Significance of halogen bonding in the synergistic nucleation of iodine oxoacids and iodine oxides

Abstract

Congeneric iodine oxoacids and iodine oxides, key nucleating vapours in the marine atmosphere, have been reported to nucleate individually. However, whether they can nucleate together remains unknown. Here, we provide molecular-level evidence that I₂O₄, the iodine oxide with the highest nucleation potential towards iodine oxoacids, can synergistically nucleate with HIO₃–HIO₂. The nucleation rate of HIO₃–HIO₂–I₂O₄ is 1.5 to 6.8 times higher than that of the known most efficient iodine-associated two-component (HIO₃–HIO₂) nucleation at 278.15 K, enhancing the role of iodine-containing species in marine atmospheric particle formation. Microscopic analysis of the three-component cluster configurations revealed that an unexpected acid–base reaction between I₂O₄ and HIO₂/HIO₃ is a key driver of this efficient synergistic nucleation, besides hydrogen bonds and halogen bonds. We identified halogen bond-induced basicity enhancement as the chemical nature of I₂O₄ behaving as a base in the nucleation process with HIO₂/HIO₃. Such a basicity enhancement effect can be extended to other iodine-containing species, e.g., HIO₂ and the more acidic HIO₃, suggesting a common feature in interactions between iodine-containing species. Our findings clarify the synergistic nucleation of iodine oxoacids and iodine oxides and highlight the necessity of considering the effect of halogen bond-induced basicity enhancement on the formation of iodine-containing particles.

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Introduction

New particle formation (NPF) initiated by the nucleation of condensable vapours produces more than half of all atmospheric aerosols.^1–3 These nascent particles act as cloud condensation nuclei (CCN), significantly influencing the earth's atmosphere radiative balance and modulating global climate patterns.^4,5 Marine NPF plays a pivotal role in the global climate model, as marine clouds have high albedo and are susceptible to changes in CCN availability.^6–10 However, the influence of marine NPF on climate remains uncertain, mainly due to the limited understanding of the nucleation process in the marine atmosphere, thus resulting in extensive uncertainty within global models.

Conventional theory has been based on the assumption that sulfuric acid (SA)–ammonia (NH₃) nucleation is the dominant mechanism in NPF in marine environments.^11,12 However, recent research has highlighted the importance of iodine oxides (I_xO_y) and iodine oxoacids (HIO_z) as crucial nucleation precursors.^10,13–28 These species are formed mainly by the transformation of iodine (I₂) and methyl iodide (CH₃I), which are emitted from the ocean surface.^29–33 Although iodine-initiated NPF events have been frequently observed,^13,34–37 the specific nucleation mechanism is still not fully understood. One study reported that in flow tube experiments, the nucleation of iodine oxides, particularly I₂O₂, I₂O₃, and I₂O₄ at high concentrations, is rapid.¹⁴ However, Cosmics Leaving Outdoor Droplets (CLOUD) chamber experiments have shown that nucleation involving iodic acid (HIO₃) and iodous acid (HIO₂) can occur rapidly under marine boundary layer conditions.³⁸ In these CLOUD chamber experiments, the concentration of formed iodine oxides is relatively low when the precursor concentration is low, which could be one of the reasons why iodine oxide nucleation cannot compete with HIO₃–HIO₂ nucleation. Iodine oxides and iodine oxoacids are known to coexist on the basis of their homology and can form strong halogen bonds (typical halogen bond energies ΔE ranging from 1 to 45 kcal mol⁻¹ calculated by Oliveira et al.³⁹), which are non-covalent interactions formed between an electrophilic halogen atom and a nucleophilic heteroatom (i.e., with lone-pair electrons).^39,40 Therefore, they may be able to nucleate together, so investigating the joint nucleation mechanism for iodine oxides and iodine oxoacids is important.

In this study, the multicomponent nucleation mechanism of iodine oxides and iodine oxoacids was investigated via quantum chemical calculations and atmospheric cluster dynamic coding. Here, multicomponent nucleation was considered to occur among HIO₃, HIO₂ and specific iodine oxides since HIO₃ and HIO₂ have been found to be able to nucleate at realistic atmospheric concentration ranges.^38,41 Since dimer can present the foundational intermolecular interaction between iodine oxides and iodine oxoacids, and the computational cost of dimer is low, the dimer formation free energy (ΔG) between iodine oxides (IO, I₂O₂, I₂O₃, I₂O₄, and I₂O₅) and iodine oxoacids (HIO₃ and HIO₂) was used to screen the propensity of specific iodine oxides towards nucleation with iodine oxoacids. I₂O₄ was found to have the greatest nucleation potential among the selected iodine oxides and can efficiently nucleate with HIO₃–HIO₂ as a base. Halogen bond-induced basicity enhancement of I₂O₄ was found to be the chemical nature for I₂O₄ behaving as a base during the nucleation with HIO₃–HIO₂. This study reveals that iodine oxides and iodine oxoacids can synergistically nucleate, breaking through the previous findings of their independent nucleation^14,38 and providing a new chemical mechanism for iodine-containing particles.

Methods

A multistep sampling scheme was employed to identify the global minimum for all of the studied clusters, including I_xO_y–HIO_2–3 dimer clusters and HIO₃–HIO₂–I₂O₄ system clusters. This procedure has been widely used in many previous studies on atmospheric cluster formation.^42–44 First, 5000–8000 initial configurations were generated for each cluster using the ABCluster program⁴⁵ and were optimized via the semiempirical PM7 method. The single point energy was subsequently calculated at the M06-2X/def2-TZVP level for all the converged geometries. Configurations up to 15 kcal mol⁻¹ higher than the lowest energy configuration were further fully optimized at the M06-2X/6-31++G(d,p) (for H O atoms) + aug-cc-pVTZ-PP (a basis set with relativistic pseudopotential for I atoms⁴⁶) level. Since there are tens of configurations we have to optimize for each cluster in this step, the adopted larger basis set such as aug-cc-pVTZ(-PP) (aug-cc-pVTZ for H O atoms and aug-cc-pVTZ-PP for I atoms) would lead to the high-cost for the computational time. Hence, we employed the smaller basis set here to reduce computational cost. Our previous study found that the adopted basis set here for optimization presents similar ΔG for HIO₃–HIO₂ clusters to that of the aug-cc-pVTZ(-PP) basis set (Table S1†).⁴¹ Moreover, we also tested several clusters including (HIO₂)₁(I₂O₄)₁, (HIO₃)₂(I₂O₄)₂ and (HIO₃)₁(HIO₂)₁(I₂O₄)₁ with the other basis set def2-TZVP. It was found that the low-energy configurations (within 1–2 kcal mol⁻¹ of the lowest-energy configuration) from def2-TZVP basis set are the same as those from 6-31++G(d,p) + aug-cc-pVTZ-PP (Fig. S1†). Therefore, the adopted basis set is acceptable for the first-round geometry optimization for HIO₃–HIO₂–I₂O₄ system. Finally, for the lowest-energy configurations within 1–2 kcal mol⁻¹, reoptimization was performed at the M06-2X/aug-cc-pVTZ(-PP) level, and the single point energy was refined at the DLPNO-CCSD(T)/aug-cc-pVTZ(-PP) level. If the calculation results failed during optimization or ended up with imaginary frequencies, the initial configurations were adjusted and reoptimized until a successful optimization without imaginary frequencies was finished. The configuration with the lowest Gibbs free energy (G) at 298.15 K and 1 atm was chosen as the global minimum. The G values at other temperatures and pressures were obtained via a GoodVibes Python script.⁴⁷ The ΔG for the global minimum was calculated by subtracting the G of the constituent molecules from that of the cluster. We also tested the influence of the dispersion correction by reoptimizing the global minima for selected three clusters ((HIO₂)₁(I₂O₄)₁, (HIO₃)₂(I₂O₄)₂ and (HIO₃)₁(HIO₂)₁(I₂O₄)₁) using M06-2X/aug-cc-pVTZ(-PP), with Grimme's dispersion correction with ZERO Damping GD3.^48–50 The root-mean-square deviation (RMSD) for optimized structure and difference in ΔG from method with and without dispersion correction are 0.001–0.003 Å and −0.004–0.012 kcal mol⁻¹, indicating that the dispersion correction causes slight influence on the results of this study (Table S2†). All the PM7 and M06-2X calculations were carried out with the Gaussian 16 program⁵¹ and DLPNO-CCSD(T) calculations were performed with the software ORCA 5.0.3.^52,53 In addition, natural bond orbital (NBO) analysis was carried out by Gaussian 16 program to give a detailed insight into intermolecular interactions.

The cluster formation rate and growth mechanism were analysed via Atmospheric Cluster Dynamics Code (ACDC) software, which simulates the cluster kinetics by means of explicit solution of the birth–death equations.⁵⁴ Herein, the simulated system was treated as a 3 × 3 box containing (HIO₃)_0–3(HIO₂)_0–3, (HIO₃)_0–3(I₂O₄)_0–3, (HIO₂)_0–3(I₂O₄)_0–3 and (HIO₃)_x(HIO₂)_y(I₂O₄)_z (x = 1–3, y + z = 2–3) clusters. The boundary cluster settings can be found in the ESI.† The simulation mainly ran at 278.15 K and 1 atm with a coagulation sink rate coefficient (k_coag) of 2 × 10⁻³ s⁻¹, a typical value in coastal regions where iodine species are nucleating.⁵⁵ Additional simulations were performed at 298.15, 253, 223.15 K to probe the effect of temperature, and further simulations were conducted at 0.5 and 0.1 atm to test the effect of pressure. The concentration of HIO₃ ([HIO₃]) was set to 10⁵ to 10⁸ cm⁻³ based on the common atmospheric concentration range.^13,36–38 The concentrations of HIO₂ and I₂O₄ were set to approximately 1/30 [HIO₃] and 1/100 [HIO₃], respectively, corresponding to the measured steady-state concentrations in the CLOUD chamber experiment.³⁸ The detailed discussion on the selection of [I₂O₄] was presented in the ESI.† We accounted for the contribution of long-range interactions via an enhancement factor of 2.4 for the collision rate coefficient.^41,56 In addition, the cluster formation rate of the SA–HIO₃–HIO₂ system ((SA)_x(HIO₃)_y(HIO₂)_z (0 ≤ x + y ≤ 3, 1 ≤ z ≤ 3) clusters) was simulated for comparison, with the concentration of SA ranging from 10⁶ to 10⁷ cm⁻³.^37,57

The similar ACDC simulations based on thermodynamics data from the same theoretical methods as ones used here have been employed in the previous studies on SA–HIO₃–HIO₂ and HIO₃–HIO₂ nucleation, producing consistent cluster formation rates with those from CLOUD experiments.^26,41 Therefore, it is reasonably believed that adopted computational level of theories combined with ACDC simulations can be reliable to describe the interactions among the iodine species and predict the cluster formation mechanism for the HIO₃–HIO₂–I₂O₄ system.

To investigate the correlation between the formation of halogen bonds (XBs) and the change in basicity of I₂O₄, a series of I₂O₄-containing dimer clusters that contain only one XB were manually constructed and optimized at the M06-2X/aug-cc-pVTZ(-PP) level. After optimization, the single point energies (E) of these dimer clusters were calculated at the DLPNO-CCSD(T)/aug-cc-pVTZ(-PP) level. The bond energy (ΔE) was calculated to represent the strength of the formed XB:

ΔE = |E(precursor–I₂O₄ dimer) − E(precursor) − E(I₂O₄)| (1)

Previous study has shown that the change in electrostatic potential (ΔESP) at specific basic site can be employed to present the change in basicity of the compounds.⁵⁸ Herein, we employed ΔESP for the basic site of I₂O₄ to represent the change in basicity of I₂O₄ when it forms XBs with various precursors. The computational details for ΔESP was presented in the ESI.† Furthermore, we also directly calculated the gas basicity (GB) of I₂O₄ before and after the formation of XBs, which is defined as the Gibbs free energy change (ΔG) for reactions (2) and (3), respectively:

I₂O₄H⁺ (g) → I₂O₄ (g) + H⁺ (g) (2)

precursor–I₂O₄H⁺ (g) → precursor–I₂O₄ (g) + H⁺ (g) (3)

It is noted that the terminal O atom of I₂O₄ with the most negative average ESP after forming XB was taken as the basic site for ΔESP and GB calculation. The geometries of positive precursor–I₂O₄H⁺ dimers and I₂O₄H⁺ were manually constructed by adding H⁺ to the basic site of I₂O₄.

Results and discussion

Of all iodine oxides, I₂O₄ is the precursor with the highest potential towards iodine oxoacids

The nucleation potential of iodine oxides towards iodine oxoacids was checked by their dimerization with HIO₂ or HIO₃. Fig. 1 presents the ΔG values and global minimum configurations of the HIO₂-containing and HIO₃-containing dimer clusters. The ΔG values for all dimers except IO–HIO₂ and IO–HIO₃ are negative, ranging from −9.7 to −21.6 kcal mol⁻¹. Of all the HIO₂-containing and HIO₃-containing dimers, HIO₂–I₂O₄ and HIO₃–I₂O₄ exhibit the lowest ΔG values, followed by HIO₂–I₂O₂ and HIO₃–I₂O₂, respectively. Therefore, I₂O₄ is expected to have the greatest intrinsic nucleation potential towards iodine oxoacids, followed by I₂O₂. In addition, the ΔG values of HIO₂–I₂O₄ and HIO₃–I₂O₄ are even lower than that of HIO₃–HIO₂ (−16.79 kcal mol⁻¹), indicating that I₂O₄ has a greater ability to bind with HIO₂ or HIO₃ than HIO₃ and HIO₂ do with each other. It is noteworthy that Engsvang et al. also calculated ΔG values for dimers of iodine oxides (I₂O₄ and I₂O₅) with iodine oxoacids in a recent study.⁵⁹ They found I₂O₄–HIO_2–3 dimers have lower ΔG values than I₂O₅–HIO_2–3 dimers, consistent with results predicted here, although the specific ΔG values in this study are lower.

Fig. 1 Formation free energy (ΔG) (A) and global minimum configurations (B) of I_xO_y–HIO_2–3 dimers at the DLPNO-CCSD(T)/aug-cc-pVTZ(-PP)//M06-2X/aug-cc-pVTZ(-PP) level of theory at 298.15 K. The red balls represent oxygen atoms, purple ones are for iodine atoms, and white ones are for hydrogen atoms. The red dashed lines in the configurations represent hydrogen bonds (HBs), and the blue dashed lines represent XBs. The red and blue numbers indicate the bond lengths of HBs and XBs, respectively. The bond lengths are given in Å.

Observation of the configurations and NBO analysis of the dimers found that both I₂O₄ and I₂O₂ accept a proton from HIO₃ in HIO₃–I₂O₄ and HIO₃–I₂O₂ clusters in addition to forming XBs and hydrogen bonds (HBs). Accordingly, both I₂O₄ and I₂O₂ behave as bases towards HIO₃. However, for dimers of other iodine oxides with HIO₃, there is no proton transfer even though XBs and HBs are formed. Therefore, the additional electrostatic interaction caused by the proton transfer reaction is expected to be one reason that I₂O₄ and I₂O₂ have lower dimer ΔG values with HIO₃ than other iodine oxides do. It is noted that the structure of (HIO₃)₁(I₂O₄)₁ resembles two IO₃ radicals clustered with a hypoiodous acid HOI. However, (HIO₃)₁(I₂O₄)₁ could not dissociate into HOI + 2·IO₃ rather than HIO₃ + I₂O₄, since the ΔG value for (HIO₃)₁(I₂O₄)₁ dissociating into HOI + 2·IO₃ (76.14 kcal mol⁻¹) is much higher than HIO₃ + I₂O₄ (18.01 kcal mol⁻¹). For the dimers of HIO₂ with I₂O₄ and I₂O₂, two XBs are formed. Two XBs are known to form for the dimers of HIO₂ with other iodine oxides except for IO. The lower dimer ΔG values of I₂O₄ and I₂O₂ with HIO₂ result from the stronger strength of XBs formed between them, as evidenced by the lower average energy gap between antibonding orbital δ*(O–I) and lone-pair orbital LP(O), which are two critical molecular orbitals for the formation of XBs with HIO₂ (Table S3†). As a representative example, Fig. S2† illustrates the δ*(O–I) and LP(O) orbitals involved in the (I₂O₄)₁(HIO₂)₁ dimer. Therefore, although I₂O₅ has more electronically deficient iodine centers than I₂O₄/I₂O₂, the additional electrostatic interaction caused by the proton transfer reaction between I₂O₄/I₂O₂ and HIO₃, and the stronger average strength of two XBs between I₂O₄/I₂O₂ and HIO₂, make I₂O₄/I₂O₂ form a more stable complex with iodine oxoacids compared to I₂O₅.

As discussed above, I₂O₄ is expected to have the highest intrinsic nucleation potential towards iodine oxoacids. In addition, in photochemical reactions of I₂ or CH₃I with ozone (O₃) under laboratory conditions, the gaseous concentration of I₂O₄ produced was higher than that of all other iodine oxides except IO.^15,60 Therefore, I₂O₄ has the greatest nucleation potential towards iodine oxoacids. In the following section, we describe our detailed investigation of the joint nucleation of I₂O₄ and iodine oxoacids.

Configurations of HIO₃–HIO₂–I₂O₄ clusters featuring halogen-induced acid–base reaction

We present the cluster configurations for the HIO₃–HIO₂–I₂O₄ system in Fig. 2 and S3.† Since HIO₃–HIO₂ configurations have already been investigated in our previous study,⁴¹ we mainly focus on HIO₃–I₂O₄ and HIO₂–I₂O₄ two-component clusters (Fig. S3†) and HIO₃–HIO₂–I₂O₄ three-component clusters (Fig. 2) here. Observation and analysis of the cluster configurations shows that I₂O₄ accepts a proton from HIO₃ and HIO₂ in almost all HIO₃–I₂O₄ and HIO₂–I₂O₄ two-component clusters. Therefore, I₂O₄ behaves as a Brønsted–Lowry base when it clusters with HIO₃ or HIO₂. To our knowledge, this is the first time that I₂O₄ has been revealed to behave as a base in clustering with HIO₃ or HIO₂. In HIO₃–HIO₂–I₂O₄ three-component clusters, only HIO₃, with the greater acidity, can donate a proton, and I₂O₄ or HIO₂ can accept a proton. In addition, I₂O₄ has a greater ability to accept a proton from HIO₃ than HIO₂ does. Therefore, the behaviour of I₂O₄ as a base is a common feature of HIO₃–I₂O₄ and HIO₂–I₂O₄ two-component clusters and HIO₃–HIO₂–I₂O₄ three-component clusters, in addition to the formation of typical XBs and HBs.

Fig. 2 Global minimum configurations of the (HIO₃)_x(HIO₂)_y(I₂O₄)_z (x = 1–3, y + z = 2–3) clusters calculated at the DLPNO-CCSD(T)/aug-cc-pVTZ(-PP)//M06-2X/aug-cc-pVTZ(-PP) level of theory. The red balls represent oxygen atoms, purple ones are for iodine atoms, and white ones are for hydrogen atoms. The red dashed lines represent HBs, and the blue dashed lines represent XBs. The red and blue numbers indicate the bond lengths of HBs and XBs, respectively. The bond lengths are given in Å.

Why I₂O₄ can behave as a base towards HIO_2–3 is an interesting topic for discussion. The calculated gas basicity (GB) of I₂O₄ is 199 kcal mol⁻¹, close to that of NH₃ (196 kcal mol⁻¹), which has been found to be unable to accept a proton from HIO₃ in the (HIO₃)₁(NH₃)₁ dimer.^17,18 Therefore, the GB of I₂O₄ cannot explain its acid–base reaction with HIO₂ and HIO₃. According to observation of the configurations of HIO₃–HIO₂–I₂O₄ clusters, the occurrence of acid–base reactions with I₂O₄ as a base is always accompanied by the formation of XBs. Therefore, it is reasonable to speculate that the formation of XBs can induce the basicity enhancement of I₂O₄, further driving the acid–base reaction.

To verify this speculation, ΔESP for the basic site and GB of I₂O₄ when it forms XBs with various precursors, were determined. Here, the selected precursors included amines, carbonyl compounds, sulfides, alcohols, benzothiazole, peroxides and hydroperoxymethyl, which can form XBs with I₂O₄ at various bond strengths. Since I₂O₄ can form two types of XBs via its two lowest energy antibonding orbitals δ*(O–I), the effects of these two types of XBs on ΔESP and GB were considered. Fig. 3A shows that the ΔESP values for the O atom as a basic site are negative when I₂O₄ forms a XB with precursors (identity of selected precursors was presented in Table S4†), which leads to an increased basicity of I₂O₄. Moreover, a higher XB energy generally results in a greater (more negative) ΔESP value. As shown in Fig. 3B, the GB of I₂O₄–precursor dimer clusters is significantly greater than that of the I₂O₄ monomer regardless of the type of XBs. In addition, a roughly positive correlation between the formed XB energy and the GB values of I₂O₄–precursor dimer clusters is observed. More importantly, even when a relatively weak XB (approximately 13 kcal mol⁻¹) is formed, the GB of I₂O₄ can be increased to 215 kcal mol⁻¹, which is close to that of dimethylamine (DMA) (215 kcal mol⁻¹), a typical base for enhancing SA-driven nucleation.⁵⁷ Therefore, the formation of XBs indeed increases the basicity of I₂O₄, increasing it from a level similar to that of NH₃ to a level that is comparable to or even greater than that of DMA.

Fig. 3 Change in electrostatic potential (ΔESP) values (kcal mol⁻¹) for the O atom as a basic site of I₂O₄ (A) and the gas basicity (GB) (kcal mol⁻¹) of precursor–I₂O₄ dimers (B) as a function of the halogen bond energy (kcal mol⁻¹). The purple and red spheres represent two different types of XBs. O-atom 1 is the basic site of I₂O₄ when it forms XB type 1 with precursors. O-atom 2 is the basic site of I₂O₄ when it forms XB type 2 with precursors.

Notably, the present study and an earlier study also revealed that HIO₂ behaves as a base towards HIO₃.⁴¹ Similarly, the ΔESP for the basic site of HIO₂ when it forms XBs with various precursors was determined. An effect similar to that of the formed XB on the ΔESP for the terminal O atom as a basic site was also found for the HIO₂ system (Fig. S4†). Therefore, the formation of XBs can greatly increase the basicity of I₂O₄ and HIO₂. To our knowledge, this is the first study to reveal that XBs induce acid–base reactions in HIO₃–HIO₂ and HIO₃–HIO₂–I₂O₄ nucleation systems.

Since XBs are weak non-covalent interactions, it is interesting to check whether other weak non-covalent interactions like HBs, commonly formed in the acid–base nucleation system, can also induce the basicity enhancement of compounds. Here, possible basicity enhancement effect of the HBs was checked by taking NH₃ as the test case. It was found that HBs indeed can induce the basicity enhancement of NH₃ (see ΔESP values for the N atom as the basic site of NH₃ when it forms HBs with precursors in Table S5†). Still, when XBs and HBs are considered as non-covalent interactions, the correlation of non-covalent interaction energy with ΔESP is similar to that of XB energy with ΔESP, i.e. a higher non-covalent interaction energy generally results in a greater (more negative) ΔESP value (Fig. S5†). Since the HB energy is weaker than XB energy considered here, the basicity enhancement effect of HBs is much lower than that of the XBs (Fig. S5†). If the stronger or more HBs are formed in the SA–base systems, the basicity enhancement effect of HBs could be improved. In view of potential role of HBs in inducing basicity enhancement, future investigation on effect of HB-induced basicity enhancement in different nucleation systems is warranted.

Low formation free energy of I₂O₄-containing clusters

The cluster formation free energy of the HIO₃–HIO₂–I₂O₄ system at 278.15 K and 1 atm is presented in Fig. S6.† As shown in Fig. S6,† the ΔG values of all HIO₃–I₂O₄ and HIO₂–I₂O₄ two-component clusters are lower than those of the corresponding HIO₃–HIO₂ two-component clusters. The ΔG values of all I₂O₄-rich clusters are lower than those of the corresponding HIO₃ or HIO₂-rich clusters in these two-component clusters. In addition, the ΔG values of the I₂O₄-containing three-component clusters are lower than those of the corresponding HIO₃–HIO₂ two-component clusters with the same number of acids (HIO₃) and bases (HIO₂ and I₂O₄). All of the aforementioned results indicate that I₂O₄ has a greater ability to bind with HIO₂ or HIO₃ than HIO₃ and HIO₂ do with each other, which is consistent with the conclusion from the ΔG analysis of the dimers of I₂O₄ with HIO₂ and HIO₃. The higher binding ability of I₂O₄ leads to the high stability of most I₂O₄-containing clusters, as evidenced by their low evaporation rates (Fig. S7†). Therefore, the participation of I₂O₄ in HIO₃–HIO₂ nucleation may be favorable. It is noteworthy that (HIO₂)₃(I₂O₄)₃ and (HIO₂)₃(I₂O₄)₂ clusters own high evaporation rates despite they have low ΔG values. It is understandable since the evaporation rate is not only dependent on the ΔG value of the individual cluster, but also on the stability of its all possible daughter clusters.⁵⁴ The high evaporation rate of (HIO₂)₃(I₂O₄)₃ and (HIO₂)₃(I₂O₄)₂ clusters result from the higher stability of their daughter clusters (e.g. (HIO₂)₂(I₂O₄)₂). Tables S6 and S7† also display the ΔG values of the HIO₃–HIO₂–I₂O₄ system clusters at other temperatures and pressures. The ΔG values of most clusters become more negative with decreasing temperature, while they become higher with decreasing pressure.

Previous experimental and theoretical studies have shown that HBs are favorable for new particle formation, particularly for those involving organic acids.^61,62 Herein, we also compared the effects of HBs and XBs on cluster formation by examining the formation free energy of two types of specific dimers: organic acids (benzoic acid, cis-pinonic acid, formic acid)–NH₃ dimers formed by HBs,⁶² and HIO₂–I₂O₄ and HIO₂–HIO₂ dimers formed by XBs.⁴¹ It is found that the formation free energies of HIO₂–I₂O₄ and HIO₂–HIO₂ dimers are lower than those of organic acids (benzoic acid, cis-pinonic acid, formic acid)–NH₃ dimers (Table S8†). This implies that XBs here are stronger than HBs.

Cluster formation rates of the HIO₃–HIO₂–I₂O₄ system

The variation in the cluster formation rates (J) of the three-component HIO₃–HIO₂–I₂O₄ system with [HIO₃] (10⁵–10⁸ cm⁻³) ([HIO₂] = 1/30 [HIO₃], I₂O₄ = 1/100 [HIO₃]) at 278.15 K, 1 atm and k_coag = 0.002 s⁻¹, along with that of the two-component HIO₃–HIO₂ system, is presented in Fig. 4A. The detailed computational methods for J are presented in ESI.† Note that pure I₂O₄ nucleation is not compared with three-component nucleation since its rate is much lower than that of HIO₃–HIO₂ nucleation when [I₂O₄] = 1/100 [HIO₃] (Fig. S8†). As shown in Fig. 4A, the J values of the HIO₃–HIO₂–I₂O₄ system increase with [HIO₃]. The J values of the HIO₃–HIO₂–I₂O₄ system are higher than those of the two-component HIO₃–HIO₂ system under the studied conditions, especially at low [HIO₃]. Therefore, I₂O₄ can enhance HIO₃–HIO₂ nucleation. To clearly demonstrate the enhancement effect of I₂O₄, the enhancement coefficient (R_I2O4), which is the ratio of the J value of the HIO₃–HIO₂–I₂O₄ system relative to that of the HIO₃–HIO₂ system, was calculated. The calculated R_I2O4 ranges from 1.5 to 6.8 at 278.15 K, depending on [HIO₃]. The lower [HIO₃] is, the higher R_I2O4 is. The R_I2O4 of 6.8 applies when the absolute J is very low and the maximum R_I2O4 for non-negligible absolute J (around 7.5 cm⁻³ s⁻¹) is about 2–3. The higher enhancement effect of I₂O₄ at low [HIO₃] decreases the lower limit concentration that HIO₃-driven nucleation has a pronounced nucleation rate. The required [HIO₃] values are 3.45 × 10⁶ cm⁻³ and 4.35 × 10⁶ cm⁻³ for J values of approximately 1 cm⁻³ s⁻¹ in the systems with and without I₂O₄, respectively. This provides further support for the idea that iodine oxides play a key role in iodine oxoacid nucleation. We also noted that a very recent study by Engsvang and Elm found “oxoacid-assisted oxide” nucleation efficient.⁶³ In their study, it was found that the predicted rate of HIO₃–HIO₂ nucleation is much lower than the experimental rates based on their selected theoretical method.⁶³ In our early studies, the predicted HIO₃–HIO₂ and SA–HIO₃–HIO₂ nucleation rates using the same theoretical methods as in this study are comparable to that from CLOUD data.^26,41 Besides, the concentration of iodine oxide is much lower than that of iodine oxoacid in the ambient atmosphere.³⁸ Hence, we treat HIO₃–HIO₂–I₂O₄ synergistic nucleation as “oxide-assisted oxoacid” here. In fact, both studies found that iodine oxoacid and iodine oxide can nucleate together.

Fig. 4 Cluster formation rates (J) (cm⁻³ s⁻¹) of the HIO₃–HIO₂ and HIO₃–HIO₂–I₂O₄ systems and enhancement coefficient (R_I2O4) (the ratio of the J value of the HIO₃–HIO₂–I₂O₄ system relative to that of the HIO₃–HIO₂ system) (A) and comparison coefficient (r) (the ratio of the J value of the HIO₃–HIO₂–I₂O₄ system relative to that of the SA–HIO₃–HIO₂ system) (B) as a function of precursor concentration at 278.15 K, 1 atm and k_coag = 0.002 s⁻¹.

The J of HIO₃–HIO₂–I₂O₄ system and R_I2O4 as a function of temperature at 1 atm are presented in Fig. S9.† J values rise as temperature declines, while further decreasing temperature exhibits a diminished effect on J below 253 K. The temperature dependence of J is more pronounced at lower [HIO₃]. As shown in Fig. S9B,† enhancement of I₂O₄ on HIO₃–HIO₂ nucleation becomes higher at higher temperature (298.15 K). Fig. S10† illustrates the J and R_I2O4 as a function of pressure at 278.15 K. J of HIO₃–HIO₂–I₂O₄ system and R_I2O4 increase slightly as pressure decreases from 1 to 0.5 atm but remain nearly constant when pressure declines from 0.5 to 0.1 atm.

A recent study revealed that SA can also enhance HIO₃–HIO₂ nucleation.²⁶ Therefore, comparing the enhancement potential of I₂O₄ with that of SA would be interesting. The variation in the comparison coefficient (r), which is the ratio of the J value of the HIO₃–HIO₂–I₂O₄ system relative to that of the SA–HIO₃–HIO₂ system, with [HIO₃] and [SA], is presented in Fig. 4B. At low [HIO₃] and therefore lower [I₂O₄], r is much less than 1, indicating that the enhancement potential of I₂O₄ is lower than that of SA. When [HIO₃] ≥ 5 × 10⁶ cm⁻³ and the corresponding [I₂O₄] ≥ 5 × 10⁴ cm⁻³, r becomes approximately 1, i.e., 1.12–1.50 for [SA] = 1 × 10⁶ cm⁻³; 0.20–1.38 for [SA] = 5 × 10⁶ cm⁻³, indicating that the enhancement potential of I₂O₄ is comparable to or even greater than that of SA for HIO₃–HIO₂ nucleation. In most cases for which r is approximately 1, [I₂O₄] is much lower than [SA]. Therefore, I₂O₄, as a base, has a greater enhancement efficiency than SA for HIO₃–HIO₂ nucleation.

Synergistic nucleation mechanism of the HIO₃–HIO₂–I₂O₄ system

The cluster growth pathway for the HIO₃–HIO₂–I₂O₄ system is shown in Fig. 5. Overall, the cluster growth pathway involves three channels: the (I) HIO₃–HIO₂ pathway, (II) HIO₃–I₂O₄ pathway and (III) HIO₃–HIO₂–I₂O₄ pathway. The contributions of the two-component pathways (HIO₃–HIO₂ and HIO₃–I₂O₄) are 30% and 12%, respectively, and the contribution of the HIO₃–HIO₂–I₂O₄ pathway is 38%. At the very early cluster formation stage, two-component clusters of HIO₃–HIO₂ and HIO₃–I₂O₄ evolved into three-component HIO₃–HIO₂–I₂O₄ clusters. Note that almost all clusters growing out of the box had O/I ratios ranging from 2.3 to 2.5, which is consistent with the O/I ratio of approximately 2.5 reported in a previous laboratory study,¹⁵ supporting the occurrence of the proposed synergistic nucleation mechanism of iodine oxoacids and iodine oxides in the atmosphere.

Fig. 5 Cluster formation pathways for the HIO₃–HIO₂–I₂O₄ system at 278.15 K, [HIO₃] = 1 × 10⁷ cm⁻³, [HIO₂] = 3.33 × 10⁵ cm⁻³, [I₂O₄] = 1 × 10⁵ cm⁻³ and k_coag = 0.002 s⁻¹. The pathways contributing less than 15% to the flux of cluster formation are not show.

Implications

This study reveals that I₂O₄, HIO₃ and HIO₂ can nucleate together, breaking through the previous findings that iodine oxoacids and iodine oxides independently nucleate.^14,38 More importantly, I₂O₄, HIO₃ and HIO₂ nucleate in a synergistic way. This synergistic nucleation increases the contribution of iodine-containing species to NPF beyond what was previously thought. Fig. 6 shows the significance of HIO₃–HIO₂–I₂O₄ nucleation on a global scale. It is noted that HIO₃–HIO₂ system was selected as the base case, since HIO₃–HIO₂ is the only two-component system that was verified to have high nucleation rate at the realistic atmospheric concentration ranges of HIO₂ and HIO₃ (ref. 38) and has the highest nucleation rate among three two-component systems in most conditions. As shown in Fig. 6, the nucleation rate increased by at least 1.5 times in areas where HIO₃ was detected once I₂O₄ was involved in nucleation. Under conditions of relatively high temperature and 10⁷ cm⁻³ HIO₃ in Helsinki, the nucleation rate can be increased by up to 23.3 times. In addition, I₂O₄ enhances HIO₃–HIO₂ nucleation as a base. Atmospheric acids such as SA and methanesulfonic acid (MSA) have been proposed to enhance HIO₃–HIO₂ nucleation.^25,26,64,65 Therefore, multicomponent nucleation involving HIO₂, HIO₃, I₂O₄, SA, MSA and other acids can further increase the contribution of iodine-containing species to NPF, which deserves future ambient field and laboratory study.

Fig. 6 Cluster formation rate (J) (cm⁻³ s⁻¹) of the HIO₃–HIO₂–I₂O₄ and HIO₃–HIO₂ systems and the enhancement coefficient (R_I2O4) in different areas with different temperatures (T) and [HIO₃]. The T and [HIO₃] in different areas were obtained from He et al.³⁸ The k_coag in Helsinki and Mace Head was set to 2 × 10⁻³ s⁻¹,⁵⁵ and k_coag in Aboa, Greenland, and Ny-Ålesund was set to 1 × 10⁻⁴ s⁻¹.³⁸

This study revealed that XBs can induce the basicity enhancement of I₂O₄ and HIO₂, further driving their acid–base reactions and therefore facilitating nucleation. Since the formation of XBs is common in iodine and oxygen-containing clusters, the mechanism by which XBs induce basicity enhancement could also be extended to other nucleation systems containing iodine oxoacids and iodine oxides. We found that XBs even can induce the basicity enhancement of more acidic HIO₃ in our preliminary study. Therefore, the mechanism by which XBs induce basicity enhancement is expected to be a common mechanism in nucleation systems containing iodine oxoacids and iodine oxides, necessitating further study. In addition, XB-induced basicity enhancement is also expected to occur during the growth of iodine oxoacids and iodine oxides-containing particles. However, more species and more complicated interactions should be involved in particle growth. The possible role of such a mechanism in particle growth is worthy of further investigation.

Conclusions

In this study, quantum chemical methods and ACDC were employed to investigate the nucleation mechanism and kinetics of iodine oxides and iodine oxoacids. Of all iodine oxides, I₂O₄ was found to have the strongest nucleation potential towards HIO₃–HIO₂. I₂O₄ can synergistically nucleate with HIO₃–HIO₂, breaking through the previous findings that iodine oxoacids and iodine oxides independently nucleate.^14,38 The synergistic nucleation rate of HIO₃–HIO₂–I₂O₄ is 1.5 to 6.8 times higher than that of the known most efficient iodine-associated two-component (HIO₃–HIO₂) nucleation at 278.15 K. The high synergistic nucleation rate enhances the role of iodine-containing species in marine atmospheric particle formation. Microscopic analysis of the three-component cluster configurations revealed that an unexpected acid–base reaction between I₂O₄ and HIO₂/HIO₃ is a key driver of this efficient synergistic nucleation, in addition to traditional HBs and XBs. The halogen bond-induced basicity enhancement was further identified as the chemical nature of I₂O₄ behaving as a base in the nucleation with HIO₂ or HIO₃. Such a basicity enhancement effect can be extended to other iodine-containing species, e.g., HIO₂ and even more acidic HIO₃, suggesting that this is a common feature in interactions between iodine-containing species. Our findings clarify the synergistic nucleation of iodine oxoacids and iodine oxides and highlight the importance of halogen bond-induced basicity enhancement in the formation of iodine-containing particles.

Data availability

The data supporting this article have been included as part of the ESI.†

Author contributions

H. B. X. and J. S. F. designed the study. R. J. Z. and Y. Y. L. performed the quantum chemical calculation and analyzed data. R. J. Z., Y. Y. L., R. J. Y., F. F. M., H. B. X. and J. S. F. wrote the manuscript. D. M. X., J. W. C., H. B. X. and J. S. F. commented on and revised the manuscript. All coauthors participated in relevant scientific discussion of the manuscript.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

This work was supported by the National Key Research and Development Program of China (2022YFC3701000, Task 1) and the National Natural Science Foundation of China (22236004, 22176022 and 22406017).

Notes and references

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5sc02517f

‡ R. J. Z. and Y. Y. L. contributed equally.

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