Application of Thomas-Fermi model to fullerene molecule and nanotube

TL;DR

This paper applies a semiclassical Thomas-Fermi model to estimate the electronic shell dimensions and dipole oscillation frequencies of fullerenes and nanotubes, showing good agreement with experimental data.

Contribution

It demonstrates the effectiveness of the Thomas-Fermi model in predicting electronic shell sizes and oscillation frequencies in fullerenes and nanotubes.

Findings

Calculated electronic shell radii closely match experimental values.

Identified and computed frequencies of dipole oscillations.

Extended the model to nanotubes with specific radii.

Abstract

Semiclassical description, based on electrostatics and Thomas-Fermi model is applied here to calculate dimensions of the electronic shell of a fullerene molecule and a nanotube. The internal radius of the electronic shell of a fullerene molecule, calculated within the framework of the model is 0.2808 nm. The external radius is 0.4182 nm. The experimental values are 0.279 nm and 0.429 nm correspondingly. This shows that semiclassical approach provides rather good description of the dimensions of the electronic shell in a fullerene molecule. Two types of dipole oscillations in a fullerene molecule are considered and their frequencies are calculated. Similar calculations are performed for a nanotube also. For a nanotube with a radius of the cylinder of the ions, Rn = 0.7 nm, the internal radius of the electronic shell, calculated within the framework of the model is 0.577 nm. The external radius is 0.816 nm. Three types of dipole oscillations in nanotube are considered and their frequencies are calculated.