Fixed-nuclei and laboratory-frame formalisms for electron scattering by a spherical top,with full incorporation of symmetry

We discuss molecule-frame and laboratory-frame symmetry-adapted formalisms for electron scattering by a spherical top. The molecule-frame formalism is based on the fixed-nuclear-orientation approximation, both for electronically elastic scattering by a vibrationally rigid molecule and also for the more general case where electronic excitation and vibrational degrees of freedom are included. The laboratory-frame formalism is based on the exact symmetries of the problem, which are carefully related to the approximate symmetries of the molecule-frame treatment. We present both the forward and backward transformations between the two representations.     

Theory of chirality functions,generalized for molecules with chiral ligands

The theory of chirality functions described in a previous publication is generalized to allow for chiral ligands. In the earlier theory, all symmetry operations of the molecular frame could be thought of as permutations of the ligands among the sites; in the present work, improper rotations not only permute the ligands, but convert them into mirror images. The group that generates all isomers from a given ordered molecule belonging to a frame with n sites is now the hyperoctahedral group of order 2ⁿ n! consisting of all possible combinations of permutations and site reflections. The representation theory of these groups is described, and applied to the problem of constructing qualitatively complete chirality functions, and of deciding which ligand partitions, and which isomer mixtures, are chiral. It is found useful to classify chiral representations of the covering group as ligand specific and class specific. The ligand specific representations describe chiral properties which are common to all frames and arise purely from the chirality of the ligands, while the class specific representations describe the chiral properties of the frame. A number of examples are explicitly worked out.     

Energetics of the loss of H2 from [C3H7]+

The internal energies of [C₃H₇]⁺ ions contributing to the metastable peak [C₃H₇]⁺ → [C₃H₅]⁺ + H₂ are higher (by perhaps > 100 kJ mol^?1) than those of the ion contributing to the threshold current in appearance energy measurements on [C₃H₅]⁺. The measured appearance energy may lead to an underestimation of the activation energy, i.e. negative ‘kinetic shift’, due to quantum, mechanical tunnelling. The distribution of energy released in the decomposition can be explained on the basis that much of the reverse activation energy and a statistical proportion of the excess energy is released as translation.     

Studies towards diarylheptanoid synthesis. Part 1: Synthesis and ring cleavage reactions of hexahydro-2H,5H-pyrano[2,3-b]pyran-2-ones

Lewis acid promoted anomeric substitution reactions of a stereoselectively prepared hexahydro-2H,5H-pyrano[2,3-b]pyran-2-one derivative was studied as a model for diarylheptanoid synthesis. Aromatic nucleophiles consistently provided the expected thermodynamic C-aryl pyranoside product.     

Synthesis of Quinolines from N-Tosyl-1-azadienes

A route to aryl-substituted quinolines from N-tosyl 1-azadienes is described. The key steps are a [4 + 2] cycloaddition with benzyne followed by base treatment of the 1,4-dihydroquinoline product. The N-tosyl 1-azadienes were prepared from readily accessible cinnamaldehyde and chalcone substrates by condensation with p-TsNH₂.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communications® to view the free supplemental file.     

Mono-coupled periodic systems with a single disorder: Response to convected loadings

This paper presents a general theory of the forced response under convected loading of mono-coupled periodic systems with a single disorder. The general expressions derived have been used to study the response of an infinite periodic beam on simple supports with one of the support spacings different from all the others. Convected harmonic pressure fields and frozen random pressure fields have been considered. Computer studies are presented showing the moment response at supports and the space-time-averaged responses in the disorder and in the nearby periodic beam elements. High response levels can occur due to (i) resonances of the beam length disorder against the stiffness of the attached periodic systems and (ii) hydrodynamic coincidence vibration occurring in the periodic beam. The frequency zones in which these high responses may occur are identified. The high response due to the resonance (ii) is restricted to the vicinity of the disorder, whereas that due to coincidence occurs throughout the system. Computed results show that the highest response levels do not necessarily occur in the beam length disorder, but may occur in one of the nearby periodic beam elements. The dependence of the maximum response levels on the magnitude of the disorder has been investigated. The conditions under which small disorders may be neglected have been pointed out.     

Stability of a Pivoting Strategy for Parallel Gaussian Elimination

Gaussian elimination with partial pivoting achieved by adding the pivot row to the kth row at step k, was introduced by Onaga and Takechi in 1986 as means for reducing communications in parallel implementations. In this paper it is shown that the growth factor of this partial pivoting algorithm is bounded above by _n <#60; 3 ^n–1, as compared to 2 ^n–1 for the standard partial pivoting. This bound _n, close to 3 ^n–2, is attainable for class of near-singular matrices. Moreover, for the same matrices the growth factor is small under partial pivoting.This revised version was published online in October 2005 with corrections to the Cover Date.