Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle

We investigate heteroclinic orbits between equilibria and rotating waves for scalar semilinear parabolic reaction-advection-diffusion equations with periodic boundary conditions. Using zero number properties of the solutions and the phase shift equivariance of the equation, we establish a necessary and sufficient condition for the existence of a heteroclinic connection between any pair of hyperbolic equilibria or rotating waves.     

Quasiparticle bandstructures of covalent semiconductors and their surfaces

The exchange-correlation self-energies and quasiparticle shifts are calculated for band states of covalent materials (diamond, silicon) and their (001) 2×1 surface in order to solve the bulk and surface band-gap problem of the LDA. The screening properties are described by a model dielectric function taking into account the spatial nonlocality in the surface case assuming specular electron reflection. The wave functions are expanded in terms of localized orbitals. The quasiparticle bandstructures obtained are in reasonable agreement with experimental results.     

Das asymptotische Verhalten der Peanokerne einiger interpolatorischer Quadraturverfahren

Summary Interpolatory quadrature formulae consist in replacing by wherep _f denotes the interpolating polynomial off with respect to a certain knot setX. The remainder may in many cases be written as wherem=n resp. (n+1) forn even and odd, respectively. We determine the asymptotic behaviour of the Peano kernelP _X (t) forn for the quadrature formulae of Filippi, Polya and Clenshaw-Curtis.

     

Synthesis, structure determination, and spectroscopic/computational characterization of a series of Fe(II)-thiolate model complexes: implications for Fe-S bonding in superoxide reductases

A combined synthetic/spectroscopic/computational approach has been employed to prepare and characterize a series of Fe(II)-thiolate complexes that model the square-pyramidal [Fe(II)(N(His))(4)(S(Cys))] structure of the reduced active site of superoxide reductases (SORs), a class of enzymes that detoxify superoxide in air-sensitive organisms. The high-spin (S = 2) Fe(II) complexes [(Me(4)cyclam)Fe(SC(6)H(4)-p-OMe)]OTf (2) and [FeL]PF(6) (3) (where Me(4)cyclam = 1,4,8,11-tetramethylcyclam and L is the pentadentate monoanion of 1-thioethyl-4,8,11-trimethylcyclam) were synthesized and subjected to structural, magnetic, and electrochemical characterization. X-ray crystallographic studies confirm that 2 and 3 possess an N(4)S donor set similar to that found for the SOR active site and reveal molecular geometries intermediate between square pyramidal and trigonal bipyramidal for both complexes. Electronic absorption, magnetic circular dichroism (MCD), and variable-temperature variable-field MCD (VTVH-MCD) spectroscopies were utilized, in conjunction with density functional theory (DFT) and semiemperical INDO/S-CI calculations, to probe the ground and excited states of complexes 2 and 3, as well as the previously reported Fe(II) SOR model [(L(8)py(2))Fe(SC(6)H(4)-p-Me)]BF(4) (1) (where L(8)py(2) is a tetradentate pyridyl-appended diazacyclooctane macrocycle). These studies allow for a detailed interpretation of the S-->Fe(II) charge transfer transitions observed in the absorption and MCD spectra of complexes 1-3 and provide significant insights into the nature of Fe(II)-S bonding in complexes with axial thiolate ligation. Of the three models investigated, complex 3 exhibits an absorption spectrum that is particularly similar to the one reported for the reduced SOR enzyme (SOR(red)), suggesting that this model accurately mimics key elements of the electronic structure of the enzyme active site; namely, highly covalent Fe-S pi- and sigma-interactions. These spectral similarities are shown to arise from the fact that 3 contains an alkyl thiolate tethered to the equatorial cyclam ring, resulting in a thiolate orientation that is very similar to the one adopted by the Cys residue in the SOR(red) active site. Possible implications of our results with respect to the electronic structure and reactivity of SOR(red) are discussed.     

Electronic spectroscopy of C2 in solid rare gas matrixes

Electronic spectroscopy of the C(2) molecule is investigated in Ar, Kr, and Xe matrixes in the 150-500 nm range. In the Ar matrix, the D ((1)Sigma(u)(+)) <-- ((1)Sigma(g)(+)) Mulliken band near 240 nm is the sole absorption in the UV range, whereas in the Kr matrix additional bands in the 188-209 nm range are assigned to the Kr(n)()(+)C(2)(-) <-- Kr(n)()C(2) charge-transfer absorptions. Because of the formation of a bound C(2)Xe species, the spectral observations in the Xe matrix differ dramatically from the lighter rare gases: the Mulliken band is absent and new bands appear near 300 and 423 nm. The latter is assigned to the forbidden B'((1)Sigma(g)(+)) <-- X ((1)Sigma(g)(+)) transition, but the origin of the former remains unclear. The spectral assignments are aided by electronic structure calculations at the MCSCF, CCSD(T), and BCCD(T) levels of theory and correlation consistent basis sets. A significant presence of multireference character of the C(2)Xe system was noted and a linear ground-state structure is predicted. The computational results contradict previous density functional studies on the same system.     

Synthesis of 3-hexahelicenol and its transformation to 3-hexahelicenylamines,diphenylphosphine, methyl carboxylate,and dimethylthiocarbamate

A nonphotochemical synthetic route to 3-hexahelicenol is reported. It involves a key [2+2+2] cycloisomerization of CH(3)O-substituted triyne that is readily available from 1-methoxy-3-methylbenzene and 1-bromo-2-(bromomethyl)naphthalene. Further functional group transformations led to 3-CO(2)CH(3), 3-NH(2), 3-PPh(2), and 3-SC(O)N(CH(3))(2) substituted hexahelicenes.