Spline collocation for strongly elliptic equations on the torus

Summary We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4].     

The reaction of iodine monochloride and monobromide with tetraorganotins

The reactions of iodine monochloride and iodine monobromide with a tetraalkyltin (butyl) and a tetraaryltin (phenyl) have been studied with a view to establishing their utility as routes to organotin chlorides and bromides respectively. Rapid high yield syntheses of the triorganotin bromides, diorganotin dichlorides and trialkyltin chloride were achieved. Some further suggestions are made on the mechanism of interhalogen fission of tincarbon bonds.     

Optimal double-configuration study of the lowest excited Π states of H2

Various levels of approximation (Hartree-Fock, configuration interaction and double-configuration Hartree-Fock method) are compared for extensive and limited exponent optimization of the atomic orbitals of the wavefunctions. The potential energy curves for the lowest-lying ¹ _u, ³ _u, ¹ _g, ³ _g states of the hydrogen molecule are presented. The shapes of the curves on the highest level of approximation, i.e. with the optimal double-configuration wavefunction, are basically in agreement with previous, more sophisticated and time-consuming work. The influence of the various approximations is also studied for several one-electron properties: charge distribution of the wavefunction along and perpendicular to the molecular axis, quadrupole moment and core attraction energy distribution. Differences arise to the work of Zemke et al. [1], who used a limited exponent optimization with a larger basis set, in the _g states where the orbitals are very diffuse. The differences concern magnitude and location of minima and maxima of potential curves, as well as considerable changes in one-electron properties which depend strongly on the spatial distribution of the orbitals.

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Zusammenfassung Verschiedene Approximationsstufen (Hartree-Fock, Konfigurationenwechselwirkung und Doppelkonfigurationen-Hartree-Fock-Methode) werden für ausgedehnte und begrenzte Exponentenoptimisierung von Atomorbitalen der Wellenfunktionen verglichen. Die Potentialkurven für die niedrigsten ¹ _u, ³ _u, ¹ _g, ³ _g Zustände des Wasserstoffmoleküls werden angegeben. Die Form der Kurven im Rahmen der besten Näherung, d. h. mit Doppelkonfiguration, stimmen im wesentlichen mit früheren aufwendigeren Rechnungen überein. Der Einfluß der verschiedenen Approximationen wird auch an einigen Einelektroneneigenschaften studiert: Ladungsverteilung der Wellenfunktion längs und senkrecht zur Molekülachse, Quadrupolmoment und Verteilung der Rumpfenergie. Unterschiede erscheinen zur Arbeit von Zemke et al. [1], die einen größeren Basissatz mit begrenzter Optimisierung verwandten, bei den _g Zuständen, wo die -Orbitale sehr diffus sind. Die Unterschiede betreffen Größe und Lage der Minima und Maxima der Potentialkurven sowie beträchtliche Änderungen in solchen Einelektroneneigenschaften, die stark von der räumlichen Verteilung der Orbitale abhängen.

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Résumé Comparaison de différents niveaux d'approximation (Hartree-Fock, interaction de configuration et Hartree-Fock à deux configurations) pour des optimisations étendues et limitées des orbitales atomiques de base. Calcul des courbes d'énergie potentielle pour les plus bas états ¹ _u, ³ _u, ¹ _g, ³ _g de la molécule d'hydrogène. Pour la fonction d'onde la plus raffinée: H.F. à deux configurations, la forme des courbes est en accord avec les résultats obtenus dans des travaux précédents plus complexes et plus coûteux. On étudie aussi l'influence des diverses approximations sur plusieurs propriétés monoélectroniques: distribution de charge le long de l'axe moléculaire et perpendiculairement à celui-ci, moment quadrupolaire et distribution de l'énergie d'attraction de coeur. On trouve des différences avec le travail de Zemke et al. (1), qui utilisent une plus grande base partiellement optimisée, pour les états _g où les orbitales sont très diffuses. Les différences concernent la grandeur et la position des extrema des courbes de potentiel, ainsi que des variations importantes des propriétés monoélectroniques qui dépendent fortement de la distribution spatiale des orbitales.

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On leave to: Institut für Theoretische Chemie, Universität Stuttgart.

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On leave to: Office of Computing Activities, National Science Foundation, Washington, D.C.     

Ion mobility–mass spectrometry: a new paradigm for proteomics

Matrix-assisted laser desorption/ionization (MALDI) coupled with ion mobility–mass spectrometry (IM–MS) provides a rapid (μs–ms) means for the two-dimensional (2D) separation of complex biological samples (e.g., peptides, oligonucleotides, glycoconjugates, lipids, etc.), elucidation of solvent-free secondary structural elements (e.g., helices, β-hairpins, random coils, etc.), rapid identification of post-translational modifications (e.g., phosphorylation, glycosylation, etc.) or ligation of small molecules, and simultaneous and comprehensive sequencing information of biopolymers. In IM–MS, protein-identification information is complemented by structural characterization data, which is difficult to obtain using conventional proteomic techniques. New avenues for enhancing the figures of merit (e.g., sensitivity, limits of detection, dynamic range, and analyte selectivity) and optimizing IM–MS experimental parameters are described in the context of deriving new information at the forefront of proteomics research.