Theoretical Studies on the Potential of Hypoiodous Acid to Self-Nucleate in Marine Regions

— The formation of new marine particles is closely correlated with the iodine-containing substances emitted by marine algae. Hypoiodous acid (HIO) is a common iodine oxoacid in marine regions. However, the potential of HIO to take part in the nucleation process and the relevant mechanism remain to be fully investigated. Herein, this study investigated the self-nucleation of HIO in marine regions and found that, although HIO can form (HIO) 2-6 clusters via medium hydrogen bonds, the (HIO) 2-6 clusters are inherently unstable. Therefore, the self-nucleation of HIO in marine regions is almost impossible. Moreover, compared with HIO molecules, HIO monomer is more inclined to bond with iodic acid (HIO 3 ) molecules. This work may help to understand the new particle formation involving iodine oxoacids more comprehensively.


Introduction
Atmospheric aerosol refers to the liquid or solid particles suspended in the atmosphere [1] , such as haze particles, smoke, clouds. The mass formation of aerosol particles can cause serious air pollution, leading to the worsening of environmental quality, and even seriously harm human health through diseases related to respiratory system and cardiovascular system [2] . Thus, it is important to explore the composition and formation mechanism of aerosol particles. New particle formation (NPF) is an important source of atmospheric aerosols [3] , and the nucleation process is the key stage in NPF [4] . Marine aerosols are indispensable in the global aerosol system since the ocean occupy 71% of the Earth. NPF events have been observed frequently in marine regions, and existing studies have shown that the nucleation of iodine-containing substances is an important contributor to the marine NPF [5,6] . At present, it is generally believed that iodine oxides (I 2 O 3-5 ) and iodine oxoacids (HIO 2-3 ) are important iodinecontaining species involved in the NPF in marine areas [7] .
The relevant studies about iodine oxoacids mainly focus on iodic acid (HIO 3 ) and iodous acid (HIO 2 ), showing that HIO 3 and HIO 2 are important participants in the NPF in marine regions [8][9][10] . Apart from HIO 3 and HIO 2 , another iodine oxoacid -hypoiodous acid (HIO) can contribute to atmospheric ozone depletion, and the concentration of HIO in marine boundary layer can reach 2~15 pptv based on recent model prediction [11] . Furthermore, in addition to gaseous HIO 3 and HIO 2 , HIO with a concentration of at least 10 6 molecules cm -3 was also observed in the atmosphere during the intense NPF events at Mace head, a coast in Ireland [8] . Similarly, aside from IO 3and IO 2 -, IOwas also detected in the 10-18 nm particles at Xiangshan gulf of the east China coast [12] .
These results suggest that HIO may also be a potential nucleation precursor for marine NPF. Therefore, in order to have a more comprehensive and clear understanding of the formation of new aerosol particles involving iodine oxoacids in marine regions, whether HIO can selfnucleate and the corresponding mechanism are worthy to be investigated.
Herein, quantum chemical calculations combining with Atmospheric Cluster Dynamics Code (ACDC) simulations were employed to investigate the formation of (HIO) 2-6 clusters with the aim of exploring the potential to self-nucleation of HIO and the corresponding nucleation mechanism under various atmospheric conditions. The current work may help to better understand the marine NPF.

Quantum chemical calculations
To obtain the global energy minimum structure of the (HIO) 2-6 clusters, a multi-step cluster conformation screening method was employed here and the details can be seen in our previous work about (HIO 2 ) 2-6 clusters [13] . The final structure optimizations and frequency calculations were performed at the level of 6-311++G(3df,3pd) (for O, H) + aug-cc-pVTZ-PP with ECP28MDF (for I) using ωB97X-D [14] function by Gaussian 09 [15] . Furthermore, for each of the global energy minimum structure of (HIO) 2-6 clusters, the single-point correction by the RI-CC2 [16] method was also carried out using the Turbomole program [17] as this for (HIO 2 ) 2-6 clusters in our previous work [13] . Thus, the Gibbs free energy (G, kcal mol -1 ) of (HIO) 1-6 molecule/cluster is calculated as: (1) where is the electron binding energy obtained at RI-CC2/aug-cc-pVTZ (for O, H) + aug-cc-pVTZ-PP with ECP28MDF (for I) level of theory, and thermal B97X-D is the thermal contribution calculated at ωB97X-D/6-311++G(3df,3pd) (for O, H) + aug-cc-pVTZ-PP with ECP28MDF (for I) level of theory. And then the Gibbs free energy of formation (ΔG, kcal mol -1 ) of (HIO 2 ) 2-6 clusters can be obtained.

Atmospheric cluster dynamics code (ACDC) simulations
In ACDC [18] simulations, the smallest clusters out of the simulation system assumed to be stable can be set as the boundary conditions. And then the thermodynamic data of (HIO 2 ) 2-6 clusters obtained by quantum chemistry calculations can be brought into ACDC to obtain the cluster formation rates and pathways by solving the birthdeath equations describing the formation and destruction of clusters. The details can be seen in our previous work about (HIO 2 ) 2-6 clusters [13] .

Conformational analysis of (HIO)2-6 clusters
Molecular clusters are mainly stabilized by intermolecular interactions within clusters. For instance, there are hydrogen bonds (HBs) and halogen bonds (XBs) interactions in pure HIO 3 or HIO 2 molecular clusters [13] . Particularly, the molecular surface electrostatic potential (ESP) analysis is helpful to predict possible intermolecular interaction sites. The sites possessing negative ESP values tend to attract the sites possessing more positive ESP values to form non-covalent interactions. Hence, in order to predict the potential interaction sites in (HIO) 2-6 clusters, the ESP-mapped molecular van der Waals (vdW) surfaces of HIO molecule was generated by VMD [19] and Multiwfn 3.7 [20] . As shown in Fig. 1, the H atom of HIO possessing a maximal ESP value (+52.0 kcal mol -1 ) can act as HB donor, the I atom of HIO possessing a maximal ESP value (+43.3 kcal mol -1 ) can act as XB donor, and the O atom of HIO possessing minimal ESP values (-23.9 kcal mol -1 ) can act as HB or XB acceptor. In summary, HIO molecules have binding sites for HB or XB, suggesting that it has the potential to form pure HIO molecular clusters through HB or XB. Figure 2 shows the obtained most stable structures of (HIO) 1-6 molecule/clusters. As can be seen from Fig. 2, there are HBs in (HIO) 2-6 clusters, and the number of HBs in clusters increases with the increase of HIO molecule number. For (HIO) n (3 ≤ n ≤ 6) clusters, the O atom and H atom of HIO molecules form a ring plane through covalent bonds and HBs (…O-H…(…O-H…) n-2 …O-H…), and the heavy atom I in HIO molecules extend out of the ring plane to different directions in space. Moreover, to further quantify the strength of HBs in (HIO) 2-6 clusters, the electron density ρ(r), Laplacian of electron density ∇ 2 ρ(r) and energy density H(r) at the corresponding bond critical points (BCPs) based on atoms in molecules (AIM) theory [21] were calculated using Multiwfn 3.7 [20] . The calculation results show that the ρ(r) and ∇ 2 ρ(r) values at the BCPs of HBs in (HIO) [2][3][4][5][6] clusters are in the range of 0.0284-0.0466a.u. and 0.0935-0.1106 a.u., respectively. Besides, all the ∇ 2 ρ(r) are positive values and all the H(r) are negative values. According to the ρ(r) and ∇ 2 ρ(r) values and the strength criteria of HBs in reference [22] , there are medium HBs in (HIO) 2-6 clusters.   (Fig. 3). At 298.15 K, the G of (HIO) 3-a and (HIO) 4-a are 8.06 and 7.89 kcal mol -1 higher than those of the corresponding globally most stable structures, respectively. As shown in Fig. 3, for (HIO

The stability analysis of (HIO)2-6 clusters
The stability of the clusters is of great importance to whether they can participate in NPF process. Fig. 4 shows the ΔG of (HIO) 2-6 clusters at 298.15, 278.15 and 258.15 K. It can be seen that the ΔG of (HIO) 2 cluster is positive value at 298.15 or 278.15 K and negative value at 258.15 K, so taking the calculation error into consideration, the stability of (HIO) 2 cluster is weak from a thermodynamic perspective. Moreover, the ΔG of (HIO) 2-6 clusters is much higher than that of (HIO 3 ) 2-6 or (HIO 2 ) 2-6 clusters at the same level of theory in our previous work [13] , suggesting that the thermodynamic stability of (HIO) 2-6 clusters is lower than that of (HIO 3 ) 2-6 or (HIO 2 ) 2-6 clusters. From a dynamic point of view, a molecular cluster can keep growing up or evaporate back towards smaller sizes. Table 1 shows the ratio of the collision frequency between the (HIO) 2-6 clusters and HIO monomer with a concentration of C to the evaporation frequency of (HIO) 2-6 clusters (βC/∑γ) at 298.15, 278.15 and 258.15 K. As can be seen from Table 1, the βC/∑γ of each (HIO) 2-6 cluster is far less than 1, so the evaporation rate of each (HIO) 2-6 cluster is much higher than its growth rate by collision. Thus, the (HIO) 2-6 clusters are unstable, so the selfnucleate of HIO is almost impossible in marine regions.
Furthermore, it can be seen from Fig. 4 and Table 2 that ΔG (HIO 3 ·HIO) ＜ ΔG ((HIO) 2 ). Compared with HIO molecules, HIO monomer is more inclined to bond with HIO 3 molecules to form small bimolecular HIO 3 ·HIO cluster. However, Table 2 shows that ΔG (HIO 3 ·HIO 2 ) ＜ ΔG ((HIO 3 ) 2 ) ＜ ΔG (HIO 3 ·HIO). Among the three small bimolecular clusters, the thermodynamic stability of HIO 3 ·HIO cluster is lower than that of HIO 3 ·HIO 2 and (HIO 3 ) 2 clusters, suggesting that the potential of HIO to participate in the nucleation process of HIO 3 is weaker than that of HIO 3 and HIO 2 . At present, it is still unclear whether HIO can participate in the nucleation process of HIO 3 , which needs to be further investigated in the future studies. Table 1 The ratio of the collision frequency between the (HIO)2-6 clusters and HIO monomer with a concentration of C (10 8 molecules cm -3 ) to the evaporation frequency of (HIO)2-6 clusters (βC/∑γ).

Conclusion
Herein, the potential of HIO to self-nucleate have been investigated by analyzing the intermolecular interactions and the stability of (HIO) 2-6 clusters. The results show that there are medium HBs in (HIO) 2-6 clusters, and the evaporation rate of each (HIO) 2-6 cluster is much higher than its growth rate, which means that the (HIO) 2-6 clusters are unstable. Therefore, the self-nucleation of HIO is almost impossible in marine regions. This is the first theoretical study on the self-nucleation of HIO, which is helpful to understand the NPF involving iodine oxoacids more clearly. Moreover, compared with HIO molecules, HIO monomer is more inclined to bond with HIO 3 molecules. Further studies are necessary to determine the potential involvement of HIO in the nucleation process of