ENUMERATION, GENERATION, AND CONSTRUCTION OF STEREOISOMERS OF HIGH-VALENCE STEREOCENTERS

Fundamental tools of molecular structure elucidation are computer prog rams generating constitutional isomers and configurational isomers. A general disadvantage of the methods of algebraic stereoisomer generati on by Nourse, Smith, Carhart, and Djerassi is the restriction of the v alences of the stereocenters to four. The present paper discusses an e xtension of this concept to higher-valence centers. Methods for counti ng and generating all stereoisomers are provided. Moreover, for some t ypes of isomers algorithms for constructing spatial realizations geome trically are presented. The main mathematical tool is the theory of gr oup actions and double cosets.