On the exceptional series,and its descendantsLa série exceptionnelle,et sa descendance

Many of the striking similarities which occur for the adjoint representation of groups in the exceptional series (cf. [1–3]) also occur for certain representations of specific reductive subgroups. The tensor algebras on these representations are easier to describe (cf. [4,5,7]), and may offer clues to the original situation.The subgroups which occur form a Magic Triangle, which extends Freudenthal's Magic Square of Lie algebras. We describe these groups from the perspective of dual pairs, and their representations from the action of the dual pair on an exceptional Lie algebra. To cite this article: P. Deligne, B.H. Gross, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 877–881.     

Temperaturmessung

Ohne Zusammenfassung     

Magnetic properties of lanthanum orthoferrite fine powders prepared by different chemical routes

Fine powders of lanthanum iron oxide, LaFeO₃, have been prepared by solid state reaction as well as sol-gel synthesis and nebulized spray pyrolysis. Structures, morphologies and magnetic susceptibility measurements of these powders have been examined. The powders prepared by all the three low-temperature routes contain nearly spherical particles with an average diameter of 40 nm. These samples show a lower Neel temperature than the powder prepared by solid state reaction besides showing much lower magnetic susceptibility at low temperatures. Dedicated to Professor C N R Rao on his 70th birthday     

Potentiometrische Bestimmung von Seltenen Erden (z. B. Erbium)

Zusammenfassung Eine schnelle und zuverlässige, potentiometrische Titrationsmethode zur Bestimmung von Erbium mit Ammoniumoxalatlösung in wäßrig-acetonischem Medium im Verhältnis 11 wurde ausgearbeitet. Man titriert in dem System Pt | ErCl₃ | Hg₂Cl₂ + KCl | Hg. Der Potentialsprung im Äquivalenzsättigungspunkt ist bereits auf Zugabe eines Tropfens Reagenslösung sehr deutlich. Der Meßfehler überschreitet nicht die Grenzen ±0,5%.Die Methode ist bei Metallionen, die mit Ammoniumoxalat schwerlösliche Niederschläge bilden, nicht anwendbar.

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Summary A rapid and accurate method for the potentiometric titration of erbium by means of ammonium oxalate solution in a water-acetone medium (11) has been worked out. The system Pt | ErCl₃ | Hg₂Cl₂ + KCl | Hg was used. The potential jump at the neutral point is distinct, even if only one drop of the reagent is added. The error of the measurement is not greater than ±0,5%- Metal ions forming insoluble precipitates with ammonium oxalate interfere with this method.

     

The canonical ensemble via symplectic integrators using Nosé and Nosé-Poincaré chains

Simulations that sample from the canonical ensemble can be generated by the addition of a single degree of freedom, provided that the system is ergodic, as described by Nosé with subsequent modifications by Hoover to allow sampling in real time. Nosé-Hoover dynamics is not ergodic for small or stiff systems and the addition of auxiliary thermostats is needed to overcome this deficiency. Nosé-Hoover dynamics, like its derivatives, does not have a Hamiltonian structure, precluding the use of symplectic integrators which are noted for their long term stability and structure preservation. As an alternative to Nosé-Hoover, the Hamiltonian Nosé-Poincaré method was proposed by Bond, Laird, and Leimkuhler [J. Comput. Phys. 151, 114 (1999)], but the straightforward addition of thermostatting chains does not sample from the canonical ensemble. In this paper a method is proposed whereby additional thermostats can be applied to a Hamiltonian system while retaining sampling from the canonical ensemble. This technique has been used to construct thermostatting chains for the Nosé and Nosé-Poincaré methods.     

Intercalating lithium into the lattice of silver nanoparticles boosts catalytic hydrogenation of carbon–oxygen bonds

Coinage metal nanoparticles with high dispersion can serve as highly efficient heterogeneous catalysts. However, owing to their low melting point, poor thermal stability remains a major obstacle towards their application under reaction conditions. It is a common practice to use porous inorganic templates such as mesoporous silica SBA-15 to disperse Ag nanoparticles (NPs) against aggregation but their stability is far from satisfactory. Here, we show that the catalytic activity for hydrogenation of dimethyl oxalate (DMO) to methyl glycolate (MG) over Ag NPs dispersed on SBA-15 silica can be further promoted by incorporation of alkali metal ions at small loading, which follows the inverse order of their cationic size: Li⁺ > Na⁺ > K⁺ > Rb⁺. Among these, 5Ag₁–Li_0.05/SBA-15 can double the MG yield compared to pristine 5Ag/SBA-15 under identical conditions with superior thermal stability. Akin to the effect of an ionic surfactant on stabilization of a micro-emulsion, the cationic charge of an alkali metal ion can maintain dispersion and modulate the surface valence of Ag NPs. Interstitial Li in the octahedral holes of the face center packed Ag lattice is for the first time confirmed by X-ray pair distribution function and electron ptychography. It is believed that this interstitial-stabilization of coinage metal nanoparticles could be broadly applicable to multi-metallic nanomaterials for a broad range of C–O bond activating catalytic reactions of esters.

Coinage metal nanoparticles with high dispersion can serve as highly efficient heterogeneous catalysts.     

Allylic interactions in organometallics: probing Electronic structure in (η5-C5H5)Fe(CO)2R,R = CH3, η1-C3H5, η1-C5H5.

The He(I) photoelectron spectra of (η⁵-C₅H₅)Fe(CO)₂R, where R = CH₃, η¹-C₃H₅ and η¹-C₅H₅, have been recorded. The lowest lying ion states result from ionization of molecular orbitals with large Fe 3d character; these move to lower anergy when R places double bonds in an allylic relationship to the metal atom. The cyclic voltammetric oxidation potential correlates well with the energies of the lowest ion states. A significant interaction between olefin π orbitals and the allylic metal center is proposed.     

Metal ion scrambling in hexanuclear M(6)(Et(2)NCO(2))(12) complexes (M = Co,Mg). Synthesis,solid state structure,and solution dynamics of heteronuclear Co(n)Mg(6-n)(Et(2)NCO(2))(12) complexes

Heteronuclear diethylcarbamato complexes of the form Co(n)()Mg(6)(-)(n)()(Et(2)NCO(2))(12) were prepared from the isostructural homonuclear precursors Mg(6)(Et(2)NCO(2))(12), 1, and Co(6)(Et(2)NCO(2))(12), 2, via a solvothermal methodology. Two materials were selected for single-crystal X-ray diffraction analysis: Co(1.6)Mg(4.4)(Et(2)NCO(2))(12) and Co(2.7)Mg(3.3)(Et(2)NCO(2))(12). Both compounds crystallize in the orthorhombic space group Ccca, as do 1 and 2. The molecular structure is best described as two trinuclear M(3) units cross-linked by diethylcarbamate ligands and twisted about one another, so that the complex has overall D(2) symmetry and is chiral. Each trinuclear unit consists of two terminal pentacoordinate metal ions and one central hexacoordinate metal ion. The X-ray diffraction data were unambiguous that the Co(2+) ions migrate exclusively to the pentacoordinate sites in the heteronuclear complexes, thus demonstrating that metal ion scrambling at the molecular level must occur. The composition of individual crystals can be continuously varied for Co(2+) mole fractions chi(Co) < 0.5, and the a and c unit cell distances are linearly related to chi(Co). This indicates that the compounds behave as solid solutions. There appears to be either a chemical or crystallographic phenomenon inherent in the synthetic methodology that prevents isolation of heteronuclear materials having chi(Co) > 0.5. Solution electronic spectroscopy and molecular weight measurements show that 2 can dissociate in chloroform and cyclohexane solution to give a dimeric complex 2'. This behavior contrasts with the stability of 1 in solution, as shown by NMR. The kinetic rate profile for formation of Co(n)Mg(6-n)(Et(2)NCO(2))(12) reveals saturation kinetics and is consistent with direct attack by 2' on 1 to give the heteronuclear complex via a higher nuclearity intermediate. This study illustrates a general method for the preparation of solids based on heteronuclear Werner-type complexes of the M(6)(Et(2)NCO(2))(12) structure type, and the mechanism by which such compounds can be formed from isostructural homonuclear precursors.