The C($^3$P) + O$_2$($^3 \Sigma_g^-$) $\leftrightarrow$ CO$_2$ $\leftrightarrow$ CO($^1 \Sigma^+$)+ O($^1$D)/O($^3$P) Reaction: Thermal and Vibrational Relaxation Rates from 15 K to 20000 K

TL;DR

This study uses quasi classical trajectory simulations on multiple potential energy surfaces to analyze the reaction rates, vibrational relaxation, and atom exchange barriers of the C($^3$P) + O$_2$ reaction over a wide temperature range, aligning well with experimental data.

Contribution

It provides detailed computational insights into reaction dynamics, vibrational relaxation, and energy barriers for the C + O$_2$ system across a broad temperature spectrum, extending understanding beyond previous experimental limitations.

Findings

Forward reaction rates match measurements from 15 K to 295 K.

Vibrational relaxation involves both reactive and non-reactive processes with distinct contact times.

The atom exchange barrier is approximately 7 kcal/mol, consistent with experimental values.

Abstract

Thermal rates for the C($^3$P) + O$_2$($^3 \Sigma_g^-$) $\leftrightarrow$ CO($^1 \Sigma^+$)+ O($^1$D)/O($^3$P) reaction are investigated over a wide temperature range based on quasi classical trajectory (QCT) simulations on 3-dimensional, reactive potential energy surfaces (PESs) for the $^1$A$'$, $(2)^1$A$'$, $^1$A$''$, $^3$A$'$ and $^3$A$''$ states. The forward rate matches measurements at 15 K to 295 K whereas the equilibrium constant determined from the forward and reverse rates are consistent with those derived from statistical mechanics at high temperature. Vibrational relaxation, O+CO($\nu=1, 2$) $\rightarrow$ O+CO$(\nu=0)$, is found to involve both, non-reactive and reactive processes. The contact time required for vibrational relaxation to take place is $\tau \geq 150$ fs for non-reacting and $\tau \geq 330$ fs for reacting (oxygen atom exchange) trajectories and the two processes are shown to probe different parts of the global potential energy surface. In agreement with experiments, low collision energy reactions for the C($^3$P) + O$_2$($^3 \Sigma_g^-$, $v=0$) $\rightarrow$ CO($^1 \Sigma^+$)+ O($^1$D) lead to CO($^{1}\Sigma^{+}$, $v'=17$) with an onset at $E_{\rm c} \sim 0.15$ eV, dominated by the $^1$A$'$ surface with contributions from the $^3$A$'$ surface. Finally, the barrier for the CO$_{\rm A}$($^1\Sigma^+$) + O$_{\rm B}$($^3$P) $\rightarrow$ CO$_{\rm B}$($^{1}\Sigma^{+}$) + O$_{\rm A}$($^3$P) atom exchange reaction on the $^3$A$'$ PES yields a barrier of $\sim 7$ kcal/mol (0.300 eV), consistent with an experimentally reported value of 6.9 kcal/mol (0.299 eV).