Adamantane isomers with given symmetries. Systematic enumeration by unit subduced cycle indices

Abstract

Tricyclic isomers of adamantane (C 10H 16) are characterized by polymethylene indices (PMI s) and molecular symmetry. The PMI is a partition denoted as [1 m 1/ , 2 m 2/ , ..., 6 m 6/ ](m 1, + 2m 2 + ... + 6m 6 = 6), in which each integer is the length of a polymethylene unit and the power (m r) denotes the number of the units. The isomers are then enumerated by starting from tetrahedron (Td and cyclobutadiene (D 2h) as parent skeletons, in which the edges are considered to be substituted by polymethylenes. From the tetrahedrane skeleton, there emerge 32 isomers, which are classified in terms of PMI and subsymmetries of T The cyclobutadiene skeleton yields 89 isomers classifed by PMIs and subsymmetries of D2. Isomer enumerations are also discussed regarding noradamantane and homoadamantane.