Quantum Rate Coefficients and Kinetic Isotope Effect for the Reaction

Article pubs.acs.org/JPCA

Quantum Rate Coefficients and Kinetic Isotope Effect for the Reaction Cl + CH4 → HCl + CH3 from Ring Polymer Molecular Dynamics Yongle Li,† Yury V. Suleimanov,*,‡,§ William H. Green,‡ and Hua Guo*,† †

Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States § Department of Mechanical and Aerospace Engineering, Combustion Energy Frontier Research Center, Princeton University, Olden Street, Princeton, New Jersey 08544, United States ‡

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

I. INTRODUCTION The reaction between chlorine atom and methane is of great importance in atmospheric chemistry.1−3 Many kinetic measurements have been reported,4−15 and the rate coefficients near room temperature have been critically evaluated.16,17 A particularly interesting issue is the fractionation of methane isotopomers in the atmosphere, which yields unique isotopic signatures.18,19 These kinetic isotope effects (KIEs) stem from isotopic-dependent reaction rates, which are quite significant for the title reaction due to its tunneling nature, particularly at low temperatures. This reaction is one of prototypical polyatomic bimolecular reactions.20−23 Because of the strong tunneling and recrossing dynamics,24 this heavy−light−heavy reaction presents a challenge to transition-state theory.25−29 In addition, it has served as a testing ground for mode specificity and bond selectivity in bimolecular reactions.30−34 As the reaction involves the transfer of a hydrogen atom, its dynamics and kinetics need be treated quantum mechanically to accurately account for quantum effects, such as tunneling and zero-point energy (ZPE). However, accurate full-dimensional quantum scattering calculations remain a formidable challenge because it requires twelve coordinates.35 So far, all quantum dynamical calculations on this reaction have been based on reduceddimensional models.36−41 Fortunately, the accurate determination of the rate coefficients does not necessarily need all the state-to-state attributes because reactivity is essentially controlled by the transition state.42 In this work, we compute the canonical rate coefficients for the title reactions using the © 2014 American Chemical Society

recently proposed ring polymer molecular dynamics (RPMD) method,43 which can be considered as an approximate quantum mechanical approach with full dimensionality. RPMD differs from the traditional transition-state theory methods, which are based on various static approximations to the real-time correlation functions used to describe chemical reactions, in its explicit, though approximate, consideration of the real-time dynamics.43 This feature can be particularly important for systems similar to the title reaction, which is affected not only by tunneling but also by strong recrossing of the transition state, thanks to the chattering motion of the transferring hydrogen between two heavy atoms. Hence, the present work can be considered as an important step in a series of benchmark studies aimed at assessing the accuracy of RPMD for various complex polyatomic systems. This publication is organized as follows. The RPMD theory and computational details are outlined in section II. The results are presented and discussed in section III, and conclusions are given in section IV.

II. THEORY The ring polymer molecular dynamics (RPMD) method43 exploits the isomorphism between the statistical properties of a quantum system and those of a fictitious classical ring polymer made up of harmonically connected beads.44 Its adaptation to the calculation of rate coefficients for chemical reactions has Received: December 1, 2013 Revised: February 21, 2014 Published: February 24, 2014 1989

dx.doi.org/10.1021/jp501043z | J. Phys. Chem. A 2014, 118, 1989−1996

The Journal of Physical Chemistry A

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Table 1. Results from RPMD Calculations of the Rate Coefficients (cm3 molecule−1 s−1) for the Cl + CH4 Reaction on the RNCE and CB PESs and Comparison with Other Theoretical and Experimental Results 300a Nbeads ξ⧧ ΔG(ξ⧧)/kcal·mol−1 kQTST κ kRPMD CUS/μOMT65 CVT/μOMT Nbeads ξ⧧ ΔG(ξ⧧)/ kcal·mol−1 kQTST κ kRPMD CUS/μOMT CVT/μOMT expt9 expt16 expt17 a

400a

64 0.996 5.40 4.02 × 10−13 0.235 9.43 × 10−14 9.9 × 10−14 1.19 × 10−13

−14

4.05 × 10 6.09 × 10−14 1.00 × 10−13 1.00 × 10−13

600a

800a

RNCE PES 32 0.988 7.98 5.66 × 10−12 0.390 2.21 × 10−12 1.6 × 10−12 1.81 × 10−12 CB PES 32 0.995 8.97 2.18 × 10−12 0.531 1.15 × 10−12 −13 1.80 × 10 1.09 × 10−12 2.68 × 10−13 1.64 × 10−12 −13 (3.0 ± 0.2) × 10 (1.26 ± 0.09) × 10−12

32 0.985 5.74 1.30 × 10−12 0.308 4.02 × 10−13 3.4 × 10−13 4.06 × 10−13

16 0.978 8.09 1.46 × 10−11 0.417 6.06 × 10−12 4.1 × 10−12 4.67 × 10−12

−12

3.33 × 10 5.15 × 10−12 (3.0 ± 0.2) × 10−12

1000a 8 0.977 8.58 2.87 × 10−11 0.429 1.23 × 10−11 8.3 × 10−12 9.27 × 10−12 8 0.993 11.38 1.31 × 0.535 7.03 × 7.28 × 1.17 ×

10−11 10−12 10−12 10−11

3.00 × 10−13

T/K.

where μR is the reduced mass between the two reactants, β = (kBT)−1, and W(ξ⧧) − W(0) is the free-energy difference which is obtained via umbrella integration along the reaction coordinate.62,67,68 The dynamical correction is provided by the second factor (κ(t→∞;ξ⧧)) in eq 1, which is the long-time limit of a timedependent ring-polymer transmission coefficient, accounting for recrossings 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.47,68 An added advantage of the RPMD rate theory is that it approaches the classical limit when only one bead is used. In this limit, the static and dynamical components of eq 1 become identical to the classical transition-state theory rate coefficient and the classical transmission coefficient, respectively.50 These quantities thus establish the limit to which the quantum effects such as ZPE and tunneling can be evaluated by using more beads. The minimal number of beads needed to account for the quantum effects can be estimated by the following formula:69

been shown to have several desirable features.45−47 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. More recently, it was shown to be equivalent to the quantum transition-state theory in the limit of no recrossing.48,49 Furthermore, the RPMD rate coefficient is independent of the choice of the dividing surface, a property highly desirable because the dividing surface is difficult to define for highdimensional systems. RPMD is accurate even in the deep tunneling regime due to a connection to semiclassical instanton theory.48 Finally, it is numerically efficient because of the favorable scaling laws associated with classical trajectories. The RPMD approach has been successfully employed to obtain accurate rate coefficients for several bimolecular reactions, in which comparison with full-dimensional quantum dynamical calculations indicated that RPMD reliably captures quantum effects such as zero-point energy and tunneling.50−59 Taking advantage of the Bennett−Chandler factorization,60,61 the RPMD rate coefficient can be conveniently presented in the following form:50,51,62 kRPMD = k QTST(T ; ξ ⧧)κ(t →∞;ξ ⧧)

nmin ≡ β ℏωmax

(1)

where ωmax is the largest vibrational frequency of the system. All calculations reported here used RPMDrate developed by Suleimanov and co-workers and the remaining details of the computational procedure can be found in the RPMDrate manual.62 The calculations were first performed with one bead, which provides the classical limit. The number of beads was then increased until convergence. Two full-dimensional analytical PESs were used in our RPMD calculations in the range of 300−1000 K. The first was an empirical PES calibrated to limited ab initio data by Espinosa-Garcia and co-workers (RNCE).70 This PES was chosen because it has been used for many previous theoretical studies,70 including rate coefficient calculations using the canonical unified statistical model with the microcanonical optimized multidimensional tunneling

The first term denotes the static contribution, while the second is the dynamical correction. In particular, kQTST (T;ξ⧧) is the centroid-density quantum transition-state theory (QTST63−65) rate coefficient,47,66 evaluated at the top of the free-energy barrier, ξ⧧, along the reaction coordinate ξ(q). This quantity depends on the position of the dividing surface and is determined entirely by static equilibrium properties. In practice, it is calculated from the centroid potential of mean force (PMF):50,51,62 ⎛ 1 ⎞1/2 ⧧ ⎟⎟ e−β[W (ξ ) − W (0)] k QTST(T , ξ ⧧) = 4πR ∞2⎜⎜ ⎝ 2πβμR ⎠

(3)

(2) 1990



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Table 2. Results from RPMD Calculations of the Rate Coefficients (cm3 molecule−1 s−1) for the Cl + CD4 Reaction on the RNCE and CB PESs and Comparison with Other Theoretical and Experimental Results 300a Nbeads ξ⧧ ΔG(ξ⧧)/kcal·mol−1 kQTST κ kRPMD CUS/μOMT CVT/μOMT Nbeads ξ⧧ ΔG(ξ⧧)/kcal·mol−1 kQTST κ kRPMD CUS/μOMT CVT/μOMT expt12 (298 K) expt8 (298 K) expt10 (298 K) a

32 0.991 6.53 2.29 × 0.483 1.11 × 8.84 × 1.09 ×

5.87 × 6.82 × (5.4 ± (6.1 ± (8.2 ±

10−14 10−14 10−15 10−14

−15

10 10−15 0.4) × 10−15 0.4) × 10−15 0.4) × 10−15

400a

600a

RNCE PES 32 0.987 7.29 1.55 × 10−13 0.520 8.06 × 10−14 6.67 × 10−14 7.53 × 10−14 CB PES

−14

4.78 × 10 5.74 × 10−14

32 0.983 8.44 1.45 × 0.557 8.06 × 6.67 × 6.78 × 32 0.995 10.47 6.23 × 0.645 4.01 × 5.37 × 6.90 ×

800a

10−12 10−13 10−13 10−13

16 0.980 9.27 5.40 × 0.557 3.00 × 2.41 × 2.44 ×

1000a

10−12 10−12 10−12 10−12

10−13 10−13 10−13 10−13

−12

2.14 × 10 2.97 × 10−12

8 0.978 9.94 1.34 × 0.569 7.63 × 5.53 × 5.92 × 8 0.993 12.82 6.95 × 0.607 4.22 × 5.35 × 7.92 ×

10−11 10−12 10−12 10−12

10−12 10−12 10−12 10−12

T/K.

correction (CUS/μOMT).25,71 The other is the more recent PES developed by Czako and Bowman (CB) based on a large number of high-level ab initio points.72 The evaluation of the latter is much slower. As a result, we have computed the rate coefficients at only two temperatures (600 and 1000 K). In the calculation of the PMF, windows with an equal size (Δξ = 0.01) were used with the force constant of the biasing potential of k = 2.72 (T/K) eV. In each sampling window, the system was first equilibrated for 20 ps, following by a production run (20 and 5 ns on RNCE PES and CB PES, respectively). The Andersen thermostat73 was used in all simulations. The time step is 0.1 and 0.5 fs on RNCE and CB PESs, respectively. Due to the larger time step and shorter simulation time, the results on the CB PES are expected to be less accurate. However, tests on the RNCE PES using the same parameters indicated that the uncertainty is within 5%. After the PMF calculations, the transmission coefficients were computed. This was initiated by running a long (20 ns) mother trajectory with the ring-polymer centroid fixed at the top of the free energy barrier via the SHAKE algorithm.74 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 0.1 ps where the transmission coefficients reach plateau values. The time step in this stage was set to 0.1 fs for both PESs. The final RPMD rate coefficients were corrected with an electronic partition function ratio of the following form: TS Q elec reactants Q elec

=

1 2 + exp( −β ΔE)

III. RESULTS AND DISCUSSION The RPMD rate coefficients for the Cl + CH4 reaction obtained on the RNCE and CB PESs are listed in Table 1, and those for the Cl + CD4 reaction are given in Table 2. It is clear from these tables that the hydrogen/deuterium abstraction reactions are characterized by strong recrossing, as evidenced by much smaller RPMD transmission coefficients than those in the H/O + CH4 reactions.53,55 The word recrossing, which is a wellknown feature of heavy−light−heavy reactions,24 is used here loosely as it includes not only classical recrossing over the barrier but also quantum mechanical tunneling. Indeed, the RPMD transmission coefficients are larger for the Cl + CD4 reaction, reflecting the less facile tunneling of the heavier deuterium atom. In both cases, the transmission coefficients generally increase with temperature, as seen in the previous RPMD studies.50,51,55,56 In Figure 1, the time dependence of the computed transmission coefficients is shown for both the Cl + CH4 and Cl + CD4 reactions on the RNCE PES. It is clear that they experience a fast initial drop apparently due to recrossing near the barrier. This is followed by some oscillations, particularly at low temperatures. Such oscillatory behaviors, which have been observed in the previous RPMD studies,52,54,55,68 might not be physically relevant as they depend on the definition of the dividing surface. The time required for converging the correlation functions for these two reactions (∼0.1 ps at 300 K) is significantly longer than that required for the H + CH4 reaction,55 in which the transmission coefficients take only 30 fs to reach plateau values. The RPMD rate coefficients for the Cl + CH4 reaction are compared in the upper panel of Figure 2 with the previous CUS/μOMT results on the RNCE PES.70 In addition, the rate coefficients obtained with the CVT/μOMT (CVT for canonical variational transition-state theory) method are also included in comparison. These TST results were generated with POLYRATE using curvilinear coordinates and the harmonic

(4)

in order to take into account the spin−orbit splitting of Cl(2P1/2,3/2) (ΔE = 882 cm−1).26 1991



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reasonably good agreement with TST results in our previous work on H/O + CH4 reactions.53,55 Several considerations should be taken into account when trying to find possible explanations for this departure from expectation. First, RPMD is known to overestimate the rate constant for asymmetric reactions.50 However, this is expected to happen at low temperatures in the so-called deep-tunneling regime.50 At high temperatures, such as 1000 K, tunneling should play a less important role than the ZPE effect for the current system because the crossover temperature is 178 K. At high temperatures, RPMD is expected to be very reliable and close to the exact quantum mechanical result and to converge to it in the high-temperature limit (where quantum and classical results coincide).50,51 Second, the quantum mechanical interference effects in the real time dynamics such as quantum reactive scattering resonances tend to be more pronounced for reactions with a small skew angle, such as the Cl + CH4 reaction. However, these effects are not included in any of the computations shown here, and, in the absence of the exact QM results, it is difficult to elucidate their role in the thermal rate coefficients. Third, the TST results might underestimate the rate coefficient at high temperatures due to the harmonic approximation employed. We have carried out a purely classical calculation at 1000 K by using RPMDrate code and RNCE PES with the same calculation parameters but with one ring polymer bead, which ignores all quantum effects. The classical rate coefficient corrected for the recrossing dynamics calculated by using RPMDrate is 5.52 × 10−12 s−1 molecule−1 cm3, which is about half of the RPMD rate coefficient (1.23 × 10−11 s−1 molecule−1 cm3). The difference between these two calculations shows that quantum effects are important for this reaction and their improper treatment could lead to a noticeable error in the rate coefficient even at 1000 K. Indeed, the RPMD rate coefficients for the Mu + CH4 reaction were much larger than the CVT/μOMT counterparts, presumably due to the harmonic approximation in the latter, while the corresponding agreement for the H/D + CH4 reactions is quite good.55 Apparently, further investigations are required in order to elucidate the underlying reason for the discrepancy. Rigorous quantum mechanical calculations, which should become possible in the near future, will be of invaluable help in solving this puzzle. In the lower panel of Figure 2, the RPMD rate coefficients obtained on the ab initio based CB PES are compared with results obtained by the two versions of TST. It is interesting to note that although the CUS/μOMT and CVT/μOMT results are quite similar on the RNCE PES, the difference is much larger on the CB PES. More importantly, the RPMD values are very close to CUS/μOMT ones, but are smaller than the CVT/ μOMT counterparts. This behavior is in line with our initial expectations. However, we note again that only rigorous quantum mechanical calculations can confirm or refute our speculations. As shown in Table 1, RPMD rate coefficients obtained on the CB PES are somewhat lower than those on the RNCE PES, reflecting the higher free-energy barrier in the ab initio PES (vide infra). The transition state on the RNCE PES has much lower vibrational frequencies than those of the CB PES, and the underestimated frequencies lead to a lower RPMD free-energy barrier, as shown in Figure 3, and thus larger rate coefficients. In both panels of Figure 2, the calculated rate coefficients are compared with representative experimental results. The overall agreement of these theoretical results with experimental data is

Figure 1. Time dependence of transmission coefficients for the Cl + CH4 (upper panel) and Cl + CD4 (lower panel) reactions at different temperatures.

Figure 2. Comparison of rate coefficients for the Cl + CH4 reaction obtained with RPMD and TST methods on the RNCE (upper panel) and CB PESs (lower panel). For comparison experimental values5,9,14,16,17 are also included in both panels.

approximation for the vibrational partition functions,75 and the CUS/μOMT results of Rangel et al.70 on the RNCE PES were reproduced. Interestingly, the CUS/μOMT and CVT/μOMT results are very close at high temperatures (10% deviation at 1000 K). The RPMD rate coefficients are somewhat larger than the CUS/μOMT and CVT/μOMT counterparts, except at low temperatures, and the difference increases with temperature. This is unusual as the RPMD rate coefficients were in 1992



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are higher than those on the CB PES. The overall agreement with experimental rate coefficients,10,12,15 all near 300 K, is very reasonable, given the differences among the experimental results. The KIEs are displayed in Figure 5 for the CH4 and CD4 isotopomers. The experimental values were those of Chiltz et

Figure 3. Comparison of the potentials of mean force (PMFs) for the Cl + CH4 reaction at 600 K obtained with RPMD on two PESs.

reasonably good, given the fact that the experimental results5,9,14,16,17 are quite scattered. We note that the RPMD results on the CB PES are quite close to the experimental data of Pilgrim et al.9 The comparison for the Cl + CD4 reaction is displayed in Figure 4 in the same fashion as Figure 2. Similar to the Cl + CH4 case, the RPMD rate coefficients are slightly larger than the CUS/μOMT and CVT/μOMT counterparts on the RNCE PES, but lower on the CB PES. In the latter case, the RPMD rate coefficients are closer to the CUS/μOMT values, as expected. Also, the RPMD rate coefficients on the RNCE PES

Figure 5. Comparison between calculated KIEs (kH/kD) and measured ones.4,5,8,10,12,15

al.,4 Clyne et al.,5 Wallington et al.,8 Matsumi et al.,10 Boone et al.,12 and Feilberg et al.15 For comparison, three other theoretical results, CUS/μOMT on the CB PES, CUS/ μOMT on the RNCE PES,70 and SCTST based on ab initio calculations,29 are also added. It is clear from Figure 5 that the experimental values differ considerably, even between the two newest ones. The SCTST results at 298 K are near the high end of the experimental data range, essentially following the experimental values from Clyne et al.5 On the other hand, the CUS/μOMT KIEs on RNCE PES are close to the lower end of the experimental data. The CUS/μOMT numbers on the CB PES are much lower than the experimental values. It is interesting that the calculated RPMD KIEs are in reasonable agreement at the two temperatures where the calculations were performed for both PESs employed in the present work, and both are in the middle of the experimental range.

IV. CONCLUSIONS In this work, we employed a recently developed fulldimensional approximate quantum mechanical method, ring polymer molecular dynamics (RPMD), to calculate the rate coefficients and KIEs for the hydrogen/deuterium abstraction reactions of CH4/CD4 by the chlorine atom on two different potential energy surfaces (PESs). It is shown that these heavy− light−heavy reactions are strongly influenced by recrossing and quantum mechanical effects such as zero point energy and tunneling. A discrepancy has been found between RPMD and tunneling corrected variational transition-state theory (TST) rate coefficients at high temperatures. Depending on the underlying PES, RPMD rate coefficients can be higher or lower than the TST counterparts. In the absence of accurate quantum mechanical results for the title system, it is rather difficult to elucidate the reason for the observed discrepancy and to compare accuracy of RPMD and TST approaches. Nevertheless, the overall agreement of RPMD and TST rate

Figure 4. Comparison of rate coefficients for the Cl + CD4 reaction obtained with RPMD, TST, and QCT methods on the RNCE (upper panel) and CB PESs (lower panel). For comparison, experimental counterparts10,12,15 are also included in both panels. 1993



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(11) Wang, J. J.; Keyser, L. F. Kinetics of the Cl(2Pj)+CH4 Reaction: Effects of Secondary Chemistry Below 300 K. J. Phys. Chem. A 1999, 103, 7460−7469. (12) Boone, G. D.; Agyin, F.; Robichaud, D. J.; Tao, F.-M.; Hewitt, S. A. Rate Constants for the Reactions of Chlorine Atoms with Deuterated Methanes: Experiment and Theory. J. Phys. Chem. A 2000, 105, 1456−1464. (13) Takahashi, K.; Yamamoto, O.; Inomata, T. Direct Measurements of the Rate Coefficients for the Reactions of Some Hydrocarbons with Chlorine Atoms at High Temperatures. Proc. Combust. Inst. 2002, 29, 2447−2453. (14) Bryukov, M. G.; Slagle, I. R.; Knyazev, V. D. Kinetics of Reactions of Cl Atoms with Methane and Chlorinated Methanes. J. Phys. Chem. A 2002, 106, 10532−10542. (15) Feilberg, K. L.; Griffith, D. W. T.; Johnson, M. S.; Nielsen, C. J. The 13C and D Kinetic Isotope Effects in the Reaction of CH4 with Cl. Int. J. Chem. Kinet. 2005, 37, 110−118. (16) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Crowley, J. N.; Hampson, R. F.; Hynes, R. G.; Jenkin, M. E.; Rossi, M. J.; Troe, J. Evaluated Kinetic and Photochemical Data for Atmospheric Chemistry: Volume II; Gas Phase Reactions of Organic Species. Atmos. Chem. Phys. 2006, 6, 3625−4055. (17) Sander, S. P.; Abbatt, J.; Barker, J. R.; Burkholder, J. B.; Friedl, R. R.; Golden, D. M.; Huie, R. E.; Kolb, C. E.; Kurylo, M. J.; Moortgat, G. K.; et al. Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies, Evaluation No. 17; JPL Publication 10-6;Jet Propulsion Laboratory: Pasadena, 2011. (18) McCarthy, M. C.; Boering, K. A.; Rice, A. L.; Tyler, S. C.; Connell, P.; Atlas, E. Carbon and Hydrogen Isotopic Compositions of Stratospheric Methane: 2. Two-Dimensional Model Results and Implications for Kinetic Isotope Effects. J. Geophys. Res.: Atmos. 2003, 108, 4461. (19) Röckmann, T.; Brass, M.; Borchers, R.; Engel, A. The Isotopic Composition of Methane in the Stratosphere: High-Altitude Balloon Sample Measurements. Atmos. Chem. Phys. Discuss. 2011, 11, 13287− 13304. (20) Michelsen, H. A.; Simpson, W. R. Relating State-Dependent Cross Sections to Non-Arrhenius Behavior for the Cl+CH4 Reaction. J. Phys. Chem. A 2001, 105, 1476−1488. (21) Liu, K. Crossed-Beam Studies of Neutral Reactions: StateSpecific Differential Cross Sections. Annu. Rev. Phys. Chem. 2001, 52, 139−164. (22) Althorpe, S. C.; Clary, D. C. Quantum Scattering Calculations on Chemical Reactions. Annu. Rev. Phys. Chem. 2003, 54, 493−529. (23) Murray, C.; Orr-Ewing, A. J. The Dynamics of Chlorine-Atom Reactions with Polyatomic Organic Molecules. Int. Rev. Phys. Chem. 2004, 23, 435−482. (24) Skodje, R. T. The Adiabatic Theory of Heavy-Light-Heavy Chemical Reactions. Annu. Rev. Phys. Chem. 1993, 44, 145−172. (25) Truhlar, D. G.; Issacson, A. D.; Garrett, B. C., Generalized Transition State Theory. In Theory of Chemical Reaction Dynamics; Bear, M., Ed.; CRC: Boca Raton, 1985; pp 65−137. (26) Duncan, W. T.; Truong, T. N. Thermal and Vibrational-State Selected Rates of the CH4 + Cl ↔ HCl + CH3 Reaction. J. Chem. Phys. 1995, 103, 9642−9652. (27) Espinosa-García, J.; Corchado, J. C. Analytical Potential Energy Surface for the CH4+Cl → CH3+ClH Reaction: Application of the Variational Transition State Theory and Analysis of the Kinetic Isotope Effects. J. Chem. Phys. 1996, 105, 3517−3523. (28) Corchado, J. C.; Truhlar, D. G.; Espinosa-García, J. Potential Energy Surface, Thermal, and State-Selected Rate Coefficients, and Kinetic Isotope Effects for Cl + CH4 → HCl + CH3. J. Chem. Phys. 2000, 112, 9375−9389. (29) 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.

coefficients with measured rate coefficients and KIEs is reasonably good, although the experimental results are quite scattered. These results suggest that RPMD provides a reliable alternative to TST for the present system. Further investigations, including rigorous quantum mechanical calculations of the rate coefficients as well as RPMD calculations for other complex reactive systems, are required for further assessing the accuracy of this novel approach.

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AUTHOR INFORMATION

Corresponding Authors

*Y.V.S.: e-mail, [email protected]. *H.G.: e-mail, [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Y.L., H.G., and W.H.G. were supported by the Department of Energy (DE-FG02-05ER15694 to H.G. and DE-FG0298ER14914 to W.H.G.). Y.V.S. acknowledges the support of a Combustion Energy Research Fellowship through the Combustion Energy Frontier Research Center, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Basic Energy Sciences under Award Number DE-SC0001198. H.G. thanks Gabor Czakó and Joel Bowman for sending us their PES.

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REFERENCES

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Quantum Rate Coefficients and Kinetic Isotope Effect for the Reaction

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