A Generalized Wreath Product Method for the Enumeration of Stereo and Position Isomers of Polysubstituted Organic Compounds

Extensive expositions of the isomer enumeration methods can be found in the review Dipers of Rouvray [1, 2]. The problem of enumerating isomers essentially reduces to finding what is known as the cycle index of a permutation group [3] and then obtaining a generating function for isomers using a theorem of Polya [3]. Read [4] stated that a method is yet to be developed for the enumeration of stereo-isomers of polysubstituted organic compounds. Read [5] recently enumerated the stereoisomers of certain specific compounds like C,Hz,XY, where X and Y are attached to the end carbons. We report here a general method for the enumeration of stereo and position isomers of polysubstituted organic compounds containing any number of functional groups. The group of permutations for the enumeration of isomers at room temperature should contain the point group operations and the permutations induced by any additional internal degrees of freedom. Leonard [6, 7] enumerated the isomers of nonrigid cyclohexane molecules by including the permutations induced by a ring-flip operator in the permutation group of the rigid molecule. Davidson [8] investigated the three-fold rotors in alkanes, two-fold rotors in polyphenyls and certain higher-fold rotors in metal complexes from the standpoint