Abstract
By constructing symmetry-adapted wavefunctions and investigating the topological structure, a systematic method is proposed for resolving the π-electron Hamiltonian of a fullerene with a certain symmetry and for treating second-neighbour hopping analytically. Calculations for fullerenes with different symmetries show that second-neighbour hopping has almost no influence for small molecules but may play an important role in the electronic and bonding properties of large carbon clusters.
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