the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 29 Sep 2026
Rapid formation of nitric acid during the daytime and its critical contribution to methanesulfonic acid-methylamine nucleation in coastal industrial areas
Abstract. Nitric acid (HNO3) is critically involved in aerosol formation, acid deposition, and atmospheric nitrogen cycling. However, the mechanisms underlying its daytime formation, particularly the influences of gaseous and interfacial water molecules, and its effect on methanesulfonic acid-methylamine (MSA-MA)-driven nucleation remains poorly understood. Here, we employed quantum chemical calculations, atmospheric cluster dynamics code (ACDC) simulations, and Born-Oppenheimer molecular dynamics (BOMD) to investigate how water catalyzes HNO3 formation in both gaseous and interfacial environments, as well as the contribution of HNO3 to MSA-MA-driven new particle formation (NPF). Results show that water-catalyzed HNO3 formation in the gas phase proceeds through a barrierless pathway and becomes significantly faster than the uncatalyzed NO2 + OH reaction under typical atmospheric water vapor concentrations. At the air-water interface, NO2 and OH not only show pronounced surface affinity, but also can lead to the rapid formation of HNO3 within picoseconds. Against the backdrop of declining global SO2 emissions, this work further reveals that HNO3 substantially promotes NPF and aerosol particle growth via two main mechanisms (i) in high HNO3 concentrations (~ 1.0 × 1012 molecules∙cm-3), such as the North China Plain and New Delhi areas, HNO3-involved pathways contribute up to 10 % of the total nucleation flux; (ii) NO3- exhibits a markedly enhanced capacity to promote aerosol hygroscopic growth by facilitating vapor uptake and stabilizing molecular clusters, thereby driving aerosol nucleation and growth. These findings offer molecular-level insights into the formation pathways of HNO3 and the growth of aerosol particles in polluted boundary layer.
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Status: open (until 10 Nov 2026)
- RC1: 'Comment on egusphere-2026-3408', Jonas Elm, 13 Oct 2026 reply
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RC2: 'Comment on egusphere-2026-3408', Anonymous Referee #3, 14 Oct 2026
reply
General Assessment: This study combines quantum chemical calculations, BOMD, classical molecular dynamics, and ACDC kinetic simulations to systematically investigate the gas-phase water-catalyzed pathway and the air–water interfacial pathway for daytime HNO₃ formation via the NO₂ + OH reaction, and further evaluates the contribution of HNO₃ to MSA–MA-driven new particle formation and aerosol hygroscopic growth. Against the backdrop of continuously declining global SO₂ emissions and the increasingly prominent role of MSA in nucleation, the topic is of clear atmospheric chemical significance. By linking microscopic reaction mechanisms with cluster dynamics simulations, the paper adopts a relatively comprehensive methodological framework and provides molecular-level insights into the rapidity of interfacial reactions, the hydration ability of NO₃⁻, and the condition-dependent role of NA in nucleation, which are the main strengths of this work. However, several key aspects of the current version still need to be strengthened: some conclusions are stated too strongly; the logical connection between the interfacial and gas-phase pathways and their applicable conditions need to be clarified; the choice and consistency of methods require additional validation; the quantitative conclusions regarding NA’s contribution are strongly affected by temperature and precursor concentrations and should not be overgeneralized; and the figures and some methodological details also need further standardization. Overall, this study has publication potential, but there remain many issues in logical rigor, data interpretation, and clarity of expression. It is recommended that the authors consider publication after supplementing the literature, improving the methodological description, cautiously phrasing the conclusions, and optimizing the figures.
Major Comments
- The abstract and conclusions overstate the role of water-catalyzed HNO₃ formation and are inconsistent with the results. The abstract states that water-catalyzed HNO₃ formation “becomes significantly faster than the uncatalyzed NO₂ + OH reaction under typical atmospheric water vapor concentrations” (Page 1, lines 18–20), but the results on Page 9, lines 203–208 report effective rate coefficients for the water-catalyzed Path 1 of to , compared with for the uncatalyzed reaction. The water-catalyzed rate is therefore about an order of magnitude lower, and the authors describe it as “comparable” and “non-negligible,” with a contribution of only – in Table 1. The abstract and conclusions must be rewritten to reflect the actual results, and the claim of “significantly faster” should be removed or replaced with a statement that the water-catalyzed pathway makes a non-negligible but secondary contribution under typical conditions.
- In the Introduction section, the authors cite Sun et al. (2016) to motivate the key scientific question whether H₂O can catalyze the NO₂ + OH reaction. However, the overview of existing theoretical and experimental progress concerning water‑mediated catalysis for this reaction remains somewhat limited. Furthermore, the manuscript jumps directly from homogeneous gas‑phase chemistry to air‑water interfacial reaction mechanisms without sufficient logical transition. It does not elaborate on the distinct chemical roles of interfacial water molecules in atmospheric NOₓ transformation, nor rationalize why interfacial modelling is still necessary even after exploring gas‑phase reaction channels. A concise transitional paragraph should be added to clarify the atmospheric importance of chemical processes occurring at aqueous micro‑ and nanodroplet interfaces, contrast their mechanistic differences and intrinsic links with gas‑phase pathways, and incorporate foundational published works addressing unique interfacial reactivity within confined droplet environments (org/10.1016/j.chempr.2023.09.019.; doi.org/10.1016/j.atmosenv.2024.120574.; doi.org/10.1016/j.atmosenv.2024.120574.; doi.org/10.1021/jacs.6b04338.; doi.org/10.1016/j.jes.2026.03.031). These references can help set the general background for interface‑specific chemistry before diving into NOₓ‑related reactions, which will make the subsequent introduction of interfacial simulations more coherent and well‑grounded.
- The reported interfacial rate constants, for Path 3 and for Path 4, cannot be interpreted as ordinary gas-phase bimolecular rate constants. If taken literally, they exceed the gas-phase collision limit by about 18 orders of magnitude. The collision limit for a gas-phase bimolecular reaction is typically on the order of , and even the uncatalyzed reaction has a rate coefficient of only about . Therefore, values of –in the same units are physically impossible for a conventional gas-phase bimolecular reaction. The comparison between interfacial and gas-phase HNO₃ formation is not sufficiently justified. Using Eqn (4), the authors obtain at 300 K and conclude that the interfacial reaction dominates over the gas-phase reaction. However, the notation in Eqn (4) is inconsistent and unclear, and the assumed surface density, water-film thickness, and reactant concentrations require stronger justification. The authors should provide a sensitivity analysis for relative humidity, NO2 and OH concentrations, droplet surface area, and interfacial coverage, and they should discuss whether the conclusion holds for cloud droplets, aqueous nanodroplets, and polluted boundary layer aerosols. If the interfacial pathway is indeed dominant by three orders of magnitude, this would have major implications for atmospheric HNO₃ budgets, and the evidence must be correspondingly robust.
- The ACDC simulations and regional extrapolations require more rigorous treatment. The boundary clusters are chosen as and , but it is not clear whether these are sufficient when HNO3 is included, and whether the results are converged with respect to cluster size and boundary conditions. The sink coefficient of should be justified for the different polluted and clean regions considered. The MA concentration range in Fig. 6c appears as to , which is almost certainly a typographical error and is inconsistent with the values discussed in the text. The reported regional contribution of HNO₃ to MSA–MA nucleation, –, depends strongly on assumed MSA, MA, HNO₃, temperature, and relative humidity, so a systematic sensitivity analysis is needed before such regional conclusions can be drawn.
- 3e may be misleading. The figure uses contour rendering, but contour lines should reflect changes in the reaction coordinate and energy direction rather than being arbitrarily overlaid or annotated. Four minima appear in the figure, yet the authors do not specify whether the collective variable (CV) changes directly along the diagonal direction or separately along the X and Y directions. Different definitions of the CV will lead to different shapes of the free-energy surface and different interpretations of the reaction pathway, so this must be clearly stated. In addition, the definition of the CV should be provided in the main text.
- The conclusions regarding NO₃⁻ hygroscopic growth are interesting but currently overextended. The hydration distributions and binding free energies suggest that NO₃⁻ is more strongly hydrated than NO₂, OH, and HNO₃, and that it can stabilize MSA- and HNO₃-containing clusters. However, these conclusions are based mainly on thermodynamic calculations, and the influence of interfacial electric fields, ion pairing, HNO₃ volatilization, and kinetic limitations is not fully considered. The comparison with HCOOH, CH₃COOH, and dicarboxylic acids should also ensure that the clusters are comparable in size, charge state, and protonation. The claim that NO₃⁻ “provides a direct pathway for enhanced aerosol particle growth” should be softened or supported by additional kinetic or experimental evidence.
- The authors’ simulations demonstrate that NA-mediated MSA–MA nucleation is negligible at 298.15 K but contributes up to 29% at 258.15 K, indicating a strongly temperature-dependent effect. Nevertheless, the title, abstract, and conclusions imply a general contribution of HNO₃ to NPF in coastal industrial areas, where summer temperatures approach 300 K. This overgeneralization is potentially misleading. The authors should qualify the title and abstract to indicate that HNO₃ promotion is significant primarily under low-temperature conditions, and should specify the temperature assumed in the regional analysis.
Citation: https://doi.org/10.5194/egusphere-2026-3408-RC2
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- 1
Review of Wang et al for ACP
Wang et al studies the role of water in the formation of HNO3 in the gas phase and HNO3 formation at the air-water interface using quantum chemical methods and molecular dynamics simulations. In addition, the role of HNO3 on methane sulfonic aicd–methylamine (MSA–MA) cluster formation is studied using quantum chemistry and atmospheric cluster dynamic simulations. The calculations are performed at a decent level of theory throughout.
The paper essentially consists of four separate topics: 1) Gas-phase kinetics, 2) Uptake of NO2 at the air-water interface, 3) Cluster formation of MSA–MA and 4) Enhanced growth due to ion formation. While the common theme is nitric acid, the separate sections feel a bit disjoint and impairs an overall coherent story.
Overall, the paper is relatively well-written and interesting. However, there are many instances where I do not believe that the data fully supports the conclusions. Hence, a careful major revision is needed before I can recommend publication.
Comments
Line 47: ” Experimentally, Okimura et al. (Mollner et al., 2010)”
Line 49: ”Percival et al. (Winiberg et al., 2020)”
Please carefully check all references.
Line 103: “The M06-2X functional (Mardirossian and Head-Gordon, 2016; Pereira et al., 2017) has proven effective in accurately describing weak intermolecular interactions and reliably predicting thermochemical properties and equilibrium geometries in atmospheric cluster systems.”
To the best of my knowledge neither Mardirossian nor Pereira studies atmospheric cluster systems. Please refer to benchmarks carried out on atmospheric molecular clusters to justify the application of the M06-2X functional.
Line 107: “... at the M06-2X/6-311++G(2df,2pd) level”
Why was the 6-311++G(2df,2pd) basis set chosen? Is this adequate enough to describe your systems?
Line 111: “The relative Gibbs free energies were subsequently refined through single-point calculations at the DLPNO-CCSD(T)/aug-cc-pVTZ level”
Why was DLPNO-CCSD(T) and aug-cc-pVTZ chosen? Please refer to atmospheric benchmarks to ensure that this leads to an accurate description of the binding energies.
Lines 114-116: What does n refer to here? Is it related to size of the clusters or a random number?
Line 130: For the umbrella sampling, what was the chosen collective variable? I assume it was center of mass?
Line 131: Also please comment on the application of a harmonic potential. I assume this was chosen to avoid the water molecules evaporating from the slab. How will this this influence the results?
Line 145-148: Is BLYP/DZVP accurate enough to describe the desired reaction? It would be beneficial to have some idea about the potential errors this level will introduce. The BLYP/DZVP level should be applied to the gas-phase reactions studied in section 3.1 to elucidate how large errors there are in the obtained barriers.
Line 161: “Thermodynamic parameters, including binding free energies, were derived from quantum chemical calculations at the M06-2X/6-311++G(2df,2pd) level.”
DFT by itself is usually not accurate enough to be used for ACDC simulations. Were DLPNO-CCSD(T)/aug-cc-pVTZ single point energies not applied here? From the methods and SI it appears so, but please clarify
Line 199-201: The calculated complex concentrations are on the order of 104 molecules cm-3. Will such a complex live long enough to ever hit the other reactant? Also I assume one of the HO --- H2O complexes should be HO --- NO2 here?
Line 210: “To quantitatively assess the catalytic effect of water molecules, the total rate coefficient ktot was defined according to Eqns (2).”
I am missing some more details on exactly how the rate calculations are performed here. This is just the rate constant. For the reaction to be relevant you also need to take the concentrations into account.
Line 222: “In addition, independent 5 ps BOMD simulations at the droplet interface confirm that both NO2 and OH can stably reside at the interface.”
Is a 5 ps simulation sufficiently long to state that they are stable? They might still evaporate.
Line 224: “Together, these results confirm a clear interfacial preference for both NO2 and OH, supporting the likelihood of interfacial reaction initiation”
This is a very idealized system and thereby not taking competing reactions into account. I am missing some critical reflection on to what extent this is a viable system under realistic conditions. Will the OH radical not react with something else before reaching the NO2 molecule? A back-of-the-envelope type estimate is needed, where the lifetime of the reactants is taken into account. I am not saying these reactions might never happen, and even if it is only a small fraction that goes to the nitric acid channel compared to competing channels, it is still an interesting finding.
Line 255: What was the sigma value set to? I assume that there is only one path and it should be unity. Perhaps omit it in the equation.
Line 256: The calculated rate of 4.59 x 107 cm3 molecules-1 s-1 is a bit puzzling. How can the rate be higher than the collision rate of NO2 with the surface. I suspect this is a breakdown of the applied transition state theory in equation (3). What is the electronic energy barrier? Is it negative?
Line 265: The different paths are getting a bit confusing. Perhaps already in the methods section define all the paths in one list of reaction schemes. That should make it easier to follow later on.
Line 273: Why is pathway 4 treated as a diffusion reaction, while the other paths are treated as gas-phase reactions?
Line 277: “This result indicates that HNO3 is predominantly formed via the reaction of gaseous NO2 with adsorbed OH at the gas-liquid interface.”
Again, here I am missing some kinetic estimates. Will the OH radical live long enough on the surface to be hit by a gas-phase NO2? In next section some estimate is attempted. However, it is not entirely clear how all the parameters are obtained. What is the concentration used for the interfacial OH?
Line 303: I am missing some overall motivation to what atmospheric region these simulations correspond to. Will there be MSA, MA, NA simultaneously in high concentrations and at low temperature? This is further commented in the section on atmospheric implications but would be beneficial to mention earlier.
Line 304: I am missing more detailed discussion on the cluster structures and comparison to the existing literature. Do you find lower free energy clusters compared to the literature? How do the structures compare to the previous work by Knattrup et al:
https://doi.org/10.1021/acsomega.2c04278
https://doi.org/10.1021/acs.jpca.3c04393
https://doi.org/10.1039/d4ra03021d
Some even larger clusters than studied here are present in these works. Would it not make sense to include these in your simulations?
Line 321: “In summary, NA enhances cluster stability by promoting both hydrogen bonding networks and proton transfer processes.”
I do not believe stability can be directly estimated from the electron density. You need the free energies for that. Perhaps rephrase to that NA enhances the number of hydrogen bond interactions in the clusters.
Line 329: “As shown in Fig. 5(b), along the MSA-MA-NA growth pathway, the conversion from the MSA·MA cluster to (MSA)2·(MA)3·NA is exothermic”
It is not entirely exothermic, as there are several barriers along the free energy profile.
Line 364: “Therefore, NA exerts the strongest influence under conditions of low temperature, low [MSA], and high [MA].”
Is this congruent with the findings of Knattrup et al (https://doi.org/10.1021/acs.jpca.3c04393), that find that NA suppress the role of MSA?
Line 371: What temperature was used for the simulations in Figure 7?
Line 391: “This distinction is consistently supported by the hydration distribution analysis (Fig. 8, Fig. S13-S14, and Table S17), which shows that NO3- remains predominantly hydrated across a wide range of conditions”
Indeed, an ion will be strongly hydrated. What happened to your proton here? Is HNO3 fully dissociated? I believe the appropriate analysis would be to look at the HNO3-water clusters.
Line 424: “Overall, the interfacial NO2 + OH reaction not only produces highly hygroscopic NO3- but also promotes vapor uptake, cluster stabilization, and nucleation, providing a direct pathway for enhanced aerosol particle growth.”
This is quite a stretch. I do not believe that the fact that an ion interacts stronger with a given species can be used to directly infer properties about nucleation and aerosol growth, without further explicit evidence. Section 3.3.2 is very disjoint from the remaining part of the manuscript and I suggest removing it.