Equivalence of a Scalar and a Vector Equilibrium Problem for a Pair of Functions Forming a Nikishin System

Mathematical Notes - We prove the equivalence of a vector and a scalar equilibrium problem that naturally arise when studying the limit distribution of zeros of type I Hermite–Padé...     

The Lp dual Minkowski problem for p > 1 and q > 0

General $L_p$ dual curvature measures have recently been introduced by Lutwak, Yang and Zhang [24]. These new measures unify several other geometric measures of the Brunn–Minkowski theory and the dual Brunn–Minkowski theory. $L_p$ dual curvature measures arise from qth dual intrinsic volumes by means of Alexandrov-type variational formulas. Lutwak, Yang and Zhang [24] formulated the $L_p$ dual Minkowski problem, which concerns the characterization of $L_p$ dual curvature measures. In this paper, we solve the existence part of the $L_p$ dual Minkowski problem for $p>1$ and $q>0$, and we also discuss the regularity of the solution.     

Unsupervised Pattern Recognition Chemometrics for Distinguishing Different Egyptian Olive Varieties Using a New Integrated Densitometric Reversed-Phase High-Performance Thin-Layer Chromatography—Image Analysis Technique

JPC – Journal of Planar Chromatography – Modern TLC - The merits of chemometrics in categorizing different Egyptian olive chemovarieties based on their compositional integrity were...     

Solid-State NMR Spectroscopy: A Powerful Technique to Directly Study Small Gas Molecules Adsorbed in Metal–Organic Frameworks

Metal–organic frameworks (MOFs) have shown great potential in gas separation and storage, and the design of MOFs for these purposes is an on-going field of research. Solid-state nuclear magnetic resonance (SSNMR) spectroscopy is a valuable technique for characterizing these functional materials. It can provide a wide range of structural and motional insights that are complementary to and/or difficult to access with alternative methods. In this Concept article, the recent advances made in SSNMR investigations of small gas molecules (i.e., carbon dioxide, carbon monoxide, hydrogen gas and light hydrocarbons) adsorbed in MOFs are discussed. These studies demonstrate the breadth of information that can be obtained by SSNMR spectroscopy, such as the number and location of guest adsorption sites, host–guest binding strengths and guest mobility. The knowledge acquired from these experiments yields a powerful tool for progress in MOF development.     

Copper-Catalyzed Trifunctionalization of Alkynes: Rapid Formation of Oxindoles Bearing Geminal Diboronates

A copper-catalyzed trifunctionalization of alkynes that provides rapid access to oxindoles bearing a geminal diboronate side chain, highlighted by the simultaneous formation of one C−C bond and two C−B bonds, is reported. This new reaction features simple reaction conditions (ligand-free catalysis), a general substrate scope, and excellent chemoselectivity. Mechanistic study revealed a reaction sequence constituted by, in the order, borylation, intramolecular cross-coupling, hydroboration, which has been rarely documented.     

Peculiar Photoinduced Electron Transfer in Porphyrin–Fullerene Akamptisomers

Porphyrin–fullerene dyads are promising candidates for organic photovoltaic devices. The electron-transfer (ET) properties of the molecular devices depend significantly on the mutual position of the donor and acceptor. Recently, a new type of molecular isomerism (akamptisomerism) has been discovered. In the present study, we explore how photoinduced ET can be modulated by passing from one akamptisomer to another. To this aim, four akamptisomers of the quinoxalinoporphyrin–[60]fullerene complex are selected for computational study. The most striking finding is that, depending on the isomer, the porphyrin unit in the dyad can act as either electron donor or electron acceptor. Thus, the stereoisomeric diversity allows one to change the direction of ET between the porphyrin and fullerene moieties. To understand the effect of akamptisomerism on the photoinduced ET processes, a detailed analysis of initial and final states involved in the ET is performed. The computed rate for charge separation is estimated to be in the region of 1–10 ns⁻¹. The formation of a long-living quinoxalinoporphyrin anion radical species is predicted.     

Synthesis,Crystal Structure,and Selected Properties of [Au(S2CNH2)2]SCN: A Precursor for Gold Macro-Needles Consisting of Gold Nanoparticles Glued by Graphitic Carbon Nitride

A new preparation route is developed for the synthesis of needle-like crystals of [Au(S₂CNH₂)₂]SCN, which avoids disproportionation of the Au^I salt used as a starting material. In the crystal structure, the two crystallographically independent Au^III centers are in a square-planar environment of two S₂CNH₂ ligands. The Hirshfeld surface analysis reveals the presence of noncovalent intermolecular S⋅⋅⋅S interactions, which are essential for the spatial arrangement of the molecules. Density functional theory (DFT) calculations including dispersion and damping corrections result in a unit cell volume very close to the value determined experimentally. Thermal decomposition in an inert atmosphere generates black needles with lengths of up to 500 μm. X-ray powder diffraction and pair distribution function analyses demonstrate that the needles are composed of nanosized crystals with a volume-weighted average domain size of 20(1) nm. According to results of X-ray photoemission experiments, the black needles are covered by a nitrogen-rich carbon nitride with composition near (CN)₂N. ¹³C solid-state NMR investigations indicate that two different carbon species are present, with signals corresponding well to heptazine units as in melon and triazine units as in poly(triazin imide) type compounds. Scanning transmission electron microscopy tomography evidences that the needles are composed of slightly elongated nanoparticles.     

Alkylation of Allyl/Alkenyl Sulfones by Deoxygenation of Alkoxyl Radicals

A challenging deoxygenation of alkoxyl radicals from readily accessible alcohol derivatives was developed, affording facile synthesis of functionalized alkenes with good functional group tolerance under mild reaction conditions. Because alkoxyl radicals can easily undergo β-fragmentations or hydrogen abstractions, this new strategy for deoxygenation of alkoxyl radicals is highly valuable. Moreover, mechanistic studies revealed that the electron-neutral phosphine acts as the deoxygenation reagent.     

Stereoselective Cascade Cyclizations with Samarium Diiodide to Tetracyclic Indolines: Precursors of Fluorostrychnines and Brucine

A series of γ-indolylketones with fluorine, cyano or alkoxy substituents at the benzene moiety was prepared and subjected to samarium diiodide-promoted cyclization reactions. The desired dearomatizing ketyl cascade reaction forming two new rings proceeded in all cases with high diastereoselectivity, but with differing product distribution. In most cases, the desired annulated tetracyclic compounds were obtained in moderate to good yields, but as second product tetracyclic spirolactones were isolated in up to 29 % yield. The reaction rate was influenced by the substituents at the benzene moiety of the substrate as expected, with electron-accepting groups accelerating and electron-donating groups decelerating the cyclization process. In case of a difluoro-substituted γ-indolylketone a partial defluorination was observed. The intermediate samarium enolate of the tetracyclic products could be trapped by adding reactive alkylating agents as electrophiles delivering products with quarternary carbons. In the case of a dimethoxy-substituted tetracyclic cyclization product a subsequent reductive amination stereoselectively provided a pentacyclic compound that was subsequently N-protected and subjected to a regioselective elimination. The obtained functionalized pentacyclic product should be convertible into the alkaloid brucine by four well-established steps. Overall, the presented report shows that functionalized tetracyclic compounds with different substituents are rapidly available with the samarium diiodide cascade cyclization as crucial step. Hence, analogues of the landmark alkaloid strychnine, for example, with specific fluorine substitutions, should be easily accessible.     

Cover Feature: How Many O-Donor Groups in Enterobactin Does It Take to Bind a Metal Cation? (Chem. Eur. J. 28/2019)

The E. coli siderophore enterobactin, the strongest Fe^III chelator known to date, forms hexacoordinate complexes with Si^IV, Ge^IV, and Ti^IV. Synthetic protocols have been developed to prepare non-symmetric enterobactin analogues with varying denticities. Various benzoic acid residues were coupled to the macrocyclic lactone to afford a diverse library of ligands. These enterobactin analogues were bound to Si^IV, Ge^IV, and Ti^IV, and the complexes were investigated through experimental and computational techniques. The binding behavior of the synthesized chelators enabled assessment of the contribution of each of the phenolic hydroxy groups in enterobactin to metal-ion complexation. It was found that at least four O-donors are needed for enterobactin derivatives to act as metal binders. Density functional theory calculations indicate that the strong binding behavior of enterobactin can be ascribed to a diminished translational entropy penalty, a common feature of the chelate effect, coupled with the structural arrangement of the three catechol moieties, which allows the triseryl base to be installed without distorting the preferred local metal-binding geometry of the catecholate ligands.