MTO and OsO4: an efficient catalytic couple for mild H2O2-based asymmetric dihydroxylation of olefins

A novel and robust system for osmium-catalyzed asymmetric dihydroxylation of olefins by aqueous H2O2 with methyltrioxorhenium (MTO) as electron transfer mediator (ETM) has been developed. The MTO is catalyzing the H2O2 oxidation of the chiral ligand to its mono-N-oxide, which in turn reoxidizes OsVI to OsVIII. Thus the (DHQD)2PHAL plays a dual role serving as the chiral inductor as well as the tertiary amine generating the N-oxide required for the recycling of osmium. The present catalytic system gives vicinal diols in good isolated yields and high enantiomeric excess (up to 99 % ee).     

Spectral asymptotics for an elliptic operator in a locally periodic perforated domain

We consider the homogenization of an elliptic spectral problem with a large potential stated in a thin cylinder with a locally periodic perforation. The size of the perforation gradually varies from point to point. We impose homogeneous Neumann boundary conditions on the boundary of perforation and on the lateral boundary of the cylinder. The presence of a large parameter 1/ε in front of the potential and the dependence of the perforation on the slow variable give rise to the effect of localization of the eigenfunctions. We show that the jth eigenfunction can be approximated by a scaled exponentially decaying function that is constructed in terms of the jth eigenfunction of a one-dimensional harmonic oscillator operator.     

Geometric Generalisations of shake and rattle

A geometric analysis of the shake and rattle methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the two methods, and the exact relation between them. In addition, the geometric insight naturally generalises shake and rattle to allow for a strictly larger class of constrained Hamiltonian systems than in the classical setting. In order for shake and rattle to be well defined, two basic assumptions are needed. First, a nondegeneracy assumption, which is a condition on the Hamiltonian, i.e., on the dynamics of the system. Second, a coisotropy assumption, which is a condition on the geometry of the constrained phase space. Non-trivial examples of systems fulfilling, and failing to fulfill, these assumptions are given.     

Electric field gradient at111In on Cu (100) surfaces and its utilization for indium surface diffusion

The electric field gradient at¹¹¹In probe atoms on Cu (100) surfaces was studied. At clean surfaces all probes are exposed to a well-defined surface field gradient. This is used to investigate indium surface diffusion, where the applied PAC method allows to observe diffusion steps on an atomistic scale. The jump rate for indium on Cu (100) was found to be in the order of 10^–3 Hz at 200 K.