Stereoisograms for reorganizing the theoretical foundations of stereochemistry and stereoisomerism. Part 1: diagrammatic representations of RS-stereoisomeric groups for integrating point groups and RS-permutation groups

Three types of groups, that is, point groups, RS-permutation groups, and ligand-reflection groups, are integrated in a consistent way. As a result, RS-stereoisomeric groups are generated so as to be capable of constructing a strict and succinct mathematical framework for reorganizing modern stereochemistry. A stereoisogram is proposed as a diagrammatic expression of an RS-stereoisomeric group, which contains a quadruplet of promolecules derived from a given skeleton in terms of the proligand–promolecule model. The four promolecules of the quadruplet are correlated to one another by means of enantiomeric, RS-diastereomeric, and holantimeric relationships according to the three types of groups. These relationships are respectively correlated to three pairs of attributes, that is, chirality/achirality, RS-stereogenicity/RS-astereogenicity, and sclerality/asclerality. The mathematical rationalization of the three pairs of attributes is in sharp contrast to the presumption of a single pair of attributes (i.e., chirality/achirality) supporting modern stereochemistry. By simple mathematical treatments, it is proven that there are only five types of stereoisograms (type I–V). The group-subgroup relationship concerned with an RS  -stereoisomeric group, for example, Tdσ∼I^ for a tetrahedral skeleton, allows us to accomplish qualitative and quantitative discussions for reorganizing modern stereochemistry. As Part 1 of this series, this article is devoted to a theoretical formulation of the stereoisogram approach.

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