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

International Journal of Molecular Sciences

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

Zehua Wang 1, Chenxi Zhang 2, Guochun Lv 1, Xiaomin Sun 1,*, Ning Wang 1 and Zhiqiang Li 3,*

1 Environment Research Institute, Shandong University, Jinan 250100, China 2 College of Biological and Environmental Engineering, Binzhou University, Binzhou 256600, China 3 Center for Optics Research and Engineering (CORE), Shandong University, Qingdao 266237, China * Correspondence: [email protected] (X.S.); [email protected] (Z.L.)

Received: 24 June 2019; Accepted: 29 July 2019; Published: 31 July 2019

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.

Keywords: sulfuric acid; sulfur dioxide; nitrogen dioxide; synergistic oxidation; hydrolysis reaction

1. Introduction

Sulfur dioxide (SO2), a major air pollutant, is released into the atmosphere via the combustion of sulfur containing fuels and industrial production [1–3], volcanic eruptions, and decomposition of sulfides in nature. SO2 can be oxidized to form sulfuric acid (H2SO4) through the homogeneous or heterogeneous processes [4–6], which include gas-phase oxidation by hydroxyl radical (OH ) • and in-cloud oxidation by dissolved ozone (O3) and hydrogen peroxide (H2O2)[7–9]. 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 [10–12]. Thus, it is significant to investigate the SO2 oxidation mechanism in the atmosphere. In hazy weather, researchers have found that a considerable amount of PM2.5 can be formed in the atmosphere, and sulfate is the significant component of the fine particulate matter [13–18]. 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 [19–24]. Wang et al. have

Int. J. Mol. Sci. 2019, 20, 3746; doi:10.3390/ijms20153746 www.mdpi.com/journal/ijms Int. J. Mol. Sci. 2019, 20, 3746 2 of 14

considered that NO2 could eﬀectively react with SO2 in the presence of H2O and NH3 during the severe haze period [25]:

+ 2 SO (g) + 2NO (g) + 2H O(aq) 2H (aq) + SO −(aq) + 2HONO(g) (1) 2 2 2 → 4 + 2 2NH (g) + SO (g) + 2NO (g) + 2H O(aq) 2NH (aq) + SO −(aq) + 2HONO(g) (2) 3 2 2 2 → 4 4 2 From Reaction (1) and (2), it can be seen that the final products primarily include SO4 − 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 [28–30]. 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 [31–34]. 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 Figure1, Tables1 and2 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 SO . The IM1 (a binding of 23.27 kcal/mol) is formed via 2 − 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+NO − 3− fragments transforms into SO2 to lead to the formation of SO3. As shown in Table S1, the reaction SO -2NO IM1 is exothermic and spontaneous (∆H of 24.50 kcal/mol and ∆G of 0.29 kcal/mol at 2 2→ − − 298.15K). Due to the absence of H2O molecule, the hydrolysis process cannot be carried out, and HONO cannot be generated, ﬁnally. Int. J. Mol. Sci. 2019, 20, x FOR PEER REVIEW 2 of 14

SOg 2NOg 2HOaq →2H aq SO aq 2HONOg (1) 2NHg SOg 2NOg 2HOaq → 2NH aq SO aq 2HONOg (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 [28–30]. 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 [31–34]. 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, Tables 1 and 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 Int. J. Mol. Sci. 2019, 20, 3746 3 of 14 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 Energy Barrier Reaction Energy Energy Barrier Reaction Energy Reaction Systems (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) 45.48 11.49 SO -2NO − 2 2 52.45 5.77 − 41.80 13.16 0.29 3.27 SO -2NO -H O − − 2 2 2 47.54 13.05 0.29 3.27 − − 40.14 14.75 4.36 3.94 SO -2NO -2H O − − 2 2 2 41.47 15.87 3.06 1.85 − − 36.49 19.48 2.63 4.15 SO -2NO -3H O − − 2 2 2 38.77 21.34 1.87 6.56 − − 40.60 20.10 SO -2NO -NH − 2 2 3 48.85 13.76 − 38.92 17.85 6.44 13.45 SO -2NO -H O-NH − − 2 2 2 3 40.30 18.60 8.55 13.06 − − 39.21 18.61 6.26 3.36 SO -2NO -2H O-NH − 2 2 2 3 39.77 18.46 12.43 14.42 − − 38.85 18.80 9.04 19.46 SO -2NO -H O-2NH − − 2 2 2 3 40.26 19.51 12.68 16.28 − − Int. J. Mol. Sci. 2019, 20, 3746 4 of 14

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

2.1.2. The Reaction of SO2-2NO2-H2O

Figure2 explores the equilibrium structures and potential energy of SO 2-2NO2-H2O. The corresponding energy data and the numerical value of charge distribution are put in Tables1 and2. 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). 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 IM0-1W 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 IM0-1W 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 IM0-1W 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 (IM0-1W to SO3-2HONO). The reactant (IM0-1W) 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. Int. J. Mol. Sci. 2019, 20, x FOR PEER REVIEW 4 of 14 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.Int. J. Mol. Sci. 2019, 20, 3746 5 of 14

Figure 2. Potential energy profile for the reaction of SO2-2NO2-H2O. The yellow spheres are S atoms, Figurethe red 2. Potential spheres areenergy O atom, profile the for blue the spheresreaction are of SO N atom,2-2NO2 and-H2O. the The white yellow spheres spheres represent are S atoms, H atom, therespectively. red spheres (Unit:are O Energiesatom, the in blue kcal spheres/mol; bond are lengthsN atom, in and angstroms). the white The spheres black represent and red lines H atom, are the 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 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. the reaction of c-ONONO2-H2O-SO2. 2.1.3. The Reaction of SO2-2NO2-2H2O 2.1.3. The Reaction of SO2-2NO2-2H2O Figure3 presents the optimized geometries of molecular species involved in the reaction of SOFigure2-2NO 23-2H presents2O to examinethe optimized the role geometries of an additional of molecular H2O species molecule. involved Tables in1 andthe 2reaction show theof SOcorresponding2-2NO2-2H2O to energy examine data the and role the of charge an additional distribution. H2O molecule. Table S3 showsTables the1 and relative 2 show energies, the correspondingenthalpies and energy Gibbs freedata energiesand the in charge all relevant distri speciesbution. for Table the SOS32 -2NOshows2-2H the2O. relative In these energies, pathways, enthalpiesthe pre-reactive and Gibbs complexes free energies (RC1-2W in all andrelevant RC2-2W) species are for produced the SO2-2NO via2 the-2H interaction2O. In these betweenpathways, the thecomplexes pre-reactive (t-ONONO complexes2-2H (RC1-2W2O and and c-ONONO RC2-2W)2-2H are2O) produced and SO 2via, or the a collisioninteraction of thebetween complexes the complexes(t-ONONO (t-ONONO2-H2O-SO22-2Hand2O c-ONONO and c-ONONO2-H2O-SO2-2H2)2O) with and H2 O.SO2, or a collision of the complexes (t-ONONOStarting2-H2O-SO with2 theand complexc-ONONO RC1-2W2-H2O-SO (2)25.32 with H kcal2O./ mol), the intermediate complex IM1-2W − ( 40.06Starting kcal with/mol) the is formed complex via RC1-2W TS1-2W with(−25.32 the kcal/mol), energy barrier the ofintermediate 40.14 kcal/ mol.complex The isomerizedIM1-2W − + (−40.06intermediate kcal/mol) complex is formed IM1 via0-2W TS1-2W ( 40.89 with kcal the/mol) energy is formed barrier byof 40.14 the H kcal/mol.2O(a) closing The toisomerized NO NO2 −. −+ + − intermediateThe H2O(a) moleculecomplex IM1’-2W reacts with (− NO40.89NO kcal/mol)2− with anis formed energy barrierby the andH2O reaction(a) closing energy to NO of 4.36NO2 kcal. The/mol H2andO(a) molecule3.94 kcal reacts/mol, with respectively. NO+NO2 The− with other an pathwayenergy barrier is analogous and reaction with theenergy above of process,4.36 kcal/mol and the − andbarrier −3.94 (41.47kcal/mol, kcal /respectively.mol) is slightly The higher other than pathway the reaction is analogous pathway with involving the above in TS1-2W. process, and the barrier In(41.47 the presencekcal/mol) of is two slightly H2O higher molecules, than the the H reaction2O(a) serves pathway as reactant involving to form in TS1-2W. 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. Int. J. Mol. Sci. 2019, 20, x FOR PEER REVIEW 5 of 14

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/molInt. J. Mol. for Sci. TS2-1W.2019, 20, 3746 It shows that the second-water molecule plays a certain role in lowering6 the of 14 energy barrier and stabilizing the complexes structures.

FigureFigure 3. 3. PotentialPotential energy proﬁleprofile forfor the the reaction reaction of SOof 2SO-2NO2-2NO2-2H2-2H2O.2O. The The yellow yellow spheres spheres are Sare atoms, S atoms,the red the spheres red spheres are O are atom, O atom, the blue the spheresblue sphe areres N are atom, N atom, and theand white the white spheres spheres represent represent H atom, H atom,respectively. respectively. (Unit: (Unit: Energies Energies in kcal in/ mol;kcal/mol; bond bo lengthsnd lengths in angstroms). in angstroms). The black The black and red and lines red arelines the aredi ﬀtheerent different pathways. pathways. The black The line black represents line represents the reaction the reaction of t-ONONO of t-ONONO2-2H2O-SO2-2H2, and2O-SO the2, redand line the is redthe line reaction is the ofreaction c-ONONO of c-ONONO2-2H2O-SO2-2H2. 2O-SO2.

2.1.4. The Reaction of SO2-2NO2-3H2O 2.1.4. The Reaction of SO2-2NO2-3H2O

The consequence of three H2O molecules taking part in reaction is shown in Figure4. The consequence of three H2O molecules taking part in reaction is shown in Figure 4. The correspondingThe corresponding energy energy data dataand andthe charge the charge distribution distribution are areput putin inTables Tables 1 1 andand 22.. Table S4S4 summarizessummarizes the the relative relative energies, energies, enthalpies enthalpies and and Gi Gibbsbbs free free energies energies in in all all relevant relevant species species for for the the SO2-2NO2-3H2O. The reactant complex RC1-3W ( 30.18 kcal/mol) and RC2-3W ( 28.19 kcal/mol) may SO2-2NO2-3H2O. The reactant complex RC1-3W −(−30.18 kcal/mol) and RC2-3W− (−28.19 kcal/mol) be formed after SO2 attacks the tetramer complexes (t-ONONO2-(H2O)3 and c-ONONO2-(H2O)3), may be formed after SO2 attacks the tetramer complexes (t-ONONO2-(H2O)3 and or H2O attacks t-ONONO2-(H2O)2-SO2 and t-ONONO2-(H2O)2-SO2, respectively. To form the c-ONONO2-(H2O)3), or H2O attacks t-ONONO2-(H2O)2-SO2 and t-ONONO2-(H2O)2-SO2, respectively. ToIM1-3W form the from IM1-3W RC1-3W, from there RC1-3W, is an energy there barrieris an energy of 36.49 barrier kcal/mol of at36.49 the transitionkcal/mol at state the TS1-3W transition and statereducing TS1-3W reaction and reducing energy of reaction 19.48 kcal energy/mol. of The 19.48 reactant kcal/mol. complex The ofreactant hydrolysis complex reaction of hydrolysis is IM10-3W, + and NO NO2− is divided by+ the− closing of H2O molecule. Through the TS1’-3W ( 45.75 kcal/mol), reaction is IM1’-3W, and NO NO2 is divided by the closing of H2O molecule. Through− the TS1’-3W a stable product complex SO3-2HONO-2H2O-1 ( 52.53 kcal/mol) is produced eventually. The oxidation (−45.75 kcal/mol), a stable product complex SO− 3-2HONO-2H2O-1 (−52.53 kcal/mol) is produced eventually.reaction of The the otheroxidation pathway reaction is approximately of the other pathway similar to is RC1-3Wapproximately to IM1-3W. similar It isto di RC1-3Wfferent from to the above hydrolytic processes, and H O reacts as a transporter to transmit a proton forming IM1-3W. It is different from the above hydrolytic2 (c) processes, and H2O(c) reacts as a transporter to H O+ intermediate. The relevant energy barrier and reaction energy of the process are shown in transmit3 a proton forming H3O+ intermediate. The relevant energy barrier and reaction energy of Table1. As shown in Table S4, the reaction SO 2-2NO2-3H2O SO3-2HONO-2H2O-1 is exothermic the process are shown in Table 1. As shown in Table S4,→ the reaction SO2-2NO2-3H2O → and spontaneous. SO3-2HONO-2H2O-1 is exothermic and spontaneous. In comparison to one-water molecules in the process of SO oxidation, three H O molecules In comparison to one-water molecules in the process of SO2 2oxidation, three H2O2 molecules havehave successfully successfully reduced reduced the the energy energy barrier barrier height height by 5.35 by 5.35 kcal/mol kcal/mol and and8.77 8.77kcal/mol. kcal/ mol.In these In thesetwo two pathways, the two additional H O molecules act only as a solvent without entering into the pathways, the two additional H2O molecules2 act only as a solvent without entering into the reaction. Itreaction. shows that It shows the third-water that the third-water moleculemolecule plays a si playsgnificant a significant role in rolestabilizing in stabilizing the complexes the complexes and and lowering the energy barrier. As the number of H O increases, the releasing energy gets more and lowering the energy barrier. As the number of H2O increases,2 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. Int. J. Mol. Sci. 2019, 20, x FOR PEER REVIEW 6 of 14 more, and the configurations of product complexes are more and more stable. The hydrolysis Int. J. Mol. Sci. 2019, 20, 3746 7 of 14 reaction is still favorable thermodynamically with the number of H2O molecule increasing.

Figure 4. Potential energy proﬁle for the reaction of SO2-2NO2-3H2O. The yellow spheres are S atoms, Figurethe red 4. spheres Potential are energy O atom, profile the blue for spheres the reaction are N atom,of SO2 and-2NO the2-3H white2O. The spheres yellow represent spheres H are atom, S atoms,respectively. the red (Unit: spheres Energies are O inatom, kcal /themol; blue bond sphe lengthsres are in N angstroms). atom, and the The white black spheres and red represent lines are the H

atom,diﬀerent respectively. pathways. (Unit: The black Energies line represents in kcal/mol; the bo reactionnd lengths of t-ONONO in angstroms)2-3H2O-SO. The 2black, and and the redred line lines is arethe the reaction different of c-ONONO pathways.2-3H The2O-SO black2 .line represents the reaction of t-ONONO2-3H2O-SO2, and the red line is the reaction of c-ONONO2-3H2O-SO2. 2.2. The Reaction of SO2-2NO2-nH2O-mNH3 (n = 0, 1, 2; m = 1, 2)

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

2.2.1. FigureThe Reaction5 explores of SO the2-2NO equilibrium2-NH3 structures and potential energy of the system 2NO 2-SO2-NH3. Table S5 summarizes the relative energies, enthalpies and Gibbs free energies in all relevant species. Figure 5 explores the equilibrium structures and potential energy of the system 2NO2-SO2-NH3. TableThe corresponding S5 summarizes thermodynamic the relative en dataergies, and enthalpies the charge and distribution Gibbs free are en putergies in Tables in all 1relevant and2. Reactant species. Thecomplexes corresponding (RC1-1A andthermodynamic RC2-1A) are formeddata and through the char the collisionge distribution between are complexes put in (t-ONONOTables 1 and2-NH 2.3 Reactantand c-ONONO complexes2-NH 3(RC1-1A) and SO and2, which RC2-1A) is equivalent are formed to replacingthrough the one collision H2O molecule between from complexes RC1-1W and RC2-1W with NH3. RC1-1A ( 15.12 kcal/mol) is converted into IM1-1A ( 35.22 kcal/mol) via the (t-ONONO2-NH3 and c-ONONO−2-NH3) and SO2, which is equivalent to− replacing one H2O transformation of an O molecule with the energy barrier and reaction energy of 40.60 kcal/mol and molecule from RC1-1W and RC2-1W with NH3. RC1-1A (–15.12 kcal/mol) is converted into IM1-1A 20.10 kcal/mol, respectively. The other pathway is similar to the above pathway with the energy barrier (−−35.22 kcal/mol) via the transformation of an O molecule with the energy barrier and reaction and reaction energy of 48.85 kcal/mol and 13.76 kcal/mol, respectively. The hydrolytic process cannot occur energy of 40.60kcal/mol and −20.10 kcal/mol,− respectively. The other pathway is similar to the above because of the absence of H O molecule. As we can see in Table S5, the reaction SO -2NO -NH IM1-1A pathway with the energy2 barrier and reaction energy of 48.85 kcal/mol and2 −13.762 3kcal/mol,→ is exothermic and spontaneous (∆H = 37.16 kcal/mol and ∆G = 3.12 kcal/mol). respectively. The hydrolytic process cannot− occur because of the− absence of H2O molecule. As we Compared with the reaction pathway of SO2-2NO2 to IM1 and IM2, the result indicates that NH3 can see in Table S5, the reaction SO2-2NO2-NH3→IM1-1A is exothermic and spontaneous (ΔH = −molecule37.16kcal/mol can serve and asΔG catalyst = −3.12kcal/mol). and solvent to reduce the energy barrier and stable structures. The NH3 molecule cannot trigger the hydrolysis reaction to produce HONO. 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.

Int. J. Mol. Sci. 2019, 20, 3746 8 of 14 Int. J. Mol. Sci. 2019, 20, x FOR PEER REVIEW 7 of 14

Figure 5. Potential energy proﬁle for the reaction of SO2-2NO2-NH3. The yellow spheres are S atoms, 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, 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 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 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. the reaction of c-ONONO2-NH3-SO2.

2.2.2. The Reaction of SO2-2NO2-H2O-NH3 2.2.2. The Reaction of SO2-2NO2-H2O-NH3 The relative energies, enthalpies and Gibbs free energies in all relevant species for SO2-2NOThe 2relative-H2O-NH energies,3 are summarized enthalpies in Tableand S6.Gibbs As shown free inenergies Figure 6,in RC1-1W-1A all relevant and RC2-1W-1Aspecies for 2 2 2 3 SOare formed-2NO -H afterO-NH SO2 attacksare summarized the complex tin/c-ONONO Table S6.2-H 2AsO-NH shown3 or NH in3 attacksFigure t/c-ONONO6, RC1-1W-1A2-H2O-SO and2. TheRC2-1W-1A product complexare formed IM1-W-A after (SO43.262 attacks kcal/mol) the iscomplex formed throught/c-ONONO TS1-W-A2-H2O-NH (13.513 kcal or /mol)NH3 withattacks the − t/c-ONONOenergy barrier2-H and2O-SO reaction2. The energy product of 38.92 complex kcal/mol IM1-W-A and 17.85 (−43.26 kcal/ mol,kcal/mol) respectively. is formed When through the only + − waterTS1-W-A molecule (13.51 getskcal/mol) close to with the NOthe energyNO2−, barrier the reactant and reaction complex energy (IM10-W-A) of 38.92 of hydrolysiskcal/mol and reaction −17.85 is + + 2− kcal/mol,formed through respectively. separating When the twothe parts,only NOwaterand molecule NO2−. Thegets IM1 close0-W-A to releasesthe NO theNO reaction, the energyreactant of + 13.45complex kcal (IM1’-W-A)/mol to form of the hydrolys productis complex reaction SO is 3formed-HONO-NH through4NO separating2-1 ( 56.27 the kcal two/mol) parts, via TS1’-W-A NO and 2− − withNO . the The energy IM1’-W-A barrier releases of 6.44 kcalthe /reactionmol. The energy NH3 molecule of 13.45 andkcal/mol the H to2O form molecule the product not only complex serve as 3 4 2 SOcatalyst-HONO-NH and stabilizer,NO -1 but (−56.27 also kcal/mol) act as reactants via TS1’-W-A to produce with HONO the energy and NH barrier4NO of2. It6.44 is dikcal/mol.ﬀerent from The 3 2 NHthe pathway molecule of twoand Hthe2O H molecules,O molecule because not theonly NH serve3 is moreas catalyst protophilia and thanstabilizer, water but and also the HONOact as 4 2 2 reactantsis liable to to provide produce a HONO proton toand form NH NHNO4NO. It 2is. Thedifferent other from pathway the pathway is analogous of two with H O RC1-W-A molecules, to becauseSO -HONO-NH the NH3 isNO more-1. Theprotophilia energy barrier than water and energy and the reaction HONO are is 40.30liable kcal to provide/mol and a proton18.60 kcal to form/mol 3 4 2 − NHin oxidation4NO2. The reaction other andpathway 8.55 kcalis analogous/mol and with13.06 RC1-W-A kcal/molin to hydrolysis SO3-HONO-NH reaction,4NO respectively.2-1. The energy barrier and energy reaction are 40.30 kcal/mol− and −18.60 kcal/mol in oxidation reaction and 8.55 Compared with the one-water reaction, the energy barrier for the SO2-oxidation reaction is kcal/molreduced byand 2.92 −13.06 kcal kcal/mol/mol and in 7.24 hydrolysis kcal/mol, reaction, respectively. respectively. Compared with the two-water reaction, Compared with the one-water reaction, the energy barrier for the SO2-oxidation reaction is it shows that the NH3 molecule plays a more important role in stabilizing the complexes and lowering reduced by 2.92 kcal/mol and 7.24 kcal/mol, respectively. Compared with the two-water reaction, it the energy barrier. When ammonia (NH3) is present in hydrolysis reaction, the product complexes shows that the NH3 molecule plays a more important role in stabilizing the complexes and lowering form ammonium nitrite (NH4NO2). The most important reason is that the ability of NH3 to acquire the protonenergy isbarrier. stronger When than ammonia water. (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.

Int. J. Mol. Sci. 2019, 20, 3746 9 of 14 Int. J. Mol. Sci. 2019, 20, x FOR PEER REVIEW 8 of 14

Figure 6. Potential energy proﬁle for the reaction of SO2-2NO2-H2O-NH3. The yellow spheres are S 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 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 atom, respectively. (Unit: Energies in kcal/mol; bond lengths in angstroms). The black and red lines the diﬀerent pathways. The black line represents the reaction of t-ONONO2-H2O-NH3-SO2, and the are the different pathways. The black line represents the reaction of t-ONONO2-H2O-NH3-SO2, and red line is the reaction of c-ONONO2-H2O-NH3-SO2. the red line is the reaction of c-ONONO2-H2O-NH3-SO2.

2.2.3. The Reaction of SO2-2NO2-2H2O-NH3 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 H OThe molecule structure from of reactant RC1-3W complex and RC2-3W RC1-2W-A with NHand RC2-2W-Ain Figure7 is. formed IM1-2W-A by replacing ( 51.74 kcalone /Hmol)2O 2 3 − moleculeis formed from via RC1-3W TS1-2W-A and (6.08 RC2-3W kcal/ mol),with NH in3 which in Figure the 7. energy IM1-2W-A barrier (−51.74 and energykcal/mol) reaction is formed are via TS1-2W-A (6.08 kcal/mol), in which the energy barrier and energy reaction are 39.21 kcal/mol 39.21 kcal/mol and 18.61 kcal/mol, respectively. IM10-2W-A ( 51.78 kcal/mol) is formed by the and −18.61 kcal/mol,− respectively. IM1’-2W-A (−51.78 kcal/mol) is− formed by the migration process migration process of H2O(a) molecule. The IM10-2W-A is converted into the product complex ofSO H-2HONO-H2O(a) molecule.O-NH The IM1’-2W-A-1 ( 48.42 kcalis converted/mol) via into the the transition product state complex TS1’-2W-A SO3-2HONO-H ( 45.522 kcalO-NH/mol).3-1 3 2 3 − − (The−48.42 corresponding kcal/mol) via reaction the transition energy and state energy TS1’-2W-A barrier ( are−45.52 3.36 kcal/mol). kcal/mol and The 6.26 corresponding kcal/mol, respectively. reaction energyOn account and ofenergy the similarity barrier are to the3.36 above kcal/mol pathway, and 6. we26 willkcal/mol, not describe respectively. the details On aboutaccount the of other the similaritypathway. to The the energy above barrier pathway, and we reaction will not energy describe are shown the details in the about Table 1the. As other shown pathway. in Table The S7, energy barrier and reaction energy are shown in the Table 1. As shown in Table S7, the reaction the reaction SO2-2NO2-2H2O-NH3 SO3-2HONO-H2O-NH3-2 is exothermic and spontaneous. SO2-2NO2-2H2O-NH3→SO3-2HONO-H→ 2O-NH3-2 is exothermic and spontaneous. In presence of one NH3 molecule, the NH3 molecule and two H2O molecules serve as solvent to 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 reduce energy barrier and stable structures, and the one H2O molecule and the NH3 molecule serve reactant to produce HONO and NH4NO2. as reactant to produce HONO and NH4NO2.

Int.Int. J. J. Mol. Mol. Sci. Sci. 20192019, ,2020, ,x 3746 FOR PEER REVIEW 910 of of 14 14

Figure 7. Potential energy proﬁle for the reaction of SO2-2NO2-2H2O-NH3. The yellow spheres are S 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 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 atom, respectively. (Unit: Energies in kcal/mol; bond lengths in angstroms). The black and red lines the diﬀerent pathways. The black line represents the reaction of t-ONONO2-2H2O-NH3-SO2, and the are the different pathways. The black line represents the reaction of t-ONONO2-2H2O-NH3-SO2, and red line is the reaction of c-ONONO2-2H2O-NH3-SO2. the red line is the reaction of c-ONONO2-2H2O-NH3-SO2.

2.2.4. The Reaction of SO2-2NO2-H2O-2NH3 2.2.4. The Reaction of SO2-2NO2-H2O-2NH3 Figure8 explores the equilibrium structures and potential energy of SO 2-2NO2-H2O-2NH3. TableFigure S8 summarizes 8 explores the the relative equilibrium energies, structures enthalpies and and potential Gibbs free energy energies of SO in2 all-2NO relevant2-H2O-2NH species.3. TableSimilar S8 tosummarizes the previous the reactions,relative en theergies, reactant enthalpies complexes and Gibbs (RC1-W-2A free energies and RC2-W-2A) in all relevant are species. formed Similarthrough to combining the previous NH reactions,3-NH3 and the t/ c-ONONOreactant complexes2-H2O-SO (RC1-W-2A2 or SO2 and and t/c-ONONO RC2-W-2A)2-H are2O-(NH formed3)2 , 3 3 2 2 2 2 2 2 3 2 throughwhich equals combining replacing NH two-NH H 2andO molecules t/c-ONONO from-H RC1-3WO-SO or or SO RC2-3W and t/c-ONONO with two NH-H3 molecules.O-(NH ) , whichStarting equals with replacing the reactant two complex H2O molecules RC1-W-2A, from the RC1-3W reaction or occursRC2-3W through with two the NH transition3 molecules. state StartingTS1-W-2A with forming the reactant the product complex complex RC1-W-2A, IM1-W-2A. the Thereaction process occurs requires through an energy the transition barrier of 38.85state TS1-W-2Akcal/ and reaction forming energy the product of 18.80 complex kcal/ mol,IM1-W-2A. respectively. The process The IM1 requires-W-2A, an with energy a binding barrier energy of 38.85 of − 0 kcal/51.69 and kcal reaction/mol, can energy serve asof the−18.80 reactant kcal/mol, complex respectively. in the next The step. IM1’-W-2A, The SO3 -HONO-NHwith a binding4NO energy2-NH 3of-1 51.69( 71.15 kcal/mol, kcal/mol) can is serve resulted as the from reacta IM1nt-W-2A complex by thein the only next H Ostep. molecule The SO reacting3-HONO-NH between4NO the2-NH NO3-1 − 0 2 − (and−71.15 NO kcal/mol), along is with resulted energy from barrier IM1’-W-2A and energy by the reaction only H2O of molecule 9.04 kcal /reactingmol and between19.46 kcalthe /NOmol,− 2− − andrespectively. NO2−, along As shownwith energy in Figure barrier8, the and other ener pathwaygy reaction is similar of 9.04 to kcal/mol the reaction and of−19.46 RC1-W-2A kcal/mol, to respectively.SO3-HONO-NH As shown4NO2-NH in 3Figure-1. There 8, the are other energy path barrierway is and similar reaction to the energy reaction of 40.26 of RC1-W-2A kcal/mol and to SO19.513-HONO-NH kcal/mol4 inNO oxidation2-NH3-1. reaction,There are respectively. energy barrier In the and hydrolysis reaction process,energy of the 40.26 energy kcal/mol barrier and and − −reaction19.51 kcal/mol energy in are oxidation 12.68 kcal reaction,/mol and respectively.16.28 kcal In/mol, the hydrolysis respectively. process, Table the S8 energy indicates barrier that bothand − reactionreaction energy pathways are SO 12.68-2NO kcal/mol-H O-2NH and −16.28SO kcal/mol,-HONO-NH respectively.NO -1 and Table SO -HONO-NH S8 indicates NOthat -2both are 2 2 2 3→ 3 4 2 3 4 2 reactionexothermic pathways and spontaneous. SO2-2NO2-H2O-2NH3→SO3-HONO-NH4NO2-1 and SO3-HONO-NH4NO2-2 are exothermicIn presence and spontaneous. of two NH3 molecules, two NH3 molecules and the only H2O molecule serve as catalyst 3 3 2 and stabilizer,In presence and of thetwo one NH NH molecules,3 molecule two and HNH2O moleculemolecules serve and asthe reactant only H toO produce molecule NH serve4NO 2as. 3 2 catalystCompared and stabilizer, with the and three-water the one NH reaction, molecule the proportion and H O ofmolecule H2O and serve NH3 asmolecules reactant is to 2:1 produce and 1:2. NHThe4NO result2. indicates that the energy barrier is slighting diﬀerent from the three-water molecule in the 2 3 SO2-oxidationCompared reaction.with the Inthree-water the hydrolytic reaction, reaction, the proportion the energy of barrier H O and is higher NH molecules than the three-water is 2:1 and 1:2.molecule, The result and theseindicates processes that the release energy more barrier reaction is slighting energy. different Moreover, from the bindingthe three-water energyof molecule product 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

Int. J. Mol. Sci. 2019, 20, 3746 11 of 14 Int. J. Mol. Sci. 2019, 20, x FOR PEER REVIEW 10 of 14 energy of product complexes is lower than that of the SO3-2HONO-2H2O. This result shows that the complexes is lower than that of the SO3-2HONO-2H2O. This result shows that the NH3 molecule plays aNH signiﬁcant3 molecule role plays in stabilizing a significant complexes. role in stabilizing complexes.

Figure 8. Potential energy proﬁleprofile forfor thethe reactionreaction ofof SO SO22-2NO-2NO22-H-H22O-2NH3.. The The yellow yellow spheres spheres are S atoms, the red spheres are O atom, the blue spheresspheres are N atom, and the white spheres represent H atom, respectively.respectively. (Unit:(Unit: EnergiesEnergies in in kcal kcal/mol;/mol; bond bond lengths lengths in angstroms).in angstroms). The The black black and and red red lines lines are

theare ditheﬀ erentdifferent pathways. pathways. The The black black line lin representse represents the reactionthe reaction of t-ONONO of t-ONONO2-H2O-2NH2-H2O-2NH3-SO32-SO, and2, and the

redthe red line line is the is reactionthe reaction of c-ONONO of c-ONONO2-H22O-2NH-H2O-2NH3-SO3-SO2. 2. 3. Materials and Methods 3. Materials and Methods All quantum chemistry calculations are performed by Gaussian 09 programs (vB.01, Gaussian, 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), 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 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 (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 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 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 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, 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 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) characteristics and thermodynamic properties. All the enthalpies (H) and Gibbs free energies (G) are are calculated with thermal correction at 298.15 K. Moreover, the intrinsic reaction coordinate (IRC) 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 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 intermediates [40]. The single-point energies of all stationary points are refined using the more basis set for M06-2X/6-311++G (3df, 3pd) [41]. The ultrafine integration grid is applied to improving precise basis set for M06-2X/6-311++G (3df, 3pd) [41]. The ultrafine integration grid is applied to the accuracy during the whole gas-phase calculation. We also calculated electrostatic potential (ESP) improving the accuracy during the whole+ gas-phas+e calculation. We also calculated electrostatic to analyze charge distribution for NO NO3− and NO NO2− fragments of RC and IM with the same potential (ESP) to analyze charge distribution for NO+NO3− and NO+NO2− fragments of RC and IM basis [42,43]. The geometries are visualized using the CYL view software package (v1.0b, Université with the same basis [42,43]. The geometries are visualized using the CYL view software package de Sherbrooke, Montreal, QC, Canada) [44]. (v1.0b, Université de Sherbrooke, Montreal, QC, Canada) [44]. 4. Conclusions 4. Conclusions In this paper, the reaction mechanism of SO2 with NO2 to form SO3 in the presence of H2O In this paper, the reaction mechanism of SO2 with NO2 to form SO3 in the presence of H2O and and NH3 is investigated. Table S9 represents that Cartesian coordinates for all relative Optimized 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

Int. J. Mol. Sci. 2019, 20, 3746 12 of 14 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.

Supplementary Materials: The following are available online at http://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.

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

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