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

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.


Introduction
Sulfur dioxide (SO 2 ), 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. SO 2 can be oxidized to form sulfuric acid (H 2 SO 4 ) 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 (O 3 ) and hydrogen peroxide (H 2 O 2 ) [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 SO 2 oxidation mechanism in the atmosphere.
In the presence of water, the process of NO 2 dimerization is likely to occur in polluted atmospheric conditions [26,27]. Some studies have demonstrated that N 2 O 4 , the dimer of NO 2 , serves as the oxidant to oxidize SO 2 on the aerosol surface [28][29][30]. For NO 2 dimer, three isomers, symmetric sys-O 2 N-NO 2 , and asymmetric t-ONONO 2 , c-ONONO 2 , can be found. The sys-O 2 N-NO 2 is very stable due to its symmetry, while asymmetric ONO-NO 2 can be rapidly converted to NO + and NO 3 − in the presence of water [31][32][33][34]. The ion pairs (NO + NO 3 − ) can also oxidize many organic and inorganic compounds [35].
Although these studies have shown that SO 2 can react with NO 2 to produce H 2 SO 4 , the reaction mechanism is not completely understood.
In this paper, we researched the gas-phase reaction of SO 2 with NO 2 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 NH 3 in the oxidation reaction also is considered.  Table S1. Two main pathways are found due to the formation of two NO 2 dimers, t-ONONO 2 and c-ONONO 2 . The pre-reactive complexes (RC1 and RC2) are produced by a collision of SO 2  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.    Table S2. In these two pathways, the complexes (t-ONONO 2 -H 2 O and c-ONONO 2 -H 2 O) are firstly produced via the interaction between an N 2 O 4 molecule and a water molecule. Through a collision with SO 2 , the two complexes can transform into the pre-reactive complex (RC1-1W and RC2-1W).

Results and Discussion
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 + NO 3 − fragment is transferred to SO 2 , leading to the formation of SO 3 . The complex IM1-1W can undergo an isomerization process to form IM -1W with the energy absorption of 0.14 kcal/mol. Because the H 2 O molecule gets involved, the NO + NO 2 − fragments are divided into two parts, and the NO + fragment rotates by an angle. Once the IM -1W is produced, the final complex SO 3 -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 SO 3 -2HONO, the water molecule reacts with the isolated NO + fragment and NO 2 − 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 SO 3 -2HONO). The reactant (IM -1W) is formed via IM2-1W releasing the energy of 0.09 kcal/mol. In the same way, the SO 3 -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 H 2 O molecule and the hydrolysis reaction cannot produce HONO. The result indicates that H 2 O molecule reacts as the solvent to reduce activation energy and stable structures and also is a critical reactant in the formation of HONO.
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.  Tables 1 and 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.
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.  Tables 1 and 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 SO 2 -2NO 2 -2H 2 O. In these pathways, the pre-reactive complexes (RC1-2W and RC2-2W) are produced via the interaction between the complexes (t-ONONO 2  The H 2 O (a) molecule reacts with NO + NO 2 − 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 H 2 O molecules, the H 2 O (a) serves as reactant to form HONO, and the other H 2 O (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.
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.

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 Tables 1 and 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.
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

The Reaction of SO
The consequence of three H 2 O molecules taking part in reaction is shown in Figure 4. The corresponding energy data and the charge distribution are put in Tables 1 and 2. Table S4 summarizes the relative energies, enthalpies and Gibbs free energies in all relevant species for the  Table 1. As shown in Table S4, the reaction SO 2 -2NO 2 -3H 2 O→SO 3 -2HONO-2H 2 O-1 is exothermic and spontaneous. In comparison to one-water molecules in the process of SO 2 oxidation, three H 2 O 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 H 2 O 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 H 2 O 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 H 2 O molecule increasing.

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 Tables 1 and 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 40.60kcal/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 = −37.16kcal/mol and ΔG = −3.12kcal/mol).
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.   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 Tables 1 and 2. Reactant complexes (RC1-1A and RC2-1A) are formed through the collision between complexes (t-ONONO 2 -NH 3 and c-ONONO 2 -NH 3 ) and SO 2 , which is equivalent to replacing one H 2 O molecule from RC1-1W and RC2-1W with NH 3 . 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 H 2 O molecule. As we can see in Table S5, the reaction SO 2 -2NO 2 -NH 3 →IM1-1A is exothermic and spontaneous (∆H = −37.16 kcal/mol and ∆G = −3.12 kcal/mol).
Compared with the reaction pathway of SO 2 -2NO 2 to IM1 and IM2, the result indicates that NH 3 molecule can serve as catalyst and solvent to reduce the energy barrier and stable structures. The NH 3 molecule cannot trigger the hydrolysis reaction to produce HONO.

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.
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.

The Reaction of SO 2 -2NO 2 -H 2 O-NH 3
The relative energies, enthalpies and Gibbs free energies in all relevant species for SO 2 -2NO 2 -H 2 O-NH 3 are summarized in Table S6. As shown in Figure 6, RC1-1W-1A and RC2-1W-1A are formed after SO 2 attacks the complex t/c-ONONO 2  Compared with the one-water reaction, the energy barrier for the SO 2 -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 NH 3 molecule plays a more important role in stabilizing the complexes and lowering the energy barrier. When ammonia (NH 3 ) is present in hydrolysis reaction, the product complexes form ammonium nitrite (NH 4 NO 2 ). The most important reason is that the ability of NH 3 to acquire the proton is stronger than water.
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. 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 SO 2 -2NO 2 -2H 2 O-NH 3 →SO 3 -2HONO-H 2 O-NH 3 -2 is exothermic and spontaneous.
In presence of one NH 3 molecule, the NH 3 molecule and two H 2 O molecules serve as solvent to reduce energy barrier and stable structures, and the one H 2 O molecule and the NH 3 molecule serve as reactant to produce HONO and NH 4 Table S8 indicates that both reaction pathways SO2-2NO2-H2O-2NH3→SO3-HONO-NH4NO2-1 and SO3-HONO-NH4NO2-2 are exothermic and spontaneous.
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  Compared with the three-water reaction, the proportion of H 2 O and NH 3 molecules is 2:1 and 1:2. The result indicates that the energy barrier is slighting different from the three-water molecule in the SO 2 -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 SO 3 -2HONO-2H 2 O. This result shows that the NH 3 molecule plays a significant role in stabilizing complexes. 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.

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].

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

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 + NO 3 − and NO + NO 2 − 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].

Conclusions
In this paper, the reaction mechanism of SO 2 with NO 2 to form SO 3 in the presence of H 2 O and NH 3 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 H 2 O and NH 3 have been studied in detail. The results indicate that HONO cannot be formed in the absence of H 2 O molecules. In the oxidation step of the system SO 2 -2NO 2 -nH 2 O (n = 0, 1, 2, 3), H 2 O plays a catalytic role to produce SO 3 , which reduces the energy barrier. In the hydrolytic step, the energy barrier of two H 2 O molecules is larger than that of one or three H 2 O molecules. But it is still thermodynamically favorable. When NH 3 is involved in the reaction, the energy barrier is lower than SO 2 -2NO 2 in the oxidation step. For SO 2 -2NO 2 -2H 2 O, when the ratio of NH 3 to H 2 O is 1:1, the energy barrier changes more greatly than SO 2 -2NO 2 -2H 2 O. For SO 2 -2NO 2 -3H 2 O, when the ratio of NH 3 to H 2 O is 1:2 and 2:1, the change of the energy barrier is not obvious. Compared to pure water reactions, the role of NH 3 in stabilizing product complexes and acquiring protons is more effective than H 2 O. 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.