Chirality and stereogenicity for allene derivatives. Observance and violation of chirality fittingness

Allene derivatives have been combinatorially enumerated under a point group D-2d as well as under a permutation group S-9([4]), which is a subgroup of the symmetric group of degree 4 and is isomorphic to the point group D-2d. These enumerations have been compared in terms of the observance and the vilolation of chirality fittingness, where two types of Young's tableaus (point-group symmetry and permutation-group symmetry) have been used to clarify the relationship between stereochernistry and permutability of allene derivatives. The concept of chirality/achirality for stereochemistry has been compared with the concept of stereogenicity/astereogenicity for permutability. Enantiomers, which have been characterized by equivalency under point-group symmetry, have been classified into two classes according to whether or not they have been assigned to orbits (equivalence classes) under permutation-group symmetry. On the other hand, diastereomers have been related to equivalence classes (orbits) under permutation-group symmetry only. The terms enantiostereogenic and diastereogenic have been coined to discuss the behavior under permutaiton-group symmetry. The CIP (Cahn-Ingold-Prelog) system is examined in terms of stereogenicity/astereogenicity. A new combination of chirality and stereogenicity described in the present paper provides us with a tool for restructuring stereochemistry.