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

Abstract

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 T^1.96 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.

1. Introduction

CH₃OH is known to be an important organic pollutant in the troposphere with concentrations averaged to be 600 pptv, next to that of CH₄.¹ The origin of CH₃OH is primarily of terrestrial rather than anthropogenic sources. In the troposphere, CH₃OH may be removed by reactions with various known radicals such as OH and NO₃; among them, the destruction by OH is dominant on account of its high reactivity and concentration in the troposphere.² In addition, oxidation by larger nitrogen oxides, N₂O_x (x = 4 and 5), is also possible under the tropospheric condition as discussed recently by Trac et al.³ and by Sarkar and Bandyopadhyay⁴ on the reactivities of N₂O₄ and N₂O₅ toward NH₃, 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 N₂O₄ is known to be lower than that of N₂O₅.³

The facile reaction of N₂O₄ with CH₃OH at low temperatures was first reported by Harris and Siegel who noted the disappearance of NO₂ upon mixing.⁵ Joffe and Gray identified methyl nitrite (CH₃ONO) and nitric acid as the products of the reaction but not methyl nitrate (CH₃ONO₂).⁶ The first kinetic measurement for the N₂O₄ + CH₃OH reaction and several other small alcohols was carried out by Fairlie et al.⁷ at 273–298 K following the NO₂ decay kinetics by visible light absorption; they reported a negative temperature dependence, obeying the third-order rate law, – d[NO₂]/dt = 2 k [NO₂]² [CH₃OH], with k = 4.8 × 10^–37 cm⁶/molecule²-s at 298 K. Nikki and co-workers⁸ investigated the reactions of NO₂ with CH₃OH and C₂H₅OH by FTIR spectroscopy monitoring the growth of RONO which followed the rate law, d[RONO]/dt = k [NO₂]² [ROH]. The rate constant for both alcohol reactions was reported to be the same, k = 5.7 × 10^–37 cm⁶/molecule²-s at 298 K. Koda et al.⁹ employed a reactor with spray-mixing to improve the mixing of the two reactants and monitored the kinetics of NO₂ decay photometrically; they reported the termolecular rate constant to be k = 1.79 × 10^–36 cm⁶/molecule2-s at 294 K. Based on their mechanistic analysis of the NO₂ decay kinetics, they postulated that the asymmetric N₂O₄, or ONONO₂, might be involved in the reaction giving CH₃ONO + HNO₃, instead of the more abundant symmetric N₂O₄. More recently, Wojcik-Pastuszka et al.¹⁰ studied the reactions of N₂O₄ with CH₃OH and several other small alcohols between 293 and 358 K by UV–vis spectroscopy, which allowed them to detect not only NO₂ and N₂O₄ but also the RONO products. The kinetics of these reactions were determined by measurement of NO₂ decay at 450 nm. They kinetically simulated the NO₂ decay–time profiles with the mechanism: 2 NO₂ ⇌ N₂O₄ and N₂O₄ + ROH ⇌ RONO + HNO₃. The second-order rate constants for CH₃ONO formation and its reverse reaction were reported in detail for the CH₃OH reaction. To date, the mechanism for the N₂O₄reaction with CH₃OH and other small alcohols remains unknown, however.

The reactivity of N₂O₄ toward NH₃ and RNH₂, including methyl amine³ (R = CH₃) and hydrazines^11,12 [R = NH₂, CH₃NH and (CH₃)₂N], 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 N₂O₄, which can undergo isomerization producing a highly reactive isomer ONONO₂ via a roaming-like transition state (TS) during the course of bimolecular collisions by lengthening of the N–N bond (O₂N–NO₂) and rotating one of the O₂N groups¹³ with barriers below the dissociation limit, ranging from 12.8 to 13.1 kcal/mol depending on collision partners.^3,11−14 Significantly, the roaming-like TS was also found to exist in the condensed phases including H₂O¹³ and solid N₂H₄,¹⁴ in which the isomerization reaction produces the reactive ONONO₂ isomer within the solid lattice producing N₂H₅⁺ONO₂^– with a large 70 kcal/mol exothermicity. The half-life of an embedded N₂O₄ in solid N₂H₄ at 218 K was predicted to be 0.5 s, which could reasonably explain the explosion observed when the N₂O₄–N₂H₄ solid mixture was warmed up slowly from 77 to 218 K during an experiment.¹⁴ Parenthetically, it should be mentioned that the conventional isomerization energies for N₂O₄ → ONONO₂ reported in the literature lie in the range of 30–45 kcal/mol,¹³ too high for the hypergolic reactions of N₂O₄ with hydrazines to occur.^11,12,14

In the present study, we investigate the mechanism for the redox reaction of N₂O₄ with CH₃OH producing the experimentally observed products, CH₃ONO and HNO₃ by quantum-chemical calculations. If the mechanism of this reaction is similar to those of its isoelectronic analogues, CH₃NH₂³ and NH₂NH₂,¹¹ then one would expect the production of CH₃ONO + HNO₃ and CH₃NO₃ + HONO via a fast and a slow reaction channel, respectively. The significance of CH₃ONO formation under the tropospheric condition will be examined on the basis of the predicted kinetics.

2. Computational Methods

2.1. Ab Initio Calculations

The electronic structures of all species involved in the oxidation of CH₃OH by N₂O₄ were optimized with UB3LYP/6-311+G(3df,2p),¹⁵ including the association step 2NO₂ + CH₃OH. 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 analyses¹⁶ 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

2.2. Kinetic Calculations

The kinetics for the reaction of N₂O₄ with CH₃OH 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 theory²⁰ 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 TST²¹ to determine the association rate for a barrierless channel. The potential energy function for the barrierless step N₂O₄ + CH₃OH → N₂O₄/CH₃OH (LM1) was estimated to cover the separation range of N₂O₄ and CH₃OH from 3.19 to13.19 Å with a step size of 0.1 Å at the UB3LYP/6-311 + G(3df,2p) level. The Morse function represents the minimum 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 N₂O₄:CH₃OH (LM1) → N₂O₄ + CH₃OH can be represented with β = 1.38 Å^–1, and the corresponding value of D_e is shown in Figure 1.

Figure 1.

Potential energy profile for the N₂O₄ (D_2h) + CH₃OH reaction calculated at the UCCSD(T)/6-311+G(3df,2p)//UB3LYP/6-311+G(3df,2p) level with ZPE corrections. Relative energies at 0 K are given in kcal/mol.

3. Results and Discussion

3.1. PES of the N₂O₄ (D_2h) + CH₃OH Reaction

We have established the PES for the reaction between N₂O₄ and CH₃OH in the gas phase using the UCCSD(T)/6-311+G(3df,2p)//UB3LYP/6-311 + G(3df,2p) level. In Table 1, we first compare the heats of reaction for 2 potential product pairs predicted at the CCSD(T)/6-311 + G(3df,2p) level based on 2 different DFT optimization methods, UB3LYP/6-311 + 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_rH^o with a slightly better agreement with available experimental data.

Table 1. Comparison of the Predicted Heats of Reaction at 0 K Based on 2 Different Optimization Methods with Experimental Values.

reaction	ΔrHo (kcal/mol)
	predicted (I)a	predicted (II)a	literature
N2O4+CH3OH = HNO3+CH3ONO	–2.5	–2.7	–2.428
N2O4+CH3OH = HONO + CH3ONO2	–2.5	–2.9	–2.528

^aPredicted values (I) by UCCSD(T)/6-311+G(3df,2p)//UB3LYP/6-311+G(3df,2p) and (II) by CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ.

Figure 1 shows the PES for the title reaction predicted using the UCCSD(T)/6-311+G(3df,2p)//UB3LYP/6-311+G(3df,2p) method. Their related structures optimized with the UB3LYP/6-311+G(3df,2p) method are presented in Figure 2. The relative energies and corresponding molecular parameters (vibrational frequencies and moments of inertia) for all involved species are summarized in Tables 2 and S2, respectively.

Figure 2.

Electronic structures of the key intermediates and TSs involved in the N₂O₄ (D_2h) + CH₃OH reaction optimized at the UB3LYP/6-311+G(3df,2p) level. Bond angles and bond lengths are in degree (°) and angstroms (Å), respectively.

Table 2. Relative Energies of Species in the N₂O₄ + CH₃OH Reaction^a.

	ZPEb	UB3LYP/6-311+G(3df,2p)c	UCCSD(T)/6-311+G(3df,2p)c
N2O4+CH3OH	46.7	–526.031	–525.103
LM1	47.4	–3.1	–6.4
LM2	47.3	6.5	2.9
LM3	47.6	–3.6	–9.6
LM4	47.5	–1.4	–7.3
TS1	44.3	8.7	7.9
TS2	45.4	6.5	4.3
TS3	44.9	25.6	28.1

^aThe energies are in kcal/mol, relative to that of N₂O₄ + CH₃OH, whose total energy is in Hartree/molecule as given.

^bThe ZPE in kcal/mol was calculated at the UB3LYP/6-311+G(3df,2p) level.

^cThe single-point energies are based on electronic structures calculated using UB3LYP/6-311+G(3df,2p) with ZPE corrections.

In Figure 1, the reaction occurs through the N₂O₄:CH₃OH (LM1) complex with a binding energy of 6.4 kcal/mol, which is slightly more stable than that of the N₂O₄/H₂O complex, 5.0 kcal/mol,¹³ but is very close to its isoelectronic N₂O₄/NH₂NH₂ complex, 6.7 kcal/mol¹¹, and N₂O₄/CH₃NH₂ complex, 6.8 kcal/mol.³ In the present reaction, the LM1 complex can undergo further reaction by lengthening N₂O₄’s N–N bond to 3.343 Å concurrently rotating one of its NO₂ groups at TS1 forming the ONONO₂/CH₃OH (LM2) complex, which lies 2.9 kcal/mol above the reactants or 9.3 kcal/mol above LM1. The bond ON–ONO₂ in the LM2 complex is lengthened to 1.854 Å, which is similar to those in the ONONO₂/NH₂NH₂ complex, 2.282 Ź¹, and ONONO₂/CH₃NH₂ complex, 2.092 Å.³ Both are longer than those in cis- and trans-ON-ONO₂ isomers, 1.685, and 1.622 Å, respectively,¹³ again suggesting that CH₃OH can induce ionization of ON-ONO₂ to form [ON⁺] [NO₃^–]. Mulliken charge analysis shows that the NO and NO₃ group charges are +0.367 and −0.507e, respectively (Figure 3).

Figure 3.

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

In the present case, the same roaming-like TS TS1 exists for the isomerization of N₂O₄ to trans-ONONO₂, 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: N₂O₄ + NH₂NH₂ 5.9 kcal/mol and N₂O₄ + CH₃NH₂ 8.0 kcal/mol. From LM2, the NO₃ group can abstract the H atom of the terminal OH group in CH₃OH via TS2 with a very small barrier of 1.4 kcal/mol to give the postreaction complex LM3 (HNO₃:CH₃ONO) with 9.6 kcal/mol exothermicity. The complex can readily separate to produce the product pair CH₃ONO + HNO₃ barrierlessly. To illustrate the effect of CH₃OH complexation with N₂O₄, we have added the potential energy profile for the isomerization of N₂O₄ to ONONO₂ without CH₃OH predicted by Raghunath and Lin¹³ 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 N₂O₄:CH₃OH to ONONO₂:CH₃OH by 1.5 kcal/mol, which may be attributed to the complexation effect. Other examples on the effect can be found in Table 3.

Table 3. Comparison of LM1, TS1, LM2, and TS2 for Various N₂O₄ Reactions (Energies in kcal/mol)^a.

reaction	LM1	TS1	LM2	TS2
N2O4= ONONO2		12.813
N2O4+ CH3OH = CH3ONO + HNO3	–6.4	7.9	–2.9	–4.3
N2O4+ CH3NH2= CH3NHNO + HNO3	–6.8	8.0	2.0	–1.63
N2O4+ NH3= NH2NO + HNO3	–5.3	8.7	4.6	9.93
N2O4+ H2O = HONO + HNO3	–5.0	8.7	2.7	12.613
N2O4+ N2H4= N2H3NO + HNO3	–6.7	5.9	–3.8	–4.911
N2O4+ N2H4= N2H3NO + HNO3(in CCl4solvent)	–5.9	7.4	–8.6	–6.729
N2O4@HZ23= NO3–+ N2H3NO + N2H5+	0.0	13.1	–45.0	–43.614
N2O4+ CH3NHNH2= CH3NHN(H)NO + HNO3	–6.9	6.3	1.4	1.211
N2O4+ (CH3)2NNH2= (CH3)2NN(H)NO + HNO3	–6.0	7.2	0.6	–0.112
N2O4+ CH3NHNHCH3= CH3N(H)N(CH3)NO + HNO3	–6.1	9.9	–1.9	–2.112

^aUCCSD(T)/6-311+G(3df,2p)//UB3LYP/6-311+G(3df,2p) was employed in refs (3),¹¹, and¹³ and this work, CCSD(T)/6-311+G(3df,2p)//B3LYP/6-311+G(3df,2p) was employed for the reaction in refs (12) and²⁹ while UCCSD(T)/CBS//UB3LYP/6-311+G(3df) was employed in the N₂O₄ isomerization reaction ref (13), and the reaction occurring in N₂H₄ solid was predicted with the DFT method in the VASP code.¹⁴

From LM1, another reaction path involves an H-transfer from CH₃OH to N₂O₄ via a tight five-member-ring TS (TS3) with a 28.1 kcal/mol barrier (or 34.5 kcal/mol above LM1) producing CH₃ONO₂ + trans-HONO. The reaction was predicted to be exothermic by 2.5 kcal/mol, which is exactly the same as the formation of CH₃ONO + HNO₃. This product channel cannot compete with the RTS-like channel producing CH₃ONO and HNO₃; 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 N₂O₄ hydrolysis¹³ to N₂O₄–hydrazine rocket propellants,^11,12,14 and to the reactions relevant to tropospheric chemistry.³ The implication of these data will be remarked later.

3.2. Kinetics of the Reaction

The kinetics of the N₂O₄ + CH₃OH 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 N₂O₄ with CH₃OH, the dominant product channel produces CH₃ONO + HNO₃, 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

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 CH₃ONO + HNO₃ 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 N₂O₄ + CH₃OH producing CH₃ONO + HNO₃ is solely controlled by TS1. The rate expression for the formation of CH₃ONO + HNO₃ in cm³molecule^–1s^–1 is determined by fitting the computed result with the 3 parameter Arrhenius equation at T = 200–2000 K

Figure 4 compares the predicted bimolecular rate constant for CH₃ONO + HNO₃ production with the result of Wojcik-Pastuszka et al.¹⁰ evaluated by kinetic modeling of NO₂ decay–time profiles using the 4 reaction mechanism including the forward and reverse processes: 2 NO₂ ⇌ N₂O₄ and N₂O₄ + CH₃OH ⇌ CH₃ONO + HNO₃ as mentioned in the Introduction. In the figure, we also present the results of Nikki⁸ and Koda,⁹ whose original third-order rate constants were kinetically modeled for N₂O₄ + CH₃OH by Wojcik-Pastuszka et al.¹⁰ with the 4-reaction mechanism. The agreement between the predicted value and 3 sets of experimental results appears to be reasonable.

Figure 4.

Comparison of the predicted bimolecular rate constant for N₂O₄ + CH₃OH→CH₃ONO + HNO₃ reaction with the values evaluated by Wojcik-Pastuszka et al.¹⁰ through kinetic modeling of NO₂-time profiles. The third-order rate constants of both Nikki⁸ and Koda⁹ were kinetically modeled by Wojcik-Pastuszka et al.¹⁰ to give the second-order rate constants as shown.

The modeling of Wojcik-Pastuszka et al.¹⁰ also gave the rate constant for the reverse reaction, CH₃ONO + HNO₃ → N₂O₄ + CH₃OH, k_–1. In Figure 5, we compare the predicted value of k_–1 with those obtained by the modeling based on the 4 reactions. The predicted value exhibits a substantial T dependence reflecting the reverse 10.4 kcal/mol barrier as indicated in Figure 1, whereas the model results showed no T dependence. This may reflect the result of poor initial static mixing of the reactants at low temperatures in a tubular reactor typically employed in a photometric measurement.

Figure 5.

Comparison of the predicted bimolecular rate constant for the reverse reaction CH₃ONO + HNO₃→N₂O₄ + CH₃OH with the values evaluated by Wojcik-Pastuszka et al.¹⁰ through kinetic modeling of NO₂-time decay profiles.

Estimation of the Contribution from the Termolecular 2NO₂ + CH₃OH Reaction

The relative average concentration of NO₂ and N₂O₄ 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 CH₃OH 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 2NO₂ + H₂O reaction,²² which had been reliably measured in laboratories²³ for comparison. In the present system, we can approximately account for the formation of CH₃ONO + HNO₃ by the stepwise mechanism

2

-2

3

The mechanism is similar to that invoked by Koda et al.,⁹ who initially assumed N₂O₄ instead of ONONO₂ as the intermediate. However, based on their analysis of the measured NO₂ decay kinetics, they concluded that ONONO₂, rather than N₂O₄, was actually involved in the reaction.⁹ Interestingly, 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 ONONO₂ intermediate leads to the rate for removal of CH₃OH

4

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

Under the tropospheric condition, it can be shown that k_–2 ≫ k₃ [CH₃OH]; eq 4 becomes

where K₂ = k₂/k_–2 is the equilibrium constant for reaction (2). Take 200 K and 760 Torr, for example, the concentration of CH₃OH in the troposphere is 9.63 × 10¹¹ molecules cm^–3, k₂ = 2.93 × 10^–14 cm³molecule^–1s^–1, k_–2 = 5.41 × 10⁶ s^–1, and k₃ = 2.56 × 10^–14 cm³ molecule^–1 s^–1; therefore, k_–2 = 5.41 × 10⁶ s^–1 ≫ k₃ x [CH₃OH] = 2.47 × 10^–2 s^–1.

Therefore, at 200 K in the troposphere, we can show that the rate of CH₃OH reaction by the termolecular mechanism presented above is about 4.4 × 10⁵ times smaller than that of the bimolecular N₂O₄ + CH₃OH reaction as estimated below by taking [NO₂]/[N₂O₄] = 100/7 × 10^–5,²⁴

[bimolecular rate constant; k₁] × [N₂O₄] = 8.85 × 10^–21 × [7 × 10^–5] = 6.20 × 10^–25;

[3-step termolecular rate constant; k_tf ] × [NO₂]² = 1.40 × 10^–34 × [100]² = 1.40 × 10^–30, where the termolecular forward rate constant

Accordingly, k₁ [N₂O₄]/k_tf [NO₂]2 = 4.4 × 10⁵ under the tropospheric condition; CH₃OH can therefore be more effectively removed by the bimolecular N₂O₄ reaction, rather than the termolecular process.

3.3. Comparison of the Predicted Termolecular Rate Constant with Experimental Data

As the termolecular kinetics for 2NO₂ + CH₃OH → CH₃ONO + HNO₃ had been reported experimentally by Fairlie et al.,⁷ Nikki et al.,⁸ and Koda and co-workers⁹ 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 2NO₂ + CH₃OH reaction with that of the analogous 2NO₂ + H₂O → HONO + HNO₃ reaction measured experimentally by England and Corcoran²³ together with our previously computed result based on the analogous 3-step mechanism²² shown above. In the case of the H₂O 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.

Figure 6.

Comparison of the predicted third-order rate constant for 2NO₂ + CH₃OH with the experimental values of Fairlie et al.,⁷ Nikki et al.,⁸ and Koda and co-workers,⁹ as well as with that of the analogous 2NO₂ + H₂O reaction reported by Zhu et al.²² who compared the predicted third-order rate constant with the experimental result of England and Corcoran.²³

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 k₃ for the ONONO₂ + H₂O reaction (due to its high exit barrier) and the weak T effect on the ONONO₂ + CH₃OH reaction as shown in Figure S3 because of its low exit barrier.

3.4. Relevancy to the Tropospheric Chemistry

Based on the rate constant k₁ given above for the formation of CH₃ONO and the concentration levels of NO₂, N₂O₄, and CH₃OH in the polluted urban atmosphere, [NO₂] ∼ 2 × 10¹¹ molecules cm^–3,²⁵ [N₂O₄] ∼ 2 × 10⁵ molecules cm^–3,²⁴ and [CH₃OH] ∼ 1 × 10¹² molecules cm^–3,²⁶ we can estimate the effective rate constant for removal of CH₃OH by N₂O₄ at the lower troposphere at 298 K: k₁ × [N₂O₄] = 2.7 × 10^–18 × [1.6 × 10⁵] = 4.4 × 10^–13 s^–1. The result suggests that the reaction is too slow to be significant.

4. Concluding Remarks

In this study, we have investigated the mechanism for the redox reaction of N₂O₄ with CH₃OH 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 CH₃ONO + HNO₃ as reported in 1951 by Joffe and Gray⁶ was controlled by the isomerization process forming trans-ONONO₂ from N₂O₄ in the presence of CH₃OH during the bimolecular collision. The highly polar and reactive trans-ONONO₂ rapidly attacks the CH₃OH molecule producing CH₃ONO and HNO₃ via a 6-member-ring TS with a negligible barrier.

For the N₂O₄ → ONONO₂ isomerization via the roaming-like TS within the N₂O₄–CH₃OH 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).²⁷ The predicted rate constant for CH₃ONO + HNO₃ formation can be given by k₁ = 1.43 × 10^–8T^1.96 exp(−9092/T) cm³molecule^–1s^–1 at T = 200–2000 K, independent of pressure. The result agrees very closely with that of the isoelectronic reaction N₂O₄ + CH₃NH₂ as shown in Figure S2.

We have also predicted the kinetics of the 2NO₂ + CH₃OH termolecular reaction based on the mechanism employed for the analogous 2NO₂ + H₂O → HONO + HNO₃ reaction.²² Comparing our predicted second- and third-order rate constants with available, but scarce, experimental data in the literature for CH₃OH reactions with N₂O₄ and NO₂, 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 N₂O₄ in the gas phase and in the H₂O solution¹³ to the hypergolic ignition of N₂O₄ in contact with hydrazine propellants,^11,12,14 and the processes relevant to the tropospheric chemistry involving potential pollutants such as NH₃³ and CH₃OH 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 N₂O₄ to trans-ONONO₂ via a very loose, roaming-like TS1, lying above the complex well at about 14 ± 2 kcal/mol. The highly polar ONONO₂ isomer is much more reactive than N₂O₄ 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 H₂O was predicted to be about 10 kcal/mol, which may be compared with that of its isoelectronic reaction with NH₃, 5.3 kcal/mol, and the very small value of 1.4 kcal/mol for CH₃OH, reflecting entirely the strength of the bond to be broken by the abstraction reaction of the NO₃ group producing HNO₃.

In view of the fact that both N₂O₄ and CH₃OH are known pollutants in the lower troposphere, we have examined the potential effect of the formation of CH₃ONO and HNO₃ from their reaction based on the predicted kinetics given above. Based on the known concentration levels of N₂O₄²⁴ and CH₃OH,²⁶ the rate of their reaction at 298 K was found to be too slow to be relevant to the troposphere chemistry.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpca.4c02433.

• Studying the impact of pressure on the N₂O₄ + CH₃OH reaction and comparing rate constants for product formation in the N₂O₄ reaction with CH₃OH and CH₃NH₂, as well as comparing bimolecular rate constants predicted for ONONO₂ reactions with CH₃OH and H₂O (PDF)

The authors declare no competing financial interest.