H\"uckel--Hubbard-Ohno modeling of $\boldsymbol{\pi}$-bonds in ethene and ethyne with application to trans-polyacetylene

TL;DR

This paper models pi-bonds in ethene and ethyne using a Hückel-Hubbard-Ohno approach and applies it to trans-polyacetylene, providing insights into bond energies and electronic excitations.

Contribution

It introduces a Hückel-Hubbard-Ohno model for pi-bonds in small molecules and extends it to describe properties of conjugated polymers like trans-polyacetylene.

Findings

Peierls coupling can be estimated with some precision.

Hubbard-Ohno parameters are insignificant at certain distances.

The model successfully describes bond lengths and electronic excitations in trans-polyacetylene.

Abstract

Quantum chemistry calculations provide the potential energy between two carbon atoms in ethane (H$_3$C$-$CH$_3$), ethene (H$_2$C$=$CH$_2$), and ethyne (HC$\equiv$CH) as a function of the atomic distance. Based on the energy function for the $\sigma$-bond in ethane, $V_{\sigma}(r)$, we use the H\"uckel model with Hubbard--Ohno interaction for the $\pi$~electrons to describe the energies $V_{\sigma\pi}(r)$ and $V_{\sigma\pi\pi}(r)$ for the $\sigma\pi$ double bond in ethene and the $\sigma\pi\pi$ triple bond in ethyne, respectively. The fit of the force functions shows that the Peierls coupling can be estimated with some precision whereas the Hubbard-Ohno parameters are insignificant at the distances under consideration. We apply the H\"uckel-Hubbard-Ohno model to describe the bond lengths and the energies of elementary electronic excitations of trans-polyacetylene, (CH)$_n$, and adjust the $\sigma$-bond potential for conjugated polymers.