Cu4O12-Baugruppen aus planaren CuO4-Polygonen im Barium-Vanadyl-Oxocuprat(II)-phosphat Ba(VO)Cu4(PO4)4

Cu₄O₁₂ Groups Built of Square Planar CuO₄ Polygones in the Barium Vanadyl Oxocuprate(II) Phosphate Ba(VO)Cu₄(PO₄)₄ Single crystals of Ba(VO)Cu₄(PO₄)₄ have been prepared by solid state reactions just below the melting points of the reaction mixtures of BaP₂O₆, Cu₃(PO₄)₂, CuO, V₂O₅ and V₂O₃ in evacuated closed quartz glas tubes. The compound crystallizes with tetragonal symmetry, Space group D? P42₁2, a = 9.560(2), c = 7.160(2) Å, Z = 2. Special and new features of the crystal structure are to each other isolated Cu₄O₁₂ and (VO)(PO₄)₄ groups. The crystal chemistry of the Cu₄O₁₂ groups is discussed with respect to other compounds containing out of plane connected square planar MO₄ polygones.     

Zwei neue Metatitanate mit fünffach koordiniertem Titan: CsNaTiO3 und RbNaTiO3

Two New Metatitanates with Five-coordinated Titanium: CsNaTiO₃ and RbNaTiO₃ [1] The new oxides CsNaTiO₃ (I) and RbNaTiO₃ (II) are obtained by heating well grounded mixtures of the binary oxides in Ni-tubes as colourless platelike crystals. I: CsO_0.56, NaO_0.48 and TiO₂, Cs:Na:Ti = 1.1:1.1:1.0; 600°C, 61 d as well as CsO_0.97, NaO_0.48 and Ti₂O₃, Cs:Na:Ti = 1.5:3.0:1.0; 760°C, 27 d. II: RbO_0.52, NaO_0.48 and TiO₂, Rb:Na:Ti = 1.1:1.1:1.0; 750°C, 14 d as well as RbO_0.98, NaO_0.48 and Ti₂O₃, Rb:Na:Ti = 1.5:3.1:1.0; 760°C, 27 d. CsNaTiO₃ (orthorhombic, Cmcm) is nearly isostructural with KNaTiO₃ [2]; a = 601.4(1) pm, b = 1 120.3(1) pm, c = 563.4(1) pm (Guinier-Simon-Data, Z = 4). RbNaTiO₃ (monoclinic, C2/c) is isostructural with KNaTiO₃; a = 590.3(1) pm, b = 1 098.4(1) pm, c = 555.1(0) pm, β = 92.15° (Guinier-Simon-Data, Z = 4). Both structures are determined by using four-circle diffractometer data (CsNaTiO₃: Siemens AED2, 2 896I_o(hkl), MoKα , R = 2.4%, R_w = 2.3%; RbNaTiO₃: Philips PW 1 100, 2 743I_o(hkl), AgKα , R = 9.9%, R_w = 8.9%; additional data see text). The Madelung Part of Lattice Energy (MAPLE), Effective Coordination Numbers (ECoN), Mean Fictive Ionic Radii (MEFIR) and the Charge Distribution in Solids are calculated and discussed.     

The hydrophobic effect in aqueous solutions of nonelectrolytes. I. Self-interactions of alkylureas

In order to clarify some aspects of the hydrophobic interactions, the enthalpies of dilution of monoethylurea, 1,3-dimethylurea, and 1,3-diethylurea have been determined calorimetrically at 25°C. The calorimetric data, expressed in terms of excess enthalpy, permit the evaluation of the pair and triplet interaction coefficients. The analyses of these and of the analogous coefficientsg _xx andg _xxx, derived from osmotic data, indicate a driving force favorable to the interactions among the hydrated solute molecules. Nevertheless, the positive values of theh _xx andh _xxx coefficients seem to suggest that the source of the effect is a rearrangement of the water molecules rather than a direct association of the solute molecules. There are evidences of a strict correlation between the enthalpic and the entropic effects. Preliminary data were presented at the International Conferences on Chemical Thermodynamics at Baden (1973) and Montpellier (1975). The experimental part was carried out at the Istituto Chimico of the University of Trieste. To whom correspondence should be addressed.     

Zur Kenntnis von BaTiVO4 und SrTiVO4

On BaTiVO₄ and SrTiVO₄ BaTiVO₄ and SrTiVO₄ were prepared in closed systems by solid state reactions. They crystallize with orthorhombic symmetry (BaTiVO₄: space group D-Pmnb; a = 5.889; b = 7.889; c ?10.397 Å; Z = 4; SrTiVO₄: space group D-P2¹,2¹,2¹,2¹; a = 5.855; b = 7.572; c = 10.012 Å; Z = 4) and belong to β-K₂SO₄-type. The ordered occupation of point positions by Ba²⁺ and Tl⁺ as well as the decrease in symmetry of SrTiVO₄ are discussed.     

On the calculation of arbitrary multielectron molecular integrals over Slater‐type orbitals using recurrence relations for overlap integrals. III. Auxiliary functions \documentclass{article}\pagestyle{empty}\begin{document}$Q_{nn'}^{q}$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$G_{-nn'}^{q}$\end{document}

The auxiliary functions $Q_{nn'}^{q}(p,pt)$ and $G_{-nn'}^{q}(p_{a},p,pt)$ which are used in our previous paper [Guseinov, I. I.; Mamedov, B. A. Int J Quantum Chem 2001, 81, 117] for the computation of multicenter electron‐repulsion integrals over Slater‐type orbitals (STOs) are discussed in detail, and the method is given for their numerical computation. The present method is suitable for all values of the parameters p_a, p, and pt. Three‐ and four‐center electron‐repulsion integrals are calculated for extremely large quantum numbers using relations for auxiliary functions obtained in this paper. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

The crystal structures of two Mercury Perrhenates

The mercury perrhenates with the empirical formulas HgReO₄ and Hg₂ReO₅ were prepared by annealing powdered mixtures of mercury(II)oxide and mercury(II)metaperrhenate Hg(ReO₄)₂ in sealed silica tubes. Their crystal structures were determined from single-crystal X-ray data. HgReO₄ crystallizes dimeric with nearly linear O₃Re? O? Hg? Hg? O? ReO₃ molecular units and Hg₂ReO₅ has a solid state structure, where Hg(I) and Hg(II) together with oxygen atoms form 14-membered rings, which are condensed to two-dimensionally infinite polycationic nets of composition (Hg₂²⁺ · 2 HgO)_n. These nets are separated from each other by tetrahedral ReO₄^? anions.     

An unequivocal synthesis of some substituted 1,2,4-triazolo[1,5-a]pyrimidines

An unequivocal synthesis of 5-chloro-7-methyl- (8) and 7-methyl-1,2,4-triazolo[1,5-a]pyrimidine (10) from 2-amino-4-chloro-6-methylpyrimidine (5) through the corresponding amidine6 and formamide oxime7 was developed. It was unambigously shown by comparison of the chemical shifts and the magnitude of coupling constants that the compounds obtained by condensation of 3-amino-1,2,4-triazole (12) and ethyl acetoacetate (13) and some further transformations are isomeric 5-methyl substituted 1,2,4-triazolo[1,5-a]pyrimidines1,9, and11.

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Eine eindeutige Synthese einiger substituierter 1,2,4-Triazolo[1,5-a]pyrimidine

Zusammenfassung Es wurde ein eindeutiger Syntheseweg für 5-Chlor-7-methyl- (8) und 7-Methyl-1,2,4-triazolo[1,5-a]pyrimidin (10) ausgehend von 2-Amino-4-chlor-6-methylpyrimidin (5) über das entsprechende Amidin6 und das Formamidoxim7 entwickelt. Durch Vergleich von chemischen Verschiebungen und Kopplungskonstanten konnte eindeutig gezeigt werden, daß die Verbindungen, die bei der Kondensation von 3-Amino-1,2,4-triazol (12) and Ethylacetoacetat (13), sowie einige weitere Transformationsprodukte, isomere 5-Methylsubstituierte 1,2,4-Triazolo[1,5-a]pyrimidine sind (1,9,11).

     

Application of coset representations to the construction of symmetry adapted functions

Summary A coset representation (G(/G _i )), which is defined algebraically by a coset decomposition of a finite groupG by its subgroupG _i , is shown to be a method for the decomposition of a regular body into its point group orbits. This proof also shows that each member of theG(/G _i ) orbit belongs to theG _i site-symmetry. In addition, a general equation concerning the multiplicities of such coset representations is derived and shown to involve Brester's equations and thek-value equations of framework groups as special cases. The relationship of the coset representation and the site-symmetry affords a general procedure for obtaining symmetry adapted functions.     

A modified steepest descent method with applications to maximizing likelihood functions

In maximizing a non-linear function G(), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1–1 transformation on the variables , so that in the space of the transformed variables, the steepest descent method produces the solution faster. The final solution in the original space is obtained by taking the inverse transformation. We apply the procedure in maximizing the likelihood functions of some generalized distributions which are widely used in modeling count data. It was shown that for these distributions, the steepest descent method via transformations produced the solutions very fast. It is also observed that the proposed procedure can be used to expedite the convergence rate of the first derivative based algorithms, such as Polak-Ribiere, Fletcher and Reeves conjugate gradient methods as well.