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A methodology to evaluate the kinetic stability of molecular nanostructures is presented based on the assumption of the independent and random nature of thermal vibrations, calculated at the density functional theory (DFT) level of theory using the harmonic approximation . The kinetic stability (KS) is directly correlated to the cleavage probability for the weakest bond of a given molecular geometry. The application of the presented method to a selection of fullerenes (see Fig. 1) and carbon nanotubes yields clear correlation to their experimentally observed relative isomer abundances.
Moreover, we present good agreement of harmonic vibrational eigenmodes between DFT and the computationally more efficient density-functional tight-binding (DFTB) method [2-4]. Thus, DFTB-based KS calculations allow the estimation of kinetic stability for more than 100,000 isomers of the fullerenes C20-C100. We found that the experimentally observed isomer abundances, as recorded for instance by mass spectroscopic investigations, are reasonably well reproduced by the Boltzmann-weighted kinetic stabilities of the cage isomers. This result suggests a mechanism of fullerene formation involving cage destruction, such as recently predicted by quantum chemical molecular dynamics (QM/MD) simulations [5-6].
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