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The reaction between D$^+$ and H$_2$ plays an important role inastrochemistry at low temperatures and also serves as a prototype for simpleion-molecule reaction. Its ground $\tilde{X}~^1A^{\prime}$ state has a verysmall thermodynamic barrier (up to 1.8$\times 10^{-2}$ eV) and the reactionproceeds through the formation of an intermediate complex lying within thepotential well of depth of at least 0.2 eV thus representing a challenge fordynamical studies. In the present work, we analyze the title reaction withinthe temperature range of 20 $-$ 100 K by means of ring polymer moleculardynamics (RPMD) and quasi-classical trajectory (QCT) methods over thefull-dimensional global potential energy surface developed by Aguado et al. [A.Aguado, O. Roncero, C. Tablero, C. Sanz, and M. Paniagua, J. Chem. Phys., 2000,112, 1240]. The computed thermal RPMD and QCT rate coefficients are found to bealmost independent of temperature and fall within the range of 1.34 $-$2.01$\times$10$^{-9}$ cm$^3$ s$^{-1}$. They are also in a very good agreementwith the previous time-independent quantum mechanical and statistical quantummethod calculations. Furthermore, we observe that the choice of asymptoticseparation distance between the reactants can markedly alter the ratecoefficient in the low temperature regime (20 $-$ 50 K). Therefore it is ofutmost importance to correctly assign the value of this parameter for dynamicalstudies, particularly at very low temperatures of astrochemical importance. Wefinally conclude that experimental rate measurements for the title reaction arehighly desirable in future.

physical chemistry chemical physics/pccp. physical chemistry chemical physics

The low temperature D$^+$ + H$_2$ $\rightarrow$ HD + H$^+$ reaction rate  coefficient: a ring polymer molecular dynamics and quasi-classical trajectory  study