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  • 1
    ISSN: 0009-2940
    Keywords: Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Azaborolinyl Complexes, X1). Synthesis and Properties of (1-tert-Butyl-2-methyl-η-1,2-azaborolinyl)carbonylmanganese and-molybdenum Complexes1-tert-Butyl-2-methyl-1,2-azaborolinyllithium (1) reacts with [CH3CN)3Mn(CO)3]PF6 to give (1-tert-butyl-2-methyl-η-1,2-azaborolinyl)tricarbonylmanganese (2). Neutral 1-tert-butyl-2-methyl-1,2-azaboroline (3) and Mo(CO)6 form π-ally(1-tert-butyl-2-methyl-η-1,2-azaborolinyl)-dicarbonylmolybdenum (4). The formation of the allyl group is due to the decomposition of an azaborolinyl ring under the reaction conditions. 2 and 4 are characterized by mass, IR, and NMR spectra. 4 could be investigated by X-ray analysis. Orthorhombic, space group Pbca, Z = 8, a = 1697.4(9), b = 1441.8(5), c = 1219.4(7) pm. The chirality of the azaborolinyl ring causes the formation of enantiomers which exist as a racemate in the crystal.
    Notes: 1-tert-Butyl-2-methyl-1,2-azaborolinyllithium (1) reagiert mit [(CH3CN)3Mn(CO)3]PF6 zum (1-tert-Butyl-2-methyl-η-1,2-azaborolinyl)tricarbonylmangan (2). Neutrales 1-tert-Butyl-2-methyl-1,2-azaborolin (3) und Mo(CO)6 bilden π-Allyl(1-tert-butyl-2-methyl-η-1,2-azaborolinyl)-dicarbonylmolybdän (4). Die Bildung der Allygruppe ist auf den Zerfall eines Azaborolin-Ringes unter den Reaktionsbedingungen zurückzuführen. 2 und 4 werden durch Massen-, IR- und NMR-Spektren charakterisiert. Von 4 konnte eine Röntgenstrukturanalyse durchgeführt werden: orthorhombisch, Raumgruppe Pbca, Z = 8, a = 1697.4(9), b = 1441.8(5), c = 1219.4(7) pm. Die Chiralität des Azaborolinyl-Ringes bedingt die Bildung von Enantiomeren, die im Kristall als Racemat vorliegen.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 118 (1985), S. 1949-1958 
    ISSN: 0009-2940
    Keywords: Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Azaborolinyl Complexes, XVI. Synthesis and Investigation of (1,2-Azaborolinyl)tricarbonyl Complexes of Chromium, Molybdenum, and Tungsten1-tert-Butyl-2-methyl-1,2-azaborolinyllithium reacts with the hexacarbonyls of chromium, molybdenum, and tungsten to give the complex salts Li[(Ab)M(CO)3] (Ab = azaborolinyl ligand, M = Cr (2), Mo (3), and W (4)). With Me3ECl (E = Ge, Sn, Pb) they form the corresponding germyl, stannyl, and plumbyl derivatives. The molecular and crystal structures of (Ab)(CO)3Cr—SnMe3 (2b) and (Ab)(CO)3Mo—SnMe3 (3b) show the azaborolinyl rings to be pentahapto-bonded, inspite of a small folding of the rings, leading to a longer distance of the boron atoms to the metal atoms. The IR, 1H, 11B, and 13C NMR data prove equivalent structures for the other complexes. The existence of enantiomers in the cell results from the crystal structure investigations of 2b and 3b and is caused by the prochiral character of the azaborolinyl rings.
    Notes: 1-tert-Butyl-2-methyl-1,2-azaborolinyllithium reagiert mit den Hexacarbonylen von Chrom, Molybdän und Wolfram zu den komplexen Salzen Li[(Ab)M(CO)3] (Ab = Azaborolinyl-Ligand, M = Cr (2), Mo (3) und W (4)). Diese bilden mit Me3ECl (E = Ge, Sn, Pb) die entsprechenden Germyl-, Stannyl- und Plumbylderivate. Die Molekül- und Kristallstrukturen von (Ab)(CO)3Cr—SnMe3 und (2b) und (Ab)(CO)3Mo—SnMe3 (3b) weisen die Azaborolinylringe als pentahapto-gebunden aus, trotz einer leichten Faltung der Ringe, durch die die Boratome einen größeren Abstand zu den Metallatomen erreichen. Die IR-, 1H-, 11B- und 13C-NMR-Daten beweisen äquivalente Strukturen für die übrigen Komplexe. Aus den Kristallstrukturuntersuchungen von 2b und 3b geht die Anwesenheit von Enantiomeren in der Zelle hervor, verursacht durch den prochiralen Charakter der Azaborolinylringe.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 0009-2940
    Keywords: Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Dihydroazaborolyl ComplexesAnmerkung zur Nomenklatur: Die traditionelle Bezeichnung „Azaborolinyl“ ist nach der IUPAC-Regel RB-1.2 durch „Dihydroazaborolyl“ zu ersetzen (Pure Appl. Chem. 55, 409, 1983. , XX. The Dynamic Behavior of BN Perturbed Cyclopentadienyl Ligands  -  Synthesis and Properties of (1-tert-Butyl-2,5-dihydro-2-methyl-η5-1H-1,2-azaboroloyl)-(η4-1,5-cyclooctadiene)cobalt1-tert-Butyl-2,5-dihydro-2-methyl-1H-1,2-azaborole (1) and Co2(CO)8 react in petroleum ether at 60-80°C with 40% yield to give the half sandwich complex (1-tert-butyl-2,5-dihydro-2-methyl-η5-1H-1,2-azaborolyl)dicarbonylcobalt (2), a red liquid. The CO ligands in 2 are substituted photolytically by 1,5-cyclooctadiene with formation of the liquid orangered title complex 3 in 54% yield. The hindered mobility of the ligands is discussed by means of temperature dependent NMR spectra.
    Notes: 1-tert-Butyl-2,5-dihydro-2-methyl-1H-1,2-azaborol (1) und Co2(CO)8 reagieren in Petrolether bei 60-80°C mit 40% Ausbeute zu dem Halbsandwichkomplex (1-tert-Butyl-2,5-dihydro-2-methyl-η5-1H-1,2-azaborolyl)dicarbonylcobalt (2), einer roten Flüssigkeit. Die CO-Liganden in 2 können photolytisch durch 1,5-Cyclooctadien ersetzt werden, wobei sich der flüssige organgerote Titel-Komplex 3 mit 54% Ausbeute bildet. Die behinderte Beweglichkeit der Liganden wird an Hand der temperaturabhängigen NMR-Spektren diskutiert.
    Additional Material: 1 Ill.
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  • 4
    Publication Date: 2022-07-07
    Description: {\bf Efficient eigenmode computation for the design of integrated optical chips.}The paper deals with adaptive multigrid methods for 2D Helmholtz eigenvalue problems arising in the design of integrated optical chips. Typical features of the technological problem are its geometric complexity, its multiscale structure, the possible occurrence of eigenvalue clusters, and the necessity of quite stringent required relative error tolerances. For reasons of sheer computational complexity, multigrid methods must be used to solve the discretized eigenvalue problems and adaptive grids must be automatically constructed to avoid an undesirable blow-up of the required number of nodes for these accuracies. In view of the problem specifications, an adaptive multigrid method based on Rayleigh quotient minimization, simultaneous eigenspace iteration, and conjugate gradient method as smoother is carefully selected. Its performance in the numerical simulation of a component of a rather recent optical chip (heterodyne receiver of HHI) is documented.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 5
    Publication Date: 2022-07-07
    Description: The paper presents a construction scheme of deriving transparent , i. e. reflection-free, boundary conditions for the numerical solution of Fresnel's equation (being formally equivalent to Schrödinger's equation). These boundary conditions appear to be of a nonlocal Cauchy type. As it turns out, each kind of linear implicit discretization induces its own discrete transparent boundary conditions.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 6
    Publication Date: 2022-07-07
    Description: An adaptive approach to the numerical solution of the wave propagation in integrated optics devices with 1D cross sections is described. First, Fresnel's approximation of the exact wave equation resulting from Maxwell's equations is considered. A criterion to estimate the validity of this approximation is derived. Fresnel's wave equation being formally equivalent to Schroedinger's equation uniquely defines an initial-boundary-value problem, which is solved numerically by a stepwise calculation of the propagating field. Discretization in longitudinal direction first with stepsize control leads to a stationary subproblem for the transversal field distribution, which is then handled by an adaptive finite element method. Thus full adaptivity of the algorithm is realized. The numerical examples are concentrated on taper structures playing an essential role in integrated optics devices for telecommunication systems.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 7
    Publication Date: 2022-07-07
    Description: We present a general technique for constructing nonlocal transparent boundary conditions for one-dimensional Schrödinger-type equations. Our method supplies boundary conditions for the $\theta$-family of implicit one-step discretizations of Schrödinger's equation in time. The use of Mikusi\'nski's operator approach in time avoids direct and inverse transforms between time and frequency domains and thus implements the boundary conditions in a direct manner.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 8
    Publication Date: 2022-07-07
    Description: We present a general technique for constructing nonlocal transparent boundary conditions for time-discretized one-dimensional Schrödinger type equations. The main tool of construction is the discrete counterpart to Mikusi\'nski's continuous algebraic operator approach. Existing techniques are simplified and generalized. Both adaptive time-steps and time-dependent exterior potentials are taken into account.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 9
    Publication Date: 2022-07-07
    Description: We present a family of nonlocal transparent boundary conditions for the 2D Helmholtz equation. The whole domain, on which the Helmholtz equation is defined, is decomposed into an interior and an exterior domain. The corresponding interior Helmholtz problem is formulated as a variational problem in standard manner, representing a boundary value problem, whereas the exterior problem is posed as an initial value problem in the radial variable. This problem is then solved approximately by means of the Laplace transformation. The derived boundary conditions are asymptotically correct, model inhomogeneous exterior domains and are simple to implement.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 10
    Publication Date: 2022-07-07
    Description: The reference wave vector of the paraxial Helmholtz equation is determined using various strategies which result all in similar expressions. The effort for its evaluation is so small that the reference wave vector can be adapted for each propagation step of an arbitrary BPM-algorithm.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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