Quantitative calculations of the excitonic energy spectra of semiconducting single-walled carbon nanotubes within a $\pi$-electron model

TL;DR

This study uses a semiempirical $b5$-electron model with parameters from conjugated polymers to accurately calculate excitonic spectra of 29 semiconducting single-walled carbon nanotubes, revealing a fundamental link between these materials.

Contribution

It introduces a quantitative method to determine exciton energies in S-SWCNTs using parameters from $b5$-conjugated polymers, bridging the understanding between PCPs and nanotubes.

Findings

Accurately calculated exciton energies for 29 S-SWCNTs.

Established a fundamental relationship between PCPs and S-SWCNTs.

Validated the semiempirical $b5$-electron Hamiltonian for nanotube spectra.

Abstract

Using Coulomb correlation parameters appropriate for $\pi$-conjugated polymers (PCPs), and a nearest neighbor hopping integral that is arrived at by fitting the energy spectra of three zigzag semiconducting single-walled carbon nanotubes (S-SWCNTs), we are able to determine quantitatively the exciton energies and exciton binding energies of 29 S-SWCNTs within a semiempirical $\pi$-electron Hamiltonian that has been widely used for PCPs. Our work establishes the existence of a deep and fundamental relationship between PCPs and S-SWCNTs.