An accurate potential energy surface and ring polymer molecular dynamics study of the Cl + CH₄ → HCl + CH₃ reaction

Abstract

The reaction Cl + CH₄ → HCl + CH₃, a prototypical bimolecular reaction, has been established as an important proving ground for studying chemical reaction kinetics and dynamics of polyatomic molecules. In this work, a globally accurate full-dimensional potential energy surface (PES) for this reaction is developed by using the permutationally invariant polynomial neural network (PIP-NN) approach based on 74 000 points calculated at the level of the explicitly correlated unrestricted coupled cluster single, double, and perturbative triple level with the augmented correlation corrected valence triple-zeta basis set (UCCSD(T)-F12a/AVTZ). For points in the entrance channel, spin–orbit corrections stemming from Cl(²P) are determined at the level of complete active space self-consistent field (CASSCF) with the AVTZ basis set. With this PES, thermal rate coefficients and kinetic isotope effects are computed for reactions Cl + CH₄ → HCl + CH₃ and Cl + CD₄ → DCl + CD₃ using the ring polymer molecular dynamics (RPMD) method, which can provide reliable estimations for thermal rate coefficients effectively. Generally, the agreement with the scattered experimental results is reasonably satisfactory.

---

I. Introduction

Due to its significance in atmospheric chemistry,^1–4 extensive theoretical^5–28 and experimental^29–74 investigations have been reported for the reaction, Cl + CH₄ → HCl + CH₃, and its isotopic analogues. This reaction is a prototypical bimolecular reaction and has been established as a benchmark system for studying chemical reaction kinetics and dynamics of polyatomic molecules,^4,75 in particular, on the state-to-state and thermal rate coefficients, kinetic isotope effects (KIEs), mode-specific and bond-selective chemistry, stereodynamics, non-adiabaticity effects, and scattering resonances, etc.

Theoretically, due to the chattering motion of the transfer of a light hydrogen atom between two heavy atoms (chlorine and carbon atoms), the title reaction is expected to be affected strongly by quantum tunneling and recrossing, thus presenting a challenge to transition-state theory.^7,8,10,21 Therefore, its kinetics and dynamics need be treated quantum mechanically for accurate description of quantum effects, such as tunneling, recrossing and zero-point vibrational energy (ZPVE). However, for the title reaction system with six atoms, it is still impractical to perform exactly full-dimensional (12D) quantum scattering calculations. So far, all quantum mechanical computations on this reaction were based on reduced-dimensional models,^{9,12,19,25,76–78} by using several different potential energy surfaces (PESs), which play a key role in the reactive kinetics and dynamics. Indeed, an inaccurate PES is not expected to yield reliable results no matter how accurate the kinetics or dynamical method might be.⁷⁹ For the title system, Espinosa-Garcia and Corchado and co-workers have developed several semi-empirical full-dimensional PESs with relatively simpler function forms based on ab initio results for the stationary points and some experimental measurements.^8,10,14 The most recent PES from them, denoted as the RNCE PES hereafter, can reproduce the available experimental kinetics effectively.¹⁴ Using the Shepard interpolation, Castillo et al. developed a full-dimensional PES for the title system based on QCISD(T)/AVDZ calculations and scaling-all-correlation level of theory.⁸⁰ In 2011, Czako and Bowman fitted a high-quality, full-dimensional global PES (denoted as CB PES hereafter) to a permutationally invariant polynomial (PIP) function form⁸¹ based on ca. 16 000 ab initio energy points calculated by an efficient composite method, which can provide accuracy almost equivalent to all-electron CCSD(T)/aug-cc-pCVQZ.^18,20 In the CB PES, spin–orbit (SO) corrections were also considered for 1600 points in the entrance channel at the level of multi-reference configuration interaction (MRCI) with Davison correction (+Q) and the augmented correlation corrected valence triple-zeta (AVTZ) basis set.²⁰

In this work, we report a new full-dimensional PES for the title reaction developed by using the PIP-neural network (PIP-NN) method,^82–84 which has been employed successfully to fit PESs for polyatomic reaction systems, such as OH + H₂O,⁸⁵ OH + HO₂ → H₂O + O₂,⁸⁶ H/OH + CH₄ → H₂/H₂O + CH₃^87–89 and F + CH₃OH → HF + CH₃O/CH₂OH⁹⁰ with high fidelity. About 74 000 points were sampled and calculated at the explicitly correlated unrestricted coupled cluster single, double, and perturbative triple level with the augmented correlation corrected valence triple-zeta basis set (UCCSD(T)-F12a/AVTZ).^91,92 In order for the correct description of the entrance channel within the adiabatic framework, the SO correction was calculated at the state-averaged level of complete active space self-consistent field (CASSCF) with the AVTZ basis set. Indeed, this PES has been already used to construct vibrationally and SO coupled diabatic potentials for the title reaction using an ansatz scheme by Manthe and co-workers very recently.²⁸ Using this newly fitted PES, thermal rate coefficients for reactions Cl + CH₄/CD₄ → HCl/DCl + CH₃/CD₃ are then computed with the ring polymer molecular dynamics (RPMD) method,⁹³ an approximate quantum mechanical approach with full dimensionality. It has been shown that the RPMD approach can efficiently provide accurate rate coefficients for several bimolecular reactions with reliable quantum effects such as ZPVE and tunneling.^22,94–115 The remaining of the publication is organized as follows. The next section (Section II) details the ab initio calculations, the PES fitting, and RPMD theory briefly. Section III presents and discusses the results. A summary and conclusions are given in Section IV.

II. Theory

II.A Ab initio calculations

In this work, all electronic calculations were performed using MOLPRO.¹¹⁶ The geometries, energies, and harmonic frequencies of all stationary points, including the reactants, products, intermediates, and transition states, were obtained at the UCCSD(T)-F12a/AVXZ (X = D, T) levels,¹¹⁷ which have been recommended for developing reliable PESs since it can efficiently provide results of accuracy similar to those obtained at the UCCSD(T)/AV5Z level.^117,118

In the entrance channel, the ground state of the Cl(²P) atom splits by 881 cm⁻¹ into the four-fold degenerate ground Cl(²P_3/2) and twofold degenerate excited Cl*(²P_1/2) SO states. The SO ground state Cl(²P_3/2) lies 294 cm⁻¹ below the non-relativistic (spin-averaged) ground state of Cl(²P), while the SO excited state Cl*(²P_1/2), 587 cm⁻¹ above, has been found to play a negligible role in the reaction with CH₄.^40,46 Thus, only the SO ground state was considered in this work by adding the SO correction, which can be obtained effectively in the adiabatic representation, to the ground electronic state of the title reaction system under the adiabatic framework. This strategy is similar to the CB PES for the same reaction,^18,20 the PES for the F + CH₄ reaction,¹¹⁹ and to our previous work for the F + H₂O reaction.¹²⁰ In particular, the SO coupling matrix elements were determined using the Breit–Pauli Hamiltonian with the unperturbed CASSCF wavefunctions.¹²¹ The SO energies were then obtained by diagonalizing the combined matrix of the electronic and SO Hamiltonians, and the SO corrections taken as the difference between the SO energies and their corresponding non-relativistic counterparts. As a compromise between efficiency and computational costs, the SO corrections in the entrance channel were calculated at the state-averaged CASSCF level with the AVTZ basis set using an active space consisting of all valence electrons, namely, (15e, 12o). The 1s, 2s, 2p orbitals of the Cl atom and the 1s orbital of the C atom were kept doubly occupied.

II.B PIP-NN fitting

Developing PESs consists of three procedures: sampling data points in the dynamically relevant configuration space, calculating their energies by the ab initio method, and fitting them to a specific function. Following our previous strategy,^87,88,90 possible reaction channels were firstly surveyed to determine the ranges of the energy and configuration space. For the Cl + CH₄ reaction, two reaction channels, namely the hydrogen abstraction and substitution pathways, were considered with the focus on the former with a barrier height of only ca. 7 kcal mol⁻¹, since the barrier height of the latter is about 35 kcal mol⁻¹ higher than the former, making it only available at very high temperatures or energies.^18,20 Then we started to sample the configuration space along the two reaction pathways with other coordinates fixed at the corresponding transition states. In this way, the main feature of the PES was captured. Further for the reactant and product asymptotes, the internal coordinates were sampled in dense grids while the intramolecular coordinates were sampled with relatively sparse grids. In order to avoid sampling points of unreasonably high energy, direct dynamical calculations were also carried out at a low level of theory, e.g., B3LYP/6-31+G(d), starting from different initial conditions.

Ab initio calculations were then performed at the level of UCCSD(T)-F12a/AVTZ for the initial set of data points, and a primitive PES can be fit. To further explore regions that are not described well due to lacking points, trajectory calculations with various initial conditions were performed on this PES. In order for efficient sampling, only those points that are not close to the existing data set will be added to improve these regions. In this work, the judgement is with the generalized Euclidean distance, χ, defined in terms of the internuclear distances between a new point {r_i} and a data point {r_i′} in the existing data set. Note that all permutationally equivalent points, namely, those configurations generated by permutations with respect to all four identical hydrogen atoms (4! = 24), were included in such screenings. The PES was also examined by checking the properties of stationary points, such as geometries, energies, and harmonic frequencies, as well as the minimum energy paths. With new points added, the PES was improved gradually. After several iterations, the outcome on the PES was converged. Finally, for points in the entrance channel, additional calculations were carried out at the CASSCF/AVTZ level to obtain their SO corrections.

All ab initio points were fitted to a permutation invariant polynomial-neural network (PIP-NN) form with two hidden layers,^82–84

where I denotes the number of the PIPs as the input layer;^81,122J and K stand for the numbers of the neurons in the first and second hidden layers, respectively; f₁ and f₂ are the transfer functions (hyperbolic tangent) of the two hidden layers; ω^(l)_j,i are weights that connect the ith neuron of (l − 1)th layer and the jth neuron of the lth layer, and b^(l)_j for biases of the jth neurons of the lth layer. Fitting parameters ω and b were determined iteratively by non-linear least squares fitting of NN with the root mean square error (RMSE) as the performance function: . The input layer of the NN consists of low-order PIPs, namely, symmetrized monomials of Morse-like variables of internuclear distances, , p_ij = exp(−r_ij/α) (α = 1.0 Å), and Ŝ the symmetrization operator, which contains all the permutation operations among four identical hydrogen atoms in the system.^122–124 In this work, all PIPs up to a maximum order of 5, namely, , resulting in 1052 PIP terms (I = 1052), were used as the input layer of NN to ensure the adequate permutation symmetry of the system.⁸³

To avoid overfitting, the “early stopping” algorithm¹²⁵ was employed with the entire data set divided randomly into three parts, i.e., the training (90%), validation (5%), and test (5%) sets. To minimize false extrapolation due to possible edge points randomly selected in the validation or test sets, only fits with similar RMSEs for all three sets were accepted as the final optimal PES. Besides, the absolute maximum deviation was considered for choosing the final PIP-NN PES. Several different NN architectures with two hidden layers were tested. For each architecture, 100 NN trainings with different initial fitting parameters, and different training, validation, and test sets were performed due to the non-linear fitting nature of the NN.

II.C RPMD

The RPMD rate code¹²⁶ developed by Suleimanov et al. was employed to calculate the thermal rate coefficients of the Cl + CH₄/CD₄ reactions. Since the methodology and theoretical details are available in ref. 126 and 127, only a brief description was given here. According to the Bennett–Chandler factorization,¹²⁸ the RPMD rate coefficient is expressed as:

k_RPMD = k_QTST(T;ξ^‡)κ(t → ∞;ξ^‡) (2)

The first factor k_QTST(T;ξ^‡) stands for the static contribution while the second factor κ is the dynamical correction. In particular, k_QTST(T;ξ^‡) is the quantum transition state theory (QTST) rate coefficient and can be determined at the top of the free energy barrier. In practice, it is calculated from the centroid potential of mean force (PMF):where R_∞, the distance between reactants, should be sufficient long to guarantee that the initial interaction between reactants is negligible, μ_R the reduced mass between the two reactants (Cl and CH₄ in this work). W(ξ^‡) − W(ξ = 0) is the free-energy difference between the bottleneck and reactant asymptote, which is obtained via umbrella integration along the reaction coordinate.

The second factor κ(t → ∞;ξ^‡) in eqn (2) counterbalances the first factor k_QTST(T;ξ^‡), ensuring that the final RPMD rate coefficient does not depend on the choice of the dividing surface, a highly desirable property since it is difficult to define the dividing surface for high-dimensional systems. It is the long-time limit of a time-dependent ring-polymer transmission coefficient, accounting for recrossing at the bottleneck of the PMF. In practice, it reaches a plateau relatively fast in reactions with explicit barrier, as in the title reaction, along the minimal energy path. Technically, the transmission coefficient is calculated by sampling ring polymer trajectories starting with their centroid pinned at the bottleneck.

An extra advantage of the RPMD rate theory is that it would reduce to the classical limit when only one bead is used. In this limit, the static and dynamical components become identical to the classical transition state theory rate coefficient and the classical transmission coefficient, respectively. The quantum effects such as ZPVE and tunneling can be captured well by more beads. The following formula is used to estimate the minimal number of beads needed to account for these quantum effects:

n_min = ħω_max/k_BT (4)

where ω_max is the largest vibrational frequency of the system. For the title reaction, this frequency is the vibration of C–H (3305 cm⁻¹) in CH₃, which corresponds to 29 beads at T = 200 K.

III. Results and discussions

III.A Ab initio calculations

The reaction between Cl + CH₄ has two reaction pathways, the dominated abstraction channel to HCl + CH₃ and the negligible substitution channel to H + CH₃Cl, as shown in Fig. 1. In this work, only the low energy pathway is reported, although the sampling covers other high energy regions. As shown in Fig. 1, there exists two van der Waals complexes between Cl and CH₄, RvdW1 and RvdW2, which are expected to play some roles in reaction dynamics especially at low collision energies.¹⁸ The geometries of the stationary points, optimized at the levels of UCCSD(T)-F12a/AVDZ and UCCSD(T)-F12a/AVTZ, are presented in Fig. 2, with the harmonic frequencies listed in Table 1. Note that all the energies are relative to the spin-averaged reactant asymptote Cl(²P) + CH₄ if not specified. For clarity, the high-level theoretical results on the CB PES,²⁰ which considered counterpoise and SO corrections, are also included for comparison. For the stationary points in the entrance channel, namely, the reactants, RvdW1, RvdW2, and TS1, their energies consist of two contributions, the non-SO electronic energy at the level of UCCSD(T)-F12a/AVTZ and the SO correction calculated at the level of CASSCF(15e, 12o)/AVTZ. Generally, the results are consistent with each other. For instance, the energy differences between the current work, UCCSD(T)-F12a/AVTZ + CASSCF(15e, 12o)/AVTZ and CB PES are all less than 0.13 kcal mol⁻¹ for these stationary points. Besides, at the level of CASSCF(15e, 12o)/AVTZ, the SO corrections of the reactant asymptote, RvdW1, RvdW2 and TS1 are −279, −231, −165, and −4 cm⁻¹, respectively, consistent with those by MRCI + Q/AVTZ used in the CB PES.²⁰

Fig. 1 Schematic illustration of the energetics for the reaction Cl + CH₄ on the lowest doublet state PES with the SO correction in the reactant channel. All energies are in kcal mol⁻¹ and relative to the Cl(²P) + CH₄ asymptote at various levels: PIP-NN PES, UCCSD(T)-F12a/AVTZ, and CB PES,²⁰ from top to bottom.

Fig. 2 Comparison of geometries in internal coordinates (distances in Å and angles in degrees) for the stationary points. The values correspond to PIP-NN PES, UCCSD(T)-F12a/AVTZ, UCCSD(T)-F12a/AVDZ, and UCCSD(T)/AVTZ²⁰ from top to bottom.

Table 1 Vibrational harmonic frequencies (cm⁻¹) of the stationary points along the reaction Cl + CH₄ → HCl + CH₃

Species	Method	Frequencies (cm^−1)
		1	2	3	4	5	6	7	8	9	10	11	12
a This work, fitted PIP-NN PES. b This work, UCCSD(T)-F12a/AVTZ. c This work, UCCSD(T)-F12a/AVDZ. d CCSD(T)/AVTZ, see ref. 20 for details.
Cl + CH4	PES^a	1343(t)	1565(e)	3028	3154(t)
	F12a^b	1344(t)	1569(e)	3033	3156(t)
	F12a^c	1340(t)	1563(e)	3032	3154(t)
	CCSD(T)^d	1351	1574	3028	3146
HCl + CH3	PES^a	2983	517	1421(e)	3118	3305(e)
	F12a^b	2991	518	1421(e)	3120	3304(e)
	F12a^c	2993	520	1419(e)	3117	3301(e)
	CCSD(T)^d	2990	496	1419	3114	3294
RvdW1	PES^a	i57	i53	32	1338	1338	1344	1565	1566	3035	3140	3151	3151
	F12a^b	i135	i109	58	1304	1321	1336	1549	1550	2661	3115	3157	3159
	F12a^c	i108	i102	53	1320	1321	1338	1545	1546	3029	3144	3158	3158
RvdW2	PES^a	53	60	62	1336	1347	1347	1572	1572	3017	3144	3144	3144
	F12a^b	71	155	165	1335	1348	1353	1572	1574	3028	3149	3150	3153
	F12a^c	i84	i73	80	1335	1338	1341	1557	1557	3027	3145	3145	3151
PvdW	PES^a	97	135	136	318	318	641	1415	1415	2847	3107	3293	3293
	F12a^b	95	101	105	309	314	609	1418	1420	2835	3110	3294	3294
	F12a^c	104	141	141	334	335	612	1418	1419	2828	3108	3292	3292
	CCSD(T)^d	101	136	136	328	328	600	1419	1419	2834	3104	3285	3285
TS1	PES^a	i1021	366	367	501	925	925	1189	1438	1438	3096	3251	3251
	F12a^b	i1006	359	361	505	924	925	1196	1432	1432	3088	3251	3251
	F12a^c	i976	254	254	504	863	863	1207	1428	1428	3084	3245	3245
	CCSD(T)^d	i1024	364	364	514	924	924	1197	1437	1437	3082	3242	3242

---

III.B Potential energy surface

In total, ca. 74 000 points were sampled and calculated at the level of UCCSD(T)-F12/AVTZ. Among them, ca. 27 000 points were located in the reactant channel, and their SO corrections were computed at the level of CASSCF(15e, 12o)/AVTZ. Then the PIP-NN method^82–84 was employed to fit the PES of the title reaction system. After several tests, the final hidden layers (J and K) were chosen to be of 5 and 100 neurons, respectively, resulting in 5966 nonlinear fitting parameters with a total RMSE of 7.4 meV, which is comparable to that of H + CH₄, 5.1 meV.⁸⁷ Thanks to the high fidelity of the PIP-NN fitting approach, the properties of the stationary points, including the energies, geometries, and harmonic frequencies, are reproduced well on the PIP-NN PES, as shown in Fig. 1, 2, and Table 1, respectively. Note that the geometries and harmonic frequencies were calculated at the level of UCCSD(T)-F12a/AVTZ without SO correction. As can be seen in Fig. 1, for the energies of the stationary points along the abstraction channel, the largest deviation between PIP-NN PES and ab initio calculations is only 0.02 kcal mol⁻¹. For the geometries in Fig. 2, all rigid coordinates, including bond distances and angles, are well produced with the deviations less than 0.0007 Å and 0.1°, respectively. For floppy coordinates in the weakly interacted complexes RvdW1 and RvdW2, the deviation can be as large as 0.3 Å. This is partly due to that the PIP-NN PES includes the SO correction in the reactant channel, which is not considered in the UCCSD(T)-F12a/AVTZ calculation.

Fig. 3 represents the contour plot along the two reactive distances r_CH and r_HCl with other coordinates constrained at the transition state TS1. Along the reaction path, TS1 and the post-reaction complex PvdW can be clearly seen. The pre-reaction complexes RvdW1 and RvdW2 cannot be shown due to the geometric constraints. The fitting errors are also shown in the inset of the same figure. It can be seen that small errors are evenly distributed in the energy range of −0.1 to 8.5 eV, which is sufficient for high temperature simulations up to 3000 K. It should be noted that some additional points at high-energy regions were included for reliable quantum dynamical simulations in the future. Besides, we also present in Fig. 4(a and b) the non-SO (E) and the SO corrected energies (E + SO) as a function of the r_CCl distance when Cl approaches CH₄ at the configuration of RvdW1 or RvdW2 in the entrance channel. Clearly, the SO corrections lower the reactant asymptote by about 0.78 kcal mol⁻¹, then start to decrease at 4–5 Å in both cases, and finally vanishes around 2.0 Å, as shown in Fig. 4(c). The PES is available from the corresponding author upon request.

Fig. 3 The contour plot of the PIP-NN PES (energy in kcal mol⁻¹) for the Cl + CH₄ → HCl + CH₃ reaction as a function of the two reactive distances with the other coordinates fixed at TS1. The inset shows the fitting errors as a function of the ab initio energy.

Fig. 4 One-dimensional plots of the non-SO electronic energy (E) and the SO corrected energy (E + SO) when Cl approaching CH₄ at the configuration of RvdW1 (a) or RvdW2 (b). The energies are relative to the spin-free reactant asymptote Cl(²P) + CH₄(eq). The corresponding SO corrections are plotted in (c).

III.C RPMD rate coefficients

The thermal rate coefficients of the Cl + CH₄ → HCl + CH₃ and Cl + CD₄ → DCl + CD₃ reactions were determined with the PIP-NN PES interfaced to the RPMDrate code.¹²⁶ Most parameters are essentially the same as those used in ref. 22 for the same reaction but on the RNCE and CB PESs. Briefly, for the calculation of the PMF, the reaction coordinate (−0.06 to 1.10) was divided by an equal size (dξ = 0.01) with the force constant of the biasing potential of 2.72 (T/K) eV using the umbrella sampling technique. In each sampling window, 60 constrained sampling trajectories of 100 ps were carried out, before which the system was equilibrated for 20 ps with the Andersen thermostat¹²⁹ for thermalization. After determining the PMF at each temperature, the transmission coefficient was computed. Specifically, a long (20 ns) mother trajectory was carried out with the ring-polymer centroid fixed at the top of PMF via the SHAKE algorithm.¹³⁰ Configurations were sampled once every 2 ps to serve as the starting positions for the child trajectories used to calculate the flux-side correlation function. For each starting position, 100 separate ring polymer trajectories were spawned with different initial momenta sampled from a Boltzmann distribution. These trajectories were then propagated without constraints for 100 fs, which is sufficiently long for the transmission coefficients to reach plateau values for the title activated reaction with apparent barriers. The time step is selected to be 0.3 fs in all RPMD calculations, comparable to 0.5 fs used in the RPMD computations on the CB PES due to the expensive evaluations.²² Several tests have been performed to guarantee that the results are converged with respect to the parameters above, as shown in Fig. S1 of the ESI.†

The final RPMD rate coefficients were corrected by an electronic partition function ratio of the following form,

to account for the SO splitting of Cl(²P_1/2,3/2) (ΔE = 881 cm⁻¹) statistically.⁷

For Cl + CH₄ → HCl + CH₃, the rate coefficients were calculated at 200, 300, 400, 600, 800, 1000, 1100, 1500, and 2000 K. At each temperature, the RPMD calculations were firstly performed with one bead, which provides the classical limit. Then we performed calculations with a sufficiently large number of beads, which were estimated according to eqn (4). Specifically, the RPMD calculations were done with 32 beads for 200, 300, 400, 600 K, 16 beads for 800 K, 8 beads for 1000, 1100, 1500, 2000 K, respectively. Similar parameters were used in the work by Li et al.,²² albeit only at 600 and 1000 K on the CB PES due to the expensive evaluations of this PES. It should be noted that the evaluation of the PIP-NN PES is even much more expensive. In addition, the previous RPMD calculations were calculated at 300, 400, 600, 800, and 1000 K on the much faster RNCE PES.²²

Fig. 5(a) presents the converged RPMD PMFs for the reaction Cl + CH₄ → HCl + CH₃. As shown, the peaks of the PMFs are all nearly at ξ = 1 within 200–3000 K for this activated reaction. With the temperature increased, the top positions show a negative shift slightly. The barriers of the PMFs are increased significantly from low to high temperatures due to the reduction in entropy from reactants to the transition state: they are 4.68, 5.68, 6.57, 7.99, 9.15, 10.12, 10.49, 11.89, and 13.22 kcal mol⁻¹, at 200, 300, 400, 600, 800, 1000, 1100, 1500, and 2000 K, respectively. The quantum effects, including ZPVE and tunneling, are significant especially at low temperatures, and can be described well by the RPMD method. The transmission coefficient, κ(t), another important factor, is shown in Fig. 5(b). Clearly, all the transmission coefficients show a fast drop initially. After some oscillations, it becomes flat eventually. Similar behaviors have been found and discussed by Li et al. on the same reaction.²² Fig. S2–S10 of the ESI† provide additional tests on the RPMD calculations of Cl + CH₄.

Fig. 5 (a) Converged PMFs and (b) transmission coefficients at 200, 300, 400, 600, 800, 1000, 1100, 1500, 2000 K for the Cl + CH₄ → HCl + CH₃ reaction.

For Cl + CD₄ → DCl + CD₃, the RPMD calculations were carried out at 300, 400, 600, 800, and 1000 K with 32, 32, 32, 16, and 8 beads, respectively. Fig. 6(a) presents the converged RPMD PMFs for the reaction Cl + CD₄ → DCl + CD₃. Similar to Cl + CH₄, the barrier heights of the PMFs, all essentially at ξ = 1, are increased along with the temperature due to the decrease in the entropy from reactants to the transition state. At 300, 400, 600, 800, and 1000 K, they are 7.22, 8.05, 9.39, 10.42, 11.29 kcal mol⁻¹, respectively. It can be seen that, the barrier heights at the same temperature are higher than those in Cl + CH₄ due to the differences in the ro-vibrational energy levels, ZPVE, and tunneling effects. Fig. 6(b) presents the corresponding transmission coefficients. After initial drops, they finally reach plateau values, which are larger than those for Cl + CH₄, whose recrossing effect is less significant than those in Cl + CD₄. Additional comparisons and tests on the RPMD calculations of Cl + CD₄ are given in Fig. S11–S15 of the ESI.†

Fig. 6 (a) Converged PMFs and (b) transmission coefficients at 300, 400, 600, 800, 1000 K for the Cl + CD₄ → DCl + CD₃ reaction.

In Fig. 7, the RPMD rate coefficients for the Cl + CH₄ reaction are compared with available experimental^{29–34,37,38,41,42,54,62} and theoretical results.^21,22 The current results are essentially the same as those on the CB PES at 600 and 1000 K,²² since both PESs are fitted to tens of thousands of points calculated at similar ab initio levels.²⁰ The RPMD predictions are apparently lower than other available results at low temperatures, 200–400 K, at which the barrier height can affect the low temperature rate coefficients significantly. With a reduction of only 0.22 kcal mol⁻¹ in the barrier, the scaled RPMD results agree well with others in the entire temperature range of 200–3000 K, as shown in Fig. 7. Nonetheless, the overall agreement is reasonably good, given the fact that the experimental results are quite scattered. On the RNCE PES, the RPMD results were slightly overestimated at temperatures higher than 500 K and agreed well with experiment at low temperatures 300–500 K.²² With anharmonicity and energies calculated at advanced levels, rate coefficients of the title reaction and its isotopologues determined by the semiclassical transition state theory (SCTST) were in good agreement with experiments,²¹ as shown in Fig. 7. Careful scrutiny shows that SCTST results are slightly overestimated especially at temperatures above 600 K.

Fig. 7 Comparison of the rate coefficients for the reaction Cl + CH₄ → HCl + CH₃ from available theoretical and experimental results.

Similarly, Fig. 8 displays the corresponding rate coefficients for the Cl + CD₄ → DCl + CD₃ reaction within 300–1000 K. The RPMD results on the CB PES at 600 and 1000 K²² again are consistent with the current RPMD ones. Around room temperatures, the RPMD calculations on the PIP-NN PES are slightly lower than experiment.^131–133 After reduction in the barrier by 0.22 kcal mol⁻¹, the scaled RPMD results agree well with the scattered experimental results around 300 K. On the RNCE PES, the RPMD results²² were evidently overestimated due to the empirical nature of this PES.¹⁴ Particularly, the imaginary frequency on the RNCE PES is only i782 cm⁻¹,¹⁴ significantly smaller than i1021 cm⁻¹ in magnitude on the current PIP-NN PES. Interestingly, the SCTST results²¹ are very close to the current RPMD results for the Cl + CD₄ reaction.

Fig. 8 Comparison of the rate coefficients of the reaction Cl + CD₄ → DCl + CD₃ from available theoretical and experimental results.

Fig. 9 The kinetics isotopic effect (KIE) defined as k_CH4/k_CD4 within the temperature range of 300–1000 K. Available theoretical and experiment results are included for comparison.

The KIEs, defined as the ratios between Cl + CH₄ and Cl + CD₄ rate coefficients, k_CH4/k_CD4, are displayed in Fig. 9 within 300–1000 K. Available theoretical^21,22 and experimental results^29,131–135 are also compared in the same figure. Clearly, experimental values differ considerably within the temperature range. The RPMD KIEs on the current PES, the CB PES, and the RNCE PES are consistent with each other at temperatures above 400 K. At temperatures between 300 and 400 K, the current RPMD KIEs, larger than those on the RNCE PES,²² are close to the lower end of the experimental data. On the contrary, the SCTST results²¹ are much higher, near the high end of the experiments.

IV. Conclusions

In the present work, we developed a new full-dimensional accurate PES for the reaction Cl + CH₄ → HCl + CH₃ based on ca. 74 000 points calculated at the UCCSD(T)-F12a/AVTZ level with the SO corrections considered at the CASSCF/AVTZ level for ca. 27 000 points in the entrance channel. The full-dimensional approximate quantum mechanical approach, ring polymer molecular dynamics (RPMD), was employed to calculate the thermal rate coefficients within 200–2000 K for Cl + CH₄ and 300–1000 K for Cl + CD₄. The RPMD predicted results are in reasonable agreement with the experimental measurements, which are scattered. If the barrier height is reduced by only 0.22 kcal mol⁻¹, the agreement becomes much better at temperatures below 400 K. The RPMD rate coefficients and the KIEs on the new PES are in good agreement with experiment in a large temperature range, suggesting that RPMD provides a reliable and efficient alternative to transition state theory for polyatomic reactions, for which it is still challenging to carry out rigorous quantum mechanical calculations. The previous RPMD results on the CB PES, including rate coefficients for Cl + CH₄/CD₄ and KIEs, are in excellent agreement with those on the current PES within 600–1000 K. As has been discussed in ref. 22, the rate coefficients on the more efficient RNCE PES were slightly overestimated within 500–1000 K for Cl + CH₄, and significantly overestimated within 300–1000 K for Cl + CD₄. Hence, the KIEs were significantly underestimated within 300–400 K on the RNCE PES.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This work was financially supported by the Chongqing Municipal Natural Science Foundation (grant no. cstc2019jcyj-msxmX0087) and the National Natural Science Foundation of China (contract no. 21573027 and 21973009). Prof. Hua Guo is thanked for helpful discussion on the work.

References

1. A. A. P. Pszenny, W. C. Keene, D. J. Jacob, S. Fan, J. R. Maben, M. P. Zetwo, M. Springer-Young and J. N. Galloway, Geophys. Res. Lett., 1993, 20, 699–702.
2. A. R. Douglass, M. R. Schoeberl, R. S. Stolarski, J. W. Waters, J. M. Russell III, A. E. Roche and S. T. Massie, J. Geophys. Res.: Atmos., 1995, 100, 13967–13978.
3. M. L. Santee, L. Froidevaux, G. L. Manney, W. G. Read, J. W. Waters, M. P. Chipperfield, A. E. Roche, J. B. Kumer, J. L. Mergenthaler and J. M. Russell, J. Geophys. Res.: Atmos., 1996, 101, 18835–18859.
4. H. A. Michelsen, Acc. Chem. Res., 2001, 34, 331–337.
5. T. N. Truong, D. G. Truhlar, K. K. Baldridge, M. S. Gordon and R. Steckler, J. Chem. Phys., 1989, 90, 7137–7142.
6. K. D. Dobbs and D. A. Dixon, J. Phys. Chem., 1994, 98, 12584–12589.
7. W. T. Duncan and T. N. Truong, J. Chem. Phys., 1995, 103, 9642–9652.
8. J. Espinosa-García and J. C. Corchado, J. Chem. Phys., 1996, 105, 3517–3523.
9. H. G. Yu and G. Nyman, Phys. Chem. Chem. Phys., 1999, 1, 1181–1190.
10. J. C. Corchado, D. G. Truhlar and J. Espinosa-García, J. Chem. Phys., 2000, 112, 9375–9389.
11. L. Zhang, M.-D. Chen, M.-L. Wang and K.-L. Han, J. Chem. Phys., 2000, 112, 3710–3716.
12. S. Skokov and J. M. Bowman, J. Chem. Phys., 2000, 113, 4495–4497.
13. C. Rangel, J. Espinosa-García and J. C. Corchado, J. Phys. Chem. A, 2005, 109, 8071–8073.
14. C. Rangel, M. Navarrete, J. C. Corchado and J. Espinosa-García, J. Chem. Phys., 2006, 124, 124306.
15. J. Sansón, J. C. Corchado, C. Rangel and J. Espinosa-García, J. Chem. Phys., 2006, 124, 074312.
16. J. Sansón, J. C. Corchado, C. Rangel and J. Espinosa-García, J. Phys. Chem. A, 2006, 110, 9568–9574.
17. S. J. Greaves, R. A. Rose, F. Abou-Chahine, D. R. Glowacki, D. Troya and A. J. Orr-Ewing, Phys. Chem. Chem. Phys., 2011, 13, 11438–11445.
18. G. Czakó and J. M. Bowman, Science, 2011, 334, 343–346.
19. Z. Zhang, Y. Zhou, D. H. Zhang, G. Czakó and J. M. Bowman, J. Phys. Chem. Lett., 2012, 3, 3416–3419.
20. G. Czakó and J. M. Bowman, J. Chem. Phys., 2012, 136, 044307.
21. J. R. Barker, T. L. Nguyen and J. F. Stanton, J. Phys. Chem. A, 2012, 116, 6408–6419.
22. Y. Li, Y. V. Suleimanov, W. H. Green and H. Guo, J. Phys. Chem. A, 2014, 118, 1989–1996.
23. R. Liu, F. Wang, B. Jiang, G. Czakó, M. Yang, K. Liu and H. Guo, J. Chem. Phys., 2014, 141, 074310.
24. W. Yan and D. Wang, Chem. Phys. Lett., 2014, 603, 41–45.
25. N. Liu and M. Yang, J. Chem. Phys., 2015, 143, 134305.
26. B. Hornung, J. N. Harvey, T. J. Preston, G. T. Dunning and A. J. Orr-Ewing, J. Phys. Chem. A, 2015, 119, 9590–9598.
27. A. J. Totenhofer, J. N. L. Connor and G. Nyman, J. Phys. Chem. B, 2016, 120, 2020–2032.
28. T. Lenzen, W. Eisfeld and U. Manthe, J. Chem. Phys., 2019, 150, 244115.
29. M. A. A. Clyne and R. F. Walker, J. Chem. Soc., Faraday Trans. 1, 1973, 69, 1547–1567.
30. R. G. Manning and M. J. Kurylo, J. Phys. Chem., 1977, 81, 291–296.
31. D. A. Whytock, J. H. Lee, J. V. Michael, W. A. Payne and L. J. Stief, J. Chem. Phys., 1977, 66, 2690–2695.
32. M. S. Zahniser, B. M. Berquist and F. Kaufman, Int. J. Chem. Kinet., 1978, 10, 15–29.
33. A. R. Ravishankara and P. H. Wine, J. Chem. Phys., 1980, 72, 25–30.
34. S. P. Heneghan, P. A. Knoot and S. W. Benson, Int. J. Chem. Kinet., 1981, 13, 677–691.
35. W. R. Simpson, T. P. Rakitzis, S. A. Kandel, A. J. Orrewing and R. N. Zare, J. Chem. Phys., 1995, 103, 7313–7335.
36. W. R. Simpson, T. P. Rakitzis, S. A. Kandel, T. LevOn and R. N. Zare, J. Phys. Chem., 1996, 100, 7938–7947.
37. J. V. Seeley, J. T. Jayne and M. J. Molina, J. Phys. Chem., 1996, 100, 4019–4025.
38. J. S. Pilgrim, A. McIlroy and C. A. Taatjes, J. Phys. Chem. A, 1997, 101, 1873–1880.
39. S. A. Kandel and R. N. Zare, J. Chem. Phys., 1998, 109, 9719–9727.
40. Z. H. Kim, A. J. Alexander, H. A. Bechtel and R. N. Zare, J. Chem. Phys., 2001, 115, 179–183.
41. K. Takahashi, O. Yamamoto and T. Inomata, Proc. Combust. Inst., 2002, 29, 2447–2453.
42. M. G. Bryukov, I. R. Slagle and V. D. Knyazev, J. Phys. Chem. A, 2002, 106, 10532–10542.
43. S. Yoon, S. Henton, A. N. Zivkovic and F. F. Crim, J. Chem. Phys., 2002, 116, 10744–10752.
44. Z. H. Kim, H. A. Bechtel and R. N. Zare, J. Chem. Phys., 2002, 117, 3232–3242.
45. S. Yoon, R. J. Holiday, E. L. Sibert III and F. F. Crim, J. Chem. Phys., 2003, 119, 9568–9575.
46. J. Zhou, J. J. Lin, B. Zhang and K. Liu, J. Phys. Chem. A, 2004, 108, 7832–7836.
47. H. A. Bechtel, Z.-H. Kim, J. P. Camden and R. N. Zare, J. Chem. Phys., 2004, 120, 791–799.
48. H. A. Bechtel, J. P. Camden, D. J. A. Brown, M. R. Martin, R. N. Zare and K. Vodopyanov, Angew. Chem., Int. Ed., 2005, 44, 2382–2385.
49. B. L. Zhang and K. P. Liu, J. Chem. Phys., 2005, 122, 101102.
50. M. J. Bass, M. Brouard, R. Cireasa, A. P. Clark and C. Vallance, J. Chem. Phys., 2005, 123, 094301.
51. Z. H. Kim, H. A. Bechtel, J. P. Camden and R. N. Zare, J. Chem. Phys., 2005, 122, 084303.
52. H. A. Bechtel, Z. H. Kim, J. P. Camden and R. N. Zare, Mol. Phys., 2005, 103, 1837–1846.
53. R. J. Holiday, C. H. Kwon, C. J. Annesley and F. F. Crim, J. Chem. Phys., 2006, 125, 133101.
54. R. Atkinson, D. L. Baulch, R. A. Cox, J. N. Crowley, R. F. Hampson, R. G. Hynes, M. E. Jenkin, M. J. Rossi and J. Troe, Atmos. Chem. Phys., 2006, 6, 3625–4055.
55. S. Yan, Y. T. Wu, B. Zhang, X.-F. Yue and K. Liu, Science, 2007, 316, 1723–1726.
56. H. Kawamata, S. Tauro and K. Liu, Phys. Chem. Chem. Phys., 2008, 10, 4378–4382.
57. Y.-T. Wu and K. Liu, J. Chem. Phys., 2008, 129, 154302.
58. S. Yan, Y.-T. Wu and K. Liu, Proc. Natl. Acad. Sci. U. S. A., 2008, 105, 12667–12672.
59. J. Riedel, S. N. Yan and K. Liu, J. Phys. Chem. A, 2009, 113, 14270–14276.
60. J. Riedel and K. Liu, J. Phys. Chem. A, 2009, 113, 4249–4254.
61. H. Kawamata and K. Liu, J. Chem. Phys., 2010, 133, 124304.
62. S. P. Sander, J. Abbatt, J. R. Barker, J. B. Burkholder, R. R. Friedl, D. M. Golden, R. E. Huie, C. E. Kolb, M. J. Kurylo, G. K. Moortgat, V. L. Orkin and P. H. Wine, Chemical kinetics and photochemical data for use in atmospheric studies, Evaluation No. 17, JPL Publication 10-6, Pasadena, 2011.
63. F. Wang, J.-S. Lin and K. Liu, Science, 2011, 331, 900–903.
64. B. L. Zhang, K. P. Liu, G. Czako and J. M. Bowman, Mol. Phys., 2012, 110, 1617–1626.
65. F. Wang, K. Liu and T. P. Rakitzis, Nat. Chem., 2012, 4, 636–641.
66. A. E. Berke, E. H. Volpa, C. J. Annesley and F. F. Crim, J. Chem. Phys., 2013, 138, 224306.
67. F. Wang, J.-S. Lin, Y. Cheng and K. Liu, J. Phys. Chem. Lett., 2013, 4, 323–327.
68. L. M. T. Joelsson, R. Forecast, J. A. Schmidt, C. Meusinger, E. J. K. Nilsson, S. Ono and M. S. Johnson, Chem. Phys. Lett., 2014, 605, 152–157.
69. F. Wang, H. Pan and K. Liu, J. Phys. Chem. A, 2015, 119, 11983–11988.
70. F. Wang and K. Liu, J. Chem. Phys., 2016, 145, 144305.
71. F. Wang and K. Liu, J. Chem. Phys., 2016, 145, 144306.
72. H. Pan, Y. Cheng and K. Liu, J. Phys. Chem. A, 2016, 120, 4799–4804.
73. H. Pan, F. Wang, G. Czako and K. Liu, Nat. Chem., 2017, 9, 1175–1180.
74. H. Pan, O. Tkac and K. Liu, J. Chem. Phys., 2018, 148, 244307.
75. C. Murray and A. J. Orr-Ewing, Int. Rev. Phys. Chem., 2004, 23, 435–482.
76. G. Nyman, H. G. Yu and R. B. Walker, J. Chem. Phys., 1998, 109, 5896–5904.
77. H. G. Yu and G. Nyman, J. Chem. Phys., 1999, 110, 7233–7244.
78. F. Meng, W. Yan and D. Wang, Phys. Chem. Chem. Phys., 2012, 14, 13656–13662.
79. J. Li, B. Jiang, H. Song, J. Ma, B. Zhao, R. Dawes and H. Guo, J. Phys. Chem. A, 2015, 119, 4667–4687.
80. J. F. Castillo, F. J. Aoiz and L. Banares, J. Chem. Phys., 2006, 125, 124316.
81. C. Qu, Q. Yu and J. M. Bowman, Annu. Rev. Phys. Chem., 2018, 69, 151–175.
82. B. Jiang and H. Guo, J. Chem. Phys., 2013, 139, 054112.
83. J. Li, B. Jiang and H. Guo, J. Chem. Phys., 2013, 139, 204103.
84. B. Jiang, J. Li and H. Guo, Int. Rev. Phys. Chem., 2016, 35, 479–506.
85. M. Bai, D. Lu and J. Li, Phys. Chem. Chem. Phys., 2017, 19, 17718–17725.
86. Y. Liu, M. Bai, H. Song, D. Xie and J. Li, Phys. Chem. Chem. Phys., 2019, 21, 12667–12675.
87. J. Li, J. Chen, Z. Zhao, D. Xie, D. H. Zhang and H. Guo, J. Chem. Phys., 2015, 142, 204302.
88. J. Li and H. Guo, J. Chem. Phys., 2015, 143, 221103.
89. J. Li, K. Song and J. Behler, Phys. Chem. Chem. Phys., 2019, 21, 9672–9682.
90. M. L. Weichman, J. A. DeVine, M. C. Babin, J. Li, L. Guo, J. Ma, H. Guo and D. M. Neumark, Nat. Chem., 2017, 9, 950–955.
91. T. B. Adler, G. Knizia and H.-J. Werner, J. Chem. Phys., 2007, 127, 221106.
92. G. Knizia, T. B. Adler and H.-J. Werner, J. Chem. Phys., 2009, 130, 054104.
93. S. Habershon, D. E. Manolopoulos, T. E. Markland and T. F. Miller III, Annu. Rev. Phys. Chem., 2013, 64, 387–413.
94. R. Collepardo-Guevara, Y. V. Suleimanov and D. E. Manolopoulos, J. Chem. Phys., 2009, 130, 174713.
95. Y. V. Suleimanov, R. Collepardo-Guevara and D. E. Manolopoulos, J. Chem. Phys., 2011, 134, 044131.
96. R. Pérez de Tudela, F. J. Aoiz, Y. V. Suleimanov and D. E. Manolopoulos, J. Phys. Chem. Lett., 2012, 3, 493–497.
97. Y. Li, Y. V. Suleimanov, M. Yang, W. H. Green and H. Guo, J. Phys. Chem. Lett., 2013, 4, 48–52.
98. Y. V. Suleimanov, R. Pérez de Tudela, P. G. Jambrina, J. F. Castillo, V. Sáez-Rábanos, D. E. Manolopoulos and F. J. Aoiz, Phys. Chem. Chem. Phys., 2013, 15, 3655–3665.
99. Y. Li, Y. V. Suleimanov, J. Li, W. H. Green and H. Guo, J. Chem. Phys., 2013, 138, 094307.
100. J. W. Allen, W. H. Green, Y. Li, H. Guo and Y. V. Suleimanov, J. Chem. Phys., 2013, 138, 221103.
101. J. Espinosa-Garcia, A. Fernandez-Ramos, Y. V. Suleimanov and J. C. Corchado, J. Phys. Chem. A, 2014, 118, 554–560.
102. R. Pérez de Tudela, Y. V. Suleimanov, M. Menendez, F. Castillo and F. J. Aoiz, Phys. Chem. Chem. Phys., 2014, 16, 2920–2927.
103. Y. Li, Y. V. Suleimanov and H. Guo, J. Phys. Chem. Lett., 2014, 5, 700–705.
104. E. Gonzalez-Lavado, J. C. Corchado, Y. V. Suleimanov, W. H. Green and J. Espinosa-Garcia, J. Phys. Chem. A, 2014, 118, 3243–3252.
105. K. M. Hickson, J.-C. Loison, H. Guo and Y. V. Suleimanov, J. Phys. Chem. Lett., 2015, 6, 4194–4199.
106. D. J. Arseneau, D. G. Fleming, Y. Li, J. Li, Y. V. Suleimanov and H. Guo, J. Phys. Chem. B, 2016, 120, 1641–1648.
107. Y. V. Suleimanov, F. Javier Aoiz and H. Guo, J. Phys. Chem. A, 2016, 120, 8488–8502.
108. M. Bai, D. Lu, Y. Li and J. Li, Phys. Chem. Chem. Phys., 2016, 18, 32031–32041.
109. K. M. Hickson and Y. V. Suleimanov, J. Phys. Chem. A, 2017, 121, 1916–1923.
110. J. F. Castillo and Y. V. Suleimanov, Phys. Chem. Chem. Phys., 2017, 19, 29170–29176.
111. J. X. Zuo, C. J. Xie, H. Guo and D. Q. Xie, J. Phys. Chem. Lett., 2017, 8, 3392–3397.
112. X. X. Lu, Q. Y. Meng, X. G. Wang, B. N. Fu and D. H. Zhang, J. Chem. Phys., 2018, 149, 174303.
113. H. Wang, J. Fang, H. Yang, J. Song and Y. Li, Chem. Phys. Lett., 2019, 730, 227–233.
114. X. X. Lu, X. G. Wang, B. N. Fu and D. H. Zhang, J. Phys. Chem. A, 2019, 123, 3969–3976.
115. J. Li, Chin. J. Chem. Phys., 2019, 32, 313–318.
116. H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. Schütz, et al., MOLPRO, version 2015, a package of ab initio programs, see http://www.molpro.net.
117. L. Kong, F. A. Bischoff and E. F. Valeev, Chem. Rev., 2011, 112, 75–107.
118. G. Czakó, I. Szabó and H. Telekes, J. Phys. Chem. A, 2014, 118, 646–654.
119. G. Czakó and J. M. Bowman, Phys. Chem. Chem. Phys., 2011, 13, 8306–8312.
120. J. Li, B. Jiang and H. Guo, J. Chem. Phys., 2013, 138, 074309.
121. A. Berning, M. Schweizer, H. J. Werner, P. J. Knowles and P. Palmier, Mol. Phys., 2000, 98, 1823–1833.
122. Z. Xie and J. M. Bowman, J. Chem. Theory Comput., 2010, 6, 26–34.
123. J. N. Murrell, K. Sobie and A. J. C. Varandas, Mol. Phys., 1976, 32, 1359–1372.
124. A. Schmelzer and J. N. Murrell, Int. J. Quantum Chem., 1985, 28, 287–295.
125. L. M. Raff, R. Komanduri, M. Hagan and S. T. S. Bukkapatnam, Neural Networks in Chemical Reaction Dynamics, Oxford University Press, Oxford, 2012.
126. Y. V. Suleimanov, J. W. Allen and W. H. Green, Comput. Phys. Commun., 2013, 184, 833–840.
127. Y. V. Suleimanov, F. J. Aoiz and H. Guo, J. Phys. Chem. A, 2016, 120, 8488–8502.
128. D. Chandler, J. Chem. Phys., 1978, 68, 2959–2970.
129. H. C. Andersen, J. Chem. Phys., 1980, 72, 2384–2393.
130. J. P. Ryckaert, G. Ciccotti and H. J. Berendsen, J. Comput. Phys., 1977, 23, 327–341.
131. T. J. Wallington and M. D. Hurley, Chem. Phys. Lett., 1992, 189, 437–442.
132. Y. Matsumi, K. Izumi, V. Skorokhodov, M. Kawasaki and N. Tanaka, J. Phys. Chem. A, 1997, 101, 1216–1221.
133. G. D. Boone, F. Agyin, D. J. Robichaud, F.-M. Tao and S. A. Hewitt, J. Phys. Chem. A, 2000, 105, 1456–1464.
134. G. Chiltz, R. Eckling, P. Goldfinger, G. Huybrechts, H. S. Johnston, L. Meyers and G. Verbeke, J. Chem. Phys., 1963, 38, 1053–1061.
135. K. L. Feilberg, D. W. T. Griffith, M. S. Johnson and C. J. Nielsen, Int. J. Chem. Kinet., 2005, 37, 110–118.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9cp05693a

---