Abstract
Abstract The stereoisomerism of propane derivatives with bond rotations is investigated by means of correlation diagrams of stereoisograms, where the diagrams are governed by epimeric RS-stereoisomeric groups formulated as subgroups of stereoisomeric groups. A molecular-symmetry group GCσ for specifying the eight positions of a propane skeleton is obtained as a wreath product with chirality fittingness (C2v[C3v, C∞v]), where bond rotations are taken into consideration. The group GCσ of order 36 is extended to give the corresponding RS-stereoisomeric group $\boldsymbol{{G}}_{\boldsymbol{{C}}\boldsymbol{{\sigma}}\tilde{\boldsymbol{{\sigma}}}\skew2\hat{\boldsymbol{{I}}}}$ of order 72, which characterizes the global symmetry of the propane skeleton. Then the group $\boldsymbol{{G}}_{\boldsymbol{{C}}\boldsymbol{{\sigma}}\tilde{\boldsymbol{{\sigma}}}\skew2\hat{\boldsymbol{{I}}}}$ is further extended to give a stereoisomeric group H of order 288 for treating chiral and achiral proligands (or $\ddot{\boldsymbol{{H}}}$ of order 144 for treating achiral proligands only) by considering epimerizations at the three RS-stereogenic carbon centers (for Ci, i = 1,2,3). The groups H or $\ddot{\boldsymbol{{H}}}$ are useful to investigate thestereoisomerism of propane derivatives. An epimeric RS-stereoisomeric group $\boldsymbol{{G}}_{\boldsymbol{{C\boldsymbol{{\sigma}}} }}^{\tilde{{\boldsymbol{{\sigma}}}}_{\boldsymbol{{i}}}}$ (or $\ddot{\boldsymbol{{G}}}_{\boldsymbol{{C\boldsymbol{{\sigma}}} }}^{\tilde{{\boldsymbol{{\sigma}}}}_{\boldsymbol{{i}}}}$) is selected as a subgroup of H (or $\ddot{\boldsymbol{{H}}}$) in order to show the local RS-stereogenicity at a given RS-stereogenic center (Ci), where the element $\tilde{\sigma }_{i}$ represents an epimerization at the Ci atom. Such an epimeric RS-stereoisomeric group $\boldsymbol{{G}}_{\boldsymbol{{C\boldsymbol{{\sigma}}} }}^{\tilde{{\boldsymbol{{\sigma}}}}_{\boldsymbol{{i}}}}$ (or $\ddot{\boldsymbol{{G}}}_{\boldsymbol{{C\boldsymbol{{\sigma}}} }}^{\tilde{{\boldsymbol{{\sigma}}}}_{\boldsymbol{{i}}}}$) corresponds to a correlation diagram of stereoisograms for showing RS-stereoisomeric relationships at the Ci atom, i.e., enantiomeric, RS-diastereomeric, and holantimeric relationships. Two RS-diastereomers of each pair are pairwise specified by a pair of RS-stereodescriptors of the CIP system.
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