The formal combination of three singlet biradicaloid entities to a singlet hexaradicaloid metalloid Ge14[Si(SiMe3)3]5[Li(THF)2]3 cluster

The reaction of GeBr with LiSi(SiMe(3))(3) leads to the metalloid cluster compound [(THF)(2)Li](3)Ge(14)[Si(SiMe(3))(3)](5) (1). After the introduction of a first cluster of this type, in which 14 germanium atoms form an empty polyhedron, [(THF)(2)Li](3)Ge(14)[Ge(SiMe(3))(3)](5) (2), we present here further investigations on 1 to obtain preliminary insight into its chemical and bonding properties. The molecular structure of 1 is determined via X-ray crystal structure solution using synchrotron radiation. The electronic structure of the Ge(14) polyhedron is further examined by quantum chemical calculations, which indicate that three singlet biradicaloid entities formally combine to yield the singlet hexaradicaloid character of 1. Moreover, the initial reactions of 1 after elimination of the [Li(THF)(2)](+) groups by chelating ligands (e.g., TMEDA or 12-crown-4) are presented. Collision induced dissociation experiments in the gas phase, employing FT-ICR mass spectrometry, lead to the elimination of the singlet biradicaloid Ge(5)H(2)[Si(SiMe(3))(3)](2) cluster. The unique multiradicaloid bonding character of the metalloid cluster 1 might be used as a model for reactions and properties in the field of surface science and nanotechnology.     

Zur Diskretisierung einer Klasse Fredholmscher Integralgleichungen mit singulärem Wert der Ordnung 1

Summary Two analoguous classes of integral equations respectively systems of linear equations, both singular in operator sense, are defined. Linking them by means of a discretisation technique and utilizing the Fredholm theory we prove, that the solution of the associated discrete problem converges rapidly to that of the integral equation. An error bound of the orderO (n q ⁿ ),tO < q < 1, is given.

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Gekürzte Fassung der von der Fakultät für Mathematik und Physik der Technischen Hochschule Darmstadt genehmigten Dissertation des Verfassers (Referenten Prof. Dr. E.Martensen und Prof. Dr. D.Laugwitz).