Quantum scattering of hot H/D on CO$_2$: Cross sections and rate coefficients for planetary atmospheres and their evolution

TL;DR

This work addresses the need for accurate quantum data on H/D collisions with CO2 to model energy transfer and atmospheric escape in CO2-rich environments. It employs a $j_z$-conserving coupled-states scattering approach with a RCCSD(T) potential energy surface to compute state-to-state, total, and transport cross sections up to $5$ eV. Key results show that mass-scaling from heavier partners significantly overestimates cross sections by factors of 30–45 and that isotopic differences are energy dependent, influencing Maxwellian-averaged rate coefficients (e.g., $k_H(300~K) = 1.84e-11$ cm^3 s^-1 and $k_D(300~K) = 1.14e-11$ cm^3 s^-1). These quantum data imply exobase shifts of order $10-20$ km and potential order-unity changes in hydrogen escape, with broad implications for Mars, early Earth, and CO2-rich exoplanets; the results provide essential inputs for revisiting atmospheric evolution and are made available as supplementary data.

Abstract

Collisions between hot hydrogen atoms and CO$_2$ play a central role in energy transfer and atmospheric escape in CO$_2$-rich planetary atmospheres. We present quantum mechanical $j_z$-conserving coupled-states calculations of state-resolved cross sections for H/D--CO$_2$ collisions at energies up to 5~eV, benchmarked to within 7\% of close-coupling results. Scattering is strongly forward-peaked, yielding momentum-transfer cross sections substantially smaller than commonly assumed: mass-scaling from O/C--CO$_2$ systems overestimates H--CO$_2$ total cross sections by factors of 30--45, while existing empirical fits underestimate the low-energy regime by up to $\sim$45\%. Isotopic substitution (H/D) produces energy-dependent differences of up to 35\% at $E<0.1$~eV, invalidating uniform scaling approaches for D/H fractionation. Maxwellian-averaged rate coefficients derived from our cross sections are significantly smaller than mass-scaled values, implying reduced H--CO$_2$ energy transfer efficiency. In atmospheric escape modelling, these revisions can shift Martian exobase altitudes by 10--20~km, leading to order-unity changes in thermal escape rates, and have implications for hydrogen loss in early CO$_2$-dominated planetary atmospheres. Our results provide essential quantum-mechanical inputs for revisiting atmospheric evolution scenarios on Mars, early Earth, and CO$_2$-rich exoplanets.

Figures (5)

• Figure 1: State-to-state cross sections $\sigma_{j=0 \to j'}$ for the scattering of CO$_2$ with H for selected collision energies.
• Figure 2: Total cross sections $\sigma_{j=0}^{\rm tot}$ for CO$_2$ in collisions with H, D, O, and C as a function of collision energy. The O--CO$_2$ and C--CO$_2$ results are shown after reduced-mass scaling for comparison. The thick red line denotes the error margin of the H--CO$_2$ total cross sections from lewkow2014precipitation. Dashed red and blue lines show the elastic contributions for H--CO$_2$ and D--CO$_2$, respectively.
• Figure 3: Angular dependence of H--CO$_2$ differential cross sections (left panel) and relative deviations upon H/D isotopic substitution (right panel) for selected collision energies. The horizontal line marks perfect agreement. Large relative deviations at very small angles occur in a strongly forward-peaked regime and should be interpreted together with the corresponding absolute cross sections.
• Figure 4: Dependence of state-specific transport cross sections on collision energy for H--CO$_2$($j=0$). Dashed lines show the elastic contribution. Comparison between close-coupling and coupled-states calculations.
• Figure 5: Maxwellian-averaged momentum-transfer rate coefficients $k_{\rm mt}(T)$ for H--CO$_2$ (blue circles and line) and D--CO$_2$ (red squares and line) collisions. Solid curves show the smoothly interpolated values, while symbols mark the temperatures listed in Table \ref{['tab:rate_coeff']}. The behaviour is well approximated by power laws (dashed lines) of the form $k(T) = A T^{B}$ with $A_{\rm H}=2.00 \times 10^{-10}$ cm$^3$ s$^{-1}$, $B_{\rm H}=-0.410$ for H--CO$_2$ and $A_{\rm D}=1.35 \times 10^{-10}$ cm$^3$ s$^{-1}$, $B_{\rm D}=-0.429$ for D--CO$_2$.