Jing Li et al. reports a theoretical study on the iodic acid (HIO₃) – iodous acid (HIO₂) based nucleating process enhanced by methanesulfonic acid (MSA) by quantum chemical calculation and cluster dynamic simulation. They found that the MSA can enhance the HIO₃-HIO₂-based nucleation, especially in polar oceanic regions. This manuscript has systematically studied the HIO₃-HIO₂-MSA ternary nucleation system, covering cluster stability, thermodynamic/kinetic analysis, and molecular-level mechanism. These interesting findings show the significance of sulfur and iodine synergistic nucleation, providing deeper insights into marine secondary particle formation, given chemical complexity of real atmosphere. This well-written manuscript has important atmospheric implications, such as in the studies of marine aerosol formation and the sulfur/iodine cycling. Hence, I recommend the publication of this study in Atmospheric Chemistry and Physics after considering my comments listed below.

General comments:

Comment 1: Although the authors have provided sufficient computational details, it would be better to add the grid settings for DFT calculations and the optimization convergence in method section of the main text.

Comment 2: In general, the nucleation process involves competition between cluster collision and its evaporation processes. In the ACDC simulations presented in this manuscript, could the authors specify which types of collision and evaporation processes considered? If possible, these details would be better to added in the ACDC methodology section.

Comment 3: In this work, the authors systematically investigated the HIO₃-HIO₂-MSA ternary nucleation process, where HIO₂ appears to play a crucial role in all clustering pathways. How should this be interpreted?

Comment 4: For the formed HIO₃-HIO₂-MSA clusters, especially large-sized clusters, are there any unoccupied binding sites that can enable further molecular binding and cluster growth? The authors would better provide theoretical evidence by quantum chemical calculations, such as using wave function analysis, or others. If done, this will provide the readers with an intuitive understanding of the growth potential of the cluster.

Specific comments:

Comment 5.

Page 4, Line 96: Please provide more details of the calculations of the volume of cluster i (V_i).

Comment 6.

Page 5, Figure 1: The authors seem to have forgotten to plot the hydrogen and halogen bonds with dotted lines in Fig. 1(d), please correct it.

Comment 7.

Page 6, Line 141: In the sentence, ‘Here, the condensation sink (CS) coefficient is set to be 2.0 × 10^-3’, there is a missing unit after the CS value.

Comment 8.

Page 7, Figure 3: To enhance data clarity for readers, consider enlarging the font size in Fig. 3, which appears relatively small.

Comment 9.

Page 12, Line 252: The word ‘play’ should be ‘plays’.

Li et al. explored the role of methanesulfonic acid (MSA) in iodine oxoacids nucleation. Detailed molecular-level mechanisms of cluster formation were studied using quantum chemical methods and cluster dynamics, providing theoretical evidence for the contribution of MSA to the formation of marine iodine clusters. After carefully reading the manuscript, I find that the main argument that MSA may enhance the nucleation rate of iodine oxoacids is convincing. The contribution of MSA to the formation of marine iodine particles remains an open question because other acids and bases such as sulfuric acid and amines may also affect the HIO3-HIO2 nucleation process in the real atmosphere - as the authors have addressed at the end of this manuscript - while this study provides an important theoretical basis for this question. This manuscript is well written. I recommend it be accepted by Atmospheric Chemistry and Physics. A few minor comments on the interpretation of the theoretical results are given below.

General comments:

1. Figures 1-3 seem to suggest that the significant enhancement of MSA on HIO3-HIO2 nucleation is robust against the uncertainties of cluster stability. However, would it be possible to have a supplementary or appendix figure for the general audience, showing the uncertainty range of the enhancement or relative contribution of MSA to the cluster formation rate?

2. I found it challenging to interpret the relative importance of the MSA-involved path in HIO3-HIO2-MSA nucleation. Figure 3a shows that the MSA-involved path is a major path (74 %), yet this was simulated with a [MSA] 5 times of [HIO3]. With the same [MSA] and [HIO3], the MSA-involved path was expected to contribute ~20 %, showing that MSA was a bit less efficient than HIO3 in clustering with HIO2. This comparatively lower efficiency does not affect the main conclusion as the [MSA] may exceed [HIO3] in atmospheric environments. However, Figures 4 and 5 show a high enhancement factor (> 2) with the same [MSA] and [HIO3]. This high enhancement factor indicates that MSA is more efficient than what I interpreted above. I hope this can be clarified in the revised manuscript.

Specific comments:

3. Line 180, "Overall, the results suggest that MSA's contribution to cluster formation is positively related to [MSA] but negatively linked to [HIO3]." This sentence is correct in terms of the relative contribution but awkward. How about removing this sentence and adding discussions on the relative importance of the MSA path (see comment 2)?

4. Line 207, "To sum up, MSA can promote nucleation, particularly in marine regions characterized by lower T, lower [HIO3] and [HIO2]." I was confused that MSA can promote nucleation at low [HIO2] within the context of this manuscript, as [HIO2] is the starting point of cluster formation. This might be caused by overemphasizing the relative contribution. Also, [HIO2] is usually associated with [HIO3]. Replacing [HIO3] (implicitly indicated to be independent of [HIO2]) with [HIO3]/[HIO2] in some discussions may help with understanding.

5. Line 222, "observed J of 2.1 × 10-4 cm-3 s-1". This J value is too low from a measurement point of view. In a scatter plot showing the correlation between J and precursor concentrations, some small values of J are often given, though they might be obtained during weak or non-NPF periods. I checked the SI of Beck et al. and found that they have clarified that "Data with J-values < a few 10-3 cm-3 s-1 are highly unreliable and reflect mainly the noise levels...". Figure 2a in their main manuscript shows that the J value is ~0.1 cm-3 s-1 during typical NPF events.

6. Figure 6. It is recommended to adjust the shaded area of field observation. Now the measured J shares a similar style with the simulated J. Some readers may wonder why there is no correlation between the measured J and [HIO3].

7. Figure 6 caption. Please explain why there is a single line for HIO3-HIO2 while [HIO2] ranges from 2e3 to 2e4. Is it because of a constant [HIO2]/[HIO3] in the simulation?

8. Figure S5. Please give the reference for field observation data herein. It is surprising to see a high formation rate of 1e4-1e6 cm-3 s-1.

9. Line 248, "...thermodynamic analyses suggest that MSA-involved clustering is nearly barrierless". I do not disagree with this statement, yet it may confuse some readers, especially considering that the horizontal axes in Figs. 5-6 are [HIO3] rather than [HIO2]. How about emphasizing that the HIO2 addition, as the rate-limiting step for cluster formation and growth, is nearly barrierless?

This manuscript explores the enhancement effects of MSA on the HIO3-HIO2 system through DFT calculations and kinetic analysis. It is found that adding MSA significantly enhances the nucleation rate, especially in colder regions. The calculations are also compared with observations and in general the MSA-HIO3-HIO2 nucleation better explains the results than the binary HIO3-HIO2 nucleation. Overall, I find this manuscript clearly written and it is a nice contribution to the literature. The manuscript can be published after the following comments are addressed.

Major comments:

1. What is the criterion for stable clusters (based on which nucleation rates can be defined)? Are they determined based on the growth rate/dissociation rate ratio? A clear definition should be given in the main text.
2. Section 3.4: how J is defined/calculated in the measurements should be discussed here, since I assume it is different from the definition used in the simulation. In other words, more justification of why the simulated rates and observed rates are directly comparable should be provided.
3. I suggest the authors do two types of calculations corresponding to polluted (CS larger than 0.002/s) and relatively clean environments. This could benefit future research in more polluted coastal regions.
4. Figure 6. I believe the blue line should be an area as the other two. Also, how does the rates differ if the uncertainties of the DFT calculations for key clusters are considered? A table might be provided for this uncertainty analysis.

Technical:

Line 24: nucleating -> nucleation. This replacement should be done in several places in the text.

Line 27: remove the second comma.

Line 35: might be rewritten as: Although the efficient nucleation of HIO3 and HIO2 is overall consistent with the CLOUD measurements, this mechanism does not account for all HIO3-induced nucleation in the real atmosphere.

Line 48: might be rewritten as: the importance of the HIO3-HIO2-MSA nucleating mechanism may differ under distinct ambient conditions.

Line 72: remove ‘and’

Line 116: present -> presented

Line 144: observed -> shown

Line 160: across-> through

Line 169: contribute to 74% of cluster formation

Line 214: access-> assess

This manuscript investigates the enhancement effects of methanesulfonic acid (MSA) on the iodic acid (HIO₃)-iodous acid (HIO₂) nucleation system, which has been reported as an important mechanism of marine new particle formation (NPF). The intermolecular interactions, cluster stability, the formation pathway/ free energy surface of cluster formation as well as the enhancement of formation rate of the HIO₃-HIO₂-MSA ternary nucleation system was systematically studied with the combination of quantum chemical simulation and ACDC approach. This paper provide theoretical evidence that the involvement of MSA can structurally stabilize HIO₃-HIO₂-based clusters and has positive synergistic effect on the nucleation with HIO₃ and HIO₂. This manuscript is nicely written and fits the scope of ACP. I recommend the manuscript to be published after the following comments are addressed.

General comments:

1. Although sufficient theoretical details of the cluster conformations have been provided, the authors should also clarify the definition of “stable cluster”. We should derive a cluster’s concentration by the competition between its collisional formation and evaporation, instead of only judging the formation free energy. Since the authors have conducted ACDC calculations, the evaporation rates of the major clusters should be discussed, as well as the time dependent concentration variations of these major clusters.
2. I find the results in section 3.2 a bit confusing when trying to interpret the relative importance of the MSA-involved path in HIO₃-HIO₂-MSA nucleation under different conditions. For example, Figure 3a (upper panel) shows that the MSA-involved path contribute to 74 % of the cluster formation, under [MSA] of 5.0 × 10⁶ molec. cm^-3, [HIO₃] of 1.0 × 10⁶ molec. cm^-3, while the MSA-involved path contribute to ~20 % under [MSA] of 1.0 × 10⁶ molec. cm^-3, [HIO₃] of 1.0 × 10⁶ molec. cm^-3. This result indicates that MSA is less efficient in clustering with HIO₂, comparing with HIO₃. The authors have mentioned the atmospheric concentration level of MSA in line 40, the authors should also include the discussion about the concentration of iodine oxoacids in the revised manuscript. Since if the concentration of HIO₃ is comparable or higher than MSA, the scenario of ACDC simulation cannot reflect the condition of real atmosphere.
3. The comparison with field measurements seems to be a bit arbitrary. What’s the atmospheric condition such as precursor concentration and temperature of the measurement sites reported? What’s the definition of the J in the reported field measurements? Can the reported J be directly compared with the ACDC simulated J?  Moreover, in Line 222, “the observed J of 2.1 × 10^-4 cm^-3 s^-1”. This J value is too low for a typical NPF event. Is this value obtained from a non-NPF day? Please check the original paper.More explanation and discussion are needed in this section, which can sharpen the significance of the theoretical study on the merit of atmospheric implication.

Specific comments:

1. It would be preferable to avoid including reference in the abstract.
2. Abbreviations such as ESP HB XB should be explained at least once in the main text.
3. Line 47, " Furthermore, given the coexistence of MSA and HIO₃ in different marine regions (Quéléver et al., 2022; Beck et al., 2021), the HIO₃-HIO₂-MSA nucleating mechanism may differ under distinct ambient conditions, but it remains unrevealed." First, nucleating should be nucleation. Second, I feel a bit confusion about this sentence. Is the different HIO₃/MSA and HIO₂/MSA concentration ratio leads to different nucleation mechanism? The authors have concluded that MSA can promote nucleation, particularly in marine regions characterized by lower T, lower [HIO₃] and [HIO₂]. It will be more preferable to add some discussion about the [HIO₃]/ [HIO₂] in different marine atmosphere.
4. More explanation of ACDC model setting is needed. For example, the setting of condensation sink and other model parameters.
5. Figure 6. The HIO₃-HIO₂ curve should be an area as the other two.
6. It would be preferable to include some uncertainty analysis.