A general method for convergent synthesis of functionalized exo-glycals based on halogenation and Suzuki cross-coupling of 1-exo-methylene sugars

Functionalized exo-glycals can be readily obtained by palladium catalyzed Suzuki cross-coupling of halo-exo-glycals with boronic acids.     

Molecular compasses and gyroscopes. II. Synthesis and characterization of molecular rotors with axially substituted bis[2-(9-triptycyl)ethynyl]arenes

We have developed a simple convergent procedure for the synthesis of molecular rotors consisting of a central aromatic group coupled with two axially positioned ethynyltriptycenes. Molecular rotors with 1,4-phenylene (1), 1,4'-1,1'-biphenylene (2), 9,10-anthracenylene (3), and 2,7-pyrenylene (4) groups were prepared by Pd(0)-catalyzed coupling of ethynyl triptycenes with the corresponding dibromoarenes. Although compounds 1-4 were not expected to have free rotation in the solid state, the rotational potentials of 1 and 3 were analyzed by semiempirical methods and the crystal packing of 1 was analyzed to design the structures most likely to yield a functional rotor in the solid state. Semiempirical PM3 calculations predict compounds 1, 2, and 4 to have frictionless internal rotation even at temperatures as low as 25 K, while compound 3 is expected to have a barrier of ca. 4 kcal/mol.     

Energy transfer in the nanostar: the role of coulombic coupling and dynamics

We present a theoretical investigation of energy transfer in the phenylene ethynelene dendrimer known as the nanostar. Data from extensive molecular dynamics simulations are used to model the dynamical effects caused by torsional motion of the phenyl groups. We compare rate constants for energy transfer between the two-ring chromophore and the three-ring chromophore obtained via the F?rster model, the ideal dipole approximation (IDA), and the transition density cube (TDC) method, which has as its limit an exact representation of the Coulombic coupling. We find that the rate constants obtained with the TDC are extremely sensitive to the phenyl group rotation, whereas the constants computed with the F?rster model and the IDA are not. The implications of these results for the interpretation of recent pump-probe experiments on the nanostar are discussed in detail. Finally, we predict the temperature dependence of the rate constant for energy transfer.     

Novel oxa-di-pi-methane and Norrish type I reactions in the S2 (pi,pi*) excited state of a series of beta,gamma-unsaturated ketones

[reaction: see text] Beta,gamma-unsaturated methyl ketones with electron-withdrawing groups at the gamma-position of the ene moiety undergo ODPM rearrangements and Norrish type I reactions on direct irradiation at 254 nm. The results are consistent with the involvement of alkene S(2) (pi,pi*) as reactive excited states in these processes.     

Equivalence between entanglement and the optimal fidelity of continuous variable teleportation

We devise the optimal form of Gaussian resource states enabling continuous-variable teleportation with maximal fidelity. We show that a nonclassical optimal fidelity of N-user teleportation networks is necessary and sufficient for N-party entangled Gaussian resources, yielding an estimator of multipartite entanglement. The entanglement of teleportation is equivalent to the entanglement of formation in a two-user protocol, and to the localizable entanglement in a multiuser one. Finally, we show that the continuous-variable tangle, quantifying entanglement sharing in three-mode Gaussian states, is defined operationally in terms of the optimal fidelity of a tripartite teleportation network.     

On the Path of a Quasi-static Crack in Mode III

A method for finding the path of a quasi-static crack growing in a brittle body is presented. The propagation process is modelled by a sequence of discrete steps optimizing the elastic energy released. An explicit relationship between the optimal growing direction and the parameters defining the local elastic field around the tip is obtained for an anti-plane field. This allows to describe a simple algorithm to compute the crack path. Mathematics Subject Classifications (2000) 74R05, 74B05, 74G70.Gerardo E. Oleaga: Supported by EU-Project Front Singularities University of Leipzig and the Max Planck Institute MIS. Partial support was also provided by the Spanish DGES project BFM2000-0605.     

Determination of continuous variable entanglement by purity measurements

We classify the entanglement of two-mode Gaussian states according to their degree of total and partial mixedness. We derive exact bounds that determine maximally and minimally entangled states for fixed global and marginal purities. This characterization allows for an experimentally reliable estimate of continuous variable entanglement based on measurements of purity.