Triplet acetylenes as synthetic equivalents of 1,2-bicarbenes, part II: new supramolecular scaffolds from photochemical cycloaddition of diarylacetylenes to 1,4-cyclohexadienes

1,5-Diaryl substituted homoquadricyclanes which are readily available through cascade photocycloaddition of diarylacetylenes to 1,4-cyclohexadienes are useful supramolecular scaffolds with an angle of about 60 degrees formed by the two aromatic rings defining a hydrophobic cavity. These structural features of pyridinyl homoquadricyclanes were applied to the design of composite organic/inorganic materials with topologies depending on the ratio of ligand to metal. The crystal structure of complex 1 (L1/AgNO(3) in a 1:1 ratio) shows an alternating ligand-metal polymer in which each of the silver ions in its linear coordination geometry is shared between two L1 molecules. A small change in the crystallization method yields a supramolecular rhomboid (complex 2, L1/AgNO(3) 3:2 ratio) which has two ligands that occupy opposite corners of the rhomboid and two silver atoms occupy the other two corners. Connection of the rhomboids units through a third molecule forms unique "beads on a string" polymeric chains. In complex 2, the silver ions adopt a distorted tetrahedral geometry with the nitrate anion occupying one of the vertices of the tetrahedron. The crystal packing of the chain of rhomboids generates cavities which are filled with disordered solvent molecules. Non-symmetrical homoquadricyclane L3 coordinates with silver only through the nitrogen of the pyridine ring but not through the nitrogen of the tetrafluoropyridine ring in which the electron density of the nitrogen lone-pair is very low. The substituents on the polycyclic moiety of the homoquadricyclane cause restricted rotation of the pyridine rings which suggests that the flexibility of such systems can be fine-tuned to create a family of supramolecular scaffolds of controlled rigidity.     

Exchange coupling of paramagnetic ions in a polyoxometalate matrix: density functional study of diiron(III) substituted gamma-silicotungstates

The quantum chemical (density functional) analysis of the antiferromagnetic interactions between the two iron centers incorporated into the gamma-silicotungstate is performed. The influence of the polyoxometalate framework on the exchange coupling within the diiron core unit is studied. The dependence of the strength of antiferromagnetic exchange on the protonation of the core bridges is considered. It is shown that the magnetic coupling is very sensitive to the distortions in core geometry. Variations in the core structure induced by the environment (such as the polyoxometalate framework) change the significance of superexchange pathways and give rise to new superexchange mechanisms. This effect is especially pronounced in the case of the hydroxo-bridged diiron core.     

C1-c5 photochemical cyclization of enediynes

This study reports a new photochemical cyclization of tetrafluoropyridinyl (TFP)-substituted enediynes that is accompanied with four formal hydrogen-atom abstractions from organic substrates and is mechanistically different from the Bergman cyclization.     

The excitonic insulator route through a dynamical phase transition induced by an optical pulse

We consider a dynamical phase transition induced by a short optical pulse in a system prone to thermodynamical instability. We address the case of pumping to excitons whose density contributes directly to the order parameter. To describe both thermodynamic and dynamic effects on equal footing, we adopt a view of the excitonic insulator for the phase transition and suggest a formation of the Bose condensate for the pumped excitons. The work is motivated by experiments in donor–acceptor organic compounds with a neutral- ionic phase transition coupled to the spontaneous lattice dimerization and to charge transfer excitons. The double nature of the ensemble of excitons leads to an intricate time evolution, in particular, to macroscopic quantum oscillations from the interference between the Bose condensate of excitons and the ground state of the excitonic insulator. The coupling of excitons and the order parameter also leads to self-trapping of their wave function, akin to self-focusing in optics. The locally enhanced density of excitons can surpass a critical value to trigger the phase transformation, even if the mean density is below the required threshold. The system is stratified in domains that evolve through dynamical phase transitions and sequences of merging. The new circumstances in experiments and theory bring to life, once again, some remarkable inventions made by L.V. Keldysh.     

Radical cascade transformations of tris(o-aryleneethynylenes) into substituted benzo[a]indeno[2,1-c]fluorenes

Oligomeric o-aryleneethynylenes with three triple bonds undergo cascade radical transformations in reaction with a Bu 3SnH/AIBN system. These cascades involve three consecutive cycle closures with the formation of substituted benzo[ a]indeno[2,1- c]fluorene or benzo[1,2]fluoreno[4,3- b]silole derivatives. The success of this sequence depends on regioselectivity of the initial attack of the Bu 3Sn radical at the central triple bond of the o-aryleneethynylene moiety. The cascade is propagated through the sequence of 5-exo-dig and 6-exo-dig cyclizations which is followed by either a radical attack at the terminal Ar substituent or radical transposition which involves H-abstraction from the terminal TMS group and 5-endo-trig cyclization. Overall, the transformation has potential to be developed into an approach to a new type of graphite ribbons.     

Graphs with full rank 3-color matrix and few 3-colorings

We exhibit a counterexample to a conjecture of Thomassen stating that the number of distinct 3-colorings of every graph whose 3-color matrix has full column rank is superpolynomial in the number of vertices.     

Rademacher multiplicator spaces equal to

Let be a rearrangement invariant function space on [0,1]. We consider the Rademacher multiplicator space of measurable functions such that for every a.e. converging series , where are the Rademacher functions. We characterize the situation when . We also discuss the behaviour of partial sums and tails of Rademacher series in function spaces.

     

The Number of Open Paths in an Oriented <Emphasis Type="Italic">ρ</Emphasis>-Percolation Model

We study the asymptotic properties of the number of open paths of length n in an oriented ρ-percolation model. We show that this number is e ^{n α(ρ)(1+o(1))} as n→∞. The exponent α is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitly computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show that the number of such paths is n ^−1/2 We ^{n α(ρ)}(1+o(1)) for some nondegenerate random variable W. We build on connections with the model of directed polymers in random environment, and we use techniques and results developed in this context.     

Theoretical Study of Glycidol Hyperbranching Polymerisation

Bulk hyperbranched anionic polymerisation of glycidol initiated by methoxide anion has been studied at B3PW91/6‐311+G(2d,p)//HF/6‐31G/d′) and MP2/6‐31+G(d′)//MP2/6‐31+G(d′) levels of theory. The Isodensity Polarised Continuum model was applied to take into account the environment effect. The results of molecular modelling are in good agreement with experimental data. According to the calculations glycidol polymerisation is thermodynamically controlled. The attack on the unsubstituted glycidol end is thermodynamically preferred except for the very first polymerisation step. Fast proton exchange reaction takes place during the polymerisation giving rise to the branching reaction. While the linear growth is caused by primary alkoxide attack, the branching reaction occurs by secondary alkoxide attack on the next glycidol molecule. It was found that cyclisation reactions show higher activation energies and are less favourable thermodynamically compared to polymerisation.     

A Novel,One‐Pot Synthesis of Novel 3F, 5F,and 8F Aromatic Polymers

A series of novel, linear, soluble, high‐molecular‐weight, fluorinated aromatic polymers has been obtained for the first time using a superacid‐catalyzed polyhydroxyalkylation reaction of fluorinated carbonyl‐containing compounds: 1,1,1,‐trifluoroacetone ( 1 ), 2,2,2‐trifluoroacetophenone ( 2 ), 2,3,4,5,6,‐pentafluorobenzaldehyde ( 3 ), and octafluoroacetophenone ( 4 ) with aromatic hydrocarbons such as biphenyl ( a ), phenyl ether ( b ), terphenyl ( c ), and 4,4′‐diphenoxybenzophenone ( d ). These Friedel‐Crafts‐type aromatic electrophilic substitution reactions are performed at room temperature in trifluoromethane sulfonic acid or in its mixtures with dichloromethane. The polymers obtained are soluble in common organic solvents, and colorless transparent films could be cast from the solutions. ¹H and ¹³C NMR analyses of the polymers synthesized reveal their linear, highly regular structure. The polymers also possess high thermostability.