Enumeration of stereoisomers of chiral and achiral derivatives of monocyclic cycloalkanes having heteromorphous alkyl substituents with the same length k
Alphonse Emadak, Robert Martin Nemba, Issofa Patouossa, Ibrahim Mbouombouo Ndassa, Beauregard Thomas Makon
A combinatorial method based on the determination of the averaged weight of permutations controlling the chirality/achirality fittingness of 2n substitution sites of the monocyclic cycloalkane allows to obtain generalized functional equations for direct enumeration of enantiomers pairs and achiral skeletons of any derivatives of monocyclic cycloalkanes having heteromorphous alkyl substituents of the same length or order k with the empirical formula , wherein at least two alkyl substituents of the same size k have each a distinct steric configuration y(1< y< sk), sk is the total number of chiral and achiral alkyl radicals sterically different of same order k. my is the number of alkyl radicals of steric configuration g of the system verifying the relation . The integer sequences of enantiomer pairs and achiral skeletons are established for substituted derivatives of monocyclic cycloalkane for n=3, 4 and k=3, 4, 5. The composite stereoisomerisms of this particular compounds is also highlighted.