Generalized structural motif model for studying the thermodynamic stability of fullerenes: from C60 to graphene passing through giant fullerenes

We present an extension of the structural motif model [Cioslowski et al., J. Am. Chem. Soc., 2000, 122, 8265], originally proposed to predict the relative stability of medium-sized neutral fullerenes (C60–C102), to account for the correct graphene limit, thus widening its range of applicability to giant and supergiant icosahedral fullerenes. The new model has been parameterized using the density functional theory (DFT) energies of 426 distinct fullerenes ranging from C60 to C180, most of which correspond to the lowest-energy isomers of each cage size. While the original model is inapplicable for fullerenes larger than C150, the new model performs very well for these systems, with typical deviations of 3.4 kcal mol−1 from the DFT energies. Based on the optimized parameters, we have obtained the actual energy contributions for all motifs, which we show are closely related to the number and separation of pentagonal rings, in contrast to the original version of the model. We also point out that, in general, motif models result in large deviations for largely aspherical fullerenes and propose a way to correct the errors.