Syntheses and structural characterizations of anionic borane-capped ammonia borane oligomers: evidence for ammonia borane H2 release via a base-promoted anionic dehydropolymerization mechanism

Studies of the activating effect of Verkade's base, 2,8,9-triisobutyl-2,5,8,9-tetraaza-1-phosphabicyclo[3.3.3]undecane (VB), on the rate and extent of H(2) release from ammonia borane (AB) have led to the syntheses and structural characterizations of three anionic aminoborane chain-growth products that provide direct support for anionic dehydropolymerization mechanistic steps in the initial stages of base-promoted AB H(2) release reactions. The salt VBH(+)[H(3)BNH(2)BH(2)NH(2)BH(3)](-) (1) containing a linear five-membered anionic aminoborane chain was produced in 74% yield via the room-temperature reaction of a 3:1 AB/VB mixture in fluorobenzene solvent, while the branched and linear-chain seven-membered anionic aminoborane oligomers VBH(+)[HB(NH(2)BH(3))(3)](-) (2a) and VBH(+)[H(3)BNH(2)BH(2)NH(2)BH(2)NH(2)BH(3)](-) (2b) were obtained from VB/AB reactions carried out at 50 °C for 5 days when the AB/VB ratio was increased to 4:1. X-ray crystal structure determinations confirmed that these compounds are the isoelectronic and isostructural analogues of the hydrocarbons n-pentane, 3-ethylpentane, and n-heptane, respectively. The structural determinations also revealed significant interionic B-H···H-N dihydrogen-bonding interactions in these anions that could enhance dehydrocoupling chain-growth reactions. Such mechanistic pathways for AB H(2) release, involving the initial formation of the previously known [H(3)BNH(2)BH(3)](-) anion followed by sequential dehydrocoupling of B-H and H-N groups of growing borane-capped aminoborane anions with AB, are supported by the fact that 1 was observed to react with an additional AB equivalent to form 2a and 2b.     

Diborabutatriene: An Electron‐Deficient Cumulene

The complexation of two equivalents of a cyclic (alkyl)(amino)carbene (CAAC) to tetrabromodiborane, followed by reduction with four equivalents of sodium naphthalide, led to the formation of the CAAC‐stabilized linear diboracumulene (CAAC)₂B₂. The capacity of the CAAC ligand to facilitate B₂→CAAC donation of π‐electron density resulted in important differences between this species and a previously reported complex featuring a B?B triple bond stabilized by cyclic di(amino)carbenes, including a longer B? B bond and shorter B? C bonds. Frontier orbital analysis indicated sharing of valence electrons across the entire linear C‐B‐B‐C unit in (CAAC)₂B₂, which is supported by natural population analysis and cyclic voltammetry.     

A mechanophysical phase transition provides a dramatic example of colour polymorphism: the tribochromism of a substituted tri(methylene)tetrahydrofuran-2-one

Background

Derivatives of fulgides have been shown to have interesting photochromic properties. We have synthesised a number of such derivatives and have found, in some cases, that crystals can be made to change colour on crushing, a phenomenon we have termed “tribochromism”. We have studied a number of derivatives by X-ray crystallography, to see if the colour is linked to molecular structure or crystal packing, or both, and our structural results have been supported by calculation of molecular and lattice energies.

Results

A number of 5-dicyanomethylene-4-diphenylmethylene-3-disubstitutedmethylene-tetrahydrofuran-2-one compounds have been prepared and structurally characterised. The compounds are obtained as yellow or dark red crystals, or, in one case, both. In two cases where yellow crystals were obtained, we found that crushing the crystals gave a deep red powder. Structure determinations, including those of the one compound which gave both coloured forms, depending on crystallisation conditions, showed that the yellow crystals contained molecules in which the structure comprised a folded conformation at the diphenylmethylene site, whilst the red crystals contained molecules in a twisted conformation at this site. Lattice energy and molecular conformation energies were calculated for all molecules, and showed that the conformational energy of the molecule in structure IIIa (yellow) is marginally higher, and the conformation thus less stable, than that of the molecule in structure IIIb (red). However, the van der Waals energy for crystal structure IIIa, is slightly stronger than that of structure IIIb – which may be viewed as a hint of a metastable packing preference for IIIa, overcome by the contribution of a more stabilising Coulomb energy to the overall more favourable lattice energy of structure IIIb.

Conclusions

Our studies have shown that the crystal colour is correlated with one of two molecular conformations which are different in energy, but that the less stable conformation can be stabilised by its host crystal lattice.

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Graphical abstract Graphical representation of the structural and colour change in the tribochromic compound (III).

     

Multilevel numerical solutions of convection‐dominated diffusion problems by spline wavelets

In this article, we utilize spline wavelets to establish an adaptive multilevel numerical scheme for time‐dependent convection‐dominated diffusion problems within the frameworks of Galerkin formulation and Eulerian‐Lagrangian localized adjoint methods (ELLAM). In particular, we shall use linear Chui‐Quak semi‐orthogonal wavelets, which have explicit expressions and compact supports. Therefore, both the diffusion term and boundary conditions in the convection‐diffusion problems can be readily handled. Strategies for efficiently implementing the scheme are discussed and numerical results are interpreted from the viewpoint of nonlinear approximation. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

An improved synthesis of [1H]-isoindolin-1-one-3-carboxylic acid

Preparation of the title compound in one operation from commercially available phthalaldehydic acid in 34% yield is described.     

Making Mathematical Connections Across the Curriculum: Activities to Help Teachers Begin

Ample evidence is available to support the contention that, for learning to be meaningful, concepts must be connected and integrated within the experiences of the learner. In mathematics, at least three kinds of connections are particularly beneficial: connections within mathematics, across the curriculum, and with real world contexts. The authors' work with preservice and inservice teachers has convinced them that teachers possess both the willingness and the capability to help students make meaningful connections, given encouragement and support. This article focuses on making mathematical connections across the curriculum; activities which help teachers learn how to design their own are shared.     

The analysis of multigrid algorithms for cell centered finite difference methods

In this paper, we examine multigrid algorithms for cell centered finite difference approximations of second order elliptic boundary value problems. The cell centered application gives rise to one of the simplest non-variational multigrid algorithms. We shall provide an analysis which guarantees that the W-cycle and variable V-cycle multigrid algorithms converge with a rate of iterative convergence which can be bounded independently of the number of multilevel spaces. In contrast, the natural variational multigrid algorithm converges much more slowly.