A study of carbon nanosystems using the Hubbard model

The Hubbard model is used as a framework for analyzing carbon nanosystems: the fullerenes C₆₀ and C₈₀ and open-ended carbon nanotubes with chiralities (5, 5) and (10, 10) of various lengths. In the strong-correlation limit, the model predicts that open carbon nanotubes have a lower energy per atom as compared to C₆₀ and C₈₀ fullerenes. This finding contradicts the conventional view that dangling bonds increase the energy of a system. However, the increase, if any, is due to the presence of five-member carbon rings in fullerenes. The energy per atom should be higher for the five-member carbon ring compared to the six-member one, because the former cannot exist in a lower energy singlet state. Carbon nanotube growth is explained. The ionization energies and electron affinities of C₆₀ and C₈₀ fullerenes are calculated and found to agree well with experimental data.