Klein Four-Group as the Factor Group for Elucidating RS-Stereoisomerism of Cubane Derivatives. The Factor-Group Method for Type-Itemized Enumeration of Stereoisograms
Abstract
Van't Hoff's way (asymmetry, stereogenicity) and Le Bel's way (dissymmetry, chirality) are compared from the viewpoint of two ways for investigating organic stereochemistry, where cubane derivatives of the point group \(\mathbf{O}_{h}\) are selected as
probes. For emphasizing Le Bel's way, combinatorial enumerations of 3D structures under point groups are first discussed to develop Fujita's proligand method and Fujita's USCI approach. The foundations of these enumerations are applied
to support synthetic studies of stereoisomers for emphasizing van't Hoff's way after the proposal of Fujita's stereoisogram approach based on RS-stereoisomeric groups, e.g., \(\mathbf{O}_{h\widetilde{\sigma}\widehat{I}}\).
Importance of the proligand-promolecule model is emphasized in enumerations under point groups (Fujita's proligand method and Fujita's USCI approach) as well as in enumerations of RS-stereoisomeric groups (Fujita's stereoisogram
approach). After the five types (type I to type V) of stereoisograms are classified into three categories (i.e., Category 1 (types I/IV), Category 2 (types II/III/V), and the co-existence case), the half-size-subgroup method and the factor-group
method have been developed for type-itemized enumerations of stereoisograms. Type-V stereoisograms for characterizing "extended pseudoasymmetry" are discussed by assigning their configuration numbers and CA-descriptors.
