The vital role of sulfuric acid in iodine oxoacids nucleation: impacts of urban pollutants on marine atmosphere

The nucleation of iodic acid (HIO3) and iodous acid (HIO2) play a significant role in marine new particle formation (NPF) events. However, the inability to explain intensive NPF bursts in polluted coasts indicates the participation of potential precursors. Herein, we identified a novel nucleation mechanism of HIO3–HIO2 system enhanced by the urban pollutant sulfuric acid (H2SO4). We found that H2SO4 could largely enhance the cluster formation rates (J, cm−3 s−1) of HIO3–HIO2 system, especially in high [H2SO4] regions near H2SO4 emission sources. The enhanced J of HIO3–HIO2–H2SO4 system performs better match than that of HIO3–HIO2 system with the observational rates of polluted coasts and polar regions, such as Zhejiang and Marambio. Moreover, the H2SO4-involved cluster formation is realized without Gibbs free energy barrier and dominate broadly in marine regions with rich H2SO4 and scarce iodine concentrations. These findings may help to explain some missing fluxes of marine new particles and emphasize the impact of urban components on marine nucleation processes.


Introduction
Atmospheric particulate pollution is a serious environmental threat worldwide, exerting farreaching influences on climate and human health (Collaborators 2019, Gokul et al 2023).These particulate matters not only directly cause urban air pollution, but also affect the marine atmosphere through long-range transportation (Zhu et al 2019, Liu et al 2022b).Although effective strategies have been taken to reduce the air pollution in recent years, the coastal areas, where there are the most industrialized and densely populated, are still suffering from atmospheric particulate pollution (Liu et al 2019, Du et al 2021).Due to the influences from both marine biological and urban anthropogenic sources (Du et al 2021, Liu et al 2022a), the evolution process of atmospheric particulate matter is quite complex and ambiguous in coastal areas.Hence, revealing the formation mechanism of atmospheric particulate matter in polluted coastal regions is one of the most important issues facing atmospheric environmental protection.
New particle formation (NPF), encompassing nucleation and subsequent growth (Zhang 2010), has been considered essential to the formation of atmospheric particulate matter through gas-to-particle conversion processes (Ning et al 2022).Initial nucleation is identified as the decisive process of marine NPF events (Hoffmann et al 2001, O'Dowd et al 2002, Ehn et al 2010, McFiggans et al 2010), which is closely related to the iodine species originated from the biological emissions of macroalgae (O'Dowd et al 2002, Zhang et al 2012).Among the iodine species, the critical role of iodic acid (HIO 3 ) in marine nucleation has been consistently highlighted (Sipila et al 2016, Yu et al 2019, Baccarini et al 2020, Rong et al 2020).Field observations on the west coast of Ireland showed that the rapid nucleation process was predominantly driven by HIO 3 with high concentration (Sipila et al 2016).The Cosmics Leaving OUtdoor Droplets chamber experiments in European Organization for Nuclear Research found that the homologous iodous acid (HIO 2 ) played an important role in stabilizing the neutral HIO 3 clusters (He et al 2021).Subsequent theoretical studies revealed the base-like behavior of HIO 2 in HIO 3 -HIO 2 binary nucleation (Zhang et al 2022, Liu et al 2023).Hence, HIO 3 -HIO 2 nucleation may play a crucial role in the primitive marine atmosphere.However, with the impact of urban pollution, NPF events have occurred frequently in coastal areas.The HIO 3 -HIO 2 binary nucleation can poorly explain the intensive NPF bursts in heavily polluted coasts (Ma et al 2023).This emphasizes the involvement of air pollutants in marine nucleation process.
The sulfuric acid (H 2 SO 4 ) has been detected in both gas and particulate phases in polluted coastal areas of China (Yu et al 2019, Zhu et al 2019).Notably, compared with the clean marine atmosphere, the concentration of H 2 SO 4 in polluted coastal areas is two orders of magnitude higher (up to 10 8 molecules cm −3 ) due to the air pollution from cities (Zhu et al 2019).Considering its strong nucleating ability (Faloona 2009, Sipila et al 2010), H 2 SO 4 molecules are likely to nucleate together with iodine oxoacids in marine regions (He et al 2023).However, neither the corresponding nucleation mechanism nor the potential environmental significance of HIO 3 -HIO 2 system enhanced by H 2 SO 4 is investigated.Hence, we aim to reveal the marine nucleation mechanism involving urban pollutants and assess the influence of pollutants on the marine atmosphere via studying HIO 3 -HIO 2 nucleation with the participation of H 2 SO 4 .

Quantum chemical calculations
The HIO 3 -HIO 2 -H 2 SO 4 system is composed of ternary clusters (HIO 3 -HIO 2 -H 2 SO 4 ), binary clusters (HIO 3 -HIO 2 , HIO 3 -H 2 SO 4 , HIO 2 -H 2 SO 4 ) and the unary clusters (HIO 3 , HIO 2 , and H 2 SO 4 ) clusters.The most stable configuration of HIO 3 -HIO 2 -H 2 SO 4 ternary clusters was proposed for the first time in this research.Additionally, the structures of binary clusters and unary clusters presented in this work were adopted from the stable configurations with the lowest Gibbs free energy of formation in previous studies at the same level of theory (Rong et al 2020, Zhang et al 2022, Liu et al 2023).A multistep method that can systematically screen the most stable structures of clusters was adopted in this study (Supplementary data).All structure optimizations and frequency calculations were carried out using Gaussian 09 package (Frisch et al 2009), and the Cartesian coordinates of these clusters with the lowest energies were collected in table S1.For each cluster with the lowest energy, the single-point correction was carried out at the RI-CC2/aug-cc-pVTZ (for O, H atoms) + aug-cc-pV(T + d)Z (for S atom) + augcc-pVTZ-PP with ECP28MDF (for I atom) level of theory using the Turbomole program (Ahlrichs et al 1989), since there is a good agreement between the simulated results (e.g. the cluster formation rates) at this theoretical level with the experimental or field measurements through a random cancellation of errors (Almeida et al 2013, Kurten et al 2018, Lu et al 2020).
The Gibbs free energy (G, kcal mol −1 ) of each molecule or cluster presented in this work was calculated as: thermal where E RI−CC2 is the electronic contribution calculated at RI-CC2/aug-cc-pVTZ (for O, H atoms) + aug-cc-pV(T + d)Z (for S atom) + augcc-pVTZ-PP with ECP28MDF (for I atom) level of theory, and G ωB97X−D thermal is the thermal contribution obtained at ωB97X−D/6−311++G(3df,3pd) (for O, H, and S atoms) + aug-cc-pVTZ-PP with ECP28MDF (for I atom) level of theory.
Considering the influence of actual precursor concentrations, the actual Gibbs free energy of formation (∆G actual , kcal mol −1 ) of clusters can be calculated as follows: where ∆G is the actual Gibbs free energy of formation of clusters at corresponding precursor concentrations, ∆G ref is the Gibbs free energy of formation at the reference pressure P ref (1 atm), n is the number of components within the cluster, k B denotes the Boltzmann constant, T signifies the temperature, N i refers to the number of molecules of type i in the number of components in the cluster and P i is the partial pressure of component i in the vapor phase.

Electrostatic potential analysis
The clusters are mainly stabilized by intermolecular interactions among the molecules, such as hydrogen bonds (HBs) or halogen bonds (XBs where c i is the concentration of cluster i, β i,j is the collision coefficient between cluster i and cluster j, γ (i +j)→i is the evaporation coefficient of the cluster (i + j) evaporating into cluster i and cluster j, Q i is the external source term of cluster i, and S i is the potential sink term for cluster i.Details for calculating β i,j and γ (i +j)→i are presented in Supplementary data.
The detailed collision and total evaporation frequencies of the HIO 3 -HIO 2 -H 2 SO 4 system at all simulated temperatures and condensation sinks are listed in table S3.The boundary conditions of the ACDC simulations are closely related to the ratio of the collision frequency between the clusters and monomer molecule at concentration c to the total evaporation frequency of clusters (details in Supplementary data).

Cluster configuration analysis
The formation of stable ternary clusters is crucial for the synergistic nucleation involving H 2 SO 4 .To assess the interacting potential of HIO 3 , HIO 2 , and H 2 SO 4 , the ESP distribution on the molecular vdW surfaces of three monomer molecules was determined.The electron-deficient regions with red color tend to attract the electron-rich regions with blue color.As shown in figure S1, the hydrogen atoms of HIO 3 , HIO 2 , and H 2 SO 4 possess relatively positive ESP values, which can act as the donors of HBs.The iodine atoms of HIO 3 and HIO 2 have positive ESP sites, which can act as the donors of XBs.The terminal oxygen atoms of HIO 3 , HIO 2 , and H 2 SO 4 has strong electron-rich property with quite negative ESP value, which can act as HB or XB acceptors.These donor and acceptor sites bind to each other, laying the foundation for the formation of molecular clusters.Moreover, the difference in ESP values among the three precursors indicates that H 2 SO 4 molecules may provide protons to HIO 3 and HIO 2 .The potential proton transfer process can be crucail for the strong connection of H 2 SO 4 and iodine oxoacids.
The ESP analysis indicates the presence of ternary nucleation tendencies, thus we obtained the most stable configurations (figure 1 and Cartesian coordinates in Supplementary data table S1) of ( HIO 3 ) x •(HIO 2 ) y •(H 2 SO 4 ) z (x + y + z ⩽ 5; x, y, z ⩾ 1) clusters.As shown in figure 1, the actual binding sites within the ternary clusters are consistent with the results predicted by the ESP analysis.H 2 SO 4 can form cage-like clusters with HIO 3 and HIO 2 through the space network of HBs and XBs.Moreover, the ternary clusters are generated through the proton transfer between H 2 SO 4 and HIO 3 /HIO 2 (indicated by red dashed boxes in figure 1).In these clusters, the H 2 SO 4 molecules provide protons to HIO 3 or HIO 2 , forming ion pairs to stabilize the ternary clusters, during which the HIO 3 molecules perform basic behavior for the first time.Hence, H 2 SO 4 molecules trigger the acidbase reactions through their stronger acidity, which may become the key point to enhance HIO 3 -HIO 2 nucleation.Additionally, there are some unoccupied binding sites outside the cage-like clusters, providing possibility of further growth via the combination with monomers or small clusters.

Cluster stability analysis
To further explore the potential role of pollutant H 2 SO 4 in HIO 3 -HIO 2 nucleation, a stability analysis of (HIO 3 ) x •(HIO 2 ) y •(H 2 SO 4 ) z (x + y + z ⩽ 5; x, y, z ⩾ 1) clusters was conducted.The stability of clusters mainly encompasses two aspects: thermodynamic stability and kinetic stability.The Gibbs free energy of formation (∆G, kcal mol −1 ) of (HIO 3 ) x •(HIO 2 ) y •(H 2 SO 4 ) z (x + y + z ⩽ 5; x, y, z ⩾ 1) clusters under standard marine atmospheric conditions (T = 258.15,278.15, 298.15 K, and p = 1 atm) were calculated (table S2) to assess the thermodynamic stability.As can be seen from table S2, all ternary clusters containing air pollutant H 2 SO 4 possess negative ∆G values, and the ∆G further decreases with the increase of the total number of molecules in ternary clusters.Hence, H 2 SO 4 molecules can jointly nucleate with HIO 3 and HIO 2 in a thermodynamically spontaneous way.Moreover, the ∆G also decreases with the decrease of T, indicating the higher thermodynamic stability of ternary clusters at lower T corresponding to relatively highlatitude marine areas.
Different from thermodynamic stability, the kinetic stability, describing the competition of cluster between formation and decomposition processes, is influenced by monomer concentrations (details in Supplementary data).To study the impact of pollutant H 2 SO 4 , the evolution of kinetic stability (indicated by lg[βc/ ∑ γ], details can be found in Supplementary data) of ternary clusters was evaluated (figure 2).As shown in figure 2   collision, thereby making a direct contribution to the nucleation process in polluted regions.Moreover, the kinetic stability of ternary cluster is also rising along with the decrease of T, similar to trend of thermodynamic stability.In this case, as the T decreases, the collision process of clusters slows down slightly.At the same time, the evaporation process is significantly inhibited, resulting in a more favorable condition for nucleation process at a relatively lower T.This indicates that it is favorable for H 2 SO 4 to jointly nucleate with HIO 3 and HIO 2 , especially at higher [H 2 SO 4 ] corresponding to heavily polluted coasts and lower T corresponding to high latitudes polar regions.Hence, the environmental significance of HIO 3 -HIO 2 -H 2 SO 4 ternary nucleation may be influential and deserve further exploration.

Cluster formation rates
To evaluate the guiding significance of HIO 3 -HIO 2 -H 2 SO 4 ternary nucleation on a global scale, the cluster formation rates (J, cm −3 s −1 ) were simulated and compared with the observational nucleation rates (detailed simulation conditions can be found in Supplementary data).Considering the differences in precursor concentrations, T, and the removal of pre-existing particles (indicated by Condensation Sink, CS) caused by geographical location variation, the simulations were performed under four typical The Zhejiang observation site is situated along the south-eastern coast of China and subject to the regions that suffering long-term atmospheric sulfur pollution (Zhu et al 2019).Despite the presence of polluted particles inhibiting the formation of new particles, the NPF events in this region remain significant (Wang et al 2017).However, the rapid nucleation in Zhejiang cannot be adequately explained by HIO 3 -HIO 2 nucleation (blue lines in figure 3(a)).Compared with the original HIO 3 -HIO 2 nucleation, the involvement of air pollutant H 2 SO 4 in nucleation significantly enhances the J (figure 3(a)).To quantitatively assess the influence of H 2 SO 4 on J, the enhancement factor (R), defined as the ratio of J between ternary HIO 3 -HIO 2 -H 2 SO 4 system and binary HIO 3 -HIO 2 system, is studied.When [H 2 SO 4 ] is elevated to 10 8 molecules cm −3 by the severe air pollution, R ranges from 2.6 × 10 3 -1.7 × 10 7 (purple columns in figure 3(b)).The substantial enhancement of H 2 SO 4 leads to a good agreement between the J of ternary system (orange lines) and the field observation results (black dashed lines).Hence, the enhancement of H 2 SO 4 on J is significant and indispensable in polluted coasts with relatively abundant sulfur and scarce iodine precursors such as Zhejiang.
The Mace Head station is located on the northwestern coast of Ireland and characterized by clean atmosphere and abundant iodine species (Sipila et al 2016).Notably, have also been reports of pollution and subsequent high [H 2 SO 4 ] in Mace Head (Berresheim et al 2002, O'Dowd et al 2002), albeit at a relatively lower frequency.We found that the simulated J of HIO 3 -HIO 2 -H 2 SO 4 system remains consistently high throughout the entire [HIO x ] (x = 2,3) range, closely agreed with field observations at Mace Head (figure 3(c)).This indicates that pollutant H 2 SO 4 may also play a role in HIO 3 -HIO 2 nucleation within clean environment.However, the rare pollution incidents and high [HIO x ] (x = 2,3) limit the enhancement effect of H 2 SO 4 to a large extent.As shown in figure 3(d), the R of H 2 SO 4 ranges from 1.0 to 1.1 × 10 7 , highly sensitive to [HIO x ] (x = 2,3).The enhancement of H 2 SO 4 on J remains noteworthy at relatively low [HIO x ] (x = 2,3).However, when [HIO 3 ] is equal to 10 8 molecules cm −3 , the enhancement of H 2 SO 4 on J is inhibited and the R of H 2 SO 4 is no more than 2.3 even though considering the impact of high [H 2 SO 4 ] (up to 10 8 molecules cm −3 ) from air pollution.Hence, for clean coastal regions with abundant iodine precursors such as Mace Head, H 2 SO 4 can enhance the J of HIO 3 -HIO 2 system, but the enhancement is less important compared with polluted coastal regions.
The simulation was also performed under the conditions of two polar observation sites, Ny-Ålesund and Marambio (Beck et al 2021, Quéléver et al 2022).These polar regions are characterized by the relatively primitive atmosphere, low concentrations of gas-phase precursors, and low T. The anthropogenic pollution from, such as vessel transportation, would increase [H 2 SO 4 ] to 10 7 molecules cm −3 .Consequently, the role of H 2 SO 4 in polar areas cannot be underestimated.The distinction lies in that there is a relatively higher [H 2 SO 4 ] and J at the Marambio site of Antarctic.The participation of H 2 SO 4 will increase the J by more than two orders of magnitude (183-fold at least) and match the observational results suitably at [H 2 SO 4 ] = 10 7 molecules cm −3 (figures 3(g) and (f)).Conversely, the relatively higher [HIO x ] (x = 2,3) at the Ny-Ålesund site of Arctic lead to sufficient J for explaining the field observations.Although co-nucleation can enhance the J of Ny-Ålesund for more than 5.5-fold when [H 2 SO 4 ] is equal to 10 7 molecules cm −3 , the actual involvement of H 2 SO 4 may be inapparent since the presence of high [HIO x ] (x = 2,3) and discrepant J (orange lines and black dashed lines in figure 3(e)).Despite the generally lower precursor concentrations in polar regions, the role of H 2 SO 4 in enhancing the J of HIO 3 -HIO 2 system exhibits a similar pattern to midlatitude regions.As illustrated in figure 3, relatively high [H 2 SO 4 ] and low [HIO x ] (x = 2,3) is the most favourable condition for the significant enhancement of H 2 SO 4 on HIO 3 -HIO 2 nucleation.Furthermore, we compared the J of HIO 3 -HIO 2 -H 2 SO 4 , HIO 3 -HIO 2 -dimethylamine (DMA), HIO 3 -HIO 2 -methanesulfonic acid (MSA), and classic H 2 SO 4 -DMA systems, aiming to assess the relative importance of different nucleation systems (see Supplementary data for detailed discussions).The results showed that the observed NPF events may result from multiple rapid nucleation systems or may be solely attributed to a specific system, depending significantly on the variations of precursor concentrations in different regions.Notably, the nucleation capability of HIO 3 -HIO 2 -H 2 SO 4 ternary system in marine atmosphere is relatively strong, especially at high [H 2 SO 4 ] derived from urban pollution.
In summary, H 2 SO 4 can enhance the J of HIO 3 -HIO 2 globally across various environments.The enhancement effect is more significant in polluted coastal areas and polar regions with relatively high [H 2 SO 4 ] and low [HIO x ] (x = 2,3).To investigate the essence of these phenomena, mechanisms involved H 2 SO 4 need to be further revealed via the simulation of cluster formation pathways.

Cluster formation pathways
To elucidate the detailed mechanism through which air pollutant H 2 SO 4 influences HIO 3 -HIO 2 nucleation, the cluster formation pathways of HIO 3 -HIO 2 -H 2 SO 4 system were revealed based on field observation results.The typical formation pathways in polluted coastal areas, exemplified by Zhejiang, are illustrated in figures 4 and S2.The simulation results for Mace Head, Ny-Ålesund, and Marambio are also provided in supplementary figures S3-S8.Without the impact of urban pollution, [H 2 SO 4 ] is approximately 10 6 molecules cm −3 , relying solely on biological sources (Hoffmann et al 2016, Sipila et al 2016, Park et al 2017).The relatively low [H 2 SO 4 ] limits the involvement of H 2 SO 4 in cluster formation pathways by the actual Gibbs free energy barrier of 3.6 kcal mol −1 (figure 5).The binary HIO 3 -HIO 2 nucleation dominate under this circumstance, proceeding through the sequential addition of HIO 3 and HIO 2 molecules.However, the direct impact of urban pollution can elevate [H 2 SO 4 ] to 10 8 molecules cm −3 .In this case, the ∆G actual of H 2 SO 4 -containing clusters largely reduced.H 2 SO 4 molecules can directly participate in cluster formation pathways through a barrierless way.The ternary nucleation pathways involving H 2 SO 4 contributed 46% to the total J, which is the most among all the pathways.Moreover, the sequential combination of H 2 SO 4 and HIO 2 molecules also contributed 40% to J. Notably, during the field observation campaign of Zhejiang, the integrated mass spectrum detected the signals of HIO 3 , HIO 2 , and H 2 SO 4 in nanoparticles simultaneously (Yu et al 2019).Therefore, the proposed ternary nucleation mechanism may provide a reasonable explanation at the molecular level for the sources of HIO 3 , HIO 2 , and H 2 SO 4 molecules in nanoparticles, which is also strong evidence for the participation of H 2 SO 4 in marine HIO 3 -HIO 2 nucleation process.
By contrasting the pathways of Zhejiang under high and low [H 2 SO 4 ], we found the significant involvement of H 2 SO 4 in nucleation processes.The simulation results from other regions (figures S3-S8) can also reflect the influence of [HIO x ] (x = 2,3) on the main formation mechanism.Hence, to explore the evolution of main cluster formation pathways of HIO 3 -HIO 2 -H 2 SO 4 system, we summarized the proportions of cluster formation pathways under a broad range of [H 2 SO 4 ] and [HIO x ] (x = 2,3) conditions.As shown in figure 6, the contributions of formation pathways involving H 2 SO 4 to the total J rise together with the increase of [H 2 SO 4 ] and the decrease of [HIO 3 ] and [HIO 2 ].This implies that with the worsening of pollution, the influence of H 2 SO 4 on HIO 3 -HIO 2 nucleation will become increasingly significant.When [H 2 SO 4 ] is lower than [HIO 3 ], corresponding to those regions characterized by relatively abundant [HIO x ] (x = 2,3) and scarce [H 2 SO 4 ], such as Mace Head and Ny-Ålesund during non-pollution period (figure S9), the widely concerned HIO 3 -HIO 2 nucleation dominate the formation pathways.When [H 2 SO 4 ] is equal to [HIO 3 ], the ternary HIO 3 -HIO 2 -H 2 SO 4 nucleation will dominate, whereby H 2 SO 4 molecules become extensively involved in formation pathways.This condition is met in those regions  characterized by abundant [HIO x ] (x = 2,3) and [H 2 4 ], such as Mace Head and Ny-Ålesund during pollution period (figure S9).When [H 2 SO 4 ] surpasses [HIO 3 ] by an order of magnitude or more, corresponding to those regions characterized by relatively scarce [HIO x ] (x = 2,3) and abundant [H 2 SO 4 ], such as Zhejiang and Marambio (figure S9), binary H 2 SO 4 -HIO 2 nucleation also be observed and occasionally dominate the cluster formation pathways (tables S4-S7).The excess H 2 SO 4 molecules may preferentially bind with HIO 2 molecules, as the latter have a stronger tendency to perform base-like behavior compared with HIO 3 .In general, H 2 SO 4 and HIO 3 , as the proton donors, will compete based on the concentrations.The dominant component, possessing a higher concentration, can engage in binary nucleation with HIO 2 through acid-base interactions.The ternary nucleation mechanism predominates when there is a relatively balanced competition between H 2 SO 4 and HIO 3 .Furthermore, the decrease of T and the increase of CS values would also promote the synergistic nucleation of H 2 SO 4 (tables S4-S7).It is worth noting that higher CS values typically occur in polluted coastal areas concomitant with higher [H 2 SO 4 ].And lower T is the inherent characteristic of polar regions.Consequently, the polluted coasts and polar regions can be the hotspots where pollutant H 2 SO 4 involves in and promotes the original HIO 3 -HIO 2 nucleation.

Conclusion
We found that H 2 SO 4 can form stable ternary clusters with HIO 3 and HIO 2 through XBs, HBs, and electrostatic interaction formed after the acid-base proton transfer.H 2 SO 4 can largely enhance the cluster formation rates of HIO 3 -HIO 2 system, especially in polluted coasts and polar regions with strong H 2 SO 4 sources.The enhanced J of HIO 3 -HIO 2 -H 2 SO 4 system performed better match than that of HIO 3 -HIO 2 system with the field observation results of polluted coasts and polar regions.Moreover, the cluster formation mechanism influenced by H 2 SO 4 was revealed.As the proton donors, H 2 SO 4 and HIO 3 will compete based on the concentrations.And H 2 SO 4 -involved pathways can be realized without Gibbs free energy barrier and dominate broadly in marine regions with rich H 2 SO 4 and scarce iodine concentrations.
The HIO 3 -HIO 2 -H 2 SO 4 nucleation mechanism revealed in this study may help to explain some missing fluxes of new particles and provide a more comprehensive understanding of the intensive NPF events in polluted marine areas.Moreover, through the simulation of H 2 SO 4 -involved iodine oxoacids nucleation mechanism, the significant influence of urban pollutants on the marine atmosphere has been substantiated.Future research can focus on the potential role of other air pollutants to establish a more universal nucleation mechanism with the complex influence of urban pollution in marine atmosphere.

Figure 1 .
Figure 1.The most stable configurations of ternary clusters.The (HIO3)x•(HIO2)y•(H2SO4)z (x + y + z ⩽ 5; x, y, z ⩾ 1) clusters identified at the ωB97X-D/6-311++G(3df,3pd) (for O, H, and S atoms) + aug-cc-pVTZ-PP with ECP28MDF (for I atom) level of theory.The white, red, yellow, and purple spheres represent the H, O, S, and I atoms, respectively.The black dashed lines represent the halogen bonds (XBs) or hydrogen bonds (HBs) in clusters, the bond lengths of XBs are indicated by blue numbers, and the bond lengths of HBs are indicated by black numbers.The bond lengths are given in Å.The red dashed boxes indicate the ternary clusters with the occurrence of proton transfers.