Symmetry-Itemized Enumeration of Cubane Derivatives as Three-Dimensional Entities by the Fixed-Point Matrix Method of the USCI Approach

Abstract

Abstract Cubane derivatives with chiral and achiral proligands are counted as three-dimensional (3D) structural isomers by the fixed-point matrix method of the unit-subduced-cycle-index (USCI) approach (S. Fujita, “Symmetry and Combinatorial Enumeration in Chemistry,” Springer-Verlag, 1991). The numbers of such 3D structural isomers are itemized with respect to their point-group symmetries, which are subgroups of the point group Oh for a cubane skeleton. For this purpose, the full list of unit subduced cycle indices with chirality fittingness (USCI-CFs) of Oh is constructed in a tabular form. Fixed-point vectors or fixed-point matrices, which are calculated by starting from USCI-CFs, are used to count 3D structural isomers in the form of isomer-counting matrices. A Maple program source for counting cubane derivatives as 3D structural isomers is given as an example of practical calculation.