Kekulénoid Addition Patterns for Fullerenes and Some Lower Homologs
Additional Document Info
The challenging problem of the enumeration and generation of addition patterns for fullerenes such that the remnant -network has a Kekul structure (i.e., a nearest neighbor pairing pattern) is studied. A methodology to generate (and thence also to enumerate) these Kekulnoid addition patterns is described, and applied to several fullerenes of up to 36 carbons. Plya-theoretic (coloring) pattern counts which ignore Kekul structures are found to be much larger than the Kekulnoid-restricted counts. Evidence is marshaled for simple yet general approximate "asymptotic-flavored" formulas for the various counts. As a consequence, the number of Kekulnoid addition patterns C NH2m for buckminsterfullerene C60 is estimated. Overall, this is but 0.1% of the Plya-theoretic addition pattern counts for all numbers of addition sites.