Stereoisomerism Accompanied with Bond Rotations. Characterization of Propane Derivatives by Correlation Diagrams of Epimeric Stereoisograms

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.