Combinatorial Enumeration of Cubane Derivatives as Three-Dimensional Entities. IV. Gross Enumeration by the Extended Superposition Method

The extended superposition method, which has been developed by us as an extension of the concept of elementary superposition (S. Fujita, Theor. Chim. Acta, 82, 473–498 (1992)), is applied to enumeration of cubane derivatives with chiral and achiral proligands. This method provides us with a tool for evaluating the respective contribution of each USCI-CF (unit subduced-cycle index with chirality fittingness) to the corresponding CI-CF (cycle index with chirality fittingness), which is in turn calculated by means of the proligand method, the markaracter method, the characteristic-monomial method or others. The extended superpositionmethod does not require generating functions but requires cycle indices (CI) for regular and irregular cases, which depend upon permutational features of chiral and/or achiral (pro)ligands. Calculated values by the extended superposition method are clarified to be identical with those obtained in terms of generating functions. Effects of chiral proligands (as three-dimensional structures) on the numbers of cubane derivatives are detailedly compared with those of the corresponding graphs (as two-dimensional constitutions). MATCH Communications in Mathematical and in Computer Chemistry MATCH Commun. Math. Comput. Chem. 67 (2012) 669-686