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Wepresent the adiabatic quantum dynamics of the proton-transferreaction H(2S) + HeH+(X1Σ+) → H2+(X2Σg+) + He(1S) on the HeH2+X̃2Σ+RMRCI6 (M = 6) PES of C. N. Ramachandran et al. (Chem. Phys. Lett.2009, 469, 26). We considerthe HeH+molecule in the ground vibrational–rotationalstate and obtain initial-state-resolved reaction probabilities andthe ground-state cross section σ0and rate constant k0by propagating time-dependent, coupled-channel,real wavepackets (RWPs) and performing a flux analysis. Three differentwavepackets are propagated to describe the wide range of energiesexplored, from cold (0.0001 meV) to hyperthermal (1000 meV) collisionenergies, and in a temperature range from 0.01 to 2000 K. We compareour time-dependent results with the time-independent ones by D. DeFazio and S. Bovino et al., where De Fazio carried out benchmark coupled-channelcalculations whereas Bovino et al. employed the negative imaginarypotential and the centrifugal-sudden approximations. The RWP crosssection is in good agreement with that by De Fazio, except at thelowest collision energies below ∼0.01 meV, where the former is larger than the latter.However, neither the RWP and De Fazio results possess the huge resonancein probability and cross section at 0.01 meV, found by Bovino et al.,who also obtained a too low σ0at high energies.Therefore, the RWP and De Fazio rate constants compare quite well,whereas that by Bovino et al. is in general lower. [ABSTRACT FROM AUTHOR]