The rhombidodecahedral tessellation of 3-space and a particular 15-vertex triangulation of the 3-dimensional torus

It is well known that the unique 7-vertex triangulation of the 2-dimensional torus S¹×S¹ is a consequence of the relationship between two hexagonal lattices in the euclidean plane: it is just the quotient of the triangular tessellation of the plane by a translation group. Each vertex star is a regular hexagon and the symmetry group of this triangulation is the affine group A(1,₇) in one dimension over ₇. In this paper we describe a particular 15-vertex triangulation of the 3-dimensional torus S¹×S¹×S¹ whose symmetry group is the affine group A(1,₁₅) and which is similarly related to two lattices in euclidean 3-space: it is just the quotient of a particular tessellation of 3-space by a translation group. Each vertex star happens to be a rhombidodecahedron, the dual of a (semiregular) cuboctahedron.     

Copper—A “Modern” Bioelement

Copper is a bioessential element in biology with truly unique chemical characteristics in its two relevant oxidation states +I and +II. Significant progress has been made in recent years in the elucidation of the frequently surprising biochemistry of this trace element. Those advances were especially furthered through mutual stimulation involving results from biochemistry, molecular biology, and medicine on one hand and the synthesis as well as the structural and spectroscopic characterization of low molecular weight model complexes on the other. The most notable features of protein-bound active copper are its almost exclusive function in the metabolism of O₂ or N/O compounds (NO, N₂O) and its frequent association with oxidizing organic and inorganic radicals such as tyrosyl, semiquinones, superoxide, or nitrosyl. This unique biological role of copper can be rationalized given its chemical and assumed evolutionary background.     

Development and validation of a method for the determination of trace alkylphenols and phthalates in the atmosphere

An analytical method has been developed for the simultaneous extraction and determination of trace tertiary octylphenol (t-OP), technical nonylphenol isomers (NP), nonylphenol monoethoxylate isomers (NP1EO) and seven phthalates in the atmosphere using gas chromatography-mass spectrometry (GC-MS). High volume samples were collected using a high-volume pump equipped with a PUF/XAD-2 column for air and glass fiber filter for particles. The detection limits of the method for alkylphenols (APs) and the phthalates ranged from 0.0006 to 0.034 ng m⁻³ in air. The recoveries of t-OP, NP, NP1EO and the phthalates for the entire procedure were satisfactory (>69%). The method was successfully applied to the determination of the analytes in the atmosphere samples collected over land and the ocean. The concentrations of t-OP, NP, NP1EO showed decline trends from land to the open sea, and the phthalates present over land and the North Sea were comparable. It is suggested that the atmosphere is a significant pathway for the transport of alkylphenols and the phthalates in the environment.     

Determination of the Insect Repellent Bayrepel® in Pool and Lake Water by Gas Chromatography after Preconcentration with Solid-Phase Extraction and Stir-Bar-Sorptive Extraction

A method for the determination of the new insect repellent Bayrepel in bathing lakes and public pools is presented. Sample preconcentration is performed either by solid-phase extraction (SPE) or stir bar sorptive extraction (SBSE). Analysis of the enriched analyte using gas chromatography-mass spectrometry (GC-MS) led to almost identical limits of detection (LOD) of 25ngL^–1 for Bayrepel with both extraction methods. Because of the slightly reduced handling effort involved, the method based on preconcentration by SBSE was finally chosen for the analysis of real samples.     

A Convergent Synthesis of (±)-α- and β-Himachalenes

(±)-α and β-Himachalene, 5 and 6 , have been synthesized in a convergent manner from 3,3-dimethylacrolein ( 9 ), the ester enolate 10 and the silyloxypentadienyllithium 7 . The key steps are the regioselective γ-addition of the dienal 13 to 7 and the intramolecular Diels-Alder addition 15 → 16 . Hydrogenolysis of the diethylphosphate group and functionalization at C (5) completed the synthesis of 5 and 6 .     

A three‐dimensional framework of bis­[tris­(ethyl­enediamine)zinc] tetra­iodo­cadmate diiodide assisted by N—H⋯I hydrogen bonds

The title salt, [Zn(C₂N₂H₈)₃]₂[CdI₄]I₂, conventionally abbreviated [Zn(en)₃]₂[CdI₄]I₂, where en is ethyl­enediamine, contains discrete [Zn(en)₃]²⁺ cations and [CdI₄]²⁻ anions with distorted octa­hedral and nearly tetra­hedral geometries, respectively, as well as uncoordinated I⁻ ions. The cation and the free I⁻ anion lie on twofold rotation axes and the [CdI₄]²⁻ anion lies on a axis in the space group I2d. The structure exhibits numerous weak inter‐ionic hydrogen bonds of two types, viz. N—H⋯I⁻(free ion) and N—H⋯I([CdI₄]²⁻), which support the resulting three‐dimensional framework.     

Ein- und zweikernige Dinitrosylkomplexe von Molybdän und Wolfram. Die Kristallstrukturen von (PPh3Me)2[WCl4(NO)2], (PPh3Me)2[MoCl3(NO)2]2 und von (PPh3Me)2[WCl3(NO)2]2

Mono- and Binuclear Dinitrosyl Complexes of Molybdenum and Tungsten. Crystal Structures of (PPh₃Me)₂[WCl₄(NO)₂], (PPh₃Me)₂[MoCl₃(NO)₂]₂, and (PPh₃Me)₂[WCl₃(NO)₂]₂ The complexes (PPh₃Me)₂[MCl₄(NO)₂] (M = Mo, W), and (PPh₃Me)₂[MCl₃(NO)₂]₂, respectively, are prepared by reactions of the polymeric compounds MCl₂(NO)₂ with triphenylmethylphosphonium chloride in CH₂Cl₂, forming green crystals. According to the IR spectra the nitrosyl groups are in cis-position in all cases. The tungsten compounds as well as (PPh₃Me)₂[MoCl₃(NO)₂]₂ were characterized by structure determinations with X-ray methods. (PPh₃Me)₂[WCl₄(NO)₂]: space group C2/c, Z = 4. a = 1874, b = 1046, c = 2263 pm, β = 119.99°. Structure determination with 3492 independent reflexions, R = 0.057. The compound consists of PPh₃Me^⊕ ions, and anions [WCl₄(NO)₂]^2? with the nitrosyl groups in cis-position (symmetry C_2v). (PPh₃Me)₂[WCl₃(NO)₂]₂: Space group C2/c, Z = 4. Structure determination with 2947 independent reflexions, R = 0.059. (PPH₃Me)₂[MoCl₃(NO)₂]₂: Space group P1 , Z = 1. a = 989, b = 1134, c = 1186 pm; α = 63.25°, β = 80.69°, γ = 69.94°. Structure determination with 3326 independent reflexions, R = 0.046. The compounds consist of PPh₃Me^⊕ ions, and centrosymmetric anions [MCl₃(NO)₂]₂^2?, in which the metal atoms are associated via MCl₂M bridges of slightly different lengths. One of the NO groups is in an axial position, the other one in equatorial position (symmetry C_2h).     

Combined electron diffraction,conformational energy and vibrational investigations of cis-1,4-ditertiary butyl-cyclohexane

The structure of cis-1,4-ditertiarybutylcyclohexane(DTBC) was investigated by combined electron diffraction, conformational and vibrational analyses in order to obtain results which are more conclusive than those previously obtained by electron diffraction alone. In this study, first the minimum energy conformations for DTBC were calculated by the Westheimer-Hendrickson procedure using various force fields described in the literature; the same fields and the minimum energy conformations were used in subsequent vibrational analyses to calculate the mean amplitudes of vibration for each minimum energy conformation of DTBC; these mean amplitudes and the corresponding internuclear distances were then used to calculate the theoretical electron diffraction radial distribution curves which were compared to the experimental curves. The results indicate that the conformational energies of all the minimum energy chair and non-chair forms of DTBC are very similar. In excellent agreement with this, the theoretical radial distribution curves of all minimum energy forms have to be mixed for a best fit to the experimental radial distribution curve. A least squares analysis of the mixture under the described conditions yields for 110 °C a composition of approximately one third chair and two thirds non-chair forms. The quality of the empirical conformational force fields has a definite influence on the reliability of these results.     

Structures of Addition Products of Acetylenedicarboxylic Acid Esters with Various Dinucleophiles. An application of C,H-spin-coupling constants

Heterocyclic compounds obtained by addition of acetylenedicarboxylic acid esters to thioureas, cyclic amidines and o-difunctionalized aromatic systems have been studied by ¹³C-NMR. In particular, C, H-spin-coupling constants over two and three bonds were used to differentiate between the various constitutional isomers and to establish the configuration of trisubstituted exocyclic C, C-double bonds. The configurational significance and diagnostic value of vicinal cis and trans C,H-spin coupling is again demonstrated in the present series.