Mechanism of the Gaseous Hydrolysis Reaction of SO2: Effects of

Dec 15, 2014 - Theoretical study of the hydrolysis of HOSO+NO2 as a source of atmospheric HONO: effects of H2O or NH3. Environmental Chemistry 2016 ...
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Mechanism of the Gaseous Hydrolysis Reaction of SO2: Effects of NH3 versus H2O Jingjing Liu,† Sheng Fang,† Wei Liu,† Meiyan Wang,† Fu-Ming Tao,*,‡ and Jing-yao Liu*,† †

Institute of Theoretical Chemistry, State Key Laboratory of Theoretical and Computational Chemistry, Jilin University, Changchun 130023, People’s Republic of China ‡ Department of Chemistry and Biochemistry, California State University, Fullerton, California 92834, United States S Supporting Information *

ABSTRACT: Effects of ammonia and water molecules on the hydrolysis of sulfur dioxide are investigated by theoretical calculations of two series of the molecular clusters SO2(H2O)n (n = 1−5) and SO2-(H2O)n-NH3 (n = 1−3). The reaction in pure water clusters is thermodynamically unfavorable. The additional water in the clusters reduces the energy barrier for the reaction, and the effect of each water decreases with the increasing number of water molecules in the clusters. There is a considerable energy barrier for reaction in SO2-(H2O)5, 5.69 kcal/mol. With ammonia included in the cluster, SO2-(H2O)n-NH3, the energy barrier is dramatically reduced, to 1.89 kcal/mol with n = 3, and the corresponding product of hydrated ammonium bisulfate NH4HSO3-(H2O)2 is also stabilized thermodynamically. The present study shows that ammonia has larger kinetic and thermodynamic effects than water in promoting the hydrolysis reaction of SO2 in small clusters favorable in the atmosphere.

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molecules and almost zero with four water molecules,24 while there is still considerably high energy barrier (20.1−21.9 kcal/ mol)18 for the reaction of SO2 + 3H2O. This result indicates that the hydrolysis reaction of SO2 may require more water molecules to further lower the energy barrier such that the reaction would become kinetically favorable. Clearly, a theoretical study of the hydrolysis reaction of SO2 involving more water molecules (n > 3) is very desirable. On the other hand, ammonia (NH3) is the most abundant alkaline component in the atmosphere, released primarily from animal wastes, NH3-based fertilizers, and industrial emissions.28 Ammonia was found to be an effective component of the precursors in the formation of atmospheric aerosols. Previous theoretical calculations have presented the important role of ammonia in stabilizing the hydrates of sulfuric acid (H2SO4− H2O−NH3)29−31 and of sulfur trioxide (SO3−H2O−NH3).32,33 Recent experimental studies suggested that the SO2−H2O− NH3 gas phase reaction may play an important role in the particle formation.34−36 It is thus reasonable to expect that ammonia may also participate in the gaseous hydrolysis reaction of SO2, ultimately leading to sulfate aerosols. To the best of our knowledge, there has been little theoretical effort in elucidating the possible role of ammonia in the gaseous hydrolysis of SO2. In this work, we attempt to analyze the effect of ammonia in the hydrolysis reactions of SO2 (SO2 + nH2O + NH3, n = 1−3) using quantum chemical calculations. In order to show the unique role of NH3, the hydrolysis reactions SO2 +

INTRODUCTION Sulfur dioxide (SO2) is an important gaseous pollutant from both industrial and natural sources.1 The interaction and hydrolysis reaction between SO2 and H2O in the gas phase or aqueous interfacial region play an important role in the formation of sulfur-containing aerosols, acid rain, and cloud condensation nucleation (CCN)2,3 and thus have drawn much attention experimentally and theoretically.4−16 The existence of hydrated SO2 complexes at the water surface prior to hydrolysis in water droplets has been directly demonstrated by vibrational sum-frequency spectroscopy (VSFS).4−6 Several microwave7 and infrared spectroscopic8−10 studies were reported on the structures of gaseous SO2−(H2O)n (n = 1−3) complexes. Quantum chemical calculations at different levels of theory were carried out to study the structures and energies of the SO2−(H2O)n (n = 1−6) clusters,11−13 and molecular dynamics (MD) simulations were used to model the behavior of SO2 at the aqueous/air interface.14−16 A number of theoretical studies have been reported on the reaction mechanism of SO2 + nH2O → H2SO3−(H2O)n−1 (n = 1−3).17−20 These results showed that the introduction of additional water molecule(s) in the gaseous hydrolysis reaction of SO2 has an important influence on the barrier height reduction, similar to hydrolysis reactions of other species, such as sulfur trioxide,19,21−24 carbon dioxide,25,26 and nitrogen dioxide.27 However, unlike the hydrolysis of SO3,24 the catalytic effect of water molecules for the hydrolysis of SO2 is not so significant, and the resulting hydrated H2SO3 complexes are unstable with respect to the corresponding hydrated SO2 complexes.18−20 For example, the energy barrier is only 2.8− 4.0 kcal/mol21,24 for the reaction of SO3 with three water © XXXX American Chemical Society

Received: August 26, 2014 Revised: December 14, 2014

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Figure 1. Potential energy profile of the SO2 + nH2O (n = 1−5) reactions at the CCSD(T)/aug-cc-pVDZ//MP2/aug-cc-pVDZ + ZPE level of theory (in kcal/mol).

nH2O → H2SO3−(H2O)n−1 (n = 1−5) were also investigated using the same methods. Given the importance of SO2 and NH3 in atmospheric aerosols, our results may give new insights into the atmospheric nucleation mechanism for sulfurcontaining aerosols.

SO2-(H2O)4 and SO2-(H2O)5, respectively. TIP3P water model50 and Generalized Amber Force Field (GAFF)51 were used for the simulation. From the simulations, we extracted 50 and 100 snapshots of the clusters SO2-(H2O)4 and SO2(H2O)5, respectively. The resulting snapshots were then used as the initial structures for geometry optimization at the level of B3LYP/6-311++G(d,p). The local minima within 3.0 kcal/mol of the global minimum were further optimized at the level of MP2/aug-cc-pVDZ.

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COMPUTATIONAL METHODS All electronic structure calculations were carried out using Gaussian 09 suite of program.37 Molecular geometries of the stationary points were optimized using second-order Møller− Plesset perturbation approximation (MP2) with Dunning’s augmented double-ζ correlation-consistent basis set, aug-ccpVDZ.38−40 Harmonic vibrational frequencies were calculated using the same method to confirm the stationary points (i.e., all real frequencies for a local minimum) and only one imaginary frequency for a transition state. The zero-point energy (ZPE) corrections were included in the determination of energy barriers and reaction energies. The intrinsic reaction coordinate (IRC)41,42 calculations were done to ensure that the transition states connect to the correct reactants and products. To obtain more reliable relative energies, single-point energies of all stationary points at the MP2/aug-cc-pVDZ geometries were calculated using coupled-cluster theory including single, double, and noniterative triple excitations43−45 [CCSD(T)] with the basis set aug-cc-pVDZ. Thermodynamic properties (enthalpy and Gibbs energy) at 1 atm and 298.15 K were calculated at the MP2/aug-cc-pVDZ level with energy corrections from CCSD(T)/aug-cc-pVDZ. Initial structures for the clusters SO2-(H2O)n (n = 2−3) were obtained by adding a water molecule to the stable complexes of SO2-(H2O)n‑1. For the larger clusters, SO2-(H2O)n (n = 4−5), molecular dynamics (MD) simulations were carried out using Amber 946 to search for possible stable configurations and the global minimum. The MD sampling scheme has been successfully applied to hydrated sulfuric acid47 and other hydrated clusters.48,49 We ran a two-step MD simulation, as described in refs 47−49, first a simulation of heating processes from 0 K to the final temperature Tf for 1 ns, followed by a production run at Tf for 10 ns. The Tf was 200 and 210 K for

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RESULTS AND DISCUSSION Hydrolysis Reactions of SO2 + nH2O (n =1−5). The equilibrium geometries of the clusters SO2-(H2O)n (n = 1−5) as well as the corresponding pathways for the hydrolysis of SO2 in the clusters were examined. As the number of water molecules increases in a given cluster, the number of possible configurations for the cluster increases quickly, and each of the configurations becomes increasingly complicated. For the larger clusters SO2-(H2O)n (n = 4,5), initial geometries of possible configurations were obtained from MD simulations, followed by geometry optimization at B3LYP/6-311++G(d,p) and further geometry optimization at MP2/aug-cc-pVDZ. Equilibrium geometries for the stable configurations and global minima were determined from the relative energies and reported in the present study (Figure 2, and Figures S1 and S2 of the Supporting Information). In the global minimum geometries of SO2-(H2O)n (n = 4, 5), the water molecules form a ring by hydrogen bonds, while SO2 is connected to the adjacent water through the interaction of electron donor− acceptor type (see SO2-4W-3 and SO2-5W-5 in Figures S1 and S2 of the Supporting Information), similar to hydrated carbon dioxide.52 Since our main objective is to look for the catalytic effect of H2O, we focus our attention on the stable configurations of the clusters that could provide the most favorable pathways for the hydrolysis of SO2, which are outlined in Figure 1. The equilibrium geometries and transition state geometries involved in these pathways are given in Figure 2 and the corresponding energetic data are given in Table 1. The equilibrium geometries and energies for other hydrated B

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Figure 2. Complexes, transition states, and products for the SO2 + nH2O (n = 1−5) reactions at the MP2/aug-cc-pVDZ level of theory (bond lengths in angstroms).

(H(4)OS, O(b)···H(2)), with a binding energy of 10.83 kcal/mol. The reaction proceeds via the transition state TS−2W to form the product complex H2SO3-H2O, lying 3.67 kcal/mol below SO2 + 2H2O but 7.16 kcal/mol above SO2-2W. At the transition state TS−2W, the double-proton transfer takes place simultaneously with the S−O bond formation, while H2O(b) serves as a shuttle to transfer a proton from H2O(a) to the oxygen atom of SO2. The energy barrier for this process is 20.86 kcal/mol. As shown in Table 1, our results are in good agreement with the previous studies. Compared to the one-water reaction, the energy barrier for the two-water reaction is reduced by ca. 12 kcal/mol. It shows that the second water molecule plays a significant role in lowering the energy barrier (see Table 1). However, the reaction is still not favorable both kinetically and thermodynamically.

complexes, unrelated to the reaction pathways considered in this work, are given in Figures S1 and S2 and Tables S1 and S2 of the Supporting Information. The stick structures presented in this work were drawn using CYLview.53 The hydrolysis reaction of SO2 with a single water molecule is initiated with the hydrated complex SO2-1W, followed by a four-membered ring transition state TS-1W to produce sulfurous acid H2SO3. The complex SO2-1W has a doubledecker-type structure with a binding energy of 3.82 kcal/mol. The transition state TS-1W lies 33.11 kcal/mol above SO2-1W, and the product H2SO3 is 4.50 kcal/mol less stable than the separated reactants SO2 + H2O and is 8.32 kcal/mol less stable than SO2-1W. As shown in Table 1, our calculated results are in reasonable agreement with the previous studies. The SO2 + 2H2O reaction begins with the formation of the six-membered ring complex SO2-(H2O)2 (SO2-2W), in which the second water molecule H2O(b) forms two hydrogen bonds C

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energy of SO2-4W is calculated to be 25.67 kcal/mol. The reaction goes through the transition state TS-4W, in which the proton transfer is assisted by a chain of three water molecules. An eight-membered ring structure occurs in TS-4W with one water molecule acting as a solvent molecule. Beyond TS-4W, the proton transfer leads to an ion-pair, [H3O]+[HSO3]−, instead of H2SO3-H2O, in the product complex. This reaction has an energy barrier of 11.56 kcal/mol. Compared to the three-water reaction, the additional water molecule results in a small reduction of 2.74 kcal/mol in the energy barrier. The ionpair intermediate [H3O]+[HSO3]-(H2O)2 is unstable, and the proton-transfer process between H3O+ and HSO3− occurs with no barrier to form the final product complex H2SO3-(H2O)3, which lies 4.19 kcal/mol above SO2-4W. The similar reaction occurs in the cluster of five water molecules, SO2-5W. The lowest energy pathway involves a twostep process through an ion-pair intermediate [H3O]+[HSO3]−-(H2O)3. At the transition state TS-5W, two protons transfer simultaneously between two active water molecules in an eight-membered ring structure. A considerable reduction in energy barrier, 5.87 kcal/mol, is found to be attributed to the fifth water molecule. The product complex H2SO3-(H2O)4 is only 3.34 kcal/mol above the reactant complex SO2-5W. Hydrolysis Reactions of SO2 + nH2O + NH3 (n = 1−3). Theoretical studies for the similar systems, such as NH3(H2O)n54 and SO3-(H2O)n-NH3,29 show that the structures of the clusters containing an ammonia molecule are similar to those determined for the corresponding water clusters, with NH3 replacing one of the water molecules. In the present study, the initial structures of SO2-(H2O)n−1-NH3 were generated by replacing one of the water molecules in SO2-(H2O)n with an ammonia molecule. Additional different pathways may occur as ammonia is introduced in the clusters. Ammonia could first be hydrated to form NH3-(H2O)m (m = 0−n), followed by a reaction with the cluster SO2-(H2O)n−m (n = 1−3). All of the different combinations of the intermediate clusters NH3(H2O)m (m = 0−n) and SO2-(H2O)n−m (n = 1−3) lead to the overall reactant clusters SO2−(H2O)n−NH3 (n = 1−3) via

Table 1. Binding Energies for Hydrated SO2 Complexes SO2-nW, Energy Barriers, and Reaction Energies for the Subsequent Hydrolysis Reactions SO2-nW → H2SO3(H2O)n−1 (n = 1−5), Obtained from CCSD(T)/aug-ccpVDZ//MP2/aug-cc-pVDZ + ZPE Calculations (Unit: kcal/ mol) SO2-nW → H2SO3−(H2O)n−1

SO2-nW n

binding energy

energy barrier

reaction energy

1

3.82 (5.0a, 3.5b, 2.6c, 3.2d) 10.83 (14.7a, 10.0b, 8.0c, 10.5d) 18.18 (13.6c, 17.1d) 25.67 31.09

33.11 (33.3−35.4a, 35.6b) 20.86 (20.0−23.0a, 22.2b) 14.31

8.32 (6.8−11.6a, 9.3b) 7.16 (4.5−9.4a, 6.6b) 4.67

11.56 5.69

4.19 3.34

2 3 4 5 a

From ref 19. bFrom ref 20. cFrom ref 12. dFrom ref 13.

For the hydrolysis of SO2 with three water molecules, the reaction occurs via an eight-membered cyclic reactant complex SO2-3W, in which the four moieties are held together by four hydrogen bonds, (H(6)···OS, H(3)···OS, O(b)···H(2), O(c)···H(4)), and there is an electron donor−acceptor (EDA) type of interaction between H2O(a) and SO2. The equilibrium geometry and binding energy (18.18 kcal/mol) of SO2-3W are consistent with the previous results. The reaction undergoes a transition state TS-3W where a double transfer of protons occurs, leading to formation of the product complex H2SO3-(H2O)2. Two water molecules are actively involved in the process of proton transfer while the third water molecule (H2O(c)) only acts as a solvent molecule. The transition state TS-3W contains a sixmembered ring structure similar to that of TS-2W. The stabilizing effect of the solvent water molecule leads to a decrease of 6.55 kcal/mol in energy barrier. The product complex H2SO3-(H2O)2 is 13.57 kcal/mol below the separate reactants SO2 + 3H2O, while it is 4.67 kcal/mol above SO2-3W. In the case of four water molecules, the most favorable pathway starts with a reactant complex SO2-4W. The binding

Figure 3. Potential energy profile for the reaction of SO2 + H2O + NH3 at the CCSD(T)/aug-cc-pVDZ//MP2/aug-cc-pVDZ + ZPE level of theory (in kilocalories per mol). D

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Figure 4. Potential energy profile of the reaction SO2 + 2H2O + NH3 at the CCSD(T)/aug-cc-pVDZ//MP2/aug-cc-pVDZ + ZPE level of theory (in kcalories per mol).

Figure 5. Potential energy profile of the hydrolysis reaction of SO2 + 3H2O + NH3 at the CCSD(T)/aug-cc-pVDZ//MP2/aug-cc-pVDZ + ZPE level of theory (in kcal/mol).

bonds with H2O. The binding energies of SO2-1W-A-1 and SO2-1W-A-2, from the separate molecules, are 12.10 and 11.10 kcal/mol, respectively, which are greater than that of SO2-2W (by 2.15 and 1.15 kcal/mol, respectively). To form the product complex H2SO3-NH3 from SO2-1W-A1, there is an energy barrier of 12.53 kcal/mol at the transition state TS-1W-A-1 and also an increase of 5.93 kcal/mol in energy. The transition state TS-1W-A-1 is analogous to that of the transition state obtained for the two-water reaction SO2 + 2H2O. Starting with the reactant complex SO2-1W-A-2, the reaction occurs through the transition state TS-1W-A-2 to form the product complex HSO2NH2-H2O. The reaction involves the formation of an S−N bond and a synchronous double-proton transfer. The process requires an energy barrier of 21.19 kcal/

a barrierless association process, as shown in the potential energy profiles for the hydrolysis of SO2 with NH3 in Figures 3−5. As a result, our following discussions will focus on the overall reactant complexes SO2−(H2O)n−NH3. SO2 + H2O + NH3. Figure 3 shows the potential energy profile and the corresponding equilibrium geometries for the reaction of SO2 + H2O in the presence of NH3. The two reactant complexes, SO2-1W-A-1 and SO2-1W-A-2, are very similar in structure to SO2-2W, with NH3 being in place of one of the two water molecules in SO2-2W. The reactant complex SO2-1W-A-1 contains three hydrogen bonds, in which NH3 serves as an acceptor as well as a double donor of hydrogen bonds. In addition, there is an EDA type of interaction between H2O and SO2. In the reactant complex SO2-1W-A-2, there is an EDA interaction between NH3 and SO2 along with hydrogen E

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NH3, as shown in the transition state TS-3W-A-2. Apparently, the presence of NH3 immediately next to the hydrolyzing water allows NH3 to directly receive the leaving proton, which is kinetically favorable. The observation is also consistent with the reaction of SO2 + 2H2O + NH3 discussed earlier. Roles of NH3 in the Hydrolysis Reactions of SO2. It is clear from the above discussion that the energy barrier and the energy of reaction are strongly affected by the presence of ammonia as a catalyst and are systematically dependent on the number of water molecules in the two series of reactions, SO2 + nH2O and SO2 + nH2O + NH3. Each additional water molecule can either participate directly in the reaction as a proton carrier or serve simply as a solvent, stabilizing the transition state and the product complex. Although ammonia appears to simply replace one of the water molecules as a catalyst or proton transmitter, it is more efficient than water in stabilizing the transition state and the final product complex. To further examine the effective roles of ammonia on the hydrolysis reaction of SO2 in the different clusters, Table 2 presents the

mol, and the product complex is 9.42 kcal/mol higher in energy than the reactant complex SO2-1W-A-2. In general, the reactant complex containing an EDA type of interaction between NH3 and SO2 leads to the product HSO2NH2. Such a reaction is much less favorable than the reaction to form the product H2SO3 initiated from the reactant complex containing an EDA type of interaction between H2O and SO2. As a result, the formation of HSO2NH2 will not be considered in the following reactions. SO2 + 2H2O + NH3. Two stable reactant complexes, SO22W-A-1 and SO2-2W-A-2, were obtained for the system of SO2 + 2H2O + NH3, as shown in Figure 4. The ammonia molecule in SO2-2W-A-1 is located between the two water molecules, and it forms two hydrogen bonds (H(2)···N, H(5)···O(b)). The ammonia molecule in SO2-2W-A-2 is located between one water and the SO2 molecule and it forms three hydrogen bonds (N···H(4), OS···H(5), and OS···H(7)). The binding energies for the two complexes are 18.30 and 19.55 kcal/mol, respectively, with SO2-2W-A-2 being slightly more stable. The reaction initiated from SO2-2W-A-1 goes through the transition state TS-2W-A-1 with an energy barrier of 5.87 kcal/ mol to form an intermediate of hydrated ammonium bisulfate INT-1 ([NH4]+[HSO3]−-H2O). At the transition state TS-2WA-1, the transfer of a proton, from the first H2O(a) to ammonia molecule, and the formation of a S−O bond takes place simultaneously. The intermediate INT-1 is unstable and is converted into the product complex H2SO3-W-A-1 without an energy barrier. This two-step hydrolysis mechanism is similar to the reaction of SO2 with four water molecules. The product complex H2SO3-W-A-1 is 16.67 kcal/mol below the separate reactants SO2 + 2H2O + NH3 and is 1.63 kcal/mol above the reactant complex SO2-2W-A-1. Similarly, the reaction complex SO2-2W-A-2 goes through the transition state TS-2W-A-2, resulting in anion-pair intermediate INT-2 and eventually a stable product complex H2SO3-W-A-2. Different from the reaction with SO2-2W-A-1, the reaction with SO2-2W-A-2 involves a double-proton transfer, from H2O(a) to NH3 and again to H2O(b), and has a much larger energy barrier of 12.41 kcal/mol. Furthermore, the product complex H2SO3-W-A-2 is less stable than H2SO3-W-A1. The first pathway is clearly preferred over the second one both kinetically and thermodynamically. SO2 + 3H2O + NH3. As shown in Figure 5, the reaction of SO2 + 3H2O + NH3 is considered to start with forming two reactant complexes, SO2-3W-A-1 and SO2-3W-A-2. The complex SO2-3W-A-2 is 2.68 kcal/mol more stable than SO23W-A-1. The first reaction pathway involving SO2-3W-A-1, however, has a very small energy barrier of only 1.89 kcal/mol, while the second one involving SO2-3W-A-2 has a much higher barrier. It indicates that the first reaction pathway is kinetically more favorable. On the other hand, the corresponding product complex from the first pathway, NH4HSO3-2W-1, is slightly less stable than that from the second pathway, NH4HSO3-2W2. It shows that the second reaction pathway is thermodynamically more favorable. It is worthwhile to note in the first pathway that, as shown in the transition state TS-3W-A-1, only one water molecule actively participates in the proton transfer from H2O(a) to NH3, leading to the formation of the NH4+ cation and HSO3− anion, while the other two water molecules serve as solvent molecules to stabilize the transition state. In contrast, the second pathway is characterized by a double-proton transfer involving two active water molecules, from H2O(a) to H2O(b) and further to

Table 2. Relative Energies ΔE, Enthalpies ΔH, and Gibbs Free Energies ΔG (in kcal/mol) with Respect to the Separate Reactants for the Reactant Complexes and Product Complexes (ΔH and ΔG Values are Given at 1.0 atm and 298.15 K).a reactant complexes SO2 + H2O SO2 + 2H2O SO2 + 3H2O SO2 + 4H2O SO2 + 5H2O SO2 + H2O + NH3 pathway1 pathway2 SO2 + 2H2O + NH3 pathway1 pathway2 SO2 + 3H2O + NH3 pathway1 pathway2

product complexes

ΔE

ΔH

ΔG

ΔE

ΔH

ΔG

−3.82 −10.83 −18.18 −25.67 −31.09

−3.67 −11.60 −19.77 −28.02 −33.88

2.24 4.43 5.97 7.12 9.29

4.50 −3.67 −13.57 −21.48 −27.75

3.32 −3.62 −16.32 −24.99 −31.93

13.29 15.57 12.20 13.34 15.13

−12.10 −11.10

−12.76 −11.77

3.72 4.53

−6.17 −1.68

−7.89 −3.65

11.02 16.23

−18.30 −19.55

−19.63 −20.96

5.82 4.48

−16.67 −14.07

−19.50 −16.52

9.97 11.78

−23.33 −26.01

−24.92 −28.28

7.46 7.41

−23.80 −24.84

−27.44 −28.57

11.87 10.46

ΔE values are from CCSD(T)/aug-cc-pVDZ//MP2/aug-cc-pVDZ + ZPE calculations, ΔH and ΔG values are from MP2/aug-cc-pVDZ +ZPE calculations with energy corrections from CCSD(T)/aug-ccpVDZ calculations. a

electronic energies, enthalpies, and Gibbs free energies of the reactant complexes and product complexes relative to the separate reactants. The corresponding energies, enthalpies, and Gibbs free energies of reaction can be obtained by taking the difference in the values between the reactant and product complexes. Figure 6 (panel a) plots the energy barrier and (panel b) the energy of reaction as a function of the number of water molecules for the two series of reactions. As shown in Figure 6a, the first additional water molecule has the most dramatic effect in reducing the energy barrier for the reactions without ammonia, a reduction of about 12 kcal/mol. Such a catalytic effect of each water molecule decreases with the total number of water molecules present in the reaction. There is still a significant energy barrier, 5.69 kcal/mol, in the F

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Figure 6. (a) Energy barriers and (b) energies of reaction, all with respect to the corresponding reactant complexes, as a function of the number of monomers in the reactant complexes.

strengthened hydrogen bond leads to increasing the population of σ*(Oa −H) by the lone pair electrons from N atom and, thus, promotes the proton transfer from σ*(Oa−H) to the N atom. On the other hand, the ammonia molecule also strengthens the intermolecular interactions between SO2 and H2O. As can be seen from Figure 7b, the second-order stabilization energies between the lone pair of the H2Oa and the antibonding orbitals π* (S−O) are larger (4.66−6.79 kcal/mol) in SO2-nW-A-1 (n = 1−3) complexes than those (3.44−6.55 kcal/mol) in SO2-nW (n = 2−4) complexes with the same monomers, which indicates that the ammonia molecule can also promote the S−O bond formation in the hydrolysis reactions. Overall, when NH3 acts as a proton acceptor, the interactions between N···H−Oa of H2O and between SO2 and H2O become stronger, thus reducing the energy barrier and enhancing the proton transfer process. The energy of reaction for SO2-(H2O)n → H2SO3-(H2O)n−1, given as a difference between the ΔE values for the reactant and product complexes, respectively, in Table 2 and also shown in Figure 6b, is all positive, which is consistent with the fact that the hydrolysis of SO2 in pure water is not thermodynamically favorable. In other words, sulfur dioxide in water is simply solvated as SO2-(H2O)n, rather than hydrolyzed as H2SO3(H2O)n. Without NH3, the product complex of hydrolysis, H2SO3-(H2O)n−1, is less stable than the corresponding hydrated complex SO2-(H2O)n, although the relative stability of H2SO3-(H2O)n−1 increases steadily with increasing the number of water molecules in the clusters. In contrast, as ammonia is added, the energy of reaction decreases much more quickly and even has a slightly negative value for the reaction SO2-(H2O)n-NH3 → NH4HSO3-(H2O)n−1. It indicates that the hydrolyzed product may eventually be stabilized in the presence of NH3. The Gibbs free energy of reaction, obtained as a difference in ΔG between the reactant and product complexes in Table 2, further demonstrates the effective role of NH3 in preferentially stabilizing the product complex over the reactant complex. Without NH3, the values of the Gibbs energy of reaction for SO2-(H2O)n → H2SO3-(H2O)n−1, n = 1−5, are 11.12, 11.14, 6.23, 6.22, and 5.84 kcal/mol, respectively. With NH3, the values for SO2-(H2O)n-NH3 → NH4HSO3-(H2O)n−1, n = 1−3, are 7.30, 4.15, and 3.05 kcal/mol, respectively. Comparing the Gibbs energies of reaction for the two series of the clusters, it is

reaction of SO2 + 5H2O. Further reduction of the energy barrier by adding more water molecules is expected to be very limited because the added water molecules are located far away from the reacting molecules. Replacing the first additional water molecule, as in the reaction SO2 + H2O + NH3, ammonia has a dramatic effect in reducing the energy barrier, a reduction over 20 kcal/mol. With one additional water, as in the reaction of SO2 + 2H2O + NH3, the energy barrier of about 6 kcal/mol is already nearly equal to that for the reaction with four additional water molecules without ammonia, SO2 + 5H2O. The energy barrier for the reaction SO2 + 3H2O + NH3 is only 1.89 kcal/ mol. As an efficient catalyst, ammonia plays a critical role in the kinetics of hydrolysis reaction of SO2: it dramatically increases the rate of the reaction by extremely lowering the energy barrier. The great catalytic effect of ammonia for the hydrolysis of SO2 is attributed to the fact that the ammonium NH4+, formed at the transition state during the hydrolysis process in the presence of NH3, is more stable than the hydronium cation H3O+ formed at the transition state in the absence of NH3. It is related to the higher basicity of NH3 than that of H2O, as noted in a previous study of the SO3−NH3−H2O system.31 To show further evidence of the greater catalytic effect of NH3 than that of H2O on the hydrolysis of SO2, natural bond orbital (NBO) analysis was carried out to describe the donor− acceptor interactions in reactant complexes SO2-nW (n = 2−4) and SO2-nW-A-1 (n = 1−3), respectively. Figure 7 shows the NBO overlap of the Ob (or N)···H−Oa hydrogen bonds (7a) and Oa···S−O intermolecular interactions (7b) in SO2-nW (n = 2−4) and SO2-nW-A-1(n = 1−3) complexes, respectively. The figure was drawn with Multiwfn55 along with VMD.56 The second-order stabilization energies, also given in Figure 7, are used to quantitatively estimate the relative strength of the interactions. In Figure 7a, the electron is donated from the lone pair of Ob (or N) atom to the antibonding orbital σ* (H−Oa). It is seen that, in complexes SO2-nW (n = 2−4), the secondorder stabilization energies of LP (Ob) → σ*(Oa−H) range from 14.46 to 27.14 kcal/mol. As the ammonia replaces a water molecule, the stabilization energies of LP (N) → σ*(Oa−H) in complexes SO2-nW-A-1 (n = 1−3) become much larger, ranging from 25.56 to 47.13 kcal/mol. The larger stabilization energies are consistent with the larger overlap of the interacting orbitals in SO2- nW-A-1 (n = 1−3) than in SO2-nW (n = 2−4), indicating the stronger hydrogen bonding interaction between the NH3 and H2O than that between two H2O molecules. The G

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Figure 7. NBO analysis of donor−acceptor orbital interactions in complexes SO2-(H2O)n (n = 2−4) and SO2-(H2O)n-NH3 (n = 1−3) with (a) H2Oa as acceptor and (b) SO2 as acceptor (0.05 e/Å3 isosurface from MP2/aug-cc-pVDZ model chemistry). The second-order stabilization energies are given in parentheses.

the energy barrier for the reaction and also stabilize the product, the energy barrier is too large and the product complex is less stable than the reactant complex. With ammonia, as shown from the results with the clusters SO2(H2O)n-NH3, n = 1−3, the energy barrier is lowered dramatically, allowing the kinetically favorable conversion of SO2 into H2SO3 or HSO3−. Ammonia is also shown to be more effective than water in stabilizing the product complex, ultimately making the hydrolysis of SO2 thermodynamically favorable. In summary, ammonia is shown to have large kinetic

seen that ammonia is about 2 kcal/mol more effective than a water molecule in lowering the Gibbs energy of reaction.

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CONCLUSION

Ammonia is shown to play an effective role in the hydrolysis of sulfur dioxide. Without ammonia, as shown from the results with the clusters SO2-(H2O)n, n = 1−5, the conversion of SO2 into H2SO3 or HSO3− in the water clusters has a rather large energy barrier and is thermodynamically unfavorable. Although water molecules in the clusters have catalytic roles in lowering H

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and thermodynamic effects that promote the hydrolysis reaction of SO2 in small clusters.

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ASSOCIATED CONTENT

S Supporting Information *

The corresponding relative energetic data for SO2 + nH2O (n = 1−5) reactions. The equilibrium geometries and transition state geometries involved in other pathways. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Tel: +17142784517. *E-mail: [email protected]. Tel: 86-431-88498016. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the National Natural Science Foundation of China (Grants 21373098, 20973077, and 21203073) and the U.S. National Science Foundation (Award 1012994) for the support of this work.

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REFERENCES

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