Synthesis and Crystal Structure of an Oligomeric Lithium Bis(amido)hydridooxidoaluminate Cluster, [{Li(C14H30N2)AlHO1/2}4]

The lithium bis(amido)hydridooxidoaluminate cluster [{Li(C₁₄H₃₀N₂)AlHO_1/2}₄] has been synthesized during systematic metallation/hydrometallation studies of a series of 1,4‐diazabut‐1‐enes with lithium aluminiumhydride. Formation of the complex is presumably derived from partial hydrolysis of the related lithium bis(amido)dihydridoaluminate and has been characterized using single crystal X‐ray diffraction. The complex crystallizes in the monoclinic space group C2/c (No. 15) with a = 25.012(2) Å, b = 10.673(2) Å, c = 28.673(3) Å, β = 115.855(7)°, V = 6887(1) ų, Z = 4. The complex exhibits an oligomeric structure of crystallographic C₂ symmetry, comprised of complex multicyclic units arising from extensive metal, hydride, oxide and ligand bridging interactions. These associations give rise to edge‐fused, non‐planar NAlOLi four‐membered rings tightly binding two of the diamido‐chelated aluminate units, with these in turn aggregating further via two of the μ²‐hydrides involving lithium atoms.     

Reactivity variations within Group 4 complexes of 1,4-di-tert-butyl-1,4-diazabuta-1,3-diene: Structures of [(C5H5)TiCl{(t-BuNCH)2}] and [(C5H5)2Zr{(t-BuNCH)2}]

The reactions of the metallocene dichlorides [(η⁵-C₅H₅)₂MCl₂], M = Ti and Zr, with the 1,4-di-tert-butyl-1,4-diazabuta-1,3-diene radical anion (lithium complex) in diethyl ether reveal a reactivity difference within the series, yielding [(C₅H₅)TiCl{(t-BuNCH)₂}] and [(C₅H₅)₂Zr{(t-BuNCH)₂}] through the elimination of Li(C₅H₅) and/or LiCl, respectively. We report the X-ray crystal structures of these complexes, and discuss their reactivity patterns and solution fluxional properties.     

Imaging of a <Emphasis Type="Italic">β</Emphasis>-peptide distribution in whole-body mice sections by MALDI mass spectrometry

Mass spectrometric imaging was applied to assess compound distributions on whole-body sections of mice after i.v. dosing of a beta-peptide and an alpha-peptide control. Animals were sacrificed at different time points (5 min, 1 h, 24 h) post-dose, providing simultaneous spatial as well as kinetic information. As a result of this study, no detection of the alpha-peptide control was observed at 1 h post-dose, while retention of the beta-peptide was observed for longer than 24 h post-dose.     

Bragg scattering of cooper pairs in an ultracold Fermi gas

We present a theoretical treatment of Bragg scattering of a degenerate Fermi gas in the weakly interacting BCS regime. Our numerical calculations predict correlated scattering of Cooper pairs into a spherical shell in momentum space. The scattered shell of correlated atoms is centered at half the usual Bragg momentum transfer, and can be clearly distinguished from atoms scattered by the usual single-particle Bragg mechanism. We develop an analytic model that explains key features of the correlated-pair Bragg scattering, and determine the dependence of that scattering on the initial pair correlations in the gas.     

Preparation and structures of aryloxy- and alkoxy-Ti(IV) complexes and their evaluation in ethylene oligomerisation and polymerisation

A range of aryloxy and alkoxy ligands, both monodenate and chelating, have been coordinated to Ti(IV) to yield complexes of the form [Ti(OAr)(2)Cl(2)], [Ti(RO^O)Cl(3)] and [Ti(RO^O)(2)Cl(2)] (R = aryl, alkyl). The complexes vary in their Lewis base solvation and/or aggregation state, as revealed by X-ray crystallography of selected examples. The complexes have been evaluated as catalysts for ethylene oligomerisation and polymerisation following activation with alkylaluminium reagents (AlEt(3), methylaluminoxane). While polyethylene is the major product, ethylene oligomers also result, ranging from dimers to higher oligomers. The results indicate a number of different active species are formed upon activation, with oligomers likely arising through a metallacyclic mechanism. The findings are discussed in the context of the commercial Alphabutol dimerisation system [Ti(OR)(4)], and the development of group 4 based ethylene trimerisation catalysts.     

Children’s Use of Variables and Variable Notation to Represent Their Algebraic Ideas

In this article, we analyze a first grade classroom episode and individual interviews with students who participated in that classroom event to provide evidence of the variety of understandings about variable and variable notation held by first grade children approximately six years of age. Our findings illustrate that given the opportunity, children as young as six years of age can use variable notation in meaningful ways to express relationships between co-varying quantities. In this article, we argue that the early introduction of variable notation in children’s mathematical experiences can offer them opportunities to develop familiarity and fluency with this convention as groundwork for ultimately powerful means of representing general mathematical relationships.     

Understanding, Integration, and Epistemic Value

Understanding enjoys a special kind of value, one not held by lesser epistemic states such as knowledge and true belief. I explain the value of understanding via a seemingly unrelated topic, the implausibility of veritism. Veritism holds that true belief is the sole ultimate epistemic good and all other epistemic goods derive their value from the epistemic value of true belief. Veritism entails that if you have a true belief that p, you have all the epistemic good qua p. Veritism is a plausible and widely held view; I argue that it is untenable. I argue that integration among beliefs possesses epistemic value independent from the good of true belief, and so has value veritism cannot account for. I argue further that this integration among beliefs comprises the distinctive epistemic value of understanding.     

Supported palladium catalysis using a heteroleptic 2-methylthiomethylpyridine-N,S-donor motif for Mizoroki-Heck and Suzuki-Miyaura coupling, including continuous organic monolith in capillary microscale flow-through mode

Flow-through catalysis utilising (2-methylthiomethylpyridine)palladium(II) chloride species covalently attached to a macroporous continuous organic polymer monolith synthesised within fused silica capillaries of internal diameter 250 μm is described, together with related studies of ground bulk monolith compared with supported catalysis on Merrifield and Wang beads and homogeneous catalysis under identical conditions to bulk supported catalysis. The monolith substrate, poly(chloromethylstyrene-co-divinylbenzene), has a backbone directly related to Merrifield and Wang resins. The homogeneous precatalyst PdCl₂(L²) (L²=4-(4-benzyloxyphenyl)-2-methylthiomethylpyridine) contains the benzyloxyphenyl group on its periphery as a model for the spacer between the ‘PdCl₂(N∼S)’ centre and the polymer substituent of the resins and monolith. Suzuki-Miyaura and Mizoroki-Heck catalysis exhibit anticipated trends in reactivity with variation of aryl halide reagents for each system, and show that supported catalysis on beads and monolith gives higher yields than for homogeneous catalysis. The synthesis of 2-methylthiomethylpyridines is presented, together with crystal structures of 4-bromo-2-bromomethylpyridine hydrobromide, 4-(4-hydroxyphenyl)-2-methylthiomethylpyridine (L¹), PdCl₂(L¹) and PdCl₂(L²). Hydrogen bonding occurs in 4-bromo-2-bromomethylpyridine hydrobromide as N-H?Br interactions, in 4-(4-hydroxyphenyl)-2-methylthiomethylpyridine as O-H?N to form chains, and in PdCl₂(L¹) as O-H?Cl interactions leading to adjacent π-stacked chains oriented in an antiparallel fashion.     

Quantum accelerator modes from the Farey tree

We show that mode locking finds a purely quantum nondissipative counterpart in atom-optical quantum accelerator modes. These modes are formed by exposing cold atoms to periodic kicks in the direction of the gravitational field. They are anchored to generalized Arnol'd tongues, parameter regions where driven nonlinear classical systems exhibit mode locking. A hierarchy for the rational numbers known as the Farey tree provides an ordering of the Arnol'd tongues and hence of experimentally observed accelerator modes.