.1.1) Annelated with Benzo[b]heterocycles

Understanding of the aromatic properties and magnetically induced current densities of highly conjugated chromophores is important when designing molecules with strongly delocalized electronic structure. Linear extension of the triphyrin(2.1.1) skeleton with an annelated benzo[b]heterocycle fragment modifies the aromatic character by extending the electron delocalization pathway. Two-electron reduction leads to an antiaromatic triphyrin(2.1.1) ring and an aromatic benzo[b]heterocycle subunit. Current-density calculations provide detailed information about the observed pathways and their strengths.     

Ground State of the Conformal Flow on 𝕊3

We consider the conformal flow model derived in Bizoń et al. (2017) as a normal form for the conformally invariant cubic wave equation on 𝕊³. We prove that the energy attains a global constrained maximum at a family of particular stationary solutions that we call the ground state family. Using this fact and spectral properties of the linearized flow (which are interesting in their own right due to a supersymmetric structure), we prove nonlinear orbital stability of the ground state family. The main difficulty in the proof is due to the degeneracy of the ground state family as a constrained maximizer of the energy. © 2019 Wiley Periodicals, Inc.     

Stereocontrolled Synthesis of Chiral Heteroaromatic Propellers with Small Optical Bandgaps

Chiral heteroaromatic propellers based on radially π‐extended hexapyrrolohexaazacoronenes were obtained in a concise synthesis from suitably functionalized donor–acceptor monopyrroles. To overcome steric hindrance, a new cyclodehydrogenation method was developed, and it uses bromine electrophiles as oxidative coupling agents instead of the commonly employed high‐potential oxidants. The new reaction offers high yields of propeller‐shaped targets, even for electron‐deficient precursors, and shows electrophile‐dependent stereoselectivity, with N‐bromosuccinimide and dibromine yielding, respectively D₆‐ and C₂‐symmetric products. The propeller azacoronenes are chiral and can be separated into configurationally stable enantiomers. In addition to providing steric bulk, peripheral functionalization considerably affects the electronic properties of the propellers, which exhibit reduced optical and electrochemical band gaps, and a more clearly defined electroreduction behavior.     

Mono-Aryl/Alkylthio-Substituted (Hetero)acenes of Exceptional Thermal and Photochemical Stability by the Thio-Friedel–Crafts/Bradsher Cyclization Reaction

The highly substituted mono-aryl/alkylthio-(hetero)acenes prepared in this study have been found to be thermally more stable (T_decomp.=331–354 °C) than the known di-aryl/alkylthio-substituted acenes by an average of 25 °C. They are also much more photostable at 254 and 365 nm (in both argon and air) than the parent anthracene and other reported anthracenes. The most photostable aryl/alkylthio-anthracenes at 254 nm were found to be 60–70 (in air) and 130 (in argon) times more stable in solution than the unsubstituted anthracene, and much more stable than known EDG/EWG-substituted anthracenes (EDG=electron-donating group, EWG=electron-withdrawing group) with an extended aromatic core. Furthermore, the acenes showed significantly higher photostability at 365 nm in both air and argon. The anthracenes were obtained by the novel thio-Friedel–Crafts/Bradsher cyclization reaction of hitherto unknown [o-(1,3-dithian-2-yl)aryl](aryl)methyl thioethers. The developed approach provides a general access to mono-aryl/alkylthio-substituted (hetero)acene frameworks containing at least three fused (hetero)aromatic rings. The characteristic feature of this approach, which leads to highly substituted acenes, is that the substituents, unlike in other methods, may be introduced at an early stage of the synthesis. DFT and TD-DFT calculations confirmed the stabilizing role of the aryl/alkylthio substituent in the mono-aryl/alkylthio-substituted anthracenes, which are the most stable anthracenes prepared to date. Their high photostability is mainly due to the quenching of singlet oxygen by the acene and the quenching of the acene S₁ state by molecular oxygen.     

N → Sn coordination in the complexes of tin halides with pyridine: A comparison between Sn(II) and Sn(IV)

The experimentally well‐known complexation of tin(II) and tin(IV) halides with pyridine (py) leads to structures showing N → Sn coordination. In the present work, the complexes SnX_n·mpy (where X = F, Cl, Br, I; n = 2, 4; m = 1, 2) possessing this kind of coordination were studied using a computational quantum chemical approach. Various aspects in the theoretical picture of these complexes were examined to find similarities and differences in their N → Sn coordination. The aspects included, among others, the physical nature of intermolecular interactions, and their role in establishing the structure and energetic stabilization of the complexes. In this context, the effect of tin valency was inspected in great detail. As proven by several theoretical methods, a largely ionic character with a certain covalent component can be attributed to the studied N → Sn coordination, irrespective of tin valency. All complexes are destabilized by py‐py and three‐body interactions, but the Sn(II) complexes experience it to a greater extent. Marked differences are observed in the structural behavior of N → Sn and SnX_n during complex formation. This affects the energetics of complexation and, in consequence, the penta‐coordinated Sn(IV) center shows a higher propensity to expand its coordination number, compared with the tri‐coordinated Sn(II) center. The present study supplements the experimental characterization of SnX_n·mpy and, in general, it sheds light on the coordination of heteroaromatic nitrogen to tin. The survey of the Cambridge Structural Database revealed that such coordination occurred in a number of crystal structures.     

Bis(N‐Confused Porphyrin) as a Semirigid Receptor with a Chirality Memory: A Two‐Way Host Enantiomerization through Point‐to‐Axial Chirality Transfer

The adduct formation of protonated bis(N‐confused porphyrin) (BNCP, 3,3′‐bis(meso‐tetratolyl‐2‐aza‐21‐carbaporphyrin) with chiral anions, carboxylic acids, and alcohols was studied in solution by means of ¹H NMR and circular dichroism (CD) spectroscopic analysis and DFT methods. The addition of enantiopure guests to the acidified BNCP resulted in optical activity that vanished after neutralization. Pairs of the ¹H NMR‐distinguishable diastereomers were formed when enantiopure guests were applied, although a single form was observed upon the addition of the racemic mixtures in each case. Unidirectional configuration change that led to diastereomeric excess was observed in several instances. Such an excess was memorized by metalation of the adducts with AgBF₄, thus resulting in optically active silver(III) complexes of BNCP with some enantiomeric excess. Absolute configurations of BNCP cations and bis(zinc) and bis(silver(III)) complexes were determined on the basis of time‐dependent (TD)‐DFT calculations of their CD spectra. It was shown that some of the chiral carboxylates induced opposite directions of enantiomerization of di‐ and tetracations or di‐/tetracation and bis(zinc) complexes. The source of the optical activity of the equimolar diastereomeric mixture of adducts is discussed.     

Supramolecular Recognition Influences Magnetism in [X@HVIV8VV14O54]6− Self‐Assemblies with Symmetry‐Breaking Guest Anions

Mixed‐valence polyoxovanadates(IV/V) have emerged as one of the most intricate class of supramolecular all‐inorganic host species, able to encapsulate a wide variety of smaller guest templates during their self‐assembly formation process. As showcased herein, the incorporation of guests, though governed solely by ultra‐weak electrostatic and van der Waals interactions, can cause drastic effects on the electronic and magnetic characteristics of the shell complex of the polyoxovanadate. We address the question of methodology for the magnetochemical analysis of virtually isostructural {V^IV/V₂₂O₅₄}‐type polyoxoanions of D_2d symmetry enclosing diamagnetic VO₂F₂^? (C_2v), SCN^? (C_∞v), or ClO₄^? (T_d) template anions. These induce different polarization effects related to differences in their geometric structures, symmetry, ion radii, and valence shells, eventually resulting in a supramolecular modulation of magnetic exchange between the V(3d) electrons that are partly delocalized over the {V₂₂O₅₄} shells. We also include the synthesis and characterization of the novel [V^VO₂F₂@HV^IV₈V^V₁₄O₅₄]^6? system that comprises the rarely encountered discrete difluorovanadate anion as a quasi‐isolated guest species.