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

Kinetic study of the CN + C2H6 hydrogen abstraction reaction based on an analytical potential energy surface

The temperature dependence of the thermal rate constants and kinetic isotope effects (KIE) of the CN + C2H6 gas-phase hydrogen abstraction reaction was theoretically determined within the 25-1000 K temperature range, i.e., from very low- to high-temperature regimes. Based on a recently developed full-dimensional analytical potential energy surface fitted to highly accurate explicitly correlated ab initio calculations, three different kinetic theories were used: canonical variational transition state theory (CVT), quasiclassical trajectory theory (QCT), and ring polymer molecular dynamics (RPMD) method for the computation of rate constants. We found that the thermal rate constants obtained with the three theories show a V-shaped temperature dependence, with a pronounced minimum near 200 K, qualitatively reproducing the experimental measurements. Among the three methods used in this work, the QCT and RPMD methods have the best agreement with the experiment at low and high temperatures, respectively, while the CVT model shows the largest discrepancies. The significant increase in the rate constant at very low temperatures in this very exothermic and practically barrierless reaction could be attributed to the large value of the impact parameter, possibly ruling out the role of the tunneling effect and the intermediate complexes in the entrance channel. The theoretical H/D KIE depicted a "normal" behaviour, i.e., values greater than unity, emulating the experimental measurements and improving previous theoretical results. Finally, the discrepancies between theory and experiments were analysed as a function of several factors, such as limitations of the kinetics theories and the potential energy surface, as well as the uncertainties in the experimental measurements.

First-principles surface reaction rates by ring polymer molecular dynamics and neural network potential: role of anharmonicity and lattice motion

Elementary gas-surface processes are essential steps in heterogeneous catalysis. A predictive understanding of catalytic mechanisms remains challenging due largely to difficulties in accurately characterizing the kinetics of such steps. Experimentally, thermal rates for elementary surface reactions can now be measured using a novel velocity imaging technique, providing a stringent testing ground for ab initio rate theories. Here, we propose to combine ring polymer molecular dynamics (RPMD) rate theory with state-of-the-art first-principles-determined neural network potential to calculate surface reaction rates. Taking NO desorption from Pd(111) as an example, we show that the harmonic approximation and the neglect of lattice motion in the commonly-used transition state theory overestimates and underestimates the entropy change during the desorption process, respectively, leading to opposite errors in rate coefficient predictions and artificial error cancellations. Including anharmonicity and lattice motion, our results reveal a generally neglected surface entropy change due to significant local structural change during desorption and obtain the right answer for the right reasons. Although quantum effects are found to be less important in this system, the proposed approach establishes a more reliable theoretical benchmark for accurately predicting the kinetics of elementary gas-surface processes.

Quantum versus classical unimolecular fragmentation rate constants and activation energies at finite temperature from direct dynamics simulations

In the present work, we investigate how nuclear quantum effects modify the temperature dependent rate constants and, consequently, the activation energies in unimolecular reactions. In the reactions under study, nuclear quantum effects mainly stem from the presence of a large zero point energy. Thus, we investigate the behavior of methods compatible with direct dynamics simulations, the quantum thermal bath (QTB) and ring polymer molecular dynamics (RPMD). To this end, we first compare them with quantum reaction theory for a model Morse potential before extending this comparison to molecular models. Our results show that, in particular in the temperature range comparable with or lower than the zero point energy of the system, the RPMD method is able to correctly capture nuclear quantum effects on rate constants and activation energies. On the other hand, although the QTB provides a good description of equilibrium properties including zero-point energy effects, it largely overestimates the rate constants. The origin of the different behaviours is in the different distance distributions provided by the two methods and in particular how they differently describe the tails of such distributions. The comparison with transition state theory shows that RPMD can be used to study fragmentation of complex systems for which it may be difficult to determine the multiple reaction pathways and associated transition states.

New Stable and Fast Ring-Polymer Molecular Dynamics for Calculating Bimolecular Rate Coefficients with an Example of OH + CH4

The accurate and efficient calculation of the rate coefficients of chemical reactions is a key issue in the research of chemical dynamics. In this work, by applying the dimension-free ultrastable Cayley propagator, the thermal rate coefficients of a prototypic high dimensional chemical reaction OH + CH₄ → H₂O + CH₃ in the temperature range of 200 to 1500 K are investigated with ring polymer molecular dynamics (RPMD) on a highly accurate full-dimensional potential energy surface. Kinetic isotope effects (KIEs) for three isotopologues of the title reaction are also studied. The results demonstrate excellent agreement with experimental data, even in the deep tunneling region. Especially, the Cayley propagator shows a high calculation efficiency with little loss of accuracy. The present results confirmed the applicability of the RPMD method, particularly the speed-up using a Cayley propagator, in theoretical calculations of bimolecular reaction rates.

Mechanism and Kinetics of Methane Combustion. Part II: Potential Energy Surface for Hydrogen-Abstraction Reaction of CH4 + O(3P)

Methane combustion plays an important role in various fields such as combustion chemistry and atmospheric chemistry of the stratosphere. Highly accurate study of its initial reaction remains a key challenge. Here, through extensive studies with a state-of-the-art ab initio and neural network method, we present a potential energy surface of the O(³P) + CH₄ → OH + CH₃ reaction on the ground state 1³A and the first excited state 2³A. In this work, the energies of 10 167 points covering all important regions are obtained with state-averaged complete active space self-consistent field calculations and then fitted using the Levenberg-Marquardt algorithm with a root-mean-square error of 0.391 and 0.442 kcal/mol for the 1³A and 2³A states, respectively. This study explores the characteristics of the radical van der Waals (VdW) complex and reveals a detailed mechanism of the methane combustion initial reaction. Within the scope of this mechanism, this surface gives a fairly accurate description of the regions around the saddle point, conical intersection, and vdW wells in the entrance for efficient computational simulations. As a theoretical study on a prototypical polyatomic reaction, it is hopeful that this work will modify our understanding of the primary process in hydrocarbon combustion.

Dynamics and kinetics of the Si(1D) + H2/D2 reactions on a new global ab initio potential energy surface

Recent studies on the exothermic complex-forming reactions have improved our understanding of complex-forming reactions greatly, however, so far a similar level of study on endothermic ones has been rather limited. In this work, the endothermic complex-forming reaction Si(1D) + H2 → SiH + H and its deuterated isotopic variant are investigated by quantum dynamics (QD) and ring polymer molecular dynamics (RPMD) calculations on a new global ab initio potential energy surface (PES) for the ground electronic state, which is constructed based on 8996 symmetry unique points computed at the icMRCI+Q/aug-cc-pVQZ level. The PES reproduces our ab initio data very well in the dynamically important regions, on which the ro-vibrational energy levels of SiH2 are calculated and general good agreement with experiment is obtained. The integral cross sections and product angular and state distributions are computed in a wide range of collision energies, and interesting dynamics behaviors are revealed. The rate coefficients are also investigated, which display an exponential rise from 2.09 × 10-20 to 6.00 × 10-12 cm3 s-1 for the Si(1D) + H2 reaction as the temperature increases from 300 to 1500 K, in contrast to the nearly temperature-independent behavior of exothermic complex-forming reactions. In addition, the applicability of the RPMD approach is demonstrated, and the kinetic isotope effect is investigated, the ratio of which decreases from 7.89 (300 K) to 1.70 (1500 K). The effects of tunneling and initial rotational excitation are also discussed.

Theoretical H + O3 rate coefficients from ring polymer molecular dynamics on an accurate global potential energy surface: assessing experimental uncertainties

Thermal rate coefficients and kinetic isotope effects have been calculated for an important atmospheric reaction H/D + O3 → OH/OD + O2 based on an accurate permutation invariant polynomial-neural network potential energy surface, using ring polymer molecular dynamics (RPMD), quasi-classical trajectory (QCT) and variational transition-state theory (VTST) with multidimensional tunneling. The RPMD approach yielded results that are generally in better agreement with experimental rate coefficients than the VTST and QCT ones, especially at low temperatures, attributable to its capacity to capture quantum effects such as tunneling and zero-point energy. The theoretical results support one group of existing experiments over the other. In addition, rate coefficients for the D + O3 → OD + O2 reaction are also reported using the same methods, which will allow a stringent assessment of future experimental measurements, thus helping to reduce the uncertainty in the recommended rate coefficients of this reaction.

An accurate potential energy surface and ring polymer molecular dynamics study of the Cl + CH4→ HCl + CH3reaction

Thermal rate coefficients for the Cl + CH₄/CD₄reactions were studied on a new full-dimensional accurate potential energy surface with the spin–orbit corrections considered in the entrance channel.

Path integral methods for reaction rates in complex systems

We shall use this introduction to the Faraday Discussion on quantum effects in complex systems to review the recent progress that has been made in using imaginary time path integral methods to calculate chemical reaction rates.

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.

A Machine Learning Approach for Prediction of Rate Constants

We report a machine learning approach to train and predict bimolecular thermal rate constants over a large temperature range. The approach uses Gaussian process (GP) regression to evaluate the difference between accurate quantum results and Eckart-corrected conventional transition state theory, mostly for collinear reactions. Training is done on a database of rate constants for 13 reaction/potential surface combinations, and testing is performed on a set of 39 reaction/potential surface combinations. Averaged over all test reactions, the GP method is within 80% of the accurate answer, whereas transition state theory (TST) is only within 330% and Eckart-corrected TST (ECK) is within 110%. In the tunneling region, GP is generally (with a few exceptions) more accurate and sometimes much more accurate. In the high-temperature recrossing region, GP is significantly more accurate than either TST or ECK, neither of which addresses the possibility of recrossing. The GP predictions for the 3D reactions O(³P) + H₂, OH + H₂, O(³P) + CH₄, and H + CH₄, for which accurate quantum results are available, provide further encouragement to the machine learning approach.

The hydrogen abstraction reaction H + C2H6 → H2(v,j) + C2H5. Part II. Theoretical kinetics and dynamics study

Two important issues motivated the present study: the role of the tunnelling contribution at low temperatures and the role of the alkyl fragment in the dynamics.

The low temperature D+ + H2→ HD + H+ reaction rate coefficient: a ring polymer molecular dynamics and quasi-classical trajectory study

The reaction between D⁺ and H₂ plays an important role in astrochemistry at low temperatures and also serves as a prototype for a simple ion-molecule reaction. Its ground X[combining tilde]¹A' state has a very small thermodynamic barrier (up to 1.8 × 10^-2 eV) and the reaction proceeds through the formation of an intermediate complex lying within the potential well with a depth of at least 0.2 eV, thus representing a challenge for dynamical studies. In the present work, we analyze the title reaction within the temperature range of 20-100 K by means of ring polymer molecular dynamics (RPMD) and quasi-classical trajectory (QCT) methods over the full-dimensional global potential energy surface developed by Aguado et al. [A. Aguado, O. Roncero, C. Tablero, C. Sanz and M. Paniagua, J. Chem. Phys., 2000, 112, 1240]. The computed thermal RPMD and QCT rate coefficients are found to be almost independent of temperature and fall within the range of 1.34-2.01 × 10^-9 cm³ s^-1. They are also in very good agreement with previous time-independent quantum mechanical and statistical quantum method calculations. Furthermore, we observe that the choice of asymptotic separation distance between the reactants can markedly alter the rate coefficient in the low temperature regime (20-50 K). Therefore it is of utmost importance to correctly assign the value of this parameter for dynamical studies, particularly at very low temperatures of astrochemical importance. We finally conclude that the experimental rate measurements for the title reaction are highly desirable in future.

Effects of multidimensional tunneling in the kinetics of hydrogen abstraction reactions of O (3 P) with CH3 OCHO

Quantum tunneling paths are important in reactions when there is a significant component of hydrogenic motion along the potential energy surface. In this study, variational transition state with multidimensional tunneling corrections are employed in the calculations of the thermal rate constants for hydrogen abstraction from the cis-CH₃ OCHO by O (³ P) giving CH₃ OCO + OH (R1) and CH₂ OCHO + OH (R2). The structures and electronic energies are computed with the M06-2X method. Benchmark calculations with the CBS_D-T approach give an enthalpy of reaction at 0 K for R1 (-2.8 kcal/mol) and R2 (-2.5 kcal/mol) which are in good agreement with the experiment, i.e. -2.61 and -1.81 kcal/mol. At the low and intermediate values of temperatures, small- and large-curvature tunneling dominate the kinetics of R1, which is the dominant path over the range of temperature from 250 to 1200 K. This study shows the importance of multidimensional tunneling corrections for both R1 and R2, for which the total rate constant at 298 K calculated with the CVT/μOMT method is 8.2 × 10^-15 cm³ molecule^-1 s^-1 which agrees well with experiment value of 9.3 × 10^-15 cm³ molecule^-1 s^-1 (Mori, Bull. Inst. Chem. Res. 1981, 59, 116). © 2018 Wiley Periodicals, Inc.

Automated calculation of thermal rate coefficients using ring polymer molecular dynamics and machine-learning interatomic potentials with active learning

We propose a methodology for the fully automated calculation of thermal rate coefficients of gas phase chemical reactions, which is based on combining ring polymer molecular dynamics (RPMD) and machine-learning interatomic potentials actively learning on-the-fly.

An experimental and theoretical investigation of the C(1D) + D2 reaction

Rate constants derived from ring polymer molecular dynamics calculations confirm the validity of this method for studying low-temperature complex-forming reactions

A ring polymer molecular dynamics study of the OH + H2(D2) reaction

Using ring polymer molecular dynamics we have calculated the rate coefficients for the OH + H₂ reaction.

Ring-polymer molecular dynamical calculations for the F + HCl → HF + Cl reaction on the ground 12A' potential energy surface

The reaction kinetics of the heavy-light-heavy abstraction reaction F + HCl → HF + Cl on the ground electronic state potential energy surface (PES) is investigated theoretically by a recently developed ring polymer molecular dynamics (RPMD) approach. First, a new PES is developed by the permutation invariant polynomial neural network (PIP-NN) approach based on 30 620 points sampled over a large configuration space from the latest and most accurate Deskevich-Hayes-Takahashi-Skodje-Nesbitt (DHTSN) PES (J. Chem. Phys., 2006, 124, 224303). Excellent fitting performance was achieved with only 521 parameters. The PIP-NN PES is 11 times faster than the DHTSN PES. Besides, the first analytical derivatives with respect to the coordinates of the atoms have been obtained for the PIP-NN PES. The RPMD rate coefficients on the PIP-NN PES are calculated and compared with available theoretical and experimental results. It is found that the experimental rate coefficients are significantly larger than the theoretical results on the DHTSN PES, due to its overestimated reaction barrier. We conclude that a reliable PES for this important heavy-light-heavy reaction is highly desirable.

Thermal Rate Constants for the O(3P) + CH4 → OH + CH3 Reaction: The Effects of Quantum Tunneling and Potential Energy Barrier Shape

The rate constants and kinetic isotope effects for the O(³P) + CH₄ reaction have been investigated with the quantum instanton method in full dimensionality. The calculated rate constants are in good agreement with the experimental values above 400 K, below which the measured values are scattered. Compared to other theoretical approaches, the quantum instanton method predicts the largest quantum tunneling effect, so it gives the largest rate constants at low temperatures. The calculated kinetic isotope effects are always much larger than 1 and increase with decreasing temperature, due to the zero-point energy and quantum tunneling. Our calculations on different potential energy surfaces demonstrate that the potential energy barrier shape dominates the magnitude of quantum tunneling and has a great effect on the kinetic isotope effect.

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.

Which Is Better at Predicting Quantum-Tunneling Rates: Quantum Transition-State Theory or Free-Energy Instanton Theory?

Quantum transition-state theory (QTST) and free-energy instanton theory (FEIT) are two closely related methods for estimating the quantum rate coefficient from the free-energy at the reaction barrier. In calculations on one-dimensional models, FEIT typically gives closer agreement than QTST with the exact quantum results at all temperatures below the crossover to deep tunneling, suggesting that FEIT is a better approximation than QTST in this regime. Here we show that this simple trend does not hold for systems of greater dimensionality. We report tests on several collinear and three-dimensional reactions, in which QTST outperforms FEIT over a range of temperatures below crossover, which can extend down to half the crossover temperature (below which FEIT outperforms QTST). This suggests that QTST-based methods such as ring-polymer molecular dynamics (RPMD) may often give closer agreement with the exact quantum results than FEIT.

The hydrogen abstraction reaction O(3P) + CH4: a new analytical potential energy surface based on fit to ab initio calculations

Based exclusively on high-level ab initio calculations, a new full-dimensional analytical potential energy surface (PES-2014) for the gas-phase reaction of hydrogen abstraction from methane by an oxygen atom is developed. The ab initio information employed in the fit includes properties (equilibrium geometries, relative energies, and vibrational frequencies) of the reactants, products, saddle point, points on the reaction path, and points on the reaction swath, taking especial caution respecting the location and characterization of the intermediate complexes in the entrance and exit channels. By comparing with the reference results we show that the resulting PES-2014 reproduces reasonably well the whole set of ab initio data used in the fitting, obtained at the CCSD(T) = FULL/aug-cc-pVQZ//CCSD(T) = FC/cc-pVTZ single point level, which represents a severe test of the new surface. As a first application, on this analytical surface we perform an extensive dynamics study using quasi-classical trajectory calculations, comparing the results with recent experimental and theoretical data. The excitation function increases with energy (concave-up) reproducing experimental and theoretical information, although our values are somewhat larger. The OH rotovibrational distribution is cold in agreement with experiment. Finally, our results reproduce experimental backward scattering distribution, associated to a rebound mechanism. These results lend confidence to the accuracy of the new surface, which substantially improves the results obtained with our previous surface (PES-2000) for the same system.

Communication: Imaging the effects of the antisymmetric-stretching excitation in the O(³P) + CH₄(v₃ = 1) reaction

Effects of one-quantum excitation of the antisymmetric-stretching mode of CH4(v3 = 1) on the O((3)P) + CH4 reaction were studied in a crossed-beam, ion-imaging experiment. In the post-threshold region, we found that (1) the product state distributions are dominated by the CH3(0₀) + OH(v' = 1) pair, (2) the product angular distributions extend toward sideways from the backward dominance of the ground-state reaction, and (3) vibrational excitation exerts a positive effect on reactivity, but translational energy is more efficient in promoting the rate of this central-barrier reaction. All major findings agree reasonably well with recent theoretical results. Some remaining questions are pointed out.