Atmospheric chemistry of CH₃O: its unimolecular reaction and reactions with H₂O, NH₃, and HF

Abstract

We have investigated the hydrogen atom transfer processes of CH₃O to CH₂OH without catalyst and with water, ammonia, and hydrofluoric acid as catalysts using ab initio methods, density functional theory (DFT) methods, and canonical variational transition state theory with small curvature tunneling (CVT/SCT). Herein, we have performed the benchmark barrier heights of the title reactions using W3X-L//CCSD(T)-F12a/VDZ-F12 methods. We have also performed the calculations of the combination of MPW-type, PBE-type exchange, M05-type, M06-type functional, and composite theoretical model chemistry methods such as CBS-QB3 and G4. We found that the M05-2X/aug-cc-pVTZ, mPW2PLYP/MG3S, M05-2X/aug-cc-pVTZ, and M06-2X/MG3S methods are performed better in different functionals with the unsigned errors (UEs) of 0.34, 0.02, 0.05, and 0.75 kcal mol⁻¹ for its unimolecular reaction and reactions with H₂O, NH₃, and HF, respectively. The calculated results show that NH₃ exerts the strongest catalytic role in the isomerization reaction of CH₃O to CH₂OH, compared with H₂O and HF. In addition, the calculated rate constants show that the effect of tunneling increases the rate constant of the unimolecular reaction of CH₃O by 10²–10¹² times in the temperature range of 210–350 K. Moreover, the variational effects of the transition state are obvious in CH₃O + NH₃. The calculated results also show that the direct unimolecular reaction of CH₃O to CH₂OH is dominant in the sink of CH₃O, compared with the CH₃O + H₂SO₄, CH₃O + HCOOH, CH₃O + H₂O, CH₃O + NH₃, and CH₃O + HF reactions in the atmosphere. The present results provide a new insight into catalysts that not only affect energy barriers, but have influences on tunneling and variational effects of transition states. The present findings should have broad implications in computational chemistry and atmospheric chemistry.

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1. Introduction

Alkoxy radicals have received a great amount of attention because they play a key role in both combustion and atmospheric chemistry.¹ The methoxy radical (CH₃O) is one of the simplest alkoxy radicals.² CH₃O is produced from OH-initiated oxidation of CH₄.² In the atmosphere, CH₃O undergoes unimolecular isomerization and decomposition and bimolecular reaction.¹ While CH₃O dominantly reacts with O₂, responsible for the formation of HCHO and HO₂, the CH₂OH + O₂ reaction is 10⁴ times faster than the CH₃O + O₂ reaction, where CH₂OH is formed through the hydrogen atom transfer of CH₃O.^3–5 Therefore, Radford stated that the isomerization reaction of CH₃O could be an important process for the loss of CH₃O.⁶ Exploring the unimolecular isomerization of CH₃O is required to estimate the fate of CH₃O in the atmosphere.

The reaction kinetics and dynamics of methoxy radicals (CH₃O) has been extensively investigated for both experimental and theoretical methods in the literature.^1,7–19 However, the kinetics of the unimolecular isomerization reaction of CH₃O remains unclear. With regard to the unimolecular reaction of CH₃O, the energy barrier is very high, in the range of 26–36 kcal mol⁻¹, depending on different theoretical methods.^{14,16,20–22} For example, Batt et al.¹⁶ estimated an energy barrier of 26.1 kcal mol⁻¹, Tachikawa et al.²² reported an energy barrier of 32.88 kcal mol⁻¹ calculated by CCSDST4/D95V**, Saebo et al.¹⁴ reported an energy barrier of 36 kcal mol⁻¹ calculated by MP3/6-31G**. This uncertainty of energy barrier of CH₃O unimolecular isomerization leads to the difficulty in quantitatively estimating the rate constant of CH₃O unimolecular isomerization reaction. In addition, CH₃O unimolecular isomerization is a hydrogen atom transfer (HAT) reaction. In particular, tunneling effects play a critical role in reaction kinesics for hydrogen transfer reactions,^23,24 such as the unimolecular reactions of Criegee intermediates,^25–28 CH₃OH + OH,²⁹ OH + H₂SO₄⋯NH₃,³⁰ unimolecular rearrangement of Rh(PH₃)₂ClCH₄,³¹ H/D + CO,^32,33 H/D + CH₃OH,³⁴ and Al + 3H₂O.³⁵ Therefore, it is necessary to reevaluate kinetics of the unimolecular isomerization reaction of CH₃O.

The other issue is that there are some reports that water and atmospheric acids can remarkably decrease the energy barrier of hydrogen atom transfer reaction.³⁶ More over water, sulfuric acid, and formic acid have been reported as catalysts to reduce the isomerization of methoxy to 25.7, 2.3, and 4.2 kcal mol⁻¹, respectively.³⁶ In particular, the calculated results are 25.7 kcal mol⁻¹ by Buszek et al.³⁶ and 22.9 kcal mol⁻¹ by Kumar et al.⁵ at the CCSD(T)/aug-cc-pVTZ//QCISD/6-31G(d) and CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ, respectively. It is noted that the reported water catalytic CH₃O isomerization of the energy barrier has difference of 2–3 kcal mol⁻¹. This results lead to the inaccuracy of evaluating the kinetics of the methoxy unimolecular isomerization reaction. In addition, the catalytic effect of ammonia is better than water in the literature.³⁷ Hydrofluoric acid is an important inorganic acid in the atmosphere. So, we calculated the H₂O, NH₃, and HF as catalysts in the unimolecular isomerization reaction of CH₃O.

In this work, we investigated the hydrogen atom transfer processes of CH₃O to CH₂OH catalyzed by water, ammonia, and hydrofluoric acid using ab initio methods and density functional theory (DFT) methods, and canonical variational transition state theory with small curvature tunneling (CVT/SCT). We studied following reactions:

CH₃O → CH₂OH (1)

CH₃O + M → CH₂OH + M (2)

where M stands for H₂O, NH₃, and HF. The purpose of this work is to determine which functional is best for every specific reaction studied here and estimate the catalytic capability of these catalysts, explore the tunneling effects, and obtain the quantitative rate constants. Herein, we also present definitive examples how to use theoretical methods to predict the quantitative rate constants for hydrogen atom transfer reactions.

2. Computational methods

2.1. Benchmark calculation

It is of great necessity for studying the atmospheric reactions with high-accurate electronic structure methods to obtain quantitative results. We used the CCSD(T)-F12a/VDZ-F12 (ref. 38–40) and QCISD/VTZ⁴¹ methods for optimizing the reactants, pre-reactive complexes, transition states, post-reactive complexes, and products and calculating their corresponding frequencies. Single point energy calculations were carried out using the W2X⁴² and W3X-L⁴² methods at the CCSD(T)-F12a/VDZ-F12 and QCISD/VTZ optimized geometries, respectively. We have obtained the benchmark barrier heights of hydrogen atom transfer reactions for CH₃O to CH₂OH by different catalysts at the W3X-L//CCSD(T)-F12a/VDZ-F12 level as our best estimate. It is worth noting that W3X-L composite methods have been used in the reactions of Criegee intermediates with water,²⁵ SO₂ with OH,⁴³ and HO₂ with XCHO⁴⁴ to obtain rate constants with experimental accuracy.

2.2. Composite method calculation

Quantum chemical composite methods have developed because they approaches CCSD(T)/CBS.⁴⁵ We used G4,⁴⁵ unrestricted coupled cluster spin contamination corrected [UCCSD(T)], and unrestricted Brueckner doubles [UBD(T)] variations of the Weizmann-1 theory (W1), named as W1U and W1BD,⁴⁶ and the CBS-QB3 (ref. 47) method.

2.3. Density functional theory (DFT) calculation

We studied different functionals: (1) the generalized gradient approximation (GGA) such as B98 ref. 48) and BP86 (ref. 49–51; (2) depending on the density of Laplace or kinetic energy density of meta-GGA such as M11-L;⁵² (3) hybrid GGA with the addition of Hartree–Fock (HF) exchange to non-local information of occupied orbital such as BMK,⁵³ HSEh1PBE,^54–57 MPW1K,^58–60 and MPW3LYP;⁶¹ (4) global-hybrid meta-GGA: B3LYP,⁶² M05-2X,⁶³ M06-HF,⁶⁴ and M06-2X;⁶⁵ (5) range-separated hybrid meta GGA such as M11 (ref. 66) and range-separated meta-NGA such as MN12-SX;⁶⁷ (6) double hybrid density functional using from both occupied and virtual orbital such as B2PLYP,⁶⁸ B2PLYPD,⁶⁹ and mPW2PLYP.⁷⁰ These computations were finished using aug-cc-pVTZ,^71–73 maug-cc-pVTZ,⁷⁴ MG3S,⁷⁵ and ma-TZVP⁷⁶ basis sets.

2.4. Reaction kinetics

The rate constants were calculated using canonical variational transition-state theory with small curvature tunneling (CVT/SCT).^77–81 We selected the best functional for every specific reactions to do direct dynamics calculations by comparing with our best estimate. The unimolecular rate constants of CH₃O to CH₂OH was calculated by M05-2X/aug-cc-pVTZ, while the bimolecular rate constants of the CH₃O + H₂O, CH₃O + NH₃, and CH₃O + HF reactions were calculated using mPW2PLYP/MG3S, M05-2X/maug-cc-pVTZ, and M06-2X/MG3S, respectively. Scale factors⁸² were used to scale all directly calculated harmonic vibrational frequencies, which are 0.964, 0.972, 0.964, and 0.970 for M05-2X/aug-cc-pVTZ, mPW2PLYP/MG3S, M05-2X/maug-cc-pVTZ, and M06-2X/MG3S, respectively.

The optimization and frequency calculations of all geometries including reactants, transition states, and products calculated were carried out with the Gaussian 09 (ref. 83) suites of programs. The high level geometry optimization calculations are performed using the Molpro 2012 (ref. 84) suites of programs. Rate constants were calculated using the Polyrate 2010A⁸⁵ and Gaussrate 2009 (ref. 86) dynamics codes.

3. Results and discussion

We have obtained the benchmark barrier heights of CH₃O to CH₂OH without catalyst and with water, ammonia, and hydrofluoric acid as catalysts using W3X-L//CCSD(T)-F12a/VDZ-F12 methods. We defined the unsigned error (UE) to determine which is the best functional, and UE is the absolute value of the difference between the computed barrier heights by different methods and the benchmark barrier heights calculated by W3X-L//CCSD(T)-F12a/VDZ-F12.

3.1. The unimolecular isomerization of CH₃O

The unimolecular isomerization of CH₃O into CH₂OH occurs via the transfer of the hydrogen atom of CH₃ group to the oxygen atom in CH₃O responsible for the formation of CH₂OH as shown in Fig. 1. The unimolecular isomerization of CH₃O into CH₂OH has been extensively studied using different theoretical methods; the previous calculated results indicated that the barrier heights of the unimolecular isomerization of CH₃O into CH₂OH are varies between 26.1 and 36.0 kcal mol⁻¹.^{14,16,20–22} Therefore, higher-level theoretical methods are required to obtain quantitative results. Herein, we use the benchmark calculation of beyond-CCSD(T) to obtain reliable results. The main results are summarized in Table 1 and Fig. 1, while all the results are provided in Table S1 (ESI).† The calculated results by W3X-L//CCSD(T)-F12a/VDZ-F12 indicate that the barrier height of the reaction is 29.56 kcal mol⁻¹ in Table 1. Fig. 2 shows that the results are calculated by various density functional methods and ab initio methods, where the UEs are 0.13, 0.18, 0.32, and 0.34 kcal mol⁻¹ using W1U, CBS-QB3, W1BD, and M05-2X/aug-cc-pVTZ, respectively; this results reflect slight changes for different theoretical methods. Therefore, the barrier height of the unimolecular isomerization of CH₃O into CH₂OH is computed to be 29.56 kcal mol⁻¹ (W3X-L//CCSD(T)-F12a/VDZ-F12), which should be reliable. The W2X//CCSD(T)-F12a/VDZ-F12 result is 29.64 kcal mol⁻¹, which agrees well with the value of 29.56 kcal mol⁻¹; this shows that the electronic structures in the unimolecular reaction of CH₃O to CH₂OH do not represent a multireference character. Additionally, Table 1 shows that the barrier height of CH₃O to CH₂OH by W3X-L//QCISD/cc-pVTZ is calculated to be 28.99 kcal mol⁻¹, which is 0.57 kcal mol⁻¹ different from the value (29.56 kcal mol⁻¹) calculated by W3X-L//CCSD(T)-F12/VDZ-F12; this result shows that the optimized geometries and calculated frequencies at the QCISD/cc-pVTZ are in adequate agreement with CCSD(T)-F12a/VDZ-F12 results, which has been observed in the SO₂ + OH reaction,⁴³ while the QCISD/cc-pVTZ-optimized geometries and calculated frequencies are reliable in the reactions of Criegee intermediates with H₂O.²⁵ Since the unimolecular reaction of CH₃O to CH₂OH and the SO₂ + OH reaction are open-shell systems, the reliability of QCISD-optimized geometries and calculated frequencies for open-shell systems should be particular concerned to obtain quantitative results in competition with experimental accuracy with an error bar of 0.1–0.2 kcal mol⁻¹.

Fig. 1 Variation in potential energy surface for the reactants, intermediates, transition states, and products of the CH₃O isomerization into CH₂OH in the without catalysis and catalyzed by water, ammonia, and hydrofluoric acid reactions at the W3X-L//CCSD(T)-F12a/VDZ-F12 level.

Table 1 The energy barriers of the CH₃O isomerization into CH₂OH, the CH₃O + H₂O, CH₃O + NH₃, and CH₃O + HF reactions with zero-point energy involved at 0 K (kcal mol⁻¹)^a

Methods	TS1	UE	TS2	UE	TS3	UE	TS4	UE
a Unsigned error (UE) obtained via the absolute value of the difference between the computed barrier heights and the benchmark barrier heights.
W3X-L//CCSD(T)-F12a/VDZ-F12	29.56	0.00	24.17	0.00	15.21	0.00	23.82	0.00
W2X//CCSD(T)-F12a/VDZ-F12	29.64	0.08	24.26	0.09	15.26	0.05	24.30	0.48
W2X//QCISD/cc-pVTZ	29.07	0.49	23.82	0.35	14.65	0.56	23.86	0.04
W3X-L//QCISD/cc-pVTZ	28.99	0.57	23.74	0.43	14.62	0.59	23.32	0.50
W1U	29.69	0.13	24.72	0.55	15.32	0.11	25.39	1.57
W1BD	29.88	0.32	24.88	0.71	15.47	0.26	25.11	1.29
mPW2PLYP/MG3S	31.33	1.77	24.15	0.02	15.48	0.27	22.92	0.90
M06-2X/MG3S	30.39	0.83	23.19	0.98	15.71	0.50	23.07	0.75
G4	30.09	0.53	25.87	1.70	15.97	0.76	25.55	1.73
CBS-QB3	29.74	0.18	25.24	1.07	15.06	0.15	27.62	3.80
M05-2X/aug-cc-pVTZ	29.90	0.34	21.35	2.82	15.16	0.05	20.41	3.41
M05-2X/maug-cc-pVTZ	30.04	0.48	21.65	2.52	15.40	0.19	20.80	3.02

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Fig. 2 The unsigned error for the energy barrier of unimolecular isomerization reaction of CH₃O to CH₂OH.

3.2. The bimolecular reactions of CH₃O with H₂O, NH₃, and HF

The unimolecular isomerization of CH₃O into CH₂OH catalyzed by H₂O, NH₃, and HF occurs via the prereactive complex before the corresponding transition state and subsequently undergo the postreactive complex responsible for the formation of CH₂OH as shown in Fig. 1. For example, when water acts as a catalyst, the hydrogen atom of CH₃O is transferred to the oxygen atom in H₂O and simultaneously the hydrogen atom of H₂O is transferred to the terminal oxygen atom in CH₃O responsible for the formation of CH₂OH. The recent investigations have indicated that the energy barrier with water catalysis is 25.7 (ref. 36) and 22.9 (ref. 22) kcal mol⁻¹ at the CCSD(T)/aug-cc-pVTZ//QCISD/6-31G(d) and CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ, respectively, which is 2.8 kcal mol⁻¹ difference between the CCSD(T)/aug-cc-pVTZ//QCISD/6-31G(d) and CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ calculated results; this reflects that higher-level theoretical methods are necessary to obtain reliable results. Thus, we calculate the energy barrier of the unimolecular isomerization of CH₃O into CH₂OH with water as a catalyst usingW3X-L//CCSD(T)-F12a/VDZ-F12 theoretical method. The computed energy barrier is 24.17 kcal mol⁻¹ in Table 1. Additionally, Fig. 3 shows that the UEs are 0.02, 0.55, and 0.71 kcal mol⁻¹ for the mPW2PLYP/MG3S, W1U, and W1BD theoretical methods, respectively, comparing with the barrier height of TS2 calculated by W3X-L//CCSD(T)-F12a/VDZ-F12.

Fig. 3 The unsigned error for the energy barrier of CH₃O + H₂O.

Previous investigations have shown that ammonia has remarkably catalytic role in hydrogen transfer processes in the H₂SO₄⋯NH₃ + OH,³⁰ CF₃OH + NH₃,³⁷ SO₃ + H₂O + NH₃ (ref. 87) reactions. Herein, we investigate the CH₃O + NH₃ reaction, resulting in the formation CH₂OH and NH₃, where NH₃ is acted as a catalyst. The optimized geometries of the transition state TS3 are provided in Fig. 1. The energy barrier of the CH₃O + NH₃ reaction is 15.21,15.26 kcal mol⁻¹ using the best W3X-L//CCSD(T)-F12a/VDZ-F12 method, W2X//CCSD(T)-F12a/VDZ-F12 method in Table 1, which shows that the beyond-CCSD(T) calculations are not necessary for obtain quantitative results; this shows that there are not multireference features in the CH₃O + NH₃ reaction. In addition, the QCISD-optimized geometries and frequency calculations are still not adequate accurate to obtain quantitative results because the UE of W3X-L//QCISD/VTZ is 0.59 kcal mol⁻¹, comparing with the results calculated by W3X-L//CCSD(T)-F12a/VDZ-F12 in Table 1. The calculated results also shows that NH₃ has much stronger catalytic ability in the isomerization reaction of CH₃O to CH₂OH than H₂O because the energy of the CH₃O + NH₃ reaction is about 9 kcal mol⁻¹ lower than that of the CH₃O + H₂O reaction, which also agree with the previous investigation in the CF₃OH + NH₃ reaction.³⁷ It is noted the UE of M05-2X/aug-cc-pVTZ is only 0.05 kcal mol⁻¹ in Table 1 and Fig. 4. Thus, the M05-2X/aug-cc-pVTZ theoretical method is chosen to do direct dynamics calculations in the CH₃O + NH₃ reaction.

Fig. 4 The unsigned error for the energy barrier of CH₃O + NH₃.

When HF is acted as a catalyst in the CH₃O + HF reaction responsible for the formation of CH₂OH, the energy barrier is decreased to 23.82 kcal mol⁻¹ in the CH₃O + HF reaction from 29.56 kcal mol⁻¹ in the unimolecular reaction of CH₃O to CH₂OH at the W3X-L//CCSD(T)-F12a/VDZ-F12 level in Table 1. In addition, it is particularly noted that the difference in the energy of the CH₃O + HF reaction between W3X-L/CCSD(T)-F12 and W2X//CCSD(T)-F12a/VDZ-F12 is about 0.5 kcal mol⁻¹, which shows that there are certain multireference features for the transition state TS4; this reveals that different catalyst may lead to the variation of nature of electronic structures in the transition states. Also, the W3X-L//QCISD/VTZ energy barrier is estimated to be 23.32 kcal mol⁻¹, which is about 0.5 kcal mol⁻¹ different from the W3X-L//CCSD(T)-F12a/VDZ-F12 in TS4; this shows that the QCISD/VTZ-optimized geometries and calculated frequencies still present unreliable results in estimating rate constants quantitatively for hydrogen transfer systems. It is noted that the CBS-QB3 result is 27.62 kcal mol⁻¹ and the M05-2X/aug-cc-pVTZ result is 20.41 kcal mol⁻¹ as listed in Table 1. The difference between CBS-QB3 and M05-2X/aug-cc-pVTZ is about 7.21 kcal mol⁻¹. However, compared with the benchmark result of 23.82 kcal mol⁻¹, the CBS-QB3 method overestimates the barrier height, while the M05-2X/aug-cc-pVTZ method underestimates the barrier in TS4. The UE of M06-2X/MG3S is about 0.75 kcal mol⁻¹, which is the best functional for the CH₃O + HF reaction as shown in Table 1 and Fig. 5.

Fig. 5 The unsigned error for the energy barrier of CH₃O + HF.

3.3. Rate constants

The calculated rate constants are presented in Table 2, where lists that the rate constants of the four reactions investigated herein are calculated using canonical variational transition-state theory with small curvature tunneling (CVT/SCT) in the temperature range of 210–350 K. Tunneling transmission coefficients are listed in Table 2, which shows that the tunneling transmission coefficients are very large for the hydrogen atom transfer process at 210 K. Furthermore, the tunneling transmission coefficient in the unimolecular isomerization of CH₃O to CH₂OH is even larger than the other reaction; in particular it is 3.29 × 10¹² at 210 K (Table 2). It is also noted that tunneling effects are very remarkable in the CH₃O unimolecular isomerization into CH₂OH, CH₃O + H₂O, and CH₃O + HF reactions, while the CH₃O + NH₃ reaction is not remarkable. For example, the tunneling coefficients are 4.71 × 10⁴, 6.46 × 10², and 9.18 × 10³ remarkable in the CH₃O unimolecular isomerization into CH₂OH, CH₃O + H₂O, and CH₃O + HF reactions, while the tunneling coefficient in the CH₃O + NH₃ reaction is only 5.85 at 298 K (Table 2). It is particular noted that the energy barrier in the CH₃O + NH₃ reaction is the lowest of the four reactions; this shows that although NH₃ exerts the strongest catalytic role in the CH₃O unimolecular isomerization into CH₂OH for three different catalysts, NH₃ also reduces tunneling and consequently that the rate constants of the CH₃O + NH₃ reaction is still slow.

Table 2 The calculated unimolecular rate constants (k₁, s⁻¹) and the bimolecular reaction rate constants (k₂, k₃, and k₄, cm³ per molecule per s) of the CH₃O unimolecular isomerization into CH₂OH, CH₃O + H₂O, CH₃O + NH₃, and CH₃O + HF in the temperature range of 210–350 K^a

T/K	Γ^TS1	κ^TS1SCT	k1	Γ^TS2	κ^TS2SCT	k2	Γ^TS3	κ^TS3SCT	k3	Γ^TS4	κ^TS4SCT	k4
a Γ^TS1, Γ^TS2, Γ^TS3, and Γ^TS4 are the rate constant ratios of canonical variational transition state to transition state theory in the CH3O unimolecular isomerization, CH3O + H2O, CH3O + NH3, and CH3O + HF reactions. κ^TS1SCT, κ^TS2SCT, κ^TS3SCT, and κ^TS4SCT are tunneling coefficients in the CH3O unimolecular isomerization, CH3O + H2O, CH3O + NH3, and CH3O + HF reactions.
210	0.96	3.29 × 10^12	2.90 × 10^−6	0.95	5.34 × 10^7	1.36 × 10^−30	0.53	1.73 × 10^2	3.11 × 10^−27	0.92	6.87 × 10^9	4.53 × 10^−27
230	0.96	1.07 × 10^10	5.26 × 10^−6	0.95	1.18 × 10^6	4.20 × 10^−30	0.56	4.51 × 10^1	2.02 × 10^−26	0.92	9.48 × 10^7	6.89 × 10^−27
250	0.96	1.06 × 10^8	1.06 × 10^−5	0.96	6.26 × 10^4	1.42 × 10^−29	0.59	1.85 × 10^1	1.25 × 10^−25	0.93	3.01 × 10^6	1.13 × 10^−26
270	0.96	2.57 × 10^6	2.41 × 10^−5	0.96	6.54 × 10^3	5.12 × 10^−29	0.61	1.02 × 10^1	6.93 × 10^−25	0.93	1.86 × 10^5	2.02 × 10^−26
290	0.97	1.30 × 10^5	6.12 × 10^−5	0.96	1.15 × 10^3	1.92 × 10^−28	0.63	6.68 × 10^0	3.38 × 10^−24	0.94	1.98 × 10^4	3.89 × 10^−26
298	0.97	4.71 × 10^4	9.15 × 10^−5	0.96	6.46 × 10^2	3.27 × 10^−28	0.63	5.85 × 10^0	6.14 × 10^−24	0.94	9.18 × 10^3	5.17 × 10^−26
310	0.97	1.20 × 10^4	1.72 × 10^−4	0.96	3.02 × 10^2	7.27 × 10^−28	0.64	4.92 × 10^0	1.44 × 10^−23	0.94	3.29 × 10^3	8.07 × 10^−26
330	0.97	1.83 × 10^3	5.28 × 10^−4	0.96	1.08 × 10^2	2.72 × 10^−27	0.66	3.91 × 10^0	5.37 × 10^−23	0.94	7.87 × 10^2	1.78 × 10^−25
350	0.97	4.20 × 10^2	1.73 × 10^−3	0.96	4.88 × 10^1	9.91 × 10^−27	0.67	3.26 × 10^0	1.78 × 10^−22	0.94	2.54 × 10^2	4.09 × 10^−25

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The variational effects are also different from each other in Table 2. Of particular interest is the obvious variational effects in the CH₃O + NH₃, leading in further decreasing the rate constants of the CH₃O + NH₃ reaction. Thus, the catalyst not only has influences on the energy barriers, but affects on tunneling and variational effects of transition states.

It is worth noting that the rate constants of these reactions are increased with the increase of temperature. At 298 K, the rate constants of the CH₃O isomerization into CH₂OH, CH₃O + H₂O, CH₃O + NH₃, and CH₃O + HF reactions are 9.15 × 10⁻⁵ s⁻¹, 3.27 × 10⁻²⁸ cm³ per molecule per s, 6.14 × 10⁻²⁴ cm³ per molecule per s, and 5.17 × 10⁻²⁶ cm³ per molecule per s, respectively. In addition, note that k₄ is estimated to be 6.89 × 10⁻²⁷–4.09 × 10⁻²⁵ cm³ per molecule per s between 230 and 350 K, while k₃ is computed 2.02 × 10⁻²⁶–1.78 × 10⁻²² cm³ per molecule per s between 230 and 350 K; this shows k₃ is larger than k₄. However, in 210 K k₄ is calculated to be 4.53 × 10⁻²⁷ cm³ per molecule per s, which is slightly larger than that of k₃ (3.11 × 10⁻²⁷ cm³ per molecule per s) because the tunneling of TS4 is 6.87 × 10⁹, which is much larger than that of TS3 (1.73 × 10²).

3.4. Atmospheric implications

The calculated atmospheric lifetimes are provided in Table 3. With regard to the unimolecular reaction, τ_TS1 is calculated by , where k₁ is the unimolecular rate constant of the reaction TS1, while for bimolecular reactions, τ_TS2, τ_TS3, τ_TS4 are calculated by , , , where k₂, k₃, and k₄ are the bimolecular rate constants of the reactions TS2, TS3, and TS4, respectively, and [H₂O] is the concentration of H₂O is 4.4 × 10¹⁷ molecule per cm³,⁸⁸ [NH₃] is the concentration of NH₃ is 1.32 × 10¹² molecule per cm³,^89,90 and [HF] is the concentration of HF is 1.8 × 10⁷ molecule per cm³,⁸⁸ respectively in Table 3. With regard to the bimolecular reactions of CH₃O + H₂O, CH₃O + NH₃, and CH₃O + HF, the atmospheric lifetimes are determined by both the rate constant and the corresponding concentrations of these catalysts in the atmosphere.

Table 3 The corresponding atmospheric lifetimes (s) at different temperature

T/K	τTS1^a	τTS2^b	τTS3^b	τTS4^b
a For the unimolecular reaction, , where k1 is the unimolecular rate constant of the reaction TS1.b For bimolecular reactions, , , , where k2, k3, and k4 are the bimolecular rate constants of the reactions TS2, TS3, and TS4, respectively, and [H2O] is the concentration of H2O is 4.4 × 10^17 molecule per cm^3,^88 [NH3] is the concentration of NH3 is 1.32 × 10^12 molecule per cm^3,^94,95 and [HF] is the concentration of HF is 1.8 × 10^7 molecule per cm^3,^88 respectively.
210	3.4 × 10^5	1.7 × 10^12	2.4 × 10^14	1.2 × 10^19
230	1.9 × 10^5	5.4 × 10^11	3.8 × 10^13	8.1 × 10^18
250	9.4 × 10^4	1.6 × 10^11	6.1 × 10^12	4.9 × 10^18
270	4.1 × 10^4	4.4 × 10^10	1.1 × 10^12	2.8 × 10^18
290	1.6 × 10^4	1.2 × 10^10	2.2 × 10^11	1.4 × 10^18
298	1.1 × 10^4	7.0 × 10^9	1.2 × 10^11	1.1 × 10^18
310	5.8 × 10^3	3.1 × 10^9	5.3 × 10^10	6.9 × 10^17
330	1.9 × 10^3	8.4 × 10^8	1.4 × 10^10	3.1 × 10^17
350	5.8 × 10^2	2.3 × 10^8	4.3 × 10^9	1.4 × 10^17

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The calculated results show that the direct unimolecular reaction of CH₃O to CH₂OH dominates the sink of CH₃O. In particular, the atmospheric lifetime of the direct unimolecular reaction of CH₃O to CH₂OH is 5.8 × 10² s at 350 K (Table 3). The rate constants of the CH₃O + H₂SO₄ and CH₃O + HCOOH reactions are 9.12 × 10⁻¹⁴, 4.19 × 10⁻¹⁶ cm³ per molecule per s, respectively at 298 K.³⁶ In the atmosphere, the concentration of H₂SO₄ is in the range of 10⁴–4 × 10⁸ molecules·per cm³.^91–93 When the upper limit concentration of sulfuric acid is considered, the atmospheric lifetime of CH₃O in the CH₃O + H₂SO₄ reaction is 2.7 × 10⁴ s at 298 K. The gas-phase concentration of formic acid is 1.1 × 10¹¹ molecules·per cm³.⁹³ The corresponding atmospheric lifetime is 2.2 × 10⁴ s at 298 K. However, the atmospheric lifetime is 1.1 × 10⁴ s for the direct unimolecular isomerization reaction of CH₃O to CH₂OH at 298 K, which shows that the direct unimolecular reaction of CH₃O to CH₂OH can compete well with the corresponding bimolecular reaction of CH₃O + H₂SO₄ and CH₃O + HCOOH.

4. Concluding remarks

The unimolecular reaction of CH₃O to CH₂OH catalyzed by different catalysts has been investigated by combining with W3X-L//CCSD(T)-F12a/VDZ-F12 benchmark calculations, the validated density functional, and canonical variational transition-state theory with small curvature tunneling. The main conclusions are extracted from the results as follows.

(1) We considered significant pathways for the isomerization of CH₃O to CH₂OH via the reactions with water, ammonia, and hydrofluoric acid. The results show that different catalysts can decrease the energy barrier of the unimolecular isomerization of CH₃O to CH₂OH. The reductions of energy barriers for the isomerization of CH₃O to CH₂OH catalyzed by water, ammonia, and hydrofluoric acid are 5.39, 14.35, and 5.74 kcal mol⁻¹, respectively, comparing with the energy barrier of the isomerization of CH₃O to CH₂OH without catalyst. Thus, the result shows that ammonia has the best catalytic ability among the three catalysts.

(2) We tabulate the unsigned error (UE) of the tested methods as listed in Table 1. The calculated results also show that the different functionals with basis sets have different accuracy. Among the functionals, the best method for the unimolecular isomerization of methoxy to hydroxymethyl and the bimolecular reaction of CH₃O with NH₃ are M05-2X/aug-cc-pVTZ. And, the best method for the bimolecular reactions of CH₃O with H₂O and HF are mPW2PLYP/MG3S and M06-2X/MG3S, respectively.

(3) The calculated rate constants show that catalysts can affect variational effects of transition states and tunneling. In addition, we show that the atmospheric lifetime of CH₃O is mainly determined by the direct unimolecular reaction of CH₃O to CH₂OH due to tunneling, which has not been previously considered.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This research is supported by National Natural Science Foundation of China (41775125 and 41165007), Science and Technology Foundation of Guizhou Province & Guizhou Minzu University, China([2015]7211), Science and Technology Foundation of Guizhou Provincial Department of Education, China ([2015]350).

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Footnotes

† Electronic supplementary information (ESI) available: Table S1 listing barrier heights at different theoretical methods and Table S2 providing Cartesian coordinates. See DOI: 10.1039/c7ra09167b

‡ Mei-Ling Wei and Xing-Feng Tan contributed equally.

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