Electronic Structure of Single- and Multiple-shell Carbon Fullerenes

TL;DR

This paper investigates the electronic states of large single-shell and nested multi-shell carbon fullerenes using tight-binding models, introducing efficient computational methods and formulas for energy levels, revealing a trend towards metallic behavior with increasing size.

Contribution

It presents two novel approaches for calculating electronic spectra of large fullerenes and derives formulas for HOMO and LUMO energies as functions of fullerene size.

Findings

Iteration method reduces problem dimensionality significantly.

Symmetry-based approach further simplifies calculations.

HOMO and LUMO energies approach metallic regime as size increases.

Abstract

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.