Critical Role of Iodous Acid in Neutral Iodine Oxoacid Nucleation.

Nucleation of neutral iodine particles has recently been found to involve both iodic acid (HIO3) and iodous acid (HIO2). However, the precise role of HIO2 in iodine oxoacid nucleation remains unclear. Herein, we probe such a role by investigating the cluster formation mechanisms and kinetics of (HIO3)m(HIO2)n (m = 0-4, n = 0-4) clusters with quantum chemical calculations and atmospheric cluster dynamics modeling. When compared with HIO3, we find that HIO2 binds more strongly with HIO3 and also more strongly with HIO2. After accounting for ambient vapor concentrations, the fastest nucleation rate is predicted for mixed HIO3-HIO2 clusters rather than for pure HIO3 or HIO2 ones. Our calculations reveal that the strong binding results from HIO2 exhibiting a base behavior (accepting a proton from HIO3) and forming stronger halogen bonds. Moreover, the binding energies of (HIO3)m(HIO2)n clusters show a far more tolerant choice of growth paths when compared with the strict stoichiometry required for sulfuric acid-base nucleation. Our predicted cluster formation rates and dimer concentrations are acceptably consistent with those measured by the Cosmic Leaving Outdoor Droplets (CLOUD) experiment. This study suggests that HIO2 could facilitate the nucleation of other acids beyond HIO3 in regions where base vapors such as ammonia or amines are scarce.

Introduction

New particle formation (NPF) contributes to more than half of the global cloud condensation nuclei, which in turn contribute to cloud formation.[1−4] Therefore, NPF ultimately affects climate change.[5,6] Compared to clouds over land, marine clouds play a larger role in the climate system not only due to their wider coverage but also because they significantly increase the albedo of oceans.[7−9] Hence, understanding marine particle formation processes is essential. Sulfuric acid (SA, H2SO4) and methane sulfonic acid (MSA, CH3HSO3) are commonly thought to contribute to marine particle formation.[10−15] In the critical initial clusters during nucleation, SA and MSA molecules are stabilized by base molecules such as ammonia (NH3) and amines (e.g., dimethylamine (DMA)).[16−25]

Besides SA and MSA, iodine-containing molecules were proposed to account for particle bursts observed over 20 years ago in coastal regions at the Mace Head Observatory, Ireland.[26,27] Iodine dioxide (OIO) was among the first candidates proposed to account for this rapid particle formation, and OIO was believed to form stable iodine tetroxide (I2O4) in the particles.[27,28] However, a following study examined the composition and morphology of iodine-containing particles and observed iodine pentoxide (I2O5) as the primary constituent of these particles.[29] Subsequent laboratory investigations alternatively proposed iodine oxides, e.g., I2O (y = 3–5) as the critical vapors initializing iodine particle formation, while the restructuring of these iodine oxides in the particle phase contributed to the observed O/I ratio of 2.5.[29−31] However, recent measurements with a nitrate chemical ionization mass spectrometer (nitrate-CIMS) revealed extremely high concentrations of iodic acid (HIO3), occasionally above 108 cm–3, at the Mace Head Observatory.[32] Such high concentrations of HIO3 lead to rapid particle formation.[32−35] In contrast to ambient observations, recent laboratory studies with high iodine concentrations shed doubts on this mechanism and proposed that I2O could have been interpreted as gaseous HIO3.[36,37]

Sophisticated experiments were carried out in the Cosmic Leaving Outdoor Droplets (CLOUD) chamber at CERN to study iodine particle formation at atmospherically relevant conditions to resolve the puzzles. With a finely tuned nitrate-CIMS, gaseous HIO3 was unambiguously measured.[35] By initializing an ion-induced nucleation experiment from ion-free conditions and tracing the subsequent development of charged iodine clusters, the authors obtained the time evolution of charged iodine clusters containing up to 11 iodine atoms.[35,38] The sequential charged clusters differ by the addition of a single HIO3 molecule and cannot be explained by any molecule containing two iodine atoms (I2O), confirming an earlier finding by Sipilä et al.[32] On the other hand, neutral iodine nucleation was found to proceed through a novel iodic acid (HIO3)–iodous acid (HIO2) mechanism.[35] The particle growth was primarily contributed by HIO3, while the I2O4 concentration, at ca. 1% HIO3, was too low to make a significant contribution.[35] In contrast to SA and bases such as NH3 and DMA, which can be independently controlled in the laboratory, iodine oxoacids (HIO2–3) originate from the same precursor, e.g., elemental iodine,[36,39] and so it is difficult to separate their roles in atmospheric particle formation. This poses challenges to determining the relative importance of the three channels: (1) pure HIO3, (2) mixed HIO3 and HIO2, and (3) pure HIO2 nucleation of neutral iodine oxoacids (defined as the sum of the three channels).

Besides laboratory experiments and field observations, quantum chemical calculations have also been used to predict iodine particle formation mechanisms. In polluted locations, SA, MSA, and NH3 were suggested to enhance pure HIO3 nucleation.[14,40,41] However, so far, the predicted nucleation rates for (1) pure HIO3, (2) HIO3–SA, (3) HIO3–MSA, and (4) HIO3–NH3 cannot account for the experimental results on pure iodine nucleation from CLOUD.[35] One likely reason for such discrepancies is that earlier studies considered only the sequential addition of HIO3 and did not include HIO2.[32] Very recently, Zhang et al. investigated the nucleation of pure HIO2 and found that the cluster formation rate of HIO2 is faster than that of pure HIO3,[42] yet remaining lower than the CLOUD measurements.[35]

To evaluate the role of HIO2 in neutral iodine oxoacid nucleation, we use quantum chemical calculations to optimize the geometries of (HIO3)(HIO2) (m = 0–4, n = 0–4) clusters and calculate corresponding thermodynamic data, which in turn are used as inputs for the Atmospheric Cluster Dynamics Code (ACDC) model to probe the cluster formation mechanisms and kinetics.[43] Furthermore, we provide a comparison of neutral iodine oxoacid nucleation with the benchmarks of neutral SA–DMA/NH3 nucleation under similar conditions to gauge the potential atmospheric importance of iodine oxoacid nucleation.

Computational Framework

Quantum Chemical Calculations

Here, a multistep global minimum sampling scheme was employed to search for the global minima of (HIO3)(HIO2) (m = 0–4, n = 1–4) clusters with additional geometries of (HIO3)1–4 clusters adopted from previous studies.[40,44] We used an in-house code to generate 3000–5000 initial configurations for each cluster with n molecules by randomly placing a new molecule around cluster minima with n – 1 molecules. The initial configurations were further optimized at the semiempirical PM7 level of theory.[45] Single-point energy calculations at the M06-2X/def2-TZVP level of theory were subsequently performed on all the optimized geometries. Additional optimizations and frequency calculations of conformers within 10–15 kcal mol–1 higher energy compared to the identified lowest energy conformer were performed at the M06-2X/Basis1 (Basis1 presents 6-31++G(d,p) for H and O atoms and aug-cc-pVTZ-PP with ECP28 for I atoms[46]) level of theory. If the geometry optimization failed or there were imaginary frequencies for the optimized conformers, the input geometries will be adjusted and re-optimized until a “successful” optimization without imaginary frequencies was obtained. Single-point energy calculations at the DLPNO-CCSD(T)/Basis2 (Basis2 presents aug-cc-pVTZ for H and O atoms and aug-cc-pVTZ-PP with ECP28 for I atoms) level of theory were further performed on selected low-free energy conformers optimized at the M06-2X/Basis1 level of theory. Similar to previous studies,[47] we employed the GoodVibes program[48] to recalculate the Gibbs free energy correction term (via quasi-harmonic correction) of (HIO3)(HIO2) (m = 0–4, n = 0–4) clusters at the M06-2X/Basis1 level to decrease the possible error caused by the rigid-rotor-harmonic-oscillator approximation. We used 100 cm–1 as the low-frequency cutoff value. Finally, the conformer with the lowest Gibbs free energy at 298.15 K (combining the single-point energies at the DLPNO-CCSD(T)/Basis2 level and the recalculated Gibbs free energy correction terms by GoodVibes) was selected as the global minimum for a given cluster. We note that mixing basis sets of different sizes (e.g., in Basis1, 6-31++G(d,p) was used for H and O atoms and aug-cc-pVTZ-PP with ECP28 for I atoms) could, in some cases, lead to substantial errors but, in our case, test calculations demonstrate that such mixture has a minimal effect on the calculated formation free energy (ΔG) (see the test results in Table S1). In addition, Gibbs free energies at other temperatures were obtained by combining the single-point energies at the DLPNO-CCSD(T)/Basis2 level and the recalculated Gibbs free energy correction terms by GoodVibes at the corresponding temperature. All geometry optimization, vibrational frequency calculations, and single-point energies using the PM7 and M06-2X methods were performed in the GAUSSIAN 16 program package,[49] and DLPNO-CCSD(T)/Basis2 calculations were performed using the ORCA 4.0.0 program[50] with tight SCF and PNO convergence criteria. The pure (HIO3)1–4 clusters from previous studies[40,44] were re-optimized, followed by single-point energy calculations at the same theory levels of this study. The ΔG values for individual clusters were obtained by subtracting the sum of Gibbs free energies of their constituent molecules from that of the clusters at the considered temperature.

ACDC Modeling

We employed the ACDC model to study the time evolutions of cluster formation rates, steady-state concentrations, and growth pathways of clusters.[43] The detailed description of the ACDC can be found in a previous study,[43] and we present the physical principles of ACDC in the Supporting Information (SI). In this study, the simulated clusters are (HIO3)(HIO2) (m = 0–4, n = 0–4); i.e., the maximum number of HIO3 and HIO2 molecules in the system is four of each. The diameter of the largest cluster ((HIO3)4(HIO2)4) is around 1.5 nm, which is calculated in Multiwfn version 3.7[51] by the maximum distance between two atoms considering their van der Waals radii. The size of the largest cluster is comparable to the 1.7 nm for the nucleation rates reported in the CLOUD experiment.[35] The (HIO3)5(HIO2)4 and (HIO3)4(HIO2)5 clusters are set as the boundary clusters, which are allowed to grow out of the system and contribute to the cluster formation rate (see details in the SI). In the simulation, the HIO3 concentration [HIO3] was set to between 106 and 108 cm–3 and the HIO2 concentration [HIO2] between 104 and 106 cm–3, corresponding to ambient concentrations.[32,35] The simulations were mainly carried out at 263.15 K (−10 °C), employing a constant coagulation sink (CS) coefficient of 2 × 10–3 s–1, a typical value at coastal regions[52] and similar to the CLOUD wall loss rate. In addition, a smaller CS value of 2 × 10–4 s–1, corresponding to the case of clean atmosphere over the Arctic Ocean,[33] and a larger CS value of 2 × 10–2 s–1, corresponding to the case of urban and polluted atmosphere,[53] were selected to test the effects of the CS on the nucleation rates. To make a direct comparison with CLOUD measurements, the simulations were also run under the same precursor concentrations (Table S2) and wall loss rates (Table S3) for each cluster and temperature (+10 and −10 °C). In ACDC, the collision rate coefficients were calculated by the hard sphere kinetic gas theory.[43] Previous studies have found that the actual collision coefficient is additionally enhanced by attractive van der Waals forces (e.g., dipole–dipole interaction and dispersion interaction).[54,55] Here, the enhancement factor for the iodine oxoacid system was approximately estimated to be 2.4 based on the dipole–dipole interaction or dispersion interaction (see details in the SI). For ACDC modeling of pure HIO3 and pure HIO2 nucleation, the (HIO3)5 and (HIO2)5 clusters, respectively, were set as boundary clusters, with the remaining parameterizations identical to those of the HIO3–HIO2 nucleation.

Results and Discussion

Cluster Structures

The global minimum structures of (HIO3)(HIO2) (m = 0–4, n = 0–4) clusters are presented in Figure . The geometries of homomolecular (HIO3)1–4 clusters are adopted from previous studies,[40,44] while the rest are searched and calculated in this study. It deserves mentioning that there are four reported (HIO3)2 conformers;[35,40,44,56] we used the one from Kumar et al.,[44] which has the lowest ΔG (see details for geometries and ΔG values in Table S4). A common feature for all the clusters is that halogen bonds (O–I···O bond, herein denoted as XB) or together with hydrogen bonds (O–H···O bond, herein denoted as HB) are formed. Interestingly, proton transfer reactions are observed in all (HIO3)(HIO2) (m = 1–4, n = 1–4) clusters except (HIO3)2(HIO2)1, while no proton transfer is observed in any pure HIO2 and HIO3 clusters. It deserves mentioning that the observed proton transfer is a spontaneous process. The spontaneous proton transfer was confirmed by re-optimizing the “proton-returned” conformer. The “proton-returned” conformer was manually built by pulling the proton back to the original location and increasing the distance between the two molecules. After the re-optimization, proton transfer can still occur, indicating a spontaneous process.

Figure 1

Lowest formation free energy conformers of the (HIO3)(HIO2) (m = 0–4, n = 0–4) clusters calculated at the DLPNO-CCSD(T)/Basis2//M06-2X/Basis1 level of theory. The dashed red lines indicate HBs. The dashed purple lines indicate XBs.

For most of (HIO3)(HIO2) (m = 1–4, n = 1–4) clusters, the proton is transferred from HIO3 to HIO2. Therefore, HIO2 behaves as a Brønsted–Lowry base when interacting with HIO3. To the best of our knowledge, this is the first time that HIO2 is revealed to behave as a base in the interaction with HIO3. Previous studies have found that the acidity of HIO3 (acid dissociation constant, pKa = 0.80)[57] is much higher than that of HIO2 (pKa = 6),[58] supporting our observations. Surprisingly, proton transfer can also occur between two HIO2 molecules in (HIO3)2(HIO2)3 and (HIO3)2(HIO2)4 clusters. In these cases, the HIO2 molecules acting as proton acceptor and donor have distinct interactions with their adjacent molecules: (1) the proton acceptor HIO2 forms two XBs via its I atom with adjacent molecules, and (2) the proton donor HIO2 forms two XBs via its two O atoms with adjacent molecules, while its I atom does not form additional bonds with other molecules. These surprising characteristics therefore result from certain interactions of an HIO2 molecule with its adjacent molecules that serve to modify the effective HIO2 acidity.

Cluster Formation Free Energy

We present the formation free energy surface with quasi-harmonic correction at 263.15 K for the iodine oxoacid system in Figure A, with the corresponding one at 298.15 K presented in Figure S1. Previous studies have shown that SA–DMA-driven NPF is dominant in the urban atmosphere[53] and that it almost proceeds at the SA kinetic limit.[59] Here, the ΔG values of the SA–DMA system (Figure B)[60] are used as a benchmark to compare with the calculated ΔG values of the iodine oxoacid system to show the effectiveness of HIO3–HIO2 cluster formation. The ΔG value of each of the HIO3–HIO2 clusters is lower than that of the corresponding SA–DMA clusters, with the difference in their ΔG values varying between 1.34 and 62.21 kcal mol–1. Such a large difference in ΔG values for all clusters indicates that iodine oxoacid cluster formation is thermodynamically even more favorable than SA–DMA cluster formation, which has hitherto represented one of the most efficiently known neutral nucleating mechanisms observed in the atmosphere. In addition, the ΔG values for the (HIO3)(HIO2) (m < n) clusters above the diagonal line are lower than those of the corresponding (HIO3)(HIO2) (m > n) clusters below the diagonal line, representing a reverse trend compared with the case of the SA–DMA system.[60] The lower ΔG values for HIO2-rich clusters indicate a stronger binding ability of HIO2 compared with that of HIO3, confirming the important role of HIO2 in iodine oxoacid nucleation.

Figure 2

Formation free energy (ΔG) with quasi-harmonic correction of (A) (HIO3)(HIO2) and (B) (SA)(DMA) (adopted from Xie et al.[60]) clusters (m = 0–4, n = 0–4) calculated at the DLPNO-CCSD(T)/Basis2//M06-2X/Basis1 and DLPNO-CCSD(T)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) levels, respectively. The calculations are performed at 263.15 K and 1 atm.

Since dimer formation is the critical first step of cluster formation and the dimer contains the simplest interaction between two monomers, the ΔG values and interaction patterns of (HIO2)2, (HIO3)2, and (HIO3)1(HIO2)1 are further analyzed here. As can be seen in Figure A, ΔG values decrease in the order (HIO3)2 (−11.42 kcal mol–1) > (HIO3)1(HIO2)1 (−18.29 kcal mol–1) > (HIO2)2 (−19.24 kcal mol–1). Therefore, HIO2 has a stronger ability to bind with HIO3 and HIO2, compared with HIO3, in agreement with the observation that HIO2-rich clusters are more stable. It deserves mentioning that the ΔG of the identified (HIO3)1(HIO2)1 is lower than previously reported one[44] and the identified (HIO2)2 is the same as that in a previous study[42] (see details for geometries and ΔG values in Table S4). As can be seen in Figure , (HIO2)2 contains only two XBs, while (HIO3)1(HIO2)1 contains proton-transfer-induced electrostatic attraction plus one HB and one XB, and (HIO3)2 contains two XBs and one HB. Therefore, the XB strength between two HIO2 is much stronger than that between two HIO3, indicating the higher XB formation ability of HIO2 compared with HIO3 in the formation of (HIO3)(HIO2) (m = 1–4, n = 1–4). The stronger XB strength between two HIO2 compared with that between two HIO3 is supported by their shorter XB bond length and smaller energy gap between antibonding orbital δ* (O–I) and lone-pair orbital LP(O), which are two critical molecular orbitals for forming XB (Table S5). We also located the (HIO3)1(HIO2)1 conformer with only two XBs, which has higher ΔG than the global minimum with proton-transfer-induced electrostatic interaction, one HB and one XB. This indicates that proton-transfer-induced electrostatic attraction plays a more important role than XB in the formation of (HIO3)1(HIO2)1, highlighting the critical role of the basicity of HIO2. All in all, the basicity of HIO2 and the stronger XB formation ability together explain the key role of HIO2 in the iodine oxoacid nucleation.

Evaporation Rates

The stability of clusters can be evaluated by their evaporation rates, and the difference between evaporation and collision rates (which are determined by ambient vapor concentrations) will determine whether a cluster shrinks or grows. Generally, the slower the evaporation rate is, the greater the cluster stability is.[24,60,61] As shown in Figure A, all clusters except (HIO3)2 and (HIO3)3, have an evaporation rate below 1 s–1 at 263.15 K. Notably, more than half of the clusters have evaporation rates on the order of 10–3–10–10 s–1, indicating their high stability. The iodine oxoacid system has a larger number of stable clusters within a 4 × 4 box compared with the widely studied SA/MSA–base systems.[60,62] The stable clusters consist of two types: (1) homomolecular clusters, i.e., (HIO2)2, (HIO2)3, and (HIO3)4, and (2) heteromolecular clusters, i.e., (HIO3)1(HIO2)1, (HIO3)1(HIO2)2, (HIO3)2(HIO2)1, (HIO3)2(HIO2)3, (HIO3)3(HIO2)2, (HIO3)3(HIO2)3, (HIO3)3(HIO2)4, (HIO3)4(HIO2)3, and (HIO3)4(HIO2)4, which lie on the diagonal line or its adjacent sites, and (HIO3)4(HIO2)2, which lies far from the diagonal line. Therefore, the location of stable clusters within a 4 × 4 box for the iodine oxoacid system differs from that of the SA/MSA–base systems, where stable clusters lie on or closely below the diagonal line.[24,60−62] The difference in the distribution of stable clusters between the iodine oxoacid system and MSA/SA–base systems mainly results from the difference in the binding ability of the “base” molecules. HIO2 has strong binding with itself and with HIO3, while other atmospheric bases have weak binding with themselves and only have strong binding with acids. The greater number of stable clusters and their unique distribution provide the iodine oxoacid system with a much more flexible pathway for cluster growth than the SA/MSA–base systems (see the Cluster Growth Pathway section). In addition, the evaporation rates of all clusters above the diagonal line are significantly lower than those of the corresponding clusters below the diagonal line (except clusters (HIO2)4, (HIO3)1(HIO2)4, (HIO3)2(HIO2)4, and (HIO3)2(HIO2)3), implying that HIO2-rich paths can compete for nucleation despite their lower vapor concentrations. We note that a recent study employed master equation methods to calculate the collision rate coefficient and evaporation rate for the formation of (HIO3)2 and (HIO3)1(HIO2)1 dimers.[36] Their collision rate coefficients are lower and their evaporation rates are higher than the values provided in this study (Table S6).

Figure 3

Evaporation rates of the (A) (HIO3)(HIO2) and (B) (SA)(DMA) (original data adopted from Xie et al.[60]) clusters (m = 0–4, n = 0–4) at 263.15 K and 1 atm.

Cluster Formation Rate

Our calculated cluster formation rates (J) for iodine oxoacids at atmospheric [HIO3] and [HIO2] are presented in Figure A. J increases steeply with [HIO3] and [HIO2]; an increase of either [HIO3] or [HIO2] by one order of magnitude, while keeping the other constant, leads to an increase of 18–8786 times in J. To underscore the fast cluster formation rates of iodine oxoacids, we show in Figure B comparable theoretical calculations of the nucleation rates of SA–DMA and SA–NH3 at the same temperature (263.15 K) and CS (2 × 10–3 s–1). In Figure B, we determine the iodine oxoacid cluster formation rates under two conditions. In condition 1 (blue curve), all precursor concentrations correspond to their ambient range, thus showing the difference in their cluster formation ability in the atmosphere. In condition 2 (red curve), [HIO3] is set equal to [SA] and [HIO2] is set equal to [DMA], thus showing the difference in their intrinsic cluster formation ability (mainly determined by cluster formation free energies). As seen in Figure B, J for SA–DMA is higher than that for iodine oxoacids under condition 1, indicating that the overall cluster formation ability of SA–DMA is stronger than that of iodine oxoacids under ambient conditions. Under condition 2, J for SA–DMA is lower than that for iodine oxoacids, especially under low [SA] or [HIO3], indicating the lower intrinsic cluster formation ability of SA–DMA compared with that of iodine oxoacids. This comparison shows that the availability of either HIO2 or DMA is the main determinant of whether iodine oxoacids or SA–DMA, respectively, is the faster nucleation mechanism. Moreover, since both HIO3 and HIO2 originate from the same iodine sources, there is a high probability that, when one is present, both are present, which favors iodine oxoacid nucleation. Additionally, the J value for iodine oxoacids at [HIO2] = 4.32 × 105 cm–3 is much faster than that for SA–NH3 at [NH3] = 100 ppt (about 2.79 × 109 cm–3 at 263.15 K) for [HIO3] and [SA] over the range 106 to 108 cm–3. Therefore, the cluster formation capability of iodine oxoacids is expected always to be larger than that of SA with 100 ppt NH3, which is consistent with CLOUD measurements.[35] In addition, it was found that the selection of CS value does not significantly change the revealed trend for the formation rates of these three systems by test simulations with CS = 2 × 10–2 s–1 and 2 × 10–4 s–1 (Figure S2).

Figure 4

Comparison of neutral iodine oxoacid cluster formation rates (J) with neutral SA–NH3/DMA cluster formation rates at 263.15 K and CS = 2 × 10–3 s–1. (A) Iodine oxoacid cluster formation rates versus [HIO3] and [HIO2] and (B) comparison of iodine oxoacid cluster formation rates with SA–NH3/DMA cluster formation rates. The SA–DMA rates and SA–NH3 rates are calculated based on ΔG values from the DLPNO-CCSD(T)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level (also applying quasi-harmonic correction).[60] The curves in panel (A) follow a power law, J ∝ [HIO3], with fitted slopes n of 1.7 ± 0.15 ([HIO2] = 106 cm–3), 2.8 ± 0.15 ([HIO2] = 105 cm–3), and 3.5 ± 0.04 ([HIO2] = 104 cm–3).

Cluster Growth Pathway

Figure shows iodine oxoacid cluster growth pathways at 263.15 K (−10 °C) with [HIO3] = 1.42 × 107 cm–3, [HIO2] = 4.32 × 105 cm–3 (under the same concentrations as an experiment from CLOUD (Table S2)), and CS = 2 × 10–3 s–1. The cluster growth pathway is mainly driven by heteromolecular collisions involving HIO3 and HIO2, with a minor channel of homomolecular HIO2 collisions. Homomolecular HIO3 collisions have a negligible contribution to neutral iodine oxoacid cluster growth during nucleation, consistent with CLOUD results.[35] After dimer formation, the major growth pathway becomes complicated. The (HIO3)1(HIO2)1 dimer collides with HIO2 or HIO3 to form the (HIO3)1(HIO2)2 or (HIO3)2(HIO2)1 trimer. Growth from the heteromolecular trimers continues via various pathways, eventually producing (HIO3)4(HIO2)2, (HIO3)4(HIO2)3, and (HIO3)4(HIO2)4 clusters. It deserves mentioning that the collision with small-sized clusters, i.e., (HIO3)1(HIO2)1, (HIO3)2(HIO2)1, or (HIO3)1(HIO2)2, is involved in the cluster growth besides collision with monomers. Previous studies also found that small clusters accelerate cluster growth in some cases of the SA–base, MSA–base, and HIO3–NH3 systems.[41,61,62] In most of the previous studies,[24,60−62] only coagulations of clusters on the diagonal line contribute to cluster growth, with smaller contributions of clusters immediately below the diagonal line. Surprisingly, it is found that three clusters far from the diagonal line ((HIO3)4(HIO2)2, (HIO3)2(HIO2)4, and (HIO3)1(HIO2)3) also contribute to cluster growth. The (HIO3)4(HIO2)2 cluster can directly collide with clusters to grow out of the 4 × 4 box, which accounts for 11% of the cluster formation rate. Alternatively, the (HIO3)4(HIO2)2 cluster can collide with HIO2 to form (HIO3)4(HIO2)3, which in turn has two growth pathways: the first is the collision with clusters such as (HIO3)1(HIO2)1 and (HIO3)2(HIO2)1, and the other is sequential addition of HIO2 and then HIO3 to finally form the (HIO3)5(HIO2)4 cluster, to grow out of the 4 × 4 box. The primary growth pathways emerging from (HIO3)4(HIO2)2–4 clusters contribute at least 95% to the overall cluster formation rate. The above cluster growth features for the iodine oxoacid system differ significantly from SA/MSA–base cluster formation mechanisms, which follow a more restricted stoichiometric path.[24,60−62] In addition, it was found that the selection of the temperature and concentration of precursors can affect the growth pathways, while the growth was still dominated by mixed HIO3–HIO2 clusters by test simulation at different temperatures and concentrations of precursors (Figures S3–S5).

Figure 5

Neutral iodine oxoacid cluster growth pathways at T = 263.15 K with [HIO3] = 1.42 × 107 cm–3, [HIO2] = 4.32 × 105 cm–3, and CS = 2 × 10–3 s–1. The dark red lines give the dominant growth paths between clusters, the arrows indicate the direction of the flux, and the numbers represent the contribution percentage of a small cluster to a larger cluster along the direction of the arrow. The pathways contributing less than 10% to the flux of the cluster are not shown for clarity.

Comparison with the CLOUD Experiment

To validate the predicted cluster concentrations and formation rates, here we compare our results with CLOUD measurements. The cluster formation rates at 1.7 nm of iodine oxoacids (HIO2–3) have been presented in a recent CLOUD study.[35] Additionally, the (HIO3)1(HIO2)1 dimer concentration ([(HIO3)1(HIO2)1]) from the same set of experiments are reported here (Table S2). To compare with the experimental data, we have calculated J and [(HIO3)1(HIO2)1] under the same conditions as the CLOUD experiments, including precursor concentrations, wall loss rates for individual clusters, and temperatures. The iodine oxoacid cluster formation rates at +10 and −10 °C, from both the CLOUD study and this study are shown in Figure . For comparison, we also show in Figure the simulated J for pure HIO3 clusters ((HIO3)1–4) and pure HIO2 clusters ((HIO2)1–4). In Figure , we show the calculated concentrations of homomolecular dimers ((HIO3)2 and (HIO2)2) and the heteromolecular dimer ((HIO3)1(HIO2)1) together with the [(HIO3)1(HIO2)1] measured by CLOUD.

Figure 6

Measured (CLOUD) and simulated (ACDC) neutral cluster formation rates J versus (A) [HIO3] and (B) [HIO2] at +10 °C (red symbols) and −10 °C (blue symbols). The hollow diamonds show iodine oxoacid cluster formation rates from CLOUD. The filled symbols show cluster formation rates from ACDC simulations based on our quantum chemical calculations: iodine oxoacid clusters (filled diamonds), pure HIO3 clusters (filled pyramids), and pure HIO2 clusters (filled inverted pyramids).

Figure 7

Measured (CLOUD) and simulated (ACDC) dimer concentrations ([(HIO3)1(HIO2)1], [(HIO3)2], and [(HIO2)2]) versus [HIO3] × [HIO2] (cm–6) at +10 °C (red symbols) and −10 °C (blue symbols). The hollow diamonds show [(HIO3)1(HIO2)1] measured by CLOUD. The filled symbols show dimer concentrations from ACDC simulations based on our quantum chemical calculations: filled diamonds for [(HIO3)1(HIO2)1], filled pyramids for [(HIO3)2], and filled inverted pyramids for [(HIO2)2].

As seen in Figure , the calculated J for iodine oxoacid clusters are one to four orders of magnitude faster than those for pure HIO3 and pure HIO2 clusters. This indicates that HIO3–HIO2 neutral cluster formation will dominate over HIO3–HIO3 and HIO2–HIO2 neutral cluster formation, as found experimentally by He et al.[35] The same conclusion can be drawn from the high [(HIO3)1(HIO2)1] seen in Figure ; the concentrations of (HIO3)1(HIO2)1 dimers are one to three orders of magnitude higher than those of (HIO3)2 or (HIO2)2 dimers. At −10 °C, the ratio of the calculated J divided by the measured J has a median value of 0.49 (Figure S6), a good agreement considering the systematic errors in both the experiments and our calculations (see below). Additionally, the calculated [(HIO3)1(HIO2)1] are in good agreement with the CLOUD experiments at −10 °C, with a median ratio of 1.07 (the ratio of the calculated [(HIO3)1(HIO2)1] divided by the measured value) (Figure S7). The good agreement on [(HIO3)1(HIO2)1] also suggests that (HIO3)1(HIO2)1 is well captured by the nitrate-CIMS and it is unlikely a surrogate for other iodine species as suggested by a recent study.[37] Although the agreement between our calculations and the CLOUD data is good at −10 °C, the agreement is poorer at +10 °C, but nevertheless acceptable within theoretical and experimental uncertainties (see below). The median J ratio (ACDC/CLOUD) is 56 (Figure S6) but reaches as high as 789. The calculated [(HIO3)1(HIO2)1] at +10 °C are also higher than the measured values, with the highest ratio of 8.6 (Figure S7).

The poorer prediction for [(HIO3)1(HIO2)1] and J at +10 °C implies that the temperature dependency of the nucleation rate may not be well presented in ACDC. To assess this hypothesis, we examine the prediction of ACDC against SA–NH3 nucleation rates obtained from CLOUD at different temperatures.[63] We find that predicted nucleation rates present much better consistency with the experimental results from CLOUD at −10, −30, and −50 °C than they do at +10 °C (Figure S8). This suggests that the temperature dependencies of both the iodine oxoacid and SA–NH3 systems are not accurately represented at present in ACDC, especially at +10 °C and potentially also in warmer conditions. Therefore, the temperature dependency of the quantum chemical calculations + ACDC methods and their comparison with experimental results warrant further study in the future. It is worth noting that despite the seemingly large difference factors at +10 °C, the agreement between our calculations and CLOUD is considered reasonable considering the J uncertainty of at least one order of magnitude in our simulations and a comparable uncertainty in CLOUD due to measurement uncertainties on vapor and particle concentrations. Moreover, when compared with those from previous studies,[14,40,42] the nucleation rates calculated here show significantly improved agreement with the CLOUD experimental data.

Implications

Our study reveals that the mixture of HIO3 and HIO2 vapors has an extremely high potential to form molecular clusters. We find that the iodine oxoacid system is even more (intrinsically) efficient for particle nucleation than the SA–DMA system, which is known to introduce rapid nucleation in urban environments.[53] Owing to the lower concentrations of HIO2, the overall nucleation rates observed from the iodine oxoacid system in pristine atmospheres are lower than that of SA–DMA observed in the polluted boundary layer. However, in pristine marine areas where base vapors are scarce, iodine oxoacid nucleation may provide the dominant source of new particles. Furthermore, since both HIO3 and HIO2 derive from the same precursor vapors, they are naturally found together, in contrast with SA and DMA/NH3, which are emitted by unrelated sources. That makes iodine oxoacid nucleation an especially efficient source of new particles in pristine areas.

Our study reveals the unexpected base behavior of HIO2 (accepting a proton from HIO3) and the stronger halogen bonding of HIO2 compared with that of HIO3. These characteristics produce highly stable HIO3–HIO2 clusters. The base behavior and strong halogen bonding of HIO2 suggest that it may potentially be able to stabilize other organic and inorganic acids to form particles. Combined with the fact that iodine levels have tripled since the 1950s because of the anthropogenic ozone increases and thinning sea ice,[64−66] iodine oxoacid nucleation could become more important than what we thought, especially in the regions of the atmosphere where iodine oxoacids and organic and inorganic acids can coexist and base vapors such as ammonia and amines are scarce. This warrants further studies on a potentially wider role of iodine oxoacids in aerosol nucleation of marine atmospheres. In addition, this study provides necessary thermodynamic data for the three branches of neutral iodine oxoacid cluster formation, which can be parameterized for simulating iodine oxoacid particle formation in the climate models in the future.