Synthesis,crystal structure,magnetism, and absorption spectra of A2UX5 Type Halides (A = K,Rb; X = Cl,Br, I)

The ternary uranium(III) halides A₂UX₅ (A = K, Rb; X = Cl, Br, I) have been prepared from the binary components AX and UX₃ in sealed tantalum containers. According to their Guinier X-ray powder patterns, they all crystallize with the K₂PrCl₅/Y₂HfS₅ type of structure. Lattice constants for ambient temperature are reported. Single-crystal structure refinemens were undertaken for K₂UI₅ and Rb₂UCl₅. Magnetic susceptibility data were recorded with a SQUID magnetometer from liquid helium to room temperature. One-dimensional (intrachain) and three-dimensional antiferromagnetic ordering occur at low temperatures dependent upon the U³⁺? U³⁺ distance. Absorption spectra were recorded between 4 000 and 28 000 cm^?1. They show f—f transitions typical for U³⁺ and, depending on the halide, very strong f—d transitions above 14 000 to 15 000 cm^?1, respectively.     

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(-)).     

NMR parameters of the tetrahedrane [Fe2(CO)6(μ-SNH)], studied by experiment and DFT

The intramolecular dynamic behavior of the tetrahedrane-type cluster [Fe₂(CO)₆(μ-SNH)] 1 was studied by ¹³C NMR spectroscopy. The ⁵⁷Fe chemical shift of 1 and the coupling constants ¹ J(⁵⁷Fe,¹³C) were measured. These NMR parameters, and also ¹ J(⁵⁷Fe,¹⁵N), were found to be in good agreement with data calculated by using density functional theory (DFT) methods (B3LYP), based on the geometry calculated at the 6-311+G(d,p) level of theory. The isolobal replacement of the Fe(CO)₃ with BH fragments leads to the tetrahedranes [Fe(CO)₃(BH)(μ-SNH)] 2 and [(HB)₂(μ-SNH)] 3. Both were identified by calculations as minima on the respective potential energy surface (PES). However, the tetrahedrane-type structure of 3 is much higher in energy when compared with the planar cyclic isomers 3a and 3b.     

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.     

Two isomeric phosphacarboranes 2,1- and 6,1-PCB(8)H(9), the first representatives of the 10-vertex closo phosphacarborane Series

The reaction between arachno-4-CB(8)H(14) and PCl(3) in the presence of PS (PS = proton sponge = 1,8-dimethylamino naphthalene) (dichloromethane, rt, 24 h) produced the neutral phosphacarborane closo-2,1-PCB(8)H(9) (35% yield), while a similar reaction of nido-1-CB(8)H(12) gave the isomeric compound closo-6,1-PCB(8)H(9) (27% yield). The structures of both compounds were derived on the basis of the combined ab initio/GIAO/NMR ((1)H, (11)B, (13)C) approach. The optimized structures at a correlated level of theory (MP2) with 6-31G* basis set were used as a basis for calculations of the (11)B and (13)C chemical shifts at GIAO-SCF/II and GIAO-MP2/II, the latter showing excellent agreement with experimental data.     

An ab initio study of the vibronic, spin-orbit, and magnetic hyperfine structure in the X2Pi electronic state of NCO

In the present study we give the results of the ab initio calculations on the vibronic, spin-orbit, and magnetic hyperfine structure in the X (2)Pi electronic state of the NCO radical. The calculations of the potential surfaces and the electronic mean values of the hyperfine coupling constants are carried out by means of the density functional theory approach (B3LYP functional combined with an atomic orbital basis set suitable for calculations of the hyperfine structure). The vibronic levels, spin-orbit splitting, and the vibronic mean values of the components of the hyperfine tensor in the vibronic species are calculated using a variational method. The results of the calculations are in good agreement with the available experimental data.     

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.