Atmospheric chemistry of CH 3 O: its unimolecular reaction and reactions with H 2 O, NH 3 , and HF †

We have investigated the hydrogen atom transfer processes of CH 3 O to CH 2 OH without catalyst and with water, ammonia, and hydro ﬂ uoric 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 di ﬀ erent functionals with the unsigned errors (UEs) of 0.34, 0.02, 0.05, and 0.75 kcal mol (cid:1) 1 for its unimolecular reaction and reactions with H 2 O, NH 3 , and HF, respectively. The calculated results show that NH 3 exerts the strongest catalytic role in the isomerization reaction of CH 3 O to CH 2 OH, compared with H 2 O and HF. In addition, the calculated rate constants show that the e ﬀ ect of tunneling increases the rate constant of the unimolecular reaction of CH 3 O by 10 2 – 10 12 times in the temperature range of 210 – 350 K. Moreover, the variational e ﬀ ects of the transition state are obvious in CH 3 O + NH 3 . The calculated results also show that the direct unimolecular reaction of CH 3 O to CH 2 OH is dominant in the sink of CH 3 O, compared with the CH 3 O + H 2 SO 4 , CH 3 O + HCOOH, CH 3 O + H 2 O, CH 3 O + NH 3 , and CH 3 O + HF reactions in the atmosphere. The present results provide a new insight into catalysts that not only a ﬀ ect energy barriers, but have in ﬂ uences on tunneling and variational e ﬀ ects of transition states. The present ﬁ ndings should have broad implications in computational chemistry and atmospheric chemistry.


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 (CH 3 O) is one of the simplest alkoxy radicals. 2 CH 3 O is produced from OH-initiated oxidation of CH 4 . 2 In the atmosphere, CH 3 O undergoes unimolecular isomerization and decomposition and bimolecular reaction. 1 While CH 3 O dominantly reacts with O 2 , responsible for the formation of HCHO and HO 2 , the CH 2 OH + O 2 reaction is 10 4 times faster than the CH 3 O + O 2 reaction, where CH 2 OH is formed through the hydrogen atom transfer of CH 3 O. [3][4][5] Therefore, Radford stated that the isomerization reaction of CH 3 O could be an important process for the loss of CH 3 O. 6 Exploring the unimolecular isomerization of CH 3 O is required to estimate the fate of CH 3 O in the atmosphere.
The reaction kinetics and dynamics of methoxy radicals (CH 3 O) has been extensively investigated for both experimental and theoretical methods in the literature. 1,[7][8][9][10][11][12][13][14][15][16][17][18][19] However, the kinetics of the unimolecular isomerization reaction of CH 3 O remains unclear. With regard to the unimolecular reaction of CH 3 O, the energy barrier is very high, in the range of 26-36 kcal mol À1 , depending on different theoretical methods. 14,16,[20][21][22] For example, Batt et al. 16 estimated an energy barrier of 26.1 kcal mol À1 , Tachikawa et al. 22 reported an energy barrier of 32.88 kcal mol À1 calculated by CCSDST4/D95V**, Saebo et al. 14 reported an energy barrier of 36 kcal mol À1 calculated by MP3/6-31G**. This uncertainty of energy barrier of CH 3 O unimolecular isomerization leads to the difficulty in quantitatively estimating the rate constant of CH 3 O unimolecular isomerization reaction. In addition, CH 3 O 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][26][27][28] CH 3 OH + OH, 29 OH + H 2 SO 4 /NH 3 , 30 unimolecular rearrangement of Rh(PH 3 ) 2 ClCH 4 , 31 H/D + CO, 32,33 H/D + CH 3 OH, 34 and Al + 3H 2 O. 35 Therefore, it is necessary to reevaluate kinetics of the unimolecular isomerization reaction of CH 3 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 À1 , respectively. 36 In particular, the calculated results are 25.7 kcal mol À1 by Buszek et al. 36 and 22.9 kcal mol À1 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 CH 3 O isomerization of the energy barrier has difference of 2-3 kcal mol À1 . 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 Hydrouoric acid is an important inorganic acid in the atmosphere. So, we calculated the H 2 O, NH 3 , and HF as catalysts in the unimolecular isomerization reaction of CH 3 O.
In this work, we investigated the hydrogen atom transfer processes of CH 3 O to CH 2 OH catalyzed by water, ammonia, and hydrouoric 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: where M stands for H 2 O, NH 3 , and HF. The purpose of this work is to determine which functional is best for every specic 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 denitive examples how to use theoretical methods to predict the quantitative rate constants for hydrogen atom transfer reactions.

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][39][40] and QCISD/VTZ 41 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 W2X 42 and W3X-L 42 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 CH 3 O to CH 2 OH 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 SO 2 with OH, 43 and HO 2 with XCHO 44 to obtain rate constants with experimental accuracy.

Composite method calculation
Quantum chemical composite methods have developed because they approaches CCSD(T)/CBS. 45 We used G4, 45

Reaction kinetics
The rate constants were calculated using canonical variational transition-state theory with small curvature tunneling (CVT/ SCT). 77

Results and discussion
We have obtained the benchmark barrier heights of CH 3 O to CH 2 OH without catalyst and with water, ammonia, and hydro-uoric acid as catalysts using W3X-L//CCSD(T)-F12a/VDZ-F12 methods. We dened 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.

The unimolecular isomerization of CH 3 O
The unimolecular isomerization of CH 3 O into CH 2 OH occurs via the transfer of the hydrogen atom of CH 3 group to the oxygen atom in CH 3 O responsible for the formation of CH 2 OH as shown in Fig. 1. The unimolecular isomerization of CH 3 O into CH 2 OH has been extensively studied using different theoretical methods; the previous calculated results indicated that the barrier heights of the unimolecular isomerization of CH 3 O into CH 2 OH are varies between 26.1 and 36.0 kcal mol À1 . 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 À1 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 À1 using W1U, CBS-QB3, W1BD, and M05-2X/augcc-pVTZ, respectively; this results reect slight changes for different theoretical methods. Therefore, the barrier height of the unimolecular isomerization of CH 3 O into CH 2 OH is computed to be 29.56 kcal mol À1 (W3X-L//CCSD(T)-F12a/VDZ-F12), which should be reliable. The W2X//CCSD(T)-F12a/VDZ-F12 result is 29.64 kcal mol À1 , which agrees well with the value of 29.56 kcal mol À1 ; this shows that the electronic Fig. 1 Variation in potential energy surface for the reactants, intermediates, transition states, and products of the CH 3 O isomerization into CH 2 OH 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, 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 CH 3 O + NH 3 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 À1 , comparing with the results calculated by W3X-L//CCSD(T)-F12a/VDZ-F12 in Table 1. The calculated results also shows that NH 3 has much stronger catalytic ability in the isomerization reaction of CH 3 O to CH 2 OH than H 2 O because the energy of the CH 3 O + NH 3 reaction is about 9 kcal mol À1 lower than that of the CH 3 O + H 2 O reaction, which also agree with the previous investigation in the CF 3 OH + NH 3 reaction. 37 It is noted the UE of M05-2X/aug-cc-pVTZ is only 0.05 kcal mol À1 in Table 1 and Fig. 4. Thus, the M05-2X/aug-cc-pVTZ theoretical method is chosen to do direct dynamics calculations in the CH 3 O + NH 3 reaction.
When HF is acted as a catalyst in the CH 3 O + HF reaction responsible for the formation of CH 2 OH, the energy barrier is decreased to 23.82 kcal mol À1 in the CH 3 O + HF reaction from 29.56 kcal mol À1 in the unimolecular reaction of CH 3 O to CH 2 OH 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 CH 3 O + HF reaction between W3X-L/CCSD(T)-F12 and W2X//CCSD(T)-F12a/VDZ-F12 is about 0.5 kcal mol À1 ,  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 À1 , which is about 0.5 kcal mol À1 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 À1 and the M05-2X/aug-cc-pVTZ result is 20.41 kcal mol À1 as listed in Table 1. The difference between CBS-QB3 and M05-2X/aug-cc-pVTZ is about 7.21 kcal mol À1 . However, compared with the benchmark result of 23.82 kcal mol À1 , 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 À1 , which is the best functional for the CH 3 O + HF reaction as shown in Table 1 and Fig. 5.

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 transitionstate 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 CH 3 O to CH 2 OH is even larger than the other reaction; in particular it is 3.29 Â 10 12 at 210 K ( Table 2). It is also noted that tunneling effects are very remarkable in the CH 3 Table 2). It is particular noted that the energy barrier in the CH 3 O + NH 3 reaction is the lowest of the four reactions; this shows that although NH 3 exerts the strongest catalytic role in the CH 3 O unimolecular isomerization into CH 2 OH for three different catalysts, NH 3 also reduces tunneling and consequently that the rate constants of the CH 3 O + NH 3 reaction is still slow.
The variational effects are also different from each other in Table 2. Of particular interest is the obvious variational effects in the CH 3 O + NH 3 , leading in further decreasing the rate constants of the CH 3 O + NH 3 reaction. Thus, the catalyst not only has inuences 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 CH 3 O isomerization into CH 2 OH, CH 3 O + H 2 O, CH 3 O + NH 3 , and CH 3 O + HF reactions are 9.15 Â 10 À5 s À1 , 3.27 Â 10 À28 cm 3 per molecule per s, 6.14 Â 10 À24 cm 3 per molecule per s, and 5.17 Â 10 À26 cm 3 per molecule per s, respectively. In addition, note that k 4 is estimated to be 6.89 Â 10 À27 -4.09 Â 10 À25 cm 3 per molecule per s between 230 and 350 K, while k 3 is computed 2.02 Â 10 À26 -1.78 Â 10 À22 cm 3 per molecule per s between 230 and 350 K; this shows k 3 is larger than k 4 . However, in 210 K k 4 is calculated to be 4.53 Â 10 À27 cm 3 per molecule per s, which is slightly larger than that of k 3 (3.11 Â 10 À27 cm 3 per molecule per s) because the tunneling of TS4 is 6.87 Â 10 9 , which is much larger than that of TS3 (1.73 Â 10 2 ).

Atmospheric implications
The calculated atmospheric lifetimes are provided in Table 3. With regard to the unimolecular reaction, s TS1 is calculated by

Concluding remarks
The unimolecular reaction of CH 3 O to CH 2 OH 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 signicant pathways for the isomerization of CH 3 O to CH 2 OH via the reactions with water, ammonia, and hydrouoric acid. The results show that different catalysts can decrease the energy barrier of the unimolecular isomerization of CH 3 O to CH 2 OH. The reductions of energy barriers for the isomerization of CH 3 O to CH 2 OH catalyzed by water, ammonia, and hydrouoric acid are 5.39, 14.35, and 5.74 kcal mol À1 , respectively, comparing with the energy barrier of the isomerization of CH 3 O to CH 2 OH 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 CH 3 O with NH 3 are M05-2X/aug-cc-pVTZ. And, the best method for the bimolecular reactions of CH 3 O with H 2 O 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 CH 3 O is mainly determined by the direct unimolecular reaction of CH 3 O to CH 2 OH due to tunneling, which has not been previously considered. Table 2 The calculated unimolecular rate constants (k 1 , s À1 ) and the bimolecular reaction rate constants (k 2 , k 3 , and k 4 , cm 3 per molecule per s) of the CH 3 O unimolecular isomerization into CH 2 OH, CH 3 O + H 2 O, CH 3 O + NH 3 , and CH 3 O + HF in the temperature range of 210-350 K a