Gold-Catalyzed Divergent Ring-Opening Rearrangement of Cyclopropenes Enabled by Dichotomous Gold−Carbenes

The gold-catalyzed ring-opening rearrangement of cyclopropenes affords an efficient route to either polysubstituted naphthols or aryl-substituted furans. Owing to the unique dichotomy of gold−carbenes, this protocol provides a switchable reaction selectivity between naphthols and furans enabled by the use of TFP−Au(MeCN)SbF₆ (tri(2-furyl) phosphine) or PNP(AuNTf₂)₂ (bis(diphenylphosphino)(isopropyl) amine) as catalysts respectively. It is proposed that the gold−carbene intermediate might be involved in the cyclopropene→naphthol rearrangement while the gold-carbocation is more likely to be involved in the cyclopropene→furan rearrangement.     

Donor-Flexible Bis(pyridylidene amide) Ligands for Highly Efficient Ruthenium-Catalyzed Olefin Oxidation

An exceptionally efficient ruthenium-based catalyst for olefin oxidation has been designed by exploiting N,N′-bis(pyridylidene)oxalamide (bisPYA) as a donor-flexible ligand. The dynamic donor ability of the bisPYA ligand, imparted by variable zwitterionic and neutral resonance structure contributions, paired with the redox activity of ruthenium provided catalytic activity for Lemieux–Johnson-type oxidative cleavage of olefins to efficiently prepare ketones and aldehydes. The ruthenium bisPYA complex significantly outperforms state-of-the-art systems and displays extraordinary catalytic activity in this oxidation, reaching turnover frequencies of 650 000 h⁻¹ and turnover numbers of several millions.     

Catalytic Behavior of Mono-N-Protected Amino-Acid Ligands in Ligand-Accelerated C−H Activation by Palladium(II)

Mono-N-protected amino acids (MPAAs) are increasingly common ligands in Pd-catalyzed C−H functionalization reactions. Previous studies have shown how these ligands accelerate catalytic turnover by facilitating the C−H activation step. Here, it is shown that MPAA ligands exhibit a second property commonly associated with ligand-accelerated catalysis: the ability to support catalytic turnover at substoichiometric ligand-to-metal ratios. This catalytic role of the MPAA ligand is characterized in stoichiometric C−H activation and catalytic C−H functionalization reactions. Palladacycle formation with substrates bearing carboxylate and pyridine directing groups exhibit a 50–100-fold increase in rate when only 0.05 equivalents of MPAA are present relative to Pd^II. These and other mechanistic data indicate that facile exchange between MPAAs and anionic ligands coordinated to Pd^II enables a single MPAA to support C−H activation at multiple Pd^II centers.     

Dimeric Manganese-Catalyzed Hydroarylation and Hydroalkenylation of Unsaturated Amides

An unprecedented Mn(I)-catalyzed selective hydroarylation and hydroalkenylation of unsaturated amides with commercially available organic boronic acids is reported. Alkenyl boronic acids have been successfully employed for the first time in Mn(I)-catalyzed carbon–carbon bond formation. A wide array of β-alkenylated amide products can be obtained in moderate to good yields, which offers practical access to five- and six-membered lactams. This protocol has predictable regio- and chemoselectivity, excellent functional group compatibility and ease of operation in air, representing a significant step-forward towards manganese-catalyzed C−C coupling.     

Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields

Let X = {X(t):t ∈ R~N} be an anisotropic random field with values in R~d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.     

Electrocatalytic Carbon Dioxide Reduction by Using Cationic Pentamethylcyclopentadienyl–Iridium Complexes with Unsymmetrically Substituted Bipyridine Ligands

Eight [Ir(bpy)Cp*Cl]⁺‐type complexes (bpy= bipyridine, Cp*=1,2,3,4,5‐pentamethylcyclopentadienyl) containing differently substituted bipyridine ligands were synthesized and characterized. Cyclic voltammetry (CV) of the complexes in Ar‐saturated acetonitrile solutions showed that the redox behavior of the complexes could be fine tuned by the electronic properties of the substituted bipyridine ligands. Further CV in CO₂‐saturated MeCN/H₂O (9:1, v/v) solutions showed catalytic currents for CO₂ reduction. In controlled potential electrolysis experiments (MeCN/MeOH (1:1, v/v), E_app=?1.80 V vs Ag/AgCl), all of the complexes showed moderate activity in the electrocatalytic reduction of CO₂ with good stability over at least 15 hours. This electrocatalytic process was selective toward formic acid, with only traces of dihydrogen or carbon monoxide and occasionally formaldehyde as byproducts. However, the turnover frequencies and current efficiencies were quite low. No direct correlation between the redox potentials of the complexes and their catalytic activity was observed.     

Aryl Boronic Acid Catalysed Dehydrative Substitution of Benzylic Alcohols for C−O Bond Formation

A combination of pentafluorophenylboronic acid and oxalic acid catalyses the dehydrative substitution of benzylic alcohols with a second alcohol to form new C−O bonds. This method has been applied to the intermolecular substitution of benzylic alcohols to form symmetrical ethers, intramolecular cyclisations of diols to form aryl-substituted tetrahydrofuran and tetrahydropyran derivatives, and intermolecular crossed-etherification reactions between two different alcohols. Mechanistic control experiments have identified a potential catalytic intermediate formed between the aryl boronic acid and oxalic acid.     

Selective Catalytic Isomerization of β-Pinene Oxide to Perillyl Alcohol Enhanced by Protic Tetraimidazolium Nitrate

A series of tetraimidazolium salts with different anions was prepared and applied in the isomerization of β-pinene oxide. After examining the activity of different catalysts, a remarkable enhancement of the selectivity of perillyl alcohol (47 %) was obtained over [PEimi][HNO₃]₄ under mild reaction conditions and using DMSO as the solvent. Furthermore, noncovalent interactions between solvent molecules and the catalyst were found by FT-IR spectroscopy and confirmed by computational chemistry. The homogeneous catalyst showed excellent stability and was reused up to six times without significant loss.     

Homogeneous variable exponent Besov and Triebel–Lizorkin spaces

We introduce homogeneous Besov and Triebel–Lizorkin spaces with variable indexes. We show that their study reduces to the study of inhomogeneous variable exponent spaces and homogeneous constant exponent spaces. Corollaries include trace space characterizations and Sobolev embeddings.