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.     

Organometallic complex compounds,part 6(1). Property-specific ligand control of stability and reactivity of (1,3-dimethyl-η3-allyl)methylnickel-ligand complexes. Separation of electronic and steric effects

Summary The property-specific ligand control of 28 ligands on the decomposition temperatures in solution, measured by d.t.a. of a four-coordinate nickel(II)-complex is reported. A quantitative separation of electronic and steric effects by a multilinear regression analysis (75% electronic and 25% steric influence for the chosen ligands) is presented. The controlling effect of the selectivity on the decomposition (fraction of the C-C-linked product) (25 P-ligands) leads to an electronic: steric ratio of the property-specific ligand control of 5545 for the chosen ligands. An increase in the relative acceptor character of the P-ligands relatively destabilizes the complexes and thereby favours formation of a C-C-bond. An increase in steric hindrance also favours C-C-bond formation. A method for revising the steric parameter of P-ligands is presented and is used to correct the -value of (PhCH₂)₃P is corrected to 135°. SCCC-MO-calculations for testing the chemical reasoning of the separated electronic and steric ligand property control are shown.     

An extended ab initio QM/MM MD approach to structure and dynamics of Zn(II) in aqueous solution

Structural and dynamical properties of Zn(II) in aqueous solution were investigated, based on an ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulation at double-zeta Hartree-Fock quantum mechanical level including the first and second hydration shells into the QM region. The inclusion of the second shell in the QM region resulted in significant changes in the properties of the hydrate. The first shell coordination number was found to be 6, the second shell consists of approximately 14 water molecules. The structural properties were determined in terms of RDF, ADF, tilt and theta angle distributions, while dynamics were characterized by mean ligand residence times, ion-ligand stretching frequencies and the vibrational and librational motions of water ligands.