Theoretical study of the Diels-Alder reactions between singlet (1Delta g) oxygen and acenes

The G3(MP2) method has been employed to study the 1,4-addition reactions between singlet oxygen and five acenes, including benzene, naphthalene, anthrecene, tetracene, and pentacene. In all, nine pathways between O(2) and the five acenes have been investigated. Our calculated results indicate that all nine pathways are concerted and exothermic and that the most reactive sites on the acenes are the center ring's meso-carbons. In addition, reactivity increases along the series benzene < naphthalene < anthrecene < tetracene < pentacene. This trend is identical to that of aromaticity for the five acenes. A correlation between reactivity and aromaticity is briefly rationalized with natural bond orbital (NBO) analysis and frontier molecular orbital (FMO) analysis. Furthermore, some experimental kinetics data from the literature supporting the calculated results are cited.     

Radial quadrature for multiexponential integrands

We introduce a Gaussian quadrature, based on the polynomials that are orthogonal with respect to the weight function ln(2)x on the interval [0, 1], which is suitable for the evaluation of radial integrals. The quadrature is exact if the non-Jacobian part of the integrand is a linear combination of a geometric sequence of exponential functions. We find that the new scheme is a useful alternative to existing approaches, particularly for integrands that exhibit multiexponential behavior.     

Existence of Resonances for Metric Scattering in Even Dimensions

Suppose _g is the (negative) Laplace–Beltrami operator of a Riemannian metric g on ⁿ which is Euclidean outside some compact set. It is known that the resolvent R()=(– _g –²)^–1, as the operator from L ² _comp( ⁿ ) to H ² _loc( ⁿ ), has a meromorphic extension from the lower half plane to the complex plane or the logarithmic plane when n is odd or even, respectively. Resonances are defined to be the poles of this meromorphic extension. We prove that when n is 4 or 6, there always exist infinitely many resonances provided that g is not flat. When n is greater than 6 and even, we prove the same result under the condition that the metric is conformally Euclidean or is close to the Euclidean metric.     

Bistable electrical switching and memory effects in a thin film of copolymer containing electron donor-acceptor moieties and europium complexes

A nonconjugated methacrylate copolymer (PCzOxEu) containing carbazole moieties (electron donors), 1,3,4-oxadiazole moieties (electron acceptors), and europium complexes in the pendant groups was synthesized via free radical copolymerization of methacrylate monomers containing the respective functional groups. The molecular structure and composition of PCzOxEu was characterized by elemental analysis, FT-IR, 1H NMR, 13C NMR, UV-vis absorption and fluorescence spectroscopies, gel permeation chromatography (GPC), X-ray photoelectron spectroscopy (XPS), and cyclic voltammetry (CyV). The resulting copolymer exhibited a relatively high glass transition temperature (Tg approximately 125 degrees C) and good solubility in common organic solvents. It could be cast into transparent films from solutions. For a thin film of PCzOxEu sandwiched between an indium-tin oxide (ITO) electrode and an Al electrode (ITO/PCzOxEu/Al), the structure behaved as a nonvolatile flash (rewritable) memory with accessible electronic states that could be written, read, and erased. The polymer memory exhibited an ON/OFF current ratio up to 10(5), switching response time of approximately 1.5 micros, more than 10(6) read cycles, retention time of more than 8 h, and write/erase voltages of about 4.4 V/-2.8 V under ambient conditions. The roles of oxadiazole moieties in improving the response time and retention time of the memory device were elucidated from the molecular simulation results.     

SG-0: a small standard grid for DFT quadrature on large systems

We report the development of a new standard quadrature grid for DFT calculations. Standard Grid 0 (SG-0) is designed to be approximately half as large as, and to provide approximately half the accuracy of, the established SG-1 grid. It is based on MultiExp and Lebedev quadrature for radial and angular coordinates, respectively. We find that SG-0 is typically 50% faster than SG-1 for energy, gradient, and hessian calculations for the exchange-correlation energy. This leads to a 35-38% speedup in the total gradient and hessian computations, and we particularly recommend its use for preliminary calculations on moderately large biochemical systems. It has been implemented as the default grid for DFT calculations in the Q-Chem 3.0 package.     

CR-invariants and the scattering operator for complex manifolds with CR-boundary

Suppose that M is a CR manifold bounding a compact complex manifold X. The manifold X admits an approximate Kähler–Einstein metric g which makes the interior of X a complete Riemannian manifold. We identify certain residues of the scattering operator as CR-covariant differential operators and obtain the CR Q-curvature of M from the scattering operator as well. Our results are an analogue in CR-geometry of Graham and Zworski's result that certain residues of the scattering operator on a conformally compact manifold with a Poincaré–Einstein metric are natural, conformally covariant differential operators, and the Q-curvature of the conformal infinity can be recovered from the scattering operator. To cite this article: P.D. Hislop et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Group cohomology and gauge equivalence of some twisted quantum doubles

We study the module category associated to the quantum double of a finite abelian group twisted by a 3-cocycle, which is known to be a braided monoidal category, and investigate the question of when two such categories are equivalent. We base our discussion on an exact sequence which interweaves the ordinary and Eilenberg-Mac Lane cohomology of . Roughly speaking, this reveals that the data provided by such module categories is equivalent to (among other things) a finite quadratic space equipped with a metabolizer, and also a pair of rational lattices with self-dual and integral.

     

Chain transfer in vinylpyridine polymerizations

Transfer constants to monomer at 55°C have been measured in 2 and 4-vinylpyridine radical polymerizations. In addition, the transfer constants to ethanol, octan-1-ol, toluene, benzyl alcohol, chloroform, and nitroethane have been measured. These values, which increase in the order above, show no significant variation between the two isomeric monomers.     

Central invariants and higher indicators for semisimple quasi-Hopf algebras

In this paper, we define the higher Frobenius-Schur (FS-)indicators for finite-dimensional modules of a semisimple quasi-Hopf algebra via the categorical counterpart developed in a 2005 preprint. When is an ordinary Hopf algebra, we show that our definition coincides with that introduced by Kashina, Sommerhäuser, and Zhu. We find a sequence of gauge invariant central elements of such that the higher FS-indicators of a module are obtained by applying its character to these elements. As an application, we show that FS-indicators are sufficient to distinguish the four gauge equivalence classes of semisimple quasi-Hopf algebras of dimension eight corresponding to the four fusion categories with certain fusion rules classified by Tambara and Yamagami. Three of these categories correspond to well-known Hopf algebras, and we explicitly construct a quasi-Hopf algebra corresponding to the fourth one using the Kac algebra. We also derive explicit formulae for FS-indicators for some quasi-Hopf algebras associated to group cocycles.

     

On the Projectivity of module coalgebras

In this paper, we derive some criteria for the projectivity of a module coalgebra over a finite dimensional Hopf algebra. In particular, we show that any Hopf algebra over a field of characteristic zero is faithfully flat over its group-like subHopf algebra. Finally, we prove that if is a finite dimensional subHopf algebra of a Hopf algebra , then is normal in if and only if . This improves a result by S. Montgomery (1993).