The H + D_2^+(v=0,1 and 2) charge transfer reaction is studied using an accurate wave packet method, using recently proposed coupled diabatic potential energy surfaces. The state-to-state cross section is obtained for three different channels: non-reactive charge transfer, reactive charge transfer, and exchange reaction. The three processes proceed via the electronic transition from the first excited to the ground electronic state. The cross section for the three processes increases with the initial vibrational excitation. The non-reactive charge transfer process is the dominant channel, whose branching ratio increases with collision energy, and it compares well with experimental measurements at collision energies around 0.5 eV. For lower energies the experimental cross section is considerably higher, suggesting that it corresponds to higher vibrational excitation of D_2^+(v) reactants. Further experimental studies of this reaction and isotopic variants are needed, where conditions are controlled to obtain a better analysis of the vibrational effects of the D_2^+ reagents.
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