Effective conjugation and Raman intensities in oligo(para-phenylene)s: a microscopic view from first-principles calculations

Electron-phonon coupling in oligo(para-phenylene)s is addressed in terms of the off-resonance Raman intensities of two distinct modes at 1220 and 1280 cm(-1). On the basis of Albrecht's theory, vibrational coupling and Raman intensities are calculated from first-principles quantum-chemical methods. A few-state model is used to evaluate the dependence of the mode intensities on oligomer length, planarity, and excitation wavelength. The link between electron delocalizationconjugation and Raman intensities is highlighted. Extending on prior studies, the present work focuses on providing an in-depth understanding of the origin of this correlation in addition to reproducing experimental findings. The model applied here allows us to interpret the results on a microscopic, quantum-mechanical basis and to relate the observed trends to the molecular orbital structure and nature of the excited states in this class of materials. We find quantitative agreement between the results of the calculations and those of measurements performed on oligo(para-phenylene)s of various chain lengths in the solid state and in solution.     

Nonlinear degenerate curvature flows for weakly convex hypersurfaces

We study the evolution of closed, weakly convex hypersurfaces in in direction of their normal vector, where the speed equals a quotient of successive elementary symmetric polynomials of the principal curvatures. We show that there exists a solution for these weakly convex surfaces at least for some short time if the elementary symmetric polynomial in the denominator of the quotient is positive. The results for this nonlinear, degenerate flow are obtained by a cylindrically symmetric barrier construction.Received: 10 November 2003, Accepted: 5 April 2004, Published online: 16 July 2004     

Flow invariance for nonlinear accretive evolutions under range conditions

Let A be a nonlinear accretive operator in a real Banach space X and f : J × X  X be continuous or of Carathéodory type, where We investigate the existence of mild solutions of the evolution system

Das Verhalten von Mono- und Diorganylphosphansulfiden gegenüber Metallcarbonylsystemen. VIII [1]; Die Kristall- und Molekülstruktur von Pentacarbonyl(dimethylmercaptophosphan)-chrom

Inhaltsübersicht. Die S-verknüpfte Verbindung (OC)₃CrSPH(CH₃)₂ isomerisiert sich oberhalb 25°C zu dem Mercaptophosphan-Komplex (OC)₅CrP(CH₃)₂SH. Dieser kristallisiert monoklin in der Raumgruppe P2₁/c mit den Citterkonstanten a = 6,882, b = 13,290, c = 13,224 Å, β = 91,60° und vier Molekeln in der Elementarzelle. In der Kristallstruktur (R = 0,085) sind die Chromatome pseudooktaedrisch koordiniert von fünf CO-Gruppen und dem Mercaptophosphanliganden (Cr—P = 2,344 Å). The Behaviour of Mono- and Diorganylphosphane Sulphides towards Metal Carbonyl Systems. VIII. Crystal and Molecular Structure of Pentacarbonyl(dimethylmereaptophosphane) chromium Abstract. The S-linked compound (OC)₅CrSPH(CH₃)₂ isomerizes to the mercaptophosphane complex (OC)₅CrP(CH₃)₂SH above 25°C. The latter crystallizes monoclinic in the space group P2₁/c with the lattice constants a = 6.882, b = 13.290, c = 13.224 Å, β = 91.60° and four molecules per unit cell. In the crystal structure (R = 0.085) the chromium atoms are pseudooctahedrally coordinated by five CO groups and the mercaptophosphane ligand (Cr—P) = 2.344 Å).