In this work the authors carried out quantum calculations to explore the gas-phase and aqueous-phase reactions of organosulfate (namely methyl sulfate and glycolic acid sulfate) with dissolved OH radicals. The simulated results clearly demonstrated the main reaction outcome is formation of inorganic sulfate and carbonyl compounds. At the same time, the results show that the nature of the substituent have some impact on the reaction mechanism. The potential reaction mechanisms were discussed in details and in general agreed with the existing experimental results. The paper is well written and provides greater mechanistic understanding of the chemistry of organosulfates in the aspect of inorganic sulfate formation.  This work fits well to the scope of this journal and I recommend publication in Atmospheric Chemistry and Physics, after the following comments have been addressed.

1. What are the atmospheric concentrations of the reactants considered in this study? Do the authors think the reactants concentrations would affect the reaction mechanism?
2. The authors highlight that chemical substitution has some impact on the course of the reaction. Is there a general rule regarding this?
3. How do the authors justify their choice of the M062X/6-311+g(2df,2pd) method for geometry optimizations and frequency calculations in the studied reactions?
4. In Figure 6, the mechanism from the intermediate lying at -43.01 kcal/mol to the product at -93.95 kcal/mol is not clear. Can the authors elucidate further on this?
5. In regards of the high atmospheric concentration of O₂, it is good that they authors consider this as an important reactant in the intermediate steps of the reactions in the aqueous-phase. However, why didn’t they examine the reaction of this oxidant (O₂) in the intermediate steps of the reaction in the gas-phase?
6. Line 130. Can the authors use a different word than “achieved” at the end of the sentence?
7. In the caption of Figure 2, it is likely that product (C) is clustered to 3 water molecules.

Manuscript review " Atmospheric fate of organosulfates through gas-phase and aqueous-phase reaction with hydroxyl radicals: implications in inorganic sulfate formation" for EGUSPHERE.

In this manuscript, the authors report on the oxidation of organosulfates, specifically methyl sulfate and glycolic acid sulfate, by OH radicals in the gas phase and in the aqueous phase. The investigations were carried out using DFT calculations with GAUSSIAN, whereby in addition to the electronic structure and thermochemistry, the reaction kinetics of the oxidation reaction and the respective intermediates were also calculated.

The questions and comments on the manuscript are listed below.

In the abstract, the authors should make it clear that they have carried out the DFT calculations.

Please check your manuscript for colloquial language, e.g. in line 17 “unfriendly”. A molecule does not have these attributes.

Line 16: How likely is the reaction of the alkyl radical with ozone (O3) in the presence of oxygen (O2), if we assume that an ozone concentration in the range of 10 to 100 ppb compared to 20% oxygen in the atmosphere?

Line 20: Why only the rate constant of OH radicals with methyl sulfonate is shown?

Why does the reader need the text from line 101 to line 113? Because none of the diffusion parameters are discussed later in the manuscript text.

Line 134: How would the unimolecular rate constant develop if the number of water molecules corresponds to the number of water molecules in the hydration shell in the aqueous phase?

Line 134: “Unimolecular rates constants” should read “Unimolecular rate constants”

Line 144: Could the authors show the rate constants instead of the lifetimes?

Beside the uni-molecular decay rate, what would be the rate constant for the alkyl radical - alkyl radical recombination reaction in the absence of any other reaction partner? That would be interesting to know?

Line 152: How meaningful is the investigation of the reaction of the alkyl radical with ozone and NO2 in term of their solubility in water? Considering the self-decay reaction as well as the reaction with O2.

Figure 1: How reliable are the decimal places in the DFT calculations?

Line 170: This statement depends on the ambient conditions, e.g. the concentration of organic substances in an aerosol particle. This is because the SO3.- could also react with organic substances. What are the intermediate steps in the formation of SO42- from SO3.-? Is there a difference in the gas phase or in the aqueous phase?

Line 234: Do the authors have an explanation, why the obtained rate constant is approx. an order of magnitude lower compared to the measured value by Gweme and Styler, 2024 (doi: 10.1021/acs.jpca.4c02877) and the references therein?

Line 278: What would be the reaction barrier of the decomposition of the alkoxy radical to SO42- and formaldehyde?

What is the authors' opinion regarding the decomposition of the peroxy radical similar to the decomposition of alkyl and alkoxyl radicals? Would that be possible?

Line 291: Since the pKa of methyl sulfate is less than zero on the pH scale, and radicals generally have a lower pKa than the parent compound, how likely the presence of the distinct radical species is to be expect?

Line 294: Why don't the authors give rate constants and lifetimes in the manuscript that are comparable to the discussion in the section on methyl sulfate? Why is there no discussion of the reactivity of similar compounds (glycolic acid) with OH to at least give an order of magnitude for the reactivity for glycolic acid sulfate?

Line 312: How likely would be the decomposition of the alkyl radical to COOH and CHO-SO3-? What would be the energy barrier and the decomposition rate?

Line 317: Why the fate of SO3.- is discussed again?

Line 334: Could the authors provide information on the contribution of the three different decomposition pathways of tetroxide? It is known from the literature that about 10-20% of tetroxide in the aqueous phase is decomposed by the formation of molecular singlet oxygen and alkoxy radicals, depending on the parent compound. What would be the contribution of the H2O2 + RCRO (ketone) formation pathway and what would be the contribution of the RCROH (alcohol), RCRO (ketone) and O2 formation pathways? What would be the influence of the organic moiety of the molecules discussed here?

Line 338: The atmospheric implication appears to be somewhat incomplete with regard to the reaction of glycolic acid sulfate with respect to the rate constants.

Line 362: What do the authors mean with low reactivity of glycolic acid sulfate relative to methyl sulfate? The rate constant of glycolic acids with OH radicals was measured with k = 5x10^8 L mol-1 s-1 (Buxton et al., 1988). The rate constant of methyl sulfate with OH is in the range of 5x10^7 to 1x10^7 L mol-1s-1 (Gweme and Styler, 2024 (doi: 10.1021/acs.jpca.4c02877)). To what extent can the presence of the SO3 group deactivate the CH2 group of glycolic acid sulfate?

To summarise, taking all comments into account, I recommend the major revision of the manuscript. The topic itself is interesting and the manuscript has its merits, but in its current form is not sufficient.

Review of Tchinda et al for ACP

Tchinda and co-workers study the transformation of glycolic acid sulfate and methyl sulfate both in the gas phase and particle phase using quantum chemical methods. The aqueous phase is modelled using a polarizable continuum model. Up to two explicit water molecules are considered in both the gas phase and aqueous phase calculations. The structure and vibrational frequencies of the stationary points are calculated at the M062X/6-311+g(2df,2pd) level of theory and the single point energies are refined using accurate CCSD(T)-F12/cc-pVDZ-F12 calculations.

This is an interesting topic that shed some further light on the atmospheric fate of organosulfates. However, the presentation is rather messy, and the study appears incomplete. Overall, I do not feel like I got wiser on the fate of organosulfates in the atmosphere and I cannot recommend publication in its current form.

Major Comments

• Not all competing pathways are studied. It seems like only some selected pathways were considered. Why were the COOH hydrogen abstraction not considered? Why was the dimer formation only considered for one of the systems, but not the others, ect?
• Why are reactions with NO₂ and O₃ taken into account, but addition of O₂, which traditional tropospheric chemistry would dictate to be the most important, just neglected?
• Gas-phase bimolecular kinetics are well-established, and the reactant complex normally does not enter the rate constant calculation. Hence, I find it curious that the authors treat the reactions as unimolecular and just start from the RC.
• I do not buy the presented argument that glycolic acid sulfate does not react with OH in the gas phase.
• What is the concentration of the organosulfates in the gas-phase compared to the condensed phase? Would they partition to the particle phase faster than they can react with OH radicals?

Specific comments

Line 96: In equation (3) quantum mechanical tunnelling is neglected. However, for hydrogen abstraction reactions tunnelling would be expected to be important. Please include the role of tunnelling for the calculated rates.

Line 104: Equation (4)-(6) does not appear to be used in the manuscript.

Line 134: It would assume that the HO• + CH₃-O-SO₃H∙∙∙(H₂O)n to H₂C•-O-SO₃H∙∙∙(H₂O)n+1 reaction should be considered as a bimolecular reaction. Any particular reason why the reaction is treated as a unimolecular reaction starting from the reactant complex? Will this not misleading make it look like the reaction is more favourable than it is? Same analysis is made in line 211.

Line 185: Could you clarify what you mean with “… while attempts to optimize the reaction with O2 did not succeed due to electronic constraints to form chemically stable species.” Are you referring to the spin states? Usually, this reaction occurs very fast and will therefore be more important than the reaction with O3.

Line 231-232: I assume the 1 M concentration is used to get the aqueous phase units right here. How well justified is it to use 1 M?

Line 280: “its formation from H₂C•-O-SO₃^- reaction with O₂ is less thermodynamically favorable than with O₃,”

Line 296: “… HOOC-CH•-O-SO₃H species was found to be without atmospheric relevance as opposed to the intermediate reactant in the reaction of methyl sulfate.”

I do not understand the argument here. The alkyl radical should be able to react barrierlessly with O₂?

Line 331: Why is the dimer from 2 peroxy radicals only formed for glycolic acid sulfate and only in the aqueous phase? What are the alternative fates of peroxy radicals?

Line 334: “… does not fragment to form in the alkoxyl radical in the singlet state, but rather transits to the triplet state before fragmentation could occur, the energy difference between the two electronic states being as low as 7.60 kcal mol-1 .”

How is it determined that it “transits” to the triplet state here? Did you do the intersystem crossing calculations?

Technical comments

Line 22: Remove either “highlight” or “unveils”

Line 44: Sentence starting with “Despite organosulfates have generally … “ please rephrase.

Line 75 and 76: M062X/6-311+g(2df,2pd) -> M06-2X/6-311+G(2df,2pd)

Line 175: I find this part of the sentence hard to understand “… and the combination of Russell (Russell, 1957) and Bennett and Summers (Bennett and Summers, 1974) mechanisms we speculated by the authors to explain this formation.”. Could you please rephrase.

Line 188: “difficulty breaking” -> “difficulty in breaking”

Line 268: “oxygen atom of the alkoxy function” -> “oxygen atom of the alkoxy functional group”

Data availability

All coordinates of the studied systems as well as energetic should be available as supporting information. Otherwise, the study is not reproducible.