Synergistic Reaction of SO₂ with NO₂ in Presence of H₂O and NH₃: A Potential Source of Sulfate Aerosol

Abstract

Effect of H₂O and NH₃ on the synergistic oxidation reaction of SO₂ and NO₂ is investigated by theoretical calculation using the molecule system SO₂-2NO₂-nH₂O (n = 0, 1, 2, 3) and SO₂-2NO₂-nH₂O-mNH₃ (n = 0, 1, 2; m = 1, 2). Calculated results show that SO₂ is oxidized to SO₃ by N₂O₄ intermediate. The additional H₂O in the systems can reduce the energy barrier of oxidation step. The increasing number of H₂O molecules in the systems enhances the effect and promotes the production of HONO. When the proportion of H₂O to NH₃ is 1:1, with NH₃ included in the system, the energy barrier is lower than two pure H₂O molecules in the oxidation step. The present study indicates that the H₂O and NH₃ have thermodynamic effects on promoting the oxidation reaction of SO₂ and NO₂, and NH₃ has a more significant role in stabilizing product complexes. In these hydrolysis reactions, nethermost barrier energy (0.29 kcal/mol) can be found in the system SO₂-2NO₂-H₂O. It is obvious that the production of HONO is energetically favorable. A new reaction mechanism about SO₂ oxidation in the atmosphere is proposed, which can provide guidance for the further study of aerosol surface reactions.

1. Introduction

Sulfur dioxide (SO₂), a major air pollutant, is released into the atmosphere via the combustion of sulfur containing fuels and industrial production [1,2,3], volcanic eruptions, and decomposition of sulfides in nature. SO₂ can be oxidized to form sulfuric acid (H₂SO₄) through the homogeneous or heterogeneous processes [4,5,6], which include gas-phase oxidation by hydroxyl radical (OH•) and in-cloud oxidation by dissolved ozone (O₃) and hydrogen peroxide (H₂O₂) [7,8,9]. It has been proved that sulfuric acid is the main contributor to the new particle formation, resulting in serious environmental issues such as haze and acid rain [10,11,12]. Thus, it is significant to investigate the SO₂ oxidation mechanism in the atmosphere.

In hazy weather, researchers have found that a considerable amount of PM_2.5 can be formed in the atmosphere, and sulfate is the significant component of the fine particulate matter [13,14,15,16,17,18]. Previous studies have indicated that, as the haze weather gets worse, the concentration of O₃ decreases, while the concentrations of NO₂ and sulfate increase [19]. However, widespread formation pathways (gas-phase oxidation and in-cloud oxidation) of sulfate cannot account for the phenomena of high content of sulfate. Some researchers have investigated that the oxidation reaction of SO₂ by NO₂ is proposed as a missing key pathway to form sulfate in a special condition [19,20,21,22,23,24]. Wang et al. have considered that NO₂ could effectively react with SO₂ in the presence of H₂O and NH₃ during the severe haze period [25]:

$${\mathrm{SO}}_2\left(\mathrm{g}\right)+2{\mathrm{NO}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{aq}\right)\to 2{\mathrm{H}}^{+}\left(\mathrm{aq}\right)+{\mathrm{SO}}_4{}^{2-}\left(\mathrm{aq}\right)+2\mathrm{HONO}\left(\mathrm{g}\right)$$ (1)

$$2{\mathrm{NH}}_3\left(\mathrm{g}\right)+{\mathrm{SO}}_2\left(\mathrm{g}\right)+2{\mathrm{NO}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{aq}\right)\to 2{\mathrm{NH}}_4{}^{+}\left(\mathrm{aq}\right)+{\mathrm{SO}}_4{}^{2-}\left(\mathrm{aq}\right)+2\mathrm{HONO}\left(\mathrm{g}\right)$$ (2)

From Reaction (1) and (2), it can be seen that the final products primarily include SO₄²⁻ and HONO.

In the presence of water, the process of NO₂ dimerization is likely to occur in polluted atmospheric conditions [26,27]. Some studies have demonstrated that N₂O₄, the dimer of NO₂, serves as the oxidant to oxidize SO₂ on the aerosol surface [28,29,30]. For NO₂ dimer, three isomers, symmetric sys-O₂N-NO₂, and asymmetric t-ONONO₂, c-ONONO₂, can be found. The sys-O₂N-NO₂ is very stable due to its symmetry, while asymmetric ONO-NO₂ can be rapidly converted to NO⁺ and NO₃⁻ in the presence of water [31,32,33,34]. The ion pairs (NO⁺NO₃⁻) can also oxidize many organic and inorganic compounds [35]. Although these studies have shown that SO₂ can react with NO₂ to produce H₂SO₄, the reaction mechanism is not completely understood.

In this paper, we researched the gas-phase reaction of SO₂ with NO₂ using the density functional theory (DFT) method. The different number of water molecules is added to the reaction so as to investigate the role of water molecules in the oxidation reaction. In addition, the effect of NH₃ in the oxidation reaction also is considered.

2. Results and Discussion

2.1. The Reaction of SO₂-2NO₂-nH₂O (n = 0, 1, 2, 3)

2.1.1. The Reaction of SO₂-2NO₂

In the absence of H₂O, the equilibrium structures and potential energy are shown in Figure 1, Table 1 and Table 2 present the corresponding energy data and the numerical value of charge distribution of NO⁺NO₃⁻ and NO⁺NO₂⁻. The relative energies, enthalpies and Gibbs free energies in all relevant species for the system SO₂-2NO₂ are summarized in Table S1. Two main pathways are found due to the formation of two NO₂ dimers, t-ONONO₂ and c-ONONO₂. The pre-reactive complexes (RC1 and RC2) are produced by a collision of SO₂. The IM1 (a binding of −23.27 kcal/mol) is formed via transient state (TS1) with the energy barrier and reaction energy of 45.48 kcal/mol and −11.49 kcal/mol, respectively. The IM2 is produced by TS2 with the energy barrier and reaction energy of 52.45 kcal/mol and −5.77 kcal/mol, respectively. These two processes are similar in that an O atom from NO⁺NO₃⁻ fragments transforms into SO₂ to lead to the formation of SO₃. As shown in Table S1, the reaction SO₂-2NO₂→IM1 is exothermic and spontaneous (ΔH of −24.50 kcal/mol and ΔG of −0.29 kcal/mol at 298.15K). Due to the absence of H₂O molecule, the hydrolysis process cannot be carried out, and HONO cannot be generated, finally.

Figure 1.

Potential energy profile for the reaction of SO₂-2NO₂. The yellow spheres are S atoms, the red spheres are O atom, and the blue spheres are N atom, respectively. (Unit: Energies in kcal/mol; bond lengths in angstroms). The black and red lines are the different pathways. The black line represents the reaction of t-ONONO₂-SO₂, and the red line is the reaction of c-ONONO₂-SO₂.

Table 1.

Energy barriers and reaction energies for the integrated reactions 2NO₂-SO₂-mH₂O-nNH₃ (m = 0, 1, 2, 3; n = 0, 1, 2) (unit: kcal/mol).

	Oxidation Reaction		Hydrolysis Reaction
Reaction Systems	Energy Barrier (kcal/mol)	Reaction Energy (kcal/mol)	Energy Barrier (kcal/mol)	Reaction Energy (kcal/mol)
SO2-2NO2	45.48	−11.49
	52.45	−5.77
SO2-2NO2-H2O	41.80	−13.16	0.29	−3.27
	47.54	−13.05	0.29	−3.27
SO2-2NO2-2H2O	40.14	−14.75	4.36	−3.94
	41.47	−15.87	3.06	−1.85
SO2-2NO2-3H2O	36.49	−19.48	2.63	−4.15
	38.77	−21.34	1.87	−6.56
SO2-2NO2-NH3	40.60	−20.10
	48.85	−13.76
SO2-2NO2-H2O-NH3	38.92	−17.85	6.44	−13.45
	40.30	−18.60	8.55	−13.06
SO2-2NO2-2H2O-NH3	39.21	−18.61	6.26	3.36
	39.77	−18.46	12.43	−14.42
SO2-2NO2-H2O-2NH3	38.85	−18.80	9.04	−19.46
	40.26	−19.51	12.68	−16.28

Table 2.

The charge distribution for the NO⁺NO₃⁻ and NO⁺NO₂⁻ in reactant complexes (RC) and intermediates (IM).

	Reactant Complexes	NO+	NO3−	Intermediate	NO+	NO2−
SO2-2NO2	RC1	0.330	−0.328	IM1	0.502	−0.201
	RC2	0.405	−0.394	IM2	0.501	−0.217
SO2-2NO2-H2O	RC1-1W	0.472	−0.437	IM1-1W	0.712	−0.250
	RC2-1W	0.506	−0.472	IM2-1W	0.688	−0.280
SO2-2NO2-2H2O	RC1-2W	0.644	−0.605	IM1-2W	0.772	−0.290
	RC2-2W	0.592	−0.532	IM2-2W	0.726	−0.259
SO2-2NO2-3H2O	RC1-3W	0.730	−0.695	IM1-3W	0.767	−0.309
	RC2-3W	0.705	−0.724	IM2-3W	0.621	−0.282
SO2-2NO2-NH3	RC1-1A	0.448	−0.442	IM1-1A	0.241	−0.222
	RC2-1A	0.458	−0.635	IM2-1A	0.643	−0.228
SO2-2NO2-H2O-NH3	RC1-1W-1A	0.599	−0.569	IM1-1W-1A	0.640	−0.261
	RC2-1W-1A	0.508	−0.672	IM2-1W-1A	0.596	−0.279
SO2-2NO2-2H2O-NH3	RC1-2W-1A	0.675	−0.673	IM1-2W-1A	0.773	−0.296
	RC2-2W-1A	0.722	−0.625	IM2-2W-1A	0.717	−0.241
SO2-2NO2-H2O-2NH3	RC1-1W-2A	0.440	−0.696	IM1-1W-2A	0.549	−0.297
	RC2-1W-2A	0.449	−0.691	IM2-1W-2A	0.488	−0.283

2.1.2. The Reaction of SO₂-2NO₂-H₂O

Figure 2 explores the equilibrium structures and potential energy of SO₂-2NO₂-H₂O. The corresponding energy data and the numerical value of charge distribution are put in Table 1 and Table 2. The relative energies, enthalpies and Gibbs free energies in all relevant species for the SO₂-2NO₂-H₂O are listed in Table S2. In these two pathways, the complexes (t-ONONO₂-H₂O and c-ONONO₂-H₂O) are firstly produced via the interaction between an N₂O₄ molecule and a water molecule. Through a collision with SO₂, the two complexes can transform into the pre-reactive complex (RC1-1W and RC2-1W).

Figure 2.

Potential energy profile for the reaction of SO₂-2NO₂-H₂O. The yellow spheres are S atoms, the red spheres are O atom, the blue spheres are N atom, and the white spheres represent H atom, respectively. (Unit: Energies in kcal/mol; bond lengths in angstroms). The black and red lines are the different pathways. The black line represents the reaction of t-ONONO₂-H₂O-SO₂, and the red line is the reaction of c-ONONO₂-H₂O-SO₂.

Beginning with the reactant complex RC1-1W (a binding energy of 17.78 kcal/mol), the complex IM1-1W (a binding energy 30.94 kcal/mol) can be formed via the TS1-1W with the energy barrier of 41.80 kcal/mol. In this process, an oxygen atom from NO⁺NO₃⁻ fragment is transferred to SO₂, leading to the formation of SO₃. The complex IM1-1W can undergo an isomerization process to form IM′-1W with the energy absorption of 0.14 kcal/mol. Because the H₂O molecule gets involved, the NO⁺NO₂⁻ fragments are divided into two parts, and the NO⁺ fragment rotates by an angle. Once the IM′-1W is produced, the final complex SO₃-2HONO can be easily formed with the energy barrier of 0.29 kcal/mol and the reaction energy of −3.27 kcal/mol. From IM′-1W to SO₃-2HONO, the water molecule reacts with the isolated NO⁺ fragment and NO₂⁻ fragment to form two HONO molecules. In the other pathway, the reaction process is similar in the above step. The IM2-1W is formed from the conversion of RC2-1W via the transition state TS2-1W with the energy barrier of 47.54 kcal/mol and the reaction energy of −13.05 kcal/mol. After that, the hydrolysis process is the same as the above reaction (IM′-1W to SO₃-2HONO). The reactant (IM′-1W) is formed via IM2-1W releasing the energy of 0.09 kcal/mol. In the same way, the SO₃-2HONO is formed with the energy barrier and reaction energy of 0.30 kcal/mol and −3.27 kcal/mol, respectively.

In the absence of water, the energy barrier is higher than one H₂O molecule and the hydrolysis reaction cannot produce HONO. The result indicates that H₂O molecule reacts as the solvent to reduce activation energy and stable structures and also is a critical reactant in the formation of HONO.

2.1.3. The Reaction of SO₂-2NO₂-2H₂O

Figure 3 presents the optimized geometries of molecular species involved in the reaction of SO₂-2NO₂-2H₂O to examine the role of an additional H₂O molecule. Table 1 and Table 2 show the corresponding energy data and the charge distribution. Table S3 shows the relative energies, enthalpies and Gibbs free energies in all relevant species for the SO₂-2NO₂-2H₂O. In these pathways, the pre-reactive complexes (RC1-2W and RC2-2W) are produced via the interaction between the complexes (t-ONONO₂-2H₂O and c-ONONO₂-2H₂O) and SO₂, or a collision of the complexes (t-ONONO₂-H₂O-SO₂ and c-ONONO₂-H₂O-SO₂) with H₂O.

Figure 3.

Potential energy profile for the reaction of SO₂-2NO₂-2H₂O. The yellow spheres are S atoms, the red spheres are O atom, the blue spheres are N atom, and the white spheres represent H atom, respectively. (Unit: Energies in kcal/mol; bond lengths in angstroms). The black and red lines are the different pathways. The black line represents the reaction of t-ONONO₂-2H₂O-SO₂, and the red line is the reaction of c-ONONO₂-2H₂O-SO₂.

Starting with the complex RC1-2W (−25.32 kcal/mol), the intermediate complex IM1-2W (−40.06 kcal/mol) is formed via TS1-2W with the energy barrier of 40.14 kcal/mol. The isomerized intermediate complex IM1′-2W (−40.89 kcal/mol) is formed by the H₂O_(a) closing to NO⁺NO₂⁻. The H₂O_(a) molecule reacts with NO⁺NO₂⁻ with an energy barrier and reaction energy of 4.36 kcal/mol and −3.94 kcal/mol, respectively. The other pathway is analogous with the above process, and the barrier (41.47 kcal/mol) is slightly higher than the reaction pathway involving in TS1-2W.

In the presence of two H₂O molecules, the H₂O_(a) serves as reactant to form HONO, and the other H₂O_(b) acts as a solvent molecule in this reaction pathway to reduce energy barrier and stable complex structures. Compare with the one-water reaction in the first step, the energy barrier for TS1-2W is reduced by 1.66 kcal/mol. Moreover, the energy barrier of TS2-2W is decreased by 6.07 kcal/mol for TS2-1W. It shows that the second-water molecule plays a certain role in lowering the energy barrier and stabilizing the complexes structures.

2.1.4. The Reaction of SO₂-2NO₂-3H₂O

The consequence of three H₂O molecules taking part in reaction is shown in Figure 4. The corresponding energy data and the charge distribution are put in Table 1 and Table 2. Table S4 summarizes the relative energies, enthalpies and Gibbs free energies in all relevant species for the SO₂-2NO₂-3H₂O. The reactant complex RC1-3W (−30.18 kcal/mol) and RC2-3W (−28.19 kcal/mol) may be formed after SO₂ attacks the tetramer complexes (t-ONONO₂-(H₂O)₃ and c-ONONO₂-(H₂O)₃), or H₂O attacks t-ONONO₂-(H₂O)₂-SO₂ and t-ONONO₂-(H₂O)₂-SO₂, respectively. To form the IM1-3W from RC1-3W, there is an energy barrier of 36.49 kcal/mol at the transition state TS1-3W and reducing reaction energy of 19.48 kcal/mol. The reactant complex of hydrolysis reaction is IM1′-3W, and NO⁺NO₂⁻ is divided by the closing of H₂O molecule. Through the TS1’-3W (−45.75 kcal/mol), a stable product complex SO₃-2HONO-2H₂O-1 (−52.53 kcal/mol) is produced eventually. The oxidation reaction of the other pathway is approximately similar to RC1-3W to IM1-3W. It is different from the above hydrolytic processes, and H₂O_(c) reacts as a transporter to transmit a proton forming H₃O⁺ intermediate. The relevant energy barrier and reaction energy of the process are shown in Table 1. As shown in Table S4, the reaction SO₂-2NO₂-3H₂O→SO₃-2HONO-2H₂O-1 is exothermic and spontaneous.

Figure 4.

Potential energy profile for the reaction of SO₂-2NO₂-3H₂O. The yellow spheres are S atoms, the red spheres are O atom, the blue spheres are N atom, and the white spheres represent H atom, respectively. (Unit: Energies in kcal/mol; bond lengths in angstroms). The black and red lines are the different pathways. The black line represents the reaction of t-ONONO₂-3H₂O-SO₂, and the red line is the reaction of c-ONONO₂-3H₂O-SO₂.

In comparison to one-water molecules in the process of SO₂ oxidation, three H₂O molecules have successfully reduced the energy barrier height by 5.35 kcal/mol and 8.77 kcal/mol. In these two pathways, the two additional H₂O molecules act only as a solvent without entering into the reaction. It shows that the third-water molecule plays a significant role in stabilizing the complexes and lowering the energy barrier. As the number of H₂O increases, the releasing energy gets more and more, and the configurations of product complexes are more and more stable. The hydrolysis reaction is still favorable thermodynamically with the number of H₂O molecule increasing.

2.2. The Reaction of SO₂-2NO₂-nH₂O-mNH₃ (n = 0, 1, 2; m = 1, 2)

2.2.1. The Reaction of SO₂-2NO₂-NH₃

Figure 5 explores the equilibrium structures and potential energy of the system 2NO₂-SO₂-NH₃. Table S5 summarizes the relative energies, enthalpies and Gibbs free energies in all relevant species. The corresponding thermodynamic data and the charge distribution are put in Table 1 and Table 2. Reactant complexes (RC1-1A and RC2-1A) are formed through the collision between complexes (t-ONONO₂-NH₃ and c-ONONO₂-NH₃) and SO₂, which is equivalent to replacing one H₂O molecule from RC1-1W and RC2-1W with NH₃. RC1-1A (−15.12 kcal/mol) is converted into IM1-1A (−35.22 kcal/mol) via the transformation of an O molecule with the energy barrier and reaction energy of 40.60 kcal/mol and −20.10 kcal/mol, respectively. The other pathway is similar to the above pathway with the energy barrier and reaction energy of 48.85 kcal/mol and −13.76 kcal/mol, respectively. The hydrolytic process cannot occur because of the absence of H₂O molecule. As we can see in Table S5, the reaction SO₂-2NO₂-NH₃→IM1-1A is exothermic and spontaneous (ΔH = −37.16 kcal/mol and ΔG = −3.12 kcal/mol).

Figure 5.

Potential energy profile for the reaction of SO₂-2NO₂-NH₃. The yellow spheres are S atoms, the red spheres are O atom, the blue spheres are N atom, and the white spheres represent H atom, respectively. (Unit: Energies in kcal/mol; bond lengths in angstroms). The black and red lines are the different pathways. The black line represents the reaction of t-ONONO₂-NH₃-SO₂, and the red line is the reaction of c-ONONO₂-NH₃-SO₂.

Compared with the reaction pathway of SO₂-2NO₂ to IM1 and IM2, the result indicates that NH₃ molecule can serve as catalyst and solvent to reduce the energy barrier and stable structures. The NH₃ molecule cannot trigger the hydrolysis reaction to produce HONO.

2.2.2. The Reaction of SO₂-2NO₂-H₂O-NH₃

The relative energies, enthalpies and Gibbs free energies in all relevant species for SO₂-2NO₂-H₂O-NH₃ are summarized in Table S6. As shown in Figure 6, RC1-1W-1A and RC2-1W-1A are formed after SO₂ attacks the complex t/c-ONONO₂-H₂O-NH₃ or NH₃ attacks t/c-ONONO₂-H₂O-SO₂. The product complex IM1-W-A (−43.26 kcal/mol) is formed through TS1-W-A (13.51 kcal/mol) with the energy barrier and reaction energy of 38.92 kcal/mol and −17.85 kcal/mol, respectively. When the only water molecule gets close to the NO⁺NO₂⁻, the reactant complex (IM1′-W-A) of hydrolysis reaction is formed through separating the two parts, NO⁺ and NO₂⁻. The IM1′-W-A releases the reaction energy of 13.45 kcal/mol to form the product complex SO₃-HONO-NH₄NO₂-1 (−56.27 kcal/mol) via TS1’-W-A with the energy barrier of 6.44 kcal/mol. The NH₃ molecule and the H₂O molecule not only serve as catalyst and stabilizer, but also act as reactants to produce HONO and NH₄NO₂. It is different from the pathway of two H₂O molecules, because the NH₃ is more protophilia than water and the HONO is liable to provide a proton to form NH₄NO₂. The other pathway is analogous with RC1-W-A to SO₃-HONO-NH₄NO₂-1. The energy barrier and energy reaction are 40.30 kcal/mol and −18.60 kcal/mol in oxidation reaction and 8.55 kcal/mol and −13.06 kcal/mol in hydrolysis reaction, respectively.

Figure 6.

Potential energy profile for the reaction of SO₂-2NO₂-H₂O-NH₃. The yellow spheres are S atoms, the red spheres are O atom, the blue spheres are N atom, and the white spheres represent H atom, respectively. (Unit: Energies in kcal/mol; bond lengths in angstroms). The black and red lines are the different pathways. The black line represents the reaction of t-ONONO₂-H₂O-NH₃-SO₂, and the red line is the reaction of c-ONONO₂-H₂O-NH₃-SO₂.

Compared with the one-water reaction, the energy barrier for the SO₂-oxidation reaction is reduced by 2.92 kcal/mol and 7.24 kcal/mol, respectively. Compared with the two-water reaction, it shows that the NH₃ molecule plays a more important role in stabilizing the complexes and lowering the energy barrier. When ammonia (NH₃) is present in hydrolysis reaction, the product complexes form ammonium nitrite (NH₄NO₂). The most important reason is that the ability of NH₃ to acquire the proton is stronger than water.

2.2.3. The Reaction of SO₂-2NO₂-2H₂O-NH₃

The structure of reactant complex RC1-2W-A and RC2-2W-A is formed by replacing one H₂O molecule from RC1-3W and RC2-3W with NH₃ in Figure 7. IM1-2W-A (−51.74 kcal/mol) is formed via TS1-2W-A (6.08 kcal/mol), in which the energy barrier and energy reaction are 39.21 kcal/mol and −18.61 kcal/mol, respectively. IM1′-2W-A (−51.78 kcal/mol) is formed by the migration process of H₂O_(a) molecule. The IM1′-2W-A is converted into the product complex SO₃-2HONO-H₂O-NH₃-1 (−48.42 kcal/mol) via the transition state TS1’-2W-A (−45.52 kcal/mol). The corresponding reaction energy and energy barrier are 3.36 kcal/mol and 6.26 kcal/mol, respectively. On account of the similarity to the above pathway, we will not describe the details about the other pathway. The energy barrier and reaction energy are shown in the Table 1. As shown in Table S7, the reaction SO₂-2NO₂-2H₂O-NH₃→SO₃-2HONO-H₂O-NH₃-2 is exothermic and spontaneous.

Figure 7.

Potential energy profile for the reaction of SO₂-2NO₂-2H₂O-NH₃. The yellow spheres are S atoms, the red spheres are O atom, the blue spheres are N atom, and the white spheres represent H atom, respectively. (Unit: Energies in kcal/mol; bond lengths in angstroms). The black and red lines are the different pathways. The black line represents the reaction of t-ONONO₂-2H₂O-NH₃-SO₂, and the red line is the reaction of c-ONONO₂-2H₂O-NH₃-SO₂.

In presence of one NH₃ molecule, the NH₃ molecule and two H₂O molecules serve as solvent to reduce energy barrier and stable structures, and the one H₂O molecule and the NH₃ molecule serve as reactant to produce HONO and NH₄NO₂.

2.2.4. The Reaction of SO₂-2NO₂-H₂O-2NH₃

Figure 8 explores the equilibrium structures and potential energy of SO₂-2NO₂-H₂O-2NH₃. Table S8 summarizes the relative energies, enthalpies and Gibbs free energies in all relevant species. Similar to the previous reactions, the reactant complexes (RC1-W-2A and RC2-W-2A) are formed through combining NH₃-NH₃ and t/c-ONONO₂-H₂O-SO₂ or SO₂ and t/c-ONONO₂-H₂O-(NH₃)₂, which equals replacing two H₂O molecules from RC1-3W or RC2-3W with two NH₃ molecules. Starting with the reactant complex RC1-W-2A, the reaction occurs through the transition state TS1-W-2A forming the product complex IM1-W-2A. The process requires an energy barrier of 38.85 kcal/ and reaction energy of −18.80 kcal/mol, respectively. The IM1′-W-2A, with a binding energy of 51.69 kcal/mol, can serve as the reactant complex in the next step. The SO₃-HONO-NH₄NO₂-NH₃-1 (−71.15 kcal/mol) is resulted from IM1′-W-2A by the only H₂O molecule reacting between the NO⁻ and NO₂⁻, along with energy barrier and energy reaction of 9.04 kcal/mol and −19.46 kcal/mol, respectively. As shown in Figure 8, the other pathway is similar to the reaction of RC1-W-2A to SO₃-HONO-NH₄NO₂-NH₃-1. There are energy barrier and reaction energy of 40.26 kcal/mol and −19.51 kcal/mol in oxidation reaction, respectively. In the hydrolysis process, the energy barrier and reaction energy are 12.68 kcal/mol and −16.28 kcal/mol, respectively. Table S8 indicates that both reaction pathways SO₂-2NO₂-H₂O-2NH₃→SO₃-HONO-NH₄NO₂-1 and SO₃-HONO-NH₄NO₂-2 are exothermic and spontaneous.

Figure 8.

Potential energy profile for the reaction of SO₂-2NO₂-H₂O-2NH₃. The yellow spheres are S atoms, the red spheres are O atom, the blue spheres are N atom, and the white spheres represent H atom, respectively. (Unit: Energies in kcal/mol; bond lengths in angstroms). The black and red lines are the different pathways. The black line represents the reaction of t-ONONO₂-H₂O-2NH₃-SO₂, and the red line is the reaction of c-ONONO₂-H₂O-2NH₃-SO₂.

In presence of two NH₃ molecules, two NH₃ molecules and the only H₂O molecule serve as catalyst and stabilizer, and the one NH₃ molecule and H₂O molecule serve as reactant to produce NH₄NO₂.

Compared with the three-water reaction, the proportion of H₂O and NH₃ molecules is 2:1 and 1:2. The result indicates that the energy barrier is slighting different from the three-water molecule in the SO₂-oxidation reaction. In the hydrolytic reaction, the energy barrier is higher than the three-water molecule, and these processes release more reaction energy. Moreover, the binding energy of product complexes is lower than that of the SO₃-2HONO-2H₂O. This result shows that the NH₃ molecule plays a significant role in stabilizing complexes.

3. Materials and Methods

All quantum chemistry calculations are performed by Gaussian 09 programs (vB.01, Gaussian, Inc, Wallingford, CT, USA) [36]. The structures of the reactant (RC), product (PC), intermediate (IM), and transition states (TS) are optimized using M06-2X density functional method with the 6-311++G (d, p) basis set [37]. This is relatively accurate and time-efficient when used to study the reaction mechanism and has been employed successfully in our previous studies [38,39]. The vibrational frequencies have been obtained to verify that the reactant complexes, intermediates, and product complexes have all positive frequencies and that the transition state (TS) geometries have only one imaginary frequency at the same level. According to the calculation of vibrational frequencies, zero-point energy (ZPE) and thermal correction are also obtained at the same level to decide their characteristics and thermodynamic properties. All the enthalpies (H) and Gibbs free energies (G) are calculated with thermal correction at 298.15 K. Moreover, the intrinsic reaction coordinate (IRC) calculation is used to verify whether each transition state is connected with the corresponding intermediates [40]. The single-point energies of all stationary points are refined using the more precise basis set for M06-2X/6-311++G (3df, 3pd) [41]. The ultrafine integration grid is applied to improving the accuracy during the whole gas-phase calculation. We also calculated electrostatic potential (ESP) to analyze charge distribution for NO⁺NO₃⁻ and NO⁺NO₂⁻ fragments of RC and IM with the same basis [42,43]. The geometries are visualized using the CYL view software package (v1.0b, Université de Sherbrooke, Montreal, QC, Canada) [44].

4. Conclusions

In this paper, the reaction mechanism of SO₂ with NO₂ to form SO₃ in the presence of H₂O and NH₃ is investigated. Table S9 represents that Cartesian coordinates for all relative Optimized geometries (reactants, transient states and products) at M06-2X/6-311++G(d,p), x coordinate, y coordinate and z coordinate. The effects of different amounts of H₂O and NH₃ have been studied in detail. The results indicate that HONO cannot be formed in the absence of H₂O molecules. In the oxidation step of the system SO₂-2NO₂-nH₂O (n = 0, 1, 2, 3), H₂O plays a catalytic role to produce SO₃, which reduces the energy barrier. In the hydrolytic step, the energy barrier of two H₂O molecules is larger than that of one or three H₂O molecules. But it is still thermodynamically favorable. When NH₃ is involved in the reaction, the energy barrier is lower than SO₂-2NO₂ in the oxidation step. For SO₂-2NO₂-2H₂O, when the ratio of NH₃ to H₂O is 1:1, the energy barrier changes more greatly than SO₂-2NO₂-2H₂O. For SO₂-2NO₂-3H₂O, when the ratio of NH₃ to H₂O is 1:2 and 2:1, the change of the energy barrier is not obvious. Compared to pure water reactions, the role of NH₃ in stabilizing product complexes and acquiring protons is more effective than H₂O. This research provides a new insight into reaction pathways of sulfuric acid formation, and can also contribute to the further study of aerosol surface reactions.

Abbreviations

PM	Particulate Matter
DFT	Density Functional Theory
RC	Reactant complex
IM	Intermediate
PC	Product
TS	Transient state
IRC	Intrinsic reaction coordinate
ESP	Electrostatic potential

Supplementary Materials

The following are available online at https://www.mdpi.com/1422-0067/20/15/3746/s1.

Author Contributions

Conceptualization, Z.W., C.Z., G.L., and X.S.; methodology, Z.W., G.L., X.S., and N.W.; writing—original draft, Z.W.; writing—review and editing, C.Z., G.L., X.S., and Z.L.

Funding

This research was funded by National Natural Science Foundation of China, grant number 21337001 and 21607011; Natural Science Foundation of Shandong Province, grant number ZR2018MB043; the Fundamental Research Fund of Shandong University, grant number 2018JC027; and Focus on research and development plan in Shandong province, grant number 2019GSF109037.

Conflicts of Interest

The authors declare no conflicts of interest.