Syntheses of seven-membered rings: ruthenium-catalyzed intramolecular [5+2] cycloadditions

The Ru-catalyzed intramolecular [5+2] cycloaddition of cyclopropylenynes is investigated with respect to the regio- and diastereoselectivity as well as the functional group compatibility of the reaction. Evidence for the mechanism as occurring through a ruthenacyclopentene intermediate is elucidated from 1) the study of the diastereoselectivity of the cycloaddition; 2) the effect of variation of substituents on the regioselectivity of cyclopropyl bond cleavage in 1,2-trans- and 1,2-cis-disubstituted cyclopropanes and 3) examples that clearly do not involve ruthenacyclohexene as intermediates as products still incorporate the cyclopropyl moiety. The scope and limitations of the Ru-catalyzed cycloaddition are discussed and compared with the Rh-catalyzed reaction. The potential power of this methodology towards natural product total synthesis is demonstrated by the formation of several polycyclic systems with the chosen reaction conditions and readily available cyclopropylenyne substrates.     

Splitting of n-fold rotationally symmetric graphs

R. A. Davidson's rules for splitting an n-fold rotationally symmetric graph can be derived from a unitary transformation on the adjacency matrix. The McClelland and D'Amato rules are special cases with n = 2 and n = 3, respectively.