Benzene derivatives with achiral and chiral substituents and relevant derivatives derived from D-6h skeletons. Symmetry-itemized enumeration and symmetry characterization by the unit-subduced cycle index approach

The unit-subduced cycle index (USCI) approach is applied to the enumeration of isomers based on D-6h skeletons, where the inverses of a mark table and a USCI table are precalculated for the point group D-6h Thus, benzene deri vatives with achiral substituents are enumerated by using partial cycle ind ices (PCIs) in an itemized manner concerning the formulas and symmetries. T he formulation of partial cycle indices with chirality fittingness (PCI-CFs ) enables us to enumerate benzene derivatives with chiral and achiral subst ituents. The USCI approach is also applied to the enumeration of isomers de rived from a coronene skeleton that also belongs to the point group D-6h. T he PCIs (or PCI-CFs) of zero or nonzero expressions are discussed in terms of a selection rule for judging the existence of subsymmetries. The symmetr ies of the resulting derivatives are discussed in terms of sphericities.