Nickel‐Catalyzed Cross‐Coupling of Redox‐Active Esters with Boronic Acids

A transformation analogous in simplicity and functional group tolerance to the venerable Suzuki cross‐coupling between alkyl‐carboxylic acids and boronic acids is described. This Ni‐catalyzed reaction relies upon the activation of alkyl carboxylic acids as their redox‐active ester derivatives, specifically N‐hydroxy‐tetrachlorophthalimide (TCNHPI), and proceeds in a practical and scalable fashion. The inexpensive nature of the reaction components (NiCl₂?6 H₂O—$9.5 mol^?1, Et₃N) coupled to the virtually unlimited commercial catalog of available starting materials bodes well for its rapid adoption.     

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Substitution of [M(bpyMe)Cl3] and [M(bpyMe-H)Cl2] (M = Pd or Pt; bpyMe =N-methyl-2,2′-bipyridylium ion) withN-heterocycles

Summary The complex Pt(bpyMe)Cl₃ (bpyMe = N-methyl-2,2-bipyridylium cation) reacts with pyridine(py) to give cis-[Pt(bpy-Me) (py)Cl₂]⁺, which on heating cyclometallates with loss of py to give Pt(bpyMe-H)Cl₂; some Pt(py)₂Cl₂ is also formed. Pt(bpyMe)Cl₃ reacts with 2,2-bipyridyl (bpy) to yield a mixture of [Pt(bpyMe-H)(bpy)]²⁺ and [Pt(bpy)₂]²⁺. The analogous reactions with Pd(bpyMe)Cl₃ proceed under very mild conditions to afford PdL₂Cl₂ (L₂ = 2py, bpy).     

The algebraic Riccati equation: conditions for the existence and uniqueness of solutions

Unmixed solutions of the matrix equation XDX+XA+AX^*?C=0, D?0 are studied.     

3,3′-Dicarbomethoxy-2,2′-bipyridyl complexes of palladium(II), platinum(II) and rhodium(III)

3,3′-Dicarbomethoxy-2,2′-bipyridyl(DCMB)reacts with K₂MCl₄(M = Pd,Pt) to give M(DCMB)Cl₂ and with RhCl₃ to give the cis-[Rh(DCMB)₂Cl₂]⁺ ion. Attempts to prepare the tris (DCMB) complex with Rh(III) and analogous Co(III) complexes were unsuccessful.     

Effect Algebras as Presheaves on Finite Boolean Algebras

For an effect algebra A, we examine the category of all morphisms from finite Boolean algebras into A. This category can be described as a category of elements of a presheaf R(A) on the category of finite Boolean algebras. We prove that some properties (being an orthoalgebra, the Riesz decomposition property, being a Boolean algebra) of an effect algebra A can be characterized in terms of some properties of the category of elements of the presheaf R(A). We prove that the tensor product of effect algebras arises as a left Kan extension of the free product of finite Boolean algebras along the inclusion functor. The tensor product of effect algebras can be expressed by means of the Day convolution of presheaves on finite Boolean algebras.     

The structure of amorphous sulfur

The λ‐transition of elemental sulfur occurring at about 159°C has long been associated with the conversion of cyclic S₈ rings (c‐S₈) to amorphous polymer (a‐S) via a ring opening polymerization. Here we demonstrate, with the use of both density functional and Hartree‐Fock quantum mechanical calculations, the existence of an energetically accessible, locally stable, hypervalent state of S that can form branch sites in the polymer. The significance of this finding is that the λ‐transition is best described as a gelation transition. The geometry of the tetravalent S atom is trigonal bipyramidal, with a lone pair occupying one of the three equatorial sites; it lies in a local energy minimum about 31 kcal/mol above the normal divalent state, and so is accessible both thermally and photochemically. Because the branched structure is formed endothermically, Le Chatelier's principle confirms that a percolation network can form on heating the element. The reactions that form branched structures are reversible, implying that the gel is fluxional. It decomposes at higher temperatures as chain scission competes with branching. The hypervalent structure provides an essential insight into the chemistry of elemental sulfur.