Ab Initio Chemical Kinetics for Oxidation of CH3OH by N2O4: Elucidation of the Mechanism for Major Product Formation and Its Relevancy to Tropospheric Chemistry

Next to CH4, CH3OH is the most abundant C1 organics in the troposphere. The redox reaction of CH3OH with N2O4 had been shown experimentally to produce CH3ONO, instead of CH3ONO2. The mechanism for the reaction remains unknown to date. We have investigated the reaction by ab initio MO calculations at the UCCSD(T)/6-311+G(3df,2p)//UB3LYP/6-311+G(3df,2p) level. The result indicates that the reaction takes place primarily by the isomerization of N2O4 to ONONO2 through a very loose transition state within the N2O4–CH3OH collision complex with a 14.3 kcal/mol barrier, followed by the rapid attack of ONONO2 at CH3OH producing CH3ONO and HNO3. The predicted mechanism for the redox reaction compares closely with the hydrolysis of N2O4. The computed rate constant, k1 = 1.43 × 10–8 T1.96 exp (−9092/T) (200–2000 K) cm3molecule–1s–1, for the formation of CH3ONO and HNO3 agrees reasonably with available low-temperature kinetic data and is found to be similar to that of the isoelectronic N2O4 + CH3NH2 reaction. We have also estimated the kinetics for the termolecular reaction, 2 NO2 + CH3OH, and compared it with the direct bimolecular process; the latter was found to be 4.4 × 105 times faster under the troposphere condition. On the basis of the known pollution levels of NO2, N2O4, and CH3OH, both processes were estimated to be of negligible importance to tropospheric chemistry, however.


INTRODUCTION
CH 3 OH is known to be an important organic pollutant in the troposphere with concentrations averaged to be 600 pptv, next to that of CH 4 . 1 The origin of CH 3 OH is primarily of terrestrial rather than anthropogenic sources.In the troposphere, CH 3 OH may be removed by reactions with various known radicals such as OH and NO 3 ; among them, the destruction by OH is dominant on account of its high reactivity and concentration in the troposphere. 2In addition, oxidation by larger nitrogen oxides, N 2 O x (x = 4 and 5), is also possible under the tropospheric condition as discussed recently by Trac et al. 3 and by Sarkar and Bandyopadhyay 4 on the reactivities of N 2 O 4 and N 2 O 5 toward NH 3 , respectively.The rate of the former redox process was predicted to be about 100 times faster than that of the latter under the tropospheric condition, although the concentration of N 2 O 4 is known to be lower than that of N 2 O 5 . 3he facile reaction of N 2 O 4 with CH 3 OH at low temperatures was first reported by Harris and Siegel who noted the disappearance of NO 2 upon mixing. 5Joffe and Gray identified methyl nitrite (CH 3 ONO) and nitric acid as the products of the reaction but not methyl nitrate (CH 3 ONO 2 ). 6he first kinetic measurement for the N 2 O 4 + CH 3 OH reaction and several other small alcohols was carried out by Fairlie et al. 7  .−14 Significantly, the roaming-like TS was also found to exist in the condensed phases including H 2 O 13 and solid N 2 H 4 , 14 in which the isomerization reaction produces the reactive ONONO 2 isomer within the solid lattice producing N 2 H 5 + ONO 2 − with a large 70 kcal/mol exothermicity.The half-life of an embedded N 2 O 4 in solid N 2 H 4 at 218 K was predicted to be 0.5 s, which could reasonably explain the explosion observed when the N 2 O 4 − N 2 H 4 solid mixture was warmed up slowly from 77 to 218 K during an experiment. 14Parenthetically, it should be mentioned that the conventional isomerization energies for N 2 O 4 → ONONO 2 reported in the literature lie in the range of 30−45 kcal/mol, 13 too high for the hypergolic reactions of N 2 O 4 with hydrazines to occur. 11,12,14n the present study, we investigate the mechanism for the redox reaction of N 2 O 4 with CH 3 OH producing the experimentally observed products, CH 3 ONO and HNO 3 by quantum-chemical calculations.If the mechanism of this reaction is similar to those of its isoelectronic analogues, CH 3 NH 2 3 and NH 2 NH 2 , 11 then one would expect the production of CH 3 ONO + HNO 3 and CH 3 NO 3 + HONO via a fast and a slow reaction channel, respectively.The significance of CH 3 ONO formation under the tropospheric condition will be examined on the basis of the predicted kinetics.

Ab Initio Calculations.
The electronic structures of all species involved in the oxidation of CH 3 OH by N 2 O 4 were optimized with UB3LYP/6-311+G(3df,2p), 15 including the association step 2NO 2 + CH 3 OH.To improve energy prediction accuracy, the UCCSD(T)/6-311+G(3df,2p) method was employed with the UB3LYP/6-311 + G(3df,2p) optimized structures.For the heats of reactions forming different products, we have also compared the results obtained with the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ method based on the structures optimized with the M06-2X/aug-cc-pVTZ method.Vibrational frequencies of all species involved were calculated at the same level employed for optimization; they were utilized to characterize the stationary points and for ZPE corrections.Unless specified otherwise, all energies cited below are obtained with the UCCSD(T)/6-311+G(3df,2p)//UB3LYP/6-311 + G(3df,2p) method.IRC analyses 16 have been carried out to confirm the connectivity of TSs with reactants and products.In the present work, all the calculations were performed using the Gaussian 16 program. 17.2.Kinetic Calculations.The kinetics for the reaction of N 2 O 4 with CH 3 OH was calculated using the Variflex program.18 We employed the canonical transition-state theory (TST) 19 to predict rate constants for a simple exchange reaction, while the RRKM theory 20 was employed to predict the kinetics of a reaction taking place via a long-lived intermediate by solving the 1-D master equation.We utilized the microcanonical TST 21

The Journal of Physical Chemistry A
G(3df,2p) and M06-2X/aug-cc-pVTZ; the result presented in the table indicates that both approaches agree closely, although the former appears to give values of Δ r H o with a slightly better agreement with available experimental data.
In Figure 1, the reaction occurs through the N 2 O 4 :CH 3 OH (LM1) complex with a binding energy of 6.4 kcal/mol, which is slightly more stable than that of the N 2 O 4 /H 2 O complex, 5.0 kcal/mol, 13 but is very close to its isoelectronic N 2 O 4 / NH 2 NH 2 complex, 6.7 kcal/mol 11 , and N 2 O 4 /CH 3 NH 2 complex, 6.8 kcal/mol. 3In the present reaction, the LM1 complex can undergo further reaction by lengthening N 2 O 4 's N−N bond to 3.343 Å concurrently rotating one of its NO 2 groups at TS1 forming the ONONO 2 /CH 3 OH (LM2) complex, which lies 2.9 kcal/mol above the reactants or 9.3   The Journal of Physical Chemistry A kcal/mol above LM1.The bond ON−ONO 2 in the LM2 complex is lengthened to 1.854 Å, which is similar to those in the ONONO 2 /NH 2 NH 2 complex, 2.282 Å 11 , and ONONO 2 / CH 3 NH 2 complex, 2.092 Å. 3 Both are longer than those in cisand trans-ON-ONO 2 isomers, 1.685, and 1.622 Å, respec-tively, 13  ].Mulliken charge analysis shows that the NO and NO 3 group charges are +0.367 and −0.507e, respectively (Figure 3).
In the present case, the same roaming-like TS TS1 exists for the isomerization of N 2 O 4 to trans-ONONO 2 , with a barrier of 7.9 kcal/mol (or 14.3 kcal/mol above LM1), which is again very similar to those of the two isoelectronic systems:   The Journal of Physical Chemistry A mol, which may be attributed to the complexation effect.Other examples on the effect can be found in Table 3.
From LM1, another reaction path involves an H-transfer from CH 3 OH to N 2 O 4 via a tight five-member-ring TS (TS3) with a 28.1 kcal/mol barrier (or 34.5 kcal/mol above LM1) producing CH 3 ONO 2 + trans-HONO.The reaction was predicted to be exothermic by 2.5 kcal/mol, which is exactly the same as the formation of CH 3 ONO + HNO 3 .This product channel cannot compete with the RTS-like channel producing CH 3 ONO and HNO 3 ; it is kinetically unimportant.
In Table 2, the relative energies of all TSs and intermediates computed at UB3LYP/6-311+G(3df,2p) and UCCSD(T)/6-311+G(3df,2p)//UB3LYP/6-311+G(3df,2p) are summarized for a more convenient inspection.In Table 3, we compare the energies of LM1, TS1, LM2, and TS2 relative to each pair of the reactants, from N 2 O 4 hydrolysis 13 to N 2 O 4 −hydrazine rocket propellants, 11,12,14 and to the reactions relevant to tropospheric chemistry. 3The implication of these data will be remarked later.The prereaction complex LM1 with the small 6.4 kcal/mol well is expected to bring about a minor P effect below room temperature as shown in Figure 1S; the formation of CH 3 ONO + HNO 3 is, however, not affected by pressure as indicated in the figure.Because TS1 (7.9 kcal/mol) is much higher than TS2 (4.3 kcal/mol) and the well depth of LM2 is only 1.4 kcal/mol, as alluded to above, the kinetics of the N   The relative average concentration of NO 2 and N 2 O 4 in the troposphere in ppbv is known to be about 100:7 × 10 −5 . 1 We, therefore, attempted to estimate the termolecular rate constant for its potential contribution to the oxidation of CH 3 OH under the tropospheric condition.The method employed is similar to the one we used earlier for our quantitative interpretation of the termolecular kinetics for the 2NO 2 + H 2 O reaction, 22 which had been reliably measured in laboratories 23 for comparison.In the present system, we can approximately account for the formation of CH 3 ONO + HNO 3 by the stepwise mechanism 2NO ONONO 2 2 (2) CH OH ONONO CH ONO HNO The mechanism is similar to that invoked by Koda et al., 9 who initially assumed N 2 O 4 instead of ONONO 2 as the intermediate.However, based on their analysis of the measured NO 2 decay kinetics, they concluded that ONONO 2 , rather than N 2 O 4 , was actually involved in the reaction. 9Interestingly, this conclusion is consistent with the PES presented in Figure 1 predicted by our high-level quantum calculations.
The steady-state assumption for the unstable ONONO 2 intermediate leads to the rate for removal of CH 3 OH The 3 rate constants in eq 4 can be reliably predicted based on the energetics and structures computed at the UCCSD(T)/ 6-311+G(3df,2p)//UB3LYP/6-311+G(3df,2p) level.Our computed results at atmospheric pressure can be represented by the 3-parameter fitted Arrhenius equations  7 Nikki et al., 8 and Koda and co-workers 9 as aforementioned, we compare the predicted value of k tf with the experimental results as shown in Figure 6.The agreement between the theory and the available experimental values is seen to be quite reasonable.In the figure, we also compare the k tf for the 2NO 2 + CH 3 OH reaction with that of the analogous 2NO 2 + H 2 O → HONO + HNO 3 reaction measured experimentally by England and Corcoran 23 together with our previously computed result based on the analogous 3-step mechanism 22 shown above.In the case of the H 2 O reaction, the agreement between the theory and experiment is seen to be excellent, reflecting the validity of the predicted PES similar to the one shown in Figure 1.
The very different temperature dependences of the termolecular rate constants, as is evident in Figure 6, can be attributed to the strong positive temperature effect on k 3 for the ONONO 2 + H 2 O reaction (due to its high exit barrier) and the weak T effect on the ONONO 2 + CH 3 OH reaction as shown in Figure S3 because of its low exit barrier.

CONCLUDING REMARKS
In this study, we have investigated the mechanism for the redox reaction of N 2 O 4 with CH 3 OH by quantum-chemical calculations.The result of the calculations carried out at the UCCSD(T)/6-311+G(3df,2p)//UB3LYP/6-311 + G(3df,2p) level indicates that the favored reaction path affording the major products CH 3 ONO + HNO 3 as reported in 1951 by Joffe and Gray 6 was controlled by the isomerization process forming trans-ONONO 2 from N 2 O 4 in the presence of CH 3 OH during the bimolecular collision.The highly polar and reactive trans-ONONO 2 rapidly attacks the CH 3 OH molecule producing CH 3 ONO and HNO 3 via a 6-memberring TS with a negligible barrier.
For the N 2 O 4 → ONONO 2 isomerization via the roaminglike TS within the N 2 O 4 −CH 3 OH complex, the barrier was predicted to be 7.9 kcal/mol above the reactants (or 14.3 kcal/ mol from the prereaction complex).This barrier is significantly lower than the typical tight TS for the unimolecular isomerization (∼30−45 kcal/mol). 27The predicted rate constant for CH 3 ONO + HNO 3 formation can be given by k 1 = 1.43 × 10 −8 T 1.96 exp(−9092/T) cm 3 molecule −1 s −1 at T = 200−2000 K, independent of pressure.The result agrees very closely with that of the isoelectronic reaction N 2 O 4 + CH 3 NH 2 as shown in Figure S2.
We have also predicted the kinetics of the 2NO 2 + CH 3 OH termolecular reaction based on the mechanism employed for the analogous 2NO 2 + H 2 O → HONO + HNO 3 reaction. 22omparing our predicted second-and third-order rate constants with available, but scarce, experimental data in the literature for CH 3 OH reactions with N 2 O 4 and NO 2 , respectively, the agreement between theory and experiments by and large appears to be reasonable.
The unusual reaction mechanism revealed from this series of studies, starting from the hydrolysis of N 2 O 4 in the gas phase and in the H 2 O solution 13 to the hypergolic ignition of N 2 O 4 in contact with hydrazine propellants, 11,12,14 and the processes relevant to the tropospheric chemistry involving potential pollutants such as NH 3 3 and CH 3 OH indicate that the redox reactions occur via prereaction complexes with about 5 ± 1 kcal/mol binding energies which have only a negligible kinetic consequence except at low temperatures.The results were summarized in Table 3.The redox process starts from the isomerization of the symmetric N 2 O 4 to trans-ONONO 2 via a very loose, roaming-like TS1, lying above the complex well at about 14 ± 2 kcal/mol.The highly polar ONONO 2 isomer is much more reactive than N 2 O 4 toward the collision partner as is evident from the small TS2 barrier above LM2 in the present case (see Figure 1).However, the barrier at TS2 above LM2 for H 2 O was predicted to be about 10 kcal/mol, which may be compared with that of its isoelectronic reaction with NH 3 , 5.3 kcal/mol, and the very small value of 1.4 kcal/mol for CH 3 OH, reflecting entirely the strength of the bond to be broken by the abstraction reaction of the NO 3 group producing HNO 3 .
In view of the fact that both N 2 O 4 and CH 3 OH are known pollutants in the lower troposphere, we have examined the potential effect of the formation of CH 3 ONO and HNO 3 from their reaction based on the predicted kinetics given above.Based on the known concentration levels of N 2 O 4 24 and CH 3 OH, 26 the rate of their reaction at 298 K was found to be too slow to be relevant to the troposphere chemistry.
Studying the impact of pressure on the N We also want to thank the reviewers and the editor for their valuable comments and suggestions.
at 273−298 K following the NO 2 decay kinetics by visible light absorption; they reported a negative temperature dependence, obeying the third-order rate law, − d[NO 2 ]/dt = 2 k [NO 2 ] 2 [CH 3 OH], with k = 4.8 × 10 −37 cm 6 /molecule 2 -s at 298 K. Nikki and co-workers 8 investigated the reactions of NO 2 with CH 3 OH and C 2 H 5 OH by FTIR spectroscopy monitoring the growth of RONO which followed the rate law, d[RONO]/dt = k [NO 2 ] 2 [ROH] N 2 O 4 , or ONONO 2 , might be involved in the reaction giving CH 3 ONO + HNO 3 , instead of the more abundant symmetric N 2 O 4 .More recently, Wojcik-Pastuszka et al. 10 studied the reactions of N 2 O 4 with CH 3 OH and several other small alcohols between 293 and 358 K by UV−vis spectroscopy, which allowed them to detect not only NO 2 and N 2 O 4 but also the RONO products.The kinetics of these reactions were determined by measurement of NO 2 decay at 450 nm.They kinetically simulated the NO 2 decay− time profiles with the mechanism: 2 NO 2 ⇌ N 2 O 4 and N 2 O 4 + ROH ⇌ RONO + HNO 3 .The second-order rate constants for CH 3 ONO formation and its reverse reaction were reported in detail for the CH 3 OH reaction.To date, the mechanism for the N 2 O 4 reaction with CH 3 OH and other small alcohols remains unknown, however.The reactivity of N 2 O 4 toward NH 3 and RNH 2 , including methyl amine 3 (R = CH 3 ) and hydrazines 11,12 [R = NH 2 , CH 3 NH and (CH 3 ) 2 N], has been investigated recently by quantum-chemical and statistical-theory calculations in our laboratory.The high reactivity of these reactions was attributed to the unique property of N 2 O 4 , which can undergo isomerization producing a highly reactive isomer ONONO 2 via a roaming-like transition state (TS) during the course of bimolecular collisions by lengthening of the N−N bond (O 2 N−NO 2 ) and rotating one of the O 2 N groups to determine the association rate for a barrierless channel.The potential energy function for the barrierless step N 2 O 4 + CH 3 OH → N 2 O 4 /CH 3 OH (LM1) was estimated to cover the separation range of N 2 O 4 and CH 3 OH from 3.19 to13.19Å with a step size of 0.1 Å at the UB3LYP/ 6-311 + G(3df,2p) level.The Morse function D Vminimum energy path obtained by fully optimizing structures along the dissociation coordinate.Here, D e , R, and R e have their usual definitions.The calculated Morse function for N 2 O 4 :CH 3 OH (LM1) → N 2 O 4 + CH 3 OH can be represented with β = 1.38 Å −1 , and the corresponding value of D e is shown in Figure 1.
N 2 O 4 + NH 2 NH 2 5.9 kcal/mol and N 2 O 4 + CH 3 NH 2 8.0 kcal/mol.From LM2, the NO 3 group can abstract the H atom of the terminal OH group in CH 3 OH via TS2 with a very small barrier of 1.4 kcal/mol to give the postreaction complex LM3 (HNO 3 :CH 3 ONO) with 9.6 kcal/mol exothermicity.The complex can readily separate to produce the product pair CH 3 ONO + HNO 3 barrierlessly.To illustrate the effect of CH 3 OH complexation with N 2 O 4 , we have added the potential energy profile for the isomerization of N 2 O 4 to ONONO 2 without CH 3 OH predicted by Raghunath and Lin 13 at the UCCSD(T)/CBS level with Dunning's correlation consistent basis set (cc-pVXZ, where X = D, T, and Q) based on the optimized structures using UB3LYP/6-311+G(3df).The barrier for the isomerization, 12.8 kcal/mol, is lower than that from N 2 O 4 :CH 3 OH to ONONO 2 :CH 3 OH by 1.5 kcal/

Figure 3 .
Figure 3. Mulliken charges of species involved in the low-energy reaction path.

3 . 2 .
Kinetics of the Reaction.The kinetics of the N 2 O 4 + CH 3 OH reaction are primarily controlled by TS1 because TS2 lies 3.6 kcal/mol below TS1 with a small 1.4 kcal/mol barrier, producing the postreaction complex with 9.6 kcal/mol exothermicity.Their rate constants were computed with the RRKM theory using the Variflex program, in the 200−2000 K range.For the reaction of N 2 O 4 with CH 3 OH, the dominant product channel produces CH 3 ONO + HNO 3 , while the second channel is not considered due to its high barrier at TS3.The low-energy reaction path shown in Figure 1 can be given as follows

Figure 4
Figure 4 compares the predicted bimolecular rate constant for CH 3 ONO + HNO 3 production with the result of Wojcik-

Figure 4 .
Figure 4. Comparison of the predicted bimolecular rate constant for N 2 O 4 + CH 3 OH→CH 3 ONO + HNO 3 reaction with the values evaluated by Wojcik-Pastuszka et al.10 through kinetic modeling of NO 2 -time profiles.The third-order rate constants of both Nikki 8 and Koda9 were kinetically modeled by Wojcik-Pastuszka et al.10 to give the second-order rate constants as shown.

Figure 5 .
Figure 5.Comparison of the predicted bimolecular rate constant for the reverse reaction CH 3 ONO + HNO 3 →N 2 O 4 + CH 3 OH with the values evaluated by Wojcik-Pastuszka et al. 10 through kinetic modeling of NO 2 -time decay profiles.

Table 1 .
Comparison of the Predicted Heats of Reaction at 0 K Based on 2 Different Optimization Methods with Experimental Values again suggesting that CH 3 OH can induce ionization of ON-ONO 2 to form [ON + ] [NO 3

Table 2 .
Relative Energies of Species in the N 2 O 4 + CH 3 OH Reaction aThe energies are in kcal/mol, relative to that of N 2 O 4 + CH 3 OH, whose total energy is in Hartree/molecule as given.bTheZPE in kcal/mol was calculated at the UB3LYP/6-311+G(3df,2p) level.c The single-point energies are based on electronic structures calculated using UB3LYP/6-311+G(3df,2p) with ZPE corrections. a