Versatile post-functionalisation strategy for the formation of modular organic–inorganic polyoxometalate hybrids

Hybrid structures incorporating different organic and inorganic constituents are emerging as a very promising class of materials since they synergistically combine the complementary and diverse properties of the individual components. Hybrid materials based on polyoxometalate clusters (POMs) are particularly interesting due to their versatile catalytic, redox, electronic, and magnetic properties, yet the controlled incorporation of different clusters into a hybrid structure is challenging and has been scarcely reported. Herein we propose a novel and general strategy for combining multiple types of metal-oxo clusters in a single hybrid molecule. Two novel hybrid POM structures (HPOMs) bis-functionalised with dipentaerythritol (R–POM₁–R; R = (OCH₂)₃CCH₂OCH₂C(CH₂OH)) were synthesised as building-blocks for the formation of heterometallic hybrid triads (POM₂–R–POM₁–R–POM₂). Such a modular approach resulted in the formation of four novel heterometallic hybrids combing the Lindqvist {V₆}, Anderson–Evans {XMo₆} (X = Cr or Al) and trisubstituted Wells–Dawson {P₂V₃W₁₅} POM structures. Their formation was confirmed by multinuclear Nuclear Magnetic Resonance (NMR), infrared (IR) and UV-Vis spectroscopy, as well as Mass Spectrometry, Diffusion Ordered Spectroscopy (DOSY) and elemental analysis. The thermal stability of the hybrids was also examined by Thermogravimetric Analysis (TGA), which showed that the HPOM triads exhibit higher thermal stability than comparable hybrid structures containing only one type of POM. The one-pot synthesis of these novel compounds was achieved in high yields in aqueous and organic media under simple reflux conditions, without the need of any additives, and could be translated to create other hybrid materials based on a variety of metal-oxo cluster building-blocks.

A versatile modular approach has been developed for incorporating different metal-oxo nanoclusters with characteristic structures into a single hybrid molecule by covalently linking them with polyol ligands.     

Fast and accurate algorithm for the simulation of NMR spectra of large spin systems

The computational cost for the simulation of NMR spectra grows exponentially with the number of nuclei. Today, the memory available to store the Hamiltonian limits the size of the system that can be studied. Modern computers enable to tackle systems containing up to 13 spins [1], which obviously does not allow to study most molecules of interest in research. This issue can be addressed by identifying groups of spins or fragments that are not or only weakly interacting together, i.e., that only share weakly coupled spin pairs. Such a fragmentation is only permitted in the weak coupling regime, i.e., when the coupling interaction is weak compared to the difference in chemical shift of the coupled spins. Here, we propose a procedure that removes weak coupling interactions in order to split the spin system efficiently and to correct a posteriori for the effect of the neglected couplings. This approach yields accurate spectra when the adequate interactions are removed, i.e., between spins only involved in weak coupling interactions, but fails otherwise. As a result, the computational time for the simulation of 1D spectra grows linearly with the size of the spin system.     

Metabolic compartmentalization in the human cortex and hippocampus: evidence for a cell- and region-specific localization of lactate dehydrogenase 5 and pyruvate dehydrogenase

Background  

For a long time now, glucose has been thought to be the main, if not the sole substrate for brain energy metabolism. Recent data nevertheless suggest that other molecules, such as monocarboxylates (lactate and pyruvate mainly) could be suitable substrates. Although monocarboxylates poorly cross the blood brain barrier (BBB), such substrates could replace glucose if produced locally.     

Existence of solutions in variational relation problems without convexity

Two main existence conditions for solutions of variational relation problems are established without convexity. The first one is based on a finite solvability property and the second one on generalized KKM mappings. These conditions unify and strengthen several existing results in the literature on the topic. A model of satisficing process by rejection is considered which gives an economic interpretation of the introduced concepts.     

Rational approximation in the complex plane using a τ-method and computer algebra

Numerous versions of the Lanczos τ-methods have been extensively used to produce polynomial approximations for functions verifying a linear differential equation with polynomial coefficients. In the case of an initial-value problem, an adapted τ-method based on Chebyshev series and the use of symbolic computation lead to a rational approximation of the solution on a region of the complex plane. Numerical examples show that the simplicity of the method does not prevent a high accuracy of results. This revised version was published online in June 2006 with corrections to the Cover Date.     

F/Si distance determination in fluoride-containing octadecasil by Hartmann–Hahn cross-polarization under fast magic-angle spinning

¹⁹F/²⁹Si Hartmann–Hahn continuous wave cross-polarization (CP) has been applied under fast magic-angle spinning (MAS) to a powder sample of octadecasil. Strong oscillations occur during CP on a sideband matching condition between the isolated ²⁹Si–¹⁹F spin pairs formed by the silicons in the D4R units and the fluoride anions. The magnitude of the dipolar coupling constant was deduced directly from the line-splitting between the intense singularities of the Pake-like patterns obtained by Fourier transformation of the oscillatory polarization transfer. The corresponding Si–F internuclear distance, r=2.62±0.05 Å, is found to be in very good agreement with the X-ray crystal structure and the value of 2.69±0.04 Å recently reported from rotational echo double resonance (REDOR) and transferred echo double resonance (TEDOR) nuclear magnetic resonance (NMR) experiments. Furthermore, the CP technique is still reliable under fast MAS where both REDOR and TEDOR sequences suffer from severe artefacts due to finite pulse lengths. In octadecasil, a spinning frequency of 14 kHz is shown to be necessary for an effective suppression of ¹⁹F–¹⁹F spin diffusion. The influences of experimental missettings and radiofrequency (RF) field inhomogeneity are taken into account.     

Genetic analysis of the GRIK2 modifier effect in Huntington's disease

Background  

In Huntington's disease (HD), age at neurological onset is inversely correlated with the length of the CAG trinucleotide repeat mutation, but can be modified by genetic factors beyond the HD gene. Association of a relatively infrequent 16 TAA allele of a trinucleotide repeat polymorphism in the GRIK2 3'UTR with earlier than expected age at neurological onset has been suggested to reflect linkage disequilibrium with a functional polymorphism in GRIK2 or an adjacent gene.     

Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier–Stokes asymptotics

In this paper, we develop a numerical method to solve Boltzmann like equations of kinetic theory which is able to capture the compressible Navier–Stokes dynamics at small Knudsen numbers. Our approach is based on the micro/macro decomposition technique, which applies to general collision operators. This decomposition is performed in all the phase space and leads to an equivalent formulation of the Boltzmann (or BGK) equation that couples a kinetic equation with macroscopic ones. This new formulation is then discretized with a semi-implicit time scheme combined with a staggered grid space discretization. Finally, several numerical tests are presented in order to illustrate the efficiency of our approach. Incidentally, we also introduce in this paper a modification of a standard splitting method that allows to preserve the compressible Navier–Stokes asymptotics in the case of the simplified BGK model. Up to our knowledge, this property is not known for general collision operators.