The primitive ideals of the Cuntz–Krieger algebra of a row-finite higher-rank graph with no sources

We catalogue the primitive ideals of the Cuntz–Krieger algebra of a row-finite higher-rank graph with no sources. Each maximal tail in the vertex set has an abelian periodicity group of finite rank at most that of the graph; the primitive ideals in the Cuntz–Krieger algebra are indexed by pairs consisting of a maximal tail and a character of its periodicity group. The Cuntz–Krieger algebra is primitive if and only if the whole vertex set is a maximal tail and the graph is aperiodic.     

Microwave Promoted Oxidative Addition Reactions of Os3(CO)12: Efficient Syntheses of Triosmium Clusters of the Type Os3(μ-X)2(CO)10 and Os3(μ-H)(μ-OR)(CO)10

Microwave heating allows for the high-yield, one-step synthesis of the known triosmium complexes Os₃(μ-Br)₂(CO)₁₀ (1), Os₃(μ-I)₂(CO)₁₀ (2), and Os₃(μ-H)(μ-OR)(CO)₁₀ with R = methyl (3), ethyl (4), isopropyl (5), n-butyl (6), and phenyl (7). In addition, the new clusters Os₃(μ-H)(μ-OR)(CO)₁₀ with R = n-propyl (8), sec-butyl (9), isobutyl (10), and tert-butyl (11) are synthesized in a microwave reactor. The preparation of these complexes is easily accomplished without the need to first prepare an activated derivative of Os₃(CO)₁₂, and without the need to exclude air from the reaction vessel. The syntheses of complexes 1 and 2 are carried out in less than 15 min by heating stoichiometric mixtures of Os₃(CO)₁₂ and the appropriate halogen in cyclohexane. Clusters 3–6 and 8–10 are prepared by the microwave irradiation of Os₃(CO)₁₂ in neat alcohols, while clusters 7 and 11 are prepared from mixtures of Os₃(CO)₁₂, alcohol and 1,2-dichlorobenzene. Structural characterization of clusters 2, 4, and 5 was carried out by X-ray crystallographic analysis. High resolution X-ray crystal structures of two other oxidative addition products, Os₃(CO)₁₂I₂ (12) and Os₃(μ-H)(μ-O₂CC₆H₅)(CO)₁₀ (13), are also presented.     

A Mild, Large-Scale Synthesis of 1,3-Cyclooctanedione: Expanding Access to Difluorinated Cyclooctyne for Copper-Free Click Chemistry

We report the large-scale synthesis of 1,3-cyclooctanedione in five steps with 29% yield. This molecule is a synthetic precursor to difluorinated cyclooctyne, which participates in a bioorthogonal copper-free click reaction with azides. The final step demonstrates the first successful application of the Wacker-Tsuji oxidation to form a cyclic 1,3-dione.