Diamond hydrocarbons revisited: partitioned formula tables of diamondoids.

Isomeric diamondoids with the same number $$n$$ of adamantane units (or cells), which share the same molecular formula $$\text{ C}_\mathrm{Q}(\text{ CH})_\mathrm{T}(\text{ CH}_{2})_\mathrm{S}$$, can be divided into valence isomers by partitioning the number $$C $$ of their carbon atoms according to whether they are Quaternary, Tertiary, or Secondary: $$C =Q +T +S$$. Each [ $$n$$]diamondoid has a dualist (or inner dual) with $$n$$ 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 $$\text{ C}_{4n+6}\text{ H}_{4n+12}$$, or irregular when the numbers of carbon and hydrogen atoms are lower than the above values for the given numbers $$n$$ of adamantane units. Regular catamantanes can have branched or non-branched dualists and they are isomeric when having the same $$n$$. 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. [ABSTRACT FROM AUTHOR]