Interpolation by positive definite functions on locally compact groups with application to SO (3)

In this research a method for interpolation on arbitrary locally compact groups is developed. The method is based on positive definite functions definable on spaces with group multiplication. To be able to use these functions two steps are necessary. First, positive semidefinite functions are determined using Bochners theorem on commutative groups respectively representation theory in the non commutative case. Then transformations are given to get positive definite out of positive semidefinite functions. For the compact group 50(3) the result is explicitly calculated and implemented in the case of three and five dimensional representations, and is applied to the approximation of energy functions of molecule interactions in 3-space.     

Exploring the phase diagram of strongly interacting matter; news from SPS and RHIC

Two experimental programs are aiming to study nuclear collisions in the energy regime in order to explore an essential part of the phase diagram of strongly interacting matter. The programs are motivated by observations that indicate a phase transition to take place in this energy domain: the onset of deconfinement. The STAR collaboration proposes an energy scan in the Relativistic Heavy Ion Collider (RHIC) at BNL. The ongoing program of the NA61/SHINE experiment consists of a two-dimensional energy-system size scan in nuclear and elementary collisions. The goal of both programs is to study the properties of the onset of deconfinement and to eventually discover the conjectured critical point of strongly interacting matter. A comparison of the strengths and limitations reveals the complementarity of the two programs.     

Physico-Chemical Properties of Magnetic Dicationic Ionic Liquids with Tetrahaloferrate Anions

A series of imidazolium-based symmetrical and asymmetrical dicationic ionic liquids (DcILs) with alkyl spacers of different length and with [FeCl₃Br]⁻ as counter ion have been synthesized. The synthesized DcILs are characterized by using FTIR and Raman spectroscopy as well as mass spectrometry, along with single-crystal XRD analysis. Physicochemical properties such as solubility, thermal stability and magnetic susceptibility are also measured. These compounds show low melting points, good solubility in water and organic solvents, thermal stability, and paramagnetism. The products of molar susceptibility and temperature (χ_mol⋅T) for the synthesized DcILs have been found between 4.05 to 4.79 emu mol⁻¹ K Oe⁻¹ and effective magnetic moment values have also been determined to be compared to that expected from the spin-only approximation.     

Mechanistic insights into NO3* induced self-terminating radical oxygenations, part 1: a computational study on NO3* and its addition to alkynes

The geometry of the nitrate radical, NO3*, for which unrestricted Hartree-Fock (HF) breaks spatial symmetry of the wave function, was optimized using hybrid density functionals that include varying fractions of Hartree-Fock exchange. Although symmetry breaking was not observed even when the functional with the highest HF exchange (BHandHLYP) was used, only B3LYP correctly describes the D(3h) symmetry of NO3* as ground-state structure with the lowest energy. Further, geometries and energies of the stationary points in the addition of NO3* to ethyne, propyne, and 2-butyne were calculated using ab initio and density functional methods. The reactions proceed through Z-configurated transition states leading to Z-configurated vinyl radicals with the activation barrier decreasing with increasing methyl substitution at the C[triple bond]C by ca. 11 kJ mol(-1) per methyl group. It was found that the results obtained at the BHandHLYP/cc-pVDZ level of theory are in good agreement with the data from single-point QCISD and CCSD(T) calculations.     

Approaches to open fullerenes: synthesis and thermal stability of cis-1 bis(isobenzofuran) Diels-Alder adducts of C60

In a quest to form wider openings within the cage of the fullerene C60 through controlled bond-breaking reactions, we have examined the double saturation of adjacent C=C bonds within a six-membered ring of C60. We have investigated the double Diels-Alder cycloaddition of two tethered isobenzofurans to the fullerene C60. We obtained cis-1 adducts in good yields after reacting the methylene- or quinoxaline-tethered bis(isobenzofuran) precursors 2a-k with parent 3,6-dihydro-1,2,4,5-tetrazine (3b). The X-ray structure of the methylene-tethered bis(isobenzofuran)-C60 adduct 4b has been obtained; four-eclipsed substituents are held rigidly by the bicyclic addends. The cis-1 bis(isobenzofuran) bisadducts 4b and 4e-j are kinetically far more stable toward thermal retro-Diels-Alder fragmentation than are mono(isobenzofuran) adducts of C60, in solution and in the solid state as determined by 1H NMR spectroscopy or thermogravimetric analysis. A methodology for the reversible solubilization of other fullerene derivatives based on this work is also presented.     

J-aggregation of a water-soluble tetracationic porphyrin in mixed LB films with a calix[8]arene carboxylic acid derivative

The molecular organization of a mixed film, containing a water-soluble tetracationic porphyrin (TMPyP) and a p-tert-butyl calix[8]arene octacarboxylic acid derivative (C8A), at the air-water interface and on a solid support (LB film), has been investigated. Although the TMPyP aggregation was not detected at the air-water interface, TMPyP J-aggregates have been found in the LB films (Y-type). Unlike tetraanionic porphyrins, for example TSPP, the TMPyP J-aggregates are not induced by a zwitterion formation. The TMPyP J-aggregation is a result of a "double comb" configuration, where porphyrins from opposite layers are interwoven in a linear infinite J-aggregate. Our results confirm that TMPyP molecules tend to self-aggregate strongly, provided the electrostatic repulsions of their peripheral groups are cancelled by the anionic groups of the C8A matrix.     

Stable cellulose nanospheres for cellular uptake

Pure, perfectly spherical cellulose nanoparticles with sizes of ≈80-260 nm can be prepared by dialysis starting from trimethylsilylcellulose (TMSC). The aqueous suspensions obtained are storable for several months. Subsequent covalent labeling of the cellulose nanoparticles with FITC has no influence on particle size, shape, and stability. The particles can be sterilized and suspended in biological media without structural changes. Incorporation of FITC-labeled cellulose nanoparticles into living human fibroblasts is studied using confocal LSM. In contrast to cellulose nanocrystals, fast cellular uptake is found for the nanospheres without transfection reagents or attachment of a receptor molecule. This suggests an influence of the geometry of biocompatible nanomaterials on endocytosis.     

Syntheses, structures and intermolecular interactions of tetraorganoammonium, -phosphonium and -stibonium dimethyl- and diphenyltetrahaloantimonates

The syntheses and spectroscopic (NMR, MS) investigations of the antimonates [Ph₄P]⁺[Me₂SbCl₄]⁻ (1), [Me₄Sb]⁺[Me₂SbCl₄]⁻ (2), [Et₄N]⁺[Ph₂SbCl₄]⁻ (3), [Bu₄N]⁺[Ph₂SbCl₄]⁻ (4), [Me₄Sb]⁺[Ph₂SbCl₄]⁻ (5), [Et₃MeSb]⁺[Ph₂SbCl₄]⁻ (6), [Et₄N]⁺[Ph₂SbF₄]⁻ (7) and [Et₄N]⁺[Ph₂SbBr₄]⁻ (8) are reported. Halogen scrambling reactions of Et₄NBr or Ph₄EBr (E = P, Sb) with R₂SbCl₃ (R = Me, Ph) produce mixtures of compounds from which crystals of [Et₄N]⁺[Ph₂SbBr_1.24Cl_2.76]⁻ (9), [Et₄N]⁺[Ph₂SbBr_2.92Cl_1.08]⁻ (10) or [Ph₄Sb]⁺[Me₂SbCl₄]⁻ (11) were isolated. The crystal and molecular structures of 1 and 3-11 are reported.     

161Dy Time‐Domain Synchrotron Mössbauer Spectroscopy for Investigating Single‐Molecule Magnets Incorporating Dy Ions

Time‐domain synchrotron Mössbauer spectroscopy (SMS) based on the Mössbauer effect of ¹⁶¹Dy has been used to investigate the magnetic properties of a Dy^III‐based single‐molecule magnet (SMM). The magnetic hyperfine field of [Dy(Cy₃PO)₂(H₂O)₅]Br₃?2 (Cy₃PO)?2 H₂O?2 EtOH is with B₀=582.3(5) T significantly larger than that of the free‐ion Dy^III with a ⁶H_15/2 ground state. This difference is attributed to the influence of the coordinating ligands on the Fermi contact interaction between the s and 4f electrons of the Dy^III ion. This study demonstrates that ¹⁶¹Dy SMS is an effective local probe of the influence of the coordinating ligands on the magnetic structure of Dy‐containing compounds.     

XUV free-electron laser desorption of NO from graphite (0001)

We report results of femtosecond laser induced desorption of NO from highly oriented pyrolytic graphite using XUV photon energies of hν = 38 eV and hν = 57 eV. Femtosecond pulses with a pulse energy of up to 40 μJ and about 30 fs duration generated at FLASH are applied. The desorbed molecules are detected with rovibrational state selectivity by (1 + 1) REMPI in the A(2)Σ(+) ← X(2)Π γ-bands around λ = 226 nm. A nonlinear desorption yield of neutral NO is observed with an exponent of m = 1.4 ± 0.2. At a fluence of about 4 mJ/cm(2) a desorption cross section of σ(1) = (1.1 ± 0.4) × 10(-17) cm(2) is observed, accompanied with a lower one of σ(2) = (2.6 ± 0.3) × 10(-19) cm(2) observable at higher total fluence. A nonthermal rovibrational population distribution is observed with an average rotational energy of = 38.6 meV (311 cm(-1)), a vibrational energy of = 136 meV (1097 cm(-1)) and an electronic energy of = 3.9 meV (31 cm(-1)).