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     

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.

---

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.     

Absolute configurations and circular dichroism of sesquiterpene-coumarin ethers

The absolute stereochemistry of 14 naturally occurring sesquiterpenecoumarin ethers is discussed. In 13 cases the coumarin moiety is isofraxidin (7-hydroxy-6,8-dimethoxycoumarin), in one case scopoletin (7-hydroxy-6-methoxycoumarin). The sesquiterpene moieties belong either to the bicyclic drimenole series or to its consecutive products (methyl migration, ring opening). The CD spectra of all compounds are given. The assignments of the absolute configurations are based on the method ofHoreau, chemical correlation by degradation reactions, extensive comparison of CD data, and biogenetic considerations.

---

Absolute Konfigurationen und Circulardichroismus von Sesquiterpen-Cumarin-Ethern

Zusammenfassung Es wird die absolute Stereochemie von 14 natürlich vorkommenden Sesquiterpen-Cumarin-Ethern diskutiert. In 13 Fällen wird die Cumarineinheit von Isofraxidin (7-Hydroxy-6,8-dimethoxycumarin) repräsentiert, in einem Fall von Scopoletin (7-Hydroxy-6-methoxycumarin). Der Sesquiterpenteil ist entweder von Drimenol oder Folgeprodukten (Methylgruppenwanderung, Ringöffnung) abgeleitet. Die CD-Spektren aller Verbindungen sind angegeben. Die Zuordnung der absoluten Konfigurationen basiert auf der Methode vonHoreau, chemischer Korrelation über Abbaureaktionen, Vergleich der CD-Spektren und biogenetischen Überlegungen.

     

Lanthanide induced shifts of aromatic 1,2,3-trimethoxy compounds: Conformational analysis of tetrahydrofurofuran-lignans in solution

Summary The solution conformations of 1,4-diaryl-tetrahydro-1H,3H-furo[3,4-c]furans were determined by means of the LIS technique using a modified LIS-simulation program specially designed for the requirements of the aromatic 1,2,3-trimethoxy arrangement as a bidentate coordination site for the NMR shift reagent. The resulting geometries were confirmed by force field calculations (MM2-87) and compared with X-ray derived structures. Reliable data for the conformations in solution allowed a quantitative estimation of the circular dichroism based on the coupled oscillator model.

---

Lanthanideninduzierte Verschiebungen von aromatischen 1,2,3-Trimethoxy-Verbindungen: Konformationsanalyse von Tetrahydrofurofuran-Lignanen in Lösung

Zusammenfassung Es wurden mittels der LIS-Technik die Konformationen von 1,4-Diaryl-tetrahydro-1H,3H-furo[3,4-c]furanen in Lösung bestimmt. Dazu mußte ein modifiziertes LIS-Simulationsprogramm entworfen werden, das auf die besonderen Verhältnisse der aromatischen 1,2,3-Trimethoxy-Gruppierung eingeht, welche in den untersuchten Verbindungen als zweizähnige Koordinationsstelle für das NMR-Verschiebungsreagens fungiert. Die resultierenden Geometrien wurden mittels Kraftfeldrechnungen (MM2-87) überprüft und soweit vorhanden auch mit Röntgenstrukturdaten verglichen. Für die Lösungskonformationen wurde eine quantitative Abschätzung des Circulardichroismus auf der Basis des Modells für gekoppelte Oszillatoren durchgeführt.

     

Die Aminoalkylierung von Chinoxalinen und Chinoxalonen 6. Mitteilung über grignard-reaktionen mit halogenalkylaminen [1]

Quinoxaline and 2(1H)-quinoxalones react with organomagnesium salts differently from the corresponding phthalazines and quinazolines. 3-Dimethylaminopropyl-magnesiumchloride alkylates quinoxaline easily by addition to the 2 and 3 position forming a tetrahydroquinoxaline 2 , which can be dehydrogenated to the corresponding dialkylated quinoxaline 3 . The monosubstituted dihydroquinoxaline 5 is obtained only with difficulty. It can equally be dehydrogenated, yielding 6 . Quinoxalones react with CH₃MgI, C₆H₅MgBr, (CH₃)₂N? (CH₂)₃? MgCl by addition to the 3,4-C?N bond (not at the CO-group), yielding 11–13 . These dihydroquinoxalones are dehydrogenated to the 3-substituted 2(1H)-quinoxalones 14–16 . Only 3-phenyl-quinoxalone adds a Grignard reagent at the CO group, forming a 2-substituted 3-phenylquinoxaline ( 26 ). 3-Methyl-quinoxalone exhibits an abnormal behaviour: It is deprotonated by the mentioned reagents at the CH3 group, and the 3-methylenequinoxalone-anion so formed attacks another molecule of methylquinoxalone, finally yielding 32 and 33 .