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 analysed 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). doi:10.1002/cphc.v21.13]. 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 behaviour 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.
