Application of the pairwise energy model to various isotopic variations of the H + H2 reaction Original Research Article

The pairwise energy model (PEM) assumes that the cross section QR for the reaction A + BC → AB + C, where B and C are isotopes of hydrogen, depends only on the pairwise relative energy Es between A and B. In this paper the PEM is applied to eight isotopic variations of the H + H2 reaction. We show that the model works well at high energy but breaks down at low energies because QR is sensitive not only to Es but also to the ratio τvibτcoll, where τvib is the vibrational period of BC, and τcoll is the collision time. In addition, at low energy reactions of HD show the effect of rotational reorientation of the HD by the incoming atom A; this favors the AD product at the expense of AH. We also consider a modified version of the PEM when the cross section is factored as QR = Qhit PR. Here Qhit is the cross section for A hitting BC, and PR is the probability for forming AB once A hits BC. We find that Qhit is a function of the relative energy E rather than Es, but PR is primarily a function of Es. Even though the PEM breaks down at low collision energy it provides a useful framework for understanding the inter- and intra-molecular isotope effects in these reactions.