The 1H and 13C NMR chemical shifts of Strychnos alkaloids revisited at the DFT level

The density functional theory calculation of ¹H and ¹³C NMR chemical shifts in a series of ten 10 classically known Strychnos alkaloids with a strychnine skeleton was performed at the PBE0/pcSseg-2//pcseg-2 level. It was found that calculated ¹H and ¹³C NMR chemical shifts provided a markedly good correlation with experiment characterized by a mean absolute error of 0.08 ppm in the range of 7 ppm for protons and 1.67 ppm in the range of 150 ppm for carbons, so that a mean absolute percentage error was as small as ~1% in both cases.     

Multinomial permutations on a circle

Multinomial permutations on a circle are considered in the framework of combinatorics. Different cases are presented and shown to agree with previously derived formula for the number of cyclic necklaces. Two applied examples are discussed with a view to illustrate the implications of derived formulas. Copyright © 2006 John Wiley & Sons, Ltd.     

Gromov's K-area and symplectic rigidity

Supported by the United States-Israel Binational Science Foundation grant 94-00302     

Enumerating disjunctions and conjunctions of paths and cuts in reliability theory

Let G=(V,E) be a (directed) graph with vertex set V and edge (arc) set E. Given a set P of source-sink pairs of vertices of G, an important problem that arises in the computation of network reliability is the enumeration of minimal subsets of edges (arcs) that connect/disconnect all/at least one of the given source-sink pairs of P. For undirected graphs, we show that the enumeration problems for conjunctions of paths and disjunctions of cuts can be solved in incremental polynomial time. Furthermore, under the assumption that P consists of all pairs within a given vertex set, we also give incremental polynomial time algorithm for enumerating all minimal path disjunctions and cut conjunctions. For directed graphs, the enumeration problem for cut disjunction is known to be NP-complete. We extend this result to path conjunctions and path disjunctions, leaving open the complexity of the enumeration of cut conjunctions. Finally, we give a polynomial delay algorithm for enumerating all minimal sets of arcs connecting two given nodes s₁ and s₂ to, respectively, a given vertex t₁, and each vertex of a given subset of vertices T₂.     

On Uniform Boundedness and Uniform Asymptotics for Orthogonal Polynomials on the Unit Circle

The known conditions due to G. Baxter, Ya. L. Geronimus, and B. L. Golinskii which guarantee the uniform boundedness and/or uniform asymptotic representation for orthonormal polynomials on the unit circle are under consideration. We show that these conditions are in general not necessary. We discuss the relation between the orthonormal polynomials on the unit circle, the best approximations, and absolutely convergent Fourier series.     

Artificial multiple criticality and phase equilibria: an investigation of the PC-SAFT approach

The perturbed-chain statistical associating fluid theory (PC-SAFT) is studied for a wide range of temperature, T, pressure, p, and (effective) chain length, m, to establish the generic phase diagram of polymers according to this theory. In addition to the expected gas-liquid coexistence, two additional phase separations are found, termed "gas-gas" equilibrium (at very low densities) and "liquid-liquid" equilibrium (at densities where the system is expected to be solid already). These phase separations imply that in one-component polymer systems three critical points occur, as well as equilibria of three fluid phases at triple points. However, Monte Carlo simulations of the corresponding system yield no trace of the gas-gas and liquid-liquid equilibria, and we conclude that the latter are just artefacts of the PC-SAFT approach. Using PC-SAFT to correlate data for polybutadiene melts, we suggest that discrepancies in modelling the polymer density at ambient temperature and high pressure can be related to the presumably artificial liquid-liquid phase separation at lower temperatures. Thus, particular care is needed in engineering applications of the PC-SAFT theory that aims at predicting properties of macromolecular materials.     

Synthesis, structure and reactivity of binuclear metal-metal bonded molybdenum(V) and tungsten(V) thioselenohalides: Molecular structure of Mo2(μ-S2)2Cl6(SeCl2)2 and W2(μ-S2)2Cl6(SeCl2)2

Thioselenohalide complexes Mo₂(μ-S₂)₂Cl₆(SeCl₂)₂ (I), Mo₂(μ-S₂)₂Br₆(SeBr₂)₂ (II), and W₂(μ-S₂)₂Br₆(SeBr₂)₂ (III) were synthesized by the reactions of corresponding metal halides or carbonyls or molybdenum metal with excesses of S₂ X ₂+Se₂ X ₂ mixtures. The complex W₂(μ-S₂)₂Cl₆(SeCl₂)₂ (IV) was obtained by an exchange reaction between (III) and excess of Se₂Cl₂. Coordination of the neutral SeX ₂ ligands to thiohalidesM ₂(μ-S₂)₂ X ₆ results in higher thermal stability, and suggests the possibility to synthesize SeX ₂ complexes of the unstable parent tungsten thiohalides. An unusual oxidative addition reaction of (I) was detected: {fx27-1} Both (I) and (IV) were characterized by X-ray crystal structure analysis. They are isostructural and form discrete molecules. Bridging S ₂ ^2? ligands are coordinated perpendicularly to the metal-metal bond;d(M?M)=2.8066 Å and 2.793 Å for I and IV, respectively. Nonequivalence of chlorine atoms which are bound to the metal atom, relate to nonequivalence of halogen atoms in the complexesM ₂(μ?S₂)₂ X ₈ ^2? . Chlorine atomstrans to SeCl₂ ligands form short bonds with the metal; the corresponding³⁵Cl NQR frequency is increased. The selenium dichloride ligand is ambidentate. The selenium atom binds as a donor to the metal and as an acceptor to two chlorine atoms which are also bound covalently to the same metal atom.     

Organo-noble-gas hydride compounds HKrCCH, HXeCCH, HXeCC, and HXeCCXeH: formation mechanisms and effect of 13C isotope substitution on the vibrational properties

We investigate the formation mechanism of HXeCCXeH in a Xe matrix. Our experimental results show that the HXeCCXeH molecules are formed in the secondary reactions involving HXeCC radicals. The experimental data on the formation of HXeCCXeH is fully explained based on the model involving the HXeCC+Xe+H-->HXeCCXeH reaction. This reaction is the first case when a noble-gas hydride molecule is formed from another noble-gas molecule. In addition, we investigate the (12)C/(13)C isotope effect on the vibrational properties of organo-noble-gas hydrides (HKrCCH, HXeCCH, HXeCC, and HXeCCXeH) in noble-gas matrixes. The present experimental results and ab initio calculations on carbon isotope shifts of the vibrational modes support the previous assignments of these molecules. Upon (12)C to (13)C isotope substitution, we observed a pronounced effect on the H-Kr stretching mode of HKrCCH (downshift of 1.0-3.6 cm(-1), depending on the matrix site) and a small anomalous shift (+0.1 cm(-1)) of the H-Xe stretching mode of HXeCCH and HXeCCXeH.     

Fluoropolyethers end‐capped by polar functional groups. III. Kinetics of the reactions of hydroxy‐terminated fluoropolyethers and model fluorinated alcohols with cyclohexyl isocyanate catalyzed by organotin compounds

The kinetics of the dibutyltin dilaurate (DBTDL)‐catalyzed urethane formation reactions of cyclohexyl isocyanate (CHI) with model monofunctional fluorinated alcohols and fluoropolyether diol Z‐DOL H‐1000 of various molecular weights (100–1084 g mol^?1) in different solvents were studied. IR spectroscopy and chemical titration methods were used for measuring the rate of the total NCO disappearance at 30–60 °C. The effects of the reagents and DBTDL catalyst concentrations, the solvent and hydroxyl‐containing compound nature, and the temperature on the reaction rate and mechanism were investigated. Depending on the initial reagent concentration and solvent, the reactions could be well described by zero‐order, first‐order, second‐order, or more complex equations. The reaction mechanism, including the formation of intermediate ternary or binary complexes of reagents with the tin catalyst, could vary with the concentration and solvent and even during the reaction. The results were treated with a rate expression analogous to those used for enzymatic reactions. Under the explored conditions, the rate of the uncatalyzed reaction of fluorinated alcohols with CHI was negligible. Moreover, there was no allophanate formation, nor were there other side reactions, catalysis by urethane in the absence of DBTDL, or a synergetic effect in the presence of the tin catalyst. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3771–3795, 2002