Copper-Catalyzed Electrophilic Thiolation of Organozinc Halides by Using N-Thiophthalimides Leading to Polyfunctional Thioethers

(Hetero)aryl, benzylic, and alkyl zinc halides were thiolated with N-thiophthalimides at 25 °C within 1 h in the presence of 5–10 % Cu(OAc)₂ ⋅ H₂O to furnish the corresponding polyfunctionalized thioethers in good yields. This electrophilic thiolation was extended to the introduction of trifluoromethylthio (SCF₃), thiocyanate (SCN), and selenophenyl (SePh) groups. The utility of this method was shown in a seven-step synthesis of a potent cathepsin D inhibitor in 34 % overall yield.     

Isotope shifts in Sm II and changes in mean-square nuclear charge radii of the stable even Sm isotopes

Isotope shifts have been measured in Sm II from which the shifts between pure configurations 4f ⁶ s and 4f ⁶5d can be determined. The specific mass shift for such a “transition” was estimated to be (?1±2)mK for a change of two neutrons. The values derived for the change in the nuclear charge distribution,δ〈r ²〉, are in good agreement with the results obtained from isotope shift measurements in Sm I (H. Brand et al.: J. Phys. B11, L99, 1978). The weighted mean values representing the best information onδ〈r ²〉 presently available are in fm²: [144, 148] 0.488(23); [148, 150] 0.285(14); [150, 152] 0.400(19); [152, 154] 0.217(11).     

Interplay of charge, spin, orbital and lattice correlations in colossal magnetoresistance manganites

We derive a realistic microscopic model for doped colossal magnetoresistance manganites, which includes the dynamics of charge, spin, orbital and lattice degrees of freedom on a quantum mechanical level. The model respects the SU(2) spin symmetry and the full multiplet structure of the manganese ions within the cubic lattice. Concentrating on the hole doped domain ( 0≤x≤0.5) we study the influence of the electron-lattice interaction on spin and orbital correlations by means of exact diagonalisation techniques. We find that the lattice can cause a considerable suppression of the coupling between spin and orbital degrees of freedom and show how changes in the magnetic correlations are reflected in dynamic phonon correlations. In addition, our calculation gives detailed insights into orbital correlations and demonstrates the possibility of complex orbital states. Received 4 September 2002 / Received in final form 8 November 2002 Published online 31 December 2002     

Regularization in Sobolev Spaces with Fractional Order

We study the minimization of a quadratic functional where the Tichonov regularization term is an H ^s -norm with a fractional s > 0. Moreover, pointwise bounds for the unknown solution are given. A multilevel approach as an equivalent norm concept is introduced. We show higher regularity of the solution of the variational inequality. This regularity is used to show the existence of regular Lagrange multipliers in function space. The theory is illustrated by two applications: a Dirichlet boundary control problem and a parameter identification problem.     

The degenerate C. Neumann system I: symmetry reduction and convexity

The C. Neumann system describes a particle on the sphere S ⁿ under the influence of a potential that is a quadratic form. We study the case that the quadratic form has ℓ +1 distinct eigenvalues with multiplicity. Each group of m _σ equal eigenvalues gives rise to an O(m _σ )-symmetry in configuration space. The combined symmetry group G is a direct product of ℓ + 1 such factors, and its cotangent lift has an Ad*-equivariant momentum mapping. Regular reduction leads to the Rosochatius system on S ^ℓ , which has the same form as the Neumann system albeit for an additional effective potential.     

Magnetic phases in Mn<Subscript>1</Subscript>_<Subscript>x</Subscript>Fe<Subscript>x</Subscript>WO<Subscript>4</Subscript> studied by neutron powder diffraction

The magnetic structures of Mn_1-xFe_xWO₄ with x = 0.0, 0.16, 0.21, 0.225, 0.232, 0.24, 0.27, 0.29, and 1.0 were refined from neutron powder diffraction data. The magnetic phase diagram could be completed in the coexistence range of different magnetic structures up to x = 0.29. For the magnetic state at 1.5 K a commensurate antiferromagnetic structure with a propagation vector = (±1/4, 1/2, 1/2) was found for x ⩽ 0.22 while the magnetic spins order with = (1/2, 0, 0) for x ≥ 0.22. In the latter phase, additionally, weak magnetic reflections indexed to an incommensurate ordering with = (- 0.214, 1/2, 0.457) occur in the diffraction pattern up to x = 0.29 indicating the occurence of a reentrant phase. For 0.12 ⩽ x ⩽ 0.29 the low temperature phases are separated from a magnetic high temperature phase showing only magnetic reflections indexed to a spin arrangement with = (1/2, 0, 0). The magnetic phase diagram is discussed qualitatively considering random superexchange between the statistically distributed Mn²⁺- and Fe²⁺-ions in the coexistence range 0.12 ⩽ x ⩽ 0.29 of different magnetic structures related to those of pure MnWO₄ and FeWO₄. Received 9 October 2002 Published online 14 March 2003