Polymer synthesis in the presence of bis(cyclopentadienyl) derivatives of Group IV–VI transition metal dichlorides: a quantum chemical study of particular reaction stages

Key pathways of interaction between growing radicals of vinyl monomers and bis(cyclopentadienyl) derivatives of Group IV–VI transition metal dichlorides were studied by the BP86/6-31G(d) and B3LYP/LanL2DZ quantum chemical methods. Prospects for use of these organometallic compounds as chain growth regulators in controlled polymerization were assessed. The character of the interaction of the compounds studied with the growing radicals is mainly determined by the metal atom. Dedicated to Academician G. A. Abakumov on the occasion of his 70th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1690–1694, September, 2007.     

Input optimization: I. Optimal realizations of mathematical models

Mathematical models are considered as input-output systems. The input is data (technological coefficients, available energy, prices) and the output is the feasible set, the set of optimal solutions, and the optimal value. We study when output is a continuous function of input and identify optimal (minimal) realizations of mathematical models. These are states of the model having the property that every stable perturbation of input results in a locally worse (higher) value of the optimal value function. In input optimization we “optimize” mathematical model rather than a specific mathematical program. This research was supported in part by the Natural Sciences and Engineering Research Council of Canada, and in part by the Gouvernement du Québec, programme de formation de chercheurs et d’action concertée.     

Riesz decompositions and subtractivity for excessive measures

The convex cone of excessive measures of a right Markov process is an example of a superharmonic semigroup in the abstract potential theory developed by Arsove and Leutwiler. We show that their theory of Riesz decompositions can be sharpened in the case of excessive measures. In particular there is always a Riesz decomposition relative to a given potential cone (resp. harmonic cone). An element of an ordered convex cone is subtractive if each majorant is a specific majorant. This notion of subtractivity features prominently in the theory of harmonic cones. We give a complete characterization of the subtractive elements in the cone of excessive measures.The research of both authors was supported in part by NSF Grant DMS 87-21347.     

Zur Chemie von Sulfiden und Seleniden primärer Phosphane — Die (1-Hydroxyalkyl)-organyl-phosphansulfide und -selenide,neue Verbindungsklassen

Investigation into Sulfides and Selenides of Primary Phosphines — The (1-Hydroxyalkyl)-organyl-phosphine Sulfides and Selenides, New Classes of Compounds Primary phosphines react with S₈ and Se₈, respectively, forming organylphosphine monosulfides, and monoselenides, respectively, RP(X)H₂ (X = S, Se) which are well characterized by ³¹P NMR spectroscopy. Organylphosphine monosulfides are detected in the reaction mixture of primary phosphines with 2,4-diaryl-1,3,2,4-dithiadiphosphetane-2,4-disulfides, too. The reaction of primary phosphines with sulfur or selenium proceeds in presence of most of the ketones without formation of any side product. The (1-hydroxyalkyl)-organyl-phosphine sulfides and selenides, respectively, RP(X)(H)C(OH)R¹R², are yielded generally in crystalline form. The X-ray crystal structure analysis of the (1-hydroxy-1-methyl-ethyl)-phenyl-phosphane sulfide (R = Ph, R¹ = R² = Me) has shown that in the crystal the molecules are chained via intermolecular O? H …? S hydrogen bridging bonds (O …? S = 328 pm). Aldehydes react with primary phosphines and sulfur forming bis(1-hydroxyalkyl)-phenyl-phosphine sulfides, RP(S)[CH(OH)R¹]₂. ¹H, ¹³C, and ³¹P NMR spectroscopic investigations allow to detect and to identify stereoisomers in some cases. Quantumchemical calculations reflect correctly which of the carbonyl compounds are able to react with the organylphosphine monosulfide formed as intermediate.     

Rotational diffusion of dyes in solvents of low viscosity from transient-dichroism experiments

Rotational diffusion data from pulsed laser experiments are presented for dye molecules dissolved in alcohols and non-alcohols. Cresyl violet and fluorescein both exhibit strong dependence of the rotational motion upon solvent molecular structure. In complete contrast the rotational diffusion of the oblong dyes pyronine G and acridine orange do not reveal any specific solute-solvent interaction.     

Orlicz capacities and Hausdorff measures on metric spaces

In the setting of doubling metric measure spaces with a 1-Poincaré inequality, we show that sets of Orlicz Φ-capacity zero have generalized Hausdorff h-measure zero provided thatwhere Θ⁻¹ is the inverse of the function Θ(t)=Φ(t)/t, and s is the “upper dimension” of the metric measure space. This condition is a generalization of a well known condition in Rⁿ. For spaces satisfying the weaker q-Poincaré inequality, we obtain a similar but slightly more restrictive condition. Several examples are also provided.     

Solvent effects on the electronic spectra of oxovanadium(IV) β-diketonates comments on the papers of ebraheem et al.

Summary Solvent effects on the electronic absorption spectra of oxovanadium(IV) 31/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-diketonates are discussed. It has been found that positions of the long-wave-length bands can be described in terms of the donor-acceptor concept including the donor numbers and the acceptor numbers.

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Lösungsmitteleffekte bei den Elektronenspektren von Oxovanadium(IV)-31/xhuge946.gif" alt="beta" align="MIDDLE" BORDER="0">-diketonaten. Kommentar zu den Arbeiten von Ebraheem et al. (Kurze Mitt.)

Zusammenfassung Es werden Lösungsmitteleffekte bei den Elektronenspektren von Oxovanadium(IV)-31/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-diketonaten diskutiert. Dabei wurde gefunden, daß die Lage der langwelligen Banden auf Basis eines Donor-Akzeptor-Modells unter Berücksichtigung der Donor- und Akzeptor-Nummern beschrieben werden kann.

     

Salze von Halogenophosphorsäuren XIX [1] Über die Bildung und den Nachweis stabiler Intermediate bei der Reaktion von Fluorid mit Phosphoroxidchlorid

Salts of Halogenophosphoric Acids. XIX Formation and Identification of Stable Intermediates on the Reaction of Fluoride with Phosphorus Oxychloride By reaction of POCl₃ with fluorides of tertiary amines in the presence of the free amines the oxo-fluorophosphates [F₂P(O? O? PF₅)]^?, [OPF₅]^2?, and [OPF₄]^? are formed as intermediates on the way to [PF₆]^?. The compounds were characterized by NMR spectroscopy.