Ring Polymer Molecular Dynamics Rate Research Articles

Rate coefficients for the O + H2 and O + D2 reactions: how well ring polymer molecular dynamics accounts for tunelling.

We present here extensive calculations of the O(3P) + H2 and O(3P) + D2 reaction dynamics spanning the temperature range from 200 K to 2500 K. The calculations have been carried out using fully converged time-independent quantum mechanics (TI QM), quasiclassical trajectories (QCT) and ring polymer molecular dynamics (RPMD) on the two lowest lying adiabatic potential energy surfaces (PESs), 13A' and 13A'', calculated by Zanchet et al. [J. Chem. Phys., 2019, 151, 094307]. TI QM rate coefficients were determined using the cumulative reaction probability formalism on each PES including all of the total angular momenta and the Coriolis coupling and can be considered to be essentially exact within the Born-Oppenheimer approximation. The agreement between the rate coefficients calculated by using QM and RPMD is excellent for the reaction with D2 in almost the whole temperature range. For the reaction with H2, although the agreement is very good above 500 K, the deviations are significant at lower temperatures. In contrast, the QCT calculations largely underestimate the rate coefficients for the two isotopic variants due to their inability to account for tunelling. The differences found in the disagreements between RPMD and QM rate coefficients for the reactions for both the isotopologues are indicative of the ability of the RPMD method to accurately describe systems where tunelling plays a relevant role. Considering that both reactions are dominated by tunelling below 500 K, the present results show that RPMD is a very powerful tool for determining rate coefficients. The present QM rate coefficients calculated on adiabatic PESs slightly underestimate the best global fits of the experimental measurements, which we attribute to the intersystem crossing with the singlet 11A' PES.

Caracal: A Versatile Ring Polymer Molecular Dynamics Simulation Package.

A new open-source program package named Caracal covering simulations of molecular systems with ring polymer molecular dynamics (RPMD) is presented. It combines a powerful RPMD implementation including chemical reaction rate calculations and biased periodic and nonperiodic samplings with a collection of easy to set up potential energy surface (PES) methodologies, thus delivering an all-inclusive approach. Most implemented PESs are based on the QMDFF and EVB-QMDFF methods. Where the quantum mechanically derived force field (QMDFF) can be set up for an arbitrary molecular system in a black-box fashion, the empirical valence bond (EVB)-QMDFF connects two QMDFFs and is able to represent the PES of a chemical reaction. With our previously published flavors of this composite method, PESs for almost arbitrary gas phase thermal ground state reactions can be set up. Given an optimized reaction path, the mechanism of the reaction can be classified and RPMD rate constants can be obtained via umbrella sampling and recrossing calculations on an EVB-QMDFF PES. Further, QMDFFs can be polymerized for the description of liquid systems. In this paper, the internal structure as well as the handling philosophy of Caracal are outlined. Further, examples of the different possible kinds of calculations are given.

Ring Polymer Molecular Dynamics Approach to Quantum Dissociative Chemisorption Rates.

A ring polymer molecular dynamics (RPMD) method is proposed for the calculation of the dissociative chemisorption rate coefficient on surfaces. The RPMD rate theory is capable of handling quantum effects such as the zero-point energy and tunneling in dissociative chemisorption, while it relies on classical trajectories for the simulation. Applications to H2 dissociative chemisorption are demonstrated. For the highly activated process on Ag(111), strong deviations from Arrhenius behavior are found at low temperatures and attributed to tunneling. On Pt(111), where the dissociation has a barrierless pathway, the RPMD rate coefficient is found to agree with the experimentally derived thermal sticking coefficient within a factor of 2 over a large temperature range. Significant quantum effects are also found.

Kinetics study of the OH + SiH4 hydrogen abstraction reaction: A theoretical analysis

AbstractThe temperature dependence of the rate constants and the kinetics isotope effects of the OH + SiH4 hydrogen abstraction reaction were theoretically studied. Three different kinetics approaches were used in this study: variational transition state theory with multidimensional tunneling (VTST/MT) corrections, quasi‐classical trajectory (QCT) calculations, and ring polymer molecular dynamics (RPMD). These studies were performed on a global analytical potential energy surface based on explicitly correlated high level ab initio calculations developed in the present work. While the experimental rate constants are practically independent with temperature, the VTST/MT results show a pronounced dependence, the QCT partially corrects this behavior, and RPMD rates are in better agreement with experiment. In this case, in the experimental common temperature range, 300–600 K, the T‐expression for the RPMD rate constants is: k(T) = 6.40 × 10−13.T0.52exp(−0.10/T). The kinetics isotope effects, H/D, are small in this temperature range, revealing the small importance of tunneling effects in this very exothermic and low barrier reaction. Different factors, such as anharmonicity, the zero‐point violation problem or limitations of the surface, without ruling out experimental uncertainties, were analyzed to explain the discrepancies.

Investigating Tunneling-Controlled Chemical Reactions through Ab Initio Ring Polymer Molecular Dynamics.

We use the ab initio ring polymer molecular dynamics (RPMD) approach to investigate tunneling-controlled reactions in methylhydroxycarbene. Nuclear tunneling effects enable molecules to overcome the barriers which cannot be overcome classically. Under low-temperature conditions, intrinsic quantum tunneling effects can facilitate the chemical reaction in a pathway that is favored neither thermodynamically nor kinetically. This behavior is referred to as the tunneling-controlled chemical reaction and is regarded as the third paradigm of chemical reaction controls. In this work, we use the ab initio RPMD approach to incorporate the tunneling effects in our quantum dynamics simulations and investigate the reaction kinetics of two competitive reaction pathways at various temperatures. The reaction rate constants obtained here agree extremely well with the experimentally measured rates. We demonstrate the feasibility of using ab initio RPMD rate calculations in a realistic molecular system and provide an interesting and important example for future investigations of reaction mechanisms dominated by quantum tunneling effects.

Assessing parameters for ring polymer molecular dynamics simulations at low temperatures: DH + H chemical reaction

Ring polymer molecular dynamics (RPMD) is an accurate method for calculating thermal chemical reaction rates. It has recently been discovered that low-temperature calculations are strongly affected by the simulation parameters. Here, for the thermally activated reaction DH + H → D + H2, we calculate the RPMD rate constants at T=50, 100, and 300 K and demonstrate that for T≥100 K the standard input parameters yield accurate results, but at low temperatures (e.g., 50 K) one must increase the asymptotic distance and force constant, and decrease the umbrella integration step.

Rate coefficients and kinetic isotope effects of Cl+XCl→XCl+Cl (X=H, D, Mu) reactions from ring polymer molecular dynamics

The ring-polymer molecular dynamics (RPMD) was used to calculate the thermal rate coefficients and kinetic isotope effects of the heavy-light-heavy abstract reaction Cl+XCl→XCl+Cl (X=H, D, Mu). For the Cl+HCl reaction, the excellent agreement between the RPMD and experimental values provides a strong proof for the accuracy of the RPMD theory. And the RPMD results are also consistent with results from other theoretical methods including improved-canonical-variational-theory and quantum dynamics. The most novel finding is that there is a double peak in Cl+MuCl reaction near the transition state, leaving a free energy well. It comes from the mode softening of the reaction system at the peak of the potential energy surface. Such an explicit free energy well suggests strongly there is an observable resonance. And for the Cl+DCl reaction, the RPMD rate coefficient again gives very accurate results compared with experimental values. The only exception is at the temperature of 312.5 K, results from RPMD and all other theoretical methods are close to each other but slightly lower than the experimental value, which indicates experimental or potential energy surface deficiency.

Ring polymer molecular dynamics and active learning of moment tensor potential for gas-phase barrierless reactions: Application to S + H2.

Ring polymer molecular dynamics (RPMD) has proven to be an accurate approach for calculating thermal rate coefficients of various chemical reactions. For wider application of this methodology, efficient ways to generate the underlying full-dimensional potential energy surfaces (PESs) and the corresponding energy gradients are required. Recently, we have proposed a fully automated procedure based on combining the original RPMDrate code with active learning for PES on-the-fly using moment tensor potential and successfully applied it to two representative thermally activated chemical reactions [I. S. Novikov et al., Phys. Chem. Chem. Phys. 20, 29503-29512 (2018)]. In this work, using a prototype insertion chemical reaction S + H2, we show that this procedure works equally well for another class of chemical reactions. We find that the corresponding PES can be generated by fitting to less than 1500 automatically generated structures, while the RPMD rate coefficients show deviation from the reference values within the typical convergence error of the RPMDrate. We note that more structures are accumulated during the real-time propagation of the dynamic factor (the recrossing factor) as opposed to the previous study. We also observe that a relatively flat free energy profile along the reaction coordinate before entering the complex-formation well can cause issues with locating the maximum of the free energy surface for less converged PESs. However, the final RPMD rate coefficient is independent of the position of the dividing surface that makes it invulnerable to this problem, keeping the total number of necessary structures within a few thousand. Our work concludes that, in the future, the proposed methodology can be applied to realistic complex chemical reactions with various energy profiles.

Quantum Effects on the D + H3+ → H2D+ + H Deuteration Reaction and Isotopic Variants.

The title reaction and its isotopic variants are studied using quasi-classical trajectory (QCT) (without taking into account corrections to account for the possible zero point energy breakdown) and ring polymer molecular dynamics (RPMD) methods with a full dimensional and accurate potential energy surface which presents an exchange barrier of approximately 0.144 eV. The QCT rate constant increases when the temperature decreases from 1500 to 10 K. On the contrary, the RPMD rate constant decreases with decreasing temperature, in semiquantitative agreement with recent experimental results. The present RPMD results are in between the thermal and translational experimental rate constants, extracted from the measured data to eliminate the initial vibrational excitation of H3+, obtained in an arc discharge. The difference between the present RPMD results and experimental values is attributed to the possible existence of non thermal vibrational excitation of H3+, not completely removed by the semiempirical model used for the analysis of the experimental results. Also, it is found that, below 200 K, the RPMD trajectories are trapped, forming long-lived collision complexes, with lifetimes longer than 1 ns. These collision complexes can fragment by either redissociating back to reactants or react to products, in the two cases tunneling through the centrifugal and reaction barriers, respectively. The contribution of the formation of the complex to the total deuteration rate should be calculated with more accurate quantum methods, as has been found recently for reactions of larger systems, and the present four atoms system is a good candidate to benchmark the adequacy of RPMD method at temperatures below 100 K.

On the calculation of quantum mechanical electron transfer rates.

We present a simple interpolation formula for the rate of an electron transfer reaction as a function of the electronic coupling strength. The formula only requires the calculation of Fermi golden rule and Born-Oppenheimer rates and so can be combined with any methods that are able to calculate these rates. We first demonstrate the accuracy of the formula by applying it to a one dimensional scattering problem for which the exact quantum mechanical, Fermi golden rule, and Born-Oppenheimer rates are readily calculated. We then describe how the formula can be combined with the Wolynes theory approximation to the golden rule rate, and the ring polymer molecular dynamics (RPMD) approximation to the Born-Oppenheimer rate, and used to capture the effects of nuclear tunneling, zero point energy, and solvent friction on condensed phase electron transfer reactions. Comparison with exact hierarchical equations of motion results for a demanding set of spin-boson models shows that the interpolation formula has an error comparable to that of RPMD rate theory in the adiabatic limit, and that of Wolynes theory in the nonadiabatic limit, and is therefore as accurate as any method could possibly be that attempts to generalize these methods to arbitrary electronic coupling strengths.

New Stress Test for Ring Polymer Molecular Dynamics: Rate Coefficients of the O(3P) + HCl Reaction and Comparison with Quantum Mechanical and Quasiclassical Trajectory Results.

In the past decade, ring polymer molecular dynamics (RPMD) has emerged as a very efficient method to determine thermal rate coefficients for a great variety of chemical reactions. This work presents the application of this methodology to study the O(3P) + HCl reaction, which constitutes a stringent test for any dynamical calculation due to rich resonant structure and other dynamical features. The rate coefficients, calculated on the 3A' and 3A″ potential energy surfaces (PESs) by Ramachandran and Peterson [ J. Chem. Phys. 2003 , 119 , 9590 ], using RPMD and quasiclassical trajectories (QCT) are compared with the existing experimental and the quantum mechanical (QM) results by Xie et al. [ J. Chem. Phys. 2005 122 , 014301 ]. The agreement is very good at T > 600 K, although RPMD underestimates rate coefficients by a factor between 4 and 2 in the 200-500 K interval. The origin of these discrepancies lies in the large contribution from tunneling on the 3A″ PES, which is enhanced by resonances due to quasibound states in the van der Waals wells. Although tunneling is fairly well accounted for by RPMD even below the crossover temperature, the effect of resonances, a long-time effect, is not included in the methodology. At the highest temperatures studied in this work, 2000-3300 K, the RPMD rate coefficients are somewhat larger than the QM ones, but this is shown to be due to limitations in the QM calculations and the RPMD are believed to be more reliable.

Ring-polymer molecular dynamical benchmarks for X + H2 insertion reactions

Rate coefficients of a class of prototypical insertion reactions, namely X + H2 → XH + H, where X = C(1D), N(1D), O(1D) or S(1D), are systematically investigated with ring polymer molecular dynamics (RPMD). Besides giving accurate rate coefficients by correctly including quantum and recrossing effects as in previous work, we have tested the effect on the results of the choice of the dividing surfaces. Our results explicitly confirm a key property of the RPMD rate theory that the choice of the dividing surface along the reaction path has no impact on the results.

Ring-polymer molecular dynamics studies of thermal rate coefficients for reaction F + H2O → HF + OH

The prototype tetra-atomic reaction F + H2O → HF + OH plays a significant role in both atmospheric and astronomical chemistry. In this work, thermal rate coefficients of this reaction are determined with the ring polymer molecular dynamics (RPMD) method on a full-dimensional potential energy surface (PES). This PES is the most accurate one for the title reaction, as demonstrated by the correct barrier height and reaction energy, compared to the benchmark calculations by the focal point analysis and the high accuracy extrapolated ab initio thermochemistry methods. The RPMD rate coefficients are in excellent agreement with those calculated by the semiclassical transition state theory and a two-dimensional master equation technique, and some experimental measurements. As has been found in many RPMD applications, quantum effects, including tunneling and zero-point energy effects, can be efficiently and effectively captured by the RPMD method. In addition, the convergence of the results with respect to the number of beads is rapid, which is also consistent with previous RPMD applications.

Theoretical Investigations of Rate Coefficients of H + H2O2 → OH + H2O on a Full-Dimensional Potential Energy Surface.

The thermal rate coefficients of H + H2O2 → OH + H2O were obtained theoretically based on a recent fundamental invariant-neural network potential energy surface. The ring polymer molecular dynamics (RPMD) calculations were performed to get the rate coefficients with quantum effects, which are in good accord with some experimental values. The rate coefficients derived from extensive quasi-classical trajectory and canonical variational transition-state calculations also predict well the experimental results at high temperatures. The RPMD rate coefficients for H + H2O2 → OH + H2O are larger than H + H2O2 → H2 + HO2, but at very low temperatures below the room temperature, the H2 + HO2 channel becomes dominant due to significant quantum tunneling effects in the H atom transfer process. Considering that the old experimental values vary widely from different groups, we expect that our theoretical investigations can motivate new experimental work, which facilitates a more reliable comparison between theory and experiment.

Ring-polymer molecular dynamics study on rate coefficient of the barrierless OH + CO system at low temperature.

Based on the recently constructed neural-network potential energy surface [Chen et al., J. Chem. Phys. 138, 221104 (2013)], ring-polymer molecular dynamics (RPMD) calculations are performed to compute rate coefficients of the barrierless OH + CO system at T ≤ 500 K. To recover the barrierless feature, a Lindemann-Hinshelwood-type mechanism and hence a reduced rate coefficient are used to approximate the overall rate coefficient. An agreement between RPMD and experimental rate coefficients can be found. These RPMD results reproduce correctly the temperature-independence of the overall rate coefficient. Finally, potential sources of errors in the present RPMD calculations are discussed.

Rate coefficients of the H + H2O2 → H2 + HO2 reaction on an accurate fundamental invariant-neural network potential energy surface.

The rate coefficients of the H + H2O2 → H2 + HO2 reaction are calculated using the ring polymer molecular dynamics (RPMD), quasi-classical trajectory (QCT), and canonical variational transition state theory (CVT) with small curvature tunneling (SCT) correction, in conjunction with the recently constructed fundamental invariant-neural network (FI-NN) potential energy surface (PES) [X. Lu et al., Phys. Chem. Chem. Phys. 20, 23095 (2018)]. In RPMD calculations, 32, 16, and 8 beads are used for computing the rate coefficients at 200 K ≤ T ≤ 400 K, 500 K ≤ T ≤ 700 K, and 700 K < T ≤ 1000 K, respectively. Given that the previous experimental rate coefficients vary widely, in particular, at low temperatures, the present RPMD rate coefficients agree well with most of the experimental results. In addition, comparing with some experimental values, the present QCT and CVT/SCT calculations on the FI-NN PES also predict accurate results at some temperatures. These results strongly support the accuracy of the present dynamics calculations as well as the full-dimensional FI-NN PES.

Accurate Determination of Tunneling-Affected Rate Coefficients: Theory Assessing Experiment.

The thermal rate coefficients of a prototypical bimolecular reaction are determined on an accurate ab initio potential energy surface (PES) using ring polymer molecular dynamics (RPMD). It is shown that quantum effects such as tunneling and zero-point energy (ZPE) are of critical importance for the HCl + OH reaction at low temperatures, while the heavier deuterium substitution renders tunneling less facile in the DCl + OH reaction. The calculated RPMD rate coefficients are in excellent agreement with experimental data for the HCl + OH reaction in the entire temperature range of 200-1000 K, confirming the accuracy of the PES. On the other hand, the RPMD rate coefficients for the DCl + OH reaction agree with some, but not all, experimental values. The self-consistency of the theoretical results thus allows a quality assessment of the experimental data.

Thermal Rate Coefficients for the Astrochemical Process C + CH+ → C2+ + H by Ring Polymer Molecular Dynamics.

Thermal rate coefficients for the astrochemical reaction C + CH+ → C2+ + H were computed in the temperature range 20-300 K by using novel rate theory based on ring polymer molecular dynamics (RPMD) on a recently published bond-order based potential energy surface and compared with previous Langevin capture model (LCM) and quasi-classical trajectory (QCT) calculations. Results show that there is a significant discrepancy between the RPMD rate coefficients and the previous theoretical results that can lead to overestimation of the rate coefficients for the title reaction by several orders of magnitude at very low temperatures. We argue that this can be attributed to a very challenging energy profile along the reaction coordinate for the title reaction, not taken into account in extenso by either the LCM or QCT approximation. In the absence of any rigorous quantum mechanical or experimental results, the computed RPMD rate coefficients represent state-of-the-art estimates to be included in astrochemical databases and kinetic networks.

ChemInform Abstract: Chemical Reaction Rate Coefficients from Ring Polymer Molecular Dynamics: Theory and Practical Applications

AbstractReview: 109 refs.

Chemical Reaction Rate Coefficients from Ring Polymer Molecular Dynamics: Theory and Practical Applications.

This Feature Article presents an overview of the current status of ring polymer molecular dynamics (RPMD) rate theory. We first analyze the RPMD approach and its connection to quantum transition-state theory. We then focus on its practical applications to prototypical chemical reactions in the gas phase, which demonstrate how accurate and reliable RPMD is for calculating thermal chemical reaction rate coefficients in multifarious cases. This review serves as an important checkpoint in RPMD rate theory development, which shows that RPMD is shifting from being just one of recent novel ideas to a well-established and validated alternative to conventional techniques for calculating thermal chemical rate coefficients. We also hope it will motivate further applications of RPMD to various chemical reactions.