Diamond hydrocarbons revisited: partitioned formula tables of diamondoids

Isomeric diamondoids with the same number of adamantane units (or cells), which share the same molecular formula , can be divided into valence isomers by partitioning the number of their carbon atoms according to whether they are Quaternary, Tertiary, or Secondary: . Each []diamondoid has a dualist (or inner dual) with vertices (situated at centers of adamantane units), and edges connecting vertices of adjacent adamantane units sharing a chair-shaped hexagon of carbon atoms. Such a dualist is characterized by a quadruplet of indices (denoted as p, s, t, q for primary, secondary, tertiary, or quaternary) specifying again the connectivity of each vertex by assimilating it with a virtual carbon atom. The diamond lattice is self-dual. Dualists help in classifying diamondoids as catamantanes with acyclic dualists, perimantanes with dualists having chair-shaped six-membered rings, or coronamantanes with dualists having only higher-membered rings. In turn, catamantanes can be either regular when they have formulas , or irregular when the numbers of carbon and hydrogen atoms are lower than the above values for the given numbers of adamantane units. Regular catamantanes can have branched or non-branched dualists and they are isomeric when having the same . Partitioned formulas reflect the branching patterns, encoded in their dualists. Partition formulas and codes are presented for all possible diamondoids with up to 7 adamantane units. A remarkable symmetry is observed for the table of partition periodic table of regular catamantanes with up to 7 adamantane units. Isomeric irregular catamantanes with six or more adamantane units may be valence-isomeric (or homomeric, sharing both the molecular and the partitioned formulas), or heteromeric when they have different partitioned formulas.