Computer-Oriented Representations of RS-Stereoisomeric Groups and Cycle Indices with Chirality Fittingness (CI-CFs) Calculated by the GAP System. Enumeration of RS-Stereoisomers by Fujita's Proligand Method

摘要

A point group for specifying chirality and an RS-permutation group for specifying RS-stereogenicity are differentiated by means of mirror-coset representations. They are integrated to generate an RS-stereoisomeric group, after the computer-oriented representation of the RS-stereoisomeric group has been developed by starting from mirror-coset representations. Thereby, the processes of combinatorial enumeration are computerized on the basis of the GAP system. The construction of an RS-stereoisomeric group stems from an appropriate generators by using the Group function of the GAP system. The calculation of the corresponding cycle index with chirality fittingness (CI-CF) is based on the function CalcConjClassCICF developed as a function of the GAP system. The calculation of the corresponding generating function and the evaluation of the coefficient of each term are conducted by using newly-developed GAP functions. The source lists of practical procedures for combinatorial enumeration of 3D structures are attached as appendices.