Combinatorial enumeration and symmetry characterization of homopoly-substituted hetero-analogue of [5]-asterane

Enumeration is a useful tool to obtain the stereochemistry of a molecular system. This study presents a bipartite algorithm as a new method of enumeration of homopoly-substituted hetero-analogue of [5]-asterane, with empirical formula C15-qH20-mXq, where the value of m is 1 and 2, respectively, for trivalent and divalent hetero-atom, X. The number of predicted stereoisomers depends on the number q1≤q≤15 of heteroatom that substitutes the carbon atom in the parent molecule [5]-asterane. In this paper, we present 1524 chiral and 360 achiral forms and their symmetry groups, obtained by varying the number of heteroatoms on the homopoly-substituted hetero-analogue of [5]-asterane. This result improves on Pólya methods, which predict 1884 (1524 + 360) stereoisomers for the same molecular system, without providing any further details of the form or symmetry group.