Rate Coefficients of the HCl + OH â Cl + H2O Reaction from Ring

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Rate Coefficients of the HCl + OH # Cl + HO Reaction From Ring Polymer Molecular Dynamics Junxiang Zuo, Yongle Li, Hua Guo, and Daiqian Xie J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b03488 • Publication Date (Web): 05 May 2016 Downloaded from http://pubs.acs.org on May 10, 2016

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The Journal of Physical Chemistry

jp-2016-034885, revised

Rate Coefficients of the HCl + OH → Cl + H2O Reaction from Ring Polymer Molecular Dynamics Junxiang Zuo,† Yongle Li,*, ‡ Hua Guo,¶ and Daiqian Xie*,†,§ †

Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210093, China

‡

Department of Physics, International Center of Quantum and Molecular Structure, Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University, Shanghai 200444, China

¶

Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, NM 87131, USA

§

Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

1

ACS Paragon Plus Environment


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ABSTRACT: Thermal rate coefficients at temperatures between 200 and 1000 K are calculated for the HCl + OH → Cl + H2O reaction on a recently developed permutation invariant potential energy surface, using ring polymer molecular dynamics (RPMD). Large deviations from the Arrhenius limit are found at low temperatures, suggesting significant quantum tunneling. Agreement with available experimental rate coefficients is generally satisfactory, although the deviation becomes larger at lower temperatures. The theory-experiment discrepancy is attributed to the remaining errors in the potential energy surface, which is known to slightly overestimate the barrier. In the deep tunneling region, RPMD performs better than traditional transition-state theory with semi-classical tunneling corrections.

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I. INTRODUCTION The reaction between HCl and OH plays an important role in atmospheric chemistry, as it produces Cl radical and water with a relatively low barrier ~ ~ ~ HCl( X 1Σ+) + OH( X 2Π) → Cl(2Pu) + H2O( X 1A1),

∆H0 = -15.36 kcal/mol.

The Cl radical is an important catalyst for the ozone destruction reaction O3 + O → 2O2 in the Chapman cycle, which is responsible to the stratosphere ozone depletion in Antarctica.1 As a result, rate coefficients of the HCl + OH reaction have been measured experimentally by many authors.2-9 For example, the rate coefficients above 200 K have been reported by Smith and Zolner,2 by Molina and coworkers,3 and by Ravishankara and coworkers.5 The low temperature rates were reported later by Sharkey and Smith,7 who found significant deviations from the Arrhenius behavior. More recently, Battin-Leclerc et al.8 and Bryukov et al.9 reinvestigated the kinetics for different isotopes as well as the pressure dependence. The potential energy surface (PES) for the title reaction has recently been investigated by a number of groups. Earlier PESs were largely empirical,10-12 some of which have been shown to give incorrect rate coefficients.13 Schaefer and coworkers have recently reported the stationary points along the reaction path using high-level ab initio methods.14 Li et al. have reported a full-dimensional PES for the title reaction by fitting 25000 Davidson corrected multi-reference configuration interaction (MRCI+Q) points,15 using the permutation invariant polynomial (PIP) method of Braams, Bowman and coworkers.16 The choice of the MRCI+Q method was due to the fact that the transitionstate region of the PES has a relatively large multi-reference character. The MRCI+Q 3



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level of theory yielded an accurate barrier for the reverse direction of the title reaction, but underestimated the reaction energy. As a result, the barrier for the forward direction is underestimated by about 0.5 kcal/mol. More recently, a much more faithful fit was reported for the same ab initio points,17 using the permutation invariant polynomialneural network (PIP-NN) method.18, 19 These two PESs have been used in several recent quasi-classical trajectory and quantum dynamical studies of both the forward and reverse directions of the title reaction,20-24 since they serve as prototypes for understanding mode specificity in reaction dynamics.25 In Figure 1, the potential along the reaction pathway is shown. In addition to a low forward barrier, there is also a significant pre-reaction well, which corresponds to a hydrogen bonded complex HO-HCl. The existence of this well is believed to facilitate tunneling at low collision energies, consistent with the experimentally observed deviations from the Arrhenius behavior at low temperatures. In addition, there have been a few direct dynamics studies on the rate coefficients,26, 27 which required no PES. The accurate characterization of tunneling in low-temperature rate coefficients remains a challenge in theoretical kinetics. The traditional transition-state theory approximates the quantum mechanical effect using semi-classical methods,28 and as a result its accuracy at low temperatures is difficult to assess.29, 30 Recrossing and tunneling become significant in heavy-light-heavy reactions, such as the one studied here, and thus posing a challenge to transition-state theory. Quantum wave packet calculations are accurate,22 but the number of thermally populated internal states of the reactants is quite large and thus difficult to account for. In this publication, we report a ring-polymer molecular dynamics (RPMD) calculation of the forward reaction rate coefficients using

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the PIP-NN PES. The RPMD method takes advantage of the isomorphism between a quantum mechanical system and a fictitious classical ring polymer consisting of harmonically connected beads.31 While the evolution of the ring polymer can be followed by Newtonian dynamics, RPMD gives the correct quantum statistics, which is important for quantum effects such as tunneling and zero-point energy. Recently, the RPMD theory for computing rate coefficients has been proposed32-35 and a general-purpose suite of programs, RPMDrate, has been developed by Suleimanov and coworkers.36 The RPMD approach has several desirable features.32, 33, 37 For example, the RPMD rate coefficient approaches the classical limit at high temperatures. It also has a well-defined short-time limit that serves as an upper bound of the RPMD rate. Furthermore, the RPMD results are independent of the choice of the dividing surface, a property highly desirable because the dividing surface is difficult to define for high-dimensional reactive systems. Formal analyses have also suggested that RPMD rate theory is consistent with quantum mechanical transition state theory,38, 39 and gives a better characterization of tunneling than the centroid molecular dynamics40 or quantum instanton theory.41 Comparison with quantum dynamical benchmarks of rate coefficients in small systems has been very promising, even in deep tunneling regions.42-54 This is important for the title reaction at low temperatures because of the apparent tunneling presence. This publication is organized as follows. The next section (Sec. II) outlines the RPMD theory and its application to rate coefficient calculations. The results are presented and discussed in Sec. III. The conclusions are given in Sec. IV.

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II. THEORY All calculations reported here used the recently developed RPMDrate code by Suleimanov and co-workers,36 with enhanced multiprocessing functionality (Y. Li, to be published). Given the fact that the RPMD rate theory has been described in detail in the literature,32-35 only a brief review is given here. Making use of the isomorphism between the quantum system and a classical ring polymer, each quantum particle is represented in RPMD by n classical beads connected by nearest neighbor harmonic potentials.55 The Hamiltonian of the reaction system of the title reaction can thus be written as bellow:

,

where

and

(1)

is the momentum and Cartesian coordinate of the jth bead of the ith

atom, mi is the mass of the ith atom, ω n = (β n h )

−1

( β n = (nk BT ) ) is the force constant −1

v0 vn between two neighboring beads and qi( ) ≡ qi( ) . The potential energy V is the PES reported by Li. et al.,17 which is PIP-NN fit of ~25000 ab initio points at the level of 2state-MRCI + Qrot/AVTZ-DW-5-state-CASSCF.15 The reaction coordinate in the RPMD calculations is defined based on two dividing surfaces in terms of the ring polymer centroids.36 The first one located in the

v reactant asymptote is defined by the vector ( R ) connecting the centers of mass (COMs) of the reactants (HCl and OH):

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v v s0 (q ) = R∞ − R ,

(2)

where R∞ is the distance where the interaction becomes negligible. The second dividing surface is placed in the vicinity of the transition state and it is defined in terms of the distance between the breaking and forming bonds:36

v v v ≠ ≠ s1 (q ) = ( qHCl − qHCl ) − ( qOH − qOH ),

(3)

v ≠ where qAB is the vector between the centroids of the atoms A and B and qAB is the corresponding distance of the atoms at the saddle point. With the two dividing surfaces defined above, the reaction coordinate ξ can be written as

v

ξ (q ) =

v s0 (q ) v v . s0 (q ) − s1 (q )

(4)

Adapting the Bennett-Chandler factorization,56, 57 the RPMD rate coefficient can be expressed by:34, 35

kRPMD (T ) = kQTST (T; ξ ≠ ) κ ( t → ∞; ξ ≠ ) ,

(

where the first term kQTST T; ξ ≠

)

(5)

is the static contribution, denoted as the centroid-

density quantum transition state theory (QTST58-60) rate coefficient,32, 34 calculated from the peak position ( ξ ≠ ) of the free-energy curve along the reaction coordinate ξ (q) . In practice, it is obtained from the potential of mean force (PMF) along the reaction coordinate:34, 35 7



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(

kQTST T ; ξ

≠

)

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12

 1  − β [W (ξ ≠ )−W (0 )]  e , = 4πR  2 πβµ R   2 ∞

(6)

( )

where µ R is the reduced mass of reactants and W ξ ≠ − W (0 ) is the change of free energy obtained via umbrella integration.36, 61

(

The second term κ t → ∞; ξ ≠

)

named the transmission coefficient represents the

dynamic correction, and accounts for recrossing at the top of the free-energy barrier ( ξ ≠ ).

(

)

This factor counterbalances kQTST T; ξ ≠ , ensuring the independence of the RPMD rate coefficient kRPMD(T) of the choice of the dividing surface.34, 35 The final RPMD rate coefficients were corrected with an electronic partition function ratio of the following form: TS Qelec. 2 = Reactant Qelec. 1+ exp ( −205K/ T )

(7)

in order to take into account the spin–orbit splitting (∆E=205 K) of OH ( 2 Π 1/2,3/2). When only one bead is used, RPMD gives the classical rate coefficients. The minimal number of beads needed to account for the quantum effects can be estimated by the following formula62 nmin ≡ β hωmax ,

(8)

where ωmax is the largest vibrational frequency of the system. There is another important parameter, namely the crossover temperature: Tc = hωb 2πk B , where iωb is 8


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the imaginary frequency at the peak position of the reaction barrier. The temperature range below Tc is often considered as the deep-tunneling region, where most semiclassical methods tend to have large errors.40 For the title reaction, the Tc is 290 K. The calculations were first performed with one bead, which provides the classical limit. The number of beads was then increased according to the calculated nmin, and twice nmin at several temperatures (200 and 1000 K) are also used to confirm the convergence of the results. In the calculation of the PMF, given the sharp peaks in the PES, two sets of windows were used. In the asymptotic region (ξ ∈ [-0.05, 0.90]), windows with an equal size (∆ξ = 0.01) were used with the force constant of the biasing potential of k=k0 = 2.727 (T/K) eV. While in the region near the barrier (ξ ∈ [0.905, 1.05]), larger k values (2 k0~4 k0) are used. To keep proper overlaps between neighboring windows, the width of windows ∆ξ is reduced to 0.005 accordingly. In each sampling window, the system was first equilibrated for 20 ps, following by a production run of 15 ns. The Andersen thermostat was used in all simulations.63 The time step is 0.1 fs. After the PMF calculations, the transmission coefficients were computed. This was initiated by running a long (10 ns) parent trajectory with the ring-polymer centroid fixed at the top of the free-energy barrier via the SHAKE algorithm.64 Configurations were sampled once every 2 ps to serve as the initial positions for the child trajectories used to compute the flux-side correlation function. For each initial position, 100 separate ring polymer trajectories are spawned with different initial momenta sampled from a Boltzmann distribution. These trajectories were then propagated with no constraint for 50 fs where the transmission coefficients reach plateau values. The time step in this state

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was also set to 0.1 fs. The variational transition-state theory calculations using the CVT/µOMT method65 are performed using POLYRATE from the Truhlar’s group.66 In this approach, the tunneling is approximated by using the micro-canonical optimized multidimensional tunneling (µOMT)67 approach, in which the larger of the small-curvature tunneling (SCT) and large-curvature ground-state tunneling (LCT) probabilities was taken as the best estimate. The same parameters are used as reported in the earlier work of Li et al.15 The same temperatures as used in RPMD calculations are selected.

III. RESULTS AND DISCUSSIONS The parameters used in all RPMDRate calculations in this work are summarized in Table 1. To elucidate how the number of beads in the RPMD calculations affects the results, the PMFs obtained with 1, 4, 8, 16, 32 and 64 beads are displayed in Figure 2 for the title reaction at 300 K. Before reaching the reaction barrier, the PMF features a shallow free-energy well, which corresponds to the HO-HCl hydrogen bonded well on the PES. A similar well was found in the Cl + O3 reaction due to a van der Waals interaction.49 The classical barrier height with a single bead is significantly higher than those obtained with more beads, suggesting that the reaction is significantly influenced by tunneling and zero-point energy. These quantum effects reduce the height of the PMF barrier from 7.65 kcal/mol with one bead in the classical limit to 5.38 kcal/mol with 64 beads in the quantum limit. It is interesting that with only 4 beads the height of the PMF peak drops already to 5.29 kcal/mol, which is quite close to its converged value. This 10


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finding is consistent with what we found previously, say in the O + CH4 reaction,44 showing the first few beads can capture the most quantum effects in RPMD. Additional beads have a relatively minor effect for energetics, but affect the shape of the peak of PMF. As discussed below, tunneling is expected to be more dominant at lower temperatures. In Figure 3, the converged RPMD PMFs are displayed for different temperatures. Two trends are apparent. First, all PMFs are dominated by a barrier near ξ =1, suggesting that this reaction is activated with a reaction bottleneck near the PES barrier. Second, the barrier height increases monotonically with temperature, which reflects a large entropic factor in the activation free energy. The free-energy barrier increases from 3.52 kcal/mol at 200 K to 14.61 kcal/mol at 1000 K, a change of 11.09 kcal/mol. This is accompanied by the disappearance of the free-energy well for the HO-HCl hydrogen bonded complex at high temperatures, which can presumably be attributed to the increased excursion of the system outside the well. Figure 4 shows the RPMD transmission coefficients as a function of time at different temperatures. Their values decay rapidly with time, and level off after ~20 fs, signaling the end of recrossing. Some oscillations are found at low temperatures, presumably due to the pre-reaction well. The transmission coefficients are typically much smaller than unity, due apparently to the heavy-light-heavy feature of the transition state, in which the transferring hydrogen oscillator between the heavy Cl and O atoms. This is very similar to other heavy-light-heavy reactions we have investigated before.44, 47 The much-less-than-unity transmission coefficients have contributions from both the classical recrossing and tunneling. The latter is manifested in the temperature dependence of 11



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κ ( t → ∞; ξ ≠ ) , which becomes smaller at lower temperatures. We note in passing that tunneling influences both the PMF and transmission coefficient in a RPMD calculation, but a separation of their contributions in the RPMD framework is difficult. The results of the RPMD calculations for the HCl + OH reaction obtained on the PIP-NN PES are summarized in Table 2. The calculated RPMD rate coefficients for the title reaction obtained at 200, 300, 500, 700, 1000 K are compared in Figure 5 with the previous theoretical and experimental results. From this figure, it is clear that the RPMD rate coefficients deviate significantly from the Arrhenius behavior at low temperatures, consistent with experimental observations. The deviation is already quite apparent above the crossover temperature (Tc = 290 K for the title reaction). They are somewhat larger than the experimental values at higher temperatures, but smaller at lower temperatures. At 300 K, for example, the RPMD rate coefficient (5.28×10-13 cm3·s-1) is about 79% times of the experimental value (6.7×10-13 cm3·s-1) of Husain et al.4 Since the dynamical treatment in RPMD is accurate, although it is known to slightly overestimates the rate coefficient of the reaction with asymmetric barrier at the temperature below the crossover temperature (Tc = 290 K for the title reaction),34 the theory-experiment discrepancies may be attributed to the inaccuracies of the PIP-NN PES. Recent work by Schaefer and coworkers have reported that the barrier height of the title reaction obtained at the CCSD(T)/cc-pVQZ level (2.4 kcal/mol)14 is somewhat lower than that at the MRCI+Q/aug-cc-pVTZ level (2.86 kcal/mol), which was used in constructing the PIPNN PES.15 Our own calculations at the CCSD(T)/aug-cc-pVTZ level have also yielded a barrier height of 2.43 kcal/mol.15 These results seem to suggest a slight overestimation of the barrier in the PES. 12


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It is interesting to compare the RPMD results with the rate coefficients obtained using the CVT/µOMT method on the same PES, which are also included in Figure 5. It is clear that the two are close in high temperatures, as they should be, but the difference increases quite dramatically at low temperatures. The rate coefficient obtained from the transition-state theory is significantly lower than its RPMD counterpart at low temperatures below Tc, suggesting underestimation of the tunneling contribution. It is known that the CVT/µOMT treatment of deep tunneling might not entirely be suitable in some cases,

especially those with

multi-dimensional

tunneling and/or large

anharmonicities.29, 30 In addition, the barrier for the title reaction is quite low and close to a pre-reaction well, which might allow multiple attempts for the system to tunnel. Interestingly, the underestimation of the tunneling contribution by the standard tunneling corrected CVT approach has also been noted in a recent calculation of the OH + OH reaction rate coefficients,68 which like the title reaction also has a low barrier with a prereaction well. For the title reaction, the CVT/µOMT rate coefficients are also significantly lower than the experiment.

IV. CONCLUSIONS In this work, we employed a full-dimensional approximate quantum mechanical method, ring polymer molecular dynamics (RPMD), to calculate the rate coefficients for the reaction HCl + OH → Cl + H2O on a newly developed permutation invariant polynomial neuro-network (PIP-NN) potential energy surface (PES). It is shown that this reaction is strongly influenced by recrossing and quantum mechanical tunneling, particularly at low temperatures. The calculated RPMD rate coefficients are in reasonably good agreement with the experimental values. Interestingly, the CVT/µOMT theory 13



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significantly underestimates the tunneling contribution at low temperatures, presumably due to the pre-reaction well. Our results also suggest that the PES, which was constructed at the MRCI level, could be improved by CCSD(T).

AUTHOR INFORMATION Corresponding Authors *Phone: +86-21-66136131. E-mail: [email protected] (YL). * Phone: +86-25-89689010. E-mail: [email protected] (DX).

ACKNOWLEDGEMENTS Y. Li acknowledges financial support from National Natural Science Foundation of China (Grant No. 21503130), and partly supported by Shanghai Key Laboratory of High Temperature Superconductors (No. 14DZ2260700). D. Q. Xie acknowledges financial support from National Natural Science Foundation of China (Grant Nos. 21133006, 21590802,

91421315),

the

Chinese

Ministry

of

Science

and

Technology

(2013CB834601), and Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase). H. Guo acknowledges financial support from US Department of Energy (Grant number DE-FG02-05ER15694). We thanks Yu. Suleimanov for many useful discussions on the RPMDRate.

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REFERENCES 1. Molina, J. J.; Tso, T. L.; Molina, L. T.; Wang, F. C. Y., Antarctic stratospheric chemistry of chlorine nitrate, hydrogen chloride, and ice: Release of active chlorine, Science 1987, 238, 1253-1257. 2. Smith, I. W. M.; Zellner, R., Rate measurements of reactions of OH by resonance absorption. Part 3.—Reactions of OH with H2, D2 and hydrogen and deuterium halides, J. Chem. Soc., Faraday Trans. 2 1974, 70. 3. Molina, M. J.; Molina, L. T.; Smith, C. A., The rate of the reaction of OH with HCl, Int. J. Chem. Kinet. 1984, 16, 1151-1160. 4. Husain, D.; Plane, J. M. C.; Xiang, C. C., Kinetic studies of the reactions of OH(X2Π) with hydrogen chloride and deuterium chloride at elevated temperatures by time-resolved resonance fluorescence (A2Σ+-X2Π), J. Chem. Soc. Faraday Trans. 2 1984, 80, 713-728. 5. Ravishankara, A. R.; Wine, P. H.; Wells, J. R.; Thompson, R. L., Kinetic study of the reaction of OH with HCl from 240–1055 K, Int. J.Chem. Kinet. 1985, 17, 1281-1297. 6. Smith, I. W. M.; Williams, M. D., Effects of isotope substitution and vibrational excitation on reaction rates. Kinetics of OH(v=0,1) and OD(v=0,1) with HCl and DCl, J. Chem. Soc. Faraday Trans. 2 1986, 82, 1043. 7. Sharkey, P.; Smith, I. W. M., Kinetics of elementary reactions at low temperatures: rate constants for the reactions of OH with HCl (298 > T/K > 138) , CH4 (298 > T/K > 178) and C2H6 (298 > T/K > 138), J. Chem. Soc. Faraday Trans. 1993, 89, 631-637. 8. Battin-Leclerc, F.; Kim, I. K.; Talukdar, R. K.; Portmann, R. W.; Ravishankara, A. R., Rate coefficients for the reactions of OH and OD with HCl and DCl between 200 and 400 K, J. Phys. Chem. A 1999, 103, 3237-3244. 9. Bryukov, M. G.; Dellinger, B.; Knyazev, V. D., Kinetics of the gas-phase reaction of OH with HCl, J. Phys. Chem. A 2006, 110, 936-943. 10. Clary, D. C.; Nyman, G.; Hernandez, R., Mode selective chemistry in the reactions of OH with HBr and HCl, J. Chem. Phys. 1994, 101, 3704-3714. 11. Yu, H.-G.; Nyman, G., Interpolated ab initio quantum scattering for the reaction of OH with HCl, J. Chem. Phys. 2000, 113, 8936-8944. 12. Rodriguez, A.; Garcia, E.; Hernandez, M. L.; Laganà, A., A LAGROBO strategy to fit potential energy surfaces: the OH+HCl reaction, Chem. Phys. Lett. 2002, 360, 304312. 13. Huarte-Larrañaga, F.; Manthe, U., Quantum mechanical calculation of the OH + HCl → H2O + Cl reaction rate: Full dimensional accurate, centrifugal sudden, and Jshifted results, J. Chem. Phys. 2003, 118, 8261-8267. 14. Guo, Y.; Zhang, M.; Xie, Y.; Schaefer III, H. F., Communication: Some critical features of the potential energy surface for the Cl + H2O → HCl + OH forward and reverse reactions, J. Chem. Phys. 2013, 139, 041101. 15. Li, J.; Dawes, R.; Guo, H., Kinetic and dynamic studies of the Cl(2Pu) + 1 H2O(X A1) → HCl(X1Σ+) + OH(X2Π) reaction on an ab initio based full-dimensional global potential energy surface of the ground electronic state of ClH2O, J. Chem. Phys. 2013, 139, 074302. 15



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16. Braams, B. J.; Bowman, J. M., Permutationally invariant potential energy surfaces in high dimensionality, Int. Rev. Phys. Chem. 2009, 28, 577–606. 17. Li, J.; Song, H.; Guo, H., Insights into the bond-selective reaction of Cl + HOD(nOH) → HCl + OD, Phys. Chem. Chem. Phys. 2015, 17, 4259-4267. 18. Jiang, B.; Guo, H., Permutation invariant polynomial neural network approach to fitting potential energy surfaces, J. Chem. Phys. 2013, 139, 054112. 19. Li, J.; Jiang, B.; Guo, H., Permutation invariant polynomial neural network approach to fitting potential energy surfaces. II. Four-atom systems, J. Chem. Phys. 2013, 139, 204103. 20. Song, H.; Guo, H., Vibrational and rotational mode specificity in the Cl + H2O → HCl + OH reaction: A quantum dynamical study, J. Phys. Chem. A 2015, 119, 61886194. 21. Song, H.; Lee, S.-Y.; Lu, Y.; Guo, H., Full-dimensional quantum dynamical studies of the Cl + HOD → HCl/DCl + OD/OH reaction: Bond selectivity and isotopic branching ratio, J. Phys. Chem. A 2015, 119, 12224-12230. 22. Song, H.; Guo, H., Mode specificity in the HCl + OH → Cl + H2O reaction: Polanyi's Rules vs. Sudden Vector Projection model, J. Phys. Chem. A 2015, 119, 826831. 23. Li, J.; Corchado, J. C.; Espinosa-García, J.; Guo, H., Final state-resolved mode specificity in HX + OH → X + H2O (X=F and Cl) reactions: A quasi-classical trajectory study, J. Chem. Phys. 2015, 142, 084314. 24. Zhao, B.; Sun, Z.; Guo, H., Communication: State-to-state dynamics of the Cl + H2O → HCl + OH reaction: Energy flow into reaction coordinate and transition-state control of product energy disposal, J. Chem. Phys. 2015, 142, 241101. 25. Li, J.; Jiang, B.; Song, H.; Ma, J.; Zhao, B.; Dawes, R.; Guo, H., From ab initio potential energy surfaces to state-resolved reactivities: The X + H2O ↔ HX + OH (X=F, Cl, and O(3P)) reactions, J. Phys. Chem. A 2015, 119, 4667-4687. 26. Steckler, R.; Thurman, G. M.; Watts, J. D.; Bartlett, R. J., Ab initio direct dynamics study of OH + HCl → Cl + H2O, J. Chem. Phys. 1997, 106, 3926-3933. 27. Buszek, R. J.; Barker, J. R.; Francisco, J. S., Water effect on the OH + HCl reaction, J. Phys. Chem. A 2012, 116, 4712-4719. 28. Truhlar, D. G.; Garrett, B. C.; Klippenstein, S. J., Current status of transition-state theory, J. Phys. Chem. 1996, 100, 12771-12800. 29. Meana-Pañeda, R.; Truhlar, D. G.; Fernández-Ramos, A., Least-action tunneling transmission coefficient for polyatomic reactions, J. Chem. Theo. Comput. 2010, 6, 6-17. 30. Barker, J. R.; Nguyen, T. L.; Stanton, J. F., Kinetic isotope effects for Cl + CH4 ⇌ HCl + CH3 calculated using ab initio semiclassical transition state theory, J. Phys. Chem. A 2012, 116, 6408-6419. 31. Habershon, S.; Manolopoulos, D. E.; Markland, T. E.; Miller III, T. F., Ringpolymer molecular dynamics: Quantum effects in chemical dynamics from classical trajectories in a extended phase space, Annu. Rev. Phys. Chem. 2013, 64, 387-413. 32. Craig, I. R.; Manolopoulos, D. E., Chemical reaction rates from ring polymer molecular dynamics, J. Chem. Phys. 2005, 122, 084106. 33. Craig, I. R.; Manolopoulos, D. E., A refined ring polymer molecular dynamics theory of chemical reaction rates, J. Chem. Phys. 2005, 123, 034102.

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Page 16 of 33

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


34. Collepardo-Guevara, R.; Suleimanov, Y. V.; Manolopoulos, D. E., Bimolecular reaction rates from ring polymer molecular dynamics, J. Chem. Phys. 2009, 130, 174713. 35. Suleimanov, Y. V.; Collepardo-Guevara, R.; Manolopoulos, D. E., Bimolecular reaction rates from ring polymer molecular dynamics: Application to H + CH4 → H2 + CH3, J. Chem. Phys. 2011, 134, 044131. 36. Suleimanov, Y. V.; Allen, J. W.; Green, W. H., RPMDrate: bimolecular chemical reaction rates from ring polymer molecular dynamics, Comput. Phys. Comm. 2013, 184, 833-840. 37. Craig, I. R.; Manolopoulos, D. E., Quantum statistics and classical mechanics: Real time correlation frunction from ring polymer molecular dynamics, J. Chem. Phys. 2004, 121, 3368-3373. 38. Hele, T. J. H.; Althorpe, S. C., Derivation of a true (t → 0+) quantum transitionstate theory. II. Recovery of the exact quatnum rate in the absense of recrossing, J. Chem. Phys. 2013, 139, 084115. 39. Hele, T. J. H.; Althorpe, S. C., Derivation of a true (t → 0+) quantum transitionstate theory. I. Uniqueness and equivalence to ring-polymer molecular dynamics transition-state-theory, J. Chem. Phys. 2013, 138, 084108. 40. Richardson, J. O.; Althorpe, S. C., Ring-polymer molecular dynamics rate-theory in the deep-tunneling regime: Connection with semi-classical instanton theory, J. Chem. Phys. 2009, 131, 214106. 41. Zhang, Y.; Stecher, T.; Cvitaš, M. T.; Althorpe, S. C., Which Is better at predicting quantum-tunneling rates: Quantum transition-state theory or free-energy instanton theory?, J. Phys. Chem. Lett. 2014, 5, 3976-3980. 42. Pérez de Tudela, R.; Aoiz, F. J.; Suleimanov, Y. V.; Manolopoulos, D. E., Chemical reaction rates from ring polymer molecular dynamics: Zero point energy conservation in Mu + H2 → MuH + H, J. Phys. Chem. Lett. 2012, 3, 493-497. 43. Suleimanov, Y. V.; Pérez de Tudela, R.; Jambrina, P. G.; Castillo, J. F.; SáezRábanos, V.; Manolopoulos, D. E.; Aoiz, F. J., A ring polymer molecular dynamics study of the isotopologues of the H + H2 reaction, Phys. Chem. Chem. Phys. 2013, 15, 36553665. 44. Li, Y.; Suleimanov, Y. V.; Yang, M.; Green, W. H.; Guo, H., Ring polymer molecular dynamics calculations of thermal rate constants for the O(3P) + CH4 → OH + CH3 reaction: Contributions of quantum effects, J. Phys. Chem. Lett. 2013, 4, 48-52. 45. Li, Y.; Suleimanov, Y. V.; Li, J.; Green, W. H.; Guo, H., Rate coefficients and kinetic isotope effects of the X + CH4 → CH3 + HX (X = H, D, Mu) reactions from ring polymer molecular dynamics, J. Chem. Phys. 2013, 138, 094307. 46. Allen, J. W.; Green, W. H.; Li, Y.; Guo, H.; Suleimanov, Y. V., Communication: Full dimensional quantum rate coefficients and kinetic isotope effects from ring polymer molecular dynamics for a seven-atom reaction OH + CH4 → CH3 + H2O, J. Chem. Phys. 2013, 138, 221103. 47. Li, Y.; Suleimanov, Y. V.; Green, W. H.; Guo, H., Quantum rate coefficients and kinetic isotope effect for the reaction Cl + CH4 → HCl + CH3 from ring polymer molecular dynamics, J. Phys. Chem. A 2014, 118, 1989-1996.

17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

48. Li, Y.; Suleimanov, Y. V.; Guo, H., Ring-polymer molecular dynamics rate coefficient calculations for insertion reactions: X + H2 → HX + H (X = N, O), J. Phys. Chem. Lett. 2014, 5, 700-705. 49. Pérez de Tudela, R.; Suleimanov, Y. V.; Menendez, M.; Castillo, F.; Aoiz, F. J., A ring polymer molecular dynamics study of the Cl + O3 reaction, Phys. Chem. Chem. Phys. 2014, 16, 2920-2927. 50. Suleimanov, Y. V.; Kong, W. J.; Guo, H.; Green, W. H., Ring-polymer molecular dynamics: Rate coefficient calculations for energetically symmetric (near thermoneutral) insertion reactions (X + H2) → HX + H(X = C(1D), S(1D)), J. Chem. Phys. 2014, 141, 244103. 51. Espinosa-Garcia, J.; Fernandez-Ramos, A.; Suleimanov, Y. V.; Corchado, J. C., Theoretical study of the F(2P) + NH3 hydrogen abstraction reaction: Mechanism and kinetics, J. Phys. Chem. A 2014, 118, 554-560. 52. Suleimanov, Y. V.; Espinosa-Garcia, J., Recrossing and tunneling in the kinetics study of the OH + CH4 → H2O + CH3 reaction, J. Phys. Chem. B 2016, 120, 1418-1428. 53. Hickson, K. M.; Loison, J.-C.; Guo, H.; Suleimanov, Y. V., Ring-polymer molecular dynamics for the prediction of low-temperature rates: An investigation of the C(1D) + H2 reaction, J. Phys. Chem. Lett. 2015, 6, 4194-4199. 54. Meng, Q.; Chen, J.; Zhang, D. H., Communication: Rate coefficients of the H + CH4 → H2 + CH3 reaction from ring polymer molecular dynamics on a highly accurate potential energy surface, J. Chem. Phys. 2015, 143, 101102. 55. Chandler, D.; Wolynes, P. G., Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids, J. Chem. Phys. 1981, 74, 4078-4095. 56. Bennett, C. H., Molecular dynamics and transition state theory: the simulation of infrequent events. In Algorithms for Chemical Computations, ACS Symposium Series, Christofferson, R. E., Ed. ACS: 1977; Vol. 46. 57. Chandler, D., Statistical mechanics of isomerization dynamics in liquids and the transition state approximation, J. Chem. Phys. 1978, 68, 2959-2970. 58. Gillan, M. J., Quantum simulation of hydrogen In metals, Phys. Rev. Lett. 1987, 58, 563-566. 59. Gillan, M. J., Quantum-classical crossover of the transition rate in the damped double well, J. Phys. C 1987, 20, 3621-3641. 60. Voth, G. A.; Chandler, D.; Miller, W. H., Rigorous formulation of quantum transition state theory and its dynamical corrections, J. Chem. Phys. 1989, 91, 7749-7760. 61. Kästner, J.; Thiel, W., Bridging the gas between thermodynamic integration and umbrella sampling provides a novel analysis method: "umbrella integration", J. Chem. Phys. 2005, 123, 144104. 62. Markland, T. E.; Manolopoulos, D. E., An efficient ring polymer contraction scheme for imaginary time path integral simulations, J. Chem. Phys. 2008, 129, 024105. 63. Andersen, H. C., Molecular dynamics simulations at constant pressure and/or temperature, J. Chem. Phys. 1980, 72, 2384-2393. 64. Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J., Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of nalkanes, J. Comput. Phys. 1977, 23, 327-341.

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65. Truhlar, D. G.; Garrett, B. C., Variational transition state theory, Annu. Rev. Phys. Chem. 1984, 35, 159-189. 66. Corchado, J. C.; Chuang, Y.-Y.; Fast, P. L.; Hu, W.-P.; Liu, Y.-P.; Lynch, G. C.; Nguyen, K. A.; Jackels, C. F.; Fernandez Ramos, A.; Ellingson, B. A., et al. POLYRATE– version 9.7, University of Minnesota, Minneapolis: 2007. 67. Liu, Y.-P.; Lu, D.-h.; Gonzalez-Lafont, A.; Truhlar, D. G.; Garrett, B. C., Direct dynamics calculation of the kinetic isotope effect for an organic hydrogen-transfer reaction, including corner-cutting tunneling in 21 dimensions, J. Am. Chem. Soc. 1993, 115, 7806-7817. 68. Nguyen, T. L.; Stanton, J. F., Ab initio thermal rate calculations of HO + HO = 3 O( P) + H2O reaction and isotopologues, J. Phys. Chem. A 2013, 117, 2678–2686.

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Table 1. Parameters for the RPMD rate coefficient calculations on the HCl + OH reaction

Parameter

Values

Note

Command line parameters Temp (K) 200,300,500,700,1000 8（1000K）;16（700K, 500K）; n 64（300K, 200K） Dividing surface parameters R∞ 30 Nbonds 1 Nchannel 1 Thermostat thermostat Andersen Biased sampling parameters 128 (200K,300K) Nwindows 112 (500K,700K,100K) ξ1 -0.05 0.01 (500K,700K,100K) 0.01 (200K,300K for -0.05≤ξ≤0.90 ) dξ 0.005 (200K,300K for 0.90＜ξ≤1.06 ) ξN 1.06 dt 0.0001 ki 2.727 (T/K) eV (200 K, 300 K, 500 K, 700 K for -0.05≤ξ≤0.9, and all windows at 1000 K) 5.454 (T/K) eV (500 K and 700 K for 0.90＜ ξ≤1.06 ) 10.908 (T/K) eV (300 K for 0.90＜ξ≤1.06 ) 13.635 (T/K) eV (200 K for 0.90＜ξ≤1.06 ) Ntrajectory 150 tequilibration 20 tsampling 100 Ni 1.5×108 Potential of mean force calculation ξ0 -0.02 ξ≠ 1.05 Nbins 5000 Recrossing factor calculation dt 0.0001 tequilibration

20

Ntotalchild

100000

tchildsampling

2

Nchild

100

tchild

0.05

Temperature Number of beads Dividing surface s1 parameter (a0 ) Number of forming and breaking bonds Number of equivalent product channels Thermostat option Number of windows Center of the first window Window spacing step Center of the last window Time step (ps )

Umbrella force constant (a.u.)

Number of trajectories Equilibration period (ps) Sampling period in each trajectory (ps) Total number of sampling points Start of umbrella integration End of umbrella integration Number of bins Time step (ps) Equilibration period (ps) in the constrained (parent) trajectory Total number of unconstrained (child) trajectories Sampling increment along the parent trajectory (ps) Number of child trajectories per one initially constrained configuration Length of child trajectories (ps)

20


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Table 2. Summary of RPMD results for the title reactions using PIP-NN PES. ξ‡ and ∆G(ξ‡) (in kcal/mol) are the peak position and barrier height of the PMF curve along the reaction coordinate ξ. κ is the plateau value of the transmission coefficient. kQTST and kRPMD are the centroid density QTST rate coefficients and the corresponding RPMD rate coefficients, respectively. All the rate coefficients are in the unit cm3·s-1.

T/K

200

300

500

700

1000

n

64

64

16

16

8

ξ‡

0.986

0.993

0.999

1.001

1.003

∆G(ξ‡)

3.52

5.38

8.36

10.97

14.61

kQTST

6.93×10-13

7.32×10-13

1.69×10-12

3.38×10-12

6.88×10-12

κ

0.400

0.542

0.567

0.578

0.597

kRPMD

4.08×10-13

5.28×10-13

1.15×10-12

2.23×10-12

4.53×10-12

CVT/µOMT a

4.14×10-14

1.22×10-13

4.84×10-13

1.13×10-12

2.70×10-12

CVT/CD-SCSAG/DLb

6.46×10-13

7.26×10-13

1.09×10-12

1.57×10-12

2.46×10-12

2D quantum b

5.60×10-13

--

1.01×10-12

--

--

MCTDH b

5.60×10-12

3.30×10-12

2.00×10-12

1.50×10-12

--

expt.1c

--

--

1.33×10-12

--

--

expt.3 c

--

6.7×10-13

--

1.46×10-12

--

expt.5 c

5.78×10-13

--

--

--

--

expt.6 c

--

--

--

1.97×10-12

--

a

The CVT/µOMT rate coefficients based on PIP-NN PES. Theoretical data of CVT/CD-SCSAG/DL, 2D quantum and MCTDH were taken from refs. 26, 11 and 13, respectively. c Experimental data of expt.1, expt.3, expt.5 and expt.6 were taken from refs. 5, 4, 8 and 9, respectively. b

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Figure 1. Reaction path for the title reaction. The geometries of the stationary points are also given. The unit is in kcal/mol.

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Figure 2. Comparison of potentials of mean force (PMFs) for the HCl + OH reaction at 300 K with different numbers of beads.

23



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Figure 3. Temperature dependence of the PMF for the HCl + OH reaction.

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Figure 4. Time dependence of the transmission coefficient for the HCl + OH reaction at different temperatures.

25



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Figure 5. Comparison rate coefficients for the HCl + OH → Cl + H2O reaction. The theoretical results include RPMD (this work), CVT/µOMT PIP-NN PES (this work), CVT/CD-SCSAG/DL,26 2D quantum on the YN PES,11 ab initio master equation (ai ME).27 Experimental data are taken from Ravishankara et al. (Expt. 1),5 Molina et al. (Expt. 2),3 Husain et al. (Expt. 3),4 Sharkey et al. (Expt. 4),7 Battin-Leckerc et al. (Expt. 5),8 and Bryukov et al. (Expt. 6).9

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TOC:

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Figure 1 592x297mm (96 x 96 DPI)


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fig2 207x164mm (96 x 96 DPI)



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fig3 219x161mm (96 x 96 DPI)


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fig4 218x156mm (100 x 100 DPI)



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Figure 5 85x84mm (300 x 300 DPI)


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TOC 85x47mm (300 x 300 DPI)


Rate Coefficients of the HCl + OH â Cl + H2O Reaction from Ring

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Rate Coefficients of the HCl + OH â Cl + H2O Reaction from Ring