On the Algebraic Index for Riemannian Étale Groupoids

In this paper, we construct an explicit quasi-isomorphism to study the cyclic cohomology of a deformation quantization over a Riemannian étale groupoid. Such a quasi-isomorphism allows us to propose a general algebraic index problem for Riemannian étale groupoids. We discuss solutions to that index problem when the groupoid is proper or defined by a constant Dirac structure on a 3-dimensional torus.     

Isolierung,Konstitution und Synthese der (R)-(−)-Eucominsäure

From the bulbs of Eucomis punctata L'Hérit. (Liliaceae) and of a hitherto undefined species of Eucomis a new optically active phenolic carboxylic acid, eucomic acid, was isolated. Structure 1 was assigned on the basis of chemical and spectral evidence. The absolute configuration of eucomic acid was determined by its correlation with piscidic acid ((2 R, 3 S)-2-(4′-hydroxybenzyl)-tartaric acid) ( 8 ). Consequently, eucomic acid is (R)-(?)-2-(4′-hydroxybenzyl)-malic acid ( 1 ). For the stereospecific synthesis, methyl cis-p-methoxybenzylidene-succinic acid ( 22 ) was transformed into the γ-lactone 24 which, by catalytic hydrogenolysis, yielded (±)-2-(4′-hydroxybenzyl)-malic acid 1-methyl ester ( 27 ). Resolution with (?)-quinine led to the enantiomeric acids 29 and 30 . The methyl ester of the levorotatory enantiomer 30 was identical with the dimethyl ester 3 of 4′-O-methyl-eucomic acid.     

Modular and Selective Arylation of Aryl Germanes (C−GeEt3) over C−Bpin,C−SiR3 and Halogens Enabled by Light-Activated Gold Catalysis

Selective C –C couplings are powerful strategies for the rapid and programmable construction of bi- or multiaryls. To this end, the next frontier of synthetic modularity will likely arise from harnessing the coupling space that is orthogonal to the powerful Pd-catalyzed coupling regime. This report details the realization of this concept and presents the fully selective arylation of aryl germanes (which are inert under Pd⁰/Pd^II catalysis) in the presence of the valuable functionalities C−BPin, C−SiMe₃, C−I, C−Br, C−Cl, which in turn offer versatile opportunities for diversification. The protocol makes use of visible light activation combined with gold catalysis, which facilitates the selective coupling of C−Ge with aryl diazonium salts. Contrary to previous light-/gold-catalyzed couplings of Ar–N₂⁺, which were specialized in Ar–N₂⁺ scope, we present conditions to efficiently couple electron-rich, electron-poor, heterocyclic and sterically hindered aryl diazonium salts. Our computational data suggest that while electron-poor Ar–N₂⁺ salts are readily activated by gold under blue-light irradiation, there is a competing dissociative deactivation pathway for excited electron-rich Ar–N₂⁺, which requires an alternative photo-redox approach to enable productive couplings.     

Replacement of the Cobalt Center of Vitamin B12 by Nickel: Nibalamin and Nibyric Acid Prepared from Metal-Free B12 Ligands Hydrogenobalamin and Hydrogenobyric Acid

The (formal) replacement of Co in cobalamin ( Cbl ) by Ni^II generates nibalamin ( Nibl ), a new transition-metal analogue of vitamin B₁₂. Described here is Nibl , synthesized by incorporation of a Ni^II ion into the metal-free B₁₂ ligand hydrogenobalamin ( Hbl ), itself prepared from hydrogenobyric acid ( Hby ). The related Ni^II corrin nibyric acid ( Niby ) was similarly synthesized from Hby , the metal-free cobyric acid ligand. The solution structures of Hbl , and Niby and Nibl , were characterized by spectroscopic studies. Hbl features two inner protons bound at N2 and N4 of the corrin ligand, as discovered in Hby . X-ray analysis of Niby shows the structural adaptation of the corrin ligand to Ni^II ions and the coordination behavior of Ni^II. The diamagnetic Niby and Nibl , and corresponding isoelectronic Co^I corrins, were deduced to be isostructural. Nibl is a structural mimic of four-coordinate base-off Cbls , as verified by its ability to act as a strong inhibitor of bacterial adenosyltransferase.