Silicon-29 diffusion-ordered NMR spectroscopy (DOSY) as a tool for studying aqueous silicates

The first use of silicon-29 diffusion-ordered NMR spectroscopy (DOSY) is reported, in a study of the speciation of aqueous silicates.     

When Ramification points meet

Summary This paper contains three applications of the technique of limit series (our [1986]) to the theory of ramification of linear series on smooth curves, and curves of compact type, overC.Let {L _t t|<}, be a family of linear series on a smooth family of smooth curves {C _t }, and letp ₁(t),p ₂(t)C _t be sections of the family which coincide (only) att=0. Setp=p ₁())=p ₂(0)C ₀.We first give a condition related to the Schubert calculus which must be satisfied by the ramification series and the . We then take up the converse problem: In what ways can a given ramification point arise as a limit? We show that if the ramification point isdimensionally proper in the sense of our [1986], then families of every kind allowed by the Schubert calculus condition can actually be constructed. Finally, we prove that dimensional propriety is in a strong sense an open condition, so that ramification points constructed as above are again dimensionally proper.In the body of the paper we work not with pairs of points, as above, but with arbitrary finite collections of points approaching (possibly) several points of the limit curve. Further, by their nature, the results are valid for families of curves of compact type.     

Integral approximations for molecular orbital theory

The electron repulsion integrals arising in LCAO-MO theory are approximated by replacement of the product of two orbitals on different centers by linear combinations of one-center products. The approximation differs from those previously proposed in that the coefficients of the various terms are determined by requiring agreement for certain integrals, and in the emphasis of the role of symmetry in selecting the one-center products. For two-center integrals, the new approximation is significantly better than older approximate methods. Reasons are given for expecting this improvement to extend also to multi-center integrals.

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Zusammenfassung Es wird ein Verfahren zur näherungsweisen Berechnung von Elektronenwechselwirkungsintegralen der LCAO-MO-Theorie beschrieben, bei welchem das Produkt zweier Zustandsfunktionen an verschiedenen Zentren durch eine Linearkombination von Produkten am gleichen Zentrum ersetzt wird. Der Unterschied zu ähnlichen Ansätzen liegt in der Justierung der Koeffizienten. Für Zweizentrenintegrale liefert die hier vorgeschlagene Methode bedeutend bessere Ergebnisse als das Mulliken-Verfahren.

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Résumé Les intégrales de répulsion électroniques intervenant dans la théorie LCAO MO sont calculées d'une manière approchée en remplaçant le produit de deux orbitales sur des centres différents par des combinaisons linéaires de produits à un centre. Cette approximation diffère de celles proposées auparavant par la détermination des coefficients des différents termes au moyen de l'ajustement de certaines intégrales et par l'importance du rôle de la symétrie dans le choix des produits monocentriques. Cette nouvelle approximation est bien meilleure que les anciennes en ce qui concerne les intégrales bi-centriques. Nous donnons des raisons d'espérer que cette amélioration s'étendra aux intégrales polycentriques.

     

Ab initio MO-SCF calculation on a model of anomalous water

Ab initio calculations are carried out on the planar hexamer model of anomalous water using a variety of basis sets. The results are compared to results of similar calculations on free water and water in the ice I-like puckered ring configurations.

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Zusammenfassung Es werden ab initio-Rechnungen für das planare Hexamer-Modell von anomalem Wasser unter Verwendung mehrerer BasissÄtze durchgeführt. Die Ergebnisse werden mit Resultaten Ähnlicher Rechnungen über freies Wasser und Wasser in der I-Eis Ähnlichen Konfiguration verzerrter Ringe verglichen.

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Résumé Calculs ab initio sur le modèle hexamérique plan de l'eau anormale en utilisant différentes bases. Les résultats sont comparés à ceux de calculs similaires sur l'eau libre et sur l'eau dans une configuration cyclique compacte analogue à celle de la glace I.

     

Acylsilanes from the pyrolysis of silyl esters of α-ketoacids

The pyrolyses of silyl esters of pyruvic acid and phenylglyoxylic acid gave rise to acylsilanes in high yield. An intramolecular rearrangement involving an intermediate siloxycarbene is proposed to account for the reaction.