Decacyclene Radical Anions Showing Strong Low‐energy Intramolecular Absorption and Magnetic Coupling of Spins in a Hexagonal Network

Two salts of the aromatic hydrocarbon decacyclene, {cryptand[2.2.2](Cs⁺)} (decacyclene^.?) ( 1 ) and {Bu₃MeP⁺}(decacyclene^.?) ( 2 ), were obtained. In both salts, decacyclene^.? radical anions formed channels occupied by cations. However, corrugated hexagonal decacyclene^.? layers could be outlined in the crystal structure of 1 with several side‐by‐side C???C approaches. The decacyclene^.? radical anions showed strong distortion in both salts, deviating from the C₃ symmetry owing to the repulsion of closely arranged hydrogen atoms and the Jahn‐Teller effect. Radical anions showed intense unusually low energy absorption in the IR‐range, with maxima at 4800 and 6000 cm^?1. According to the carculations, these bands can originate from the SOMO‐LUMO+1 and SOMO‐LUMO+2 transitions, respectively. Radical anions exhibited a S=1/2 spin state, with an effective magnetic moment of 1.72 μ_B at 300 K. The decacyclene^.? spin antiferromagnetically coupled with a Weiss temperature of ?11 K. Spin ordering was not observed down to 1.9 K owing to spin frustration in the hexagonal decacyclene^.? layers.     

Novel organomagnesium reagents in synthesis. Catalytic cyclomagnesiation of allenes in the synthesis of N-, O-, and Si-substituted 1Z,5Z-dienes

An efficient method for the synthesis of valuable N-, O-, and Si-containing 1Z,5Z-diene compounds was developed. The method comprises Cp₂TiCl₂-catalyzed homo- and cross-cyclomagnesiation of 1,2-dienes by Grignard reagents (RMgR′) to give 2,5-dialkylidenemagnesacyclopentanes in up to 96% yield. This approach was successfully used in the synthesis of 5Z,9Z-dienoic acids, precursors of acetogenins and insect pheromones.     

Unexpected cleavage of the Cpy–Cpy bond in the reaction of 2,2′-bipyridine N,N′-diimines with acetylenes

An unusual cleavage of the C_py–C_py bond in the reaction of 2,2′-bipyridine N,N′-diimine and its C-methyl substituted derivatives with acetylenes is described. The effect of the solvent on the yield of 7,7′-bipyrazolo[1,5-a]pyridine-2,2′,3,3′-tetracarboxylates and the products of cleavage of the C_py–C_py bond has been studied. The mechanism of the cleavage reaction is discussed on the basis of DFT calculations.     

Cyanide Complexes Based on {Mo6I8}4+ and {W6I8}4+ Cluster Cores

Compounds based on new cyanide cluster anions [{Mo₆I₈}(CN)₆]^2–, trans-[{Mo₆I₈}(CN)₄(MeO)₂]^2– and trans-[{W₆I₈}(CN)₂(MeO)₄]²⁻ were synthesized using mechanochemical or solvothermal synthesis. The crystal and electronic structures as well as spectroscopic properties of the anions were investigated. It was found that the new compounds exhibit red luminescence upon excitation by UV light in the solid state and solutions, as other cluster complexes based on {Mo₆I₈}⁴⁺ and {W₆I₈}⁴⁺ cores do. The compounds can be recrystallized from aqueous methanol solutions; besides this, it was shown using NMR and UV-Vis spectroscopy that anions did not undergo hydrolysis in the solutions for a long time. These facts indicate that hydrolytic stabilization of {Mo₆I₈} and {W₆I₈} cluster cores can be achieved by coordination of cyanide ligands.     

Wigner quasi-probability densities and characterization of the Gaussian distribution

A new characterization of the Gaussian distribution was given by R. Hudson in 1974. A sharpening and some extensions of this result are proposed, and connections with other characterizations of the Gaussian distribution are given. Linnik's “ridge principle” is substantially used. Bibliography: 11 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 228, 1996, pp. 142–153.     

On reconstruction of distributions by the translated moments of linear statistics

The problem of reconstruction of a multivariate distribution by means of translated moments is considered. Supported in part by the Russian Foundation for Fundamental Research (project code # 95-011-01260) and the International Science Foundation. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part II.