The non-adiabatic quantum dynamics of the H+H$_2^+$ $rightarrow$ H$_2$+ H$^+$ charge transfer reactions, and some isotopic variants, is studied with an accurate wave packet method. A recently developed $3times$3 diabatic potential model is used, which is based on very accurate {it ab initio} calculations and includes the long-range interactions for ground and excited states. It is found that for initial H$_2^+$(v=0), the quasi-degenerate H$_2$(v=4) non-reactive charge transfer product is enhanced, producing an increase of the reaction probability and cross section. It becomes the dominant channel from collision energies above 0.2 eV, producing a ratio, between v=4 and the rest of vs, that increases up to 1 eV. H+H$_2^+$ $rightarrow$ H$_2^+$+ H exchange reaction channel is nearly negligible, while the reactive and non-reactive charge transfer reaction channels are of the same order, except that corresponding to H$_2$(v=4), and the two charge transfer processes compete below 0.2 eV. This enhancement is expected to play an important vibrational and isotopic effect that need to be evaluated. For the three proton case, the problem of the permutation symmetry is discussed when using reactant Jacobi coordinates.
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