Nonclassical C_n (n=30-40, 50) fullerenes containing five-, six-, seven-member rings

Classical and heptagon-contained nonclassical fullerene isomers of C₃₀-C₄₀ and C₅₀ are generated by Spiral algorithm and optimized using DFT methods. There are much larger number of nonclassical isomers than classical ones. Energies of isomers generally increase with the number of heptagons inside and those lowest-energy nonclassical isomers contain only one heptagon. For all fullerenes considered, there is no nonclassical isomer that energetically prevails over the lowest-energy classical counterpart. But the best nonclassical isomers are more stable than most classical ones. The validity of pentagon adjacency penalty rule (PAPR) and hexagon neighbor rule (HNR) is examined for the nonclassical fullerenes. PAPR is still roughly applicable while HNR almost breaks down. A new topological index U with better performance over PAPR and HNR is presented and its superiority is further confirmed on two subsets of C₅₀ isomers. This U index can be considered as an extension of PAPR to nonclassical isomers with existence of heptagons.