Cationic molybdenum oxo alkylidenes stabilized by N-heterocyclic carbenes: from molecular systems to efficient supported metathesis catalysts

Cationic d⁰ group 6 olefin metathesis catalysts have been recently shown to display in most instances superior activity in comparison to their neutral congeners. Furthermore, their catalytic performance is greatly improved upon immobilization on silica. In this context, we have developed the new family of molecular cationic molybdenum oxo alkylidene complexes stabilized by N-heterocyclic carbenes of the general formula [Mo(O)(CHCMe₃)(IMes)(OR)[X⁻]] (IMes = 1,3-dimesitylimidazol-2-ylidene; R = 1,3-dimesityl-C₆H₃, C₆F₅; X⁻ = B(3,5-(CF₃)₂C₆H₃)₄⁻, B(Ar^F)₄, tetrakis(perfluoro-t-butoxy)aluminate (PFTA)). Immobilization of [Mo(O)(CHCMe₃)(IMes)(O-1,3-dimesityl-C₆H₃)⁺B(Ar^F)₄⁻] on silica via surface organometallic chemistry yields an active alkene metathesis catalyst that shows the highest productivity towards terminal olefins amongst all existing molybdenum oxo alkylidene catalysts.

The first cationic molybdenum oxo complexes were synthesized and immobilized on partially dehydroxylated silica. Vastly enhanced catalytic activity for terminal olefins was found compared to their neutral congeners.     

Enzyme-Catalyzed Synthesis of O-Glycopeptide Building Blocks

Abstract

In 1988, MOSBACH et aL¹ reported the synthesis of a-D-mannopyranosy1-L-serine and Q -D-N-acetylgalactosamino-L-serine by reversing the hydrolytic activity of a -mannosidase from jack beans and a -N-acetylgalactosaminidase from beef liver, respectively. The yields in these equilibrium-controlled syntheses² using high concentrations of monosaccharide and serine were highly dependent on the enzyme concentration and ranged from 5 to 10 percent in both cases.     

Eigenvalues of a statistical mechanics matrix

We consider the problem of finding the spectrum of an n × n matrix which arises in the study of a certain model of long-range interactions in a one-dimensional statistical mechanics system. Our analysis exhibits a curious resemblance of the suitably normalized distribution of eigenvalues to the Marčenko–Pastur law in the limit n → ∞.     

The (S−1,S) inventory model and its counterparts in queueing theory

We explore the relationship between the ($S?1,S$) inventory model and three well-known queueing models: the Erlang loss system, the machine-repair model and a two-node Jackson network. Exploiting this relationship allows us to obtain key performance measures of the ($S?1,S$) model, like the so-called virtual outdating time, the number of items on the shelf in steady state, the long-run rate of unsatisfied demands and the distribution of the empty shelf period.     

Ockham’s Calculus of Strict Implication

In his main work Summa Logicae written around 1323, William of Ockham developed a system of propositional modal logic which contains almost all theorems of a modern calculus of strict implication. This calculus is formally reconstructed here with the help of modern symbols for the operators of conjunction, disjunction, implication, negation, possibility, and necessity.