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 formalism. C 2015 AIP Publishing LLC. [http://dx