Convex Hamiltonian energy surfaces and their periodic trajectories

In this paper we introduce symplectic invariants for convex Hamiltonian energy surfaces and their periodic trajectories and show that these quentities satisfy several nontrivial relations. In particular we show that they can be used to prove multiplicity results for the number of periodic trajectories.This paper represents results obtained while holding a visiting position at the Courant Institute for Mathematical Sciences, New YorkResearch partially supported by NSF Grant No. DMS-8603149 and a Rutgers University Research Council Grant     

Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

Conformational analysis by LIS. II. 2-and 3-alkyl substituted 1-indanones

The preferred conformations of the alkyl groups relative to the cyclopentenone ring of 2-ethyl-, 2-benzyl-, 2-isopropyl-, and 3-isopropyl-1-indanone were determined by means of the lanthanide-induced-shift technique (LIS). Two different models were used in the calculation of LIS. Coupling data-where available-were compatible with the conformations derived from LIS data. O. Hofer, Mh. Chem.109, 405 (1978).     

Coordination and ligand exchange dynamics of solvated metal ions

Recent developments in computer speed and capacity have opened the access to highly accurate molecular dynamics simulations based on quantum mechanically calculated forces for the chemically relevant region around ions in solution (QM/MM formalism). This accuracy, although still extremely consuming (30-300 days of CP time per simulation), is needed for reliable structural details and ligand exchange rates. A large number of main group and transition metal ions have been investigated by this approach, giving very detailed insight into the properties of these ions in solution and allowing to classify the ions by various characteristics. Most first-row transition metal ions have a very stable first hexa-coordinated solvation shell, whose vibrational distortions, however, strongly influence the dynamics of the second shell. The dynamical Jahn-Teller effect - shown to be a femto- and picosecond phenomenon - can strongly influence ligand coordination and exchange dynamics. A large number of ions with very labile solvation shell such as most main group ions, but also transition metal ions, e.g. Ag(I) and Hg(II), can change their coordination within the picosecond scale, leading to an almost simultaneous presence of several species hardly accessible by present experimental techniques. Among these ions, the structure breakers are of particular interest, and it could be shown that there are two types of them, one with a large and very labile first coordination shell such as Cs(I), the other characterised by a small first but an unusually large second solvation shell such as Au(I). Investigations of metal ions coordinated to ammonia ligands have shown that coordination to hetero-atoms can accelerate the ligand exchange reaction rates by several orders of magnitude, e.g. for Cu(II) and Ni(II). Simulations of ions in aqueous ammonia gave a very detailed picture of the complexity of species almost simultaneously present and illustrate the enormous difficulties encountered when trying to fit X-ray or neutron diffraction data for such systems. In general, ligand exchange rates situated in the picosecond range are far below the NMR scale, and as femtosecond laser pulse spectroscopy could not be applied so far to ionic solutions, accurate simulations have become a very important tool to access structure and dynamics of solvated ions. A number of VIDEO clips supplied on the Web as supporting material illustrates the processes occurring in solutions of the metal ions.     

Anwendung der Streustrahl-Methode zur Bestimmung der Elemente in Mineral?lprodukten mit Hilfe der R?ntgenfluorescenz-Spektral-Analyse am Beispiel der Bleibestimmung in Ottokraftstoffen

Zusammenfassung In einem relativ einfach durchzuführenden Verbundverfahren wird Selen im Sauerstoff-strom innerhalb 15 min bei 1100–1150°C quantitativ aus den Metall- bzw. Metalloxidschmelzen verdampft und in einer mit flüssigem Stickstoff gekühlten Vorlage aufgefangen. Das aus der Vorlage mit einer definierten Menge verdünnter HNO₃ in Gegenwart von Ni-Nitrat gelöste Selen läßt sich direkt durch AAS mit dem Graphitofen (FAAS) äußerst nachweisstark und zuverlässig bestimmen. Die Nachweisgrenze (elektrodenlose Entladungslampe) liegt bei 3×10^–11 g Se. Der Verfahrensverbund erlaubt mit Probenmengen 10 g in Ag und Au Se-Gehalte 0,05 ppb,inCu 0,1 ppb,in Bi 0,2 ppb und in Pb 10 ppb zu erfassen. Für draht-, stab- und spanförmige Proben erhält man für Se-Gehalte von 2–0,002 ppm Variationskoeffizienten zwischen 3 und 6%. Die Vollständigkeit der Se-Verdampfung aus den Matrices Cu, Ag, Au und Bi wurde ebenso wie die Richtigkeit des Gesamtverfahrens durch systematische Untersuchungen belegt.

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Determination of se by furnace atomic absorption spectrometry (FAAS) in the ppb-range in Cu, Cu alloys, Ag, Au, Pb and Bi after volatilization in an oxygen stream

Summary Selenium is evaporated in a multi-stage procedure within 15 min from metals or metal oxides fused at temperatures of 1100–1150°C under a stream of oxygen and is trapped in a receiver cooled with liquid nitrogen. The condensed SeO₂ is dissolved with a definite volume of diluted HNO₃ in the presence of Ni-nitrate and determined with high sensitivity and reliability by FAAS (electrodeless discharge lamp). The detection limit of the FAAS was found to be 3 · 10^–11 g of Se. The multi-stage procedure allows to detect Se levels 0.05 ppb in Ag and Au, 0.1 ppb in Cu, 0.2 ppb in Bi, and 10 ppb in Pb, respectively, with sample weights 10 g. For wire, rod, and chip samples the coefficients of variation are found to be between 3 and 6% for Se contents of 2 to 0.002 ppm. The quantitative evaporation of Se from Cu, Ag, Au, and Bi as well as the accuracy of the whole procedure have been checked systematically.

Die Arbeit wurde durch Mittel der DFG in dankenswerter Weise unterstützt.     

Circular dichroism of sesquiterpene-umbelliferone ethers and structure elucidation of a new derivative isolated from the gum resin “Asa Foetida”

The CD spectra of 16 naturally occurring sesquiterpene-umbelliferone ethers, including the complete set of farnesiferol A isomers with all acetates and 6-oxoderivatives, are reported over the significant wavelength range of 350–200 nm. 11 compounds were isolated from an Asa Foetida sample and 5 further derivatives, already known as natural products, were obtained by acetylation orJones oxidation. In addition, a new compound — kamolonol (14) — was isolated. Its structure is characterized by twofold methyl migration in the drimenol derived sesquiterpene moiety.¹H-NMR, MS, IR, UV, and CD data of the new compound are discussed.Herrn Prof. Dr.K. Schlögl mit den besten Wünschen zum 60. Geburtstag gewidmet.