Combinatorial Enumeration of Cubane Derivatives as Three-Dimensional Entities. III. Gross Enumeration by the Characteristic-Monomial Method

The CM (characteristic monomial) method developed by us (S. Fujita, Theor. Chem. Acc., 99, 224–230 (1998), S. Fujita, J. Chem. Inf. Comput. Sci., 40, 1101–1112 (2000)) is applied to enumeration of cubane derivatives with chiral and achiral proligands. For this purpose, CM-CFs (characteristic monomials with chirality fittingness) are calculated by emphasizing the interconvertivity between Q-conjugacy characters and markaracters. Thereby, a dominant CM-CF table is constructed so as to correspond to an irreducible Q-conjugacy character table in the present article (Part III of this series), just as a dominant USCI-CF (unit subduced-cycle index with chirality fittingness) table corresponds to a dominant markaracter table as discussed in Part II of this series. The present set of tables is used to prepare dominant and non-dominant USCI-CFs, which are in turn used to prepare SCI-CFs (subduced cycle indices with chirality fittingness) and CI-CFs (cycle indices with chirality fittingness). The CI-CFs ofOh andO for enumerating cubane derivatives as threedimensional structural isomers and as steric isomers as well as for enumerating achiral and chiral cubane derivatives are clarified to be equivalent to those prepared by the proligand method (Part I of this series) as well as to those prepared by the markaracter method (Part II of this series). A Maple program source for calculating USCI-CFs from CM-CFs is given as an example of practical calculation. MATCH Communications in Mathematical and in Computer Chemistry MATCH Commun. Math. Comput. Chem. 67 (2012) 649-668