Push–Pull Buta‐1,2,3‐trienes: Exceptionally Low Rotational Barriers of Cumulenic CC Bonds and Proacetylenic Reactivity

A variety of asymmetrically donor–acceptor‐substituted [3]cumulenes (buta‐1,2,3‐trienes) were synthesized by developed procedures. The activation barriers to rotation ΔG^≠ were measured by variable temperature NMR spectroscopy and found to be as low as 11.8 kcal mol^?1, in the range of the barriers for rotation around sterically hindered single bonds. The central C?C bond of the push–pull‐substituted [3]cumulene moiety is shortened down to 1.22 Å as measured by X‐ray crystallography, leading to a substantial bond length alternation (BLA) of up to 0.17 Å. All the experimental results are supported by DFT calculations. Zwitterionic transition states (TS) of bond rotation confirm the postulated proacetylenic character of donor–acceptor [3]cumulenes. Additional support for the proacetylenic character of these chromophores is provided by their reaction with tetracyanoethene (TCNE) in a cycloaddition‐retroelectrocyclization (CA–RE) cascade characteristic of donor‐polarized acetylenes.     

Decomposition of conditionally positive definite functions on commutative hypergroups

In this paper we consider bounded, conditionally positive definite functions on commutative hypergroups. We show an integral representation that allows to decompose conditionally positive definite functions as differences of positive definite functions.     

Decomposition of conditionally positive definite functions on commutative hypergroups

In this paper we consider bounded, conditionally positive definite functions on commutative hypergroups. We show an integral representation that allows to decompose conditionally positive definite functions as differences of positive definite functions.     

NHC→SiCl4: An Ambivalent Carbene‐Transfer Reagent

The addition of BCl₃ to the carbene‐transfer reagent NHC→SiCl₄ (NHC=1,3‐dimethylimidazolidin‐2‐ylidene) gave the tetra‐ and pentacoordinate trichlorosilicon(IV) cations [(NHC)SiCl₃]⁺ and [(NHC)₂SiCl₃]⁺ with tetrachloroborate as counterion. This is in contrast to previous reactions, in which NHC→SiCl₄ served as a transfer reagent for the NHC ligand. The addition of BF₃ ? OEt₂, on the other hand, gave NHC→BF₃ as the product of NHC transfer. In addition, the highly Lewis acidic bis(pentafluoroethyl)silane (C₂F₅)₂SiCl₂ was treated with NHC→SiCl₄. In acetonitrile, the cationic silicon(IV) complexes [(NHC)SiCl₃]⁺ and [(NHC)₂SiCl₃]⁺ were detected with [(C₂F₅)SiCl₃]^? as counterion. A similar result was already reported for the reaction of NHC→SiCl₄ with (C₂F₅)₂SiH₂, which gave [(NHC)₂SiCl₂H][(C₂F₅)SiCl₃]. If the reaction medium was changed to dichloromethane, the products of carbene transfer, NHC→Si(C₂F₅)₂Cl₂ and NHC→Si(C₂F₅)₂ClH, respectively, were obtained instead. The formation of the latter species is a result of chloride/hydride metathesis. These compounds may serve as valuable precursors for electron‐poor silylenes. Furthermore, the reactivity of NHC→SiCl₄ towards phosphines is discussed. The carbene complex NHC→PCl₃ shows similar reactivity to NHC→SiCl₄, and may even serve as a carbene‐transfer reagent as well.     

Chemoenzymatic Synthesis of Nonasulfated Tetrahyaluronan with a Paramagnetic Tag for Studying Its Complex with Interleukin‐10

Implants and artificial biomaterials containing sulfated hyaluronans have been shown to improve the healing of injured skin and bones. It is hypothesized that these effects are mediated by the binding of sulfated glycosaminoglycans (GAGs) to growth factors and cytokines, resulting in the sequestering of proteins to the wound healing site and in modulated protein activity. Given that no direct synthetic access to sulfated oligohyaluronans has been available, little is known about their protein binding and the structure of the resulting protein complexes. Here, the chemoenzymatic preparation of oligohyaluronans on the gram scale is described. Oligohyaluronans are converted into anomeric azides at the reducing end, enabling the attachment of analytical labels through an anomeric ligation reaction. A nonasulfated tetrahyaluronan–ethylenediaminetetraacetic acid derivative has been produced and used as a paramagnetic tag for the elucidation of the complex of this ligand with interleukin‐10 using paramagnetic relaxation enhancement NMR analysis. The metal ion position is resolved with 1.0 Å, enabling a refined structural model of the complex.     

The Stokes conjecture for waves with vorticity

We study stagnation points of two-dimensional steady gravity free-surface water waves with vorticity.