A State-Space-View of Atom-Diatom Reactions Relevant to Rarefied Gas Flow

Abstract

A microscopically resolved picture of energy flow in atom-diatom collisions is essential for understanding the non-equilibrium chemistry in rarefied and hypersonic gas flow. Here, a comprehensive ensemble of quasi-classical trajectories on global, reactive, and ``vetted'' potential energy surfaces are employed to construct state-resolved probability maps and to determine the dependence of the outcomes on the initial ro-vibrational states $(v,j)$. The full range of processes, including elastic, inelastic, atom exchange, reactive, and atomization are quantified, revealing distinct structure reactivity relationships. For the [OOO] system consistent trends are obtained from two high-quality potential energy surfaces, despite their different electronic structure and representation techniques. The resulting state-space description provides a comprehensive picture of energy redistribution in high-energy atom-diatom collisions, forming a basis for improved modeling of non-equilibrium chemistry in hypersonic and rarefied environments.

Figures (11)

• Figure 1: Schematic of all PESs used in the present work; energies (in eV) not to scale and no barriers and intermediates shown. Panel Left: The O($^3$P) + O$_2$(X$^3\Sigma_{\rm g}^{-})$ reaction system. Atomization leads to 3O($^3$P). The energies in black are from the RKHS-PES.MM.o3:2025 Middle: The N($^4$S) + O$_2$(X$^3 \Sigma^{-}_{\rm g})$$\rightarrow$ O($^3$P) + NO(X$^2 \Pi$) reaction.MM.no2:2020 Right: The N($^4$S) + NO(X$^2 \Pi$) $\rightarrow$ O($^3$P)+N$_2$(X$^1 \Sigma_{\rm g}^+)$ collision system.MM.n2o:2020 For this last reaction the true PES involves a considerably larger number of states and transition states between them.
• Figure 2: The O($^3$P) + O$_2$(X$^3\Sigma_g^{-} )$ collision system. Panel A: Initial-state domains in $(v,j)$ defining zones I--IV: I: $v\in[0,10],\, j\in[0,50]$; II: $v\in[0,10],\, j\in[150,250]$; III: $v\in[10,30],\, j\in[50,150]$; IV: $v\in[30,50],\, j\in[0,50]$. Panel B: Process distribution: total (black outline, no fill) and zone-resolved bars (colored), with zone bars normalized to the total so they lie within the outline; percentages values are shown only for the total. Panel C: Inelastic final-state distributions $P(v',j')$ for zones I--IV (from left to right), respectively. Panel D: Reactive final-state distributions $P(v',j')$ for zones I--IV. Heat maps use a common logarithmic color scale within each row. Zone colors are consistent across panels, and the zone label appears at the top-right of each map. All simulations were carried out using the RKHS-PES for O$_3$.
• Figure 3: The O($^3$P) + O$_2$(X$^3\Sigma_g^{-} )$ collision system. Origin maps of initial rovibrational states $(v,j)$ that yield the indicated final states $(v',j')$ from simulations using the RKHS-PES for O$_3$. Panels (top–left to bottom–right) correspond to $(v',j')=(2,30)$, $(0,175)$, $(18,95)$, and $(34,45)$. Each panel shows a heat map of counts (logarithmic scale) of trajectories on the discrete grid of available initial states; white cells indicate no events.
• Figure 4: The O($^3$P) + O$_2$(X$^3\Sigma_{\rm g}^{-})$ collision system. Panel A: Initial-state domains in $(v,j)$ defining zones I--IV: I: $v\in[0,10],\, j\in[0,50]$; II: $v\in[0,10],\, j\in[150,250]$; III: $v\in[10,30],\, j\in[50,150]$; IV: $v\in[30,50],\, j\in[0,50]$. Panel B: Process distribution: total (black outline, no fill) and zone-resolved bars (colored), with zone bars normalized to the total so they lie within the outline; percentages values are shown only for the total. Panel C: Inelastic final-state distributions $P(v',j')$ for zones I--IV (from left to right), respectively. Panel D: Reactive final-state distributions $P(v',j')$ for zones I--IV. Heat maps use a common logarithmic color scale within each row. Zone colors are consistent across panels, and the zone label appears at the top-right of each map. All simulations were carried out using the PIP-PES for O$_3$.
• Figure 5: The O($^3$P) + O$_2$(X$^3\Sigma_g^{-} )$ collision system. Origin maps of initial rovibrational states $(v,j)$ that yield the indicated final states $(v',j')$ from simulations using the PIP-PES for O$_3$.varga:2017 Panels (top–left to bottom–right) correspond to $(v',j')=(2,30)$, $(0,175)$, $(18,95)$, and $(34,45)$. Each panel shows a heat map of counts (logarithmic scale) of trajectories on the discrete grid of available initial states; white cells indicate no events.