Restricted Enumerations by the Unit-Subduced-Cycle-Index (USCI) Approach. II. Restricted Subduced Cycle Indices for Treating Interactions Between Two or More Orbits

摘要

The restricted-fixed-point-matrix (RFPM) method is developed as an extension of the fixed-point-matrix (FPM) method, which is one of the four methods of the unit-subducedcycle-index (USCI) approach (S. Fujita, "Symmetry and Combinatorial Enumeration in Chemistry", Springer-Verlag (1991)). The RFPM method is capable of combinatorial enumerations of 3D structures or graphs under a restricted condition, where orbits of vertices and edges interact each other. Subduced cycle indices with chirality fittingness (SCI-CFs), which are calculated for an unrestricted condition by starting from unit subduced cycle indices with chirality fittingness (USCI-CFs), are converted into restricted SCI-CFs by means of newly-defined territory indicators (TIs) of vertices and edges. Such restricted SCI-CFs as calculated for respective subgroups are effective to evaluate the numbers of fixed points (promolecules) on the action of the subgroups under the restricted condition, where the occupation of a common vertex or the occupation of adjacent edges is avoided.