On the domain of fractional Laplacians and related generators of Feller processes

In this paper we study the domain of the generator of stable processes, stable-like processes and more general pseudo- and integro-differential operators which naturally arise both in analysis and as infinitesimal generators of Lévy- and Lévy-type (Feller) processes. In particular we obtain conditions on the symbol of the operator ensuring that certain (variable order) Hölder and Hölder–Zygmund spaces are in the domain. We use tools from probability theory to investigate the small-time asymptotics of the generalized moments of a Lévy or Lévy-type process ${(X_t)}_{t\ge 0}$,

$\underset{t\to 0}{\lim }?\frac{1}{t}({\mathbb{E}}^{x}f(X_t)?f(x)),x\in {\mathbb{R}}^d,$

for functions f which are not necessarily bounded or differentiable. The pointwise limit exists for fixed $x\in {\mathbb{R}}^d$ if f satisfies a Hölder condition at x. Moreover, we give sufficient conditions which ensure that the limit exists uniformly in the space of continuous functions vanishing at infinity. As an application we prove that the domain of the generator of ${(X_t)}_{t\ge 0}$ contains certain Hölder spaces of variable order. Our results apply, in particular, to stable-like processes, relativistic stable-like processes, solutions of Lévy-driven SDEs and Lévy processes.     

A Thioxanthone Sensitizer with a Chiral Phosphoric Acid Binding Site: Properties and Applications in Visible Light-Mediated Cycloadditions

A chiral phosphoric acid with a 2,2’-binaphthol core was prepared that displays two thioxanthone moieties at the 3,3’-position as light-harvesting antennas. Despite its relatively low triplet energy, the phosphoric acid was found to be an efficient catalyst for the enantioselective intermolecular [2+2] photocycloaddition of β-carboxyl-substituted cyclic enones (e.r. up to 93:7). Binding of the carboxylic acid to the sensitizer is suggested by NMR studies and by DFT calculations to occur by means of two hydrogen bonds. The binding event not only enables an enantioface differentiation but also modulates the triplet energy of the substrates.     

A HF Loaded Lewis-Acidic Aluminium Chlorofluoride for Hydrofluorination Reactions

The very strong Lewis acid aluminium chlorofluoride (ACF) was loaded with anhydrous HF. The interaction between the surface of the catalyst and HF was investigated using a variety of characterization methods, which revealed the formation of polyfluorides. Moreover, the reactivity of the HF-loaded ACF towards the hydrofluorination of alkynes was studied.     

Orthogonal Olefination with Organogermanes

Reported herein is a fully orthogonal olefination, which involves the site- and E-selective coupling of aryl germanes with alkenes, tolerating otherwise widely employed coupling handles such as aromatic (pseudo)halogens (C−I, C−Br, C−Cl, C−F, C−OTf, C−OSO₂F), silanes and boronic acid derivatives as well as alternative functionalities. This unprecedented [Ge]-based oxidative Heck coupling proceeds at room temperature with high speed (10 min to 2 hours) and operational simplicity owing to its base-free and air-tolerant features.     

Functional Dithienopyrazines: Structure-Property Relationships**

Dithienopyrazines are only scarcely used as building blocks in organic electronic materials. Here, we report efficient preparation and investigation of syn- and anti-dithienopyrazines, which were functionalized with triaraylamine units to provide different series of donor-acceptor-donor-type materials. The characterization of the optoelectronic properties resulted in valuable structure-property relationships and allowed for the elucidation of the influence of structural effects such as core structure (syn vs anti), type of substituents (directly arylated vs ethynylated aryl), and substitution pattern (α,α’- vs β,β’- vs fourfold substitution). Finally, first application of a dithienopyrazine derivative as model for hole-transport materials tailored for organic electronic devices has been realized.     

Stability and Conversion of Tin Zintl Anions in Liquid Ammonia Investigated by NMR Spectroscopy

Homoatomic polyanions of post‐transition main‐group metals, namely, Zintl anions, are precast in analogous Zintl phases and can react in solution to form new materials. Despite comprehensible reaction approaches, the formed products cannot be planned in advance, as hitherto undetected and therefore disregarded side reactions take place. The outcomes and interpretations of the reactions of Zintl anions are so far based mainly on crystal structures, which only allow characterization of the product that has the lowest solubility. Here we present the results of our investigation of the stability of highly charged tin Zintl anions in liquid ammonia, which is not exclusively based on solution effects but also on the oxidative influence of the solvent. This allows for a deeper understanding of the ongoing processes in solution and opens doors to the directed synthesis of transition metal complexes of Sn₄^4?, here shown by its reactivity towards MesCu.     

Direct In Situ Investigation of Milling Reactions Using Combined X‐ray Diffraction and Raman Spectroscopy

The combination of two analytical methods including time‐resolved in situ X‐ray diffraction (XRD) and Raman spectroscopy provides a new opportunity for a detailed analysis of the key mechanisms of milling reactions. To prove the general applicability of our setup, we investigated the mechanochemical synthesis of four archetypical model compounds, ranging from 3D frameworks through layered structures to organic molecular compounds. The reaction mechanism for each model compound could be elucidated. The results clearly show the unique advantage of the combination of XRD and Raman spectroscopy because of the different information content and dynamic range of both individual methods. The specific combination allows to study milling processes comprehensively on the level of the molecular and crystalline structures and thus obtaining reliable data for mechanistic studies.