Excavations in molecular crystals

Single crystals built from porous molecular networks can react with agents that penetrate the crystals, cleave fragments from the network, and thereby increase the volume available for guests, all without loss of crystallinity.     

A difluorosulfide as a Freon-free source of phosphonodifluoromethyl carbanion

The synthesis of difluoromethylphosphonates is becoming difficult due to environmental protective laws restricting the use of HCFCs and CFCs as starting chemicals. To circumvent this limitation, we report the preparation of a thioether as a new source of the lithiodifluoromethylphosphonate. This methodology avoiding the use of HCFCs involves a selective fluorination of sulfide followed by a thiaphilic addition of an organometallic reagent, which offers an alternative route to obtain phosphonodifluoromethyl carbanion. A contrasted reactivity, due to a medium effect, was also noted which allows addition of a wide range of electrophiles including nitroalkenes and DMF to thioethers.     

Molecular tectonics. Use of the hydrogen bonding of boronic acids to direct supramolecular construction

Tetraboronic acids 1 and 2 have four -B(OH)(2) groups oriented tetrahedrally by cores derived from tetraphenylmethane and tetraphenylsilane. Crystallization produces isostructural diamondoid networks held together by hydrogen bonding of the -B(OH)(2) groups, in accord with the tendency of simple arylboronic acids to form cyclic hydrogen-bonded dimers in the solid state. Five-fold interpenetration of the networks is observed, but 60% and 64% of the volumes of crystals of tetraboronic acids 1 and 2, respectively, remain available for the inclusion of disordered guests. Guests occupy two types of interconnected channels aligned with the a and b axes; those in crystals of tetraphenylmethane 1 measure approximately 5.9 x 5.9 A(2) and 5.2 x 8.6 A(2) in cross section at the narrowest points, whereas those in crystals of tetraphenylsilane 2 are approximately 6.4 x 6.4 A(2) and 6.4 x 9.0 A(2). These channels provide access to the interior and permit guests to be exchanged quantitatively without loss of crystallinity. Because the Si-C bonds at the core of tetraboronic acid 2 are longer (1.889(3) A) than the C-C bonds at the core of tetraboronic acid 1 (1.519(6) A), the resulting network is expanded rationally. By associating to form robust isostructural networks with predictable architectures and properties of porosity, compounds 1 and 2 underscore the usefulness of molecular tectonics as a strategy for making ordered materials.     

Size minimization and approximating problems

We consider Plateau type variational problems related to the size minimization of rectifiable currents. We realize the limit of a size minimizing sequence as a stationary varifold and a minimal set. Other examples of functionals to be minimized include the integral over the underlying carrying set of a power q of the multiplicity function, with .Because minimizing sequences may have unbounded mass we make use of a more general object called a rectifiable scan for describing the limit. This concept is motivated by the possibility of recovering a flat chain from a sufficiently large collection of its slices. In case the given boundary is smooth and compact, the limiting scan has finite mass and corresponds to a rectifiable current.Received: 11 February 2002, Accepted: 16 June 2002, Published online: 17 December 2002Mathematics Subject Classification (2000): 49Q15, 28A75Thierry De Pauw: The research of the first author was supported by a Marie Curie fellowship of the European Community program Human Potential under contract HMPF-CT-2001-01235Robert Hardt: The research of the second author was partially supported by NSF grant DMS-0072486     

Magnetic anisotropy in icosahedral cobalt clusters

Magnetic anisotropy has been measured in multiply twinned, icosahedral cobalt clusters. It is found that the low-temperature magnetization of deposited cluster layers is well defined with the Stoner–Wohlfarth model by averaging over clusters with a range of anisotropy energy. Anisotropy energy calculation based on Néel's pair model shows that the icosahedral structure and the layer-by-layer growth of the clusters induce oscillations of the magnetic anisotropy as a function of the filling of the outer surface of the particle. The magnetization measurement at room temperature indicates a weakly correlated cluster glass, as deduced from the approach to saturation that is well described with 2D random anisotropy model.     

Sensitivity indices for multivariate outputs

We define and study a generalization of Sobol sensitivity indices for the case of a vector output.     

2,2′-Bipyridine-3,3′-dicarboxylic carbohydrate esters and amides. Synthesis and preliminary evaluation as ligands in Cu(II)-catalysed enantioselective electrophilic fluorination

A series of 10 new carbohydrate-substituted bipyridines were prepared from 2,2′-bipyridine-3,3′-dicarboxylic acid, itself easily available from ortho-phenanthroline. As a preliminary exploration of their use as chiral ligands, Cu(II)-catalysed asymmetric electrophilic fluorination of model β-ketoesters using these simple and easily accessible chiral bipyridines was studied. Only modest enantioselectivity was observed in this reaction, although the ee was in a similar range as those provided by known and more elaborate ligands.