Hierarchical Enumeration Based on Skeletons of Ligancy 6 by Using Combined-Permutation Representations. Part 2. Prismane Derivatives

摘要

Group hierarchy for characterizing a prismane skeleton with six substitution positions has been discussed by defining the point group (PG), the RS-stereoisomeric group (RS-SIG), the stereoisomeric group (SIG), and the isoskeletal group (ISG) successively as follows: PG D-3h (order 12) subset of RS-SIG D-3h (sigma) over tilde(I) over cap (order 24) = SIG (the same as D-3h (sigma) over tilde(I) over cap) subset of ISG ([6])(S sigma(I) over cap) (order 1440). On the basis of combined-permutation representations (S. Fujita, MATCH Commun. Math. Comput. Chem. 76 (2016) 379-400), Fujita's proligand method (S. Nita, Combinatorial Enumeration of Graphs, Three-Dimensional Structures, and Chemical Compounds, University of Kragujevac, Faculty of Science, Kragujevac, 2013) is modulated and applied to the enumeration of prismane derivatives under the group hierarchy. A set of three ligand-inventory functions is introduced into cycle indices with chirality fittingness (CI-CFs) to give generating functions for the enumeration of 3D structures under PG and RS-SIG. On the other hand, a single ligand-inventory function is introduced into CI-CFs to give generating functions for the enumeration of 2D structures under SIG and MG. The enumeration results are discussed systematically in terms of isomer-classification diagrams.