The experimental gas-phase structures of 1,3,5-trisilylbenzene and hexasilylbenzene and the theoretical structures of all benzenes with three or more silyl substituents

The structures of 1,3,5-trisilylbenzene and hexasilylbenzene in the gas phase have been determined by electron diffraction, and that of 1,3,5-trisilylbenzene by X-ray crystallography. The structures of three trisilylbenzene isomers, three tetrasilylbenzenes, pentasilylbenzene and hexasilylbenzene have been computed, ab initio and using Density Functional Theory, at levels up to MP2/6-31G*. The primary effect of silyl substituents is to narrow the ring angle at the substituted carbon atoms. Steric interactions between silyl groups on neighbouring carbon atoms lead first to displacement of these groups away from one another, and then to displacement out of the ring plane, with alternate groups moving to opposite sides of the ring. In the extreme example, hexasilylbenzene, the SiCCSi dihedral angle is 17.8(8) degrees .     

Use of a Design of Experiments approach for the optimisation of a microwave assisted Ugi reaction

The utility of a Design of Experiments (DoE) approach for the rapid and efficient optimisation of a microwave assisted Ugi 3cc reaction of levulinic acid is demonstrated. DoE methods have also been applied to the assessment of the reaction scope for a range of amine and isonitrile substrates. The optimal procedure developed using this approach has enabled the preparation of lactam derivatives in moderate to excellent yields (17-90%) in a reaction time of only 30 min compared to the conventional methodology which required up to 48 h.     

Molecular structure of Hf(BH4)4 investigated by quantum mechanical calculations and gas-phase electron diffraction

The structure of the gaseous hafnium tetrakis(tetrahydroborate) molecule, Hf(BH4)4, has been investigated by detailed quantum mechanical calculations and by analysis of its gas electron-diffraction (GED) pattern. The ground-state geometry possesses T symmetry with all of the triply-bridged BH4 groups twisted equally about the Hf...B-H axes. Salient structural parameters (ra distances, r angles) deduced from the GED pattern by the SARACEN method were: r(Hf...B) 231.4(2), r(Hf-Hb) 221.5(7), r(B-Hb) 127.6(5), r(B-Ht) 121(1) pm, Hf...B-Hb 69.4(3), Hb-B-Hb 108.4(4), Hb-B-Ht 110.6(3), B...Hf...B-Hb 166(1) degrees. A notable feature is the large magnitude of the Hf...B and Hf-Hb anharmonicity parameters, attributed to the fluxional hydrogen atom exchange process. The properties are compared with those of related tetrahydroborates..     

Generalized phase diversity for wave-front sensing

Phase diversity is a phase-retrieval algorithm that uses a pair of intensity images taken symmetrically about the wave front to be determined. If these images are taken about the system input pupil this is equivalent to a curvature-sensing algorithm. Traditionally a defocus aberration kernel is used to produce the phase-diverse data. We present a generalization of this method to allow the use of other functions as the diversity kernel. We discuss the necessary and sufficient conditions that such a function must satisfy for use in a null wave-front sensor. Computer simulations were used to validate these results.     

Biosynthesis of hydroxydiphenylacetylene by regiospecific monooxygenation

Bacterial monooxygenase enzymes catalyze a regiospecific single-step hydroxylation of diphenylacetylene to yield meta- and para-hydroxydiphenylacetylene.     

Factorizations of the Complete Graph into C 5-Factors and 1-Factors

In this paper, we show that K_10n can be factored into C₅-factors and 1-factors for all non-negative integers and satisfying 2+=10n–1.Research partially supported by an NSF-AWM Mentoring Travel Grant     

Homology manifold bordism

The Bryant-Ferry-Mio-Weinberger surgery exact sequence for compact homology manifolds of dimension is used to obtain transversality, splitting and bordism results for homology manifolds, generalizing previous work of Johnston.

First, we establish homology manifold transversality for submanifolds of dimension : if is a map from an -dimensional homology manifold to a space , and is a subspace with a topological -block bundle neighborhood, and , then is homology manifold -cobordant to a map which is transverse to , with an -dimensional homology submanifold.

Second, we obtain a codimension splitting obstruction in the Wall -group for a simple homotopy equivalence from an -dimensional homology manifold to an -dimensional Poincaré space with a codimension Poincaré subspace with a topological normal bundle, such that if (and for only if) splits at up to homology manifold -cobordism.

Third, we obtain the multiplicative structure of the homology manifold bordism groups .