Synthese,Kristallstruktur und festkörper‐NMR‐spektroskopische Untersuchung neuer Oxonitridosilicate der Mischkristallreihe Ba4−xCaxSi6N10O

The new oxonitridosilicates Ba_4?xCa_xSi₆N₁₀O have been synthesized by means of high‐temperature synthesis in a radio‐frequency furnace, starting from calcium, barium, silicon diimide and amorphous silicon dioxide. The maximum reaction temperature was at about 1450 °C. The solid solution series Ba_4?xCa_xSi₆N₁₀O with a phase width 1.81 ≤ x ≤ 2.95 was obtained. The crystal structure of Ba_1.8Ca_2.2Si₆N₁₀O was determined by X‐ray single‐crystal structure determination (P2₁3, no. 198), a = 1040.2(1) pm, Z = 4, wR2 = 0.082). It can be described as a highly condensed network of corner‐sharing SiN₄ and SiON₃ tetrahedra, the voids of which are occupied by the alkaline earth ions. The structure is isotypic with that of BaEu(Ba_0.5Eu_0.5)YbSi₆N₁₁. In the ²⁹Si solid‐state MAS‐NMR spectrum two isotropic resonances at ?50.0 and ?53.6 ppm were observed.     

The chemical bond in polyphosphides: crystal structures, the electron localization function, and a new view of aromaticity in P4(2-) and P5(-)

The incongruent solvation of M(I)4P6 species (M(I) = K, Rb, Cs) in liquid ammonia leads to a broad variety of polyphosphides such as P7(3-), P11(3-), and the putatively aromatic P4(2-) and P5(-), which we investigated by using NMR spectroscopy and single-crystal X-ray structure analysis. The structures of Cs2P4 x 2 NH3, (K@[18]crown-6)3K3(P7)2 x 10 NH3, Rb3P7 x 7 NH3, and (Rb@[18]crown-6)3P7 x 6 NH3 are discussed and compared. The electron localization function ELF is used in a comparison of the chemical bonding of various phosphorus species. The variances of the basin populations provide a well-established measure for electron delocalization and therefore aromaticity. While comparable variance is calculated for P4(2-) and P5(-) it is observed in the lone pairs rather than in the basin populations of the bonds as in the prototypical aromatic hydrocarbons such as benzene or the cyclopentadienide anion. For this behavior, the term "lone pair aromaticity" is proposed.     

Memoryless near-collisions via coding theory

We investigate generic methods to find near-collisions in cryptographic hash functions. We introduce a new generic approach based on methods to find cycles in the space of codewords of a code with low covering radius. We give an analysis of our approach and demonstrate it on the SHA-3 candidate TIB3.