Partitioned-Formula Periodic Tables for Diamond Hydrocarbons (Diamondoids)

Isomeric diamond hydrocarbons (diamondoids or polymantanes) with the same number n of adamantane units share the same molecular formula C(Q)(CH)(T)(CH(2))(S) and can be divided into valence isomers (denoted as Q-T-S) by partitioning the number C = Q + T + S of their carbon atoms according to whether they are quaternary, tertiary, or secondary. Vertices of dualists are the centers of adamantane units, and dualist edges connect vertices of adjacent adamantane units (sharing a chair-shaped hexagon). Dualists of diamondoids are hydrogen-depleted skeletons of staggered alkane or cycloalkane rotamers. Diamondoids with acyclic dualists can be classified as catamantanes, those having dualists with chair-shaped six-membered rings as perimantanes, and those having dualists with higher-membered rings that are not perimeters of hexagon-aggregates as coronamantanes. Diamondoids with n adamantane units may be classified into regular catamantanes when the molecular formula is C(4n+6)H(4n+12), and irregular polymantanes (catamantanes or perimantanes) when the number of carbon atoms is lower than 4n + 6. The derivation is presented of formula-periodic tables of regular and irregular diamondoids that allow a better understanding of the shapes and properties of these hydrocarbons for which many applications are predicted.