Vibrational, non-adiabatic and isotopic effects in the dynamics of the H$_2$ + H$_2^+$ $\rightarrow$ H$_3^+$ + H reaction: application to plasma modeling

The title reaction is studied using a quasi-classical trajectory method for collision energies between 0.1 meV and 10 eV, considering the vibrational excitation of H$_2^+$ reactant. A new potential energy surface is developed based on a Neural Network many body correction of a triatomics-in-molecules potential, which significantly improves the accuracy of the potential up to energies of 17 eV, higher than in other previous fits.The effect of the fit accuracy and the non-adiabatic transitions on the dynamics are analyzed in detail.The reaction cross section for collision energies above 1 eV increases significantly with the increasing of the vibrational excitation of H$_2^+$($v'$), for values up to $v'$=6. The total reaction cross section (including the double fragmentation channel) obtained for $v'$=6 matches the new experimental results obtained by Savic, Schlemmer and Gerlich [Chem. Phys. Chem. 21 (13), 1429.1435(2020)]. The differences among several experimental setups, for collision energies above 1 eV, showing cross sections scattered/dispersed over a rather wide interval, can be explained by the differences in the vibrational excitations obtained in the formation of H$_2^+$ reactants. On the contrary, for collision energies below 1 eV, the cross section is determined by the long range behavior of the potential and do not depend strongly on the vibrational state of H$_2^+$. In addition in this study, the calculated reaction cross sections are used in a plasma model and compared with previous results. We conclude that the efficiency of the formation of H$_3^+$ in the plasma is affected by the potential energy surface used.