Enantioselective Catalysis CXLI [1]. Tridentate Ligands with 1-(Pyridin-2-yl)ethylamine as Chiral Building Block in the Enantioselective Transfer Hydrogenation of Acetophenone

Summary.  A series of novel tridentate ligands with nitrogen and oxygen donor sites was synthesized starting from enantiomerically pure (S)- and (R)-1-(pyridin-2-yl)ethylamine, the preparation and resolution of which was developed. The new optically active ligands were tested as in situ catalysts together with Ru(PPh₃)₃Cl₂ in the enantioselective transfer hydrogenation of acetophenone with isopropanol. The secondary amine ligand (S)-2,4-di-tert-butyl-6-(1-(pyridin-2-yl)ethylamino)methylphenol gave the best results with almost quantitative conversion and 47%ee. Received August 17, 2001. Accepted August 27, 2001     

Interpolation of operator ideals with an application to eigenvalue distribution problems

We derive results on the interpolation of complete quasinormed operator ideals, mainly for the absolutelyp-summing and thes-number idealsS _p ^s defined by Pietsch. By estimating theK-Functional of Peetre, we get that the interpolation ideal (S _p1 ^s ,S _p2 ^s ),_,p is contained inS _p ^s and is even equal to it in the case of the approximation numbers. A similar fact is proved for absolutely (p, q)-summing operators, interpolating the first index. We show further that the absolutelyp-summing operators onc ₀ are contained in the complex interpolation space ( _p1 (c _o), _p2 (c _o))_[].The previous results are then applied to prove summability properties for the eigenvalues of operators in Banach spaces, which are products ofS _p1 ^s -type and absolutelyp _j -summing operators. Roughly speaking, the summability order is the harmonic sum of thep _i - andp _j -indices, wherep _j 2. In the case of Hilbert spaces, this reduces to the well-known Weyl-inequality. The method uses an abstract interpolation estimate for ideal quasinorms which may be useful also for other operator ideals.     

Approximation numbers of Sobolev imbeddings over unbounded domains

Let Ω ? $\text{R}$^N be an open set with $\text{dist}\text{(x, ?Ω) = O(¦ x ¦}{}^{\mathrm{?l}}\text{)}\text{for}\text{x ? Ω}$ and some l > 0 satisfying an additional regularity condition. We give asymptotic estimates for the approximation numbers α_n of Sobolev imbeddings

over these quasibounded domains Ω. Here

denotes the Sobolev space obtained by completing $\text{C}{}_0{}^{\mathrm{staggered\infty }}\text{(Ω)}$ under the usual Sobolev norm. We prove $\text{α}{}_{\mathrm{n}}\text{(I}{}_{\mathrm{p,q}}{}^{\mathrm{m}}\text{)}\text{\$}\text{?}\text{n}{}^{\mathrm{?\gamma }}$, where

. There are quasibounded domains of this type where γ is the exact order of decay, in the case p ? q under the additional assumption that either 1 ? p ? q ? 2 or 2 ? p ? q ? ∞. This generalizes the known results for bounded domains which correspond to l = ∞. Similar results are indicated for the Kolmogorov and Gelfand numbers of I_p,q^m. As an application we give the rate of growth of the eigenvalues of certain elliptic differential operators with Dirichlet boundary conditions in $\text{L}{}_2\text{(Ω)}$, where Ω is a quasibounded domain of the above type.     

Optisch aktive übergangsmetall-komplexe LXIV. Neue optisch aktive Cp(CO)Fe-acyl-komplexe mit

The novel complexes CpFe(CO)(COR)P(C₆H₅)₂NR'R^* with Cp = C₅H₅,C₉H₇ (indenyl); R = CH₃, C₂H₅, CH(CH₃)₂, CH₂C₆H₅;R` = H, CH<sub>3</sub>, C<sub>2</sub>H<sub>5</sub>, CH<sub>2</sub>C<sub>6</sub>H<sub>5</sub> and R<sup>*</sup> = (S)-CH(CH<sub>3</sub>)(C<sub>6</sub>H<sub>5</sub>), have been synthesized by reaction of CpFe(CO)<sub>2</sub>R wiht P(C<sub>6</sub>H<sub>5</sub>)<sub>2</sub>NR`R^* and characterized analytically as well as spectroscopically. The pairs of diastereoisomers RS/SS have been separated by preparative liquid chromatography and fractional crystallization, respectively. The optically pure complexes (+)₄₃₆- und ()₄₃₆-CpFe(CO)(COR)P(C₆H₅)₂NR`R^* are configurationally stable at room temperature. At higher temperatures they equilibrate with CpFe(CO)₂R and epimerize with respect to the Fe configuration.     

Ground-state properties and static dipole polarizabilities of the alkali dimers from K2 n to Fr2 n(n=0,+1) from scalar relativistic pseudopotential coupled cluster and density functional studies

The newly adjusted energy-consistent nine-valence-electron pseudopotentials for K to Fr are used to calculate spectroscopic properties for the neutral and positively charged alkali dimers using coupled cluster and density functional theory. For the neutral dimers the static dipole polarizability was calculated. The coupled cluster results are all in excellent agreement with experimental values. The density functionals used can give quite different spectroscopic properties especially for the dipole polarizability, with the Perdew-Wang PW91 functional performing best.     

Optisch aktive übergangsmetall-komplexe : LXVIII. Darstellung,epimerisierung, röntgenstrukturanalyse und absolute konfiguration von (-)546-C7H7Mo(CO)(PN★)I

C₇H₇Mo(CO)(PN^★)I (I) (PN^★  (S)(+)-(C₆H₅)₂PN(CH₃)CH(CH₃)(C₆H₅)) is prepared in 90% yield by reaction of C₇H₇Mo(CO)₂I and PN^★. The two diastereo-isomers Ia and Ib differing only in the Mo-configuration exhibit chemical shift differences of their C₇H₇ and CH₃ signals. Ia and Ib can be separated by fractional crystallization. In solution Ia epimerizes with respect to the Mo configuration. The half lives in benzene for the equilibration Ia ? Ib are 5.5, 30, and 104 min at 60, 50, and 40°C, respectively. Phosphine exchange experiments show that the epimerization proceeds via PN^★ dissociation.An X-ray structure analysis was carried out on a single crystal of Ia. The absolute configuration at Mo was determined to be (R).     

Modellrechnungen an einigen Siliziumwasserstoffverbindungen vom Typ SiHn,SiH n + und SiH n − nach der Einzentrenmethode

Zusammenfassung Es werden molekulare Struktur, Energie des Grundzustandes, Bindungsabstände, Bindungsenergie, Ionisierungsenergie und Protonenaffinität der Siliziumwasserstoffverbindungen SiH _n , SiH _n ⁺ und SiH_n ^– (n=3, 4 oder 5) nach der Einzentrenmethode berechnet.

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OCE-calculations on some silicon hydrides of the type SiH _n , SiH _n ⁺ and SiH _n ^–

OCE-Calculations are reported for molecular structures, ground state energies, bond distances, binding energies, ionization potentials and proton affinities of the silicon hydrides SiH _n , SiH _n ⁺ and SiH _n ^– (n=3, 4 or 5).

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Résumé Calcul par la méthode monocentrique de la structure moléculaire, de l'énergie de l'état fondamental, des longueurs de liaison, des énergies de liaison, des potentiels d'ionisation et des affinités protoniques pour les hydrures de silicium SiH _n , SiH _n ⁺ et SiH _n ^– (n=3, 4 ou 5).

     

Die Lösung der Prae-Maxwellschen Gleichungen mit Hilfe vollständiger Lösungssysteme

This paper deals with the Neumann problem of the pre-Maxwell partial differential equations for a vector field v defined in a region G ? R ³. We approximate its uniquely determined solution (integrability conditions assumed) uniformly on G by explicitly computable particular integrals and linear combinations of vector fields with a “fundamental” sequence of points .     

Äquivalenzen bezüglich allgemeiner Homotopiegruppen

In the following work we present an uniform theory for proofs of theorems on local and numerably local properties of spaces and maps (over B). As applications of our two main theorems, we obtain some new results, but also theorems proven by A. Dold [3] and T. tom Dieck [2], and well-known theorems on CW-spaces.