A possible unaccounted source of atmospheric sulfate formation: amine-promoted hydrolysis and non-radical oxidation of sulfur dioxide

Abstract

Numerous field and laboratory studies have shown that amines, especially dimethylamine (DMA), are crucial to atmospheric particulate nucleation. However, the molecular mechanism by which amines lead to atmospheric particulate formation is still not fully understood. Herein, we show that DMA molecules can also promote the conversion of atmospheric SO₂ to sulfate. Based on ab initio simulations, we find that in the presence of DMA, the originally endothermic and kinetically unfavourable hydrolysis reaction between gaseous SO₂ and water vapour can become both exothermic and kinetically favourable. The resulting product, bisulfite NH₂(CH₃)₂⁺·HSO₃⁻, can be readily oxidized by ozone under ambient conditions. Kinetic analysis suggests that the hydrolysis rate of SO₂ and DMA with water vapour becomes highly competitive with and comparable to the rate of the reaction between SO₂ and OH·, especially under the conditions of heavily polluted air and high humidity. We also find that the oxidants NO₂ and N₂O₅ (whose role in sulfate formation is still under debate) appear to play a much less significant role than ozone in the aqueous oxidation reaction of SO₂. The newly identified oxidation mechanism of SO₂ promoted by both DMA and O₃ provides another important new source of sulfate formation in the atmosphere.

---

1 Introduction

Sulfuric acid in the atmosphere, mainly produced by the oxidation of gaseous sulfur dioxide, is known as the most important nucleating agent in the earliest stage of atmospheric new particle formation (NPF), as it possesses the lowest vapour pressure (<0.001 mmHg at 298 K) among the gaseous species in the atmosphere.^1–9 SO₂ in the atmosphere is mainly oxidized by OH· radicals produced from excited oxygen and water vapour.^10–12 However, numerous observations indicate that there is insufficient OH· to account for the unexpectedly rapid growth in H₂SO₄ concentration in the highly polluted atmosphere, in which the high aerosol concentration can actually block solar ultraviolet radiation and lower the concentration of OH· radicals, thereby preventing them from participating in photochemical reactions.⁵ Moreover, OH· oxidation alone cannot explain the observed level of H₂SO₄ at nighttime.¹³

On the other hand, although the abundance of the common oxidizing gases O₃ and NO_x is much higher than that of OH· radicals in the atmosphere, previous ab initio calculations show that the direct oxidation of SO₂ by O₃/NO_x in the gas phase is kinetically unfeasible due to extremely high activation barriers. The hydrolysis of gaseous SO₂ is proposed as an alternative reaction pathway to yield H₂SO₄ because sulfurous acid can be more easily oxidized to sulfuric acid by some moderate oxidants, e.g., ozone and NO_x.^14–17 However, the hydrolysis of SO₂ in the gas phase has also been shown to be both thermodynamically and kinetically unfavourable via high-level quantum mechanical (QM) calculations^10,18–20 since the hydrolysis of SO₂ with either H₂O monomer or dimer is an endothermic process and, again, entails very high energy barriers.¹⁰ Hence, new oxidation pathways must be explored to explain the fast conversion of SO₂ to atmospheric H₂SO₄.

Atmospheric bases, such as ammonia (NH₃), are another important contributor to initial sulfate aerosols.²¹ In addition, both cloud chamber studies and field measurements have revealed that atmospheric amines, especially dimethylamine (DMA), also play a surprisingly crucial role in the NPF process, even though their concentrations are two or three orders of magnitude lower than that of NH₃.^22–30 For example, Almeida et al. detected that a 5 pptv level of DMA can enhance the particle formation rate more than 1000-fold than 250 pptv NH₃.⁸ More recently, Yao et al. reported that H₂SO₄·DMA·H₂O nucleation leads to high NPF rates in urban areas of China.³⁰ Li et al. found that sulfamic acid, produced from SO₃ and high concentrations of NH₃, can directly participate in H₂SO₄·DMA clustering.³¹ Currently, it is widely accepted that DMA, similar to NH₃, can further stabilize sulfate clusters through salification with H₂SO₄. On the other hand, although Liu et al. showed that alkaline gases, such as ammonia, can promote the hydrolysis of SO₂ to form H₂SO₃ (ref. 22) and Chen et al. proposed that alkaline aerosols can trap SO₂, then being oxidized by NO₂,¹⁴ the role played by DMA molecules in atmospheric chemistry is still incompletely understood, despite its fundamental importance for exploring the role of amines in atmospheric chemistry.

Here, we show that atmospheric amines can play a key role in the formation of sulfates at high relative humidity (RH) and low illumination, thereby contributing to enhanced aerosol formation on highly polluted days. Ab initio simulations demonstrate that the presence of methylamine (MA)/DMA molecules leads to exothermic hydrolysis of SO₂ with water vapour, without a barrier, to a product that can be oxidized by O₃ and NO_x. O₃ is also found to be a stronger oxidant than NO_x in the amine-assisted oxidation of SO₂. As a result, the concentration level of atmospheric H₂SO₄ from aqueous oxidation may be mainly controlled by the concentration of O₃ rather than that of NO_x. Based on transition state theory (TST) analysis and the observed concentrations of the participating atmospheric species, the rate of the SO₂ hydrolysis reaction with the assistance of DMA at 100% RH is even higher than the rate of SO₂ oxidization by OH·. This finding may shed new light on the long-standing endeavour to identify the unknown oxidation pathway leading to atmospheric sulfate formation.

2 Results and discussion

2.1 Hydrolysis of SO₂ assisted by DMA

The potential energy surfaces (PESs) for the hydrolysis reaction of SO₂, MA/DMA and nH₂O (n = 1–3) are shown in Fig. 1(a–b) and S1 in ESI.† In the reaction with the water monomer (Fig. 1(a)), the breaking of the O–H bond of water in the presence of MA and DMA requires activation energies of 5.8 and 3.2 kcal mol⁻¹, respectively, indicating that both reactions can take place quite readily under ambient conditions. In contrast, the process of SO₂ + H₂O → H₂SO₃ in the gas phase needs to overcome a high energy barrier of 33.9 kcal mol⁻¹.¹² Note that previous quantum-mechanical (QM) calculations showed that atmospheric ammonia can also lower the barrier for the hydrolysis of SO₂ to ∼12.0 kcal mol⁻¹.²² However, this energy barrier is still quite high for a reaction to take place at room temperature. According to our calculations, the hydrolysis barriers with MA and DMA are approximately 6.0 and 9.0 kcal mol⁻¹ lower than the barrier with NH₃, respectively, suggesting that amines can promote SO₂ hydrolysis more strongly than NH₃. Furthermore, spontaneous ionization to form HSO₃⁻ and NH₃CH₃⁺/NH₂(CH₃)₂⁺ during the hydrolysis reactions is also observed.

Fig. 1 (a) Potential energy profiles for the hydrolysis reactions of MA (blue lines)/DMA (red lines), SO₂, and H₂O monomer. (b) Potential energy profiles for the hydrolysis reactions of MA (blue lines)/DMA (red lines), SO₂, and H₂O dimer. The energy profiles are calculated at the M06-2X/cc-pVDZ-F12 level with zero-point-energy (ZPE) correction.

The energy barrier for hydrolysis can be further lowered by introducing an additional water molecule to the reaction through the formation of a ring structure in the transition state, as shown in Fig. 1(b). The hydrolysis of SO₂ with a water dimer and DMA can become barrierless. Likewise, hydrolysis with (H₂O)_n (n ≥ 3) are also barrierless reactions (ESI Fig. S1†). In addition, increasing the number of water and DMA molecules also promotes further ionization of the already formed H₂SO₃ and amine molecules. As shown in ESI Fig. S2†(a), H₂SO₃ is partially ionized to HSO₃⁻ in the (DMA)₂·H₂SO₃·(H₂O)_n, (n = 1–3) clusters, while complete ionization of H₂SO₃ and DMA to (NH₂(CH₃)₂⁺)₂·SO₃²⁻ is observed in the presence of (H₂O)_n (n ≥ 4) with a very low dissociation barrier of 0.24 kcal mol⁻¹ (ESI Fig. S2(b)†). Next, we show that the complete ionization of H₂SO₃ can benefit its oxidation, a phenomenon that may occur on aerosol surfaces (with high pH) in air with high concentrations of DMA and water.

The spontaneous formation and ionization processes of bisulfite/sulfite are confirmed by Born–Oppenheimer molecular dynamics (BOMD) simulation (Fig. 2). As shown by the BOMD trajectories at 300 K in Fig. 2(a), the hydrolysis of SO₂ with a water dimer and MA molecule is a very fast process, where the OH bond of a bridging water molecule breaks during the initial 0.33 ps of the BOMD simulation. Meanwhile, the N–H and O–S bond distances decrease to ∼1.07 and ∼1.78 Å, respectively, suggesting the formation of NH₃CH₃⁺·HSO₃⁻·H₂O. It is observed that the system does not maintain the ionized form and returns back to the molecular state of SO₂ after 2.70 ps, indicating the reversible transition between SO₂ and HSO₃⁻ due to the thermal effect. It is interesting that such a chemical equilibrium can be sensitively regulated by temperature. The simulation system maintains the form of NH₃CH₃⁺·HSO₃⁻ at 300 K for ∼2.4 ps during the total BOMD simulation time of 20 ps (lower panel in Fig. 2(b)), while the time period that NH₃CH₃⁺·HSO₃⁻ lasts is approximately six times longer at 250 K (∼12.2 ps) than at 300 K (upper panel in Fig. 2(b)). The BOMD simulation of SO₂·DMA·(H₂O)₂ shows a similar trajectory as that of the SO₂·MA·(H₂O)₂ system (Fig. 2(c) and (d)), where the time periods of the NH₂(CH₃)₂⁺·HSO₃⁻ state are 9.1 and 10.6 ps at 300 and 250 K, respectively. Clearly, lower temperature is beneficial for bisulfite/sulfite formation due to its entropy being lower than that of the loose SO₂·H₂O cluster.

Fig. 2 (a) Snapshots taken from the BOMD simulation of SO₂·MA·(H₂O)₂ at 300 K. (b) Time evolution of the O–H, O–S, and N–H bond lengths in SO₂·MA·(H₂O)₂ at 250 and 300 K. (c) Snapshots taken from the BOMD simulation of SO₂·DMA·(H₂O)₂ at 300 K. (d) Time evolution of the O–H, O–S, and N–H bond lengths in SO₂·DMA·(H₂O)₂ at 250 and 300 K, respectively.

Previous studies have suggested that heterogeneous reactions on the surface of water droplets play crucial roles in atmospheric chemistry, such as the ionization of N₂O₄.^32,33 Zhong et al. found that SO₂ on a water nanodroplet tends to have an S–O bond exposed to the air that can readily react with other gaseous species in the air.³⁴ Here, BOMD simulations also confirm that increasing the size of the water cluster can move the SO₂ ↔ HSO₃⁻ equilibrium towards the right-hand side. As shown in ESI Fig. S3(a) and (b),† SO₂, MA/DMA, and two water molecules quickly convert to NH₃CH₃⁺/NH₂(CH₃)₂⁺·HSO₃⁻·H₂O cyclic structures, which remain stable on the water cluster during the BOMD simulation at 300 K. By contrast, no similar structure is formed from SO₂ and NH₃ during the BOMD simulation (ESI Fig. S3(c)†), implying that the amines have a unique promotion effect on the hydrolysis of SO₂. The NH₂(CH₃)₂⁺·HSO₃⁻ complex on the water droplet can also uptake an additional DMA molecule to form (NH₂(CH₃)₂⁺)₂·SO₃²⁻, as shown in ESI Fig. S3(d).†

2.2 Oxidation of NH₂(CH₃)₂⁺·HSO₃⁻ and (NH₂(CH₃)₂⁺)₂·SO₃²⁻ by O₃

The oxidization process of NH₂(CH₃)₂⁺·HSO₃⁻ by O₃ is divided into two steps: (1) Adsorption of O₃ and (2) dissociation of [SO₃·O₃H]⁻, as shown in the energy profiles in Fig. 3(a) and (b). The oxidation starts from the physical adsorption of O₃ with one oxygen atom approaching the HSO₃⁻ group (E_ads = −3.03 kcal mol⁻¹), and then the O₃ molecule is chemically adsorbed to HSO₃⁻ by forming a cyclic structure, NH₂(CH₃)₂⁺· [SO₃·O₃H]⁻, as an intermediate state. This process is highly exothermic (ΔE = −63.12 kcal mol⁻¹) and overcomes a low barrier of 6.37 kcal mol⁻¹, which is 9.25 kcal mol⁻¹ lower than the energy barrier without an amine (Fig. 3(a)). This energy barrier can be further lowered by adsorption of additional water molecules, where the energy barrier equals 5.85 and 4.18 kcal mol⁻¹ for one and two H₂O molecules, respectively (Fig. 3(a)). Due to the low energy barrier, formation of the NH₂(CH₃)₂⁺·[SO₃·O₃H]⁻ complex can spontaneously occur during the BOMD simulation at room temperature (ESI Fig. S4†).

Fig. 3 (a) Potential energy profiles for the oxidation reactions of H₂SO₃/CH₂(CH₃)₂⁺·HSO₃⁻·(H₂O)_n (n = 0, 1, 2) and O₃. Snapshots are taken from the BOMD simulation. (b) Potential energy versus the O–H distance in CH₂(CH₃)₂⁺·[SO₃·O₃H]⁻. The blue and red lines correspond to the singlet and triplet multiplicities, respectively. The grey line is obtained from the spin-polarized calculation with the PBE functional in the VASP. Snapshots are taken from the BOMD simulation. (c) Potential energy profiles for the oxidation reactions of (CH₂(CH₃)₂⁺)₂·SO₃²⁻·(H₂O)₄ and O₃. Snapshots are taken from the BOMD simulation. (d) Snapshots are taken from the BOMD simulation of (CH₂(CH₃)₂⁺)₂·SO₃²⁻·O₃·(H₂O)₄ at 300 K. All energy profiles are calculated at the M06-2X/cc-pVDZ-F12 level with ZPE correction.

As NH₂(CH₃)₂⁺·[SO₃·O₃H]⁻ is an extremely stable intermediate state, the dissociation of [SO₃·O₃H]⁻ needs to overcome a relatively high energy barrier (E_a = 17.58 kcal mol⁻¹) to produce HSO₄⁻ and singlet O₂ in the spin-restricted calculation (Fig. 3(b)). This barrier seems too high for a room–temperature reaction to occur. However, it is known that unstable singlet O₂ in the atmosphere can quickly convert to the triplet ground state³⁵ through collision and that, in particular, the strong spin–orbit interaction of the heavy element sulfur can greatly enhance the spin-flipping rate. Thus, the real dissociation process is accompanied by a spin-flipping process, which can greatly lower the dissociation barrier. Because the O–H stretching vibration corresponds to the main imaginary frequency of the transition state, we scan the energy surface versus the O–H distance (d_OH) of [SO₃·O₃H]⁻, as shown in Fig. 3(b). The cross-point (d_OH = 1.39 Å) between the singlet and triplet Born–Oppenheimer potential surfaces is found to yield a dissociation barrier of 7.36 kcal mol⁻¹, indicating the kinetic feasibility of the oxidation process under ambient conditions. The low dissociation barrier (E_a = 6.31 kcal mol⁻¹) is also confirmed by a calculation at the spin-polarized Perdew–Burke–Ernzerhof (PBE)/plane-wave level,³⁶ as implemented in the Vienna Ab initio Simulation Package (VASP 5.3).³⁷ The dissociation reaction is also highly exothermic (ΔE = −36.79 kcal mol⁻¹). Unlike the barrier to the adsorption of O₃, the dissociation barrier is minimally affected by additional vicinal water molecules (Fig. 3(a) and ESI Fig. S5†).

Moreover, the dissociation of HSO₃⁻ to SO₃²⁻, which generally happens on alkaline aerosol surface, can promote oxidation with O₃. A cluster containing one H₂SO₃, two DMA, and four H₂O molecules is chosen to mimic this situation, where the DMA and H₂SO₃ molecules spontaneously form NH₂(CH₃)₂⁺ and SO₃²⁻. As shown in Fig. 3(c), the oxidation becomes a one-step reaction with an extremely low barrier (E_a = 1.37 kcal mol⁻¹). This oxidation process can be reproduced in the BOMD simulation as well (Fig. 3(d)).

2.3 Oxidation of NH₂(CH₃)₂⁺·HSO₃⁻ with NO_x

NH₂(CH₃)₂⁺·HSO₃⁻ can be oxidized by NO₂ to form the radical NH₂(CH₃)₂⁺·SO₃⁻ and HNO₂ (HONO) with an energy barrier of 13.08 kcal mol⁻¹ and a potential energy change of −5.15 kcal mol⁻¹, as shown by the energy profiles and corresponding structures displayed in ESI Fig. 4(a) and S6(a),† respectively. In contrast to this oxidation reaction, the oxidation process without DMA has a relatively higher barrier (18.02 kcal mol⁻¹) and a positive energy change (6.30 kcal mol⁻¹), as shown in Fig. 4(a). Similar to the barrier for O₃ oxidation, the barrier for oxidizing NH₂(CH₃)₂⁺·SO₃⁻ with NO₂ can be lowered by extra neighbouring water molecules; e.g., the values of the oxidation barrier in the presence of the water monomer and dimer are equal to 10.20 and 8.32 kcal mol⁻¹, respectively. Such a barrier is believed to be even lower on the surface of aqueous aerosols.

Fig. 4 (a) Potential energy profiles for the oxidation reactions of H₂SO₃/CH₂(CH₃)₂⁺·HSO₃⁻·(H₂O)_n and NO₂ (n = 0–2). (b) Potential energy profiles for the oxidation reaction for H₂SO₃/NH₂(CH₃)₂⁺·HSO₃⁻·(H₂O)_n (n = 0,1–3) and N₂O₅. The energy profiles are calculated at the M06-2X/cc-pVDZ-F12 level with ZPE correction. Snapshots are taken from the BOMD simulation.

The NH₂(CH₃)₂⁺·SO₃⁻ radical product is an active radical, so it can easily react with other radicals, such as O₂, NO₂, and OH˙. For example, our calculations demonstrate that NH₂(CH₃)₂⁺·SO₃⁻·(H₂O)_n (n ≥ 1) and another NO₂ molecule can spontaneously form a NH₂(CH₃)₂⁺·HSO₄⁻·(H₂O)_n−1 cluster (ESI Fig. S6(b)†). In addition, HNO₂, the other product of this oxidation reaction, is also an important precursor of OH˙ radicals in the atmosphere.^38,39

The potential energy profiles of NH₂(CH₃)₂⁺·HSO₃⁻·(H₂O)_n (n = 0–3) oxidized by N₂O₅, another abundant oxidative NO_x species in the atmosphere, are shown in Fig. 4(b) and ESI Fig. S6(c).† Similar to O₃ oxidation, the process of (NH₂(CH₃)₂⁺·HSO₃⁻·(H₂O)_n + N₂O₅ → CH₂(CH₃)₂⁺·HSO₄⁻·(H₂O)_n−1 + HNO₃ + HNO₂) is a two-step reaction, where N₂O₅ first dissociates into a NO₂⁻·NO₃⁺ ion pair and combines with the bisulfite cluster to form a HNO₃ molecule and a stable complex [SO₃·NO₂]⁻ (Fig. 4(b)). The energy barrier of this step also decreases from 16.0 to 10.82 kcal mol⁻¹ as the number of participating water molecule increases (n = 0–3). In the second step, a H₂O molecule that attacks the sulfur atom will assist the breaking of [SO₃·NO₂]⁻, and the product CH₂(CH₃)₂⁺·HSO₄⁻·HNO₃·HNO₂·(H₂O)_n−1 is finally formed. This step is also an exothermic process (ΔE = −6.42 and −10.04 kcal mol⁻¹ for n = 2 and 3, respectively), and the barrier of this step is weakly affected by the number of water molecules (E_a = 17.37 and 15.04 kcal mol⁻¹ for n = 2 and 3, respectively). Such high energy barriers indicate that N₂O₅ plays a negligible role in the oxidation of sulfite.

2.4 Kinetics and implications for atmospheric chemistry

The reaction rate constants of hydrolysis reactions are calculated based on TST, as listed in Table 1, and details of this calculation and the reactant concentrations are listed in ESI Tables S1, S2 and S3.† The rate constant for the hydrolysis reaction of SO₂·H₂O with DMA adopts an inverse relation with temperature, decreasing from 3.35 × 10⁻¹⁰ to 1.39 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹ as the temperature changes from 240 to 300 K. According to previous observations, [SO₂] and [DMA] are ∼10¹² and ∼10⁹ molecules cm⁻³ in highly polluted air, respectively, while the concentration of H₂O decreases from 9.7 × 10¹⁷ to 9.0 × 10¹⁵ molecules cm⁻³ at 100% relative humility (RH) as the temperature drops from 300 K to 240 K.^7,30,40 On the basis of these parameters, the estimated concentrations of the SO₂·H₂O and DMA·H₂O complexes at 300 K are approximately 3.4 × 10⁸ and 1.9 × 10⁶ molecules cm⁻³, respectively, and the rate of hydrolysis for SO₂ and H₂O monomer assisted by DMA is estimated to be 4.8 × 10⁶ molecule cm⁻³ s⁻¹.

Table 1 Values of the total rate constants (k, cm³ molecule⁻¹ s⁻¹) for the hydrolysis reactions at temperatures from 240 to 300 K

Reaction	k (cm^3 molecule^−1 s^−1)
	240 K	260 K	280 K	300 K
SO2·H2O + MA	6.56 × 10^−13	3.09 × 10^−13	1.58 × 10^−13	8.96 × 10^−14
SO2·H2O + DMA	3.35 × 10^−10	9.42 × 10^−11	3.21 × 10^−11	1.39 × 10^−11
SO2·(H2O)2 + MA	3.79 × 10^−9	3.17 × 10^−9	1.18 × 10^−9	4.22 × 10^−10
SO2·(H2O)2 + DMA	9.01 × 10^−9	7.26 × 10^−9	5.64 × 10^−9	4.53 × 10^−9

---

It is interesting to compare the rate of SO₂ hydrolysis assisted by DMA to the rate of SO₂ reacting with OH· radicals under high RH conditions. The latter was previously thought to be the main reaction for SO₂ oxidation. Using the average concentration of OH· during the daytime (1 × 10⁶ molecules cm⁻³), the reaction rate of the oxidation of SO₂ by OH˙ based on a previously calculated rate constant (1.3 × 10⁻¹² cm³ molecule⁻¹ s⁻¹ at 300 K and 1 atm)⁴¹ is 1.5 × 10⁶ molecule cm⁻³ s⁻¹, which is lower than the hydrolysis rate. In this case, the consumption of SO₂ in the hydrolysis reaction can exceed that in the oxidation reaction with OH· radicals. Similarly, the estimated hydrolysis rate for atmospheric SO₂, DMA, and (H₂O)₂ at 300 K and 100% RH is 2.9 × 10⁶ molecules per cm³ per s, which is also more competitive with the reaction rate of SO₂ and OH·. Moreover, the concentration of OH· would be further lowered due to the reduced photochemistry either during heavily polluted periods or at night time, when the hydrolysis reaction would even play an even more crucial role in SO₂ oxidation.

The hydration products CH₂(CH₃)₂⁺·HSO₃⁻·(H₂O)_n are expected to be oxidized by O₃, NO₂, and N₂O₅. The estimated rate constant of the oxidation of CH₂(CH₃)₂⁺·HSO₃⁻·(H₂O)₂ by O₃ (5.82 × 10⁻¹⁵ cm³ molecule⁻¹ s⁻¹) is 3 orders of magnitude higher than that of the oxidation by NO₂ (1.73 × 10⁻¹⁸ cm³ molecule⁻¹ s⁻¹). As the concentrations of O₃, NO₂ and N₂O₅ were separately measured to be ∼10¹², ∼10¹², and ∼10¹⁰ molecules cm⁻³ in haze episodes, respectively,^7,42 we can estimate the lifetime of CH₂(CH₃)₂⁺·HSO₃⁻·(H₂O)₂ by the expression τ = (k × [oxidant])⁻¹. The lifetime of CH₂(CH₃)₂⁺·HSO₃⁻·(H₂O)₂ during oxidation by O₃ is ∼1/1000 of that during oxidation by NO₂ at 300 K. Considering the much lower oxidation rate constant and concentration of N₂O₅ than O₃ and NO₂, the oxidation by N₂O₅ is negligible. As a result, the proposed hydrolysis of SO₂ assisted by DMA in an O₃-polluted atmosphere is an important pathway for sulfate formation.

3 Conclusions

In summary, the hydrolysis and oxidation of SO₂ promoted by DMA are studied by using QM calculations and BOMD simulations. In both gaseous and heterogeneous environments, SO₂ can be easily hydrated with the assistance of DMA and then oxidized by O₃, as shown by the overall energy profile in Fig. 5. By contrast, NO₂ and N₂O₅, also viewed as important oxidants in the atmosphere, appear to play a much less important role than O₃ in the oxidation of SO₂. Kinetic analysis shows that the consumption rate of SO₂ during hydrolysis in the presence of DMA can surpass the rate of oxidation with OH· radicals under the conditions of heavily polluted air and high RH.

Fig. 5 Overall potential energy profiles for the hydrolysis of SO₂ promoted by DMA and oxidized by O₃ (M06-2X/cc-pVDZ-F12 with ZPE correction).

In the last decade, O₃ levels in the global atmosphere, according to field measurements, have greatly increased. For example, it has been reported that the yearly mean concentration of O₃ in Chinese megacities increased by 69% from 2006 to 2015.⁴³ The results from this research suggest that the hydrated oxidation of SO₂ with amines and O₃ has an important role in atmospheric chemistry.

4 Methods

4.1 Details of QM calculations and BOMD simulations

The geometries of the reactant states, transition states, and product states in all the reactions are optimized at the unrestricted M06-2X/cc-pVDZ-F₁₂ level,^44–46 which has shown good results on weak interactions and has been widely used in computational studies of atmospheric chemistry.^16,46–48 Zero-point energy (ZPE) corrections are included when calculating the potential energies, and intrinsic reaction coordinate (IRC) analysis is carried out to confirm the reaction pathways. WB97XD/cc-pVDZ-F12 and B2PLYPD/def2-TZVP methods are also employed for the total potential energy profiles for comparison, which show great consistency with energy profiles based on M06-2X. All the QM calculations for the reaction pathways are performed by using the Gaussian 09 software package.⁴⁹ The spin-polarized calculations are performed based on the generalized gradient approximation of the PBE functional, as implemented in the VASP 5.3.^37,50–52 A kinetic energy cutoff of 400 eV is chosen for the plane-wave expansion. The cell size for the NH₂(CH₃)₂⁺·[SO₃·O₃H] cluster is 15 × 15 × 15 ų.

BOMD simulations are performed in the framework of the Becke–Lee–Yang–Parr (BLYP) functional^53,54 with the Quickstep module in CP2K code.⁵⁵ The Gaussian and plane wave (GPW) basis sets (280 Ry energy cutoff) combined with the Goedecker-Teter-Hutter (GTH) pseudopotential⁵⁶ are employed to obtain a good balance between computational cost and accuracy. In addition, the dispersion correction is also included to better describe weak intermolecular interactions.⁵⁷ Periodic boundary conditions are used, and the cell sizes for the SO₂·MA/DMA·(H₂O)₂, NH₂(CH₃)₂⁺·HSO₃⁻·O₃·(H₂O)₄, and (NH₂(CH₃)₂⁺)₂·SO₃²⁻·O₃·(H₂O)₄ systems are 20 × 20 × 20 ų. A larger cell size (35 × 35 × 35 ų) is chosen for the hydrolysis reaction of SO₂ on the surface of a water nanodroplet containing 100 water molecules. The BOMD simulations are carried out at lower and higher temperatures (250 and 300 K), and the temperatures of the systems are controlled using the Nosé–Hoover thermostat. The time step of BOMD is set to 1.0 fs, which has been proven to achieve sufficient energy conservation for water systems.^34,47,58 The reaction process is unchanged with a smaller time step of 0.5 fs (ESI Fig. S7†).

4.2 Calculation of the reaction rate constant

The rate constants of hydrolysis and oxidation reactions are evaluated using TST with Wigner tunnelling corrections.^48,59,60 As [SO₂][DMA] is negligible relative to [SO₂][H₂O] and [DMA][H₂O], in the hydrolysis reaction of SO₂ assisted by DMA, two reaction pathways are considered: H₂O first binding to SO₂ and first binding to DMA. Because the concentrations of the reactants DMA, SO₂, SO₂·H₂O, and DMA·H₂O are critical to the final reaction rates, we estimate the number of SO₂·H₂O and DMA·H₂O complexes by the following expressions: [SO₂·H₂O] = K_SO2·H2O[SO₂][H₂O] and [DMA·H₂O] = K_DMA·H2O[DMA][H₂O], where K_SO2·_H2O and K_DMA·H2O are the equilibrium constants for the formation of SO₂·H₂O and DMA·H₂O dimers, respectively. The total reaction rate ν can be expressed as

Taking the reaction of SO₂·H₂O and DMA as an example, the hydrolysis process is represented by

By assuming that the reactant complex SO₂·DMA·H₂O is in equilibrium with the reactant monomers SO₂·H₂O and DMA, the total rate constant k_{SO2·DMA·H2O} for the reaction can be written as

where K_eq is the equilibrium constant for forming the reactant complex SO₂·DMA·H₂O and is expressed bywhere ΔG_eq is the free-energy change for the formation of the reactant complex, R is the gas constant, and T is the temperature. Here, k_uni is estimated by unimolecular TST and is expressed as

k_uni = Γk₂ (5)

The tunnelling effect factor Γ is given by Wigner tunnelling corrections,

where h is the Planck constant, ν⁺⁻ is the imaginary frequency of the transition state, k_B is the Boltzmann constant, and k₂ is represented byhere, ΔG is the activation free-energy change from the reactant complex to the transition state. The entropic term S is obtained from the partition function q(V,T) aswhere q(V,T) is determined from the calculation of vibrational frequency.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We thank Dr Jinrong Yang for valuable discussions. HL is thankful for the funding support from the National Natural Science Foundation of China (21773005). JSF and XCZ acknowledge computer support from UNL Holland Computing Center.

Notes and references

1. F. Bianchi, J. Trostl, H. Junninen, C. Frege, S. Henne, C. R. Hoyle, U. Molteni, E. Herrmann, A. Adamov, N. Bukowiecki, X. Chen, J. Duplissy, M. Gysel, M. Hutterli, J. Kangasluoma, J. Kontkanen, A. Kurten, H. E. Manninen, S. Munch, O. Perakyla, T. Petaja, L. Rondo, C. Williamson, E. Weingartner, J. Curtius, D. R. Worsnop, M. Kulmala, J. Dommen and U. Baltensperger, Science, 2016, 352, 1109–1112.
2. M. Kulmala, J. Kontkanen, H. Junninen, K. Lehtipalo, H. E. Manninen, T. Nieminen, T. Petaja, M. Sipila, S. Schobesberger, P. Rantala, A. Franchin, T. Jokinen, E. Jarvinen, M. Aijala, J. Kangasluoma, J. Hakala, P. P. Aalto, P. Paasonen, J. Mikkila, J. Vanhanen, J. Aalto, H. Hakola, U. Makkonen, T. Ruuskanen, R. L. Mauldin 3rd, J. Duplissy, H. Vehkamaki, J. Back, A. Kortelainen, I. Riipinen, T. Kurten, M. V. Johnston, J. N. Smith, M. Ehn, T. F. Mentel, K. E. Lehtinen, A. Laaksonen, V. M. Kerminen and D. R. Worsnop, Science, 2013, 339, 943–946.
3. A. Kürten, F. Bianchi, J. Almeida, O. Kupiainen-Määttä, E. M. Dunne, J. Duplissy, C. Williamson, P. Barmet, M. Breitenlechner, J. Dommen, N. M. Donahue, R. C. Flagan, A. Franchin, H. Gordon, J. Hakala, A. Hansel, M. Heinritzi, L. Ickes, T. Jokinen, J. Kangasluoma, J. Kim, J. Kirkby, A. Kupc, K. Lehtipalo, M. Leiminger, V. Makhmutov, A. Onnela, I. K. Ortega, T. Petäjä, A. P. Praplan, F. Riccobono, M. P. Rissanen, L. Rondo, R. Schnitzhofer, S. Schobesberger, J. N. Smith, G. Steiner, Y. Stozhkov, A. Tomé, J. Tröstl, G. Tsagkogeorgas, P. E. Wagner, D. Wimmer, P. Ye, U. Baltensperger, K. Carslaw, M. Kulmala and J. Curtius, J. Geophys. Res.: Atmos., 2016, 121, 12377–12400.
4. R. Zhang, A. Khalizov, L. Wang, M. Hu and W. Xu, Chem. Rev., 2012, 112, 1957–2011.
5. Y. Cheng, G. Zheng, C. Wei, Q. Mu, B. Zheng, Z. Wang, M. Gao, Q. Zhang, K. He, G. Carmichael, U. Pöschl and H. Su, Sci. Adv., 2016, 2016, e1601530.
6. D. L. Yue, M. Hu, R. Y. Zhang, Z. B. Wang, J. Zheng, Z. J. Wu, A. Wiedensohler, L. Y. He, X. F. Huang and T. Zhu, Atmos. Chem. Phys., 2010, 10, 4953–4960.
7. G. J. Zheng, F. K. Duan, H. Su2, Y. L. Ma, Y. Cheng, B. Zheng, Q. Zhang, T. Huang, T. Kimoto, D. Chang, U. Pöschl, Y. F. Cheng and K. B. He, Atmos. Chem. Phys., 2015, 2015, 2969–2983.
8. J. Almeida, S. Schobesberger, A. Kurten, I. K. Ortega, O. Kupiainen-Maatta, A. P. Praplan, A. Adamov, A. Amorim, F. Bianchi, M. Breitenlechner, A. David, J. Dommen, N. M. Donahue, A. Downard, E. Dunne, J. Duplissy, S. Ehrhart, R. C. Flagan, A. Franchin, R. Guida, J. Hakala, A. Hansel, M. Heinritzi, H. Henschel, T. Jokinen, H. Junninen, M. Kajos, J. Kangasluoma, H. Keskinen, A. Kupc, T. Kurten, A. N. Kvashin, A. Laaksonen, K. Lehtipalo, M. Leiminger, J. Leppa, V. Loukonen, V. Makhmutov, S. Mathot, M. J. McGrath, T. Nieminen, T. Olenius, A. Onnela, T. Petaja, F. Riccobono, I. Riipinen, M. Rissanen, L. Rondo, T. Ruuskanen, F. D. Santos, N. Sarnela, S. Schallhart, R. Schnitzhofer, J. H. Seinfeld, M. Simon, M. Sipila, Y. Stozhkov, F. Stratmann, A. Tome, J. Trostl, G. Tsagkogeorgas, P. Vaattovaara, Y. Viisanen, A. Virtanen, A. Vrtala, P. E. Wagner, E. Weingartner, H. Wex, C. Williamson, D. Wimmer, P. Ye, T. Yli-Juuti, K. S. Carslaw, M. Kulmala, J. Curtius, U. Baltensperger, D. R. Worsnop, H. Vehkamaki and J. Kirkby, Nature, 2013, 502, 359–363.
9. D. R. Hanson, J. Geophys. Res., 2002, 107, 4158.
10. W.-K. Li and M. L. McKee, J. Phys. Chem. A, 1997, 101, 9778–9782.
11. J. J. Margitan, J. Phys. Chem. A, 1984, 88, 3314–3318.
12. P. H. Wine, R. J. Thompson, A. R. Ravishankara, D. H. Semmes, C. A. Gump, A. Torabi and J. M. Nicovich, J. Phys. Chem., 1983, 88, 2095–2104.
13. R. L. Mauldin, T. Berndt, M. Sipila, P. Paasonen, T. Petaja, S. Kim, T. Kurten, F. Stratmann, V. M. Kerminen and M. Kulmala, Nature, 2012, 488, 193–196.
14. Z. Chen, C. Liu, W. Liu, T. Zhang and J. Xu, Sci. Total Environ., 2017, 575, 429–436.
15. F. Sheng, L. Jingjing, C. Yu, T. Fu-Ming, D. Xuemei and L. Jing-yao, RSC Adv., 2018, 8, 7988–7996.
16. H. Zhang, S. Chen, J. Zhong, S. Zhang, Y. Zhang, X. Zhang, Z. Li and X. C. Zeng, Atmos. Environ., 2018, 177, 93–99.
17. J. Yang, L. Li, S. Wang, H. Li, J. S. Francisco, X. C. Zeng and Y. Gao, J. Am. Chem. Soc., 2019, 141, 19312–19320.
18. R. Steudel and Y. Steudel, Eur. J. Inorg. Chem., 2009, 2009, 1393–1405.
19. T. Loerting and K. R. Liedl, J. Phys. Chem. A, 2001, 105, 5137–5145.
20. A. F. Voegele, C. S. Tautermann, C. Rauch, T. Loerting and K. R. Liedl, J. Phys. Chem. A, 2004, 108, 3859–3864.
21. J. Kirkby, J. Curtius, J. Almeida, E. Dunne, J. Duplissy, S. Ehrhart, A. Franchin, S. Gagne, L. Ickes, A. Kurten, A. Kupc, A. Metzger, F. Riccobono, L. Rondo, S. Schobesberger, G. Tsagkogeorgas, D. Wimmer, A. Amorim, F. Bianchi, M. Breitenlechner, A. David, J. Dommen, A. Downard, M. Ehn, R. C. Flagan, S. Haider, A. Hansel, D. Hauser, W. Jud, H. Junninen, F. Kreissl, A. Kvashin, A. Laaksonen, K. Lehtipalo, J. Lima, E. R. Lovejoy, V. Makhmutov, S. Mathot, J. Mikkila, P. Minginette, S. Mogo, T. Nieminen, A. Onnela, P. Pereira, T. Petaja, R. Schnitzhofer, J. H. Seinfeld, M. Sipila, Y. Stozhkov, F. Stratmann, A. Tome, J. Vanhanen, Y. Viisanen, A. Vrtala, P. E. Wagner, H. Walther, E. Weingartner, H. Wex, P. M. Winkler, K. S. Carslaw, D. R. Worsnop, U. Baltensperger and M. Kulmala, Nature, 2011, 476, 429–433.
22. J. Liu, S. Fang, W. Liu, M. Wang, F. M. Tao and J. Y. Liu, J. Phys. Chem. A, 2015, 119, 102–111.
23. Y. You, V. P. Kanawade, J. A. de Gouw, A. B. Guenther, S. Madronich, M. R. Sierra-Hernández, M. Lawler, J. N. Smith, S. Takahama, G. Ruggeri, A. Koss, K. Olson, K. Baumann, R. J. Weber, A. Nenes, H. Guo, E. S. Edgerton, L. Porcelli, W. H. Brune, A. H. Goldstein and S. H. Lee, Atmos. Chem. Phys., 2014, 14, 12181–12194.
24. J. Zheng, Y. Ma, M. Chen, Q. Zhang, L. Wang, A. F. Khalizov, L. Yao, Z. Wang, X. Wang and L. Chen, Atmos. Environ., 2015, 102, 249–259.
25. M. Chen, M. Titcombe, J. Jiang, C. Jen, C. Kuang, M. L. Fischer, F. L. Eisele, J. I. Siepmann, D. R. Hanson, J. Zhao and P. H. McMurry, Proc. Natl. Acad. Sci. U. S. A., 2012, 109, 18713–18718.
26. C. Qiu, L. Wang, V. Lal, A. F. Khalizov and R. Zhang, Environ. Sci. Technol., 2011, 45, 4748–4755.
27. S. M. Murphy, A. Sorooshian, J. H. Kroll, N. L. Ng, P. Chhabra, C. Tong, J. D. Surratt, E. Knipping, R. C. Flagan and J. H. Seinfeld, Atmos. Chem. Phys., 2007, 7, 289–349.
28. H. Yu, R. McGraw and S.-H. Lee, Geophys. Res. Lett., 2012, 39, L02807.
29. C. Qiu and R. Zhang, Phys. Chem. Chem. Phys., 2013, 15, 5738–5752.
30. L. Yao, O. Garmash, F. Bianchi, J. Zheng, C. Yan., J. Kontkanen, H. Junninen, S. B. Mazon, M. Ehn, P. Paasonen, M. Sipilä, M. Wang, X. Wang, S. Xiao, H. Chen, Y. Lu, B. Zhang, D. Wang, Q. Fu, F. Geng, L. Li, H. Wang, L. Qiao, X. Yang, J. Chen, V.-M. Kerminen, T. Petäjä, D. R. Worsnop, M. Kulmala and L. Wang, Science, 2018, 361, 278–281.
31. H. Li, J. Zhong, H. Vehkamaki, T. Kurten, W. Wang, M. Ge, S. Zhang, Z. Li, X. Zhang, J. S. Francisco and X. C. Zeng, J. Am. Chem. Soc., 2018, 140, 11020–11028.
32. B. J. Finlayson-Pitts, L. M. Wingen, A. L. Sumner, D. Syomin and K. A. Ramazan, Phys. Chem. Chem. Phys., 2003, 5, 223–242.
33. Y. Miller., B. J. Finlayson-Pitts and R. B. Gerber, J. Am. Chem. Soc., 2009, 131, 12180–12185.
34. J. Zhong, C. Zhu, L. Li, G. L. Richmond, J. S. Francisco and X. C. Zeng, J. Am. Chem. Soc., 2017, 139, 17168–17174.
35. C. Schweitzer and R. Schmid, Chem. Rev., 2003, 103, 1685–1757.
36. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868.
37. J. Furthmüller, J. Hafner and G. Kresse, Phys. Rev. B: Condens. Matter Mater. Phys., 1994, 50, 15606–15622.
38. A. J. M. Anglada, S. Olivella and A. Solé, Phys. Chem. Chem. Phys., 2014, 16, 19437–19445.
39. C. Ye, N. Zhang, H. Gao and X. Zhou, Environ. Sci. Technol., 2017, 51, 6849–6856.
40. M. E. Dunn, E. K. Pokon and G. C. Shields, J. Am. Chem. Soc., 2003, 126, 2647–2653.
41. B. Long, J. L. Bao and D. G. Truhlar, Phys. Chem. Chem. Phys., 2017, 19, 8091–8100.
42. H. Wang, K. Lu, X. Chen, Q. Zhu, Q. Chen, S. Guo, M. Jiang, X. Li, D. Shang, Z. Tan, Y. Wu, Z. Wu, Q. Zou, Y. Zheng, L. Zeng, T. Zhu, M. Hu and Y. Zhang, Environ. Sci. Technol., 2017, 4, 416–420.
43. W. Gao, X. Tie, J. Xu, R. Huang, X. Mao, G. Zhou and L. Chang, Sci. Total Environ., 2017, 603–604, 425–433.
44. C. Hattig, W. Klopper, A. Kohn and D. P. Tew, Chem. Rev., 2012, 112, 4–74.
45. G. Knizia, T. B. Adler and H. J. Werner, J. Chem. Phys., 2009, 130, 054104.
46. Y. Zhao and D. G. Truhlar, Theor. Chem. Acc., 2008, 120, 215–241.
47. J. Zhong, H. Li, M. Kumar, J. Liu, L. Liu, X. Zhang, X. C. Zeng and J. S. Francisco, Angew. Chem., Int. Ed. Engl., 2019, 58, 8351–8355.
48. R. Wu, S. Pan, Y. Li and L. Wang, J. Phys. Chem. A, 2014, 118, 4533–4547.
49. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery Jr, J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. Staroverov, T. N. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman and D. J. Fox, Gaussian 09, Revision D.01, Gaussian Inc., Wallingford, CT, 2009.
50. G. Kresse and J. Hafner, Phys. Rev. B: Condens. Matter Mater. Phys., 1993, 47, 558.
51. G. Kresse and J. FurthmüllerJ, Comput. Mater. Sci., 1996, 6, 15–50.
52. G. Kresse and J. Furthmuller, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169–11186.
53. A. D. Becke, Phys. Rev. A: At., Mol., Opt. Phys., 1988, 38, 3098.
54. C. Lee, W. Yang and R. G. Parr, Phys. Rev. B: Condens. Matter Mater. Phys., 1988, 37, 785–789.
55. J. VandeVondele, F. Mohamed, M. Krack, J. Hutter, M. Sprik and M. Parrinello, J. Chem. Phys., 2005, 122, 14515.
56. G. Lippert, J. Hutter and M. Parrinello, Mol. Phys., 2010, 92, 477–488.
57. S. Grimme, J. Antony, S. Ehrlich and H. Krieg, J. Chem. Phys., 2010, 132, 154104.
58. C. Zhu, M. Kumar, J. Zhong, L. Li, J. S. Francisco and X. C. Zeng, J. Am. Chem. Soc., 2016, 138, 11164–11169.
59. J. Elm, S. Jorgensen, M. Bilde and K. V. Mikkelsen, Phys. Chem. Chem. Phys., 2013, 15, 9636–9645.
60. H. S. Johnston and J. Heicklen, J. Chem. Phys., 1962, 66, 532–533.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9sc04756e

---