Self-Similarity and Localization

The localized eigenstates of the Harper equation exhibit universal self-similar fluctuations once the exponentially decaying part of a wave function is factorized out. For a fixed quantum state, we show that the whole localized phase is characterized by a single strong coupling fixed point of the renormalization equations. This fixed point also describes the generalized Harper model with next nearest neighbor interaction below a certain threshold. Above the threshold, the fluctuations in the generalized Harper model are described by a strange invariant set of the renormalization equations.Comment: 4 pages, RevTeX, 2 figures include

Bis-N-heterocyclic carbene aminopincer ligands enable high activity in Ru-catalyzed ester hydrogenation

Bis-N-heterocyclic carbene (NHC) aminopincer ligands were for the first time successfully applied in catalytic hydrogenation of esters. We have isolated and characterized a well-defined catalyst precursor as a dimeric [Ru2(L)2Cl3]PF6 complex and studied its reactivity and catalytic performance. Remarkable initial activities up to 283 000 h-1 were achieved in hydrogenation of ethyl hexanoate at only 12.5 ppm Ru loading. A wide range of aliphatic and aromatic esters can be converted with this catalyst to corresponding alcohols in near quan-titative yields. The described synthetic protocol makes use of air stable reagents available in multigram quantities rendering the bis-NHC ligands an attractive alternative to the conventional phosphine-based systems

Bis-N-heterocyclic carbene aminopincer ligands enable high activity in Ru-catalyzed ester hydrogenation

Bis-N-heterocyclic carbene (NHC) aminopincer ligands were for the first time successfully applied in catalytic hydrogenation of esters. We have isolated and characterized a well-defined catalyst precursor as a dimeric [Ru2(L)2Cl3]PF6 complex and studied its reactivity and catalytic performance. Remarkable initial activities up to 283 000 h-1 were achieved in hydrogenation of ethyl hexanoate at only 12.5 ppm Ru loading. A wide range of aliphatic and aromatic esters can be converted with this catalyst to corresponding alcohols in near quan-titative yields. The described synthetic protocol makes use of air stable reagents available in multigram quantities rendering the bis-NHC ligands an attractive alternative to the conventional phosphine-based systems

Triazaphospholes versus Triazoles: An Investigation of the Differences between “Click”-Derived Chelating Phosphorus- and Nitrogen-Containing Heterocycles

A new class of pyridyl-functionalized triazaphospholes bearing either ^<i>t</i>Bu or SiMe₃ substituents at the 5-position of the N₃PC heterocycle have been prepared via the “click” reaction starting from 2-(azidomethyl)­pyridine and the corresponding phosphaalkynes. In order to investigate the electronic structure and donor–acceptor properties of such novel chelating and low-coordinate phosphorus heterocycles, calculations at the DFT level have been carried out. Moreover, cyclic voltammetry measurements were performed and the results were compared with those for the structurally related triazole-based systems, demonstrating a significant influence of the phosphorus atom as well as the substitution pattern on the electronic properties of the novel compounds. The P,N hybrid ligands form Re­(I) complexes of the type [(N^∧^mN)­Re­(CO)₃Br] via coordination of the nitrogen atom N² to the metal center rather than via the phosphorus atom, as verified crystallographically