Metallaheterocumulene : III. Ungewöhnliche bildung von (CO)5Cr=C=NCPh2N=C=Cr(CO)5 bei der reaktion von [(CO)5Cr=C=N=CPh2] AlBr4 mit tetrahydrofuran

Pentacarbonyl(3,3-diphenyl-2-azaallenylidene)chromium tetrabromoaluminate, [(CO)₅Cr=C=Nz.dbnd;CPh₂]⁺ AlBr₄⁻, reacts with THF in dichloromethane to give the dinuclear bis(isonitrile) complex [(CO)₅Cr=C=N]₂CPh₂ which formally corresponds to the product of a reductive dimerization of two [(CO)₅Cr=C=N=CPh₂]⁺ moieties with concomitant elimination of one CPh₂ fragment.     

Electrochemical behaviour and chemical oxidation study of the thio- and phosphido-bridge binuclear iron complexes

The electrochemical behaviour of thio and phosphido complexes of iron(I): Fe₂XY(CO)_6nL_n (X = Y = SR, PR₂ and X = SR, Y = PR₂, L = PR₃) has been studied on platinum and mercury electrodes, in organic solvent. These complexes are reduced in a two-electron irreversible process. A large difference is observed between their oxidation potentials on mercury and platinum electrodes; this is ascribed to the formation of a mercury complex in which mercury is inserted into the metalmetal bond. In oxidation on platinum electrodes, two mono-electronic waves are observed. The influece of the ligand basicity on the cathodic E_{$\text{1}\text{2}$} values is discussed. A parallel shift is observed between the E_{$\text{1}\text{2}$} and the IR ν(CO) of the totally symmetrical mode. Chemical oxidation of the complexes shows that the dications cannot be isolated, and leads to isolation of the following species: [FeP(CH₃)₂(CO)₃]₂AgNO₃, [FeSCH₃(CO)₂P(CH₃)₃]₂(NO₃)₂, {[FeSCH₃(CO)₂P(CH₃)₃]₂F} PF₆, where NO₃^? and F^? act as ligands.     

On the hyperbolicity of Einstein's and other gauge field equations

It is shown that Einstein's vacuum field equations (respectively the conformal vacuum field equations) in a frame formalism imply a symmetric hyperbolic system of reduced propagation equations for any choice of coordinate system and frame field (and conformal factor). Certain freely specifiable gauge source functions occurring in the reduced equations reflect the choice of gauge. Together with the initial data they determine the gauge uniquely. Their choice does not affect the isometry class (conformal class) of a solution of an initial value problem. By the same method symmetric hyperbolic propagation equations are obtained from other gauge field equations, irrespective of the gauge. Using the concept of source functions one finds that Einstein's field equation, considered as second order equations for the metric coefficients, are of wave equation type in any coordinate system.Work supported by a Heisenberg-Fellowship of the Deutsche Forschungsgemeinschaft     

Pentaiodide komplexer Alkalimetall‐Kronenether‐Kationen: Darstellung und strukturelle Charakterisierung der Verbindungen [M(Benzo‐15‐Krone‐5)2]I5 mit M = Na,K, Rb,Cs

Pentaiodides of Complex Alkaline Metal Crown Ether Cations: Synthesis and Structural Characterisation of the Compounds [M(benzo‐15‐crown‐5)₂]I₅, M = Na, K, Rb and Cs The isotypic compounds [M(benzo‐15‐crown‐5)₂]I₅, M = Na, K, Rb and Cs are obtained as single crystals via the reaction of benzo‐15‐crown‐5, MI and iodine (2 : 1 : 2) from ethanol/dichloromethane (1 : 1). These compounds crystallize in the monoclinic space group P2₁/n with four formula units in the unit cell. The cations form typical sandwich complexes. The volume of the unit cell increases by 4, 3 % from the sodium to the caesium compound, corresponding to the increasing space required by the cations. The pentaiodide units consist of a elongated triiodide unit and two iodine half‐molecules. These iodine molecules are completed by centres of symmetry. The interconnection between the pentaiodide units leads to the formation of zig‐zag chains that run along [001]. Considering the strongly different ionic radii of the alkali‐metal cations, the existence of this number of isotypic structures is rather surprising.     

Carbolactonization of olefins under mild conditions by cyanoacetic and malonic acids promoted by manganese (III) acetate

A variety of olefins can be converted to γ-lactones with good efficiency by intermolecular carbolactonization using cyanoacetic acid or malonic acid derivatives in the presence of Mn (III) at 23°.     

The question of cyclic versus acyclic ions: The structure of [C10H12]+˙ gas phase ions

The extent of isomerization of acyclic and cyclic gas phase radical cations of composition [C₁₀H₁₂]⁺˙ has been investigated by using collisionally activated dissociation spectroscopy. Both electron and charge exchange ionizaiton were employed to form the ions with various internal energies. The [C₁₀H₁₂]⁺˙ ions investigated consisted of ionized phenylbutenes, ring-substituted methyl derivatives of allylbenzene and phenylpropene, 1-methyl-2-isopropenylbenzene, benzylcyclopropane, phenylcyclobutane, tetralin and 1-methylindan. The 1-methylindan and tetralin radical cations are the most stable of the C₁₀H₁₂ isomeric radical ions. The [C₁₀H₁₂]⁺˙ formed from acyclic olefins having the double bond in conjugation with the aromatic ring retain the initial structure to a significant extent. However, ions derived from olefins with the double bond out of conjugation with the benzene ring preferentially cyclize to stable five- and six-membered cyclic ions. Ring opening of small-ring cyclic ions, such as ionized benzylcyclopropane and phenylcyclobutane, occurs, followed by ring closure to the tetralin radical cation.     

Accurate and consistent particle tracking on unstructured grids

A new numerical method for particle tracking (Lagrangian particle advection) on 2‐D unstructured grids with triangular cells is presented and tested. This method combines key attributes of published methods, including streamline closure for steady flows and local mass conservation (uniformity preservation). The subgrid‐scale velocity reconstruction is linear, and this linear velocity field is integrated analytically to obtain particle trajectories. A complete analytic solution to the 2‐D system of ordinary differential equations (ODEs) governing particle trajectories within a grid cell is provided. The analytic solution to the linear system of locally mass‐conserving constraints that must be enforced to obtain the coefficients in the ODEs is also provided. Numerical experiments are performed to demonstrate that the new method has substantial advantages in accuracy over previously published methods and that it does not suffer from unphysical particle clustering. The method can be used not only in particle‐tracking applications but also as part of a semi‐Lagrangian advection scheme.Copyright © 2015 John Wiley & Sons, Ltd.