Stability of fullerenes with four-membered rings

Fullerenes with four-membered rings with up to 60 atoms were systematically generated and their stability examined by the conjugated circuits (CC) model and the topological resonance energy (TRE) model. As none of the models accounts for strain, which is important in spherically shaped conjugated systems with four-membered rings, the results are only qualitative. Values of resonance energy obtained by the two models show remarkable disagreement. Isomers selected as the most stable are quite different in dependence on the criterion used. The structures selected by TRE possess a small number or no four-membered rings (for C60, buckminsterfullerene was selected), while those selected by the CC model sometimes possess greater numbers (up to 6) of four-membered rings, paired by a common edge.