State-to-State Quantum Mechanical Calculations of Rate Coefficients for the D$^+$ + H$_2$ → HD + H$^+$ Reaction at Low Temperature

The dynamics of the D+ + H2 → HD + H+ reaction on a recent ab initio potential energy surface (Velilla, L.; Lepetit, B.; Aguado, A.; Beswick, J. A.; Paniagua, M. J. Chem. Phys. 2008, 129, 084307) has been investigated by means of a time-independent quantum mechanical approach. Cross-sections and rate coefficients are calculated, respectively, for collision energies below 0.1 eV and temperatures up to 100 K for astrophysical application. An excellent accord is found for collision energy above 5 meV, while a disagreement between theory and experiment is observed below this energy. We show that the rate coefficients reveal a slightly temperature-dependent behavior in the upper part of the temperature range considered here. This is in agreement with the experimental data above 80 K, which give a temperature independent value. However, a significant decrease is found at temperatures below 20 K. This decrease can be related to quantum effects and the decay back to the reactant channel, which are not considered by simple statistical approaches, such as the Langevin model. Our results have been fitted to appropriate analytical expressions in order to be used in astrochemical and cosmological models