Neue Fluropalladate(II)

New Fluoropalladates(II) Single crystal investigations on \documentclass{article}\pagestyle{empty}\begin{document}$ \begin{array}{*{20}c} {[6][4]} \\ {{\rm CsPdPdF}_{\rm 5} } \\ \end{array} $\end{document} (orange brown) demonstrate the close structural relationship to the CsAgFeF₆ – and CsNiNiF₆-type, respectively. One half of the Pd²⁺ ions is surrounded octahedrally, whereas the other half, because of the “absence” of one F^?, is coordinated planar quadratically. CsPd₂F₅ crystallizes orthorhombic (Imma – D, No. 74; Z = 4) with a = 6.53₃, b = 7.86₂, c = 10.79 Å (four circle diffractometer data). From Guinier data are isotypic CsMgPdF₅ (yellow, a = 6.603(2), b = 7.415(2), c = 10.548(3) Å), CsZnPdF₅ (beige, a = 6.576(1), b = 7,483(2), c = 10.645(2) Å), CsNiPdF₅ (yellow, a = 6.499(1), b = 7.504(2), c = 10.575(3) Å) and CsCoPdF₅ (brown, a = 6.527(1), b = 7.553(1), c = 10.659(2) Å). Besides of CsPd₂F₅ there exist compounds of the composition Me₃PdF₅ on the alkali-rich side of the system MeF/PdF₂. Single crystal investigations for Rb₃PdF₃ (yellow, P4/mbm–D, No. 127; Z = 2) led to a = 7.46₇, c = 6.49₇ Å (four circle diffractometer data). Isotypic are (single crystal data) Cs₃PdF₅ (yellow, a = 7.84₈, c = 6.68₈ Å) and Rb₂CsPdF₅ (yellow, ordered distribution of the alkali ions, a = 7.57₅, c = 6.44₅ Å).     

Ruthenium-catalyzed olefin metathesis double-bond isomerization sequence

A novel ruthenium-catalyzed tandem ring-closing metathesis (RCM) double-bond isomerization reaction is described in this paper. The utility of this method for the efficient syntheses of five-, six-, and seven-membered cyclic enol ethers is demonstrated. It relies on the conversion of a metathesis-active ruthenium carbene species to an isomerization-active ruthenium-hydride species in situ. This conversion is achieved by using various additives. Scope and limitations of the different protocols are discussed, and some mechanistic considerations based on (31)P and (1)H NMR spectroscopic studies are presented.     

Diphosphacarbollide analogues of the C5H5- anion: isolation of the nido-di- and triphosphacarboranes 7,8,9-P2CB8H10, [7,8,9-P2CB8H9]-, [7,8,10-P2CB8H9]-, and 7,8,9,10-P3CB7H8

Treatment of a solution of excess PCl(3) and PS (PS = "proton sponge" = 1,8-dimethylamino naphthalene) with arachno-4-CB(8)H(14) (1) in CH(2)Cl(2), followed by hydrolysis of the reaction mixture, resulted in the isolation of the eleven-vertex diphosphacarbaborane nido-7,8,9-P(2)CB(8)H(10) (2) (yield 34%) as the main product. Other products isolated from this reaction were the phosphacarboranes nido-7,8,9,10-P(3)CB(7)H(8) (3) (yield 5%) and closo-2,1-PCB(8)H(9) (4) (yield 15%). Compound 2 can be deprotonated by PS in CH(2)Cl(2) or NaH in diethyl ether to give the [nido-7,8,9-P(2)CB(8)H(9)](-) (2(-)()) anion, which gives back the original compound, 2, upon re-protonation. Thermal rearrangement of anion 2(-) (Na(+) salt) at 350 degrees C for 2 h produced the isomeric [nido-7,8,10-P(2)CB(8)H(9)](-) (5(-)()) anion, which was isolated as a PPh(4)(+) salt (yield 86%). Multinuclear ((1)H, (11)B, (31)P, and (13)C), two-dimensional [(11)B-(11)B] COSY, (1)H{(11)B(selective)}, (1)H{(31)P(selective)}, and gradient-enhanced ([(1)H-(13)C] HSQC) magnetic resonance measurements led to complete assignments of all resonances which are in excellent agreement with the structures proposed. Coupling constants, (1)J((31)P,(13)C), (2)J((31)P,C,(1)H), and (1)J((31)P,(31)P), were calculated using the DFT method B3LYP/6-311+G(d,p). The molecular geometries of all compounds were optimized ab initio at a correlated level of theory (RMP2(fc)) using the 6-31G basis set, and their correctness was assessed by comparison of the experimental (11)B and (13)C chemical shifts with those calculated by the GIAO-SCF/II//RMP2(fc)/6-31G method. The computations also include the structures and chemical shieldings of the still unknown isomers [nido-7,10,8-P(2)CB(8)H(9)](-) (6(-)) and [nido-7,9,8-P(2)CB(8)H(9)](-) (7(-)).     

Neue Ternäre Silber(II)-fluoride: Ag3IIM2IVF14 (MIV = Zr,Hf)

New Ternary Silver (II) Fluorides: Ag M F₁₄ (M^IV = Zr, Hf) Single crystals of deeply blue violet coloured fluorides Ag₃^IIM₂^IVF₁₄ (M^IV = Zr, Hf) have been obtained by heating powder samples under F₂/N₂ (1:2) at T ≈? 600°C. The isotypic compounds crystallizes monoclinic with a = 924.9, b = 668.6, c = 907.3 pm, β = 90.30° (Ag₃Hf₂F₁₄) and a = 922.5, b = 667.6, c = 906.3 pm, β = 91.30° (Ag₃Zr₂F₁₄) (Four circle diffractometer data, Philips PW 1100), spcgr. C2/m-C_2h³ (No. 12), Z = 2. There are two different sorts of Ag²⁺:Ag(1) with coordination number C.N. [Ag(1)] = 4 + 2 and Ag(2) with C.N.[Ag(2)] = 4 + 4 against F^?. Ag(1) can be substituted by Cu²⁺, Ni²⁺, Zn²⁺, Mg²⁺ (all of blue/red violet colour), Ag(2) by Ca²⁺, Cd²⁺, Hg²⁺ (bright green). From (preliminary) powder data CuAg₂Zr₂F₁₄ with a = 912.3(4), b = 661.2(2), c = 899.4(2) pm, β = 90.70° (3) is isotypic, the other compounds seems to be of closely related type of structure.     

Comparison of cartesian and lobe function Gaussian basis sets

The lobe function and cartesian (spherical harmonic) gaussian are compared with reference to calculations for second-row atoms. Single and grouped gaussian basis sets which have been reported for cartesian functions are taken over directly to construct corresponding lobe function bases with identical sets of exponents and with lobe separations chosen by a scaling procedure. Total and orbital energies and SCF coefficients resulting from calculations on the second-row atoms using the two types of functions for both primitive and grouped gaussian basis sets are seen to be in excellent agreement, thereby emphasizing the essential equivalence of lobe functions and cartesian gaussians, at the very least with respect to calculation of energy surfaces.

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Zusammenfassung Die Lobe-Funktionen und kartesischen (Kugelfunktions-) Gaußfunktionen werden in Berechnungen von Atomen der zweiten Reihe des periodischen Systems verglichen. Schon bekannte einfache und gruppierte Gaußfunktionsbasissätze für kartesische Funktionen werden direkt übernommen, um entsprechende Lobe-Funktionsbasen mit identischen Exponenten zu konstruieren, wobei die zugehörigen Lobe-Abstände nach einer Koordinatenstreckungs-(scaling) Methode berechnet werden. Gesamt- und Orbitalenergien sowie SCF-Koeffizienten für die Atome der zweiten Reihe stimmen bei Benutzung der beiden verschiedenen Funktionstypen, sowohl bei einfacher als auch bei gruppierter Gaußfunktionsbasis, außerordentlich gut überein, wodurch die wesentliche Gleichwertigkeit von Lobe-Funktionen und kartesischen Gaußfunktionen betont wird, zum allermindesten hinsichtlich der Berechnung von Energieflächen.

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Résumé La fonction de lobe et la gaussienne cartésienne (harmonique sphérique) sont comparées sur des calculs d'atomes de la seconde ligne. Des bases de gaussiennes simples et groupées utilisées pour les fonctions cartésiennes sont directement employées pour construire les bases correspondantes de fonctions à lobes avec des ensembles d'exposants identiques et des séparations de lobes choisis par calibrage. L'emploi de ces deux types de fonctions donne des résultats concordants pour l'énergie totale, les énergies orbitales et les coefficients SCF, mettant l'accent sur l'équivalence essentielle des fonctions à lobe et des gaussiennes cartésiennes, tout au moins pour le calcul des surfaces d'énergie.

     

Limit theorems under the assumption of restricted convergence on a set with a finite limit point

We consider double sequences {{X_nk}} of independent and asymptotically constant random variables. For certain constants A_n we put The central problem is the following one: Assume that {F_n} for x ? I ? R₁ converges weakly to a nonconstant limit function ψ where I is a set with a finite limit point (restricted convergence Then additional conditions ensuring the complete convergence F_n ? F to a certain limit distribution function F are given. These additional conditions are weaker than the corresponding sufficient conditions known from the classical theory. Further, these results yield two new versions of the central limit theorem, see § 2. In the case of identically distributed summands with common distribution function V the assumption a sufficient to prove F_n ? F_α, provided that (F_α stands for a stable distribution with characteristic exponent α).     

Estimates from below for Lebesgue constants of Fourier series on compact Lie groups

In this paper the Lebesque constants (L _R ^K (G))_R>0 of Fourier series on compact Lie groups G corresponding to general one-dimensional groupings on the dual object G^{^} are estimated from below by the associated (abelian) Lebesgue constants (L _R ^K (T))_R>0 on a maximal torus T in G. For spherical groupings this leads to the estimate L _R (G)const.R^(l-1)/2, l=dimT2.