Lifting problems and transgression for non-abelian gerbes

We discuss lifting and reduction problems for bundles and gerbes in the context of a Lie 2-group. We obtain a geometrical formulation (and a new proof) for the exactness of Breen’s long exact sequence in non-abelian cohomology. We use our geometrical formulation in order to define a transgression map in non-abelian cohomology. This transgression map relates the degree one non-abelian cohomology of a smooth manifold (represented by non-abelian gerbes) with the degree zero non-abelian cohomology of the free loop space (represented by principal bundles). We prove several properties for this transgression map. For instance, it reduces–in case of a Lie 2-group with a single object–to the ordinary transgression in ordinary cohomology. We describe applications of our results to string manifolds: first, we obtain a new comparison theorem for different notions of string structures. Second, our transgression map establishes a direct relation between string structures and spin structures on the loop space.     

The Shape of Germanium Clusters To Come

A different drummer : The existence of endohedral germanium clusters was predicted earlier by gas‐phase experiments. The [Co@Ge₁₀]^3? anion now synthesized is surprising, as it breaks with a long line of exclusively deltahedral structures found in the past. Instead, it has a regular pentagonal‐prismatic structure (see picture; Co gray, Ge red).

     

Ultrafast dynamics in DNA: "fraying" at the end of the helix

The dynamics of the electric fields in the interior of DNA are measured by using oligonucleotides in which a native base pair is replaced by a dye molecule (coumarin 102) whose emission spectrum is sensitive to the local electric field. Time-resolved measurements of the emission spectrum have been extended to a six decade time range (40 fs to 40 ns) by combining results from time-correlated photon counting, fluorescence up-conversion, and transient absorption. Recent results showed that when the reporter is placed in the center of the oligonucleotide, the dynamics are very broadly distributed over this entire time range and do not show specific time constants associated with individual processes (Andreatta, D.; et al. J. Am. Chem. Soc. 2005, 127, 7270). This paper examines an oligonucleotide with the reporter near its end. The broadly distributed relaxation seen before remains with little attenuation. In addition, a new relaxation with a well-defined relaxation time of 5 ps appears. This process is assigned to the rapid component of "fraying" at the end of the helix.     

Dimers of heptapnictide anions: As14 4- and P14 4- in the crystal structures of [Rb(18-crown-6)]4As14.6NH3 and [Li(NH3)4]4P14.NH3

Compounds [Rb(18-crown-6)]4As14.6NH3 (1) and [Li(NH3)4]4P14.NH3 (2) were prepared by the reaction of Rb4As6 with SbPh3 and 18-crown-6 and by the reduction of white phosphorus with elemental lithium in liquid ammonia, respectively. Both were characterized by low-temperature single-crystal X-ray structure analysis. They were found to contain the Ci symmetrical Pn14(4-) anion (Pn = P, As), which consists of two nortricyclane-like Pn7-cages connected by a single bond. Molecular complexes of [Rb(18-crown-6)(NH3)]2[Rb(18-crown-6)]2As14 are formed in 1, which are connected to fanfold sheets via N-H...O bonds. The anion is isolated in 2, and N-H...N bonds result in the formation of {[Li(NH3)4](mu-NH3)2[Li(NH3)4]}2+ cationic complexes.     

Kinetics of intramolecular charge transfer with N-phenylpyrrole in alkyl cyanides

For the electron acceptor/donor molecule N-phenylpyrrole (PP), the fast intramolecular charge transfer (ICT) reaction accompanied by dual fluorescence from a locally excited (LE) and an ICT state is investigated in alkyl cyanide solvents as a function of temperature. After a comparison of the X-ray crystal structure of PP with calculations from the literature, absorption and fluorescence spectra of PP in a series of solvents over a wide polarity range are discussed. ICT with PP strongly depends on solvent polarity and starts to appear in solvents more polar than diethyl ether. From an analysis of the ICT/LE fluorescence quantum yield ratio Phi'(ICT)/Phi(LE), approximate data for the change in enthalpy -DeltaH of the ICT reaction of PP are obtained, ranging from 9 kJ/mol in acetonitrile (MeCN) to 4 kJ/mol in n-butyl cyanide (BuCN). From ICT and LE fluorescence decays of PP measured as a function of temperature, the forward (Ea = 9 kJ/mol in ethyl cyanide (EtCN) and 6 kJ/mol in MeCN) and backward (Ed = 16 kJ/mol in EtCN and MeCN) ICT reaction barriers are determined. From these data, -Delta H (7 kJ/mol (EtCN); 10 kJ/mol (MeCN)) is calculated, in good agreement with the results coming from Phi'(ICT)/Phi(LE). The data for Ea show that the forward ICT barrier becomes smaller with increasing solvent polarity, whereas the absence of change for Ed comes from the compensating increase of -DeltaH. Both observations are indicative of a late transition state for the LE --> ICT reaction. For PP in EtCN and MeCN, the ICT radiative rate constant k'(f)(ICT) increases with temperature. This is caused by the ICT low transition dipole moment and hence does not contain information on the molecular structure (twisted or planar) of the ICT state. The fast ICT observed with PP supports our previous conclusion, based on a comparison of PP with its planarized derivative fluorazene, that the pyrrole and phenyl moieties in the ICT state of PP are coplanar and possess substantial electronic coupling.     

Hydrogen Bonds in Rubidium Amide‐Ammonia(3/2), RbNH2·2/3NH3

Rubidium amide‐ammonia(3/2), RbNH₂·2/3NH₃, was synthesized from Rubidiumhydride, RbH, in liquid ammonia at ?78 °C. The compound crystallizes in the cubic space group I2₁3 with Z = 4, a = 10.0490(12) Å, and V = 1014.77(20) Å as isometric colorless crystals. The crystal structure was solved from single‐crystal X‐ray data. The structure contains a three‐dimensional network of amide anions and ammonia molecules, which are interconnected via hydrogen bonds.     

Experimental Charge Density Studies of Cyclotetrasilazane and Metal Complexes Containing the Di‐ and Tetraanion

The homologous series of parent octamethylcyclotetrasilazane (c‐NH‐SiMe₂‐)₄, ( 1 ), the lithium complex [(THF)₂Li₂(c‐N‐SiMe₂‐NH‐SiMe₂‐)₂]₂, ( 2 ), containing the cyclic dianion, and [(THF)₂LiAl(c‐N‐SiMe₂‐)₄]₂, ( 3 ), accommodating the unprecedented tetraanion [Me₂SiN]^4‐ was synthesized to investigate the nature of the covalent Si‐N single bond in the presence of various metals. These model compounds show a wide diversity of Si‐N(H), Si‐N(M), Si‐N(H, M) and M‐N bonds and serve as bench‐mark systems to study polar bonds by high‐resolution low‐temperature X‐ray structure analysis. Experimental charge density studies reveal highly polar Si‐N bonds with remarkable ionic contribution, even in the non‐metallated starting material 1 . The Li‐N and Li‐O bonds have to be classified as almost purely ionic bonds with topological properties not far from those determined for NaCl.     

Investigation of high‐speed boundary‐layer transition by DNS

An investigation of hypersonic boundary‐layer flow along a flat plate is being presented. The high Mach number investigated calls for the consideration of the chemical reactions and the change in thermodynamical properties for temperatures up to T = 6000 K. For the current investigation a test case at M = 20 and the atmospheric conditions at an altitude of H = 50 Km is chosen. The differences to the ideal‐gas result is demonstrated. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)