On toric h-vectors of centrally symmetric polytopes

We prove tight lower bounds for the coefficients of the toric h-vector of an arbitrary centrally symmetric polytope generalizing previous results due to R. Stanley and the author using toric varieties. Our proof here is based on the theory of combinatorial intersection cohomology for normal fans of polytopes developed by G. Barthel, J.-P. Brasselet, K. Fieseler and L. Kaup, and independently by P. Bressler and V. Lunts. This theory is also valid for nonrational polytopes when there is no standard correspondence with toric varieties. In this way we can establish our bounds for centrally symmetric polytopes even without requiring them to be rational. Received: 24 March 2004     

Direct Imaging of Octahedral Distortion in a Complex Molybdenum Vanadium Mixed Oxide

Complex Mo,V‐based mixed oxides that crystallize in the orthorhombic M1‐type structure are promising candidates for the selective oxidation of small alkanes. The oxygen sublattice of such a complex oxide has been studied by annular bright field scanning transmission electron microscopy. The recorded micrographs directly display the local distortion in the metal oxygen octahedra. From the degree of distortion we are able to draw conclusions on the distribution of oxidation states in the cation columns at different sites. The results are supported by X‐ray diffraction and electron paramagnetic resonance measurements that provide integral details about the crystal structure and spin coupling, respectively.     

Poly[tetrakis(n‐propylammonium) [octa‐μ‐chlorido‐dichloridotrinickelate(II)]]: a hybrid organic–inorganic layer compound in the Cs4Mg3F10 structure type

The title compound, {(C₃H₁₀N)₄[Ni₃Cl₁₀]}_n, contains zigzag layers of tri‐μ‐chlorido‐bridged linear 2/m‐symmetric Ni₃Cl₁₂ segments, linked by mono‐μ‐chlorido quasi‐linear bridges to two other segments at each end. These inorganic layers are interleaved with interdigitated bilayers of mirror‐symmetric n‐propylammonium cations, the ammonium head groups of which are directed into the inorganic layers to form multiple N—H...Cl hydrogen bonds, while the propyl tail groups pack together in a tongue‐and‐groove manner in the center of the bilayer. The propyl groups are ordered at 100 K but disordered with opposite conformations on the mirror plane at 240 K.     

Rapid ion-exchange technique for the separation and preconcentration of chromium(VI) and chromium(III) in fresh waters

A technique for the separation and preconcentration of Cr(VI) and Cr(III) in fresh waters is presented. The analytical procedure involves the use of anion- and cation-exchange columns. The columns are eluted and the eluate is analysed for chromium using a graphite furnace atomic absorption spectrometer. The recovery of Cr(VI) and Cr(III) is 97.86 ± 1.31% and 102.36 ± 1.25% (95% confidence), respectively. The detection limits are 0.019 and 0.020 μg 1^?1 for 200 ml of sample (twice the standard deviation of eleven replicate blanks). The method is rapid and the need for minimum sample handling avoids contamination problems.     

Experimental and four‐component relativistic DFT studies of tungsten carbonyl complexes

We present a theoretical and experimental study of the structure and nuclear magnetic resonance (NMR) parameters of the pentacarbonyltungsten complexes of η¹‐2‐(trimethylstannyl)‐4,5‐dimethylphosphinine, η²‐norbornene, and imidazolidine‐2‐thione. The three complexes have a pseudo‐octahedral molecular structure with the six ligands bonded to the tungsten atom. The η¹‐2‐(trimethylstannyl)‐4,5‐dimethylphosphinine‐pentacarbonyl tungsten complex was synthesized for the first time. For all compounds, we present four‐component relativistic calculations of the NMR parameters at the Dirac–Kohn–Sham density functional level of theory using hybrid functionals. These large‐scale relativistic calculations of NMR chemical shifts and spin–spin coupling constants were compared with available experimental data, either taken from the literature or measured in this work. The inclusion of solvent effects modeled using a conductor‐like screening model was found to improve agreement between the calculated and experimental NMR parameters, and our best estimates for the NMR parameters are generally in good agreement with available experimental results. The present work demonstrates that four‐component relativistic theory has reached a level of maturity that makes it a convenient and accurate tool for modeling and understanding chemical shifts and indirect spin–spin coupling constants of organometallic compounds containing heavy elements, for which conventional non‐relativistic theory breaks down. Copyright © 2015 John Wiley & Sons, Ltd.