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Diamond hydrocarbons revisited: partitioned formula tables of diamondoids

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Abstract

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.

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  1. Department of Marine Sciences, Texas A&M University at Galveston, 200 Seawolf Parkway, Galveston, TX, 77553, USA

    Alexandru T. Balaban

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Balaban, A.T. Diamond hydrocarbons revisited: partitioned formula tables of diamondoids. J Math Chem 51, 1043–1055 (2013). https://doi.org/10.1007/s10910-012-0130-7

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