Tunneling effects in the $D+H_2$ → DH+H and $H+D_2$ → HD+D reactions

Abstract

We considered the tunneling effect on transition-state theory rate-constants for the $H+D_2$ and $D+H_2$ reactions. The method for estimating the important parameter $E_c$ (potential barrier height) was proposed. A tunneling correction factor $\Gamma_t\exp\,\theta_t$ was estimated from experimental data, and compared with the corresponding values obtained from many theoretical methods. We found that our method for calculating the tunneling correction factor is most satisfactory. According to our result, the tunneling effect cannot be neglected around $800^\circ K$ where $\Gamma_t\exp\,\theta_t$ is ca. 0.8 whereas the factor approaches to unity at $T>2400^\circ K$ where the tunneling completely disappears. In the past, however, the tunneling effect has been considered to be negligible above $450^\circ K$. We believe that our result is correct and right. In addition to the above fact, we also found that the tunneling correction factor for the two reactions is in the order of $\Gamma\exp\,\theta_t(D+H_2)>\Gamma_t\exp\,\theta_t(H+D_2)$ in agreement with Truhlar et al.``s result. In contrast to our result, however, Shavitt et al. found that the order is reversed, i.e., $\Gamma_t \exp\, \theta_t(D+H_2) < \Gamma_t \exp\, \theta_t (H+D_2)$. We discussed about the Shavitt et al.``s result.