Intervals in lattices of quasiorders

We investigate the structure of intervals in the lattice of all closed quasiorders on a compact or discrete space. As a first step, we show that if the intervalI has no infinite chains then the underlying space may be assumed to be finite, and in particular,I must be finite, too. We compute several upper bounds for its size in terms of its heighth, which in turn can be computed easily by means of the least and the greatest element ofI. The cover degreec of the interval (i.e. the maximal number of atoms in a subinterval) is less than 4h. Moreover, ifc4(n–1) thenI contains a Boolean subinterval of size 2 ⁿ , and ifI is geometric then it is already a finite Boolean lattice. While every finite distributive lattice is isomorphic to some interval of quasiorders, we show that a nondistributive finite interval of quasiorders is neither a vertical sum nor a horizontal sum of two lattices, with exception of the pentagon. Many further lattices are excluded from the class of intervals of quasiorders by the fact that no join-irreducible element of such an interval can have two incomparable join-irreducible complements. Up to isomorphism, we determine all quasiorder intervals with less than 9 elements and all quasiorder intervals with two complementary atoms or coatoms.     

Synthesis and structural characterization of novel neutral hexacoordinate silicon(IV) complexes with SiO2N4 skeletons containing cyanato-N or thiocyanato-N ligands

A series of novel hexacoordinate silicon(IV) complexes with an SiO2N4 skeleton (compounds (OC-6-12)-3, (OC-6-12)-4, (OC-6-12)-5, (OC-6-12)-6, and (OC-6-2'2)-7) were synthesized, starting from Si(NCO)4 or Si(NCS)4. These compounds contain (i) two bidentate O,N-chelate ligands (or one tetradentate O,N,N,O-chelate ligand) derived from 4-aminopent-3-en-2-ones of the formula type Me-C(NRH)=CH-C(O)-Me (R = organyl) and (ii) two monodentate cyanato-N or thiocyanato-N ligands. Formally, the bidentate singly negatively charged O,N-chelate ligands (tetradentate 2-fold negatively charged O,N,N,O-chelate ligand) behave as ligands of the imino-enolato type. In addition, the adduct trans-8 was synthesized by reaction of Si(NCS)4 with 2 molar equiv of Me-C(Ni-PrH)=CH-C(O)-Me. This hexacoordinate silicon(IV) complex contains (i) four monodentate thiocyanato-N ligands and (ii) two neutral monodentate ligands of the iminio-enolato type. All compounds synthesized were structurally characterized by single-crystal X-ray diffraction and solid-state and solution NMR spectroscopy. To get more information about the stereochemistry of these compounds, the experimental investigations were complemented by computational studies.     

Syntheses and structures of dimesitylbismuth(III) bromide, Mes2BiBr, and bis(diphenyldithiophosphinato)mesitylbismuth(III), MesBi(S2PPh2)2

Addition of BiBr₃ to Mes₃Bi (Mes = 2, 4, 6-Me₃C₆H₂) in Et₂O gives 86% of Mes₂BiBr (1) as yellow crystals. Reaction of 1 with Ph₂PS₂NH₄ in a 1 : 1 molar ratio gives a quantitative yield of MesBi(S₂PPh₂)₂ (2) rather than the expected dimesitylbismuth compound. The crystal and molecular structures of 1 and 2 were determined at 153 K and 173 K, respectively. They contain Mes₂BiBr molecules with trigonal pyramidal coordination around Bi. The mean Bi---C bond distance is 2.27 Å and the Bi---Br bond distance is 2.690(2) Å. The angles around Bi vary between 89.4 and 106.4°. Intermolecular Bi…Br contacts of 3.795 Å, indicating weak secondary bonding, give rise to zig-zag shaped (Bi---Br)_x chains. In the polymeric chain the coordination geometry around bismuth atoms can be described as pseudo-trigonal bipyramidal. The crystals of 2 consist of discrete monomeric MesBi(S₂PPh₂)₂ molecules with a symmetry plane containing the metal atom and the aromatic ring of the attached mesityl group. The dithiophosphinato ligands exhibit an anisobidentate coordination pattern with long and short phosphorus—sulfur bonds, i.e. P(1)---S(1) 2.051(31) Å and P(1)---S(2) 1.980(3) Å, related to short and long bismuth—sulfur distances, respectively, i.e. Bi---S(1) 2.662(2) Å and Bi---S(2) 3.123(3) Å. This leads to a square-pyramidal geometry around the bismuth atom, with the metal lying 0.33 Å above the basal plane formed by the four sulfur atoms.     

The hexacoordinate silicate dianions mer-tris[glycolato(2-)-O(1),O(2)]silicate and fac-tris[benzilato(2-)-O(1),O(2)]silicate: syntheses and structural characterization

Treatment of tetramethoxysilane with glycolic acid and morpholine (molar ratio 1:3:2) in methanol, followed by crystallization from methanol/tetrahydrofuran, yielded morpholinium mer-tris[glycolato(2-)-O(1),O(2)]silicate (mer-7). Treatment of benzilic acid with sodium hydride, followed by addition of tetrachlorosilane and triethylamine (molar ratio 3:4:1:2), afforded, after crystallization from 1,4-dioxane/acetonitrile/diethyl ether/n-pentane, triethylammonium fac-tris[benzilato(2-)-O(1),O(2)]silicate-hemi-1,4-dioxane (fac-8.(1)/(2)C(4)H(8)O(2)). Single-crystal X-ray diffraction studies showed that the Si-coordination polyhedra of the hexacoordinate silicon(IV) complexes mer-7 and fac-8.(1)/(2)C(4)H(8)O(2) are distorted octahedra. Both compounds were additionally characterized by solid-state VACP/MAS NMR studies ((13)C, (29)Si), and fac-8.(1)/(2)C(4)H(8)O(2) was studied in solution by (1)H, (13)C, and (29)Si NMR experiments. The structural investigations were complemented by computational studies (MP2 studies, TZP level) of the dianions of fac-7 and mer-7.     

Visuelle Titrationen unter Verwendung von Di?thyldithiocarbaminat

Zusammenfassung Als Einleitung zu einer Reihe von Berichten über visuelle Titrationen unter Verwendung von Diäthyldithiocarbaminat werden in der vorliegenden Mitteilung die analytisch wichtigen Eigenschaften der Schwermetallcarbate besprochen. Es wird eine Reaktionsreihenfolge der Metalle gegenüber dem Fällungsreagens mitgeteilt, die den noch folgenden maß-analytischen Verfahren zugrunde liegt.     

Die Analytik von Cellulose?thergruppen

Zusammenfassung Es werden Methoden und Apparaturen zur qualitativen und quantitativen Bestimmung von Äthergruppen in Cellulosederivaten mit einer oder mehreren Alkoxyl- und Hydroxyalkylgruppen (C₁-nC₄) beschrieben. Die Ätherspaltung erfolgt im allgemeinen mit Jodwasserstoffsäure und in Sonderfällen mit Bromwasserstoffsäure. Als Reaktionsprodukte entstehen Monojodalkane und Alkene oder Monobromalkane und Dibromalkane. Diese werden der gas-chromatographischen Trennung unterworfen, über die Retentionszeit identifiziert und durch Titration oder über das Gas-Chromatogramm quantitativ bestimmt.

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Analysis of cellulose ether groups

A report is given on methods and apparatus for the qualitative and quantitative determination of ether groups in cellulose derivatives with one or more alkoxyl and hydroxyalkyl groups (C₁-nC₄). Ether splitting generally takes place with hydriodic acid and in special cases with hydrobromic acid. The resulting reaction products are monoiodoalkanes and alkenes or monobromoalkanes and dibromoalkanes, which are subjected to gas chromatographic separation and identified via the retention time and quantitatively evaluated by titration or via the gas chromatogram.

     

Extended fenske-hall calculation of inner-shell binding energies using (Z + 1)-bazis sets: Sulfur-containing molecules

It is shown that the S1s and S2p binding energies and their chemical shifts in the molecules H₂S, SO₂, SF₆ and COS obtained with hole-state calculations using an extended Fenske-Hall method are in good agreement with experimental values if mixed (Z + 1)-basis sets are applied.