Determination of the Wiener molecular branching index for the general tree

The many applications of the distance matrix, D(G), and the Wiener branching index, W(G), in chemistry are briefly outlined. W(G) is defined as one half the sum of all the entries in D(G). A recursion formula is developed enabling W(G) to be evaluated for any molecule whose graph G exists in the form of a tree. This formula, which represents the first general recursion formula for trees of any kind, is valid irrespective of the valence of the vertices of G or of the degree of branching in G. Several closed expressions giving W(G) for special classes of tree molecules are derived from the general formula. One illustrative worked example is also presented. Finally, it is shown how the presence of an arbitrary number of heteroatoms in tree-like molecules can readily be accommodated within our general formula by appropriately weighting the vertices and edges of G.     

Active site reactant center geometry in the Co(II)-product radical pair state of coenzyme B12-dependent ethanolamine deaminase determined by using orientation-selection electron spin-echo envelope modulation spectroscopy

The distances and orientations among reactant centers in the active site of coenzyme B12-dependent ethanolamine deaminase from Salmonella typhimurium have been characterized in the Co(II)-product radical pair state by using X-band electron paramagnetic resonance (EPR) and two-pulse electron spin-echo envelope modulation (ESEEM) spectroscopies in the disordered solid state. The unpaired electron spin in the product radical is localized on C2. Our approach is based on the orientation-selection created in the EPR spectrum of the biradical by the axial electron-electron dipolar interaction. Simulation of the EPR line shape yielded a best-fit Co(II)-C2 distance of 9.3 A. ESEEM spectroscopy performed at four magnetic field values addressed the hyperfine coupling of the unpaired electron spin on C2 with 2H in the C5' methyl group of 5'-deoxyadenosine and in the beta-2H position at C1 of the radical. Global ESEEM simulations (over the four magnetic fields) were weighted by the orientation dependence of the EPR line shape. A Nelder-Mead direct search fitting algorithm was used to optimize the simulations. The results lead to a partial model of the active site, in which C5' is located a perpendicular distance of 1.6 A from the Co(II)-C2 axis, at distances of 6.3 and 3.5 A from Co(II) and C2, respectively. The van der Waals contact of the C5'-methyl group and C2 indicates that C5' remains close to the radical species during the rearrangement step. The C2-Hs-C5' angle including the strongly coupled hydrogen, Hs, and the C5'-Hs orientation relative to the C1-C2 axis are consistent with a linear hydrogen atom transfer coordinate and an in-line acceptor p-orbital orientation. The trigonal plane of the C2 atom defines sub-spaces within the active site for C5' radical migration and hydrogen atom transfers (side of the plane facing Co(II)) and amine migration (side of the plane facing away from Co(II)).     

Electronic properties of iron arsenic high temperature superconductors revealed by angle resolved photoemission spectroscopy (ARPES)

We present an overview of the electronic properties of iron arsenic high temperature superconductors with emphasis on low energy band dispersion, Fermi surface and superconducting gap. ARPES data is compared with full-potential linearized plane wave (FLAPW) calculations. We focus on single layer NdFeAsO_0.9F_0.1 (R1111) and two layer Ba_1?xK_xFe₂As₂ (B122) compounds. We find general similarities between experimental data and calculations in terms of character of Fermi surface pockets, and overall band dispersion. We also find a number of differences in details of the shape and size of the Fermi surfaces as well as the exact energy location of the bands, which indicate that magnetic interaction and ordering significantly affects the electronic properties of these materials. The Fermi surface consists of several hole pockets centered at Γ and electron pockets located in zone corners. The size and shape of the Fermi surface changes significantly with doping. Emergence of a coherent peak below the critical temperature T_c and diminished spectral weight at the chemical potential above T_c closely resembles the spectral characteristics of the cuprates, however the nodeless superconducting gap clearly excludes the possibility of d-wave order parameter. Instead it points to s-wave or extended s-wave symmetry of the order parameter.     

Systematic effects of carbon doping on the superconducting properties of Mg(B1-xCx)(2)

The upper critical field, H(c2), of Mg(B1-xCx)(2) has been measured in order to probe the maximum magnetic field range for superconductivity that can be attained by C doping. Carbon doped MgB2 filaments were prepared, and for carbon levels below 4% the transition temperatures are depressed by about 1 K/% C and H(c2)(T=0) rises by about 5 T/% C. This means that 3.8% C substitution will depress T(c) from 39.2 to 36.2 K and raise H(c2)(T=0) from 16.0 to 32.5 T. These rises in H(c2) are accompanied by a rise in resistivity at 40 K from about 0.5 to about 10 microOmega cm.