Systematic Enumeration of High Symmetry Molecules by Means of Unit Subduced Cycle Indices with and without Chirality Fittingness

Abstract

Abstract A novel method of enumerating isomers is presented by using adamantane as a parent skeleton. This method is based on unit subduced cycle indices with and without chirality fittingness, the indices being derived from the subduction of coset representations. The chirality fittingness, which is determined by examining the relationship between a point group and its subgroup, controls the mode of substitution by achiral and chiral substituents. The method provides detailed enumerations concerning symmetries and molecular formulas, whereas Pólya’s theorem takes only the latter into consideration.