  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.
