Evolution Semigroups and Product Formulas for Nonautonomous Cauchy Problems

In this paper, we study nonautonomous Cauchy problems (NCP) {^{u̇(t) = A(t)u(t)}_{u(s) = x ∈ X} for a family of linear operators (A(t))_t∈I on some Banach space X by means of evolution semigroups. In particular, we characterize “stability” in the so called “hyperbolic case” on the level of evolution semigroups and derive a product formula for the solutions of (NCP). Moreover, in Section 4 we connect the “hyperbolic” and the “parabolic” case by showing, that integrals ∫^t_s A(τ) dτ always define generators. This yields another product formula.     

Prearranged Glycosides,Part 12, Intramolecular Mannosylations of Glucose Derivatives via Prearranged Glycosides

A series of prearranged glycosides 5 , 17 , 23 , 28 , 37 , and 41 , having a benzyl‐protected 1‐thiomannosyl donor linked through its positions 2, 3, 4, and 6 via succinate and malonate tethers, respectively, to positions 2, 3, and 6 of a benzyl glucopyranoside acceptor, were prepared by condensation of the respective mannosyl succinates and malonates with suitably protected benzyl glucopyranosides. The prearranged glycosides were intramolecularly coupled under various conditions to give the corresponding tethered (1→4)‐linked disaccharides. The yields and anomer ratios of the products of these couplings were interpreted in terms of the thermodynamic stability of the resulting disaccharides. In the case of prearranged glycoside 17 , having positions 3 of both the donor and the acceptor linked by a succinate tether, a strong dependence of the diastereoselectivity of the intramolecular glycosylation on the activation procedure was observed. All other cases did not show a significant dependence of the outcome of the anomeric configuration in intramolecular glycosylation on the activation procedure or the solvent.     

Hexasupersilyloctaindane (tBu3Si)6In8— A Compound with a Novel In8 Cluster Framework

A doubly capped In ₆ octahedron characterizes the structure of the dark green octaindane (tBu₃Si)₆In₈ (see picture), which is obtained from (C₅Me₅)In and tBu₃SiNa in pentane at −78°C. In1/In1′ are the capping atoms, and In2/In2′ form the apexes of the stretched In₆ octahedron. Thus, in agreement with the results of ab initio calculations, the compound can be classified as a hypoprecloso-indane.     

η5-Phospholylgallium: The First Monomeric Polyhapto Compound between a Phospholyl Ligand and a Main Group Metal

Monomeric polyhapto-bound phospholyl compounds were hitherto unknown for the main group elements. Use of a solution of metastable GaBr has allowed the synthesis of monomeric η⁵-phospholylgallium, which has been characterized by X-ray structure analysis as the Cr(CO)₅ complex 1 .     

Multimodal Analysis of Light-Driven Water Oxidation in Nanoporous Block Copolymer Membranes**

Heterogeneous light-driven catalysis is a cornerstone of sustainable energy conversion. Most catalytic studies focus on bulk analyses of the hydrogen and oxygen evolved, which impede the correlation of matrix heterogeneities, molecular features, and bulk reactivity. Here, we report studies of a heterogenized catalyst/photosensitizer system using a polyoxometalate water oxidation catalyst and a model, molecular photosensitizer that were co-immobilized within a nanoporous block copolymer membrane. Via operando scanning electrochemical microscopy (SECM), light-induced oxygen evolution was determined using sodium peroxodisulfate (Na₂S₂O₈) as sacrificial electron acceptor. Ex situ element analyses provided spatially resolved information on the local concentration and distribution of the molecular components. Infrared attenuated total reflection (IR-ATR) studies of the modified membranes showed no degradation of the water oxidation catalyst under the reported light-driven conditions.     

Understanding MOF Flexibility: An Analysis Focused on Pillared Layer MOFs as a Model System

Flexible porous frameworks are at the forefront of materials research. A unique feature is their ability to open and close their pores in an adaptive manner induced by chemical and physical stimuli. Such enzyme-like selective recognition offers a wide range of functions ranging from gas storage and separation to sensing, actuation, mechanical energy storage and catalysis. However, the factors affecting switchability are poorly understood. In particular, the role of building blocks, as well as secondary factors (crystal size, defects, cooperativity) and the role of host–guest interactions, profit from systematic investigations of an idealized model by advanced analytical techniques and simulations. The review describes an integrated approach targeting the deliberate design of pillared layer metal–organic frameworks as idealized model materials for the analysis of critical factors affecting framework dynamics and summarizes the resulting progress in their understanding and application.