A density matrix renormalization group study of low-lying excitations of polythiophene within a Pariser-Parr-Pople model

Symmetrized density-matrix-renormalization-group calculations have been carried out, within Pariser-Parr-Pople Hamiltonian, to explore the nature of the ground and low-lying excited states of long polythiophene oligomers. We have exploited C-2 symmetry and spin parity of the system to obtain excited states of experimental interest, and studied the lowest dipole allowed excited state and lowest dipole forbidden two photon state, for different oligomer sizes. In the long system limit, the dipole allowed excited state always lies below the lowest dipole forbidden two-photon state which implies, by Kasha rule, that polythiophene fluoresces strongly. The lowest triplet state lies below two-photon state as usual in conjugated polymers. We have doped the system with a hole and an electron and obtained the charge excitation gap and the binding energy of the 1(1)B(u)(-) exciton. We have calculated the charge density of the ground, one-photon and two-photon states for the longer system size of 10 thiophene rings to characterize these states. We have studied bond order in these states to get an idea about the equilibrium excited state geometry of the system. We have also studied the charge density distribution of the singly and doubly doped polarons for longer system size, and observe that polythiophenes do not support bipolarons.

Gauge theory of a group of diffeomorphisms. III. The fiber bundle description

A new fiber bundle approach to the gauge theory of a group G that involves space‐time symmetries as well as internal symmetries is presented. The ungauged group G is regarded as the group of left translations on a fiber bundle G(G/H,H), where H is a closed subgroup and G/H is space‐time. The Yang–Mills potential is the pullback of the Maurer–Cartan form and the Yang–Mills fields are zero. More general diffeomorphisms on the bundle space are then identified as the appropriate gauged generalizations of the left translations, and the Yang–Mills potential is identified as the pullback of the dual of a certain kind of vielbein on the group manifold. The Yang–Mills fields include a torsion on space‐time.

Hot gaseous coronae of early-type galaxies and their radio luminosity function

Recent X-ray observations have revealed that early-type galaxies (which usually produce extended double radio sources) generally have hot gaseous haloes extending up to approx102kpc1,2. Moreover, much of the cosmic X-ray background radiation is probably due to a hotter, but extremely tenuous, intergalactic medium (IGM)3. We have presented4–7 an analytical model for the propagation of relativistic beams from galactic nuclei, in which the beams' crossing of the pressure-matched interface between the IGM and the gaseous halo, plays an important role. The hotspots at the ends of the beams fade quickly when their advance becomes subsonic with respect to the IGM. This model has successfully predicted (for typical double radio sources) the observed8 current mean linear-size (approx2Dsime350 kpc)4,5, the observed8–11 decrease in linear-size with cosmological redshift4–6 and the slope of the linear-size versus radio luminosity10,12–14 relation6. We have also been able to predict the redshift-dependence of observed numbers and radio luminosities of giant radio galaxies7,15. Here, we extend this model to include the propagation of somewhat weaker beams. We show that the observed flattening of the local radio luminosity function (LRLF)16–20 for radio luminosity Papproximately 1024 W Hz-1 at 1 GHz can be explained without invoking ad hoc a corresponding break in the beam power function Phi(Lb), because the heads of the beams with Lb < 1025 W Hz-1 are decelerated to sonic velocity within the halo itself, which leads to a rapid decay of radio luminosity and a reduced contribution of these intrinsically weaker sources to the observed LRLF.

Intermolecular Chelate Linkage Isomerism of the Hydroxyimino Group in the Nickel(II), Copper(II), and Palladium(II) Complexes of Quadridentate Schiff-base Ligands

The C-nitrosation of bivalent quadridentate β-imino ketone complexes of nickel(II), copper(II), and palladium(II), with nitrosating reagents has been investigated. The chemical analysis and spectroscopic results reveal that one of the α-CH groups of the coordinated lignad undergoes selective nitrosation forming mono(hydroxyimino) derivative. The hydroxyimino group introduced coordinates through either N- or O- atom to metal(II) by dislodging the carbonyl group already coordinated. This gives rise to two linkage isomers, one with N-bonded and the other with O-bonded hydroxyimino group in the case of nickel(II) (except for 1d) and palladium(II), and a single isomer with O-bonded hydroxyimino group in copper(II) complexes. The isomers obtained from 1b and 1i have been separated by column chromatography. In chloroform each of the isomers of nickel(II) isomerizes to give an equilibrium mixture of two isomers, but not those of copper(II) and palladium(II).

Enantioselective and Protecting Group-Free Synthesis of 1-Deoxythionojirimycin, 1-Deoxythiomannojirimycin, and 1-Deoxythiotalonojirimycin

1-Deoxythioglyconojirimycins were synthesized by using a protecting group-free strategy, starting from readily available carbohydrates, in good overall yield. Use of benzyl-triethylammonium tetrathiomolybdate, BnEt3N](2)MoS4, as a sulfur transfer reagent and borohydride exchange resin (BER) reduction of a lactone enabled the efficient synthesis of the title compounds.

Alkaloid synthesis: stereoselective approach towards fawcettimine-serratinine group of lycopodium alkaloids

The concept of carbocycle-heterocycle equivalency has been utilised to assemble the framework of fawcettimine-serratinine group of alkaloids from 1,5-cyclooctadiene through a common tricarbocyclic intermediate 3.

A multiplier theorem for the sublaplacian on the Heisenberg group

A multiplier theorem for the sublaplacian on the Heisenberg group is proved using Littlewood-Paley-Stein theory of g-functions.

Mixed Convection Induced in a Gas Flowing Past a Hot Horizontal Flat Plate

A boundary layer analysis of mixed convective motion over a hot horizontal flat plate is performed under the conditions of steady flow and low speed. Use of the Howarth-Dorodnytsyn transformation makes it possible to dispense with the usual Boussinesq approximation, and variable gas properties are accounted for via the assumption that dynamic viscosity and thermal conductivity are proportional to the absolute temperature. The formulation presented enables the entire mixed convection regime to be described by a single set of equations. Finite difference solutions when the Prandtl number is 0.72 are obtained over the entire range of the mixed convection parameter ξ from 0 (free convection) to 1 (forced convection) and heating parameter ▵ values from 2 to 12. The effects of both ξ and ▵on the velocity profiles, the temperature profiles, and the variation of skin friction and heat transfer functions are clearly illustrated in tables and graphs.

Organometallic derivatives of diphosphazanes. 2. Seven-coordinated Group 6 metal tricarbonyl complexes of diphosphazane ligands. X-ray crystal structure of [WI2(CO)3{P(OPh)2}2NPh]

The reactions of the complexes [MI2(CO)3-(NCMe)2] (M = Mo, W) with the diphosphazane ligands RN{P(OPh)2}2 (R = Me, Ph) in CH2Cl2 at room temperature afford new seven-coordinated complexes of the type [MI2(CO)3{P(OPh)2}2NR]. The molybdenum complexes are sensitive to air oxidation even in the solid state, whereas the tungsten complexes are more stable in the solid state and in solution. The structure of the tungsten complex [WI2(CO)3{P(OPh)2}2NPh] has been determined by single-crystal X-ray diffraction. It crystallizes in the orthorhombic system with the space group Pna 2(1), a = 19.372 (2) angstrom, b = 11.511 (1) angstrom, c = 15.581 (1) angstrom, and Z = 4. Full-matrix least-squares refinement with 3548 reflections (I > 2.5-sigma-(I)) led to final R and R(w) values of 0.036 and 0.034, respectively. The complex adopts a slightly distorted pentagonal-bypyramidal geometry rarely observed for such a type of complexes; two phosphorus atoms of the diphosphazane ligand, two iodine atoms, and a carbonyl group occupy the equatorial plane, and the other two carbonyl groups, the apical positions.