The Minimum Pentagon-Adjacency Rule

The most stable isomer of a particular fullerene will be an isomer with the smallest possible number A of pentagon-pentagon fusions. 

The most extensive test of this idea is a study using the QCFF/PI semiempirical method to estimate the relative stabilities of all 1812 distinct fullerene isomers of As 

A more specific form of the minimal adjacency rule has been suggested. To each fullerene isomer it is possible to attach apentagon neighbor index signature ft where Pi (k = 0. 5) is the number of pentagons with k pentagonal neighbors. Trivially, 

The calculations in Ref. 62 highlight certain isomers within the minimal-Afp class as most stable. A rule compatible with these results is as follows  

The most stable isomer of the class with minimal Np is one that minimizes 

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