Yury V. Suleimanov

Bimolecular reaction rates from ring polymer molecular dynamics: Application to H + CH4→ H2 + CH3

In a recent paper, we have developed an efficient implementation of the ring polymer molecular dynamics (RPMD) method for calculating bimolecular chemical reaction rates in the gas phase, and illustrated it with applications to some benchmark atom-diatom reactions. In this paper, we show that the same methodology can readily be used to treat more complex polyatomic reactions in their full dimensionality, such as the hydrogen abstraction reaction from methane, H + CH(4) → H(2) + CH(3). The present calculations were carried out using a modified and recalibrated version of the Jordan-Gilbert potential energy surface. The thermal rate coefficients obtained between 200 and 2000 K are presented and compared with previous results for the same potential energy surface. Throughout the temperature range that is available for comparison, the RPMD approximation gives better agreement with accurate quantum mechanical (multiconfigurational time-dependent Hartree) calculations than do either the centroid density version of quantum transition state theory (QTST) or the quantum instanton (QI) model. The RPMD rate coefficients are within a factor of 2 of the exact quantum mechanical rate coefficients at temperatures in the deep tunneling regime. These results indicate that our previous assessment of the accuracy of the RPMD approximation for atom-diatom reactions remains valid for more complex polyatomic reactions. They also suggest that the sensitivity of the QTST and QI rate coefficients to the choice of the transition state dividing surface becomes more of an issue as the dimensionality of the reaction increases.

Bimolecular reaction rates from ring polymer molecular dynamics

We describe an efficient procedure for calculating the rates of bimolecular chemical reactions in the gas phase within the ring polymer molecular dynamics approximation. A key feature of the procedure is that it does not require that one calculate the absolute quantum mechanical partition function of the reactants or the transition state: The rate coefficient only depends on the ratio of these two partition functions which can be obtained from a thermodynamic integration along a suitable reaction coordinate. The procedure is illustrated with applications to the three-dimensional H + H(2), Cl + HCl, and F + H(2) reactions, for which well-converged quantum reactive scattering results are computed for comparison. The ring polymer rate coefficients agree with these exact results at high temperatures and are within a factor of 3 of the exact results at temperatures in the deep quantum tunneling regime, where the classical rate coefficients are too small by several orders of magnitude. This is probably already good enough to encourage future applications of the ring polymer theory to more complex chemical reactions, which it is capable of treating in their full dimensionality. However, there is clearly some scope for improving on the ring polymer approximation at low temperatures, and we end by suggesting a way in which this might be accomplished.

Rate coefficients and kinetic isotope effects of the X + CH4 → CH3 + HX (X= H, D, Mu) reactions from ring polymer molecular dynamics

The thermal rate coefficients and kinetic isotope effects have been calculated using ring polymer molecular dynamics (RPMD) for the prototypical reactions between methane and several hydrogen isotopes (H, D, and Mu). The excellent agreement with the theoretical rate coefficients of the H + CH4 reaction obtained previously from a multi-configuration time-dependent Hartree calculation on the same potential energy surface provides strong evidence for the accuracy of the RPMD approach. These quantum mechanical rate coefficients are also in good agreement with the results obtained previously using the transition-state theory with semi-classical tunneling corrections for the H∕D + CH4 reactions. However, it is shown that the RPMD rate coefficients for the ultralight Mu reaction with CH4 are significantly smaller than the experimental data, presumably suggesting inaccuracies in the potential energy surface and∕or experimental errors. Significant discrepancies between the RPMD and transition-state theory results have also been found for this challenging system.

Communication: Full dimensional quantum rate coefficients and kinetic isotope effects from ring polymer molecular dynamics for a seven-atom reaction OH + CH4 → CH3 + H2O

The kinetic isotope effect (KIE) of the seven-atom reactions OH + CH4 → CH3 + H2O and OH + CD4 → CD3 + HDO over the temperature range 200-1000 K is investigated using ring polymer molecular dynamics (RPMD) on a full-dimensional potential energy surface. A comparison of RPMD with previous theoretical results obtained using transition state theory shows that RPMD is a more reliable theoretical approach for systems with more than 6 atoms, which provides a predictable level of accuracy. We show that the success of RPMD is a direct result of its independence of the choice of transition state dividing surface, a feature that is not shared by any of the transition state theory-based methods. Our results demonstrate that RPMD is a prospective method for studies of KIEs for polyatomic reactions for which rigorous quantum mechanical calculations are currently impossible.

Ring Polymer Molecular Dynamics Calculations of Thermal Rate Constants for the O(3P) + CH4 → OH + CH3 Reaction: Contributions of Quantum Effects

The thermal rate constant of the O((3)P) + CH4 → OH + CH3 reaction is investigated with ring polymer molecular dynamics on a full-dimensional potential energy surface. Good agreement with experimental and full-dimensional quantum multiconfiguration time-dependent Hartree results between 300 and 1500 K was obtained. It is shown that quantum effects, for example, tunneling and zero-point energy, can be effectively and efficiently included in this path-integral based approach implemented with classical trajectories. Convergence with respect to the number of beads is rapid, suggesting wide applicability for other reactions involving polyatomic molecules.

THEORETICAL KINETICS STUDY OF THE O(3P) + CH4/CD4 HYDROGEN ABSTRACTION REACTION: THE ROLE OF ANHARMONICITY, RECROSSING EFFECTS AND QUANTUM MECHANICAL TUNNELING

Using a recently developed full-dimensional accurate analytical potential energy surface [Gonzalez-Lavado, E., Corchado, J. C., and Espinosa-Garcia, J. J. Chem. Phys. 2014, 140, 064310], we investigate the thermal rate coefficients of the O((3)P) + CH4/CD4 reactions with ring polymer molecular dynamics (RPMD) and with variational transition-state theory with multidimensional tunneling corrections (VTST/MT). The results of the present calculations are compared with available experimental data for a wide temperature range 200-2500 K. In the classical high-temperature limit, the RPMD results match perfectly the experimental data, whereas VTST results are smaller by a factor of 2. We suggest that this discrepancy is due to the harmonic approximation used in the present VTST calculations, which leads to an overestimation of the variational effects. At low temperatures the tunneling plays an important role, which is captured by both methods, although they both overestimate the experimental values. The analysis of the kinetic isotope effects shows a discrepancy between both approaches, with the VTST values smaller by a factor about 2 at very low temperatures. Unfortunately, no experimental results are available to shed any light on this comparison, which keeps it as an open question.

Quantum Rate Coefficients and Kinetic Isotope Effect for the Reaction Cl + CH4 → HCl + CH3 from Ring Polymer Molecular Dynamics

Thermal rate coefficients and kinetic isotope effect have been calculated for prototypical heavy-light-heavy polyatomic bimolecular reactions Cl + CH4/CD4 → HCl/DCl + CH3/CD3, using a recently proposed quantum dynamics approach: ring polymer molecular dynamics (RPMD). Agreement with experimental rate coefficients, which are quite scattered, is satisfactory. However, differences up to 50% have been found between the RPMD results and those obtained from the harmonic variational transition-state theory on one of the two full-dimensional potential energy surfaces used in the calculations. Possible reasons for such discrepancy are discussed. The present work is an important step in a series of benchmark studies aimed at assessing accuracy for RPMD for chemical reaction rates, which demonstrates that this novel method is a quite reliable alternative to previously developed techniques based on transition-state theory.

Ring-Polymer Molecular Dynamics for the Prediction of Low-Temperature Rates: An Investigation of the C(1D) + H2 Reaction

Quantum mechanical calculations are important tools for predicting the rates of elementary reactions, particularly for those involving hydrogen and at low temperatures where quantum effects become increasingly important. These approaches are computationally expensive, however, particularly when applied to complex polyatomic systems or processes characterized by deep potential wells. While several approximate techniques exist, many of these have issues with reliability. The ring-polymer molecular dynamics method was recently proposed as an accurate and efficient alternative. Here, we test this technique at low temperatures (300-50 K) by analyzing the behavior of the barrierless C((1)D) + H2 reaction over the two lowest singlet potential energy surfaces. To validate the theory, rate coefficients were measured using a supersonic flow reactor down to 50 K. The experimental and theoretical rates are in excellent agreement, supporting the future application of this method for determining the kinetics and dynamics of a wide range of low-temperature reactions.

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.

Theoretical Kinetics Study of the F(2P) + NH3 Hydrogen Abstraction Reaction

The hydrogen abstraction reaction of fluorine with ammonia represents a true chemical challenge because it is very fast, is followed by secondary abstraction reactions, which are also extremely fast, and presents an experimental/theoretical controversy about rate coefficients. Using a previously developed full-dimensional analytical potential energy surface, we found that the F + NH3 → HF + NH2 system is a barrierless reaction with intermediate complexes in the entry and exit channels. In order to understand the reactivity of the title reaction, thermal rate coefficidents were calculated using two approaches: ring polymer molecular dynamics and quasi-classical trajectory calculations, and these were compared with available experimental data for the common temperature range 276-327 K. The theoretical results obtained show behavior practically independent of temperature, reproducing Walther-Wagners experiment, but in contrast with Perskys more recent experiment. However, quantitatively, our results are 1 order of magnitude larger than those of Walther-Wagner and reasonably agree with the Persky at the lowest temperature, questioning so Walther-Wagners older data. At present, the reason for this discrepancy is not clear, although we point out some possible reasons in the light of current theoretical calculations.