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

The reaction between D$^+$ and H$_2$ plays an important role in astrochemistry at low temperatures and also serves as a prototype for simple ion-molecule reaction. Its ground $\tilde{X}~^1A^{\prime}$ state has a very small thermodynamic barrier (up to 1.8$\times 10^{-2}$ eV) and the reaction proceeds through the formation of an intermediate complex lying within the potential well of depth of at least 0.2 eV thus representing a challenge for dynamical studies. In the present work, we analyze the title reaction within the temperature range of 20 $-$ 100 K by means of ring polymer molecular dynamics (RPMD) and quasi-classical trajectory (QCT) methods over the full-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 be almost 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 agreement with the previous time-independent quantum mechanical and statistical quantum method calculations. Furthermore, we observe that the choice of asymptotic separation distance between the reactants can markedly alter the rate coefficient in the low temperature regime (20 $-$ 50 K). Therefore it is of utmost importance to correctly assign the value of this parameter for dynamical studies, particularly at very low temperatures of astrochemical importance. We finally conclude that experimental rate measurements for the title reaction are highly desirable in future.