Symmetry of three-center,four-electron bonds

Three-center, four-electron bonds provide unusually strong interactions; however, their nature remains ununderstood. Investigations of the strength, symmetry and the covalent versus electrostatic character of three-center hydrogen bonds have vastly contributed to the understanding of chemical bonding, whereas the assessments of the analogous three-center halogen, chalcogen, tetrel and metallic -type long bonding are still lagging behind. Herein, we disclose the X-ray crystallographic, NMR spectroscopic and computational investigation of three-center, four-electron [D–X–D]⁺ bonding for a variety of cations (X⁺ = H⁺, Li⁺, Na⁺, F⁺, Cl⁺, Br⁺, I⁺, Ag⁺ and Au⁺) using a benchmark bidentate model system. Formation of a three-center bond, [D–X–D]⁺ is accompanied by an at least 30% shortening of the D–X bonds. We introduce a numerical index that correlates symmetry to the ionic size and the electron affinity of the central cation, X⁺. Providing an improved understanding of the fundamental factors determining bond symmetry on a comprehensive level is expected to facilitate future developments and applications of secondary bonding and hypervalent chemistry.

The factors determining the symmetry and the fundamental nature of the three-center, four-electron bonds are assessed.     

Thermo-mechanically coupled modelling of cellular MgO-C refractories under thermal shock

Refractory materials such as magnesium oxide carbon (MgO-C) composites are used in the steel-making industry for furnaces, ladles or oxygen converters. A new class of composites are cellular MgO-C materials, consisting of carbon foams filled with magnesium oxide and inclusions of gas filled pores. Cellular MgO-C composites have the advantage of significantly improving the thermo-mechanical properties [1]. This contribution focuses on the FEM implementation of a fully coupled thermo-mechanical continuum model. It is based on the theory of porous media (TPM) restricted by a kinematic coupling of the displacement field of all constituents. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

High resolution monitoring of an unsteady glass fibre drawing process

We report unsteady experimental results on the stability of fibre diameter in a continuous glass forming process, using two unique laser systems: a high resolution diffractometer and a backward phase Doppler interferometer. For draw ratios close to those used in the industry, the glass fibre diameter exhibits small fluctuations, which cannot be considered to be a result of draw resonance. It is shown that the amplitude of fibre diameter fluctuations decreases with increasing draw ratio, while the corresponding frequency increases with the temperature of the molten glass. Although the origin of these fluctuations is still not well understood, it appears that their frequency depends on the characteristics of the molten glass jet.     

Identifying Kinds of Reasoning in Collective Argumentation

We combine Peirce’s rule, case, and result with Toulmin’s data, claim, and warrant to differentiate between deductive, inductive, abductive, and analogical reasoning within collective argumentation. In this theoretical article, we illustrate these kinds of reasoning in episodes of collective argumentation using examples from one teacher’s practice. Examining different kinds of reasoning in collective argumentation can inform how students engage in generating and examining hypotheses using inductive and abductive reasoning and move toward the deductive reasoning required for proof. Mathematics educators can build on their understanding of these kinds of reasoning to support students in reasoning in productive ways.     

The Ostrovsky–Vakhnenko equation: A Riemann–Hilbert approach

We present an inverse scattering transform approach for the (differentiated) Ostrovsky–Vakhnenko equation:

u_txx−3u_x+3u_xu_xx+uu_xxx=0.$u_{txx}-3u_x+3u_x{u}_{xx}+u{u}_{xxx}=0.$

This equation can also be viewed as the short-wave model for the Degasperis–Procesi equation. The approach is based on an associated Riemann–Hilbert problem, which allows us to give a representation for the classical (smooth) solution of the Cauchy problem, to get the principal term of its long-time asymptotics, and also to find, in a natural way, loop soliton solutions.     

Research into teacher knowledge: a stimulus for development in mathematics teacher education practice

In this paper, we document some developments in teacher education practice at one university, brought about by reflection on research into mathematics teacher knowledge. The authors are three members of the Cambridge-based research team who developed the Knowledge Quartet (KQ), a theory of mathematics teacher knowledge, with a focus on classroom situations in which this knowledge is applied. At the same time as being researchers, the authors were elementary mathematics teacher education instructors. They found that the KQ research brought about new awareness of the importance of some components of mathematics didactics, as well as providing new tools for undertaking some aspects of their teacher educator role. The paper explores some of these awarenesses and tools in detail.     

Ethylene-promoted versus ethylene-free enyne metathesis

The role of ethylene in promoting metathesis of acetylenic enynes is probed within the context of ring-closing enyne metathesis, using first- and second-generation Grubbs catalysts. Under inert atmosphere, rapid catalyst deactivation is observed by calibrated GC-FID analysis for substrates with minimal propargylic bulk. MALDI-TOF mass spectra reveal a Ru(enyne)(2) derivative that exhibits very low reactivity toward both enyne and ethylene. Under ethylene, formation of this species is suppressed. Enynes with bulky propargylic groups are not susceptible to this catalyst deactivation pathway, even under N(2) atmosphere.     

Solvent-mediated charge redistribution in photodissociation of IBr(-) and IBr(-)(CO2)

A combined experimental and theoretical investigation of photodissociation dynamics of IBr(-) and IBr(-)(CO(2)) on the B ((2)Σ(1/2)(+)) excited electronic state is presented. Time-resolved photoelectron spectroscopy reveals that in bare IBr(-) prompt dissociation forms exclusively I? + Br(-). Compared to earlier dissociation studies of IBr(-) excited to the A' ((2)Π(1∕2)) state, the signal rise is delayed by 200 ± 20 fs. In the case of IBr(-)(CO(2)), the product distribution shows the existence of a second major (～40%) dissociation pathway, Br? + I(-). In contrast to the primary product channel, the signal rise associated with this pathway shows only a 50 ± 20 fs delay. The altered product branching ratio indicates that the presence of one solvent-like CO(2) molecule dramatically affects the electronic structure of the dissociating IBr(-). We explore the origins of this phenomenon with classical trajectories, quantum wave packet studies, and MR-SO-CISD calculations of the six lowest-energy electronic states of IBr(-) and 36 lowest-energy states of IBr. We find that the CO(2) molecule provides sufficient solvation energy to bring the initially excited state close in energy to a lower-lying state. The splitting between these states and the time at which the crossing takes place depend on the location of the solvating CO(2) molecule.