Three-body problem in a dilute bose-Einstein condensate

We derive the explicit three-body contact potential for a dilute condensed Bose gas from microscopic theory. The three-body coupling constant exhibits the general form predicted by Wu [Phys. Rev. 115, 1390 (1959)]] and is determined in terms of the amplitudes of two- and three-body collisions in vacuum. In the present form, the coupling constant becomes accessible to quantitative studies which should provide the crucial link between few-body collisions and the stability of condensates with attractive two-body forces.     

13C NMR spectra of diazastilbenes. I—trans-styryldiazines

The ¹³C NMR spectra of all trans-styryldiazines, methyldiazines and trans-styrylpyridines have been fully assigned. Empirical shift increments were obtained for the chemical shifts of the carbon atoms; these are discussed in the light of theoretical considerations.     

From uncharged to decacationic molecules: syntheses and spectroscopic properties of heteroarenium-substituted pyridines

Nucleophilic substitutions on pentachloropyridine with 4-(dimethylamino)pyridine, 4-aminopyridine, and 4-(pyrrolidin-1-yl)pyridine give mono-, tri- and pentacationic pyridine-hetarenium salts. The mono-, tri- and pentacationic 4-aminopyridine derivatives can be deprotonated to neutral compounds in solution, or protonated to di-, hexa- and decacationic pyridine derivatives, respectively. Successive substitutions with different heteroaromatic nucleophiles give pyridines with two distinct types of heteroarenium substituents.     

Highly stretched single polymers: atomic-force-microscope experiments versus ab-initio theory

Experimental single-molecule stretching curves for three backbone architectures (single-stranded DNA, various types of peptides, polyvinylamine) are quantitatively compared with corresponding quantum-chemical (zero-temperature) ab-initio calculations in the high-force range of up to two nanonewtons. For high forces, quantitative agreement is obtained with the contour length of the polymers as the only fitting parameter. For smaller forces, the effects of chain fluctuations are accounted for by using recent theoretical results for the stretching response of a freely-rotating-chain model.     

Spontaneous dissociation of long-range Feshbach molecules

We study the spontaneous dissociation of diatomic molecules produced in cold atomic gases via magnetically tunable Feshbach resonances. We provide a universal formula for the lifetime of these molecules that relates their decay to the scattering length and the loss rate constant for inelastic spin relaxation. Our universal treatment as well as our exact coupled channels calculations for 85Rb dimers predict a suppression of the decay over several orders of magnitude when the scattering length is increased. Our predictions are in good agreement with recent measurements of the lifetime of 85Rb(2).     

Polarity matching of radical trapping: high yielding 3-exo and 4-exo cyclizations

A catalyzed synthesis of cyclopropanes and cyclobutanes via radical chemistry is described. The method that generally proceeds in high yields uses epoxides as radical precursors and titanocene(III) complexes as the electron transfer catalysts (see scheme). The key to the success of the transformation is constituted by the chemoselectivity of radical reduction. Electrophilic enol radicals generated through cyclization are reduced rapidly whereas their precursors, nucleophilic alkyl radicals, remain unaffected.     

Close-packed floating clusters: granular hydrodynamics beyond the freezing point?

Monodisperse granular flows often develop regions with hexagonal close packing of particles. We investigate this effect in a system of inelastic hard spheres driven from below by a "thermal" plate. Molecular dynamics simulations show, in a wide range of parameters, a close-packed cluster supported by a low-density region. Surprisingly, the steady-state density profile, including the close-packed cluster part, is well described by a variant of Navier-Stokes granular hydrodynamics (NSGH). We suggest a simple explanation for the success of NSGH beyond the freezing point.     

Enantioselective [6pi]-photocyclization reaction of an acrylanilide mediated by a chiral host. Interplay between enantioselective ring closure and enantioselective protonation

The [6pi]-photocyclization of the anilides 1a and 5 was studied in the absence and in the presence of the enantiomerically pure chiral lactam 4. The relative configuration of the products was unambiguously established by single-crystal X-ray crystallography and by NMR spectroscopy. A significant enantiomeric excess was observed upon reaction of compound 1a to its photocyclization products at -55 degrees C employing lactam 4 as a chiral complexing agent in toluene as the solvent (66% yield). The trans product ent-3a was obtained in 57% ee, and the minor diastereoisomer (trans/cis = 73/27), cis product ent-2a, was obtained in 30% ee. DFT calculations were conducted modeling the complexation of intermediates 8 and ent-8 to host 4. In agreement with steric arguments concerning the conrotatory ring closure of 1a, the formation of ent-8 is favored leading to the more stable complex 4.ent-8 as compared to 4.8. Whereas the enantioselectivity in the photocyclization to trans compound ent-3a increased upon reduction in the reaction temperature, the enantiomeric excess in the formation of cis compound ent-2a went through a maximum at -15 degrees C (45% ee) and decreased at lower temperatures. Deuteration experiments conducted with the pentadeuterated analogue of 1a, d(5)-1a, revealed that the protonation of the intermediates 8 and ent-8 is influenced by chiral amide 4. In the formation of ent-3a/3a, both the enantioselective ring closure and the enantioselective protonation by amide 4 favor the observed (6aS,10aS)-configuration of the major enantiomer ent-3a. In the formation of ent-2a/2a, the enantioselective ring closure (and the subsequent diastereoselective protonation) favors the (6aR,10aS)-configuration that is found in compound 2a. Contrary to that, the enantioselective protonation by amide 4 shows a preference for ent-2a with the (6aS,10aR)-configuration.