Abstract
Molecules derived from a parent skeleton are enumerated where both achiral ligands as well as chiral ligands are allowed. Chirality fittingness of an orbit is proposed in order to permit chiral ligands. The enumeration is conducted with and without consideration of obligatory minimum valency (OMV). The effect of the OMV is formulated by assigning different weights to the respective orbits of the parent skeleton. The importance of coset representations and their subduction by subgroups is discussed. The subduced representations are classified into three classes through their chirality fittingness, which determines the mode of substitution with chiral and achiral ligands. Several novel concepts such as a unit subduced cycle index and a subduced cycle index are given in general forms.
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Fujita, S. Subduction of coset representations. An application to enumeration of chemical structures with achiral and chiral ligands. J Math Chem 5, 121–156 (1990). https://doi.org/10.1007/BF01166424
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DOI: https://doi.org/10.1007/BF01166424