Understanding the reaction between muonium atoms and hydrogen molecules: zero point energy, tunnelling, and vibrational adiabaticity

Abstract

The advent of very precise measurements of rate coefficients in reactions of muonium (Mu), the lightest hydrogen isotope, with H 2 in its ground and first vibrational state and of kinetic isotope effects with respect to heavier isotopes has triggered a renewed interests in the field of muonic chemistry. The aim of the present article is to review the most recent results about the dynamics and mechanism of the reaction Mu + H 2 to shed light on the importance of quantum effects such as tunnelling, the preservation of the zero point energy, and the vibrational adiabaticity. In addition to accurate quantum mechanical (QM) calculations, quasiclassical trajectories (QCT) have been run in order to check the reliability of this method for this isotopic variant. It has been found that the reaction with H 2 (v=0) is dominated by the high zero point energy (ZPE) of the products and that tunnelling is largely irrelevant. Accordingly, both QCT calculations that preserve the products' ZPE as well as those based on the Ring Polymer Molecular Dynamics methodology can reproduce the QM rate coefficients. However, when the hydrogen molecule is vibrationally excited, QCT calculations fail completely in the prediction of the huge vibrational enhancement of the reactivity. This failure is attributed to tunnelling, which plays a decisive role breaking the vibrational adiabaticity when v=1. By means of the analysis of the results, it can be concluded that the tunnelling takes place through the ν 1 =1 collinear barrier. Somehow, the tunnelling that is missing in the Mu + H 2 (v=0) reaction is found in Mu + H 2 (v=1).

Zero-point energy, tunnelling, and vibrational adiabaticity in the Mu + H2reaction

“…Our interpretations use some of the same concepts as Aldegunde et al [8] -tunnelling, ZPE, and vibrationally adiabatic potentials -but also consider vibrational nonadiabaticity for the excited-state reaction. ZPE and tunnelling are both QM effects and vibrational non-adiabaticity will exhibit different behaviour in quantal and classical calculations.…”

“…Two recent experiments [1][2][3] and comparison of these new measurements with earlier thermal rate constants [4] have prompted new theoretical calculations [1][2][3][5][6][7][8][9][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.…”

“…It is difficult to rigorously separate these different effects in accurate QM calculations, so it is typical to resort to approximate methods for further analysis. Aldegunde et al [8] rely on quasiclassical trajectory (QCT) methods, ring polymer molecular dynamics (RPMD), and a comparison with vibrationally adiabatic potentials that neglect bend ZPE. To help distinguish ZPE and tunnelling effects, we use ideas based on variational transition state theory (VTST) with multidimensional tunnelling corrections, which is an approximate yet well-validated approach to treat tunnelling and which does impose constraints on the ZPE in modes perpendicular to the reaction path as in vibrationally adiabatic models.…”

“…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…”

Editorial

“…Within the Topical Reviews series, another recent article with a focus on gas-phase chemical dynamics describes the quantum theory of reaction rates [2], whilst another deals with the dynamics and mechanism of the reaction between muonium and hydrogen [3]. Other recent Topical Reviews include articles on photoelectron angular distributions in molecules [4], the structure and dynamics of water [5], the hierarchical reference theory of fluids [6], multireference explicitly correlated electronic structure methods [7], microscopic scale simulations of electrokinetics [8], the theory of non-electrolyte solutions [9], and spin dynamics of solid effect dynamic nuclear polarisation [10].…”