A possible atmospheric source of HNO₃: the ammonolysis reaction of t-N₂O₄ in the presence of water monomer, water dimer, and sulfuric acid

Abstract

Although the ammonolysis of t-N₂O₄ is one of the potential sources of HNO₃ formation, the available studies have only focused on its naked reaction. Herein, the effect of important neutral and acidic trace gases, water monomer, water dimer, and sulfuric acid, on the formation of HNO₃ from the ammonolysis of t-N₂O₄ was studied by the quantum chemical method of CCSD(T)/aug-cc-pVTZ//B3LYP-D3/6-311++G(3df,2pd) and the Master equation/Rice–Ramsperger–Kassel–Marcus (ME/RRKM) rate calculations. The quantum chemical results revealed that the ammonolysis of t-N₂O₄ with (H₂O)₂ and H₂SO₄ are barrierless or nearly barrierless reactions, potentially lowering the energy barrier to 3.4–4.1 kcal mol⁻¹. The calculated effective rate constant illustrates that (H₂O)₂ (100% RH) dominates over H₂O and H₂SO₄ within the range of 280–320 K (0 km), with an effective rate constant that is 1–3 orders of larger magnitude, whereas H₂SO₄ (10⁸ mol cm⁻³) is the most favorable catalyst within the troposphere between 5 and 30 km. However, the contributions of H₂O, (H₂O)₂, and H₂SO₄ are not apparent in the gas-phase ammonolysis of t-N₂O₄ within the range of 213–320 K and 0–30 km because their effective rate constants were at least 4 orders of magnitude lower than the corresponding rate constant of the ammonolysis of t-N₂O₄. In general, the current findings shed fresh light on neutral (H₂O and (H₂O)₂) and acidic (H₂SO₄) catalysts that not only affect energy barriers but also have an impact on the ammonolysis of t-N₂O₄ in neutral and acidic conditions.

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Environmental significance

Nitrogen tetroxide (N₂O₄) is considered to be a dimer of nitrogen dioxide (NO₂) and plays an important role in the formation of acid rain. The fact is that the ammonolysis of t-N₂O₄ is one of the potential sources of HNO₃ formation; thus, the effort of water monomer, water dimer, and sulfuric acid on the ammonolysis of t-N₂O₄ was studied by quantum chemical method and Master equation rate calculations. The quantum chemical results reveal that the ammonolysis of t-N₂O₄ with (H₂O)₂ and H₂SO₄ are barrierless or nearly barrierless reactions. In terms of the effective rate constant, (H₂O)₂ outperforms the other catalysts in the temperature range 280–320 K (0 km). Moreover, the effect of H₂SO₄ on the ammonolysis reaction of t-N₂O₄ is obvious at higher altitudes of 5–30 km. In general, this work will give a new insights into how the neutral and acidic catalysts affect the formation of HNO₃.

1. Introduction

Nitrogen dioxide (NO₂),¹ as one of the most significant NO_x, is not only a precursor to the photochemical formation of ozone in the troposphere,² but it can also contribute to the formation of photochemical smog and cause significant health and environmental hazards.³ Nitrogen tetroxide (N₂O₄), a dimer of nitrogen dioxide (NO₂),⁴ can be used for nitration, nitrosation, and oxidation.⁵ In addition, N₂O₄ is an oxidizing agent for auto-igniting fuels and plays an important role in the formation of acid rain.⁶ Due to the fact that N₂O₄ is a highly toxic chemical species that hinders experimental studies,⁷ quantum calculations are a trend in current research to probe the N₂O₄-related reaction mechanisms. As the most major loss route of N₂O₄ in the atmosphere, the hydrolysis of N₂O₄ is potentially important in the lower atmosphere and plays an important role in the formation of HONO, a major source of OH pollution in the urban atmosphere.^8,9

Several investigations have shown that the less stable t-N₂O₄ (trans-N₂O₄) is substantially more reactive than s-ONONO₂ (symmetric N₂O₄); hence, it was selected as a starting point for studying the hydrolysis of NO₂ dimers.^9–12 The reaction barrier for the hydrolysis of t-N₂O₄ to form HONO was in the range of 10.8–11.9 kcal mol⁻¹ at different theoretical levels.^9,11,12 Several groups reported that using H₂O and (H₂O)₂ as catalysts stabilized the reactant complexes by 3.5–6.9 kcal mol⁻¹ and reduced the energy barrier to 6.2 kcal mol⁻¹. Consequently, Zhang et al.⁹ revealed that, for the hydrolysis of t-N₂O₄, the H₂SO₄ catalyst is more effective than H₂O and (H₂O)₂ catalysts, resulting in not only a higher binding energy of 15.0 kcal mol⁻¹ for the reactant complex but also a lower energy barrier of 3.8 kcal mol⁻¹.

In the atmosphere, the hydrolysis of t-N₂O₄ to produce HONO is the most major loss route of t-N₂O₄.^10,11 As a complement to the loss of t-N₂O₄, the ammonolysis reaction of t-N₂O₄ can form HNO₃,¹³ which could be competitive with the main source of HNO₃, the gas-phase reaction of NO₂ with the hydroxyl (OH) radical^8,14 during the day and the hydrolysis reaction of N₂O₅ ^15–17 at night, in polluted areas of NH₃. The ammonolysis of t-N₂O₄ (shown in eqn (1) and (2)) investigated by Lin et al.¹³ reveals that the energy barrier of the t-N₂O₄ + NH₃ reaction was determined to be 5.3 kcal mol⁻¹ and the corresponding rate constant at low temperature was not pressure-dependent. As far as we know, the effect of neutral and acidic gases on the ammonolysis of t-N₂O₄, which plays a significant catalytic role in hydrogen abstraction reactions,^9,15,18–37 has not been explored.

NO₂ + NO₂ ↔ t-N₂O₄ (1)

t-N₂O₄ + NH₃ → HNO₃ + NH₂NO (2)

As in the previous studies on N₂O₄ + H₂O,^11,12 HO₂ + NO₂,³⁸ H₂CO + NH₃,³⁹ and SO₂ + NO₂ ⁴⁰ reactions, water molecules were found to play an essential role in enhancing the stability of pre-reactive complexes and lowering the apparent activation energies of the transition states. In addition to water monomer, some recent works addressed the potential role of water dimer,^18,41 which may play a significant catalytic role in hydrogen abstraction reactions because its concentrations can reach 9 × 10¹⁴ mol cm⁻³.^42,43 Aside from water monomer and water dimer, acidic^9,15,30–37 gas species in the atmosphere may also be effective in lowering the energy barriers for hydrogen transfer reactions^30–34 and atmospheric hydrolysis reactions^9,15,35–37 in the gas phase. The presence of H₂SO₄ ^37,44 in the atmosphere was considered to be a more effective catalyst than neutral catalysts,^{25,28–30,33,45} which not only greatly reduces the energy barriers^27,28,33 but also facilitates the transfer of hydrogen,^30–33,46 and thus, H₂SO₄ was regarded as either good acceptors or good donors of H in the catalytic gas reactions. These situations stimulated our interest in studying the ammonolysis of t-N₂O₄ by neutral (H₂O and (H₂O)₂) and acidic (H₂SO₄) gases.

In this work, using global minimum searching combined with quantum chemical methods, we first obtained the stable structures of the reactant complexes of t-N₂O₄⋯NH₃⋯X (X = H₂O, (H₂O)₂, and H₂SO₄). The ammonolysis of t-N₂O₄ in the presence of X was then studied using the stable molecular clusters t-N₂O₄⋯NH₃⋯X. Finally, the effective rate constant for the ammonolysis of t-N₂O₄ with X was estimated at temperatures ranging from 213 to 320 K and altitudes ranging from 0 to 30 km.

2. Calculation details

2.1 Electronic structure calculations

The molecular geometries of the isolated reactants, pre-reactive complexes, transition states, post-reactive complexes, and products of the ammonolysis reaction of t-N₂O₄ without and with X were optimized using the B3LYP-D3 method^47–53 with 6-311++G(3df,2pd) basis set in Gaussian 09 suites.⁵⁴ The D3 method has been reliably utilized to describe the noncovalent interaction and the equilibrium structure of atmospheric clusters and reactions.^51,55 Notably, the keyword “stable = opt” is added in the calculations at the B3LYP-D3/6-311++G(3df,2pd) level to ensure that all the geometries are stable. Frequency calculations were calculated at the same level for all stationary points to check that all transition states have the same character as a first-order saddle point with a single imaginary frequency and that other stationary points correspond to minima on potential energy surfaces (PESs). The scaling factor employed to adjust the ZPEs was 0.969.^56,57 To ensure that the optimized transition state connects the desired pre- and post-reactive complexes, intrinsic reaction coordinate (IRC) calculations^58–60 were performed at the same level. To improve the accuracy of the relative energies, single-point energy calculation was performed at the CCSD(T)/aug-cc-pVTZ^61–63 level by using the Gaussian 09 software.⁵⁴ It was noted that the T₁ diagnostic values for closed-shell in Table S3† were 0.02 less than the standard value,^64,65 showing the multireference calculations for recovering non-dynamical correlation were not a problem, and the single reference method of CCSD(T)/aug-cc-pVTZ is reliable to single point energy calculation.

Global minimum searching combined with quantum chemical methods was employed to obtain the most stable structures of the reactant complexes of t-N₂O₄⋯NH₃⋯X. Initially, 500 structures with low energies were auto-produced by ABCluster software^66,67 with TIP4P^68,69 model for H₂O, (H₂O)₂, and CHARMM⁷⁰ force field for t-N₂O₄, NH₃, and H₂SO₄. Then, pre-optimized by the semi-empirical method of PM7 ⁷¹ in MOPAC 2016.⁷² Next, the structures with the N(t-N₂O₄)⋯N(NH₃) interaction of electron donor–acceptor (EDA) and facilitating the transfer of hydrogen atom from t-N₂O₄ to NH₃ were selected to optimize at the B3LYP-D3/6-311+G(d,p) level. Subsequently, 50 isomers with an order of electronic energies were chosen to optimize at the level of B3LYP-D3/6-311+G(2d,2p). Finally, the global minimum isomers within 5.0 kcal mol⁻¹ (the electric energy) were re-optimized at the B3LYP-D3/6-311++G(3df,2pd) level.

2.2 Rate constant calculations

The rate constants for the ammonolysis reaction of t-N₂O₄ without and with X were calculated in two steps. First, the high-pressure-limit (HPL) rate constants were calculated by using the VRC-VTST calculations in Polyrate 2017 software.⁷³ The details of VRC-VTST can be seen in Table S7 of the ESI.† Then, based on the HPL rate constants, the rate constants for the ammonolysis reaction of t-N₂O₄ without and with X at different temperatures and pressures were calculated using the Master Equation Solver for Multi-Energy Well Reactions (MESMER) program.⁷⁴ The Inverse Laplace Transform (ILT) approach was used to analyze the barrierless step from distinct reactants to the pre-reactive complex.^75,76 Meanwhile, the transition step from the pre-reactive complex to the post-reactive complex occurring through the transition state was applied to the RRKM theory.^77,78 ILT methods and RRKM theory can be, respectively, expressed in eqn (3) and (4).In eqn (3) and (4), where W(E − E₀) is the rovibrational sum of states (SOS) at the optimized transition state (TS) geometry, E₀ is the reaction threshold energy, h is Planck's constant, ρ(E) is the density of rovibrational states of the reactant, and Q(β) is the corresponding canonical partition function. Moreover, the electronic geometries, vibrational frequencies, and rotational constants were calculated at the B3LYP-D3/6-311++G(3df,2pd) level, and single-point energy calculations were refined at the CCSD(T)/aug-cc-pVTZ level for the modeling. The one-dimensional asymmetric Eckart potential was used to treat the tunneling effect in the RRKM calculation. In addition, the Lennard-Jones (L-J) parameters ε/k_B = 71.4 K and σ = 3.798 Å were used for N₂,⁷⁹ε/k_B = 200.0 K and σ = 3.50 Å were used for t-N₂O₄,⁸⁰ while ε/k_B = 481.0 K and σ = 2.92 Å were estimated for NH₃.⁸⁰

3. Results and discussions

The pre-reactive complex in each reaction channel was denoted by “IM” followed by a number, whereas the transition state and post-reactive complexes were denoted by “TS” and “IMF”, respectively. Species in the presence of H₂O, (H₂O)₂, and H₂SO₄ were denoted by the suffixes “WM”, “WD”, and “SA”.

3.1 Mechanism and rate constants for the ammonolysis reaction of t-N₂O₄

The ammonolysis reaction of t-N₂O₄ has been extensively investigated from the theoretical viewpoint.¹³ Here, this reaction has been reinvestigated at the CCSD(T)/aug-cc-pVTZ//B3LYP-D3/6-311++G(3df,2pd) level to check the catalytic effect of X. Our results shown in Fig. 1 were found to be very mechanistically and energetically similar to the work reported by Lin et al.¹³ All the relative energy values qualitatively matched (see Table S2†). As seen in Fig. 1, the t-N₂O₄ + NH₃ reaction occurred through a ring formation mechanism, resulting in the formation of a six-membered ring complex t-N₂O₄⋯NH₃ with a binding energy of 0.5 kcal mol⁻¹. Then, the terminal O1 atom of t-N₂O₄ abstracts the H atom of NH₃ along with the N–N bond formation to form the product complex HNO₃⋯NH₂NO. From an energy point of view, the barrier height of the t-N₂O₄ + NH₃ reaction was 3.7 kcal mol⁻¹, revealing that t-N₂O₄ can easily react with NH₃ in the gas phase.

Fig. 1 Potential energy profiles for the t-N₂O₄ + NH₃ → HNO₃ + NH₂NO reaction at the CCSD(T)/aug-cc-pVTZ//B3LYP-D3/6-311++G(3df,2pd) level.

The calculated rate constants for the ammonolysis reaction of t-N₂O₄ are listed in Table 1. In the ammonolysis reaction of t-N₂O₄, the hindered internal rotation (HIR)^77,81–86 correction at 760 Torr has a moderate effect, increasing the rate constants by a factor of 1.25 to 1.28. Meanwhile, the almost unchanged rate constants for the ammonolysis reaction of t-N₂O₄ at different atmospheric pressures revealed that the pressure (10–760 Torr)⁸⁷ has little effect on the ammonolysis reaction of t-N₂O₄ within the temperature range of 280–320 K.^88,89

Table 1 The rate constants (k_R) (cm³ mol⁻¹ s⁻¹) for the t-N₂O₄ + NH₃ reaction without and with HIR treatments within the temperature range of 280–320 K and pressure range of 10–760 Torr

T (K)	HIR impact^a			Pressure impact
	With HIR treatments	Without HIR treatments	Factor^b	10 Torr	50 Torr	100 Torr	300 Torr	760 Torr
a HIR impact represents the hindered internal rotations treatment. b Factor denotes the rate ratio between with HIR treatments and without HIR treatments.
280	6.67 × 10^−17	5.20 × 10^−17	1.28	5.03 × 10^−17	5.14 × 10^−17	5.16 × 10^−17	5.18 × 10^−17	5.20 × 10^−17
290	7.81 × 10^−17	6.13 × 10^−17	1.27	5.90 × 10^−17	6.07 × 10^−17	6.10 × 10^−17	6.12 × 10^−17	6.13 × 10^−17
298	8.80 × 10^−17	6.95 × 10^−17	1.27	6.65 × 10^−17	6.88 × 10^−17	6.92 × 10^−17	6.94 × 10^−17	6.95 × 10^−17
300	9.06 × 10^−17	7.17 × 10^−17	1.26	6.84 × 10^−17	7.09 × 10^−17	7.13 × 10^−17	7.16 × 10^−17	7.17 × 10^−17
310	1.04 × 10^−16	8.32 × 10^−17	1.26	7.84 × 10^−17	8.20 × 10^−17	8.26 × 10^−17	8.30 × 10^−17	8.32 × 10^−17
320	1.19 × 10^−16	9.57 × 10^−17	1.25	9.40 × 10^−17	9.40 × 10^−17	9.55 × 10^−17	9.55 × 10^−17	9.57 × 10^−17

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3.2 Mechanism and rate constants for the ammonolysis reaction of t-N₂O₄ with H₂O and (H₂O)₂

Fig. 2a and b show the ammonolysis reaction of t-N₂O₄ assisted by H₂O (Channel WM) and (H₂O)₂ (Channel WD), where both H₂O and (H₂O)₂ served as a “bridge” to promote hydrogen atom transfer from the N3 atom of NH₃ to the terminal O1 atom of t-N₂O₄. In the case of Channel WM, the reaction can occur either (a) between NH₃ and monohydrated t-N₂O₄ (t-N₂O₄⋯H₂O) or (b) between hydrated NH₃ (NH₃⋯H₂O) and t-N₂O₄. The binding energy of t-N₂O₄⋯H₂O was 2.9 kcal mol⁻¹, which was consistent with the previously calculated value of 3.5 kcal mol⁻¹ at the CCSD(T)-F12a/cc-pVDZ-F12//M06-2X/6-311++G(3df,2pd) level.⁹ The binding energy of NH₃⋯H₂O was 4.4 kcal mol⁻¹, which agreed well with the calculated values of 4.4–4.6 kcal mol⁻¹.^90,91 The stability of NH₃⋯H₂O was 1.5 kcal mol⁻¹ higher than that of t-N₂O₄⋯H₂O. So, the ammonolysis of t-N₂O₄ in the presence of H₂O mainly takes place via the collision of NH₃⋯H₂O with t-N₂O₄ to form the quasi-planar eight-membered ring reactant complex IM_WM1. The energy of the reactant complex IM_WM1 was 4.7 kcal mol⁻¹ lower than that of the isolated reactants t-N₂O₄ + H₂O + NH₃. In the complex IM_WM1, H₂O played the roles of a single acceptor and donor of hydrogen bonds. After the formation of the complex IM_WM1, the reaction proceeded to form a hydrogen-bonded complex, HNO₃⋯H₂O⋯NH₂NO (denoted IMF_WM), through the transition state TS_WM, with an energy barrier of 4.2 kcal mol⁻¹.

Fig. 2 Potential energy profiles for the t-N₂O₄ + NH₃ → HNO₃ + NH₂NO reaction catalyzed by H₂O and (H₂O)₂ at the CCSD(T)/aug-cc-pVTZ//B3LYP-D3/6-311++G(3df,2pd) level (a–c) denotes the values respectively reported from ref. 9, 90, and 91.

The reaction t-N₂O₄ + NH₃ + (H₂O)₂ can be initiated by the reactant complex IM_WD1, which can be formed from t-N₂O₄⋯(H₂O)₂ + NH₃ or t-N₂O₄ + NH₃⋯(H₂O)₂. It is clear from Fig. 2b that NH₃ was most likely bound to (H₂O)₂ prior to t-N₂O₄. The reactant complex IM_WD1 has a quasi-planar structure similar to that of complex IM_WM1 and can be regarded as H₂O in IM_WM1, which was replaced by (H₂O)₂. The binding energy of IM_WD1 was 1.7 kcal mol⁻¹ from t-N₂O₄ + NH₃⋯(H₂O)₂. After complex IM_WD1, the ammonolysis reaction of t-N₂O₄ with (H₂O)₂ can form the product complex HNO₃⋯(H₂O)₂⋯NH₂NO (labeled as IMF_WD) through the transition state TS_WD with an energy barrier of 0.3 kcal mol⁻¹. Three hydrogen atom transfer mechanisms occurred at TS_WD, as well as the simultaneous formation of the N(2)⋯N(3) bond. In comparison to H₂O in Channel WM, (H₂O)₂ in Channel WD played a more obvious catalytic role in promoting the ammonolysis reaction of t-N₂O₄. When (H₂O)₂ was used as a catalyst in Channel WD, it stabilized the reactant complex by a further 4.9 kcal mol⁻¹ and decreased the reaction barrier by 3.9 kcal mol⁻¹. The more pronounced catalytic effect of (H₂O)₂ could be attributed to two factors. On the one hand, (H₂O)₂ may improve the N(t-N₂O₄)⋯N(NH₃) interaction compared to H₂O. For example, in the reactant complex IM_WD1, the strengthening of the N(t-N₂O₄)⋯N(NH₃) interaction was shown by the shortening of the bond distance N(2)⋯N(3) (2.18 Å, shown in Fig. 2b), which is less than the corresponding value in the reactant complex IM_WM1 (2.21 Å, shown in Fig. 2a). On the other hand, when H₂O was replaced by (H₂O)₂, however, the transition state extended from an eight-member ring (TS_WM) to a ten-member ring (TS_WD). This structural change reduces the ring tension of the transition state to a certain extent, lowering the reaction energy barrier.

As shown in Table 2, within the range of 213–320 K and 0–30 km,^88,89 the rate constant for the ammonolysis reaction of t-N₂O₄ assisted by H₂O (k_WM) was predicted to be 3.94 × 10⁻²⁰ to 1.93 × 10⁻¹⁹ cm³ mol⁻¹ s⁻¹, which was 2–3 orders of magnitude lower than that of the naked ammonolysis reaction of t-N₂O₄. The calculated rate constant for the ammonolysis reaction of t-N₂O₄ assisted by (H₂O)₂ (k_WD) was 3.66 × 10⁻¹⁶ to 1.98 × 10⁻¹⁵ cm³ mol⁻¹ s⁻¹, which was 1–2 orders of magnitude greater than the naked ammonolysis reaction of t-N₂O₄. The ammonolysis reaction of t-N₂O₄ assisted by (H₂O)₂ was more kinetically favorable than the ammonolysis reaction of t-N₂O₄ with H₂O, with a rate constant that was 3–5 orders of magnitude greater.

Table 2 Calculated rate constants (k, cm³ mol⁻¹ s⁻¹) for the t-N₂O₄ + NH₃ reaction with H₂O, (H₂O)₂, and H₂SO₄ calculated by master equation within the range of 213–320 K and 0–30 km^a,b

Altitude	T (K)	k R	k WM	k WD	k SA
a k R, kWM, kWD, and kSA were respectively denoted the rate constants for the t-N2O4 + NH3, t-N2O4 + NH3⋯H2O, t-N2O4 + NH3⋯(H2O)2, and t-N2O4 + NH3⋯H2SO4 reactions. b The 0–30 km data were reported from ref. 88 and 89.
0 km	280	5.20 × 10^−17	1.16 × 10^−19	6.05 × 10^−16	1.49 × 10^−16
	290	6.13 × 10^−17	1.33 × 10^−19	5.29 × 10^−16	1.50 × 10^−16
	298	6.95 × 10^−17	1.48 × 10^−19	4.76 × 10^−16	1.50 × 10^−16
	300	7.17 × 10^−17	1.52 × 10^−19	4.64 × 10^−16	1.51 × 10^−16
	310	8.32 × 10^−17	1.72 × 10^−19	4.11 × 10^−16	1.52 × 10^−16
	320	9.57 × 10^−17	1.93 × 10^−19	3.66 × 10^−16	1.54 × 10^−16
5 km	259.3	3.59 × 10^−17	8.59 × 10^−20	8.30 × 10^−16	1.48 × 10^−16
10 km	229.7	1.92 × 10^−17	5.32 × 10^−20	1.40 × 10^−15	1.51 × 10^−16
15 km	212.6	1.24 × 10^−17	3.94 × 10^−20	1.98 × 10^−15	1.56 × 10^−16
20 km	215.5	1.28 × 10^−17	4.15 × 10^−20	1.86 × 10^−15	1.55 × 10^−16
25 km	218.6	1.37 × 10^−17	4.38 × 10^−20	1.74 × 10^−15	1.54 × 10^−16
30 km	223.7	1.55 × 10^−17	4.79 × 10^−20	1.57 × 10^−15	1.53 × 10^−16

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3.3 Mechanism and rate constants for the ammonolysis reaction of t-N₂O₄ with H₂SO₄

As shown in Fig. S3,† nine geometrical isomers of the reactant complex t-N₂O₄⋯NH₃⋯H₂SO₄ (labeled as IM_SAn, n = 1–9) were found at the B3LYP-D3/6-311++G(3df,2pd) level, with complex IM_SA1 being the most stable. Based on complex IM_SA1, Fig. 3 presents the potential energy surface (PES) for the ammonolysis of t-N₂O₄ in the presence of H₂SO₄ (Channel SA). In the case of Channel SA, the reaction can occur (a) between NH₃ and t-N₂O₄⋯H₂SO₄ or (b) between t-N₂O₄ and NH₃⋯H₂SO₄. The binding energy of NH₃⋯H₂SO₄ was 14.7 kcal mol⁻¹, which was in good agreement with the previously reported value.⁹² The large binding energy of NH₃⋯H₂SO₄ indicates that in the reaction of t-N₂O₄ + NH₃ + H₂SO₄, NH₃ is easily bound to the isolated H₂SO₄. In this sense, the ammonolysis reaction of t-N₂O₄ with H₂SO₄ mainly takes place via the collision of t-N₂O₄ with NH₃⋯H₂SO₄, resulting in the reactant complex IM_SA1.

Fig. 3 Potential energy profiles for the t-N₂O₄ + NH₃ → HNO₃ + NH₂NO reaction catalyzed by H₂SO₄ at the CCSD(T)/aug-cc-pVTZ//B3LYP-D3/6-311++G(3df,2pd) level (a) The values was reported from ref. 92.

The energy of the reactant complex IM_SA1 was 15.0 kcal mol⁻¹ lower than that of the separate reactants t-N₂O₄, NH₃, and H₂SO₄. In the complex IM_SA1, H₂SO₄ served as a single donor and acceptor of hydrogen bonds to form a ring-like structure with the binary complex of t-N₂O₄⋯NH₃. The stability of complex IM_SA1 increased by 5.4–10.3 kcal mol⁻¹ when compared to the reactant complexes IM_WM1 and IM_WD1, with the distance of the N(t-N₂O₄)⋯N(NH₃) bond reduced by 0.01–0.04 Å. After the formation of the complex IM_SA1, Channel SA proceeded through the transition state TS_SA to form a ten-membered ring hydrogen-bonded complex HNO₃⋯H₂SO₄⋯NH₂NO (labeled as IMF_SA). Similar to the transition state TS_WM described above, TS_SA was in the middle of a double hydrogen atom transfer process, with the H₂SO₄ moiety serving as a bridge for the hydrogen transfer. From the viewpoint of the energy barrier height, Channel SA was a barrierless process. In comparison to H₂O and (H₂O)₂, H₂SO₄ could lower the energy barrier, at least by 0.7–4.6 kcal mol⁻¹. Complex IMF_SA showed a ten-membered ring structure. It had a binding energy of 28.0 kcal mol⁻¹ to the separate reactants t-N₂O₄, NH₃, and H₂SO₄, which was 13.0 kcal mol⁻¹ lower than the reactant complex IM_SA1. The rate constant of the t-N₂O₄ + NH₃⋯H₂SO₄ reaction is one order of magnitude more than that of the ammonolysis reaction of t-N₂O₄ without a catalyst, as shown in Table 2. This result revealed that H₂SO₄ in the t-N₂O₄ + NH₃⋯H₂SO₄ reaction plays a favorable catalytic role in promoting the ammonolysis reaction of t-N₂O₄. Thus, the ammonolysis reaction of t-N₂O₄ assisted by (H₂O)₂ and H₂SO₄ was more kinetically favorable than the reaction with H₂O.

3.4 Kinetics and implication in atmospheric chemistry

According to previous reports,^93–96 it is clear that the rate constant listed in Table 2 is insufficient to predict the atmospheric importance of the ammonolysis reaction of t-N₂O₄ assisted by (H₂O)₂ and H₂SO₄. To understand the atmospheric effect of (H₂O)₂ and H₂SO₄ on the ammonolysis reaction of t-N₂O₄, we introduced the effective rate constants (k′) to calculate the relative efficiency of neutral and acid trace gases affecting the atmospheric reaction^97–100 and to compare the rate constant for the naked reaction.

On the basis of the rate constant for Channels WM, WD, and SA, the equilibrium constant for the bimolecular formation (NH₃⋯H₂O, NH₃⋯(H₂O)₂, and NH₃⋯H₂SO₄) and the concentrations of H₂O, (H₂O)₂, and H₂SO₄ are listed in Tables S4-6,† as stated in eqn (5)–(7).

where k_WM, k_WD, and k_SA are the bimolecular rate constants for Channel WM, Channels WD, and SA, respectively; K_eq(NH₃⋯H₂O), K_eq(NH₃⋯(H₂O)₂), and K_eq(NH₃⋯H₂SO₄) are the equilibrium constants for the formation of complexes NH₃⋯H₂O, NH₃⋯(H₂O)₂, and NH₃⋯H₂SO₄. [H₂O], [(H₂O)₂], and [H₂SO₄] represent the concentrations of H₂O, (H₂O)₂, and H₂SO₄ taken from previous reports.^44,87 The k′ for the ammonolysis reaction of t-N₂O₄ with X at 0 km altitude and at different altitudes (5–30 km) in the troposphere was calculated.

3.4.1 Zero kilometer altitude. As seen in Table 3, the calculated value of can compete with at 280 K. With increasing temperature, the calculated was ∼1–3 orders of magnitude smaller than the values of , showing that the ammonolysis reaction of t-N₂O₄ was superior to that of an acidic (H₂SO₄) catalyst in the presence of neutral (H₂O and (H₂O)₂) catalysts. However, the H₂SO₄-catalyzed reaction can be neglected because its calculated was at least 4 orders of magnitude lower than the corresponding value of k_R in the naked reaction of the ammonolysis reaction of t-N₂O₄. This indicated that the contributions of H₂SO₄ to the ammonolysis reaction of t-N₂O₄ in atmospheric chemistry are not obvious within the temperature range of 280–320 K (at 0 km altitude).

Table 3 The effective rate constants (k′, cm³ molecule⁻¹ s⁻¹) for the t-N₂O₄ + NH₃ reaction assisted by H₂O, (H₂O)₂, and H₂SO₄ within the temperature range of 280–320 K^a,b (0 km)

Catalysts	T/K	280 K	290 K	298 K	300 K	310 K	320 K
a , , and were respectively denoted the effective rate constants for the t-N2O4 + NH3⋯H2O, t-N2O4 + NH3⋯(H2O)2, and t-N2O4 + NH3⋯H2SO4 reactions. b The values of temperature were reported from ref. 88 and 89. c The values of concentrations were reported from ref. 44 and 87.
	100% RH^c	4.29 × 10^−22	6.96 × 10^−22	1.02 × 10^−21	1.11 × 10^−21	1.70 × 10^−21	2.49 × 10^−21
	100% RH^c	2.45 × 10^−21	3.68 × 10^−21	5.16 × 10^−21	5.46 × 10^−21	7.70 × 10^−21	1.02 × 10^−20
	[H2SO4]^c = 10^8 mol cm^3	1.39 × 10^−21	5.49 × 10^−22	2.72 × 10^−22	2.32 × 10^−22	1.03 × 10^−22	4.71 × 10^−23

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3.4.2 Higher altitudes. The k′ for the ammonolysis reaction of t-N₂O₄ with H₂O, (H₂O)₂, and H₂SO₄ were calculated within the 5–30 km altitude range, and the calculated k′ is listed in Table 4. It can be seen in Table 4 that the contribution of H₂SO₄ was most obvious in the catalysts of H₂O, (H₂O)₂, and H₂SO₄ within the altitude range of 5–30 km, since the value of was larger by 1–8 orders of magnitude than that of . In order to quantitatively assess the impact of H₂SO₄ on the ammonolysis reaction of t-N₂O₄, the total rate constant k_tot can be calculated using eqn (8). The branching ratio for in Table 4 was calculated to be 3.11 × 10⁻⁵–5.06 × 10⁻⁴ at 5–30 km. This indicates that the contribution of the H₂SO₄-assisted ammonolysis reaction of t-N₂O₄ can be negligible in atmospheric gas-phase chemistry.

Table 4 The effective rate constants (k′, cm³ molecule⁻¹ s⁻¹) for the t-N₂O₄ + NH₃ reaction with H₂O, (H₂O)₂, and H₂SO₄ at different altitudes in troposphere^a

Altitude (km)^b	T (K)^b	P (torr)^b
a , , and were respectively denoted the effective rate constants for the t-N2O4 + NH3⋯H2O, t-N2O4 + NH3⋯(H2O)2, and t-N2O4 + NH3⋯H2SO4 reactions; ktot = kR + + . b The values of altitude, temperature and pressure were reported from ref. 87, 88 and 89.
5	259.3	406.75	5.62 × 10^−23	1.50 × 10^−22	1.81 × 10^−21	5.05 × 10^−5
10	229.7	202.16	2.12 × 10^−23	1.74 × 10^−22	9.47 × 10^−21	4.93 × 10^−4
15	212.6	91.20	1.38 × 10^−25	2.95 × 10^−26	3.74 × 10^−21	3.02 × 10^−4
20	215.5	41.04	6.12 × 10^−26	4.52 × 10^−27	4.00 × 10^−22	3.11 × 10^−5
25	218.6	19.00	3.05 × 10^−26	8.56 × 10^−28	2.71 × 10^−21	1.97 × 10^−4
30	223.7	8.36	1.33 × 10^−26	1.12 × 10^−28	7.88 × 10^−21	5.06 × 10^−4

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4. Summary and conclusions

In this work, the favorable route for the ammonolysis reaction of t-N₂O₄ in the presence of neutral (H₂O and (H₂O)₂) and acidic (H₂SO₄) catalysts was investigated using the quantum chemical method of CCSD(T)/aug-cc-pVTZ//B3LYP-D3/6-311++G(3df,2pd) and the master equation. The calculated results show that the energy barrier for the ammonolysis reaction of t-N₂O₄ increased when H₂O was present, but when (H₂O)₂ was present, the reaction energy barrier decreased to 0.3 kcal mol⁻¹, which was 3.4 kcal mol⁻¹ lower than the ammonolysis reaction of t-N₂O₄ without the catalyst, especially when H₂SO₄ was directly involved in the reaction that is a barrierless process. In terms of the effective rate constant, (H₂O)₂ outperforms the other catalysts in the temperature range of 280–320 K (0 km). Moreover, the effect of H₂SO₄ on the ammonolysis reaction of t-N₂O₄ is obvious at higher altitudes of 5–30 km. Overall, this work will give a new insight into how the neutral and acidic catalysts affect the formation of HNO₃ from the ammonolysis reaction of t-N₂O₄. As HNO₃ is an important source of acid rain, the present work will provide a potential formation pathway for HNO₃, which plays a crucial role in the formation of acid rain.

Author contributions

Ruxue Mu: investigation, data curation, visualization, writing – original draft. Weixin Zhou: supervision, writing – review and editing, project administration. Zhaozhao Hong: visualization, data curation. Rui Wang: writing – review and editing, project administration. Quan Liu: visualization, data curation. Qiang Zhang: formal analysis. Min Jiang: formal analysis. Balaganesh Muthiah: supervision, writing – review and editing. Tianlei Zhang: writing – review and editing, project administration.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (no. 22073059, 22203052); the Natural Science Foundation of Shaanxi Province (no. 2023-YBGY-486, 2022JM-133); the Funds of Graduate Innovation of Shaanxi University of Technology (no. SLGYCX2304); the authors also thank Prof. Mark A. Blitz (from University of Leeds) for providing the use of the MESMER program.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ea00095h

‡ Ruxue Mu and Weixin Zhou have contributed equally to this work.

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