  A heavy-impact vibrational excitation and dissociation model for CO$_2$ is
presented. This state-to-state model is based on the Forced Harmonic Oscillator
(FHO) theory which is more accurate than current state of the art kinetic
models of CO$_2$ based on First Order Perturbation Theory. The first excited
triplet state $^{3}$B$_{2}$ of CO$_2$, including its vibrational structure, is
considered in our model, and a more consistent approach to CO$_2$ dissociation
is also proposed. The model is benchmarked against a few academic 0D cases and
compared to decomposition time measurements in a shock tube. Our model is shown
to have reasonable predictive capabilities, and the CO$_2$ $+$ O
$\leftrightarrow$ CO $+$ O$_2$ is found to have a key influence on the
dissociation dynamics of CO$_2$ shocked flows, warranting further theoretical
studies. We conclude this study with a discussion on the theoretical
improvements that are still required for a more consistent analysis of the
vibrational dynamics of CO$_2$, discussing the concept of vibrational chaos and
its possible application to CO$_2$. The necessity for further experimental
works to calibrate such state-to-state models is also discussed, with a
proposed roadmap for novel experiments in shocked flows.
