Benzene Derivatives with Achiral and Chiral Substituents and Relevant Derivatives Derived from D6h Skeletons. Symmetry-Itemized Enumeration and Symmetry Characterization by the Unit-Subduced Cycle Index Approach

Abstract

The unit-subduced cycle index (USCI) approach is applied to the enumeration of isomers based on D6h skeletons, where the inverses of a mark table and a USCI table are precalculated for the point group D6h. Thus, benzene derivatives with achiral substituents are enumerated by using partial cycle indices (PCIs) in an itemized manner concerning the formulas and symmetries. The formulation of partial cycle indices with chirality fittingness (PCI-CFs) enables us to enumerate benzene derivatives with chiral and achiral substituents. The USCI approach is also applied to the enumeration of isomers derived from a coronene skeleton that also belongs to the point group D6h. The PCIs (or PCI-CFs) of zero or nonzero expressions are discussed in terms of a selection rule for judging the existence of subsymmetries. The symmetries of the resulting derivatives are discussed in terms of sphericities.