Theoretical study of the D$^{-}$ + H$_2$ $\rightarrow$ H$^{-}$ + HD reaction at low energies

The rearrangement reaction D$^{-}$ + H$_2$ $\rightarrow$ H$^{-}$ + HD has been studied in a recent experimental work at low temperatures (10,19,and 23K) [1]. An upper limit of about 10$^{-18}$~cm$^3$/s for the rate coefficient is obtained. A fully-quantum reactive scattering calculation of the rate coefficient is performed using the hyperspherical coordinates and the potential energy surface in Ref. [2]. Eigenchannel R-matrix approach with modified slow variable discretization [3] is used to represent continuum wave functions of the system to obtain the scattering matrix describing the scattering from the initial rovibrational channel of the H$_2$+D$^-$ into possible channels of H$^{-}$ + HD. At low collision energies between H$_2$ in the ground state and D$^-$, only three rotational channels of HD($v,j$) + H$^-$ are open for the reaction with $v=0$ and $j=0,1,2$. Formulas for the cross section and rate coefficient for reactive scattering in hyperspherical coordinates are derived. Preliminary results for the rate coefficient of the D$^{-}$ + H$_2$ $\rightarrow$ H$^{-}$ + HD reaction is obtained. [1]Endres \textit{et al}, in press, PRA (2017) [2] Ayouz \textit{et al}, JCP \textbf{132}, 19 (2010) [3] Yuen and Kokoouline, EPJD, \textbf{71},19 (2017)