Combinatorial enumeration of ethane derivatives as three-dimensional chemical structures,not as graphs. A systematic approach for enumerating and characterizing stereoisomers of tartaric acids and related compounds

Fujita’s proligand method is applied to the enumeration of ethane derivatives, where the counting of stereoisomers of tartaric acids is examined in detail as a probe for testing the versatility of the method. The cycle index with chirality fittingness (CI-CF) for enumerating ethane derivatives is obtained by Fujita’s proligand method and compared with the CI-CF derived alternatively by the direct calculation of permutations of substitution positions. The two CI-CFs are identical with each other so that the methodology underlying in Fujita’s method is demonstrated in a concrete fashion. The enumeration results are compared with those derived by Pólya’s corona. Fujita’s proligand method is shown to be capable of enumerating stereoisomers, whereas Pólya’s corona is concluded to enumerate graphs, but not stereoisomers. The conceptually change from graphs to three-dimensional (3D) chemical structures is discussed, where the superiority of Fujita’s proligand method is demonstrated.