Mathematics achievement and interest in mathematics from a differential perspective

In this article, we present results of an empirical study with 500 German students of grades 7 and 8. The study focussed on students' mathematics achievement and their interest in mathematics as well as on the relation between these two constructs. In particular, the results show that the development of an individual student's achievement between grade 7 and grade 8 depends on the achievement level of the specific classroom and therefore on the specific mathematics instruction Interest in mathematics could be regarded a predictor for mathematics achievement Moreover, our findings suggest that the students show hardly any fear of mathematics independent of their achievement level.     

Recent advances of group 14 dimetallenes and dimetallynes in bond activation and catalysis

Since the first heavy alkene analogues of germanium and tin were isolated in 1976, followed by West''s disilene in 1981, the chemistry of stable group 14 dimetallenes and dimetallynes has advanced immensely. Recent developments in this field veered the focus from the isolation of novel bonding motifs to mimicking transition metals in their ability to activate small molecules and perform catalysis. The potential of these homonuclear multiply bonded compounds has been demonstrated numerous times in the activation of H₂, NH₃, CO₂ and other small molecules. Hereby, the strong relationship between structure and reactivity warrants close attention towards rational ligand design. This minireview provides an overview on recent developments in regard to bond activation with group 14 dimetallenes and dimetallynes with the perspective of potential catalytic applications of these compounds.

This minireview highlights the recent advances in small molecule activation and catalytic applications of homonuclear dimetallenes, dimetallynes and interconnected bismetallylenes of heavier group 14 elements.     

Negatively charged hyperbranched polyether-based polyelectrolytes

The preparation of carboxylated hyperbranched polyglycerols of narrow polydispersity was achieved by modification (78–90%) of the hydroxyl end groups via Michael addition of acrylonitrile, followed by hydrolysis. High conversion could only be achieved for low molecular weight starting materials (520 and 1,030 g mol⁻¹). The solution properties of the resulting materials were investigated by dynamic light scattering (DLS), showing the formation of large aggregates with size depending on the pH value. After deposition on a negatively charged mica surface, the structures observed by atomic force microscope (AFM) show the coexistence of aggregates and single macromolecules. Most interesting, in the case of the lower molecular weight sample (PG 520 g mol⁻¹), extended and ordered terrace structures were formed, which are unprecedented for hyperbranched polymers and are of interest for surface modification in general.     

Kinetic Analysis of the Reactions between GG-Containing Oligonucleotides and Platinum Complexes. 1. Reactions of Single-Stranded Oligonucleotides with cis-[Pt(NH(3))(2)(H(2)O)(2)](2+) and [Pt(NH(3))(3)(H(2)O)](2+)

Using concentration measurements based on high performance liquid chromatography, we have investigated the kinetics of reaction between single-stranded oligonucleotides containing a d(GpG) sequence, i.e., d(GG), d(TGG), d(TTGG), and d(CTGGCTCA), and the platinum complexes cis-[Pt(NH(3))(2)(H(2)O)(2)](2+) (1) and [Pt(NH(3))(3)(H(2)O)](2+) (2). The rate constants for the substitution of one aqua ligand of platinum in 1 or 2 by each guanine of the oligonucleotides were individually measured, as well as, for 1, those for the subsequent conversion of the monoadducts to the diadduct. For the platination of d(GG) and d(TGG), the rate constants are similar for the 5'- and 3'-guanines. The longer oligonucleotides d(TTGG) and d(CTGGCTCA) are platinated slightly faster on the 5'-G than on the 3'-G. 2 shows a similar slight preference for the 5'-guanine, but it reacts by a factor of 4-10 more slowly than 1. For both complexes, the platination rate constants increase with increasing oligonucleotide length. Platination of the 5'-G by 1 is 1 order of magnitude faster on d(CTGGCTCA) than on d(GG). Concerning the chelation step giving the GG diadduct of 1, the longer the oligonucleotide, the larger is the ratio between the rates of the cyclization of the 3'- and 5'-monoadducts k(3)(')(c) and k(5)(')(c): k(3)(')(c)/k(5)(')(c) equals 1.4 for d(GG) and 3.3 for d(CTGGCTCA).     

Dialumenes – aryl vs. silyl stabilisation for small molecule activation and catalysis

Main group multiple bonds have proven their ability to act as transition metal mimics in the last few decades. However, catalytic application of these species is still in its infancy. Herein we report the second neutral NHC-stabilised dialumene species by use of a supporting aryl ligand (3). Different to the trans-planar silyl-substituted dialumene (3Si), compound 3 features a trans-bent and twisted geometry. The differences between the two dialumenes are explored computationally (using B3LYP-D3/6-311G(d)) as well as experimentally. A high influence of the ligand''s steric demand on the structural motif is revealed, giving rise to enhanced reactivity of 3 enabled by a higher flexibility in addition to different polarisation of the aluminium centres. As such, facile activation of dihydrogen is now achievable. The influence of ligand choice is further implicated in two different catalytic reactions; not only is the aryl-stabilised dialumene more catalytically active but the resulting product distributions also differ, thus indicating the likelihood of alternate mechanisms simply through a change of supporting ligand.

Ligand controlled reactivity: a trans-bent and twisted geometry enables dihydrogen activation and enhanced catalytic activity for NHC-stabilised dialumenes.     

2,2‐Dichloro‐1,3‐bis(trimethylsilyl)‐1,3‐diaza‐2‐silacyclopentane

In the title compound, C₈H₂₂Cl₂N₂Si₃, the central Si atom is tetrahedrally coordinated by two Cl and two N atoms in a molecule that has crystallographically imposed C₂ symmetry. Comparison is made with the isomorphous structure having titanium instead of silicon at the central position in the diazacyclopentane ring [Tinkler, Deeth, Duncalf & McCamley (1996). Chem. Commun. pp. 2623–2624].     

Single-ion magnetism in the extended solid-state: insights from X-ray absorption and emission spectroscopy

Large single-ion magnetic anisotropy is observed in lithium nitride doped with iron. The iron sites are two-coordinate, putting iron doped lithium nitride amongst a growing number of two coordinate transition metal single-ion magnets (SIMs). Uniquely, the relaxation times to magnetisation reversal are over two orders of magnitude longer in iron doped lithium nitride than other 3d-metal SIMs, and comparable with high-performance lanthanide-based SIMs. To understand the origin of these enhanced magnetic properties a detailed characterisation of electronic structure is presented. Access to dopant electronic structure calls for atomic specific techniques, hence a combination of detailed single-crystal X-ray absorption and emission spectroscopies are applied. Together K-edge, L_2,3-edge and Kβ X-ray spectroscopies probe local geometry and electronic structure, identifying iron doped lithium nitride to be a prototype, solid-state SIM, clean of stoichiometric vacancies where Fe lattice sites are geometrically equivalent. Extended X-ray absorption fine structure and angular dependent single-crystal X-ray absorption near edge spectroscopy measurements determine Fe^I dopant ions to be linearly coordinated, occupying a D_6h symmetry pocket. The dopant engages in strong 3dπ-bonding, resulting in an exceptionally short Fe–N bond length (1.873(7) Å) and rigorous linearity. It is proposed that this structure protects dopant sites from Renner–Teller vibronic coupling and pseudo Jahn–Teller distortions, enhancing magnetic properties with respect to molecular-based linear complexes. The Fe ligand field is quantified by L_2,3-edge XAS from which the energy reduction of 3d_z² due to strong 4s mixing is deduced. Quantification of magnetic anisotropy barriers in low concentration dopant sites is inhibited by many established methods, including far-infrared and neutron scattering. We deduce variable temperature L₃-edge XAS can be applied to quantify the J = 7/2 magnetic anisotropy barrier, 34.80 meV (∼280 cm⁻¹), that corresponds with Orbach relaxation via the first excited, M_J = ±5/2 doublet. The results demonstrate that dopant sites within solid-state host lattices could offer a viable alternative to rare-earth bulk magnets and high-performance SIMs, where the host matrix can be tailored to impose high symmetry and control lattice induced relaxation effects.

Taking advantage of synchrotron light source methods, we present the geometric and electronic structure of iron doped in lithium nitride.     

Modular and Selective Arylation of Aryl Germanes (C−GeEt3) over C−Bpin,C−SiR3 and Halogens Enabled by Light-Activated Gold Catalysis

Selective C –C couplings are powerful strategies for the rapid and programmable construction of bi- or multiaryls. To this end, the next frontier of synthetic modularity will likely arise from harnessing the coupling space that is orthogonal to the powerful Pd-catalyzed coupling regime. This report details the realization of this concept and presents the fully selective arylation of aryl germanes (which are inert under Pd⁰/Pd^II catalysis) in the presence of the valuable functionalities C−BPin, C−SiMe₃, C−I, C−Br, C−Cl, which in turn offer versatile opportunities for diversification. The protocol makes use of visible light activation combined with gold catalysis, which facilitates the selective coupling of C−Ge with aryl diazonium salts. Contrary to previous light-/gold-catalyzed couplings of Ar–N₂⁺, which were specialized in Ar–N₂⁺ scope, we present conditions to efficiently couple electron-rich, electron-poor, heterocyclic and sterically hindered aryl diazonium salts. Our computational data suggest that while electron-poor Ar–N₂⁺ salts are readily activated by gold under blue-light irradiation, there is a competing dissociative deactivation pathway for excited electron-rich Ar–N₂⁺, which requires an alternative photo-redox approach to enable productive couplings.     

First organophosphorus radical-mediated cyclisations to afford medium-sized rings: eight-membered lactones and seven- and eight-membered lactams

The phosphorus based radical precursors N-ethylpiperidine hypophosphite (EPHP) and diethylphosphine oxide (DEPO) are efficient reagents for carrying out the formation of seven- and eight-membered rings. Esters and amides were successfully converted into the corresponding eight-membered lactones and seven- and eight-membered lactams in good to excellent yields.