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.     

Ferromagnetic spin alignment in head-to-tail coupled oligo(1, 4-phenyleneethynylene)s and Oligo(1,4-phenylenevinylene)s bearing pendant p-phenylenediamine radical cations

The intramolecular and long-range ferromagnetic coupling between p-phenylenediamine radical cations in head-to-tail coupled oligo(1, 4-phenyleneethynylene)s and oligo(1,4-phenylenvinylene)s between neighbors and next-nearest neighbors is described. UV/vis/near-IR experiments show that the radical cations are localized in the pendant p-phenylenediamine units of the conjugated oligomers. The ESR spectra of these oligo(1,4-phenyleneethynylene) and oligo(1, 4-phenylenvinylene) di(radical cation)s are consistent with those of a triplet state. A linear behavior is observed for the doubly integrated ESR intensity of the DeltaM(s) = +/-1 and DeltaM(s) = +/-2 signals with the inverse temperature (I approximately 1/T), consistent with Curie's law. This behavior indicates a triplet ground-state diradical with a large triplet-singlet energy gap or possibly a degeneracy of singlet and triplet states.     

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.