Thermal Rate Coefficients and Kinetic Isotope Effects for the Reaction

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Thermal Rate Coefficients and Kinetic Isotope Effects for the Reaction OH + CH4 → H2O + CH3 on an ab Initio-Based Potential Energy Surface Jun Li*,† and Hua Guo‡ †

School of Chemistry and Chemical Engineering, Chongqing University, Chongqing 401331, China Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States

‡

ABSTRACT: Thermal rate coefficients for the title reaction and its various isotopologues are computed using a tunneling-corrected transition-state theory on a global potential energy surface recently developed by fitting a large number of high-level ab initio points. The calculated rate coefficients are found to agree well with the measured ones in a wide temperature range, validating the accuracy of the potential energy surface. Strong non-Arrhenius effects are found at low temperatures. In addition, the calculations reproduced the primary and secondary kinetic isotope effects. These results confirm the strong influence of tunneling to this heavy-light-heavy hydrogen abstraction reaction.

I. INTRODUCTION The reaction between hydroxyl radical and methane to form water and methyl radical (OH + CH4 → H2O + CH3) plays an extraordinarily important role in both atmospheric and combustion chemistry. On the one hand, at low temperatures, this reaction represents the major methane removal pathway in the atmosphere. At high temperatures, on the other hand, the abstraction of hydrogen from methane by the hydroxyl radical is a key step in natural gas combustion. This exothermic reaction (ΔH0 = −13.5 kcal/mol) has a moderate barrier (ΔE ≈ 6−7 kcal/mol),1−3 which features the transfer of a hydrogen atom. Because of its practical importance, the thermal rate coefficients of the title reaction have been measured with different techniques over a wide range (178−2025 K) of temperatures.4−22 As shown in Figure 1, these experimental

rate measurements, although generally consistent with each other, still have some discrepancies. It is not difficult to notice from the figure that the temperature dependence of the rate coefficient is non-Arrhenius, with a significant curvature at low temperatures. Various kinetic isotope effects (KIEs) have also been reported.15,17,20,23,24 These observations strongly suggest an important role of tunneling at low temperatures for the transferring hydrogen atom between two “heavy” moieties. The title reaction has also served as a prototype for studying dynamics of bimolecular reactions involving polyatomic molecules. For instance, the state-to-state reaction dynamics of the OH + CD4 reaction have been investigated in crossed molecular beam experiments by Liu and co-workers.25−27 In addition, the vibrational spectroscopy and decay dynamics of the CH4−OH entrance channel complex have been studied by Lester and co-workers.28,29 The reaction kinetics and dynamics of the title reaction have been extensively studied using various levels of theory. Most of the previous theoretical studies have focused on the determination and characterization of stationary points along the reaction path, particularly the transition state that, to a large extent, determines the rate coefficients and KIEs.1,20,30−36 There have been some early theoretical studies of reaction dynamics as well, using empirical potential energy surfaces (PESs) in reduced dimensionality.37−39 However, a complete understanding of the kinetics and dynamics requires an accurate full-dimensional PES. In 2000, Espinosa-Garciá and Corchado reported the first global analytical PES (PES-2000) using a Received: February 3, 2018 Revised: February 24, 2018 Published: February 26, 2018

Figure 1. Comparison of the experimental rate coefficients for the reaction OH + CH4 → H2O + CH3 as a function of 1000/T. © XXXX American Chemical Society

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DOI: 10.1021/acs.jpca.8b01201 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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kcal/mol, flanked by pre- and post-transition-state wells.3 As mentioned above, the 15-dimensional PES3 for the OH + CH4 → H2O + CH3 reaction was fit to ∼135 000 points by the PIPNN approach, in which the permutation symmetry of all five hydrogens in the system is enforced by symmetry functions as the input layer of the NN.54 In PIP-NN, the PIPs are symmetrized monomials of Morse-like variables of the internuclear distances (pij = exp(−αrij) with α = 1.0 Å−1):59

simple molecular mechanics functional form parametrized by both theoretical and experimental information.40 With this PES, several kinetics and dynamical calculations have been performed, and the agreement with available experimental data has generally been satisfactory.40−45 However, the ab initio method used to parametrize PES-2000 is no longer considered state-of-the-art, and significant inaccuracies have been recently pointed out by us.3,45 A refined PES (PES-2014) was later reported by the same group parametrized with more accurate ab initio data,2 and further calculations were performed on the new PES to provide insights into the kinetics and dynamics of this reaction.2,46,47 Because of the simple analytical functional forms with a small set of adjusting parameters and the limited number of ab initio points, these pioneering PESs may not be sufficiently reliable, especially outside the region along the minimum energy path (MEP). Importantly, the experimentally measured KIEs have not been reproduced by theory. These uncertainties in these PESs are almost certainly responsible for the failure.47 In 2015, we developed a new globally accurate PES in full dimensionality using the permutation invariant polynomialneural network (PIP-NN) approach48,49 based on ∼135 000 points calculated at the explicitly correlated couple cluster singles, doubles, and perturbative triples level with the augmented correlation consistent polarized valence triple-ζ basis set (UCCSD(T)-F12a/aug-cc-pVTZ).3 The CCSD-F12 approach has been extensively used in constructing global PESs50−53 and demonstrated to be highly accurate thanks to the high fidelity of the PIP-NN method.54 Both kinetics and dynamics results, such as the rate coefficients and cross sections, on this PIP-NN PES agreed well with available experiment.3,55,56 Thanks to the ultraflexibility of the PIP-NN approach and the large number of high-level ab initio points sampled over large configuration space, the PIP-NN PES represents the most accurate PES so far for the title reactive system. It is noted that calculated reaction probabilities on the PES-2000 are remarkably different from those on the PIP-NN PES.56 In the present publication, the thermal rate coefficients for reactions OH + CH4, OD + CH4, OH + CD4, and OH + 13CH4 are computed on the accurate PIP-NN PES using the canonical variational transition-state theory (CVT) with the inclusion of multidimensional tunneling effects,57,58 as well as the standard quasi-classical trajectory (QCT) method at high temperatures. These results provide a stringent test of the PES. Good agreement in the rate coefficients and their temperature dependences is achieved. More importantly, the calculated KIEs are found to be in a much better agreement with experiment than previous theoretical calculations. The improved agreement with experiment provides strong support for the accuracy of the PES and sheds valuable light on the role of tunneling in this important reaction. The remainder of the paper is structured as follows. Section II briefly summarizes the PES and the computational details in the transition-state theory and QCT method. The results and discussion are presented in Section III. Finally, conclusions are presented in Section IV.

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G({rij}) = S ̂ ∏ pijlij

(1)

i1) over the temperature range can be attributed to tunneling under the MEP. Because of its heavier mass, the transferring deuterium has a smaller vibrational frequency and smaller tunneling probability through the reaction barrier than hydrogen. In addition, the MEP is also dependent on isotope substitution, despite the fact that the PES, namely, the electronic energy plus the nuclei repulsive energy for a given configuration, is independent of nuclei D

DOI: 10.1021/acs.jpca.8b01201 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A masses. This is because the MEP used in the CVT/μOMT calculations is determined as the path of steepest descent in mass-scaled coordinates. Besides, the eigenvectors associated with the imaginary frequency at the transition state are dependent on isotope substitution.35 As shown in the upper panel of Figure 5, the barrier height for the reactions OH +

Figure 6. Thermal rate coefficients for the reaction OD + CH4 → HOD + CH3 as a function of 1000/T.

Figure 5. Potential energy (VMEP) and the ground vibrational state adiabatic potential (VGa ) along the MEP for reactions OH + CH4, OH + CD4, and OD + CH4. For each case, the zero of the energy is defined as that at the reactant asymptote. Figure 7. OH/OD + CH4 KIE as a function of the temperature over the range of 200−2000 K.

CH4 and OH + CD4 are essentially the same; however, they have different MEPs, particularly after the transition state: VMEP for the OH + CD4 reaction is slightly thicker than that for the OH + CH4 reaction. In the lower panel of the same Figure, it can be seen that the ground vibrational state adiabatic potential (VGa ) for OH + CD4 is not only higher but also thicker than that for OH + CH4. These are also supported by the magnitudes of the imaginary frequencies at the transition state: for OH + CH4, it is 1422i cm−1, much larger than 1056i cm−1 for OH + CD4. The OD + CH4 → HOD + CH3 reaction was also studied to provide information on secondary KIEs, where the deuterium atom is not directly involved in the reaction coordinate. Since the hydrogen atom is transferred, the tunneling effect is expected to be significant particularly at low temperatures. However, the source of secondary KIEs is more subtly dependent on the topography of the PES near the transition state. Figure 6 plots the CVT/μOMT calculated rate coefficients for this reaction on the PIP-NN PES, compared to available experiment measurements4,17 and results obtained on PES-2014.47 Clearly, the current CVT/μOMT rate coefficients on the PIP-NN PES and CVT/LCG3 rate coefficients on PES-2014 agree reasonably well with experiment, although the former is somewhat higher than experiment, while the latter is slightly lower than experiment. Interestingly, the RPMD rate coefficients on PES-2014 significantly overestimate the measurements at low temperatures and underestimate for temperatures above 400 K. Figure 7 presents the corresponding the secondary KIE, defined as the ratio between the rate coefficients for the OH + CH4 reaction and those for the OD + CH4 reaction in the temperature range of 200−2000 K. The theoretical values on

PES-2014 and the available experiment measurements are also included for comparison. All the results show an “inverse” behavior, that is, KIE smaller than 1, and the same trend of the KIE, namely, increasing along with the temperature. However, their deviations are quite remarkable. In the experimental temperature range (220−415 K), the CVT/LCG3 KIEs on PES-2014 agree well with experiment, falling within 0.85−0.95, which are slightly larger those calculated by the CVT/μOMT approach on the PIP-NN PES. On one hand, the KIEs determined by the RPMD approach on PES-2014 are significantly smaller. On the other hand, both CVT/LCG3 and RPMD calculated KIEs on PES-2014 increase gradually, becoming larger than 1 at high temperatures. While the CVT/ μOMT KIEs on the PIP-NN PES oscillate within the range of temperature 500−1000 K, 0.90−1.00, and then become essentially 1 at high temperatures. This can also be rationalized by comparing VMEP and VGa along the reaction coordinates in the two reactions. As shown in Figure 5, the deuterated atom in the OD reactant does not affect VMEP and VGa , in particular, in the reactant valley and the transition state region, both of which govern the kinetics. Therefore, at high temperatures, KIEs between OH + CH4 and OH + CD4 are expected to be ∼1, as predicted by the current CVT/μOMT calculations on the PIPNN PES. Finally, the OH + 13CH4 → H2O + 13CH3 reaction was investigated, and the corresponding KIEs were analyzed. This represents a severe test of the theory, since many factors are involved. This KIE has been studied by several groups, and it has been found that these heavy-atom KIEs are very sensitive to the theoretical treatment on the torsional motion.20,35,66,67 At E

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the experimental temperatures, 273, 293, and 353 K, the CVT/ LCG3 KIEs on PES-2014 are 1.039, 1.037, 1.031, respectively, and the CUS/μOMT results on PES-2000 are 1.036, 1.033, 1.029, respectively. They are both much larger than the experimental value of 1.0054 ± 0.0009 over the temperature range of 273−353 K.23 The CVT/μOMT results on the PIPNN PES are 1.0306, 1.0100, and 0.9964, respectively, or averaged to be 1.0123, which are close to the experiment measurement. The better agreement with experiment shows that again the new PES is more accurate than previous ones.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by National Natural Science Foundation of China (Contract No. 21573027 to J.L.) and by the U.S. Department of Energy (DE-SC0015997 to H.G.). We thank Prof. W. L. Hase for sending us a modified VENUS code, in which the Boltzmann distributions for rovibrational motions of diatomic molecules are included.

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IV. CONCLUSIONS We report here an extensive investigation of the kinetics of the title reaction and its isotopologues using both the transitionstate theory (CVT/μOMT) and QCT method on an accurate global PES. The rate coefficients are non-Arrhenius at low temperatures and strongly dependent on isotopic substitution, suggesting the importance of tunneling. These effects are reproduced by the tunneling-corrected transition-state theory over a large temperature range. In addition, the calculated primary and secondary KIEs are found to be in a much better agreement with experiment than previous theory. These new calculations provide strong evidence in support of the accuracy of the PIP-NN PES. The difficulties associated with an accurate characterization of reaction kinetics arise from two major sources. One is the reliability of the PES, which is determined by the accuracy of the ab initio method and fidelity of the fitting procedure. The second is from the approximations used in the transition-state theory, including the harmonic approximation in treating the vibrational modes, the approximate treatment of the quantum effects such as tunneling, and the approximate inclusion of recrossing dynamics. In the current work, we believe that the PIP-NN PES has essentially eliminated the errors in the PES. Although the current PIP-NN PES does not include the spin− orbit correction in the reactant channel, which increases the barrier height by only 70 cm−1, its effect is approximately accounted for by an electronic partition function. In addition, the approximations in the transition-state calculations are mitigated to the best of our abilities. It is desirable to further remove the approximations in the transition-state theory treatment of the kinetics. While fulldimensional quantum scattering calculations are still not feasible at this moment for this 15-dimensional reaction,52 it is possible to achieve this goal by using an emerging theoretical tool of RPMD,68 which has been adapted for calculating rate coefficients.69,70 As the global PES is used in the RPMD calculation of the potential of mean force along the reaction path, all anharmonicities are included. The RPMD approach can also account accurately for the zero-point energy and tunneling. Thus, RPMD calculations of the reaction rate coefficients and kinetic isotope effects on the PIP-NN PES would be highly desirable, and work in that direction is in progress.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jun Li: 0000-0003-2392-8322 Hua Guo: 0000-0001-9901-053X F

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DOI: 10.1021/acs.jpca.8b01201 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpca.8b01201 J. Phys. Chem. A XXXX, XXX, XXX−XXX