Algorithm for Combinatorial Bipartite Enumeration of Chiral and Achiral Stereoisomers of Homo- and Heteropolysubstituted Derivatives of the Cubane Molecule

Abstract

This paper is devoted to the application of an algorithm for the enumeration of chiral and achiral stereoisomers of homo and heteropolysubstituted derivatives of the cubane molecule. The sequence of this algorithm is in three steps, the first of which is the determination of the permutations of 8 hydrogen atoms of the cuban molecule ( ) subjected to the action of the Oh group. The second step will be the composition of these permutations later into permutational representations and controlling respectively the chirality and achirality of this molecular system. The transformation of these 2 operators into a pair of generic formulae used for bipartite combinatorial enumeration giving chiral and achiral isomer numbers of the homo- and hetero-polysubstituted derivatives of the cubane molecule respectively symbolised by the empirical formulae and being the final step.