XVI. (2,5-C4Bu2RHN)MCl3 (M = Ti, Zr, Hf; R = H, SiMe3)—Azacyclopentadienyl-Komplexe der Gruppe 4-Metalle

The azacyclopentadienyl compounds (2,5-C₄^tBu₂RHN)MCl₃ (M = Ti, Zr, Hf; R = H, SiMe₃) have been prepared as stable solids from the lithiated pyrroles and MCl₄. The π-coordination of the azacyclopentadienyl ligands, as suggested from ¹³ C NMR data, has been confirmed for (2,5-C₄^tBu₂H₂N)TiCl₃ by an X-ray diffraction study.     

A π-acceptor series for phosphines from51V N.M.R. data on [η5-CpV(CO)3L] complexes

Summary Qualitative molecular orbital considerations of the complexes [⁵-CPV(CO)₃ L] (L = substituted phosphane, SbPh₃, AsPh₃, CN^–) suggest that s' V chemical shift parameters () obtained for these compounds should correlate with the -acceptor abilities of L. Based on observed r-values, the ligands are arranged in sequence of their -acceptor ability, which lies in the order P(OR)₃ > CN^– > PR'₃3 SbPh₃ PPhF₂ > P(i-Bu)₃ P(NR ₂ )₃ > PPh₃ > AsPh₃ Nuclear spin-spin coupling constants J (⁵¹V-³¹ P), line widths H and i.r. data in the (CO) region are also presented.P(OR)₃ = P(OEt)₃, 4-Ethyl-l-phospha-2,6,7-trioxabicyclo[2.2.2]-octane; R = Me, n-Pr; R = Me, Et.     

Cycloadditionsreaktionen der aminofluorsilane

Aminofluorsilanes are obtained by the reaction of fluorosilanes with the lithium salts of the corresponding amines. The reaction of aminofluorosilanes with butyllithium in a (2 + 2)cyclo addition reaction leads to the formation of fourmembered silicon-nitrogen ring compounds. The mechanism of the reaction is discussed, the mass, ¹H and ¹⁹F NMR spectra of the compounds are reported.     

The Yellow Polymorphs of Mercuric Iodide (HgI2)

HgI₂ crystallizes under ambient conditions from various solvents and by sublimation into three concomitant polymorphs whose colors are red, orange, and yellow. The orange and yellow phases are metastable and transform into the red phase when touched. A phase transition from red to yellow occurs at 400 K. The reverse transition from yellow to red shows a huge hysteresis. We established that the structures of the metastable yellow^M phase (determined by single‐crystal X‐ray diffraction) and the high‐temperature yellow^HT phase (determined by powder synchrotron X‐ray diffraction and second‐harmonic generation) are different, albeit closely related. Both show analogous packings of I? Hg? I molecules, which are straight in the first and bent with an angle of ca. 160° in the second. The red and orange phases are tetrahedral semiconductor structures that sublime even at room temperature. The growth of the yellow^M phase from 2‐chloroethanol and the kinetics of the reconstructive phase transition red to yellow^HT and back were studied by optical microscopy, Raman spectroscopy in solution, luminescence, and powder synchrotron X‐ray diffraction as a function of time at various temperatures. Both yellow phases grow by accretion of HgI₂ molecules, present in the solution or liberated from the red crystals, on the surface of the crystal. In contrast, the reverse transformation from yellow to red occurs in the bulk of the crystal, presumably by migration of Hg in the packing of I and subsequent rearrangement of I. The displacement parameters of Hg in both structures are considerably larger than those of I and apparently not dominated by disorder effects.     

Some non-existence results on divisible difference sets

In this paper, we shall prove several non-existence results for divisible difference sets, using three approaches:

1. character sum arguments similar to the work of Turyn [25] for ordinary difference sets,
2. involution arguments and
3. multipliers in conjunction with results on ordinary difference sets.

Among other results, we show that an abelian affine difference set of odd orders (s not a perfect square) inG can exist only if the Sylow 2-subgroup ofG is cyclic. We also obtain a non-existence result for non-cyclic (n, n, n, 1) relative difference sets of odd ordern.     

Reconstructing phase space from PDE simulations

We propose the Karhunen-Loève (K-L) decomposition as a tool to analyze complex spatio-temporal structures in PDE simulations in terms of concepts from dynamical systems theory. Taking the Kuramoto-Sivashinsky equation as a model problem we discuss the K-L decomposition for 4 different values of its bifurcation parameter . We distinguish two modes of using the K-L decomposition: As an analytic and synthetic tool respectively. Using the analytic mode we find unstable fixed points and stable and unstable manifolds in a parameter regime with structurally stable homoclinic orbits (=17.75). Choosing the data for a K-L analysis carefully by restricting them to certain burst events, we can analyze a more complicated intermittent regime at =68. We establish that the spatially localized oscillations around a so called strange fixed point which are considered as fore-runners of spatially concentrated zones of turbulence are in fact created by a very specific limit cycle (=83.75) which, for =87, bifurcates into a modulated traveling wave. Using the K-L decomposition synthetically by determining an optimal Galerkin system, we present evidence that the K-L decomposition systematically destroys dissipation and leads to blow up solutions.We would like to dedicate this paper to Klaus Kirchgässner on the occasion of his 60th birthday     

Unified treatment of fermions and bosons

Dirac's matrices can be interpreted as an 8-rank covariant antisymmetric tensor field on an 11-dimensional manifold (space-time ×S ⁷) enforcing a linkage between the Lorentz transformation and rotations ofS ⁷, conferring spinorial properties on any quantity having an index in the inner spaceS ⁷.     

Novel enantioselective strong cation exchangers based on sulfodipeptide selectors: evaluation for enantiomer separation of chiral bases by nonaqueous capillary electrochromatography

Strong cation exchange (SCX)-type chiral stationary phases (CSPs) based on beta-amino sulfonic acid-terminated dipeptide derivatives as chiral selectors, immobilized on thiol-modified silica particles (3.5 microm), were synthesized and applied to enantiomer separations of chiral bases by nonaqueous capillary electrochromatography (CEC). The effect of structural variations of the sulfodipeptide selectors on the separation factors alpha was investigated. These studies included variation of the acid-terminal amino sulfonic acid residue, variation of the configurations, i.e., comparison of the diastereomeric (S,S)- and (R,S)-configurations of the sulfodipeptides, and finally comparison of sulfodipeptide selectors with corresponding beta-amino sulfonic acid analogs. In general, the capillary columns (100 microm ID) packed with the new SCX-type CSPs showed enantioselectivity for an elaborated set of chiral basic drugs in CEC acting by an enantioselective cation-exchange retention mechanism. N-[N-(4-Allyloxy-3,5-dichlorobenzoyl)-leucyl]-2-amino-3,3-dimethylbutane sulfonic acid, in particular with (R,S)-configuration, turned out to be a more effective SCX-type selector than a more rigid analog based on N-[N-(4-Allyloxy-3,5-dichlorobenzoyl)-leucyl]-2-pyrrolidinemethane sulfonic acid. Both of the former diastereomers were capable to baseline-resolve the enantiomers of ca. 40% of the tested basic chiral solutes including sympathomimetics and beta-blockers, while for the latter SCX-type CSPs only 10-20% of the selected solutes afforded resolutions > 1.5.