This study employed a multi-step computational workflow to optimize configurations and calculate energies for (HNO3)x(HIO3)y(HIO2)z clusters (2≤x+y+z≤6, 1≤x≤3). The constraint of 1≤x≤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 (2≤y+z≤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 IO3-, NO3- and the protonated counterpart H2IO2+. 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.

The Gibbs free energies (ΔG, kcalmol-1) of the optimized clusters at a reference pressure of 1 atm were calculated using the following equation: 1ΔG=ΔEDLPNO-CCSD(T)+ΔESOC+ΔGthermalωB97X-D

The terms in Eq. (1) were derived as follows: (1) The electronic energy term (ΔEDLPNO-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 (ΔESOC) 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 (ΔGthermalωB97X-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.

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 a.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.

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: 2dcidt=12∑j<iβj,(i-j)cjc(i-j)+∑jγ(i+j)→ici+j-∑jβi,jcicj-12∑j<iγi→jci+Qi-Si, where ci denotes the concentration of cluster i, βj,(i-j) represents the collision rate coefficient between clusters j and (i-j), and γ(i+j)→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 Qi and Si, respectively. Details for calculating βj,(i-j) and γ(i+j)→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 βc/∑γ>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 βc/∑γ>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 βi,j, consistent with prior simulations (Halonen et al., 2019). Additionally, a size-dependent sink term (Lehtipalo et al., 2016) Si is used to quantify cluster losses: 3Si=CSref×(di/dref)-m, where di is the diameter of cluster i, CSref 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).

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 kcalmol-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 kcalmol-1), which is significantly more electropositive than the hydroxyl hydrogen sites in HIO3 (+59.1 kcalmol-1) or HIO2 (+57.3 kcalmol-1). This enhanced electropositivity enables HNO3 to act as a superior proton donor, favoring proton transfer to the electron-rich site during cluster formation.

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 (2≤x+y+z≤6, 1≤x≤3) as shown in Fig. 1. In these optimized clusters, HNO3 molecules form thermodynamically stable structures with iodine oxoacids (HIO3/HIO2) 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 kcalmol-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 a.u.; average bond length: 2.7 Å) than the XBs formed between iodine oxoacids (average ρ(r): 0.054 a.u.; average bond length: 2.4 Å).

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 (βcboundary/Σγ=1, where collision rate equals evaporation rate) across tropospheric temperatures (228–288 K, Fig. 2b) (Dunne et al., 2016; Williamson et al., 2019). Above cboundary, cluster growth dominates over dissociation, enabling persistent nucleation.

For HNO3-containing clusters, ambient HNO3 concentrations (10⁸–10¹¹ molec.cm-3), spanning clean polar regions to polluted coastal environments, universally exceed the cboundary 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, cboundary decreases sharply with declining temperature (Fig. 2b). For the (HNO3)1(HIO3)2(HIO2)3 cluster, cboundary drops from ∼ 10⁹ molec.cm-3 at 288 K (MBL) to ∼ 10⁵ molec.cm-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.

The widespread coexistence of HNO3 and iodine oxoacids (HIO3/HIO2) 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 molec.cm-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 molec.cm-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 [HIO3]/[HIO2] 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 molec.cm-3, and [HIO3] = 10⁷ molec.cm-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 cm-3s-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 molec.cm-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 molec.cm-3 in the MBL (anthropogenic coastal conditions), decreasing to 1 × 10⁹ molec.cm-3 in the FT, and increasing to a constant 5 × 10⁹ molec.cm-3 (sub-ppb to ppb level) in the UT (Jurkat et al., 2014). HIO3 concentration was set to 1 × 10⁷ molec.cm-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.

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(HNO3-HIO3-HIO2)/J(HIO3-HIO2)) 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.

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 HIO3/HIO2), 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.

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).

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), [HIO3]=5×106 molec.cm-3(He et al., 2021),) HNO3 at the typical concentration (Xu et al., 2018) of 1 × 10¹⁰ molec.cm-3 can enhance HIO3–HIO2 nucleation by 10-fold, consistent with its catalytic role in the MBL. Under extremely polluted conditions ([HNO3]=1×1011 molec.cm-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 molec.cm-3) (Honrath et al., 2002). However, with increasing anthropogenic NOx 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 molec.cm-3, the cluster formation rate of the HNO3-HIO3-HIO2 mechanism can reach up to 10²–10⁴ cm-3s-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 NOx 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 NOx.

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 (10-3cm-3s-1<J<102cm-3s-1). However, at the observed HNO3 concentrations in the UT (∼ ppb levels, i.e., [HNO3]=5×109 molec.cm-3) (Jurkat et al., 2014), J increases to 10³–10⁴ cm-3s-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 cm-3s-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.

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 kcalmol-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 kcalmol-1 relative to CCSD(F12^∗)/CBS results (Schmitz and Elm, 2020). These perturbations directly affect cluster stability: a +1 kcalmol-1 shift destabilizes clusters and increases evaporation rates into monomers, while a -1 kcalmol-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 kcalmol-1 shift reduces R to < 2, while -1 kcalmol-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 kcalmol-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.