A novel formation mechanism of sulfamic acid and its enhancing effect on methanesulfonic acid–methylamine aerosol particle formation in agriculture-developed and coastal industrial areas

Sulfamic acid (SFA) significantly impacts atmospheric pollution and poses potential risks to human health. Although traditional sources of SFA and their role in sulfuric acid–dimethylamine new particle formation (NPF) have received increasing attention, the formation mechanism of SFA from HNSO₂ hydrolysis with methanesulfonic acid (MSA) and its enhancing effect on MSA-methylamine (MA) NPF have not been studied, which will limit understanding on the source and loss of SFA in agriculture-developed and coastal industrial areas. Here, the gaseous and interfacial formation of SFA from HNSO₂ hydrolysis with MSA was investigated using quantum chemical calculations and Born–Oppenheimer molecular dynamics (BOMD) simulations. Furthermore, the role of SFA in the MSA-MA system was assessed using the Atmospheric Cluster Dynamic Code (ACDC) kinetic model. Our simulation results indicate that the gaseous SFA formation from the hydrolysis of HNSO₂ with MSA can be competitive with that catalyzed by H₂O within an altitude of 5–15 km. At the air–water interface, two types of reactions, the ion-forming mechanism and the proton exchange mechanism to form the SFA⁻ … H₃O⁺ ion pair, were observed on the timescale of picoseconds. Considering the overall environment of sulfuric acid emission reduction, the present findings suggest that SFA may play a significant role in NPF and the growth of aerosol particles, as (i) SFA can directly participate in the formation of MSA-MA-based clusters and enhance the rate of NPF from these clusters by approximately 10³ times at 278.15 K and (ii) the SFA⁻ species at the air–water interface can attract gaseous molecules to the aqueous surface and thus promote particle growth.

1 Introduction

As a well-studied nitrogen derivative of sulfuric acid (Rennebaum et al., 2024), sulfamic acid (SFA) was not only recognized as a potent aerosol and cloud-nucleating agent (Xue et al., 2024; Zhang et al., 2023b; Pszona et al., 2015; Li et al., 2018) but can also harm human health through atmospheric deposition into water bodies (Van Stempvoort et al., 2019). In agriculture-developed and industrial areas with high ammonia (NH₃) concentrations, such as the Yangtze River Delta in China (Yu et al., 2020), the Indo-Gangetic Plains (Kuttippurath et al., 2020), Pakistan, Bangladesh (Warner et al., 2016), and southern Italy (Tang et al., 2021), the atmospheric concentration of SFA estimated by the theoretical method of CCSD(T)-F12/cc-pVDZ-F12//M06-2X/6-311$++$G(3df,3pd) (Li et al., 2018) was expected to reach up to 10⁸ molec. cm⁻³, thus leading to it becoming a significant air pollutant; therefore, the sources of SFA in the atmosphere have been focused by several groups (Lovejoy and Hanson, 1996; Pszona et al., 2015; Li et al., 2018; Larson and Tao, 2001; Manonmani et al., 2020; Zhang et al., 2022b). The traditional source of SFA was mainly taken from the ammonolysis of SO₃ (Lovejoy and Hanson, 1996; Larson and Tao, 2001; Li et al., 2018). Experimentally, the rate coefficient for the ammonolysis of SO₃ was detected to be $\mathrm{2.0}\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ molec.⁻¹ s⁻¹ at 295 K (Lovejoy and Hanson, 1996), which was close to the value for the hydrolysis of SO₃ assisted by water molecules (10⁻¹¹–10⁻¹⁰ cm³ molec.⁻¹ s⁻¹) (Kim et al., 1998; Hirota et al., 1996; Shi et al., 1994; Kolb et al., 1994; Long et al., 2013, 2023; Ding et al., 2023; Cheng et al., 2023; Wang et al., 2024). Theoretically, the ammonolysis of SO₃ to produce SFA can be catalyzed by NH₃. In arid and heavily polluted regions with high NH₃ concentrations, the effective rate coefficient for the ammonolysis of SO₃ can be sufficiently rapid, making it competitive with the conventional loss pathway of SO₃ with water (Li et al., 2018).

In addition to the ammonolysis of SO₃, new sources of SFA formation have received increasing attention (Zhang et al., 2022b; Manonmani et al., 2020; Li et al., 2018; Xue et al., 2024). The existence of HNSO₂ was proposed in the reaction between SO₃ and NH₃ and was regarded as the most stable for nine different isomers of HNSO₂, HONSO, HOSNO, HOS(O)N, HSNO₂, HSONO, HON(O)S, HOOSN, and HOONS (Deng et al., 2016). Owing to its similarity to SO₃ and the potential role of SO₃ in the atmosphere, the hydrolysis of HNSO₂ to produce SFA formation has been the focus of several groups (Zhang et al., 2022b; Manonmani et al., 2020). As the direct hydrolysis of HNSO₂ with a high-energy barrier hardly takes place in the gas phase (Zhang et al., 2022b; Manonmani et al., 2020), the addition of a second water molecule (Manonmani et al., 2020), formic acid (H₂SO₄), and sulfuric acid (SA) (Zhang et al., 2022b) has been proven to promote the product of SFA through the hydrolysis of HNSO₂. It was noted that, with the global reduction in the concentration of H₂SO₄ resulting from SO₂ emission restrictions, the contribution of methanesulfonic acid (MSA) to aerosol nucleation has received the widespread attention of scientists. As a major inorganic acidic air pollutant (Chen et al., 2020), the concentration of MSA in the atmosphere was noted to be notably high across various regions, spanning from coastal to continental, with levels found to be between 10% and 250 % of those measured for SA (Shen et al., 2019, 2020; Dawson et al., 2012; Bork et al., 2014a; Berresheim et al., 2002; Hu et al., 2023). However, to the best of our knowledge, the gaseous hydrolysis of HNSO₂ with MSA has not yet been investigated, which will confine the understanding of the source of SFA to regions with significant pollution and high levels of MSA. Thus, understanding the hydrolysis of HNSO₂ with MSA in the gas phase was necessary for exploring its impact on aerosols and human health.

$$\begin{array}{}\text{(1)}& {\mathrm{HNSO}}_{\mathrm{2}}+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}+\mathrm{MSA}\to \mathrm{SFA}+\mathrm{MSA}\end{array}$$

As a supplement to gas-phase reactions, interfacial reactions at the air–water interface can not only accelerate the rates of atmospheric reactions but may also introduce new mechanisms (Freeling et al., 2020; Zhong et al., 2019). For instance, the Criegee intermediates reacting with MSA at the air–water interface can form the ion pair of CH₃C(H)(OOH)(SO₃CH₃) anhydride and H₃O⁺ (Ma et al., 2020), which differs from the corresponding gaseous reaction where the MSA molecule acts solely as a reactant reacting with Criegee intermediates directly. As far as we know, HNSO₂ exhibits a significant interfacial preference, due to the fact that the total duration time of HNSO₂ at the interface approximately accounts for 49.1 % of the 150 ns simulation time (Fig. S1 in the Supplement). However, the hydrolysis of HNSO₂ with MSA has not been studied at the air–water interface, which will limit our understanding of how the hydrolysis of HNSO₂ with MSA differs in the gas phase and air–water interfaces.

From a structural point of view, two functional groups of −NH₂ and −SO₃H in the SFA molecule can act as both hydrogen donors and acceptors to interact with atmospheric species. Previous studies have demonstrated that SFA has a potential role in new particle formation (NPF), as it not only clusters efficiently with itself and SA (Lovejoy and Hanson, 1996) but can also promote the nucleation rate of NPF initiated from SA-DMA by a factor of 2 in dry and severely contaminated areas with NH₃ (Li et al., 2018). Due to the concentration of SA in the atmosphere decreasing significantly with the scenario of SO₂ emission control measures, MSA-driven NPF has attracted growing attention (Dawson et al., 2012; Nishino et al., 2014; Chen and Finlayson-Pitts, 2017; Chen et al., 2020; Shen et al., 2020). Initially, the binary nucleation of MSA with inorganic ammonia and organic amines in the atmosphere was reported, where MA exhibits the strongest enhancing capability (Chen et al., 2016; Chen and Finlayson-Pitts, 2017; Shen et al., 2019; Hu et al., 2023). Subsequently, some reported results suggest that the triadic MSA-MA-driven NPF can exhibit greater nucleation rates competed to the binary of MSA-driven NPF (Zhang et al., 2022a: Hu et al., 2023). For example, both formic acid (Zhang et al., 2022a) and trifluoroacetic acid (Hu et al., 2023) exhibit an excellent catalytic influence on MSA-MA-driven NPF. However, the SFA involved in MSA-MA-driven NPF has not been investigated, so it is important to investigate whether SFA can exhibit a similar enhancing effect in MSA-MA to that observed in SA-DMA.

This work studied the catalytic effect of SFA on HNSO₂ hydrolysis and MSA-MA nucleation particle formation. Specifically, quantum chemical calculations were used firstly to assess the atmospheric processes of the gaseous hydrolysis of HNSO₂ with MSA. Then, the gaseous and interfacial mechanism differences in the HNSO₂ hydrolysis with MSA were investigated applying the Born–Oppenheimer molecular dynamics (BOMD) simulation method. Finally, the atmospheric implications and mechanism of SFA in the MSA-MA-dominated NPF process were evaluated density functional theory and Atmospheric Cluster Dynamic Code (ACDC) (McGrath et al., 2012; Hu et al., 2023; Zhao et al., 2020; Zhang et al., 2024; Tsona Tchinda et al., 2022; Liu et al., 2021b) to evaluate the potential effect of SFA on nucleation and NPF. This work will not only deepen our understanding of the source of SFA but also reveal significant implications for new particle formation and aerosol particle growth in MSA-polluted areas.

2 Methodology

2.1 Quantum chemical calculations

The gaseous hydrolysis of HNSO₂ with MSA was comprehensively studied through quantum chemistry simulations. Optimization of all the species was carried out by using the method of M06-2X with a 6-311$++$G(2df,2pd) basis set (Zhao and Truhlar, 2008; Elm et al., 2012; Bork et al., 2014b). Vibrational frequencies were subsequently computed at the M06-2X/6-311$++$G(2df,2pd) level to ensure the reality of all stationary points' frequencies and the presence of only one imaginary frequency in transition states. It is noted that the calculated bond distances and bond angles at the M06-2X/6-311$++$G(2df,2pd) level (Fig. S2) agree well with the available values (Fig. S2) from the experiment and three different theoretical levels of the M06-2X/6-311$++$G(3df,2pd), M062X/6-311$++$G(3df,3pd), and M06-2X/aug-cc-pVTZ levels. Also, at the M06-2X/6-311$++$G(2df,2pd) level, internal reaction coordinate (IRC) analyses were conducted to verify the connection from the transition states to the corresponding products (or reactants). All calculations regarding geometries and frequency were conducted with the aid of the Gaussian 09 (Frisch et al., 2009) program. Furthermore, single-point energies were performed at the CCSD(T)-F12/cc-pVDZ-F12 (Kendall et al., 1992; Adler et al., 2007) level utilizing the ORCA (Neese, 2012) program, based on the optimized geometries mentioned above. The CCSD(T)/aug-cc-pVDZ method was chosen to calculate the relative energies as the fact that, compared with unsigned error (Table S1 in the Supplement) calculated at the CCSD(T)/CBS//M06-2X/6-311$++$G(2df,2pd) level, unsigned errors calculated at CCSD(T)-F12/cc-pVDZ-F12//M06-2X/6-311$++$G(2df,2pd) were 0.71 kcal mol⁻¹.

2.2 Rate coefficient calculations

The rate coefficients for the hydrolysis of HNSO₂ with MSA were calculated through a two-step process. Initially, the high-pressure-limit (HPL) rate coefficients were computed applying VRC-VTST methods within the Polyrate package (Chuang et al., 1999). It is worth noting that the electronic structure method for VRC-TST calculations is based on the Gaussian 09 program using M06-2X/6-311$++$G(2df,2pd). Meanwhile, two pivot points were selected (Bao et al., 2016; Long et al., 2021; Georgievskii and Klippenstein, 2003; Meana-Pañeda et al., 2024) to produce a single-faceted dividing surface for the HNSO₂ hydrolysis (shown in Sect. S1 in the Supplement). Subsequently, on the basis of the HPL rate coefficients, the rate coefficients for the hydrolysis of HNSO₂ with MSA were calculated within the temperature range of 212.6–320.0 K and pressures applying the Master Equation Solver for Multi-Energy well Reactions (MESMER) program (Glowacki et al., 2012). The rate coefficients for the barrierless steps transitioning between reactants and pre-reactive complexes were assessed applying the inverse Laplace transform (ILT) method within MESMER calculations, while the step-transitioning between pre-reactive complexes and post-reactive complexes via transition states was evaluated using the RRKM theory (Mai et al., 2018) in combination with the asymmetric Eckart model. The details of the rate coefficient for the hydrolysis of HNSO₂ with and without X (X = H₂O and MSA) are given in Sect. S1 and Tables 1 and S4.

Table 1 Rate coefficients (k, cm³ molec.⁻¹ s⁻¹) and effective rate constants (k^′, cm³ molec.⁻¹ s⁻¹) for the hydrolysis of HNSO₂ with H₂O and MSA calculated by the master equation within the temperature range of 213–320 K and altitude range of 0–15 km.

k_WM and k_MSA are respectively the rate constants for the hydrolysis of HNSO₂ with H₂O and MSA; $k_{\mathrm{WM}}^{\prime }$ and $k_{\mathrm{MSA}}^{\prime }$ are respectively the effective rate constants for the hydrolysis of HNSO₂with H₂O and MSA.

2.3 BOMD simulations

BOMD simulations were conducted applying DFT implemented in the CP2K program (VandeVondele et al., 2005; Hutter et al., 2014). The exchange and correlation interactions were addressed using the Becke–Lee–Yang–Parr (BLYP) functional (Becke, 1988; Lee et al., 1988), while Grimme's dispersion was applied to address weak dispersion interaction (Grimme et al., 2010). The Goedecker–Teter–Hutter (GTH) conservation pseudopotential (Goedecker et al., 1996; Hartwigsen et al., 1998), combined with a Gaussian DZVP basis set (VandeVondele and Hutter, 2007) and an auxiliary plane wave basis set, was used to represent core and valence electrons. Energy cutoffs (Zhong et al., 2017, 2018, 2019) of 280 Ry for the plane wave basis set and 40 Ry for the Gaussian basis set were applied. The gaseous reactions were simulated in the NVT ensemble at 300 K, with $\mathrm{15}\times \mathrm{15}\times \mathrm{15}$ ų supercells and a time step of 1 fs. To simulate the water microdroplet, the system containing 191 water molecules (Zhong et al., 2017) was utilized in $\mathrm{35}\times \mathrm{35}\times \mathrm{35}$ ų supercells. This setup included HNSO₂ and MSA along with the water drop. Prior to the interfacial simulation, a 10 ps relaxation period in the BOMD simulation was used to equilibrate the water microdroplet system with 191 molecules.

2.4 ACDC kinetics simulation

The ACDC model (McGrath et al., 2012; Hu et al., 2023; Zhao et al., 2020; Zhang et al., 2024; Tsona Tchinda et al., 2022; Liu et al., 2021b) was utilized to simulate the (MSA)_x(MA)_y(SFA)_z ($\mathrm{0}\le y\le x+z\le \mathrm{3}$) cluster formation rates and explore the potential mechanisms, where the most stable structures of (SFA)_x(MSA)_y(MA)_z ($\mathrm{0}\le z\le x+y\le \mathrm{3}$) clusters were searched with ABCluster software (Zhang and Dolg, 2015) (the details are in Sect. S1). This simulation encompasses a variety of temperatures and monomer concentrations to capture the dynamics under different environmental conditions. Thermodynamic parameters, obtained from quantum chemical calculations executed at the M06-2X/6-311$++$G(2df,2pd) level, were used as inputs for the ACDC model. Notably, many benchmark studies (Zhao et al., 2020; Zhang et al., 2024; Tsona Tchinda et al., 2022; Liu et al., 2021b) show that the M06-2X functional has good performance compared to other common functionals for gaining the Gibbs free energies. For all the M06-2X calculations, the 6-311$++$G(2df,2pd) basis set was used, as it is a good compromise between accuracy and efficiency and does not yield significant errors in the thermal contribution to the free energy compared to much larger basis sets, such as 6-311$++$G(3df,3pd), with differences in relative ΔG less than 1.75 kcal mol⁻¹ (Table S7). The temporal progression of cluster concentrations was determined by numerically integrating the birth–death equation, leveraging MATLAB's ode15s solver for enhanced accuracy.

$$\begin{array}{}\text{(2)}& \begin{array}{rl}{\displaystyle \frac{\mathrm{d}{c}_i}{\mathrm{d}t}}& ={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\sum _{j<i}{\mathit{\beta }}_{j,(i-j)}{c}_j{c}_{(i-j)}+\sum _j{\mathit{\gamma }}_{(i+j)\to i}{c}_{i+j}\\ & -\sum _j{\mathit{\beta }}_{i,j}{c}_i{c}_j-{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\sum _{j<i}{\mathit{\gamma }}_{i\to j}{c}_i+Q_i-S_i\end{array}\end{array}$$

Here, c_i represents the concentration of a specific cluster, labeled as i; the term β_i,j was used to denote the collision coefficient, which was a measure of the frequency at which clusters i and j collide with each other in a given environment or system; the coefficient ${\mathit{\gamma }}_{(i+j\to i)}$ was defined as the evaporation rate constant that describes the process of a larger cluster, consisting of combined elements i and j, breaking down into the individual smaller clusters i and j; and Q_i encompasses all other source terms contributing to the formation of cluster i. S_i signifies alternative sink terms for cluster i that may remove it from the system. Considering the formation Gibbs free energy (Table S8) and evaporation rates (Table S9) of all clusters, the clusters containing pure MSA and MA molecules and the clusters containing an SFA molecule are mostly more stable and therefore are allowed to form larger clusters and contribute to particle formation rates. In this case, clusters (MSA)₄ ⋅ (MA)₃, (MSA)₄ ⋅ (MA)₄ and SFA
,⋅ (MSA)₃ ⋅ (MA)₃ are set as the boundary clusters.

3 Results and discussion

3.1 The hydrolysis of HNSO₂ with MSA in the gas phase

Given the low chance of three molecules of HNSO₂, H₂O, and MSA colliding simultaneously under atmospheric conditions, the hydrolysis of HNSO₂ with MSA (Channel MSA) was likely a sequential bimolecular process. As the concentration of water molecules (10¹⁸ molec. cm⁻³; Anglada et al., 2013) in the atmosphere is much higher than that of HNSO₂ and MSA (10⁵–10⁹ molec. cm⁻³; Shen et al., 2020), it is hard for the reaction pathway of HNSO₂ … MSA + H₂O to occur in actual atmospheric conditions. Therefore, Channel MSA proceeds through the initial formation of dimers (HNSO₂ … H₂O and MSA. … H₂O) via collisions between HNSO₂ (or MSA) and H₂O. Subsequently, the generated dimer interacts with the third reactant, either MSA or HNSO₂. As seen in Fig. 1, the calculated Gibbs free energy of the MSA … H₂O complex was −0.9 kcal mol⁻¹, which was 4.5 kcal mol⁻¹ lower than that of HNSO₂ … H₂O. Consequently, it was predicted that the primary route for the hydrolysis reaction of HNSO₂ with MSA takes place via the HNSO₂ + MSA … H₂O reaction.

Figure 1 The potential energy profile (ΔG) for the hydrolysis reaction of HNSO₂ with MSA at the CCSD(T)-F12/cc-pVDZ-F12//M06-2X/6-311$++$G(2df,2pd) level of theory.

Starting from the HNSO₂ + MSA … H₂O reactants, Channel MSA was initiated through the intermediate complex designated as IM_MSA1. From a geometric perspective, the IM_MSA1 complex exhibits a cage-like configuration by a van der Waals (vdW) force (S₁ … O₁, 2.00 Å) and the involvement of three hydrogen bonds: H₂ … O₄ (1.53 Å), H₄ … N₁ (1.60 Å), and H₅ … O₃ (2.07 Å). The Gibbs free energy of the IM_MSA1 complex relative to HNSO₂ + MSA … H₂O reactants was 1.7 kcal mol⁻¹. Subsequently, as presented in Fig. 1, Channel MSA progresses through the transition state TS_MSA1 to yield complex IMF_MSA1. At TS_MSA1, the MSA moiety facilitates two hydrogen atom transfers, with TS_MSA1 lying only 0.8 kcal mol⁻¹ above complex IM_MSA1. Complex IMF_MSA1 exhibits a cage-like structure with a Gibbs free energy 23.4 kcal mol⁻¹ lower than that of IM_MSA1, revealing thermodynamic favorability of HNSO₂ hydrolysis with MSA. To evaluate the relative catalytic impact of MSA and H₂O, Fig. S4 illustrates the profiles of Gibbs free energy for the hydrolysis of HNSO₂ and the corresponding reaction assisted by H₂O. Compared to complex HNSO₂ … (H₂O)₂, the Gibbs stabilization energy of IM_MSA1 increased by 5.6 kcal mol⁻¹, potentially shortening the S₁ … O₁ bond distance by 0.21 Å. Considering the Gibbs free energy barrier and rate coefficients, MSA demonstrates a greater catalytic role compared to H₂O in lowering the energy barrier for the hydrolysis of HNSO₂. In particular, MSA facilitates the hydrogen atom to extraction from H₂O, further reducing the reaction energy barriers to 7.7 kcal mol⁻¹. Meanwhile, the calculated rate coefficients for HNSO₂ hydrolysis with MSA were $\mathrm{3.08}\times {\mathrm{10}}^{-\mathrm{11}}$–$\mathrm{3.50}\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ molec.⁻¹ s⁻¹ within 212.6–320.0 K, exceeding corresponding values for reactions involving H₂O by 2 orders of magnitude. Besides, the Gibbs free energy of IMF_MSA1 was 2.0 kcal mol⁻¹ lower than that of the product complex IMF_WM1 (SFA … H₂O), suggesting SFA has a higher affinity for MSA compared to H₂O. Besides, MSA-assisted HNSO₂ hydrolysis is reduced by 4.9 kcal mol⁻¹ in the energy barrier, as opposed to the NH₃-assisted ammonolysis of SO₃, with its rate constant at 298 K ($\mathrm{2.85}\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ molec.⁻¹ s⁻¹) close to the value of ammonolysis of SO₃ with NH₃ ($\mathrm{4.35}\times {\mathrm{10}}^{-\mathrm{10}}$ cm³ molec.⁻¹ s⁻¹) (Li et al., 2018). However, due to the absence of the concentration of HNSO₂, the competitiveness of these two reactions cannot be further confirmed.

To evaluate the comparative catalytic ability of X (X = H₂O and MSA) in the atmosphere, the effective rate coefficients (k^′) for X-assisted HNSO₂ hydrolysis were calculated in Table 1. Notably, k^′ serves as a metric for gauging the comparative catalytic ability of a series of gaseous catalysts in atmospheric reactions (Sarkar et al., 2017; Zhang et al., 2019, 2020; Buszek et al., 2012; Gonzalez et al., 2011; Parandaman et al., 2018; Anglada et al., 2013). When X was present, the calculated k^′ was given by Eq. (3).

$$\begin{array}{}\text{(3)}& k^{\prime }X=k_X\times K_{\mathrm{eq}}\left(X\mathrm{\dots }{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right)\times \left[X\right]\end{array}$$

In Eq. (3), k_X was the rate coefficient for X-assisted HNSO₂ hydrolysis (Table 1), while K_eq (X … H₂O) denotes the equilibrium coefficients of X … H₂O (Table S2). [X] represents the available concentrations of H₂O (Anglada et al., 2013) and MSA (Shen et al., 2020). As indicated in Table 1, at experimental concentrations ([H₂O] = 5.16×10¹⁶–2.35×10¹⁸ molec. cm⁻³) within 280.0–320.0 K (at 0 km), the computed $k_{\mathrm{WM}}^{\prime }$ ranged from $\mathrm{5.99}\times {\mathrm{10}}^{-\mathrm{18}}$–$\mathrm{7.79}\times {\mathrm{10}}^{-\mathrm{17}}$ cm³ molec.⁻¹ s⁻¹. This range exceeded $k_{\mathrm{MSA}}^{\prime }$ ($\mathrm{4.60}\times {\mathrm{10}}^{-\mathrm{21}}$–$\mathrm{4.81}\times {\mathrm{10}}^{-\mathrm{20}}$ cm³ molec.⁻¹ s⁻¹) by 2–4 orders of magnitude, highlighting the pronounced impact of H₂O compared to MSA at 0 km in enhancing the rate of HNSO₂ hydrolysis. However, with the significant decrease in atmospheric water molecules with increasing altitude, the calculated $k_{\mathrm{MSA}}^{\prime }$ ranged from $\mathrm{1.96}\times {\mathrm{10}}^{-\mathrm{19}}$ s⁻¹–$\mathrm{1.30}\times {\mathrm{10}}^{-\mathrm{17}}$ cm³ molec.⁻¹ s⁻¹, surpassing $k_{\mathrm{WM}}^{\prime }$ ($\mathrm{9.85}\times {\mathrm{10}}^{-\mathrm{27}}$–$\mathrm{6.51}\times {\mathrm{10}}^{-\mathrm{22}}$ cm³ molec.⁻¹ s⁻¹) by 3–10 orders of magnitude. This illustrates that MSA has a significantly greater catalytic ability than H₂O in accelerating the rate of HNSO₂ hydrolysis within 5–15 km. So, HNSO₂ hydrolysis with MSA may represent a potential formation pathway for SFA across an altitude scope of 5–15 km.

3.2 Reactions at the air–water interface

The interfacial mechanism of MSA-assisted HNSO₂ hydrolysis at the air–water interface has not been thoroughly investigated. Interestingly, our simulations show that HNSO₂ and MSA molecules spend approximately 49.1 % and 12.1 % of the time, respectively, at the air–water interface during the 150 ns simulation (Figs. S1 and S6). This reveals that the presence of HNSO₂ and MSA at the air–water interface should not be disregarded. Therefore, BOMD simulations were performed to clarify the interfacial mechanism of MSA-assisted HNSO₂ hydrolysis at the air–water interface. Comparable to the reactions of SO₃ at the air–water interface with acidic molecules (Cheng et al., 2023; Zhong et al., 2019), the hydrolysis of HNSO₂ with MSA at the air–water interface may occur through three pathways: (i) the adsorbed MSA interacts with HNSO₂ at the air–water interface, (ii) the adsorbed HNSO₂ interacts with MSA at the air–water interface, and (iii) the HNSO₂ … MSA complex reacts at the air–water interface. Nevertheless, because of the high reactiveness of MSA at the air–water interface, the lifetime of MSA was minimal (seen in Fig. S9) on the water droplet, which was around a small number of picoseconds, leading to the rapid formation of MSA⁻ ion. Meanwhile, although HNSO₂ remains stable at the air–water interface (seen in Fig. S8) and does not dissociate within 10 ps, the hydrated form of HNSO₂ illustrated in Fig. S8 was not conducive to HNSO₂ hydrolysis at the air–water interface. Therefore, model (iii) was primarily considered for HNSO₂ hydrolysis with MSA at the air–water interface. It is worth noting that the HNSO₂ … MSA complex can persist at the air–water interface for approximately 34.2 % of the 150 ns simulation time (see in Fig. S7). For model (iii), two types of reactions were found at the air–water interface: (a) the NH₂SO${}_{\mathrm{3}}^{-}$ and H₃O⁺ ion formation mechanism and (b) the proton exchange mechanism.

NH₂SO${}_{\mathrm{3}}^{-}$ and H₃O⁺ ion formation mechanism. Figures 2a and S10 and Movie S1 illustrate the formation mechanism of NH₂SO${}_{\mathrm{3}}^{-}$ and H₃O⁺ ions through the chain structure at 4.57 ps, and a chain-hydrolyzed transition state was observed, accompanied by two proton transfer events. IN particular, an H₂ atom transferred from the OH moiety of an MSA molecule to the terminal N atom of an HNSO₂ molecule, resulting in the breaking of the O₃–H₂ bond (with a length of 1.49 Å) and the formation of an H₂–N bond (with a length of 1.14 Å). Concurrently, an interfacial water molecule decomposes, leading to the elongation of the O₁–H₁ bond to over 1.00 Å, with the S1 atom of HNSO₂ obtaining the OH moiety of the interfacial water molecule ($d_{({\mathrm{S}}_{\mathrm{1}}\text{–}{\mathrm{O}}_{\mathrm{1}}}$) = 1.60 Å). By 4.61 ps, the N–H₂ and S₁–O₁ bonds both shortened to 0.99 and 1.01 Å, revealing the formation of the SFA molecule. However, due to its strong acidity, the SFA molecule could only persist on the water droplet surface for a picosecond timescale. As a result, at 7.43 ps, the proton of SFA transferred to another interfacial water molecule, completing the deprotonation of SFA. The loop structure mechanism (Figs. 2b and S11 and Movie S2) was similar to the chain structure mechanism. However, in this case, the proton of SFA transferred to CH₃SO${}_{\mathrm{3}}^{-}$ rather than to an interfacial water molecule.

Figure 2 BOMD simulation trajectories and snapshots of the NH₂SO${}_{\mathrm{3}}^{-}$ and H₃O⁺ ion formation mechanism – chain structure (a) and loop-structure (b) – in the HNSO₂ hydrolysis with MSA at the air–water interface.

Figure 3 BOMD simulation trajectories and snapshots of the proton exchange mechanism in MSA-mediated HNSO₂ hydration with one (a) and two (b) water molecules at the air–water interface.

Proton exchange mechanism. As depicted in Fig. 3, the proton exchange mechanism illustrates the deprotonation of MSA concurrent with HNSO₂ hydration at the air–water interface. As shown in Figs. 3a and S12 and Movie S3, MSA-mediated HNSO₂ hydration with a single water molecule was observed. Initially, the HNSO₂ … MSA complex quickly associates with an interfacial water molecule and forms a loop structure complex that accelerates the rate of proton transfer. By 4.38 ps, an eight-membered loop structure complex, HNSO₂ … H₂O … MSA, emerges, characterized by two hydrogen bonds ($d_{\left({\mathrm{H}}_{\mathrm{2}}\text{–}\mathrm{N}\right)}=\mathrm{1.82}$ Å and $d_{\left({\mathrm{H}}_{\mathrm{1}}\text{–}{\mathrm{O}}_{\mathrm{2}}\right)}=\mathrm{1.92}$ Å) and a van der Waals force ($d_{\left({\mathrm{S}}_{\mathrm{1}}\text{–}{\mathrm{O}}_{\mathrm{1}}\right)}=\mathrm{2.35}$ Å). Thereafter, at 4.77 ps, a transition-state-like configuration was identified where the water molecule within the loop complex dissociated, elongating the O₁–H₁ bond to over 1.00 Å, and the S atom of HNSO₂ attached to the OH group of the interfacial water molecule. Concurrently, the CH₃SO${}_{\mathrm{3}}^{-}$ ion receives the proton from the separated interfacial water molecule. The entire reaction for MSA-mediated HNSO₂ hydration with one water molecule was completed at 4.80 ps, resulting in the formation of SFA and MSA molecules. MSA-mediated hydration of HNSO₂ with two water molecules (Figs. 3b and S13 and Movie S4) at the air–water interface was similar to the mechanism identified with one water molecule. However, the inclusion of two water molecules enlarges the loop, significantly reducing the stress on the loop structures. Consistent with the prediction in Fig. 4, the loop structures preferred to include two water molecules rather than one water molecule. This observation agrees well with the reported hydration of the Criegee intermediate at the air–water interface (Zhu et al., 2016; Kumar et al., 2018; Liu et al., 2021a; Zhang et al., 2023a). Additionally, MSA-mediated hydration of HNSO₂ with three water molecules (Fig. S14 and Movie S5) was observed in the proton exchange mechanism. However, its probability of occurrence was smaller due to the relatively larger entropy effect. It was noteworthy that the SFA and MSA molecules formed in the proton exchange mechanism were not stable at the air–water interface, which can further interact with an interfacial water molecule to form the corresponding ions of NH₂SO${}_{\mathrm{3}}^{-}$ and CH₃SO${}_{\mathrm{3}}^{-}$.

Figure 4 Percentages of different mechanisms for HNSO₂ hydrolysis with MSA at the air–water interface observed in BOMD simulations.

At the air–water interface, a sum of 50 BOMD trajectories, each lasting 10 ps, was conducted to investigate HNSO₂ hydrolysis with MSA. Two distinct mechanisms were observed: the formation of NH₂SO${}_{\mathrm{3}}^{-}$ and H₃O⁺ ions (shown in blue and yellow in Fig. 4) and the proton exchange mechanism (represented by orange, purple, and green in Fig. 4). In the mechanism involving the formation of NH₂SO${}_{\mathrm{3}}^{-}$ and H₃O⁺ ions, approximately 22 % (Figs. 2a, 4, and S10 and Movie S1) of the reactions took place via a chain structure, while the majority (∼18 %) (Figs. 2b, 4, and S11 and Movie S2) proceeded through a loop structure mechanism. This discrepancy can be attributed to the uncertainty regarding the direction of proton transfer from SFA. Since the number of water molecules near the water microdroplet far exceeded that of CH₃SO${}_{\mathrm{3}}^{-}$, protons were predominantly transferred to interface water molecules, making the loop structure mechanism weaker than the chain structure mechanism. Approximately 60 % of the reactions were observed to be due to the proton exchange mechanism in BOMD simulations. Through water-mediated mechanisms, these reactions resulted in SFA formation. Similarly to gas-phase reactions, loop structures were observed in these reactions. Approximately 10 % of the reactions formed a loop structure involving one water molecule (Figs. 3a, 4, and S12 and Movie S3), while the most common loop structure involved two water molecules (about 42 %) (Figs. 3b, 4, and S13 and Movie S4). Smaller loops were found to experience more stress than loop structures with two water molecules. In cases of loop structures with three water molecules (about 8 %) (Figs. 4 and S14 and Movie S5), the entropy effect was deemed to be more significant than the strain effect and likely played a dominant role. The two water molecules contained in the loop structure not only acted as a reactant but also facilitated proton transfer as a bridge.

3.3 New particle formation from the atmospheric products

3.3.1 The influence of SFA on the stability of atmospheric MSA-MA-based clusters

Electrostatic potential (ESP) mapping on the molecular van der Waals (vdW) surface was employed to analyze the interactions between SFA and other key nucleation precursors like MSA and MA. As shown in Fig. 5, sites with more negative ESP often attract more positive ESP sites, namely hydrogen bonds in the studied system. Specifically, the hydrogen atoms of the −SO₃H and −NH₂ groups (site 4 and 5) in SFA, possessing more positive ESP values, have the potential to attract groups with negative ESP values, such as the oxygen atom within the −SO₃H group of MSA (site 6) and the nitrogen atom of MA (site 1), thus forming hydrogen bonds as proton donors. Additionally, the sulfur atom of the −SO₃H functional group (site 7) in SFA, with a negative ESP of −30.75, acts as proton acceptor, facilitating direct binding with MSA and MA molecules via the hydrogen bonds. Therefore, the introduction of SFA was believed to enhance the stability of MSA-MA clusters by promoting the formation of more hydrogen bonds and facilitating proton transfers.

Figure 5 ESP-mapped molecular vdW surface of MA, SFA, and MSA molecules at the M06-2X/6-311$++$G(2df,2pd) level of theory. Surface local minima and maxima of ESP of the different functional groups in MA, SFA, and MSA molecules are represented as blue and yellow spheres, respectively. The values of maximum and minimum are shown in kcal mol⁻¹ in the parentheses. The green, red, and blue arrows refer to the tendencies to form hydrogen bonds and proton transfer events, respectively (green: carbon; red: oxygen; blue: nitrogen; yellow: sulfur; and white: hydrogen).

Figure 6 The J (cm⁻³ s⁻¹) (a) and R (b) versus [SFA] with [MSA] = 10⁶ molec. cm⁻³, [MA] = 2.5×10⁸ molec. cm⁻³, and four different temperatures (green line: 298.15 K; blue line: 278.15 K; red line: 258.15 K; black line: 238.15 K).

3.3.2 The cluster formation rates in the SFA-MSA-MA system

Simulations were conducted to determine the cluster formation rates (J) for the MSA-MA-SFA system, with varying parameters such as temperature and the concentrations of the precursors involved. To assess the promotional impact of SFA on J under varying atmospheric conditions, the enhancement factor (R) was computed as the ratio of J_MSA-MA-SFA to J_MSA-MA. As depicted in Fig. 6a, the J of the MSA-MA-SFA system exhibits a negative correlation with temperature, attributed to the decrease in ΔG value and evaporation rates of clusters at lower temperatures. Conversely, a positive correlation of R with temperature was observed (Fig. 6b), indicating that SFA's enhancement of nucleation was more pronounced in regions with relatively higher temperatures. Furthermore, both J and R show an increase as the [SFA] increases, suggesting a positive correlation of J and R with [SFA]. In short, in regions with high [SFA], such as the Yangtze River Delta of China, Bangladesh, and the east coast of India, SFA was expected to significantly boost the J of MSA-MA-based nucleation. It is noted that, in Fig. 6b, due to the competitive relationship between MSA and SFA, at low concentrations of SFA, the binding capacity of MSA with MA is stronger than that of SFA with MA, resulting in only a small amount of SFA participating in cluster formation. However, as the concentration of SFA increases, the number of (MSA)_x ⋅ (MA)_y ⋅ (SFA)_z (where $y\le x+z\le$3) ternary clusters increases, leading to the formation of more hydrogen bonds and a significant increase in R_SFA. Additionally, Fig. 7 illustrates the J and R of MSA-MA-SFA clusters under different [MSA] and [MA]. On the one hand, larger values of [MSA] and [MA] correspond to higher J, as the increased concentration of nucleation precursors leads to a rise in the number of MSA-MA-FSA clusters. On the other hand, increasing [MSA] and [MA] result in a decrease in the R attributed to the effect of SFA on nucleation. This was because, as [MSA] and [MA] increase, the prevalence of pure MSA-MA clusters rises during the clustering process, consequently reducing the impact of SFA.

Figure 7 The J (cm⁻³ s⁻¹) (a) and R (b) as a function of [MSA] with [SFA] = 10⁸ molec. cm⁻³ and three different [MA] (black line: [MA] = 2.5×10⁷ molec. cm⁻³; red line: [MA] = 2.5×10⁸ molec. cm⁻³; blue line: [MA] = 2.5×10⁹ molec. cm⁻³) at 278.15 K.

3.3.3 The growth paths of clusters under different atmospheric conditions

Li et al. (2018) studied the atmospheric concentration of SFA estimated by the theoretical method (Li et al., 2018) and expected it to reach up to 10⁸ molec. cm⁻³ in high NH₃ concentrations, such as the Yangtze River Delta in China (Yu et al., 2020), the Indo-Gangetic Plains (Kuttippurath et al., 2020), Pakistan, Bangladesh (Warner et al., 2016), and southern Italy (Tang et al., 2021). Considering the high atmospheric concentrations of MSA and MA detected in coastal industrial areas (Shen et al., 2020; Mao et al., 2018), SFA could be an important contributor to MSA-MA-driven NPF, such as the Yangtze River Delta in China, the east coast of India, the south of Bangladesh, and Italy. To further evaluate the implications of SFA for the MSA-MA nucleation in the atmosphere, the growth paths of clusters were calculated under different atmospheric conditions. In Fig. 8a, two main types of cluster formation routes were found: (i) the pure MSA-MA pathway and (ii) the MSA-MA-SFA pathways at 278.15 K in the studied system. In the pure MSA-MA pathway, cluster growth primarily occurs through the collisional addition of MSA or MA monomers. Conversely, in the SFA-involved pathways, SFA can directly participate in the formation of stable larger clusters, such as (MSA)₂ ⋅ (MA)₂ ⋅ SFA and (MSA)₂ ⋅ (MA)₂ ⋅ (SFA)₂ clusters, and then subsequently grow out. The involvement of SFA in the cluster formation pathway was significantly influenced by atmospheric conditions. Firstly, as the temperature rises from 238.15 to 278.15 K, the contribution of the SFA-involved cluster formation pathways rises from 68 % to 90 % (Fig. 8b), implying that the pathway involving SFA becomes increasingly important at lower altitudes or in warmer conditions. Secondly, as depicted in Figs. 8c and S22, the contribution of SFA to the MSA-MA system is primarily influenced by [SFA] and [MSA], with negligible dependence on [MA]. To assess the role of SFA in MSA-MA nucleation in the atmosphere, the specific contribution of the MSA-MA cluster growth paths at varying [SFA] to NPF was calculated at 278.15 K, as illustrated in Fig. 8c, under the ambient conditions typical of the corresponding regions. Generally, as [SFA] increases from 10⁴ to 10⁸ molec. cm⁻³, the contribution of the SFA-involved pathway increases gradually. Specifically, at low [SFA] (10⁴ molec. cm⁻³), the contributions of SFA-involved clustering pathways are 77 % and 41 % in regions with relatively low [MSA] in non-sea regions (Berresheim et al., 2002). In regions with high [SFA] (10⁶, 10⁸ molec. cm⁻³), the contributions of the SFA-MSA-MA growth pathways are dominant in their NPF. Particularly in areas with high [MSA], such as the Pacific Rim (6.26×10⁸ molec. cm⁻³; Saltzman et al., 1986), the central Mediterranean Sea (2.11×10⁸ molec. cm⁻³; Mansour et al., 2020), and the Amundsen Sea (3.65×10⁹ molec. cm⁻³; Jung et al., 2020), nucleation is primarily driven by the SFA-MSA-MA pathway, contributing to approximately 88 % of cluster formation. These results suggest that the influence of SFA is more pronounced in regions with relatively high [MSA]. It is important to note that the [SFA] values discussed in this work are estimated from limited observational data based on the reaction between SO₃ and NH₃ in the atmosphere. Accurate determination of atmospheric [SFA] requires extensive field observations to enable more comprehensive research.

Figure 8 Main cluster formation mechanism of the MSA-MA-SFA-based system at 278.15 K: [MSA] = 10⁷ molec. cm⁻³, [MA] = 2.5×10⁸ molec. cm⁻³, and [SFA] = 10⁶ molec. cm⁻³. (a) The black arrows indicate the pure MSA-MA-based growth pathways. Blue arrows represent the pathways containing SFA. The influence of (b) temperature, (c) [SFA], and [MSA] on the relative contribution of the pure MSA-MA-based clustering pathway and the SFA participation pathway to the system flux is analyzed. Other results in panels (b) and (c) indicate that the pathway contribution of the cluster growing out of the studied system is less than 5 %.

3.4 Interfacial implications of products on aerosol particle growth

As the discussion above, the formation of SFA⁻ … H₃O⁺ and MSA⁻ … H₃O⁺ ion pairs can occur within a few picoseconds at the air–water interface. The atmospheric affinity of MSA⁻, SFA⁻, and H₃O⁺ for gaseous precursors was further probed by evaluating the free energies of interaction. It was worth noting that compounds such as MSA, MA, HNO₃ (NA), and (COOH)₂ (OA) were identified as candidate species for consideration (Wang et al., 2024; Kulmala et al., 2004). As presented in Table 2, the computed binding energies demonstrate that the interactions of SFA⁻ … MSA, SFA⁻ … NA, SFA⁻ … OA, H₃O⁺ … MA, MSA⁻ … MSA, MSA⁻ … OA, and MSA⁻ … NA were stronger than those of MSA … MA (one of the primary precursors for atmospheric aerosols), with their Gibbs free energies increased by 14.3–50.9 kcal mol⁻¹. The findings indicate that the presence of SFA⁻, MSA⁻, and H₃O⁺ at the interface facilitates the capture of potential gaseous species onto the surface of the water microdroplet.

Table 2 Gibbs free energy (ΔG) for the formation of SFA⁻ … MSA, SFA⁻ … NA, SFA⁻ … OA, H₃O⁺ … MA, MSA⁻ … MSA, MSA⁻ … OA, MSA⁻ … NA, and MSA … MA,(MSA)₁ ⋅ (MA)₁ ⋅ (X)₁ at 298 K.

^a The value was taken from Zhang et al. (2022a). ^b The value was taken from Zhong et al. (2019).

Furthermore, we investigated the possibility of SFA⁻ contributing to the enlargement of particles within the MSA-MA cluster, taking into account the geometric configuration and the free energy of formation for the (MSA)₁ ⋅ (MA)₁ ⋅ (SFA⁻)₁ clusters aggregating. Compared with other clusters, such as (MSA)₁ ⋅ (MA)₁ ⋅ (X)₁ (where X = HCOOH, CH₃COOH, CHOCOOH, OA, CH₃COCOOH, HOOCCH₂COOH, HOOC(CH)₂COOH, HOOC(CH₂)₂COOH, HOOC(CH₂)₃COOH, C₆H₅(COOH), and C₁₀H₁₆O₃) clusters (Zhang et al., 2022a), the quantity of hydrogen bonds within the (MSA)₁ ⋅ (MA)₁ ⋅ (SFA⁻)₁ cluster increased, and the loop of complex was expanded. It has been demonstrated that SFA⁻ has the greatest capacity to stabilize MSA-MA clusters and facilitate MSA-MA nucleation in these clusters. This was attributed to its acidic nature and structural characteristics, which include a greater number of intermolecular hydrogen bond binding sites. Therefore, relative to the (MSA)₁ ⋅ (MA)₁ ⋅ (X)₁ cluster (Table 2), the Gibbs formation free energy ΔG of the (MSA)₁ ⋅ (MA)₁ ⋅ (SFA⁻)₁ cluster was lower, indicating that the NH₂SO${}_{\mathrm{3}}^{-}$ ion exhibits a more potent nucleation capacity at the air–water interface compared to the X species in the gas phase. Consequently, our forecast was that the presence of NH₂SO${}_{\mathrm{3}}^{-}$ at the air–water interface would foster enhanced particle growth.

4 Summary and conclusions

In this study, quantum chemical calculations, BOMD simulations, and the ACDC kinetic model were utilized to characterize the gaseous and interfacial hydrolysis of HNSO₂ with MSA and to examine the influence exerted by SFA on MSA-MA-based clusters.

In the gaseous reaction, the activation energy for the hydrolysis of HNSO₂ catalyzed by MSA was only 0.8 kcal mol⁻¹, significantly lower by 7.7 kcal mol⁻¹ than the energy barrier of H₂O-assisted HNSO₂ hydrolysis. The effective rate coefficients reveal that the SFA formation from MSA-catalyzed hydrolysis of HNSO₂ can be competitive with that catalyzed by H₂O within an altitude of 5–15 km. Moreover, kinetic simulations utilizing the ACDC have disclosed that SFA has an unexpectedly positive impact on the NPF process, markedly enhancing the assembly of the MSA-MA-based cluster. Notably, the “participant” mechanism of SFA for cluster formation was identified by tracing the growth paths of the system in agriculture-developed and coastal industrial areas, especially significant in the Yangtze River Delta of China, in Bangladesh, and on the east coast of India.

At the air–water interface, the NH₂SO${}_{\mathrm{3}}^{-}$ and H₃O⁺ ion formation mechanism (∼40 %) and the proton exchange mechanism (∼60 %) were observed in the hydrolysis of HNSO₂ with MSA, which can take place in a few picoseconds. Notably, the SFA⁻, MSA⁻, and H₃O⁺ ions formed at the air–water interface possess the ability to attract potential precursor molecules like MSA, MA, and HNO₃. This attraction facilitates the transition of gaseous molecules onto the surface of the water microdroplet. Moreover, the assessment of the potential of X in the formation of the ternary MSA-MA-X cluster revealed that SFA⁻ exhibits the greatest propensity to stabilize MSA-MA clusters and to foster the nucleation of MSA-MA in the context of X.

Overall, this work not only elucidates a novel mechanism underlying the hydrolysis of HNSO₂ with MSA but also highlights the potential contribution of SFA on aerosol particle growth and new particle formation.