Stress Test for Quantum Dynamics Approximations: Deep Tunneling in the Muonium Exchange Reaction D + HMu → DMu + H.

Quantum effects play a crucial role in chemical reactions involving light atoms at low temperatures, especially when a light particle is exchanged between two heavier partners. Different theoretical methodologies have been developed in the last decades attempting to describe zero-point energy and tunneling effects without abandoning a classical or semiclassical framework. In this work, we have chosen the D + HMu → DMu + H reaction as a stress test system for three well-established methods: two representative versions of transition state theory (TST), canonical variational theory and semiclassical instanton, and ring polymer molecular dynamics (RPMD). These calculations will be compared with accurate quantum mechanical results. Despite its apparent simplicity, the exchange of the extremely light muonium atom (0.114 u) becomes a most challenging reaction for conventional methods. The main result of this work is that RPMD provides an overall better performance than TST-based methods for such a demanding reaction. RPMD might well turn out to be a useful tool beyond TST applicability.

The reactive collision mechanism evinced: stereodynamical control of the elementary Br + H2 → H + HBr reaction.

From a kinetics standpoint, reactive molecular collisions are the building blocks of the mechanisms of chemical reactions. In contrast, a dynamics standpoint reveals molecular collisions to have their own internal mechanisms, which are not mere theoretical abstractions: through suitable preparation of the reactants internal and stereochemical states, features of the mechanisms of a reactive molecular collision can be made evident and used as "handles" to control the reaction outcome. Using time-independent quantum dynamical calculations, we demonstrate this for the Br + H2(v = 0-1, j = 2) → H + HBr reaction in the 1.0-1.6 eV range of total energies. Despite its pronounced effect on reactivity, which is in agreement with the predictions from Polanyi rules, reactant vibration is found to have little effect on the mechanism of this endoergic, late-barrier reaction. Analysis of the correlations between directional reaction properties shows that the collision stereochemistry strongly depends on the total energy, but not on how this energy is partitioned between reactant translation and vibration. The stereodynamical preferences implied by the collision mechanisms determine how and to what extent one can control the reaction. Regarding the overall reaction, the extent of control is found to be large near the reaction threshold but not when the total energy is high. Regarding state-to-state reactions, the effect of reactant stereochemistry on the product rotational state distribution is found to be nontrivial and energy dependent.

A ring polymer molecular dynamics study of the isotopologues of the H + H2 reaction.

The inclusion of Quantum Mechanical (QM) effects such as zero point energy (ZPE) and tunneling in simulations of chemical reactions, especially in the case of light atom transfer, is an important problem in computational chemistry. In this respect, the hydrogen exchange reaction and its isotopic variants constitute an excellent benchmark for the assessment of approximate QM methods. In particular, the recently developed ring polymer molecular dynamics (RPMD) technique has been demonstrated to give very good results for bimolecular chemical reactions in the gas phase. In this work, we have performed a detailed RPMD study of the H + H(2) reaction and its isotopologues Mu + H(2), D + H(2) and Heµ + H(2), at temperatures ranging from 200 to 1000 K. Thermal rate coefficients and kinetic isotope effects have been computed and compared with exact QM calculations as well as with quasiclassical trajectories and experiment. The agreement with the QM results is good for the heaviest isotopologues, with errors ranging from 15% to 45%, and excellent for Mu + H(2), with errors below 15%. We have seen that RPMD is able to capture the ZPE effect very accurately, a desirable feature of any method based on molecular dynamics. We have also verified Richardson and Althorpe's prediction [J. O. Richardson and S. C. Althorpe, J. Chem. Phys., 2009, 131, 214106] that RPMD will overestimate thermal rates for asymmetric reactions and underestimate them for symmetric reactions in the deep tunneling regime. The ZPE effect along the reaction coordinate must be taken into account when assigning the reaction symmetry in the multidimensional case.

Can quasiclassical trajectory calculations reproduce the extreme kinetic isotope effect observed in the muonic isotopologues of the H + H2 reaction?

Rate coefficients for the mass extreme isotopologues of the H + H(2) reaction, namely, Mu + H(2), where Mu is muonium, and Heµ + H(2), where Heµ is a He atom in which one of the electrons has been replaced by a negative muon, have been calculated in the 200-1000 K temperature range by means of accurate quantum mechanical (QM) and quasiclassical trajectory (QCT) calculations and compared with the experimental and theoretical results recently reported by Fleming et al. [Science 331, 448 (2011)]. The QCT calculations can reproduce the experimental and QM rate coefficients and kinetic isotope effect (KIE), k(Mu)(T)/k(Heµ)(T), if the Gaussian binning procedure (QCT-GB)--weighting the trajectories according to their proximity to the right quantal vibrational action--is applied. The analysis of the results shows that the large zero point energy of the MuH product is the key factor for the large KIE observed.

Stereodynamics of the F + HD(v = 0, j = 1) reaction: direct vs. resonant mechanisms.

The stereodynamics and mechanism of the F + HD(v = 0, j = 1) → HF (DF) + D (H) reactions have been thoroughly analysed at collision energies in the 0-160 meV range. Specifically, this study is focused on (i) the comparison between the stereodynamics of the collisions leading to HF and DF formation, and (ii) the stereodynamical fingerprints of the resonance that occurs at low collision energies in the HF channel and whose manifestation in the total cross section is greatly diminished for initial j > 0. While previous studies were limited to the analysis of integral cross sections (ICS), differential cross sections (DCS) and reaction probabilities, in the present work we have included the analysis of vectorial quantities such as the direction of the initial rotational angular momentum and internuclear axis, and their effect on reactivity. In particular, polarisation parameters (PP) and polarisation dependent differential cross sections (PDDCS), quantities that describe how the intrinsic HD rotational angular momentum and molecular axis polarisations contribute to reaction, are calculated and examined. The evolution of the PPs with the collision energy differs markedly between the two reaction channels. For the DF channel, the PP values are small and change very little in the energy range in which DF formation is appreciable. In contrast, rapid fluctuations in the magnitude and sign of the PPs are observed in the HF channel at low collision energies in and around the resonance. As the collision energy increases, direct (non-resonant) scattering prevails, and the various quantities are reasonably well accounted for by the QCT calculations, as in the case of the DF channel. The intrinsic directional information has been used to access the extent of control that can be achieved through polarisation of the HD molecule prior to collision. It was found that the same extrinsic preparation leads to very different outcomes on the HF channel DCS when the collision energy is close to the resonance. It is also shown that polarisation of the HD internuclear axis along the initial relative velocity enhances the effect of the resonance and allows its clear identification. Finally, the effect of different extrinsic preparations on the angle-velocity DCS is found to be strong, thus allowing considerable control of product angular distributions.

Quantum mechanical mechanisms of inelastic and reactive H + D(2)(v = 0, j = 2) collisions.

This article analyses the mechanisms of inelastic and reactive H + D(2)(v = 0, j = 2) collisions that result in highly vibrationally excited products when the collision energy is 1.70 eV. The analytical method is entirely quantum mechanical and focuses on correlations between the polarization of the reactant molecule and the direction of product scattering. Two viewpoints are used. The "intrinsic" viewpoint reveals the reactant polarizations that lead to the largest cross section at each value of the scattering angle (the angle between the reactant-approach and product-recoil directions); the "extrinsic" viewpoint reveals how the dependence of the collision cross section on the scattering angle changes when the reactant polarization is fixed at each one of a set of experimentally feasible alternatives. Comparison of processes correlating with the same range of impact parameters is also used, to facilitate isolation and identification of directional effects. When products are scattered in the backward and sideways regions, the results for inelastic and reactive collisions are rather similar. When products are scattered in the forward region, the results for inelastic and reactive collisions are clearly different: a side-on collision geometry that largely increases the inelastic cross section hardly affects the reactive cross section. This feature is the quantum mechanical signature of the so-called "tug-of-war" mechanism.

Reaction dynamics of the D+ + H2 system. A comparison of theoretical approaches.

The dynamics of the deuteron-proton exchange D(+) + H(2) → HD + H(+) reaction on its ground 1(1)A' potential energy surface has been the subject of a theoretical study for collision energies below 1.5 eV. The results obtained with three theoretical approaches: quasi-classical trajectory (QCT), statistical quasi-classical trajectory (SQCT), and accurate time-independent quantum mechanical (QM) calculations are compared in the range of collision energies from 5 meV to 0.2 eV. The QM calculations included all total angular momentum quantum numbers, J, up to J(max) ≈ 40 and all the Coriolis couplings. For higher collision energies, the comparison was restricted to the QCT and SQCT results given the enormous computational cost implied in the QM calculations. Reaction cross sections as a function of collision energy (excitation functions) for various initial rovibrational states have been determined and compared with the corresponding results for the endothermic H(+) + D(2) → HD + D(+) isotopic variant. The excitation function for the title reaction decays monotonically with collision energy as expected for an exothermic reaction without a barrier, in contrast to the behaviour observed in the mentioned H(+) + D(2) (v = 0, j ≤ 3). Reaction probabilities as a function of J (opacity functions) at several collision energies calculated with the different approaches were also examined and important differences between them were found. The effect of using the gaussian binning procedure that preserves, to a large extent, the zero point energy, as compared to the standard histogram binning in the QCT calculations, is also examined. At low collision energy, the best agreement with the accurate QM results is given by the SQCT data, although they tend to overestimate the reactivity. The deviations from the statistical behaviour of the QCT data at higher energies are remarkable. Nevertheless, on the whole, the title reaction can be deemed more statistical than the H(+) + D(2) reaction.

The canonical and other mechanisms of elementary chemical reactions.

This article introduces a definition of the concept of elementary reaction mechanism that, while conforming to the traditional view of reaction mechanisms as dynamical processes whereby reagents are transformed into products, sharpens it by requiring reagent and product states to be completely specified and fully correlated. This leads to well-defined mathematical requirements for classification of a dynamical process as a reaction mechanism and also to a straightforward mathematical procedure for the determination of a special class of independent collision mechanisms that are dubbed "canonical". Canonical mechanisms result from an exact decomposition of the differential cross section of the reaction and form a complete orthogonal basis in terms of which all reaction mechanisms can be described. Examples involving the benchmark F + H2 and D + H2 reactions at energies ranging from ultralow to hyperthermal illustrate how canonical and other reaction mechanisms can be visualised and also how analysis of a reaction in terms of its canonical mechanisms can provide insight into its dynamics.