Restricted Enumerations by the Unit-Subduced-Cycle-Index (USCI) Approach. III. The Restricted-Partial-Cycle-Index (RPCI) Method for Treating Interactions Between Two or More Orbits
نویسنده
چکیده
The restricted partial-cycle-index (RPCI) method has been developed by starting from the partial-cycle-index (PCI) method of the unit-subduced-cycle-index (USCI) approach (S. Fujita, “Symmetry and Combinatorial Enumeration in Chemistry”, Springer-Verlag (1991)), where enumerated derivatives are generated by means of vertex substitution (monodentate ligands) and/or edge substitution (bidentate ligands) under a restriction condition that occupation of a common vertex (or occupation of adjacent edges) is avoided. Thus, restricted partial cycle indices with chirality fittingness (PCI-CFs) are derived from unit subduced cycle indices with chirality fittingness (USCI-CFs) via restricted subduced cycle indices with chirality fittingness (SCI-CFs). The resulting restricted PCI-CFs enable us to enumerate derivatives under the restricted condition in a symmetry-itemized fashion. The restricted PCI-CFs are further transformed into restricted cycle indices with chirality fittingness (restricted CI-CFs) for gross enumerations of total, achiral, chiral derivatives. A maple program for the RPCI method is reported as an appendix. MATCH Communications in Mathematical and in Computer Chemistry MATCH Commun. Math. Comput. Chem. 69 (2013) 311-332
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