Dependence of Binding Energy on the Number of Atoms for Carbon Fullerences

Using a molecular orbital method with non-local-density and Harris-functional approximations, the bond lengths, binding energies and HOMO-LUMO energy gaps of the carbon fullerenes C(n) have been calculated on the assumption that all bond lengths in each fullerene are the same. The results are as follows. (1) The binding energies (per atom) of C(n) containing hexagonal and pentagonal rings are expressed as F-A/n, where F and A are the binding energy (per atom) of an infinitely long carbon fullerene and the excess strain energy of pentagonal rings, respectively. (2) The values of A for C(n) (n=24-36) are larger than those for C(n)(n=60-120), because of the adjoining pentagonal rings in the former. (3) C60, C70, C100, C90, C32 and C120, in decreasing order, have especially large HOMO-LUMO energy gaps and are expected to be less reactive.