Symmetry and Systematic Enumeration of Twistane Derivatives. Global/Local Chirality and Global/Local RS-Stereogenicity Revisited by Fujita's Stereoisogram Approach

Fujita's stereoisogram approach (S. Fujita, Mathematical Stereochemistry; De Gruyter: Berlin, 2015) has been applied to the discussion on the stereochemistry of twistane derivatives. In addition to chirality as the first kind of handedness, RS-stereogenicity is emphasized as the second kind of handedness, where an R-twistane skeleton and an S-twistane skeleton are recognized to be a pair of RS-diastereomers as a result of RS-stereogenicity. The contrast between global/local chirality and global/local RS-stereogenicity is clearly demonstrated by introducing the names, R-twistane and S-twistane, which are based on the globality of RS-stereogenicity. Among the five types of stereoisograms (type I to type V) as the full repertoire, there appear only type-I and type III stereoisograms during the discussions on twistane derivatives. Combinatorial enumeration of twistane derivatives are discussed on the basis of Fujita's proligand method (S. Fujita, Combinatorial Enumeration of Graphs, Three-Dimensional Structures, and Chemical Compounds; University of Kragujevac, Faculty of Science: Kragujevac, 2013).