Darstellung von (s) -2,5-dimethyl-2-isopropyl-2,3-dihydrofuran,einem der beiden enantiomeren des sexuallockstoffs des werftkäfers hylecoetus dermestoides L.

The optical pure title compound II is synthesized by conversion of the branched chain sugar methyl-2-C-acetyl-4,6-O-benzylidene-3-deoxy-α-d-ribo-hexopyranose (I) which is available from d-glucose. 2,5-Di-methyl-2-isopropyl-2,3-dihydrofuran is found for the first time as a natural product and represents a new type of insect pheromones.     

Some new equivalences of Anderson's paving conjectures

Anderson's paving conjectures are known to be equivalent to the Kadison-Singer problem. We prove some new equivalences of Anderson's conjectures that require the paving of smaller sets of matrices. We prove that if the strictly upper triangular operators are paveable, then every 0 diagonal operator is paveable. This result follows from a new paving condition for positive operators. In addition, we prove that if the upper triangular Toeplitz operators are paveable, then all Toeplitz operators are paveable.

     

Chemical Bonds and Spin State Splittings in Spin Crossover Complexes. A DFT and QTAIM Analysis

Summary. Density functional theory (DFT) calculations have been performed for the high-spin (HS) and low-spin (LS) isomers of a series of iron(II) spin crossover complexes with nitrogen ligands. The calculated charge densities have been analyzed in the framework of the quantum theory of atoms in molecules (QTAIM). For a number of iron(II) complexes with substituted tris(pyrazolyl) ligands the energy difference between HS and LS isomers, the spin state splitting, has been decomposed into atomic contributions in order to rationalize changes of the spin state splitting due to substituent effects.     

Every completely polynomially bounded operator is similar to a contraction

It is proved that a bounded operator on a Hilbert space is similar to a contraction if and only if it is completely polynomially bounded. This gives a partial answer to Problem 6 of Halmos (Bull. Amer. Math. Soc.76 (1970). 877–933). The set of completely bounded maps between C¹-algebras is studied to obtain some structure, representation, and extension theorems for this class of maps. These allow a characterization of the completely bounded representations, on a Hilbert space, of any subalgebra of a C¹-algebra to be obtained. The result in the title follows by applying this characterization to the disk algebra.     

Adding Remnant Magnetization and Anisotropic Exchange to Propeller‐like Single‐Molecule Magnets through Chemical Design

The selective replacement of the central iron(III) ion with vanadium(III) in a tetrairon(III) propeller‐shaped single‐molecule magnet has allowed us to increase the ground spin state from S=5 to S=13/2. As a consequence of the pronounced anisotropy of vanadium(III), the blocking temperature for the magnetization has doubled. Moreover, a significant remnant magnetization, practically absent in the parent homometallic molecule, has been achieved owing to the suppression of zero‐field tunneling of the magnetization for the half‐integer molecular spin. Interestingly, the contribution of vanadium(III) to the magnetic anisotropy barrier occurs through the anisotropic exchange interaction with iron(III) spins and not through single ion anisotropy as in most single‐molecule magnets.     

Rational enantioselective design of chiral heterobimetallic single-chain magnets: synthesis, crystal structures and magnetic properties of oxamato-bridged M(II)Cu(II) chains (M=Mn, Co)

A new series of neutral oxamato-bridged M(II)Cu(II) chiral chains of general formula [MCuL(x)(S)(m)(H(2)O)(n)]·aS·bH(2)O [L(1)=(M)-1,1'-binaphthalene-2,2'-bis(oxamate) with M=Mn (1a) and Co (1b); L(2)=(P)-1,1'-binaphthalene-2,2'-bis(oxamate) with M=Mn (2a) and Co (2b)] and the analogous racemic chains of formula [MCuL(3)(S)(m)(H(2)O)(n)]·aS·bH(2)O [L(3)=1,1'-binaphthalene-2,2'-bis(oxamate) with M=Mn (3a) and Co (3b)] have been prepared by reaction of the corresponding dianionic oxamatocopper(II) complex [Cu(L(x))](2-) with Mn(2+) or Co(2+) cations in either dimethylformamide (DMF) or dimethyl sulfoxide (DMSO). Solid circular dichroism (CD) spectra of the bimetallic chain compounds were recorded to establish their chiral and enantiomeric nature. They exhibit maximum positive and negative Cotton effects, each pair of enantiomeric chains being non-superimposable mirror images. The crystal structures of the Mn(II)Cu(II) (1a-3a) and the Co(II)Cu(II) (1b and 2b) chain compounds were solved by single-crystal X-ray diffraction methods. Our attempts to obtain X-ray quality crystals of 3b were unsuccessful. The values of the shortest interchain Mn···Mn and Co···Co distances are indicative of a good isolation of neighbouring chains in the crystal lattice, which is caused by the bulky aromatic ligand. Although all the Mn(II)Cu(II) and Co(II)Cu(II) chains exhibit ferrimagnetic behaviour (-J(MnCu)=18.9-26.6 cm(-1) and -J(CoCu)=19.5-32.5 cm(-1)), only the enantiopure Co(II)Cu(II) chains (1b and 2b) show slow magnetic relaxation at low temperatures (T(B)=0.6-1.8 K), which is a characteristic of single-chain magnets (SCMs) and is related to the magnetic anisotropy of the high-spin Co(II) ion. Analysis of the SCM behaviour of 1b and 2b, based on Glauber's theory for an Ising one-dimensional system, shows a thermally activated mechanism for the magnetic relaxation (Arrhenius law dependence). The energy barriers (E(a)) to reverse the magnetisation direction are 8.2 (1b) and 8.1cm(-1) (2b), whereas the pre-exponential factor (τ(0)) is 1.9×10(-8) (1b) and 6.0×10(-9) s (2b). Interestingly, the racemic Co(II)Cu(II) chain analogue, 3b, showed no evidence of SCM behaviour.