Altitude-dependent role of nitric acid in iodic acid-iodous acid nucleation: from marine boundary layer catalyst to upper troposphere core component

With global sulfur emissions declining and concurrent marine iodine emissions rising, new particle formation (NPF) driven by iodic acid (HIO₃) and iodous acid (HIO₂) has become critical to global aerosol and cloud condensation nuclei (CCN) budget. However, the role of ubiquitous nitric acid (HNO₃) in this iodine-driven nucleation across altitudes from the marine boundary layer (MBL) to the upper troposphere (UT) remains poorly understood. Here, we integrated quantum chemical calculations with Atmospheric Cluster Dynamics Code (ACDC) simulations to unravel the altitude-dependent enhancement mechanism by which HNO₃ enhances HIO₃–HIO₂ nucleation. Under MBL conditions, HNO₃ acts as a catalyst to promote nucleation via collision and re-evaporation processes, yielding a modest 2–3-fold enhancement in nucleation. In contrast, as altitude increases to the UT, where cluster evaporation is effectively suppressed by low temperature, HNO₃ becomes a core component of nucleation clusters, driving a 200-fold enhancement on the cluster formation rate. Consequently, the simulated cluster formation rates of the HNO₃–HIO₃–HIO₂ mechanism reach 10³–10⁴ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}$, exceeding those of the well-documented H₂SO₄–NH₃–HNO₃ mechanism under comparable UT conditions. Our findings establish HNO₃ as a critical atmospheric agent that amplifies iodine oxoacid nucleation across altitudes, providing a critical chemical explanation for intense NPF events in both polluted coastal regions and the UT. This altitude-dependent role of HNO₃ links marine iodine emissions to troposphere-wide particle formation, with important implications for global CCN budgets and the refinement of climate models.

1 Introduction

Atmospheric aerosols exert critical impacts on air quality, human health, and global climate change (Haywood and Boucher, 2000; Pope and Dockery, 2006; Fan et al., 2016; Hirshorn et al., 2022), primarily by acting as cloud condensation nuclei (CCN) that modulate cloud microphysics (Fan et al., 2016; Li et al., 2022). New particle formation (NPF) accounts for ∼ 50 % of global CCN (Kulmala et al., 2013; Williamson et al., 2019) and is the dominant particle source in the upper troposphere (UT) (Gordon et al., 2017), thus serving as a key process linking atmospheric chemistry to climate regulation. Nucleation is recognized as the key step in NPF processes (Zhang, 2010; Kulmala et al., 2013). Due to the chemical complexity of nucleation precursors and the sensitivities to ambient conditions, identifying molecular-level mechanisms during the critical nucleation stage remains a persistent challenge in atmospheric chemistry (Zhang et al., 2012).

Conventional sulfuric acid (H₂SO₄)-dominated nucleation mechanisms fail to account for the observed concentrations of particulate matter in the boundary layer and cloud condensation nuclei in the upper troposphere (Williamson et al., 2019). With declining global sulfur emissions (Aas et al., 2019) and rising marine iodine emissions (Cuevas et al., 2018; Legrand et al., 2018), recent studies have identified marine-derived iodine oxoacids, iodic acid (HIO₃) (Sipilä et al., 2016) and iodous acid (HIO₂) (He et al., 2021), as important nucleation precursors in marine (Liu et al., 2023; Bai et al., 2025), polar (Baccarini et al., 2020; He et al., 2021; Li et al., 2024a), and even high-altitude environments (Koenig et al., 2020; Salignat et al., 2024; Li et al., 2024a). Studies show that HIO₃ and HIO₂ can form stable clusters via acid–base interactions and halogen bonds (Liu et al., 2023; Ma et al., 2023). However, this binary HIO₃–HIO₂ nucleation mechanism alone cannot explain the intense NPF events observed in polluted coastal regions (e.g., Zhejiang, China), suggesting that additional atmospheric species may participate in and promote iodine oxoacid-driven nucleation processes (Yu et al., 2019; Ma et al., 2023), yet these species remain unidentified and uncharacterized.

Nitric acid (HNO₃) is one of the most widespread and abundant inorganic acids in the atmosphere, present throughout the marine boundary layer (MBL) and upper troposphere (UT), with sources including anthropogenic emissions (Wang et al., 2021) and natural processes such as lightning (Tost, 2017). Previous studies have confirmed that HNO₃ stabilizes atmospheric molecular clusters via hydrogen bonds and proton-transfer driven electrostatic interactions in both H₂SO₄–dimethylamine (DMA) (Liu et al., 2021) and H₂SO₄–NH₃ (Liu et al., 2018; Wang et al., 2022) nucleation systems, and since iodine oxoacids readily form hydrogen- and halogen-bond networks, the ubiquitous and co-located HNO₃ is a strong candidate for the additional species that promotes iodine-driven nucleation (Zhang et al., 2024; Zu et al., 2024a, b). Importantly, HNO₃ and iodine precursors extensively coexist across altitudes. Specifically, nitrate and iodate are simultaneously detected in the free troposphere (FT) (Frege et al., 2017), and both iodine species (Koenig et al., 2020) and HNO₃ are observed in the UT (Jurkat et al., 2014). However, nitrate-based chemical ionization, commonly used for neutral cluster detection, tends to mask HNO₃'s involvement in iodine-driven nucleation (Sipilä et al., 2016), leaving its molecular mechanism and environmental dependence unclear.

Notably, atmospheric temperature, condensation sink, and precursor concentrations vary sharply with altitude, giving rise to strong altitude-dependent behavior in atmospheric nucleation. To date, no study has revealed how HNO₃ regulates iodine oxoacid nucleation from the MBL to the UT. Consequently, fundamental questions remain unanswered: Can HNO₃ interact with HIO₃ and HIO₂ to form critical nucleation clusters? What is the molecular mechanism by which HNO₃ interacts with HIO₃–HIO₂ clusters? How does the role of HNO₃ in HIO₃–HIO₂ nucleation shift with altitude from the MBL to the UT? Answering these questions will help us elucidate how marine iodine emissions shape troposphere-wide NPF and the global CCN budget under the sulfur emission reduction.

Here, we combine high-level quantum chemical calculations and Atmospheric Cluster Dynamics Code (ACDC) (McGrath et al., 2012) simulations to systematically unravel the altitude-dependent mechanism of the role of HNO₃ in HIO₃–HIO₂ nucleation. We reveal the molecular nature of iodine-containing cluster stabilization by HNO₃, quantify nucleation rates and pathway evolution along the vertical atmospheric profile, and evaluate the new mechanism against classic nucleation schemes. Our results establish the functional transition of HNO₃ from a catalyst in the MBL to a core cluster component in the UT, providing critical theoretical support for interpreting global iodine-driven NPF and improving aerosol representations in climate models.

2 Methods

2.1 Configurational sampling workflow

This study employed a multi-step computational workflow to optimize configurations and calculate energies for (HNO₃)_x(HIO₃)_y(HIO₂)_z clusters ($\mathrm{2}\le x+y+z\le \mathrm{6}$, $\mathrm{1}\le x\le \mathrm{3}$). The constraint of $\mathrm{1}\le x\le \mathrm{3}$ is applied because HNO₃ exhibits a relatively weak self-binding ability (Liu et al., 2021; Zu et al., 2024b), requiring the participation of HIO₂ to form stable clusters. The initial structures of (HIO₃)_y(HIO₂)_z ($\mathrm{2}\le y+z\le \mathrm{6}$) clusters were adopted from our previous study (Liu et al., 2023; Zu et al., 2024a). Initially, the ABCluster program (Zhang and Dolg, 2015) with the UFF force field (Rappe et al., 1992) was employed to systematically generate initial configurations, yielding 5000 low-energy candidate structures for each cluster. Given the inability of the Universal Force Field (UFF) to describe proton transfer, ions in distinct protonation states were utilized to model hydrogen bonding and proton transfer (Kubečka et al., 2019). The ionic species considered include ${\mathrm{IO}}_{\mathrm{3}}^{-}$, ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and the protonated counterpart ${\mathrm{H}}_{\mathrm{2}}{\mathrm{IO}}_{\mathrm{2}}^{+}$. These structures were then subjected to preliminary optimization with the PM7 (Stewart, 2013) semi-empirical method in MOPAC2016 program (Stewart, 2016) to filter for 100 low-energy configurations. Despite exhaustive sampling within the computational budget, selecting the lowest 100 configurations based on PM7 calculations may still result in the true global minimum being missed (Kurfman et al., 2021). In addition, we manually constructed a set of candidate structures with multiple hydrogen- and halogen-bonding structures based on chemical intuition. All subsequent Density Functional Theory (DFT) optimizations were performed with the Gaussian 09 (Frisch et al., 2009), consistently using the ωB97X-D functional and a FineGrid for integration, which has been benchmarked and widely adopted for describing noncovalent interactions in atmospheric molecular clusters (Elm et al., 2013). This DFT stage proceeded in two steps with different basis sets. First, the 100 most stable configurations were reoptimized using the 6-31+G^∗ (for H, O, and N) + Lanl2DZ (for I) basis sets (Elm and Kristensen, 2017). Subsequently, a final high-precision reoptimization with tight convergence criteria was performed on the 10 most stable isomers. To ensure accuracy for atmospheric systems, the 6-311++G(3df,3pd) basis set was assigned to H, O, and N, in combination with the aug-cc-pVTZ-PP basis set and ECP28MDF for I (Francl et al., 1982; Peterson et al., 2003). As demonstrated by previous benchmark studies, this combination provides highly reliable estimates of binding energies (Elm et al., 2012, 2013). Vibrational frequency calculations were performed at this final level to confirm the optimized structures were true energy minima.

2.2 Quantum Chemistry Calculation

The Gibbs free energies (ΔG, kcal mol⁻¹) of the optimized clusters at a reference pressure of 1 atm were calculated using the following equation:

$$\begin{array}{}\text{(1)}& \mathrm{\Delta }G=\mathrm{\Delta }{E}_{\text{DLPNO-CCSD(T)}}+\mathrm{\Delta }{E}_{\text{SOC}}+\mathrm{\Delta }{G}_{\text{thermal}}^{\mathit{\omega }\text{B97X-D}}\end{array}$$

The terms in Eq. (1) were derived as follows: (1) The electronic energy term (ΔE_{DLPNO-CCSD(T)}), intended to refine binding energies with high accuracy, was obtained from the single point calculations using ORCA 5.0 program (Neese, 2012) at the DLPNO-CCSD(T)/aug-cc-pVTZ (for H, O, and N) + aug-cc-pVTZ-PP with ECP28MDF (for I) level of theory with TightPNO and TightSCF settings. (2) Spin-orbit coupling (SOC) effects play a significant role in the thermodynamic properties of atmospheric iodine species due to their heavy-atom nature, as previously demonstrated by foundational studies (Khanniche et al., 2016, 2017; Engsvang et al., 2024). In this study, the SOC correction (ΔE_SOC) was evaluated by computing the energy difference between calculations performed with and without SOC potential. These calculations were performed using Gaussian 16 (Frisch et al., 2016) at the ωB97X-D/6-311++G(3df,3pd) (for H, N and O) + dhfTZVP-2c (for I) level of theory (Chan and Yim, 2013; Kühn and Weigend, 2015; Sarr et al., 2021; Holzer et al., 2022). (3) Temperature-dependent free energy corrections ($\mathrm{\Delta }{G}_{\text{thermal}}^{\mathit{\omega }\text{B97X-D}}$) were computed at the ωB97X-D/6-311++G(3df,3pd) (for H, O, and N) + aug-cc-pVTZ-PP with ECP28MDF (for I) level. The Shermo 2.6 code (Lu and Chen, 2021) was used to calculate free energy values at specified atmospheric temperatures (204–288 K). The ΔG of the optimized clusters at various temperatures are summarized in Table S1 in the Supplement.

2.3 Wave Function Analysis

The wavefunction from quantum calculations was analyzed using Multiwfn 3.7 (Lu and Chen, 2012) with results visualized via VMD software (Humphrey et al., 1996), to investigate the intermolecular interactions responsible for the identified cluster conformations. Potential binding sites were identified by mapping the electrostatic potential (ESP) onto the Van der Waals (vdW) surface, defined by the 0.001 $\mathrm{a}.\mathrm{u}.$ electron density contour, to distinguish electron-rich (electronegative) and electron-deficient (electropositive) regions prone to noncovalent bonding. For quantitative evaluation of interaction strengths, the Atoms in Molecules (AIM) theory (Lane et al., 2013) was employed to calculate key topological properties at bond critical points (BCPs), including electron density ρ(r), Laplacian of electron density ∇²ρ(r), and local energy density H(r), as shown in Table S2.

2.4 Atmospheric cluster dynamics code (ACDC) simulation

To quantitatively investigate nucleation kinetics, including cluster formation rates and growth pathways, the ACDC (McGrath et al., 2012) was employed to numerically solve the birth-death equations (Eq. 2). These equations describe the temporal evolution of cluster concentrations by integrating collision, evaporation, source, and sink processes:

$$\begin{array}{}\text{(2)}& \begin{array}{rl}{\displaystyle \frac{\mathrm{d}{c}_i}{\mathrm{d}t}}=& {\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\sum _{j<i}{\mathit{\beta }}_{j,(i-j)}{c}_j{c}_{(i-j)}+\sum _j{\mathit{\gamma }}_{(i+j)\to i}{c}_{i+j}\\ & -\sum _j{\mathit{\beta }}_{i,j}{c}_i{c}_j-{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\sum _{j<i}{\mathit{\gamma }}_{i\to j}{c}_i+Q_i-S_i,\end{array}\end{array}$$

where c_i denotes the concentration of cluster i, ${\mathit{\beta }}_{j,(i-j)}$ represents the collision rate coefficient between clusters j and (i−j), and ${\mathit{\gamma }}_{(i+j)\to i}$ corresponds to the evaporation rate coefficient for cluster (i+j) dissociating into clusters i and j. External sources and size-dependent sinks are quantified by Q_i and S_i, respectively. Details for calculating ${\mathit{\beta }}_{j,(i-j)}$ and ${\mathit{\gamma }}_{(i+j)\to i}$ are presented in the Supplement. In the ACDC simulations, kinetically stable clusters are characterized as those capable of continuous growth rather than dissociation via evaporation, as quantified by the criterion $\mathit{\beta }c/\sum \mathit{\gamma }>\mathrm{1}$. Correspondingly, the boundary conditions are set as seven-molecule clusters, representing the smallest kinetically stable clusters that grow beyond the six-molecule simulation system. Boundary clusters were determined individually for each ACDC simulation: temperature-dependent β and ∑γ coefficients were first calculated for each cluster, and those satisfying the criterion $\mathit{\beta }c/\sum \mathit{\gamma }>\mathrm{1}$ at the given monomer concentration (c) were defined as boundary clusters. Here, the c denotes the gas-phase concentration of the actual colliding species (HNO₃, HIO₃, or HIO₂). Representative boundary conditions under various temperature and concentration scenarios are provided in Table S3.

To account for intermolecular vdW force enhancement, a factor of 2.3 was applied to β_i,j, consistent with prior simulations (Halonen et al., 2019). Additionally, a size-dependent sink term (Lehtipalo et al., 2016) S_i is used to quantify cluster losses:

$$\begin{array}{}\text{(3)}& S_i={\text{CS}}_{\text{ref}}\times (d_i/d_{\text{ref}}{)}^{-m},\end{array}$$

where d_i is the diameter of cluster i, CS_ref is the condensation sink for a reference monomer, and m is set to 1.7, which depends on scavenger distributions and is consistent with typical atmospheric aerosols (Lehtinen et al., 2007).

3 Results and Discussion

3.1 Molecular Interactions

The formation of thermodynamically stable atmospheric clusters is governed by intermolecular interactions between nucleation precursors, primarily hydrogen bonds (HB) and halogen bonds (XB). To identify potential binding sites between HNO₃ and iodine oxoacids, we analyzed their molecular electrostatic potential (ESP, Fig. S1 in the Supplement), which maps the electron-rich (electronegative) and electron-deficient (electropositive) regions on the molecular surface, where noncovalent bonds are prone to form. The ESP analysis indicates that HNO₃ can interact with iodine oxoacids through diverse bonding modes, reflecting its dual role as both a halogen bond acceptor and a hydrogen bond donor. For halogen bonding, the nitro oxygen atoms of HNO₃ exhibit a localized negative ESP (−18.7 kcal mol⁻¹), providing accessible sites to accept halogen bonds from the electrophilic iodine centers of HIO₃ and HIO₂. More importantly, the hydroxyl hydrogen of HNO₃ displays a highly positive ESP (+67.9 kcal mol⁻¹), which is significantly more electropositive than the hydroxyl hydrogen sites in HIO₃ (+59.1 kcal mol⁻¹) or HIO₂ (+57.3 kcal mol⁻¹). This enhanced electropositivity enables HNO₃ to act as a superior proton donor, favoring proton transfer to the electron-rich site during cluster formation.

Figure 1 Representative most stable structures of HNO₃–HIO₃–HIO₂ clusters identified at the ωB97X-D/6-311++G (3df, 3pd) (for H, N, and O atoms) and aug-cc-pVTZ-PP with ECP28MDF (for I atom) levels of theory. The complete set of all identified structures is provided in Fig. S2. The white, blue, red, and pink balls represent the H, N, O, and I atoms, respectively. The hydrogen bonds and halogen bonds are shown in dashed blue and purple lines, respectively.

To confirm the dominant binding modes, we employed a multi-step conformational search strategy, we identified the most stable configurations of (HNO₃)_x(HIO₃)_y(HIO₂)_z clusters ($\mathrm{2}\le x+y+z\le \mathrm{6}$, $\mathrm{1}\le x\le \mathrm{3}$) as shown in Fig. 1. In these optimized clusters, HNO₃ molecules form thermodynamically stable structures with iodine oxoacids (${\mathrm{HIO}}_{\mathrm{3}}/{\mathrm{HIO}}_{\mathrm{2}}$) via an interaction network bridged by hydrogen bonds and halogen bonds. Within this ternary system, HNO₃ and HIO₃ act as proton donors (acids), while HIO₂ serves as the proton acceptor (base) due to its stronger basicity relative to the acids. Both HNO₃ and HIO₃ undergo proton transfer to HIO₂, thereby forming ion pairs that substantially enhance cluster stability by strengthening electrostatic interactions.

To quantitatively characterize the strength of these intermolecular interactions, we performed AIM analysis (Table S2). The results confirm that HNO₃ acts primarily as a hydrogen bond donor rather than a halogen bond acceptor. HNO₃ accounts for 80 % of all HBs, the majority of which are medium-strength bonds (Emamian et al., 2019) (68.3 % exhibit binding energies of 12.0–24.0 kcal mol⁻¹, with ∇²ρ(r) > 0 and H(r) < 0). These HBs are comparable in strength to those formed between iodine oxoacids themselves, highlighting HNO₃'s contribution to the hydrogen bonding network. By comparison, HNO₃ contributes 37 % of all XBs in the ternary clusters. The N–O⋯I XBs formed between HNO₃ and iodine oxoacids are weaker (average ρ(r): 0.036 $\mathrm{a}.\mathrm{u}.$; average bond length: 2.7 Å) than the XBs formed between iodine oxoacids (average ρ(r): 0.054 $\mathrm{a}.\mathrm{u}.$; average bond length: 2.4 Å).

Figure 2 (a) Gibbs free energies of formation (ΔG, kcal mol⁻¹) for the most stable six-molecule HNO₃–HIO₃–HIO₂ clusters at the DLPNO-CCSD(T)/aug-cc-pVTZ(-PP)//ωB97X-D/6-311++G(3df,3pd) + aug-cc-pVTZ-PP level of theory (288 K). (b) Minimum HNO₃ concentrations (c_boundary) required for six-molecule clusters to reach kinetic stability at various tropospheric temperatures, defined by the condition where the collision frequency equals the total evaporation coefficients (βc_boundary=Σγ). Clusters are sorted in ascending order of c_boundary. Since pure iodine oxoacid clusters, such as (HIO₃)₃(HIO₂)₃, do not contain HNO₃, their evaporation rates cannot substitute for those of the clusters formed upon collision with HNO₃. Consequently, the c_boundary values for these HNO₃-free clusters are not provided here. Figure S4 presents data for clusters collisions involving other monomers (HIO₃ and HIO₂).

3.2 Cluster Stability

To elucidate the stability of the HNO₃-HIO₃-HIO₂ clusters, we evaluated their thermodynamic and kinetic properties (Fig. 2). Thermodynamic analysis reveals a distinct acid-base stoichiometry dependence of cluster stability (Fig. 2a). Consistent with established thermodynamic patterns in acid-base clustering (Olenius et al., 2013; Elm, 2017), six-molecule clusters with an acid-to-base ratio of 1:1 (HNO₃ and HIO₃ as acids, HIO₂ as base) exhibit the lowest Gibbs free energies of formation (ΔG). This 1:1 stoichiometry preference is consistent across all cluster sizes (Fig. S3). Notably, for clusters with fixed number of molecules and acid-base ratio, increasing the HNO₃ fraction elevates ΔG across all sizes (Fig. S3). This trend indicates that HNO₃–HIO₂ clusters and HNO₃–HIO₃–HIO₂ clusters are less thermodynamically stable than HIO₃–HIO₂ clusters, reflecting the combined effects of hydrogen bonding and halogen bonding on overall cluster stability.

While negative ΔG reflects the thermodynamic feasibility of cluster formation, the kinetic competition between collision–driven growth and evaporation–driven dissociation ultimately determines whether clusters can persist and grow into larger clusters. To assess kinetic feasibility, we calculated the minimum HNO₃ concentration required for clusters to achieve kinetic stability ($\mathit{\beta }{c}_{\text{boundary}}/\mathrm{\Sigma }\mathit{\gamma }=\mathrm{1}$, where collision rate equals evaporation rate) across tropospheric temperatures (228–288 K, Fig. 2b) (Dunne et al., 2016; Williamson et al., 2019). Above c_boundary, cluster growth dominates over dissociation, enabling persistent nucleation.

Figure 3 Heatmaps of cluster formation rates (J, in ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}$) as a function of HNO₃ and HIO₃ concentrations, simulated under various temperature (T) and CS conditions. The HIO₂ concentration was set to $\left[{\mathrm{HIO}}_{\mathrm{3}}\right]/\mathrm{50}$. J is represented by a color gradient from blue (10⁻¹³ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}$) to red (10⁷ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}$), with contour lines indicating J values of 10⁻⁹, 10⁻⁷, 10⁻⁵, 10⁻³, 10¹, 10³, and 10⁵ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}$.

For HNO₃-containing clusters, ambient HNO₃ concentrations (10⁸–10¹¹ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$), spanning clean polar regions to polluted coastal environments, universally exceed the c_boundary across all tropospheric temperatures. This confirms that HNO₃-containing clusters are kinetically viable for growth under real atmospheric conditions. Critical to our altitude-dependent hypothesis, c_boundary decreases sharply with declining temperature (Fig. 2b). For the (HNO₃)₁(HIO₃)₂(HIO₂)₃ cluster, c_boundary drops from ∼ 10⁹ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ at 288 K (MBL) to ∼ 10⁵ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ at 228 K (UT). This four-order-of-magnitude reduction demonstrates that high-altitude low temperatures drastically suppress cluster evaporation, allowing HNO₃ to more effectively stabilize clusters by lowering the concentration threshold for kinetic stability.

3.3 Cluster Formation Rates under Different Atmospheric conditions

The widespread coexistence of HNO₃ and iodine oxoacids (${\mathrm{HIO}}_{\mathrm{3}}/{\mathrm{HIO}}_{\mathrm{2}}$) across diverse atmospheric environments, from polluted coastal MBL to remote UT, motivates a systematic investigation of the cluster formation rate (J) of the HNO₃–HIO₃–HIO₂ ternary system under altitude-resolved tropospheric conditions (Fig. 3), focusing on how HIO₃'s contribution to J evolves with altitude. We selected four temperatures strictly matching tropospheric vertical gradients: 288 K (MBL), 268 K (polar boundary layer), 248 K (FT), and 228 K (UT) (Dunne et al., 2016). The condensation sink (CS), which quantifies cluster scavenging, was set to 1 × 10⁻² s⁻¹ (polluted MBL, high background aerosols) and 1 × 10⁻⁴ s⁻¹ (clean UT, low background aerosols) (Ranjithkumar et al., 2021), directly reflecting observed CS vertical trends. HNO₃ concentrations were set to 10⁸–10¹¹ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ (from remote polar regions (Honrath et al., 2002; Jones et al., 2014) to polluted coastal areas; Xu et al., 2018), and HIO₃ concentrations ranged between 10⁵ and 10⁸ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ (from inland to coastal environments), mirroring their observed environmental gradients (Sipilä et al., 2016). Given that HIO₂ and HIO₃ are homologous iodine species with co-varying concentrations, [HIO₂] was defined as a fraction of [HIO₃]. Reported $\left[{\mathrm{HIO}}_{\mathrm{3}}\right]/\left[{\mathrm{HIO}}_{\mathrm{2}}\right]$ ratios range from ∼ 20 to 100 (Sipilä et al., 2016; Baccarini et al., 2020; He et al., 2023), and we adopted a ratio of 50, consistent with field observations at Mace Head (Sipilä et al., 2016) and our previous studies (Li et al., 2024b; Zu et al., 2024a, b).

High-altitude environments drastically boost the ternary nucleation efficiency via the synergistic decline of temperature and CS with altitude. Thermodynamically, lower temperatures suppress cluster evaporation. At a constant CS ([HNO₃] = 10¹⁰ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$, and [HIO₃] = 10⁷ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$), the temperature decline from MBL (288 K) to UT (228 K) enhances J by more than four orders of magnitude (from ∼ 10¹ to ∼ 10⁵ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}$). Kinetically, the CS reduction from 1 × 10⁻² s⁻¹ (polluted lower atmosphere) to 1 × 10⁻⁴ s⁻¹ (clean UT) minimizes scavenging of nascent clusters. This enhancement is especially important at low iodine oxoacid and HNO₃ concentrations, where clusters form slowly and are therefore more easily scavenged.

Moreover, J exhibits a strong dependence on the concentrations of HNO₃ and iodine oxoacids. As expected, higher precursor concentrations lead to higher J. Notably, the system's sensitivity to nucleation precursor concentrations is strongly altitude-dependent, as visualized by J contour orientations (Fig. 3). In the MBL (e.g., 288 K), contours are nearly vertical, which indicates iodine oxoacids dominate nucleation, and HNO₃ only effectively enhances J at high HNO₃ concentrations (> 10¹⁰ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$). In contrast, as temperature decreases with increasing altitude, the contours gradually pivot towards the [HNO₃] axis. At typical UT temperatures (e.g., 228 K), the contour slope approaches −1 across all simulated CS values, demonstrating that HNO₃ exerts a pronounced influence over a broader concentration range than at lower altitudes. Consistent with this, HNO₃'s enhancement factor rises to ∼ 10² in the UT (Fig. S5), confirming its transition to a critical contributor to nucleation. Given the ppb-level HNO₃ concentrations observed in the UT, this enhanced sensitivity underscores the amplified importance of HNO₃ in iodine oxoacid nucleation at high altitudes.

High-altitude regions are critical for nucleation, as they significantly influence global CCN (Gordon et al., 2017). While HNO₃'s regulatory role is expected to be altitude-dependent, its quantitative variation across the troposphere remains unclear. To address this gap, we quantified the HNO₃–HIO₃–HIO₂ nucleation mechanism by simulating the evolution of its J along idealized and representative vertical atmospheric profiles. For clarity and ease of discussion, the vertical atmosphere was approximately stratified into the MBL (0–2 km), FT (2–12 km), and UT, (12–14 km), matching the concentration distributions of the nucleation precursors at different altitudes in the atmosphere (Jurkat et al., 2014).

A uniform temperature lapse rate of 6 K km⁻¹ (starting from 288 K at the surface) (Catling and Kasting, 2017) and a CS decline from 2 × 10⁻³ to 1 × 10⁻⁴ s⁻¹(Ranjithkumar et al., 2021), were applied to reflect the transition from particle–rich MBL to clean FT. Precursor vertical concentrations were constrained as follows: the HNO₃ concentration was set to 1 × 10¹⁰ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ in the MBL (anthropogenic coastal conditions), decreasing to 1 × 10⁹ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ in the FT, and increasing to a constant 5 × 10⁹ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ (sub-ppb to ppb level) in the UT (Jurkat et al., 2014). HIO₃ concentration was set to 1 × 10⁷ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ in the MBL (coastal emission hotspot) (Sipilä et al., 2016) and reduced by one order of magnitude in the FT. Due to limited field constraints on HIO₃ at high altitudes, its concentration was held constant above the FT. This assumption is based on the fact that the concentration of iodine monoxide (IO) radical, a key precursor of HIO₃ in the troposphere with relatively stable concentrations across altitudes (Koenig et al., 2020; Finkenzeller et al., 2023), exhibits an observed positive correlation with that of HIO₃ in the troposphere (Koenig et al., 2020; Finkenzeller et al., 2023). HIO₂ concentration was fixed at a ratio of 1/50 relative to HIO₃ across all altitudes, consistent with the conditions in Fig. 3.

Figure 4 Altitude-dependent simulation inputs and the corresponding cluster formation rates (J, ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}$). (a) Temperature; (b) CS; (c) HNO₃ concentration; and (d) HIO₃ concentration as functions of altitude. (e) J versus altitude for the HIO₃–HIO₂ (purple) and HNO₃–HIO₃–HIO₂ (blue) mechanisms, simulated under the vertical profiles in (a–d); dashed lines denote boundaries of the four altitude stages. (f) Altitude-dependent enhancement factor of HNO₃ (R, $J({\mathrm{HNO}}_{\mathrm{3}}-{\mathrm{HIO}}_{\mathrm{3}}-{\mathrm{HIO}}_{\mathrm{2}})/J({\mathrm{HIO}}_{\mathrm{3}}-{\mathrm{HIO}}_{\mathrm{2}})$) of HIO₃-HIO₂ nucleation by HNO₃.

Based on the above constrained simulation conditions, we partitioned the altitude–dependent evolution of J into four stages (Fig. 4e and f). In Stage 1 (0–2 km, from the MBL to the lower FT), as altitude increases, the suppressive effects of decreasing HNO₃ and HIO₃ concentrations outweigh the promoting effects of lower temperature and reduced CS, resulting in a J minimum. Near 2 km, J is ∼ 70-fold lower than that in the MBL. At this stage, the enhancement factor of HNO₃ (R, defined as $J({\mathrm{HNO}}_{\mathrm{3}}-{\mathrm{HIO}}_{\mathrm{3}}-{\mathrm{HIO}}_{\mathrm{2}})/J({\mathrm{HIO}}_{\mathrm{3}}-{\mathrm{HIO}}_{\mathrm{2}})$) is approximately 1.5–2, which indicates a modest promotional effect of HNO₃. In Stage 2 (2–12 km, FT), with precursor concentrations held constant, the continuous decline in temperature emerges as the dominant driver, boosting J for both the binary (HIO₃–HIO₂) and ternary (HNO₃–HIO₃–HIO₂) mechanisms. Notably, the ternary mechanism shows a steeper altitude-dependent increase in J, reflecting stronger HNO₃ stabilization at low temperatures, with R reaching 10² at 8 km. Comparison of altitude–dependent trends reveals distinct “sensitive zones” where J responds most sharply to altitude. For the binary HIO₃–HIO₂ mechanism, this zone is confined to a relatively narrow layer (8–10 km). By comparison, the J of the ternary HNO₃–HIO₃–HIO₂ mechanism not only achieves a higher peak but also sustains rapid growth over a broader vertical range (2–8 km), highlighting its efficacy across a wider altitude span. In Stage 3 (12–13 km, UT), J becomes less sensitive to further temperature decreases (Fig. S6). At these ultra-low temperatures, thermodynamically favorable HNO₃-containing clusters (e.g., HNO₃–HIO₂ clusters) are effectively stabilized against evaporation (Fig. 2b), while elevated UT HNO₃ becomes the key driver of enhancement. Under these conditions, the elevated HNO₃ concentrations in the UT, sustained by lightning–driven chemical production and long–range transport, become the key driver of R for HIO₃–HIO₂ nucleation, further elevating R. In Stage 4 (13–14 km, upper UT), J approaches a steady state as HNO₃ concentrations stabilize at ppb levels and temperature effects saturate.

Overall, J for both HIO₃–HIO₂ and HNO₃–HIO₃–HIO₂ mechanisms exhibit non-monotonic altitude profiles, declining from the MBL to ∼ 2 km then increasing toward the UT. Critically, while HNO₃'s enhancement on J is modest at lower altitudes, its influence increases significantly with altitude, particularly in the UT where the synergy of elevated HNO₃ concentrations and ultra-low temperatures strongly accelerates J. Deep convective systems can actively transport iodine oxoacids upward into the UT (Twohy et al., 2002; Randel et al., 2010; Williamson et al., 2019), while lightning-driven oxidation sustains ppb-level HNO₃; conversely, UT-nucleated particles may descend via large-scale subsidence to replenish lower-tropospheric CCN (Wang et al., 2016; Xiao et al., 2023; Mehra et al., 2026). Through this bidirectional vertical coupling, HNO₃ acts as a bridge between marine iodine emissions at the surface and particle formation across the full tropospheric column.

Figure 5 Altitude-dependent nucleation pathways and cluster composition under atmospheric conditions in Fig. 4. (a) Three primary nucleation pathways identified by ACDC simulations: binary HIO₃–HIO₂, ternary HNO₃–HIO₃–HIO₂, and binary HNO₃–HIO₂ pathway. (b) Branching ratios of the flux out for three nucleation pathways at different altitudes. (c) Number contributions of HNO₃, HIO₃, and HIO₂ molecules to the total outflux clusters at different altitudes. Left: HIO₃–HIO₂ mechanism; Right: HNO₃–HIO₃–HIO₂ mechanism.

3.4 Altitude-Dependent Nucleation Mechanisms

To uncover the molecular origin of HNO₃'s altitude-dependent enhancement, we analyzed the nucleation pathways of the HNO₃–HIO₃–HIO₂ system (Fig. 5). As illustrated in Fig. 5a, ACDC simulations identify three primary nucleation routes: the binary HIO₃–HIO₂ pathway, the ternary HNO₃–HIO₃–HIO₂ pathway, and the binary HNO₃–HIO₂ pathway. Their branching ratios evolve systematically with altitude, with HNO₃-involved pathways gaining dominance at higher altitude, directly reflecting HNO₃'s role transition (Fig. 5b). Specifically, the binary HIO₃–HIO₂ pathway dominates at 0–6 km; above 6 km, the ternary HNO₃–HIO₃–HIO₂ pathway takes the lead, while the binary HNO₃–HIO₂ pathway also begins to contribute. In the UT, the high concentration of HNO₃ drives the binary HNO₃–HIO₂ pathway to become predominant.

HNO₃ promotes nucleation via both direct and indirect pathways. Directly, as a core component, HNO₃ is stably incorporated into growing clusters. For instance, in the binary HNO₃–HIO₂ pathway, nucleation proceeds via the stepwise addition of (HNO₃)₁(HIO₂)₁ dimers to form (HNO₃)₂(HIO₂)₂ tetramers, which subsequently collide to exceed cluster size. Additionally, HNO₃ participates in forming kinetically stable clusters (e.g., (HNO₃)₁(HIO₃)₂(HIO₂)₃, (HNO₃)₂(HIO₃)₁(HIO₂)₃, and (HNO₃)₂(HIO₂)₄). Indirectly, as a catalyst, HNO₃ promotes nucleation via a collision–re-evaporation cycle. Specifically, HNO₃ forms intermediates with HIO₂ (e.g., (HNO₃)₁(HIO₂)₁). When these intermediates collide with iodine-containing clusters, HNO₃ molecule re-evaporates into the gas phase while HIO₂ is retained, efficiently transferring HIO₂ to particles and accelerating nucleation.

To further elucidate HNO₃'s role across altitudes, Fig. 5c presents the weighted average molecular composition of outflux clusters (weighted by pathway branching ratios), capturing its altitude-driven functional shift. In the low-to-mid troposphere (0–6 km), HNO₃ constitutes < 10 % of outflux clusters (dominated by ${\mathrm{HIO}}_{\mathrm{3}}/{\mathrm{HIO}}_{\mathrm{2}}$), confirming its catalytic role (collision-re-evaporation cycle), resulting in modest enhancement (< 10-fold). Above 6 km, the proportion of HNO₃ in outflux clusters rises steadily, exceeding 40 % in the UT, signaling its transition to a core component. This shift is accompanied by a much more significant promotional effect, with R reaching up to 200-fold (Fig. 4f).

The altitude-dependent role transition of HNO₃ is driven by the different temperature sensitivities of evaporation (far more sensitive) versus collision coefficients (Supplementary Methods). This temperature sensitivity leads to fundamentally different nucleation behaviors: at low altitudes, rapid evaporation ensures that only the most thermodynamically stable clusters survive; at high altitudes, suppressed evaporation shifts the controlling factor to precursor availability.

Figure 6 Cluster formation rates (J, ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}$) for HIO₃–HIO₂ (purple dashed line), HNO₃–HIO₃–HIO₂ (blue) and H₂SO₄–DMA or H₂SO₄–NH₃–HNO₃ (red) systems under the corresponding atmospheric conditions in (a) Zhejiang, where gray shaded areas represent locally observed cluster formation rates (Yu et al., 2019); (b) Mace Head, where the dashed line marks the upper limit of cluster formation rates reported in field observations (Sipilä et al., 2016); (c) Greenland; and (d) the UT.

At low altitudes (MBL), evaporation-limited conditions favor 1:1 acid-base stoichiometry (minimal evaporation rates, Fig. 5c) in both binary HIO₃–HIO₂ and ternary HNO₃–HIO₃–HIO₂ pathways. With increasing altitude and decreasing temperature, evaporation is suppressed and nucleation becomes collision-limited, favouring the most abundant species. For ternary nucleation mechanism, high HNO₃ concentrations (exceeding iodine oxoacids) drive more frequent HNO₃–HIO₂ collisions, making HNO₃–involved pathways dominant in the UT (Fig. 5b).

3.5 Comparison with Typical Nucleation Systems

To assess the atmospheric significance of the proposed HNO₃–HIO₃–HIO₂ mechanism and identify the specific environments where it plays a role, we compared it against well-established nucleation mechanisms. We selected four representative environments: a polluted coastal area (Zhejiang, China), a clean marine site (Mace Head, Ireland), a polar region (Greenland), and UT, encompassing pollution gradients (polluted-to-clean) and temperature ranges (high-to-low) to cover the core application scenarios of the nucleation mechanism. The comparison analysis included three key mechanisms: (1) the binary HIO₃–HIO₂ nucleation (purple dashed line, as a baseline), (2) the ternary HNO₃–HIO₃–HIO₂ nucleation proposed in this study (blue solid and dashed lines), and (3) the competing H₂SO₄-driven mechanism (i.e., H₂SO₄–DMA (Almeida et al., 2013) for polluted coastal regions or H₂SO₄–NH₃–HNO₃ for the UT; Wang et al., 2022) (red solid line). All data (Liu et al., 2018, 2021, 2023) related to quantum chemical calculations of the mechanisms were re-calculated at the same level of theory to ensure the result comparability.

For the polluted coastal environment of Zhejiang (Fig. 6a, 288 K, CS = 1.0 × 10⁻² s⁻¹(Ning et al., 2022), $\left[{\mathrm{HIO}}_{\mathrm{3}}\right]=\mathrm{5}\times {\mathrm{10}}^{\mathrm{6}}$ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$(He et al., 2021),) HNO₃ at the typical concentration (Xu et al., 2018) of 1 × 10¹⁰ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$ can enhance HIO₃–HIO₂ nucleation by 10-fold, consistent with its catalytic role in the MBL. Under extremely polluted conditions ($\left[{\mathrm{HNO}}_{\mathrm{3}}\right]=\mathrm{1}\times {\mathrm{10}}^{\mathrm{11}}$ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$), this enhancement reaches 10²-fold, enabling the HNO₃–HIO₃–HIO₂ mechanism to achieve better agreement with field observations (Yu et al., 2019) (gray shaded area in Fig. 6a). With ongoing global sulfur emission reductions, the HNO₃–HIO₃–HIO₂ mechanism emerges as an increasingly significant, and potentially dominant, pathway for NPF in polluted coastal regions. At the clean coastal site of Mace Head (Fig. 6b, 288 K, CS = 2.0 × 10⁻³ s⁻¹) (Sipilä et al., 2016), elevated ambient [HIO₃] (Heard et al., 2006) limits HNO₃'s contribution, leading to modest enhancement (< 1.5-fold). Both the HNO₃–HIO₃–HIO₂ and HIO₃–HIO₂ mechanisms generally reach, and at higher concentrations modestly exceed, the upper limit of field-observed cluster formation rates. This potential overestimation of J likely originates from methodological limitations: specifically, the finite seven-molecule boundary may not encompass the critical cluster size (Besel et al., 2020), and the applied quantum chemical level of theory might inherently produce slightly overbound clusters (Engsvang et al., 2024).

With decreasing temperature or increasing altitude, the enhancement effect of HNO₃ on HIO₃–HIO₂ nucleation becomes progressively pronounced. In the cold polar environment of Greenland (Fig. 6c, 268 K, CS = 1.0 × 10⁻⁴ s⁻¹), an [HIO₃] of 10⁶–10⁷ (Baccarini et al., 2020), HNO₃ can provide an enhancement of ∼ 2–3 times at typical ambient HNO₃ concentrations (e.g., 10⁹ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$) (Honrath et al., 2002). However, with increasing anthropogenic NO_x emissions from shipping activities due to Arctic warming (Dalsøren et al., 2013; Gong et al., 2018; Qi et al., 2024), local HNO₃ concentrations may rise significantly. Our simulations show that if local [HNO₃] reaches 10¹⁰ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$, the cluster formation rate of the ${\mathrm{HNO}}_{\mathrm{3}}-{\mathrm{HIO}}_{\mathrm{3}}-{\mathrm{HIO}}_{\mathrm{2}}$ mechanism can reach up to 10²–10⁴ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}$, an enhancement of 20-fold compared to the binary HIO₃−HIO₂ mechanism. Under cold Arctic conditions with a low condensation sink, cluster evaporation and scavenging losses are strongly suppressed, allowing HNO₃ to participate more effectively in cluster stabilization. Consequently, modest increases in HNO₃ concentrations from rising shipping NO_x emissions translate directly into substantial enhancements in the cluster formation rate. This significant enhancement highlights the potential importance of this mechanism for local NPF under the influence of high concentrations of anthropogenic NO_x.

In the UT (Fig. 6d, 228 K, CS = 1.0 × 10⁻⁴ s⁻¹) (Williamson et al., 2019), conventional pathways (e.g., pure HIO₃–HIO₂ nucleation) are inefficient (${\mathrm{10}}^{-\mathrm{3}}{\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}<J<{\mathrm{10}}^{\mathrm{2}}{\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}$). However, at the observed HNO₃ concentrations in the UT (∼ ppb levels, i.e., $\left[{\mathrm{HNO}}_{\mathrm{3}}\right]=\mathrm{5}\times {\mathrm{10}}^{\mathrm{9}}$ $\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}$) (Jurkat et al., 2014), J increases to 10³–10⁴ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}$, an enhancement of 10² to 10⁶ times over the pure HIO₃–HIO₂ mechanism, establishing HNO₃ as a core component of UT nucleation clusters. This rate far exceeds that of the reported H₂SO₄–NH₃–HNO₃ mechanism in this region (1–100 ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}$), establishing HNO₃–HIO₃–HIO₂ nucleation as the potentially critical nucleation pathway in the UT, supported by the enhanced stability of HNO₃–HIO₂ clusters at low temperatures (Tables S4 and S5).

In summary, the enhancement of HIO₃–HIO₂ nucleation by HNO₃ is widespread across diverse atmospheric environments, and it emerges as a potentially dominant mechanism under high-altitude or low-temperature conditions, consistent with its altitude-dependent functional transition from MBL catalyst to UT core component. In the context of SO₂ emission reductions, the high atmospheric abundance and broad spatial distribution of HNO₃ are anticipated to exert a profound and far-reaching impact on global NPF, highlighting the need to incorporate its altitude-dependent role into atmospheric models.

3.6 Uncertainty Analysis

To evaluate the robustness of our results, specifically HNO₃'s altitude-dependent transition from MBL catalyst to UT core component, we systematically analyzed uncertainties arising from two primary sources: quantum chemical calculations of Gibbs free energies of cluster formation (ΔG) and the atmospheric constraints on precursor concentrations (HIO₃ and HIO₂).

Regarding quantum chemical calculations, we examined the sensitivity of J to calculated ΔG variations by applying ± 1 kcal mol⁻¹ perturbations to all clusters (Fig. S8), a magnitude consistent with prior benchmarks showing that DLPNO-CCSD(T) typically exhibits a potential ΔE error of < 1 kcal mol⁻¹ relative to CCSD(F12^∗)/CBS results (Schmitz and Elm, 2020). These perturbations directly affect cluster stability: a +1 kcal mol⁻¹ shift destabilizes clusters and increases evaporation rates into monomers, while a −1 kcal mol⁻¹ shift enhances stabilization against evaporation (evaporation rate coefficient γ in Eq. S2 in the Supplement). Under MBL conditions, where HNO₃ acts primarily as a catalyst and cluster evaporation is inherently rapid, these perturbations significantly affect the enhancement factor (R) of HNO₃: +1 kcal mol⁻¹ shift reduces R to < 2, while −1 kcal mol⁻¹ shift increases it to > 10 (baseline R = 2–3). As indicated by prior benchmarks (Schmitz and Elm, 2020; Engsvang et al., 2024), the DLPNO-CCSD(T) method may slightly underestimate ΔG (i.e., over-bind the clusters). Therefore, the +1 kcal mol⁻¹ perturbation is likely the most realistic scenario. Notably, this sensitivity diminishes rapidly with the increasing altitude. In the UT, where HNO₃ serves as a core component and its evaporation is effectively suppressed, the impact of ΔG perturbations on J becomes negligible. This altitude-dependent sensitivity not only validates HNO₃'s functional transition (from MBL catalyst to UT core component), but also confirms its robust enhancement at high altitudes.

We further conducted sensitivity tests for the concentrations of HIO₂ and HIO₃ (Figs. S9 and S10) to assess the mechanism's applicability across varying atmospheric conditions. Consistent with the flux composition (Fig. 5c), the HNO₃–HIO₃–HIO₂ mechanism shows strong sensitivity to HIO₂ concentrations: HNO₃ enhances nucleation even at low [HIO₂], both J and R increase substantially with HIO₂ abundance. Although atmospheric HIO₂ concentrations remain poorly constrained, our simulated concentration ranges are consistent with CLOUD chamber observations under UT conditions (Shen et al., 2024). Furthermore, theoretical studies have confirmed HIO₂'s stability against tropospheric photolysis (De Souza and Brown, 2014) and oxidation (Khanniche et al., 2017), supporting the mechanism's robustness under realistic conditions.

It is also worth noting the potential uncertainties related to the relativistic effects. A recent benchmark (Engsvang et al., 2024) has demonstrated that the ZORA-DLPNO-CCSD(T) approach, which incorporates the zeroth-order regular approximation (ZORA) (Lenthe et al., 1993) provides thermodynamic estimates that are highly consistent with reference ZORA-CCSD(T) calculations. To address this, we performed single-point energy calculations at the ZORA-DLPNO-CCSD(T)/ma-ZORA-def2-TZVPP (for H, N, and O) (Neese, 2012) + SARC-ZORA-TZVPP (for I) (Rolfes et al., 2020) level of theory using the ORCA program. To provide more precise thermodynamic energies, the ZORA-corrected results are listed in Table S6 in the Supplement, and the subsequently simulated J are presented in Fig. S11 in the Supplement. Although it includes more comprehensive physical corrections, the ZORA-corrected energies tend to yield lower J values than the CLOUD measurements. Given that DLPNO-CCSD(T) method demonstrates closer agreement, we have retained it for single-point correction.

4 Conclusion

This study combines quantum chemical calculations and ACDC simulations, to elucidate the role of HNO₃ in iodine oxoacid nucleation, establishing an altitude-dependent HNO₃–HIO₃–HIO₂ nucleation mechanism. Specifically, at the molecular level, HNO₃ can stabilize HIO₃–HIO₂ clusters through a network of hydrogen bonding, halogen bonding, and proton transfer-driven electrostatic interactions. Thermodynamically, the stability of HNO₃-containing clusters exhibits a strong temperature dependence and increases significantly with decreasing temperature, which directly drives the altitude-dependent functional transition of HNO₃. Kinetically, the J shows a non-monotonic vertical profile governed by temperature, CS, and precursor concentrations.

In the low-altitude MBL, high temperatures drive rapid cluster evaporation, thus restricting HNO₃ to a catalytic role via a collision-re-evaporation cycle that confers modest J enhancement (∼ 1.5–2-fold). In the UT, low temperatures strongly suppress evaporation, allowing HNO₃ to serve as a core cluster component. This shift leads to the dominance of HNO₃-involved pathways and boosts the nucleation rate by up to 200-fold relative to the binary HIO₃–HIO₂ mechanism. Consequently, the simulated J reaches reaching 10³–10⁴ ${\mathrm{cm}}^{-\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}$ in the UT, exceeding the classic H₂SO₄–NH₃–HNO₃ nucleation pathway.

The proposed HNO₃–HIO₃–HIO₂ nucleation mechanism provides a new theoretical perspective for interpreting the intense NPF events in both polluted coastal regions and the upper troposphere. It grows in importance as global sulfur emissions decline, while also becoming relevant to rapid NPF in the Arctic under increasing anthropogenic nitrogen emissions. By mediating iodine nucleation across the troposphere, HNO₃ effectively links marine iodine emissions to troposphere-wide CCN production, with implications for cloud formation and Earth's radiative balance.

These findings highlight the critical need to incorporate altitude-dependent HNO₃-iodine nucleation into global climate and aerosol models. Future work should explore interactions with other atmospheric bases (e.g., ammonia, amines) and acids (e.g., organic acids, methanesulfonic acid), as well as joint laboratory, field, and modeling studies, to further constrain the role of HNO₃ in complex atmospheric environments.