Non-adiabatic couplings and dynamics in proton transfer reactions of H n + systems: Application to H 2 + H 2 + → H + H 3 + collisions

Analytical derivatives and non-adiabatic coupling matrix elements are derived for H n + systems (n = 3-5). The method uses a generalized Hellmann-Feynman theorem applied to a multi-state description based on diatomics-in-molecules (for H 3 +) or triatomics-in-molecules (for H 4 + and H 5 +) formalisms, corrected with a permutationally invariant many-body term to get high accuracy. The analytical non-adiabatic coupling matrix elements are compared with ab initio calculations performed at multi-reference configuration interaction level. These magnitudes are used to calculate H 2 (v ′ = 0, j ′ = 0) + H 2 + (v, j = 0) collisions, to determine the effect of electronic transitions using a molecular dynamics method with electronic transitions. Cross sections for several initial vibrational states of H 2 + are calculated and compared with the available experimental data, yielding an excellent agreement. The effect of vibrational excitation of H 2 + reactant and its relation with non-adiabatic processes are discussed. Also, the behavior at low collisional energies, in the 1 meV-0.1 eV interval, of interest in astrophysical environments, is discussed in terms of the long range behaviour of the interaction potential which is properly described within the triatomics-in-molecules formalismWe also thank the support from the European Research Council under the European Union’s Seventh Framework Programme (No. FP/2007-2013)/ERC Grant Agreement No. 610256 (NANOCOSMOS). We also acknowledge the COST Action No. CM1401 “Our Astrochemical History