Automorphismes induits et valeurs propres

Summary Let T be an aperiodic automorphism on a non atomic probability space (W,A,P), A being a countably generated tribe. It is shown that for all >0 and all alo, there exists A, such that P(A)1–, and such that the automorphism T_A induced by T on A admits exp(2 i a) as a proper value.     

Binding energy for inhomogeneous nuclear matter

For a spatial finite nuclear density distribution a binding energy formula is developed. A modified Thomas-Fermi method which deduces the mixed density by taking into account an anisotropic local momentum space occupation is used. This method presents the binding energy as a functional of the proton and neutron density distributions. It was possible within this framework to derive in a consistent way the energy correction terms due to density inhomogeneities. The structure of these energy correction terms is shown and an estimate is given for the adjustable parameters of this model to fit the experimental nuclear masses.     

Surface segregation and surface electronic interactions in PtCu

Photoemission and Auger electron spectroscopy on Pt_0.98Cu_0.02 show that the (110) face has over twice as much Cu surface segregation as the (111) face. The Cu 3d-derived surface “density of states” differ strikingly in peak shape and in width (by 0.5 eV). The centroids, compared with bulk Cu d states, are shifted by more than 0.3 eV towards the Fermi level. This is the first experimental correlation between surface segregation and surface bonding.     

Zum Randverhalten der Lösungen gewisser zweidimensionaler Variationsprobleme mit freien Randbedingungen

Ohne Zusammenfassung     

Four-dimensional quantum study on exothermic complex-forming reactions: Cl- + CH3Br-->ClCH3+Br-

The exothermic gas-phase bimolecular nucleophilic substitution (S(N)2) reaction Cl(-)+CH(3)Br (upsilon1',upsilon2',upsilon3')-->ClCH(3) (upsilon1,upsilon2,upsilon3)+Br- and the corresponding endothermic reverse reaction have been studied by time-independent quantum scattering calculations in hyperspherical coordinates on a coupled-cluster potential-energy surface. The dimensionality-reduced model takes four degrees of freedom into account [Cl-C and C-Br stretching modes (quantum numbers upsilon3' and upsilon3); totally symmetric modes of the methyl group, i.e., C-H stretching (upsilon1' and upsilon1) and umbrella bending vibrations (upsilon2' and upsilon2)]. Diagonalization of the Hamiltonian was performed employing the Lanczos algorithm with a variation of partial reorthogonalization. A narrow grid in the total energy was employed so that long-living resonance states could be resolved and extracted. While excitation of the reactant umbrella bending mode already leads to a considerable enhancement of the reaction probability, its combination with vibrational excitation of the broken C-Br bond, (0, 1, 1), results in a strong synergic effect that can be rationalized by the similarity with the classical transitional normal mode. Exciting the C-H stretch has a non-negligible effect on the reaction probability, while for larger translational energies this mode follows the expected spectatorlike behavior. Combination of C-Br stretch and symmetric C-H, (1,0,1), stretch does not show a cooperative effect. Contrary to the spectator mode concept, energy originally stored in the C-H stretching mode is by no means conserved, but almost completely released in other modes of the reaction products. Products are most likely formed in states with a high degree of excitation in the new C-Cl bond, while the internal modes of the methyl group are less important. Reactants with combined umbrella/C-Br stretch excitation, (0, 1, 1), may yield products with two quanta in the umbrella mode.     

Direct assignment of enantiofacial discrimination on single heterocyclic substrates by self-induced CD

The first direct assignment of highly dynamic enantiofacial discrimination acting on a single heterocyclic substrate has been achieved by a combination of experimental and theoretical CD spectroscopy. The interaction of chirally modified hosts based on triphenylene ketals with appropriate prochiral guests can lead to the preferential formation of one diastereomeric host-guest complex. This reversible stereoselective binding transmits the chiral information from remote chiral groups in the host to the strongly absorbing triphenylene chromophore, which gives rise to self-induced CD. This effect was exploited for the determination of the enantiofacial recognition in various host-guest systems. Inversion of the steric demand either of the chiral substituents at the host or of the prochiral guest leads to almost complete inversion of the resulting CD spectra. For the assignment of the absolute stereochemistry of the complexes, a combined molecular dynamics/quantum-chemical approach was successfully employed. Despite the size and the highly dynamic character of the supramolecular systems, fundamental properties of the systems and details of the spectra were simulated accurately, providing access to fast and reliable assignment of the enantiofacial preference. The results are highly consistent with available X-ray data.     

Supramolecular control of valence-tautomeric equilibrium on nanometer-scale gold clusters

This communication describes the preparation and characterization of a valence tautomer complex covalently attached to gold nanoparticles. Variable-temperature IR spectroscopy is used to determine the equilibrium thermodynamic parameters for the valence tautomerization. These results are compared with a nonsurface combined valence tautomer complex. The results show that surface confinement attenuates both DeltaH degrees and DeltaS degrees . We attribute these changes to a reduced accessible molecular surface area.