Geometrical Understanding of Fullerene Structures and Electronic States

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Abstract
For the geometrical understanding of general fullerenes, we propose the use of a projection method based on a honeycomb lattice. The formation of general fullerenes is completely specified by the distribution of twelve pentagonal defects on a honeycomb lattice. Utilizing this projection method, we exhibit the geometric specification of icosahedral hyperfullerenes and other fullerenes with lower symmetry. The conception of the “phason line” is introduced for the arrangement of pentagonal defects, where the bond alternation gives rise to misfit in the Kekulé structure. We demonstrate the lattice distortion and the charge distribution of the fullerenes with the phason line, taking account of the electron-phonon interaction to this system.