Electronic Structure of Single- and Multiple-shell Carbon Fullerenes

Details Electronic Structure of Single- and Multiple-shell Carbon Fullerenes Electronic Structure of Single- and Multiple-shell Carbon Fullerenes

1993-12-09

arxiv.org/abs/cond-mat/9312040v1

Phys. Rev. B 49 (1994) 5020-5023

Physics

Condensed Matter

Materials Science

5 pages, RevTex, 2 figures upon request (to be published in Physical Review B, Feb. 1994)

Scientific paper

10.1103/PhysRevB.49.5020

We study the electronic states of giant single-shell and the recently discovered nested multi-shell carbon fullerenes within the tight-binding approximation. We use two different approaches, one based on iterations and the other on symmetry, to obtain the $\pi$-state energy spectra of large fullerene cages: $C_{240}$, $C_{540}$, $C_{960}$, $C_{1500}$, $C_{2160}$ and $C_{2940}$. Our iteration technique reduces the dimensionality of the problem by more than one order of magnitude (factors of $\sim 12$ and $20$), while the symmetry-based approach reduces it by a factor of $10$. We also find formulae for the highest occupied and lowest unoccupied molecular orbital (HOMO and LUMO) energies of $C_{60{\cdot}n^{2}}$ fullerenes as a function of $n$, demonstrating a tendency towards metallic regime for increasing $n$. For multi-shell fullerenes, we analytically obtain the eigenvalues of the intershell interaction.

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