Asymptotic observables on scattering states

In quantum mechanical potential scattering theory we use selected observables to describe the asymptotic properties of scattering states for long times. E.g., we show for the position and momentum operators that for Ωε?^cont(H), $$\left( {m\frac{x}{t} - p} \right)e^{ - iHt} \Psi \to 0,$$ and that the set of outgoing states is absorbing. This is obtained easily without any detailed analysis of the interacting time evolution. The class of forces includes highly singular and very long range potentials. The results may serve as an intermediate step in a proof of asymptotic completeness; as a particular application we present a simple proof of completeness for Coulomb systems.     

New dimension in nano-imaging: breaking through the diffraction limit with scanning near-field optical microscopy

In recent years scanning near-field optical microscopy (SNOM) has developed into a powerful surface analytical technique for observing specimens with lateral resolution equal to or even better than 100 nm. A large number of applications, from material science to biology, have been reported. In this paper, two different kinds of near-field optical microscopy, aperture and scattering-type SNOM, are reviewed together with recent studies in surface analysis and biology. Here, near-field optical techniques are discussed in comparison with related methods, such as scanning probe and standard optical microscopy, with respect to their specific advantages and fields of application.     

Combinatorial diversity of fission yeast SCF ubiquitin ligases by homo- and heterooligomeric assemblies of the F-box proteins Pop1p and Pop2p

Background  

SCF ubiquitin ligases share the core subunits cullin 1, SKP1, and HRT1/RBX1/ROC1, which associate with different F-box proteins. F-box proteins bind substrates following their phosphorylation upon stimulation of various signaling pathways. Ubiquitin-mediated destruction of the fission yeast cyclin-dependent kinase inhibitor Rum1p depends on two heterooligomerizing F-box proteins, Pop1p and Pop2p. Both proteins interact with the cullin Pcu1p when overexpressed, but it is unknown whether this reflects their co-assembly into bona fide SCF complexes.     

Fourfold tetraurea calix[4]arenes--potential cores for the formation of self-assembled dendrimers

Wide rim tetraurea calix[4]arenes monofunctionalized at the narrow rim by COOH or NH2 have been synthesized in five steps from t-butylcalix[4]arene tripropylether. Their covalent linkage via the narrow rim to a central calix[4]arene fixed in the 1,3-alternate conformation led to pentacalix[4]arenes 9 bearing four tetraurea derivatives in the cone conformation in a flexible tetrahedral arrangement. Their self-assembly via the formation of hydrogen bonded dimeric capsules has been studied under different conditions. A fourfold heterodimerisation of tetrakis-tetraurea derivatives of type 9 with tetratosylurea 10 has been confirmed by 1H NMR-spectroscopy and dynamic light scattering.     

Cyclic esters of aliphatic diacids with pyrocatechol and hydroquinone

Cyclic esters of adipic acid, suberic acid and sebacic acid were prepared by reaction of the acid dichlorides and pyrocatechol or hydroquinone in benzene under high dilution conditions. While only the cyclic dimers could be obtained from hydroquinone, pyrocatechol formed cyclic monomers as well as cyclic dimers (and also a cyclic dimer with succinic acid). The structure of all compounds was confirmed by¹H-NMR- and mass spectra. The crystal structures of the pyrocatechol esters were determined by single crystal X-ray analysis.

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Cyclische Ester aliphatischer Dicarbonsäuren mit Brenzcatechin und Hydrochinon

Zusammenfassung Es wurden cyclische Ester von Adipinsäure, Korksäure und Sebacinsäure durch Reaktion der entsprechenden Säure-Dichloride mit Brenzcatechin oder Hydrochinon bei hoher Verdünnung hergestellt. Während mit Hydrochinon lediglich die cyclischen Dimeren erhalten werden konnten, wurden mit Brenzcatechin sowohl cyclische Monomere als auch cyclische Dimere erhalten (ebenfalls das cyclische Dimer mit Bernsteinsäure). Die Strukturen wurden mittels¹H-NMR und Massenspektren gesichert. Die Kristallstrukturen der Brenzcatechin-Ester wurden mittels Röntgenstrukturanalyse bestimmt.

     

1,1,2,2-Tetraethynylethanes: Synthons for Tetraethynylethenes and Modules for Acetylenic Molecular Scaffolding

The synthesis of functionalized 1,1,2,2-tetraethynylethanes (= 3,4-diethynylhexa-1,5-diynes) as synthons for tetraethynylethenes (3,4-diethynylhex-3-ene-1,5-diynes) and as building blocks for three-dimensional acetylenic molecular scaffolding targeting the synthesis of the molecular carbon belts 3 and 4 is reported (Scheme 1). Reaction of diethyl oxalate and (trialkylsilyl)ethynyl Grignard reagents afforded the silyl-protected 3,4-diethynylhexa-1,5-diyne-3,4- diols 7 and 8 which were transformed in high yields into the cyclic carbonate 9 and the cyclic orthoesters 10–13 , respectively (Scheme 2). The solid-state structures of 9 and 10 were elucidated by X-ray crystallography. The alkyne protecting groups in 9, 10 , and 12 were smoothly removed to give the free tetraynes 14–16 as relatively stable oils in nearly quantitative yields (Scheme 3). Orthoesters 15 and 16 underwent Pd-catalyzed cross-coupling with iodobenzene to give the tetraphenyl derivatives 17 and 18 (Scheme 4). Thermal acid-catalyzed elimination of the orthoester moieties in 12 and 13 produced the silyl-protected tetraethynylethenes 19 and 20 and concluded a novel, simple three-step synthesis of these fully two-dimensionally conjugated π-chromophores (Scheme 5).     

Stereoisomeric flavor compounds,part LVIII: The use of heptakis(2,3-di-O-methyl-6-O-tert-butyldimethylsilyl)-β-cyclodextrin as a chiral stationary phase in flavor analysis

The characteristics of the new chiral stationary phase heptakis(2,3-di-O-methyl-6-O-tert-butyldimethylsilyl)-β-cyclodextrin are outlined and compared with permethyl- and perethyl-β-cyclodextrins.     

Coordination Chemistry of Acrylamide 4. Crystal Structures and IR Spectroscopic Properties of Acrylamide Complexes with CoII,NiII, and ZnII nitrates

Acrylamide complexes of metal nitrates: [M(O‐OC(NH₂)CHCH₂)_n(H₂O)_m][NO₃]₂ (M = Co( 1 ), Ni( 2 ) (n = 6 and m = 0) and Zn( 3 ) (n = 4 and m = 2)) have been determined by using single crystal X‐ray diffraction analysis. All complexes crystallize in the triclinic space group . The structures of 1 and 2 represent octahedral species [M(AAm)₆]²⁺ (AAm = O‐OC(NH₂)CHCH₂ and M = Co or Ni) and uncoordinated nitrate ions. The structure of 3 involves the octahedral cation [Zn(AAm)₄(H₂O)₂]²⁺ in which the Zn²⁺ environment includes oxygen atoms of four acrylamide and two water molecules that are stabilized using ionic nitrate ions. The observations of the solid‐state IR spectroscopic vibrational frequencies of these acrylamide complexes are in agreement with the crystal structures.     

Compensation of steric demand by cation-pi interactions,cobaltocenium cations as guests in tetraurea calix[4]arene dimers

The affinities of ferrocene (2) and the cobaltocenium cation (3+), which have roughly the same size and differ in their charge, towards the inner cavity of the dimeric capsule formed by tetraurea calix[4]arene (1) were studied in C2D4Cl2 solutions. While 3+, which occupies more than 75% of the internal volume of the dimer, is readily encapsulated this is not the case for 2. This is probably due to cation-pi interactions, which operate only between 3+ and the aromatic rings of the calix[4]arene dimer. We found that the affinity of the cobaltocenium cation is higher than that of the tropylium cation (4+) and is only 2-3 times less than that of the tetraethylammoniun cation (5+). From the variable temperature 1H NMR spectra of this capsule, the free energy of activation at 298 K (deltaGdouble dagger(298K)) for the reorientation of the hydrogen bonded belt between the two parts of the dimer could be determined by total line shape analysis for the aromatic protons of the calixarene. The value of 14.3 +/- 0.2 kcal mol(-1) for the dimeric capsules of 3+ PF6- is very similar to the free activation energy found for dimeric capsules of 1 with 4+ PF6- and 5+ PF6- in C2D4Cl2. It becomes significantly lower, if PF6- is replaced by BF4-. We also found that ten times more DMSO is needed to disrupt the capsule 1 x 3+ x 1 than the corresponding 1 x 1 dimer containing benzene as guest. This demonstrates again the importance of the cation-pi interactions for the stability of such hydrogen-bonded dimeric capsules.