Enumeration, Generation, and Construction of Stereoisomers of High-Valence Stereocenters

Fundamental tools of molecular structure elucidation are computer programs generating constitutional isomers and configurational isomers. A general disadvantage of the methods of algebraic stereoisomer generation by Nourse, Smith, Carhart and Djerassi is the restriction of the valences of the stereocenters to four. The present paper discusses an extension of this concept to higher-valence centers. Methods for counting and generating all stereoisomers are provided. Moreover, for some types of isomers algorithms for constructing spatial realizations geometrically are presented. The main mathematical tool is the theory of group actions and double cosets.