Isotopic substitution of muonium for hydrogen provides an unparalleled opportunity to deepen our understanding of quantum mass effects on chemical reactions. A recent topical review in this journal of the thermal and vibrationally state-selected reaction of Mu with H 2 raises a number of issues that are addressed here. We show that some earlier quantum mechanical calculations of the Mu + H 2 reaction, which are highlighted in this review, and which have been used to benchmark approximate methods, are in error by as much as 19% in the low-temperature limit. We demonstrate that an approximate treatment of the Born-Oppenheimer diagonal correction that was used in some recent studies is not valid for treating the vibrationally state-selected reaction. We also discuss why vibrationally adiabatic potentials that neglect bend zero-point energy are not a useful analytical tool for understanding reaction rates, and why vibrationally non-adiabatic transitions cannot be understood by considering tunnelling through vibrationally adiabatic potentials. Finally, we present calculations on a hierarchical family of potential energy surfaces to assess the sensitivity of rate constants to the quality of the potential surface.
IntroductionTwo recent experiments [1-3] and comparison of these new measurements with earlier thermal rate constants [4] have prompted new theoretical calculations [1-3,5-10] for the Mu + H 2 reaction. The reaction of Mu, the lightest isotope of the H atom (with a mass of 0.114 amu), with H 2 has received significant attention because it exhibits a large inverse isotope effect for the thermal reaction and an extremely large enhancement of the rate when H 2 is in its first excited vibrational state. Much of this recent interest has been motived by a desire to understand the causes of these unusual features, particularly as they relate to approximate methods that may be useful for the study of larger systems. Benchmarks of these methods against accurate quantum mechanical (QM) results for this very challenging test system are important to understand why some approximations work well whereas others fail badly. In a recent review, which is based partly on earlier work [5,7] but also containing new analysis for this reaction, Aldegunde et al. [8] use the concepts of tunnelling, zero-point energy (ZPE), and vibrationally adiabatic potentials in an attempt to understand the accurate results and analyse the behaviour of approximate treatments. Although the results from their computed QM calculations are in semi-quantitative agreement with ours, their interpretations of these results differ