Skip to main content
NCBI home page
RSC Advances logoLink to RSC Advances
. 2026 Jul 28;16(39):43604–43612. doi: 10.1039/d6ra02637k

Gas phase hydrolysis of organic sulfuric anhydride: the possibility and atmospheric influence in initial new particle formation

Xintong Zhang a,b, Haijie Zhang b,✉, Jiaqi Wang b, Fang Bi b, Rui Gao b, Junling Li b, Yanqin Ren b, Hong Li b, Jinjuan Li a,✉
PMCID: PMC13411313  PMID: 42524530

Abstract

Cycloaddition of carboxylic acids (RCOOH) to SO3 readily contributes to the formation of carboxylic sulfuric anhydrides (CSA), which have relatively low vapor pressures that facilitate new particle formation (NPF). Current research is primarily based on the formation and nucleation mechanisms of CSA, with limited studies addressing their stabilities. Therefore, the current study was designed to investigate the stability and nucleation potential of CSA through quantum chemical calculation on gas-phase hydrolysis of the simplest CSA, formic sulfuric anhydride (FSA), with the catalytic effects of formic acid (HCOOH, FA) and sulfuric acid (H2SO4, SA). The application of FA or SA as a catalyst decreased the Gibbs free energy barriers from 29.4–38.5 kcal mol−1 to 26.5–26.9 kcal mol−1 and 25.7–26.6 kcal mol−1, respectively, promoting hydrolysis of FSA via a proton-transfer-mediated catalysis mechanism. Even so, the gas-phase hydrolysis of FSA is still not feasible due to extremely high reaction barriers, endowing it with superior stability with pronounced participation in the initial steps of NPF. Comparative analysis regarding the inter-molecular interactions and evaporation coefficient of small FSA- and SA-containing clusters demonstrated the strong hydrogen bonding of FSA with base molecules, along with a pronounced proton transfer process. The present study proved the kinetic stability of FSA toward gas-phase hydrolysis and suggested the potential role of FSA in participating in the initial NPF in areas with abundant base molecules, such as pastoral and industrial areas. Further research should focus on the stability of various kinds of CSA on the interface or particle phase and integrate the corresponding kinetic parameters into atmospheric nucleation models.

FSA generated through cycloaddition of carboxylic acids to SO3 is kinetic stable toward gas-phase hydrolysis under different catalysts effect, enabling it a potential participator in the initial NPF in the area with abundant base molecules.graphic file with name d6ra02637k-ga.webp

1. Introduction

Atmospheric aerosol has emerged as a core topic of research in environmental science due to its significant effects on the climate, the biosphere, and human health.1–5 Along with direct emission from natural and anthropogenic sources, the new particle formation (NPF) process, including the nucleation and growth stages, contributes over half of the global aerosol budget and has been frequently observed across various environments.5–10

Sulfur chemistry plays a critical role in the nucleation and growth steps of NPF, with varying sulfur forms across diverse environmental conditions. Sulfur dioxide (SO2), a prominent trace gas, can be effectively oxidized by hydroxyl radicals (OH˙) and stabilized Criegee intermediates (sCIs), resulting in the formation of SO3, considered an important oxide of sulfur and also a key intermediate for sulfuric acid (H2SO4, SA) formation.11–14 SA has been reported to serve as the primary nucleation precursor of NPF with enhanced nucleation efficiency in the presence of various stabilizing agents, such as ammonia (NH3) and amines.10,15–17 Besides H2O molecules, SO3 readily reacts with atmospheric inorganic molecules.18 Specifically, as key inorganic acids driving NPF, SA and iodic acid (HIO3, IA) can further react with SO3 to form disulfuric acid and iodic sulfuric anhydride, potentially contributing to NPF in highly polluted regions.18,19 Sulfamic acid (NH2SO3H, SFA), formed through the reaction of SO3 and NH3, has been reported to directly participate in SA-dimethylamine (SA-DMA) nucleation with significant enhancement.20,21 Moreover, the reaction of SO3 and NH3 has been reported to form sulfonylamine (HNSO2),22 which, upon hydrolysis, gives rise to SA and NH3, directly contributing to SA-NH3 nucleation.23 Meanwhile, the hydrolysis of HNSO2, catalyzed by neutral, basic, and acidic catalysts, could also generate SFA, showing significant participation in SA-DMA nucleation.22 Recently, the atmospheric cycloaddition of SO3 to hydrogen sulfide (H2S) has been reported to form thiosulfuric acid (H2S2O3, TSA), which may act as a nucleation participant under a relatively high concentration of bases.24

Methanesulfonic acid (MSA) and methanesulfinic acid (MSIA), important organosulfur products of dimethyl sulfide oxidation with high yields and low volatility in the marine atmosphere, have also been identified to promote NPF both individually and synergistically.11,25–28 Organosulfates (OSs), the dominant organosulfur compounds accounting for 5–30% of the organic mass fraction in atmospheric particles,29,30 have been identified as important participants of NPF.31 Recent work through microwave spectrometer and quantum chemical calculations has demonstrated the reaction potential of various carboxylic acids, such as formic acid (HCOOH, FA),32 pivalic acid,33 3-methyl-1,2,3-butanetricarboxylic acid,34 and thiobenzoic acid35 with SO3 to form carboxylic sulfuric anhydrides (CSA), having relatively low vapor pressures, and are capable of initiating NPF. The formation barriers reported for most studied CSAs are small, in some cases even essentially barrierless.32,36 For example, as the simplest CSA, formic sulfuric anhydride (FSA) is formed via the barrierless gas-phase cycloaddition of FA to SO3 and is anticipated to be a potential participant in NPF. Although the generated FSA may possess excess internal energy due to the exothermic formation process, this energy is expected to be rapidly dissipated through collisions with abundant atmospheric gases, leading to collisionally stabilized FSA. Meanwhile, the CSA were speculated to produce RCOOH and SA through gas-phase or liquid-phase hydrolysis, providing a potential pathway to incorporate volatile organic acids into atmospheric aerosols.32

However, the current studies primarily focus on the formation and nucleation mechanisms of CSA, studies on their gas phase stability remain limited.37–39 Considering the high abundance of gas-phase water molecules and the potential participation of FSA in NPF, a detailed investigation of the gas-phase fate of FSA is urgently required. Therefore, high-level theoretical calculations at the CCSD(T)-F12/cc-pVDZ-F12//M06-2X/6-311++G(3df,3pd) level, in combination with wavefunction analysis and Atmospheric Cluster Dynamics Code (ACDC) kinetics simulations, were performed to (i) identify the kinetic stability of FSA toward gas-phase hydrolysis, (ii) determine and compare the catalytic potential of organic acids FA and SA on FSA hydrolysis, and (iii) evaluate the potential role of FSA in the initial stage of atmospheric NPF.

2. Computational methods

2.1. Computational details

Geometry optimizations and vibrational frequency calculations were performed through Gaussian 09, employing density functional theory (DFT) at the M06-2X/6-311++G(3df,3pd) level of theory.40–43 Furthermore, optimization of the transition state (TS) structures was carried out using a single imaginary frequency criterion.44 Subsequent intrinsic reaction coordinate (IRC) calculations were conducted to ensure that each identified TS correctly connects the corresponding reactant (React) and product complexes (Prod) throughout the reaction pathway. The accuracy of the relative energies was enhanced through single-point energy calculations using the ORCA program45 at the CCSD(T)-F12/cc-pVDZ-F12 level of theory, which could effectively suppress the Basis Set Superposition Error (BSSE) and has been used as a high-level reference method for atmospheric clusters, OH-initiated atmospheric reactions, acid-catalyzed hydrolysis reactions, and atmospheric radical H-migration processes.46–53 Based on a benchmark study showing that CCSD(T)-F12 relative energies and reaction barriers generally approach chemical accuracy, and that M06-2X performs well for proton-transfer processes and noncovalent interactions, the uncertainty of the calculated barriers is conservatively estimated to be a few kcal mol−1, including contributions from the DFT geometry optimization and CCSD(T)-F12 zero-point corrections.46 The final corrected Gibbs free energy (GF12corr) was determined by combining the binding energy (EF12) obtained at the CCSD(T)-F12/cc-pVDZ-F12 level and Gibbs free-energy correction (GDFTcorrections) derived from the M06-2X/6-311++G(3df,3pd) level, as presented in eqn (1).

GF12corr = EF12 + GDFTcorrections 1

2.2. Wavefunction analysis

Topological characteristics on bond critical points (BCPs) were examined by virtue of electron density (ρ), a parameter strongly correlated with bond strength, aiming to investigate the intensity of intermolecular hydrogen bonding interactions and the newly formed covalent bond through proton transfer processes in molecular clusters.54 Simultaneously, a color-filled map of localized orbital locator (LOL) was generated and systematically analyzed to elucidate the spatial distribution of electron localization and the underlying molecular electronic structure, with the highest and lowest localization of electron density denoted by red and blue, respectively. Furthermore, hydrogen bond energies (EH) were calculated with eqn (2), which was proposed by Espinosa et al.:55

EH = V(rbcp)/2 2

where V(rbcp) denotes the potential energy density at the corresponding BCP.

For the clusters containing a proton transfer process, the Laplacian bond order (LBO) was determined for quantitative comparison of the strength of the newly formed covalent bond formed via proton transfer, as LBO shows a positive correlation with bond strength. Multiwfn software was used for all the topological analyses performed in this study.56,57

2.3. Kinetic simulation

The atmospheric clusters' stability was further compared through the monomers' evaporation coefficients from the corresponding clusters using ACDC simulations.58 Evaporation coefficients were calculated based on the Gibbs free energy of cluster formation, as expressed in eqn (3):

2.3. 3

where i and j represent the two fragments (monomer or cluster) of cluster (i + j), and γ(i+j)→i is the evaporation coefficient of i evaporating from cluster (i + j). βij is the collision coefficient between i and j. cei represents the equilibrium concentration of i, ΔGi denotes the Gibbs free energy of formation for i, and cref is the monomer concentration of the reference vapor, measured at standard atmospheric pressure (1 atm), T is the temperature, and kb is the Boltzmann constant. It should be noticed that evaporation coefficients are calculated from ΔG, and uncertainties in the calculated ΔG may influence evaporation coefficients nonlinearly through the exponential term in eqn (3).

2.4. Cluster structure sampling

The global minimum configuration of the binary clusters formed by FSA with common atmospheric nucleation precursors such as SA and DMA, was identified using the workflow depicted in Fig. 1, a methodology validated in our previous studies. Initially, 1000 low-energy structures were generated with ABCluster software,59 followed by subsequent optimization using semi-empirical method PM7 (ref. 60) coupled with the Mopac2016 program.61 Moreover, the top 100 structures with the lowest energies were subjected to further optimization at the M06-2X/6-31+G* level of theory, providing the 30 best structures, followed by subsequent optimization at the M06-2X/6-311++G(3df,3pd) level of theory, aiming to generate the global minimum configuration. Moreover, extensive manual sampling was performed for each cluster to account for the complexity of the potential energy surface.

Fig. 1. Flowchart for the global minimum sampling.

Fig. 1

Open in a new tab

3. Results and discussion

3.1. Kinetic stability of FSA toward gas-phase hydrolysis

To evaluate the kinetic stability of FSA (HCOSO4H) toward gas-phase hydrolysis, the potential energy surfaces of the FSA hydrolysis mechanism under uncatalysed, HCOOH and H2SO4 catalytic conditions were investigated and illustrated in reactions (1A)–(1C):

HCOSO4H + H2O → HCOOH + H2SO4 1A-1
HCOSO4H + H2O → HCOOH + SO3 + H2O 1A-2
HCOSO4H + HCOOH + H2O → 2HCOOH + H2SO4 1B
HCOSO4H + H2SO4 + H2O→ HCOOH + 2H2SO4 1C

where reactions (1A-1) and (1A-2) represent two parallel pathways under uncatalysed conditions, leading to the formation of different products. Reactions (1B) and (1C) represent the formic acid (HCOOH, FA) and sulfuric acid (H2SO4, SA) catalyzed reactions, respectively.

The Gibbs free energy, thermal correction of Gibbs free energy at the M06-2X/6-311++G(3df,3pd) level, single point energy at the CCSD(T)-F12/cc-pVDZ-F12 level, corrected Gibbs free energy, and imaginary frequency of TS are summarized in Tables S1–S3 of the SI, while the Cartesian coordinates of all examined stationary points are presented in Section II of SI.

3.1.1. Hydrolysis of FSA without catalyst

This section discusses the calculation and comparison of FSA hydrolysis without any catalyst (reaction (1A-1) and (1A-2)). Fig. 2 shows that the FSA + H2O reaction proceeds through a reactive complex (React) and passes the TS, resulting in the formation of a product complex (Prod) through different channels. It should be noted that the naming of intermediates follows the isomeric configuration of the final products along each reaction pathway. Specifically, for the “cis pathway,” the products are cis-SA and cis-FA, and thus the reactant complex, TS and product complex along this pathway are labeled as Reactcis, TScis, and Prodcis. As shown in Fig. 2(a) and reaction (1A-1) yielding SA and FA as products includes a pathway leading to the formation of cis-SA with a reaction barrier of 30.7 kcal mol−1. The Gibbs free energy of the resulting product monomers (cis-SA + cis-FA) is 2.4 kcal mol−1 lower than that of the reactant monomers (FSA + H2O). For the remaining two pathways leading to the formation of trans-SA, the reaction barriers are 29.4 and 32.2 kcal mol−1, respectively, while the corresponding product monomers are thermodynamically more stable, lying 7.5 kcal mol−1 below the reactant monomers (FSA + H2O). Therefore, reaction (1A-1) is not considered feasible in the gas phase due to the high reaction barriers. From a kinetic perspective, such a barrier would result in extremely small rate coefficients, indicating that the reaction would proceed too slowly to compete with other atmospheric loss or transformation processes of FSA under relevant atmospheric conditions.

Fig. 2. Gibbs free energy profile (kcal mol−1) for the uncatalyzed hydrolysis of FSA at the CCSD(T)-F12/cc-pVDZ-F12//M06-2X/6-311++G(3df,3pd) level. (a) Reaction (1A-1) with the product of SA and FA. (b) Reaction (1A-2) with the product of SO3, H2O, and FA. The white, gray, red, and yellow spheres represent H, C, O, and S atoms, respectively.

Fig. 2

Open in a new tab

For reaction (1A-2), two distinct pathways leading to the formation of cis-FA and trans-FA were identified and are presented in Fig. 2(b), demonstrating high reaction barriers of 38.5 and 33.8 kcal mol−1 compared to the reactant monomers (FSA + H2O). Meanwhile, the generated monomers SO3, H2O, and FA (cis- or trans-) lie 7.1 and 3.1 kcal mol−1 higher in Gibbs free energy than the reactant monomers (FSA + H2O), respectively, indicating that reaction (1A-2) in the gas-phase is both kinetically hindered and thermodynamically unfavorable at 298.15 K and 1 atm. In other words, uncatalyzed hydrolysis of FSA in the gas phase is kinetically hindered, due to the relatively high reaction barriers. Therefore, the catalytic potential of acid substance was further considered and calculated.

3.1.2. Hydrolysis of FSA with FA as the catalyst

The catalytic effect of organic acids was further examined to promote the hydrolysis of FSA because of their abundant atmospheric concentrations. FA is the most abundant species with a concentration up to 20 ppbv (ref. 32 and 62) and has been identified to be an effective catalyst in the hydrolysis of several species, including SO3, (ref. 63 and 64) glyoxal,65 formaldehyde,66 and ketene.67 Hence, FA is speculated to be a potential catalyst for FSA hydrolysis.

Fig. 3(a) and (b) illustrate the two distinct reaction channels corresponding to the formation of trans-FA and cis-FA, respectively. There are three different pre-reactive dimer complexes FA---H2O, FSA---H2O and FSA---FA in the presence of FA as a catalyst, with respective Gibbs free energy changes of 0.6, −1.5 and −3.7 kcal mol−1. The dimers subsequently form trimeric complexes, Reacttrans and Reactcis, through an endergonic process with the Gibbs free energy of 8.6 and 7.1 kcal mol−1 higher than that of the reactant monomers, respectively. It should be noticed that the pathways leading to Reacttrans and Reactcis are shown only to describe the possible formation and energies of the specific ternary reactant complex involved in the IRC confirmed reactions. They are not intended to enumerate all possible atmospheric collision pathways or all possible ternary cluster conformations. Reacttrans and Reactcis subsequently overcome a reaction energy barrier to form stable clusters trans-SA---(trans-FA)2 and trans-SA---trans-FA---cis-FA, with 13.3 and 2.6 kcal mol−1 lower than that of the reactant monomers. Through a proton-transfer-mediated catalysis from FA, the total reaction barriers reduced to 26.5 kcal mol−1 (with trans-SA and 2 × trans-FA as the final products) and 26.9 kcal mol−1 (with trans-SA, trans-FA and cis-FA as the final products), respectively, slightly lower than those of the uncatalyzed reaction (29.4–38.5 kcal mol−1). This modest barrier reduction is more plausibly associated with the larger O–H–O angles in the configurations of TStrans and TScis, promoting the proton-transfer process. Even so, FA still remains unable to significantly reduce the reaction barriers. Hence, more effective atmospheric catalysts are needed for further consideration.

Fig. 3. Gibbs free energy profile (kcal mol−1) for the hydrolysis of FSA with trans-FA as the catalyst (reaction (1B)) for the formation of (a) trans-SA and 2 × trans-FA and (b) trans-SA, trans-FA, and cis-FA at the CCSD(T)-F12/cc-pVDZ-F12//M06-2X/6-311++G(3df,3pd) level. The white, gray, red, and yellow spheres represent H, C, O, and S atoms, respectively.

Fig. 3

Open in a new tab

3.1.3. Hydrolysis of FSA with SA as the catalyst

SA, an atmospheric nucleation precursor, serves as an effective catalyst in various gas-phase reactions through significantly decreased activation energies.20,24,68 For instance, SA catalyzed its own formation through the hydrolysis of SO3.68 Specifically, the O–H bonds in SA are more labile and hence may support the proton transfer during the hydrolysis. Furthermore, as a capable hydrogen donor and acceptor,69 it was speculated that SA may act as a significantly more effective catalyst than FA in FSA hydrolysis. In this case, the incorporated SA molecule may follow two possible pathways: it can either catalyze the hydrolysis of FSA expressed by eqn (1C) or directly bond with FSA to form a SA---FSA molecular cluster.

Fig. 4 provides a comparison between the two channels mentioned above. The addition of SA to the reaction of FSA with H2O results in the formation of prereactive dimer complexes, including SA---H2O, FSA---H2O, and SA---FSA, with respective Gibbs free energy changes of −1.4, −1.5, and −3.9 kcal mol−1, identifying SA---FSA as a more thermodynamically favourable cluster. Further cluster growth leads to the formation of trimer complexes Reacttrans and Reactcis, with Gibbs free energies 5.3 and 6.1 kcal mol−1 higher than those of the reactant monomers, respectively, as shown in Fig. 4(a) and (b). Starting with the Reacttrans and Reactcis entry channels, the reactions proceed with the reaction barriers of 26.6 and 25.7 kcal mol−1 to form Prodtrans and Prodcis, respectively. The TS (TStrans and TScis) complexes comprising a SA molecule have an eight-membered ring steric configuration. Even SA shows a catalytic effect due to its proton-transfer-mediated catalysis, which is beneficial to the transfer of H from H2O to FSA, the reaction barriers still remain sufficiently high to prevent competitive hydrolysis in the gas-phase.

Fig. 4. Gibbs free energy profile (kcal mol−1) for the hydrolysis of FSA with catalyst SA (Reaction (1C)) for the formation of (a) 2 × trans-SA and trans-FA and (b) trans-SA, cis-SA, and cis-FA at the CCSD(T)-F12/cc-pVDZ-F12//M06-2X/6-311++G(3df,3pd) level. The white, gray, red, and yellow spheres represent H, C, O, and S atoms, respectively.

Fig. 4

Open in a new tab

As a competing pathway, SA serving as the direct nucleating agent with the unhydrolyzed FSA was found to be more feasible. Upon collision, FSA, H2O, and SA may form several trimer clusters (including SA---FSA---H2O) with different hydrogen-bonding patterns and spatial arrangements. The prereactive complexes Reacttrans and Reactcis leading to hydrolysis are reaction-oriented clusters, but not the most thermodynamically stable clusters. As shown in Fig. 4, cluster SA---FSA---H2O in the nucleation pathway has a comparatively lower Gibbs free energy of −5.6 kcal mol−1 than the reactant monomers, and at least 10.9 and 11.7 kcal mol−1 lower than Reacttrans (5.3 kcal mol−1) and Reactcis (6.1 kcal mol−1), respectively. Meanwhile, the global minimum clusters demonstrate the presence of three strong hydrogen bonds along with various intermolecular interaction bonding sites. In other words, although hydrolysis of FSA is possible from a specific reaction-oriented complex, it is kinetically hindered with relatively high reaction barriers, whereas the nucleation pathway is more favourable and could drive subsequent cluster growth, contributing to the NPF.

3.2. Potential role of FSA in the initial NPF

SA is the most prominent atmospheric nucleation agent, and base species like amine and NH3 stabilize the SA-containing clusters by reducing the volatility of SA. However, for most atmospheric conditions close to the earth's surface, the concentrations of SA (104–108 molecules cm−3) and NH3 (ranging from 107–1011 molecules cm−3) are insufficient to explain the substantial nucleation rate responsible for the particle production rates observed in the atmosphere. Atmospheric experiments provided evidence that organic acids (OA), particularly low-volatile (LVOCs) and extremely low-volatile organic compounds (ELVOCs), are considered to be involved in NPF.7,70,71

The kinetic stability of FSA toward gas-phase hydrolysis has been verified in Section 3.1, suggesting that even in the presence of a strong catalyst, the hydrolysis reaction of FSA is not feasible due to a sufficiently high reaction barrier. Given the thermodynamically favorable cluster formation pathway of FSA, other small atmospheric clusters were further optimized, analyzed, and compared. Fig. 5 presents the most stable configurations of clusters SA---FSA, SA---SA, SA---DMA, and FSA---DMA and their color-filled LOL map. Unlike the optimized configurations, which mainly provide structural evidence, LOL analysis was performed to reveal the electron localization characteristics and support the proton transfer process from a topological perspective.

Fig. 5. The most stable configurations calculated at the M06-2X/6-311++G(3df,3pd) level of theory, as well as their corresponding color-filled LOL map of clusters (a) SA---FSA, (b) SA---SA, (c) FSA---DMA, and (d) SA---DMA. Hydrogen bonds are shown as dashed lines (Å). The red, yellow, gray, and white spheres represent O, S, C, and H atoms, respectively. In the LOL map, the highest and lowest localization of electron density is denoted by red and blue, respectively.

Fig. 5

Open in a new tab

SA---FSA demonstrates a slightly lower Gibbs free energy of formation (ΔG) of −8.66 kcal mol−1, compared to −8.42 kcal mol−1 of SA---SA. Meanwhile, there are three hydrogen bonds in cluster SA---FSA with a hydrogen bond energy (EH) of 27.32, 12.57 and 8.12 kcal mol−1, larger than the two hydrogen bonds in cluster SA---SA with an EH of 16.83 kcal mol−1. According to kinetic simulations through the ACDC model, cluster SA---FSA has a slightly higher evaporation coefficient at 3.9 × 103 s−1, compared to SA---SA (2.9 × 103 s−1), with the same orders of magnitude. Therefore, cluster SA---FSA possesses comparable thermodynamic and kinetic stability with SA---SA.

As a common atmospheric nucleation precursor, dimethylamine (DMA) could promote SA-contained cluster formation by acid–base pairs. The intermolecular interactions could be improved by changing from hydrogen bond interactions to electrostatic interactions during the proton transfer from acid to base molecule. FSA---DMA is thermodynamically more stable, as evidenced by the significantly lower ΔG of −17.66 kcal mol−1, relative to −11.25 kcal mol−1 of SA---DMA. As shown in Fig. 5(c) and (d), the protons of both FSA and SA have completely transferred to the DMA molecule. The redder area between N and H1, as well as the green area between O1 and H1 in the LOL maps, provides further evidence of the proton transfer process in both clusters. Furthermore, the LBO of the newly formed covalent bond through proton transfer in cluster FSA---DMA is 0.60, which is larger than the 0.48 in SA---DMA, suggesting the stronger covalent bond strength and providing bonding strength evidence for its enhanced thermodynamic stability. Kinetic simulations further suggest a 4 orders of magnitude lower evaporation coefficient for cluster FSA-DMA (1.4 × 10−3 s−1) compared to SA-DMA (7.1 × 101 s−1), illustrating that cluster FSA---DMA is more kinetically stable than SA---DMA.

Overall, comparative analysis of small FSA- and SA-containing clusters indicates that FSA is more tightly bound to the base molecule via hydrogen bonding and proton transfer processes, and hence may participate in the initial NPF in areas with abundant base molecules, such as pastoral and industrial areas. This is in good agreement with the recent study by Wang et al.38

4. Conclusion

The cycloaddition reaction of SO3 to carboxylic acids is known to play a significant role in carboxylic sulfuric anhydride (CSA) formation, which could have extremely low vapor pressures to kick-start NPF. This study verified the stability of the simplest organic sulfuric anhydride—FSA and its nucleation potential using quantum calculations at the CCSD(T)-F12/cc-pVDZ-F12//M06-2X/6-311++G(3df,3pd) level of theory. The results demonstrate that the gas phase hydrolysis reaction of FSA is unlikely to take place with reaction barriers as high as 29.4 to 38.5 kcal mol−1. Although FA and SA could substantially lower the reaction barriers to 25.7–26.9 kcal mol−1 through proton-transfer-mediated catalysis, the resulting barriers are still too high for gas-phase hydrolysis of FSA to represent a kinetically favourable pathway under typical atmospheric conditions. According to the comparison of the inter-molecular interactions and evaporation coefficient for small FSA- and SA-containing clusters, FSA is found to bind tightly with base molecules via hydrogen bonds and newly formed covalent bonds through proton transfer processes, and hence may participate in the initial atmospheric NPF, particularly in pastoral and industrial areas characterized by high base emissions. The present study identified the kinetic stability of CSA in the gas phase and provided a scientific foundation for future investigations on CSA-driven nucleation mechanisms. It should be noted that the present study only evaluated the kinetic stability of FSA toward gas-phase hydrolysis, and further research should focus on additional atmospheric sinks (such as oxidation reactions and photochemical degradation) of various kinds of CSA species on the interface or particle phase and integrate corresponding kinetic parameters into atmospheric nucleation models.

Conflicts of interest

The authors declare that they have no conflicts of interest.

Supplementary Material

RA-016-D6RA02637K-s001

Acknowledgments

The authors thank the Jing-Jin-Ji Regional Integrated Environmental Improvement-National Science and Technology Major Project (No. 2026ZD1212900) and the National Natural Science Foundation of China (No. 22306179) for support of this research.

Data availability

The thermodynamics data and cartesian coordinates of all optimized structures in this article have been included in the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d6ra02637k.

References

  1. Williamson C. J. Kupc A. Axisa D. Bilsback K. R. Bui T. Campuzano-Jost P. Dollner M. Froyd K. D. Hodshire A. L. Jimenez J. L. Kodros J. K. Luo G. Murphy D. M. Nault B. A. Ray E. A. Weinzierl B. Wilson J. C. Yu F. Yu P. Pierce J. R. Brock C. A. Nature. 2019;574:399–403. doi: 10.1038/s41586-019-1638-9. [DOI] [PubMed] [Google Scholar]
  2. Kerminen V.-M. Lihavainen H. Komppula M. Viisanen Y. Kulmala M. Geophys. Res. Lett. 2005;32:L14803. doi: 10.1029/2005GL023130. [DOI] [Google Scholar]
  3. Haywood J. Boucher O. Rev. Geophys. 2000;38:513–543. doi: 10.1029/1999RG000078. [DOI] [Google Scholar]
  4. Zhang R. Khalizov A. Wang L. Hu M. Xu W. Chem. Rev. 2012;112:1957–2011. doi: 10.1021/cr2001756. [DOI] [PubMed] [Google Scholar]
  5. Kulmala M. Vehkamäki H. Petäjä T. Dal Maso M. Lauri A. Kerminen V. M. Birmili W. McMurry P. H. J. Aerosol Sci. 2004;35:143–176. doi: 10.1016/j.jaerosci.2003.10.003. [DOI] [Google Scholar]
  6. Kulmala M. Science. 2003;302:1000–1001. doi: 10.1126/science.1090848. [DOI] [PubMed] [Google Scholar]
  7. Zhang R. Suh I. Zhao J. Zhang D. Fortner E. C. Tie X. Molina L. T. Molina M. J. Science. 2004;304:1487–1490. doi: 10.1126/science.1095139. [DOI] [PubMed] [Google Scholar]
  8. Ma L. Zhang Y. Lin Z. Zhou Y. Yan C. Zhang Y. Zhou W. Ma W. Hua C. Li X. Deng C. Qi Y. Dada L. Li H. Bianchi F. Petäjä T. Kangasluoma J. Jiang J. Liu S. Hussein T. Kulmala M. Liu Y. Ecotoxicol. Environ. Saf. 2022;243:114023. doi: 10.1016/j.ecoenv.2022.114023. [DOI] [PubMed] [Google Scholar]
  9. Kulmala M. Kontkanen J. Junninen H. Lehtipalo K. Manninen H. E. Nieminen T. Petäjä T. Sipilä M. Schobesberger S. Rantala P. Franchin A. Jokinen T. Järvinen E. Äijälä M. Kangasluoma J. Hakala J. Aalto P. P. Paasonen P. Mikkilä J. Vanhanen J. Aalto J. Hakola H. Makkonen U. Ruuskanen T. Mauldin R. L. Duplissy J. Vehkamäki H. Bäck J. Kortelainen A. Riipinen I. Kurtén T. Johnston M. V. Smith J. N. Ehn M. Mentel T. F. Lehtinen K. E. J. Laaksonen A. Kerminen V.-M. Worsnop D. R. Science. 2013;339:943–946. doi: 10.1126/science.1227385. [DOI] [PubMed] [Google Scholar]
  10. Yao L. Garmash O. Bianchi F. Zheng J. Yan C. Kontkanen J. Junninen H. Mazon S. B. Ehn M. Paasonen P. Sipilä M. Wang M. Wang X. Xiao S. Chen H. Lu Y. Zhang B. Wang D. Fu Q. Geng F. Li L. Wang H. Qiao L. Yang X. Chen J. Kerminen V.-M. Petäjä T. Worsnop D. R. Kulmala M. Wang L. Science. 2018;361:278–281. doi: 10.1126/science.aao4839. [DOI] [PubMed] [Google Scholar]
  11. Shen J. Scholz W. He X.-C. Zhou P. Marie G. Wang M. Marten R. Surdu M. Rörup B. Baalbaki R. Amorim A. Ataei F. Bell D. M. Bertozzi B. Brasseur Z. Caudillo L. Chen D. Chu B. Dada L. Duplissy J. Finkenzeller H. Granzin M. Guida R. Heinritzi M. Hofbauer V. Iyer S. Kemppainen D. Kong W. Krechmer J. E. Kürten A. Lamkaddam H. Lee C. P. Lopez B. Mahfouz N. G. A. Manninen H. E. Massabò D. Mauldin R. L. Mentler B. Müller T. Pfeifer J. Philippov M. Piedehierro A. A. Roldin P. Schobesberger S. Simon M. Stolzenburg D. Tham Y. J. Tomé A. Umo N. S. Wang D. Wang Y. Weber S. K. Welti A. Wollesen de Jonge R. Wu Y. Zauner-Wieczorek M. Zust F. Baltensperger U. Curtius J. Flagan R. C. Hansel A. Möhler O. Petäjä T. Volkamer R. Kulmala M. Lehtipalo K. Rissanen M. Kirkby J. El-Haddad I. Bianchi F. Sipilä M. Donahue N. M. Worsnop D. R. J. Environ. Sci. Technol. 2022;56:13931–13944. doi: 10.1021/acs.est.2c05154. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Zhang R. Science. 2010;328:1366–1367. doi: 10.1126/science.1189732. [DOI] [PubMed] [Google Scholar]
  13. Berresheim H. Elste T. Tremmel H. G. Allen A. G. Hansson H. C. Rosman K. Dal Maso M. Mäkelä J. M. Kulmala M. O'Dowd C. D. J. Geophys. Res. 2002;107:5–12. doi: 10.1029/2000JD000229. [DOI] [Google Scholar]
  14. Berndt T. Stratmann F. Sipilä M. Vanhanen J. Petäjä T. Mikkilä J. Grüner A. Spindler G. Lee Mauldin Iii R. Curtius J. Kulmala M. Heintzenberg J. Atmos. Chem. Phys. 2010;10:7101–7116. doi: 10.5194/acp-10-7101-2010. [DOI] [Google Scholar]
  15. Temelso B. Morrison E. F. Speer D. L. Cao B. C. Appiah-Padi N. Kim G. Shields G. C. J. Phys. Chem. 2018;122:1612–1622. doi: 10.1021/acs.jpca.7b11236. [DOI] [PubMed] [Google Scholar]
  16. Cai R. Yan C. Yang D. Yin R. Lu Y. Deng C. Fu Y. Ruan J. Li X. Kontkanen J. Zhang Q. Kangasluoma J. Ma Y. Hao J. Worsnop D. R. Bianchi F. Paasonen P. Kerminen V. M. Liu Y. Wang L. Zheng J. Kulmala M. Jiang J. Atmos. Chem. Phys. 2021;21:2457–2468. doi: 10.5194/acp-21-2457-2021. [DOI] [Google Scholar]
  17. Kirkby J. Curtius J. Almeida J. Dunne E. Duplissy J. Ehrhart S. Franchin A. Gagné S. Ickes L. Kürten A. Kupc A. Metzger A. Riccobono F. Rondo L. Schobesberger S. Tsagkogeorgas G. Wimmer D. Amorim A. Bianchi F. Breitenlechner M. David A. Dommen J. Downard A. Ehn M. Flagan R. C. Haider S. Hansel A. Hauser D. Jud W. Junninen H. Kreissl F. Kvashin A. Laaksonen A. Lehtipalo K. Lima J. Lovejoy E. R. Makhmutov V. Mathot S. Mikkilä J. Minginette P. Mogo S. Nieminen T. Onnela A. Pereira P. Petäjä T. Schnitzhofer R. Seinfeld J. H. Sipilä M. Stozhkov Y. Stratmann F. Tomé A. Vanhanen J. Viisanen Y. Vrtala A. Wagner P. E. Walther H. Weingartner E. Wex H. Winkler P. M. Carslaw K. S. Worsnop D. R. Baltensperger U. Kulmala M. Nature. 2011;476:429–433. doi: 10.1038/nature10343. [DOI] [PubMed] [Google Scholar]
  18. Kumar A. Iyer S. Barua S. Brean J. Besic E. Seal P. Dall'Osto M. Beddows D. C. S. Sarnela N. Jokinen T. Sipilä M. Harrison R. M. Rissanen M. J. Am. Chem. Soc. 2024;146:15562–15575. doi: 10.1021/jacs.4c04531. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Wang R. Cheng Y. Chen S. Li R. Hu Y. Guo X. Zhang T. Song F. Li H. Atmos. Chem. Phys. 2024;24:4029–4046. doi: 10.5194/acp-24-4029-2024. [DOI] [Google Scholar]
  20. Li H. Zhong J. Vehkamäki H. Kurtén T. Wang W. Ge M. Zhang S. Li Z. Zhang X. Francisco J. S. Zeng X. C. J. Am. Chem. Soc. 2018;140:11020–11028. doi: 10.1021/jacs.8b04928. [DOI] [PubMed] [Google Scholar]
  21. Zhang Y. Wang Z. Wang H. Cheng Y. Zhang T. Ou T. Wang R. J. Phys. Chem. 2023;127:8935–8942. doi: 10.1021/acs.jpca.3c04982. [DOI] [PubMed] [Google Scholar]
  22. Zhang T. Zhang Y. Tian S. Zhou M. Liu D. Lin L. Zhang Q. Wang R. Muthiah B. Phys. Chem. Chem. Phys. 2022;24:4966–4977. doi: 10.1039/D1CP04437K. [DOI] [PubMed] [Google Scholar]
  23. Manonmani G. Sandhiya L. Senthilkumar K. Int. J. Quantum Chem. 2020;120:e26182. doi: 10.1002/qua.26182. [DOI] [Google Scholar]
  24. Zhang H. Wang W. Fan L. Li J. Ren Y. Li H. Gao R. Xu Y. J. Environ. Sci. Eng. 2025;148:489–501. doi: 10.1016/j.jes.2023.09.010. [DOI] [PubMed] [Google Scholar]
  25. Ning A. Zhang X. Atmos. Environ. 2022;269:118826. doi: 10.1016/j.atmosenv.2021.118826. [DOI] [Google Scholar]
  26. Chen Q. Sherwen T. Evans M. Alexander B. Atmos. Chem. Phys. 2018;18:13617–13637. doi: 10.5194/acp-18-13617-2018. [DOI] [Google Scholar]
  27. Shen J. Xie H.-B. Elm J. Ma F. Chen J. Vehkamäki H. J. Environ. Sci. Technol. 2019;53:14387–14397. doi: 10.1021/acs.est.9b05306. [DOI] [PubMed] [Google Scholar]
  28. Ning A. Zhang H. Zhang X. Li Z. Zhang Y. Xu Y. Ge M. Atmos. Environ. 2020;227:117378. doi: 10.1016/j.atmosenv.2020.117378. [DOI] [Google Scholar]
  29. Zhang X. Lian Y. Tan S. Yin S. Atmos. Chem. Phys. 2024;24:3593–3612. doi: 10.5194/acp-24-3593-2024. [DOI] [Google Scholar]
  30. Tan S. Zhang X. Lian Y. Chen X. Yin S. Du L. Ge M. J. Am. Chem. Soc. 2022;144:16953–16964. doi: 10.1021/jacs.2c05807. [DOI] [PubMed] [Google Scholar]
  31. Katz D. J. Abdelhamid A. Stark H. Canagaratna M. R. Worsnop D. R. Browne E. C. Atmos. Chem. Phys. 2023;23:5567–5585. doi: 10.5194/acp-23-5567-2023. [DOI] [Google Scholar]
  32. Mackenzie R. B. Dewberry C. T. Leopold K. R. Science. 2015;349:58–61. doi: 10.1126/science.aaa9704. [DOI] [PubMed] [Google Scholar]
  33. Love N. Carpenter C. A. Huff A. K. Douglas C. J. Leopold K. R. J. Phys. Chem. 2022;126:6194–6202. doi: 10.1021/acs.jpca.2c04904. [DOI] [PubMed] [Google Scholar]
  34. Zhang H. Wang W. Pi S. Liu L. Li H. Chen Y. Zhang Y. Zhang X. Li Z. Chemosphere. 2018;212:504–512. doi: 10.1016/j.chemosphere.2018.08.074. [DOI] [PubMed] [Google Scholar]
  35. Reynolds A. J. Koziol K. J. Leopold K. R. ChemPhysChem. 2025;26:e202400844. doi: 10.1002/cphc.202400844. [DOI] [PubMed] [Google Scholar]
  36. Huff A. K. Mackenzie R. B. Smith C. J. Leopold K. R. J. Phys. Chem. 2019;123:2237–2243. doi: 10.1021/acs.jpca.9b00300. [DOI] [PubMed] [Google Scholar]
  37. Song X.-M. Li X.-X. Zhou X. Ni S. Bai F.-Y. Zhang K. Zhao Z. J. Environ. Sci. Eng. 2026;161:772–783. doi: 10.1016/j.jes.2025.08.006. [DOI] [PubMed] [Google Scholar]
  38. Wang R. Li R. Chen S. Mu R. Zhang C. Ma X. Khan M. Zhang T. Atmos. Chem. Phys. 2025;25:5695–5709. doi: 10.5194/acp-25-5695-2025. [DOI] [Google Scholar]
  39. Zhang H. Gao R. Li H. Li Y. Xu Y. Chai F. J. Environ. Sci. Eng. 2023;123:54–64. doi: 10.1016/j.jes.2022.01.015. [DOI] [PubMed] [Google Scholar]
  40. Frisch M. J., Trucks G. W., Schlegel H. B., Scuseria G. E., Robb M. A., Cheeseman J. R., Scalmani G., Barone V., Mennucci B. and Petersson G. A., Gaussian 09, Revision A. 01, Gaussian Inc., Wallingford CT, 2009 [Google Scholar]
  41. Zhao Y. Truhlar D. G. Theor. Chem. Acc. 2008;120:215–241. [Google Scholar]
  42. Jorge Kohanoff N. I. G., Density Functional Theory: Basics, New Trends and Applications, Wiley-Blackwell, 2003 [Google Scholar]
  43. Mardirossian N. Head-Gordon M. J. Chem. Theory Comput. 2016;12:4303–4325. doi: 10.1021/acs.jctc.6b00637. [DOI] [PubMed] [Google Scholar]
  44. Møller K. H. Otkjær R. V. Hyttinen N. Kurtén T. Kjaergaard H. G. J. Phys. Chem. 2016;120:10072–10087. doi: 10.1021/acs.jpca.6b09370. [DOI] [PubMed] [Google Scholar]
  45. Neese F. WIREs Comput. Mol. Sci. 2012;2:73–78. doi: 10.1002/wcms.81. [DOI] [Google Scholar]
  46. Knizia G. Adler T. B. Werner H.-J. J. Chem. Phys. 2009;130:054104. doi: 10.1063/1.3054300. [DOI] [PubMed] [Google Scholar]
  47. Zhang H. Chen S. Zhong J. Zhang S. Zhang Y. Zhang X. Li Z. Zeng X. C. Atmos. Environ. 2018;177:93–99. doi: 10.1016/j.atmosenv.2018.01.017. [DOI] [Google Scholar]
  48. Yousaf K. E. Peterson K. A. J. Chem. Phys. 2008;129:184108. doi: 10.1063/1.3009271. [DOI] [PubMed] [Google Scholar]
  49. Zhang J. Valeev E. J. Chem. Theory Comput. 2012;8:3175–3186. doi: 10.1021/ct3005547. [DOI] [PubMed] [Google Scholar]
  50. Szűcs T. Czakó G. Phys. Chem. Chem. Phys. 2021;23:10347–10356. doi: 10.1039/D0CP06392D. [DOI] [PubMed] [Google Scholar]
  51. Zhang T. Wen M. Zeng Z. Lu Y. Wang Y. Wang W. Shao X. Wang Z. Makroni L. RSC Adv. 2020;10:9093–9102. doi: 10.1039/D0RA00024H. [DOI] [PMC free article] [PubMed] [Google Scholar]
  52. Yang X. Wang H. Lu K. Ma X. Tan Z. Long B. Chen X. Li C. Zhai T. Li Y. Qu K. Xia Y. Zhang Y. Li X. Chen S. Dong H. Zeng L. Zhang Y. Nat. Commun. 2024;15:1648. doi: 10.1038/s41467-024-45885-w. [DOI] [PMC free article] [PubMed] [Google Scholar]
  53. Zhang Y. Huang L. Ye T. Ding C. Xu Y. Dang L. Zhang T. Xu H. Zhou K. ACS Earth Space Chem. 2022;6:2779–2789. doi: 10.1021/acsearthspacechem.2c00088. [DOI] [Google Scholar]
  54. Lu T. Chen F. J. Phys. Chem. 2013;117:3100–3108. doi: 10.1021/jp4010345. [DOI] [PubMed] [Google Scholar]
  55. Espinosa E. Molins E. Lecomte C. Chem. Phys. Lett. 1998;285:170–173. doi: 10.1016/S0009-2614(98)00036-0. [DOI] [Google Scholar]
  56. Lu T. Chen F. J. Comput. Chem. 2012;33:580–592. doi: 10.1002/jcc.22885. [DOI] [PubMed] [Google Scholar]
  57. Lu T. J. Chem. Phys. 2024;161:082503. doi: 10.1063/5.0216272. [DOI] [PubMed] [Google Scholar]
  58. McGrath M. J. Olenius T. Ortega I. K. Loukonen V. Paasonen P. Kurtén T. Kulmala M. Vehkamäki H. Atmos. Chem. Phys. 2012;12:2345–2355. doi: 10.5194/acp-12-2345-2012. [DOI] [Google Scholar]
  59. Zhang J. Dolg M. Phys. Chem. Chem. Phys. 2015;17:24173–24181. doi: 10.1039/C5CP04060D. [DOI] [PubMed] [Google Scholar]
  60. Martin B. P. Brandon C. J. Stewart J. J. P. Braun-Sand S. B. Proteins: Struct., Funct., Bioinf. 2015;83:1427–1435. doi: 10.1002/prot.24826. [DOI] [PMC free article] [PubMed] [Google Scholar]
  61. Stewart J. J. P. J. Comput.-Aided Mol. Des. 1990;4:1–103. doi: 10.1007/BF00128336. [DOI] [PubMed] [Google Scholar]
  62. Valentini F. Kozell V. Petrucci C. Marrocchi A. Gu Y. Gelman D. Vaccaro L. Energy Environ. Sci. 2019;12:2646–2664. doi: 10.1039/C9EE01747J. [DOI] [Google Scholar]
  63. Hazra M. K. Sinha A. J. Am. Chem. Soc. 2011;133:17444–17453. doi: 10.1021/ja207393v. [DOI] [PubMed] [Google Scholar]
  64. Long B. Long Z.-W. Wang Y.-B. Tan X.-F. Han Y.-H. Long C.-Y. Qin S.-J. Zhang W.-J. ChemPhysChem. 2012;13:323–329. doi: 10.1002/cphc.201100558. [DOI] [PubMed] [Google Scholar]
  65. Hazra M. K. Francisco J. S. Sinha A. J. Phys. Chem. 2014;118:4095–4105. doi: 10.1021/jp502126m. [DOI] [PubMed] [Google Scholar]
  66. Hazra M. K. Francisco J. S. Sinha A. J. Phys. Chem. 2013;117:11704–11710. doi: 10.1021/jp4008043. [DOI] [PubMed] [Google Scholar]
  67. Louie M. K. Francisco J. S. Verdicchio M. Klippenstein S. J. Sinha A. J. Phys. Chem. 2015;119:4347–4357. doi: 10.1021/jp5076725. [DOI] [PubMed] [Google Scholar]
  68. Torrent-Sucarrat M. Francisco J. S. Anglada J. M. J. Am. Chem. Soc. 2012;134:20632–20644. doi: 10.1021/ja307523b. [DOI] [PubMed] [Google Scholar]
  69. Rozenberg M. S. Loewenschuss A. Nielsen C. J. J. Phys. Chem. 2016;120:3450–3455. doi: 10.1021/acs.jpca.6b00635. [DOI] [PubMed] [Google Scholar]
  70. Jokinen T. Berndt T. Makkonen R. Kerminen V.-M. Junninen H. Paasonen P. Stratmann F. Herrmann H. Guenther A. B. Worsnop D. R. Kulmala M. Ehn M. K. Sipila M. Proc. Natl. Acad. Sci. U. S. A. 2015;112:7123–7128. doi: 10.1073/pnas.1423977112. [DOI] [PMC free article] [PubMed] [Google Scholar]
  71. Tröstl J. Chuang W. K. Gordon H. Heinritzi M. Yan C. Molteni U. Ahlm L. Frege C. Bianchi F. Wagner R. Simon M. Lehtipalo K. Williamson C. Craven J. S. Duplissy J. Adamov A. Almeida J. Bernhammer A.-K. Breitenlechner M. Brilke S. Dias A. Ehrhart S. Flagan R. C. Franchin A. Fuchs C. Guida R. Gysel M. Hansel A. Hoyle C. R. Jokinen T. Junninen H. Kangasluoma J. Keskinen H. Kim J. Krapf M. Kürten A. Laaksonen A. Lawler M. Leiminger M. Mathot S. Möhler O. Nieminen T. Onnela A. Petäjä T. Piel F. M. Miettinen P. Rissanen M. P. Rondo L. Sarnela N. Schobesberger S. Sengupta K. Sipilä M. Smith J. N. Steiner G. Tomè A. Virtanen A. Wagner A. C. Weingartner E. Wimmer D. Winkler P. M. Ye P. Carslaw K. S. Curtius J. Dommen J. Kirkby J. Kulmala M. Riipinen I. Worsnop D. R. Donahue N. M. Baltensperger U. Nature. 2016;533:527–531. doi: 10.1038/nature18271. [DOI] [PMC free article] [PubMed] [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

RA-016-D6RA02637K-s001
RA-016-D6RA02637K-s001.pdf (167KB, pdf)

Data Availability Statement

The thermodynamics data and cartesian coordinates of all optimized structures in this article have been included in the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d6ra02637k.

Articles from RSC Advances are provided here courtesy of Royal Society of Chemistry

RESOURCES