Aggregation behaviour of thallium(I) beta-diketiminates

Modulation of the steric requirements of a number of N-aryl beta-diketiminate ligands results in the isolation of a variety of Tl(I) compounds with different stabilities and nuclearities.     

Insights into the making of a stable silylene

Reduction of Cl2Si[(NR)2C6H4-1,2] (R = CH2Bu(t)) with potassium is known to lead to the stable silylene Si[(NR)2C6H4-1,2] (1). However, silylene is now shown to react further with an alkali metal (Na or K) to yield the (1)(2)2-, c-(1)(3)-*, c-(1)(3)2- or c-(1)(4)2- derivatives. Reduction of Cl2Si[(NR)2C6H4-1,2] (R = CH2CH3 or CH2CHMe2) with potassium does not lead to an isolable silylene, but such a silylene is proposed to be an intermediate and, as for 1, reacts further to afford the potassium salts of c-[Si{(NR)2C6H4-1,2}]4-* and c-[Si{(NR)2C6H4-1,2}](4)2-. The pathways leading to the anionic cyclotri- and cyclotetrasilanes are discussed and supported experimentally; including by X-ray structures of relevant intermediates.     

Neutral carbene analogues of the heaviest Group 13 elements: consideration of electronic and steric effects on structure and stability

The neutral monovalent Group 13 beta-diketiminato complexes [CH{(CF3)2CN-2,6-iPr2C6H3}2In] and [CH{(Me)2CN-2,6-iPr2C6H3}2Tl] have been synthesised by analogous 'one-pot' procedures involving reaction of [KN(SiMe3)2] with the appropriate beta-imino-enamine and Group 13 iodide. The structure of the indium complex reveals that replacement of the ligand backbone methyl groups of the previously reported complex [CH{(Me)2CN-2,6-iPr2C6H3}2In] with trifluoromethyl substituents results in only minor modifications to the dimensions of the NCCCNIn metallacycle. The electronic structures of both indium species were interrogated by DFT calculations to reveal similar frontier molecular orbital schemes. In agreement with calculations performed previously on the aluminium and gallium complexes, [CH{(Me)2CN-2,6-iPr2C6H3}2Al] and [CH{(Me)2CN-2,6-iPr2C6H3}2Ga], the HOMO in both indium species comprises a metal-based sp-hybrid while the LUMO is a ligand-based orbital of pi symmetry. The vacant indium p-orbital is represented by the LUMO + 1. Although incorporation of the fluorinated substituents results in a stabilisation of the system overall, the stabilities and observed structural features of the complexes are reasoned to be primarily a result of the steric profile of the very bulky ligands and not through any redistribution of the electron density within the cyclic species. The thallium complex is isostructural to the analogous and previously reported aluminium, gallium and indium species. The greater stability of the monovalent state however is reflected in a reordering of the orbital energies and a stabilisation of the metal-based orbitals in the frontier region of the MO scheme.     

Solid- and solution-state structures of indium 'alkene analogues'

Although the nuclearity of In(I) 'carbenes' is dependent upon the steric demands of the supporting beta-diketiminate ligand, it is shown by solution NMR diffusion (DOSY) methods that the In-In interactions observed in the solid-state are very weak and not retained in solution.     

Dynamic investigation of loci with surprising outcomes and their mathematical explanations

The locus is a very important concept in Euclidean geometry since it serves as a tool for solving different problems, and allows geometric constructions to be carried out. The teaching of the subject of loci in various mathematics courses includes solution of different exercises in which the student is required to find the locus in accordance with the data of the question. The present paper offers a different view of the subject of loci, which brings about conceptual understanding of the subject with identification of conserved properties and suitable generalizations obtained through investigation that includes the use of dynamic geometric software (GeoGebra). General formulas were developed for the equation of the locus in two cases. In the article, there are links to geometric applets which allow one to demonstrate the loci formed in some cases.     

Organoiron compounds derived from the indium 'carbene analogues', [In(N(Ar)C(Me))2CH] (Ar = dipp = 2,6-iPr2C6H3; = Mes = 2,4,6-Me3C6H2)

Oxidative insertion of the In(I) 'carbene analogues', [In{N(Dipp)C(Me))2CH] (Ar = Dipp = 2,6-iPr2C6H3; Ar = Mes = 2,4,6-Me3C6H2) into the Fe-I bond of [CpFe(CO)2I] occurred cleanly and under mild conditions to yield the In(III) compounds [CH((CH3)2CN-2,6-iPr2C6H3)2In(I)FeCp(CO)2] and [CH( (CH3)2CN-2,4,6-Me3C6H3)2In(I)FeCp(CO)2], which have been fully characterised in solution and the solid state. Attempts to abstract the iodide anion from [CH( (CH3)2CN-2,6-iPr2C6H3)2In(I)FeCp(CO)2] to form cationic species containing a coordinated indium diyl were unsuccessful and resulted in a complex mixture of products from which two ionic species were isolated. Neither cation was found to contain indium by X-ray crystallographic analysis. These observations were indicative of ill-defined decomposition pathways as have been noted by previous workers. A further attempt to form a cationic iron species containing a coordinated [In(N(Dipp)C(Me) )2CH] fragment resulted in oxidation of the iron centre from Fe(II) to Fe(III), with deposition of indium metal, and the isolation of a cationic Fe(III) beta-diketiminate complex.     

The effectiveness of ‘what if not’ strategy coupled with dynamic geometry software in an inquiry-based geometry classroom

In this paper we present the results of a study which was carried out in an inquiry-based teaching and learning environment with the use of ‘what if not’ methodology coupled with the integration of dynamic geometry software. The vast majority of the students reported that they perceived themselves as participants rather than spectators. Most of the prospective teachers came to the conclusion that the implementation of the findings of this study in their future teachings was a good idea and that it will raise the students’ motivation and enhance and deepen the knowledge pool of the learners.     

On teaching extrema triangle problems using dynamic investigation

An important and interesting area in the study of triangle geometry is the related issue of extrema problems and inequalities. These problems play a significant role in the mathematics study program in high school. In tasks such as these, the difficulty level is high when one does not know in advance what the expected answer is. When one knows what to prove, the difficulty level is lower and most of the effort is aimed at attaining a proof of the expected answer. This can be done using dynamic geometric software. The possibility of making frequent changes to the geometric objects and the ability of dragging objects, contributes to the process of deducing properties, checking hypotheses and generalizing. In this paper, eight investigative tasks in Euclidean geometry are presented together with the applets developed for carrying out the dynamic investigation. Some of the tasks are well known, while others are almost unknown and are worthy of presentation as enrichment for those interested in the subject. The tasks were given to preservice teachers of mathematics as part of an advanced course for integrating technological tools in the teaching of mathematics.