In this work the authors carried out quantum calculations to explore the aqueous-phase reactions of organic peroxides (MHP, PAA and BZP) with dissolved SO2 or S(IV) species under various pH conditions. The simulated results clearly demonstrated the effects of pH on the major reaction pathways between various organic peroxides with S(IV) species leading to form inorganic sulfate and organosulfate. The potential reaction mechanisms were discussed with details and in general agreed with the existing experimental results. The paper is well written and provide greater mechanistic understanding of the organic peroxides chemistry in aspect of inorganic and organic sulfur formation.  I only have a few minor comments

General comments:

For the quantum chemical calculations, what are the concentrations of the reactants used in the calculations? Would the reaction pathways and kinetics  potentially affect by the reactant concentrations?

For the reaction pathways,  would there be any other possible reaction pathways between the organic peroxides and S(IV) in addition to the ones discussed and considered in the calculations?

In the atmospheric implications, it is very nice the authors  to show and discuss the effective rate constants for different reaction systems under different values of pH and temperature and their corresponding lifetimes. the authors have pointed out  such reactions may be important for sulfate formation under oxidant-limiting conditions. Can the authors further elaborate this point? Also, could the authors comment the yield of inorganic sulfate and organosulfates in different reaction systems and environmental conditions.

Minor comments.

Line 100, “The diffusion coefficient for a reactant is related to its radius in any medium of viscosity 𝜂 by the Stokes-Einstein approach (Einstein, 1905).” It is not clear what is the viscosity of the aqueous solutions. How the diffusion would affect the reaction pathways if the solutions or aqueous aerosols were hlghly viscous?

Line 115, “The formation of SO2•H2O•MHP is relatively endergonic at 298.15 K and standard concentration of 1 M.” Can the authors elaborate why the concentration of 1M was chosen for the calculations? Would the concentration of the reactants affect the reaction pathways and kinetics?

Line 155, “The high proportion of sulfate relative to methyl sulfate observed by Lind et al. can further be explained by the demonstrated fast hydrolysis of methyl sulfate at acidic pH (Hu et al., 2011) and its effective oxidation by OH radicals (Kwong et al., 2018) to form inorganic sulfate.” Could the authors comment how significance of these two processes in the formation of inorganic sulfate and organosulfates relative to the reactions between organic peroxides and S(IV) species?

Line 183, “In general, the reaction of PAA is much more favorable to the formation of inorganic sulfate than the reaction of MHP at all pH ranges, while the formation of organosulfate is slightly prevented. This is in line with the experimental observation that the reaction of PAA with dissolved SO2 almost exclusively forms inorganic sulfate (Lind et al., 1987).”  What would be the ratios of the inorganic sulfate to organosulfate formed upon the reaction of PAA and dissolved SO2 at pH 1.81 – 6.97 and pH > 6.97? Also, what would be ratios for other reaction systems? 

This new contribution explores theoretically the aqueous condensed phase chemistry of organic peroxides (Ops) with dissolved sulfur in its (+IV) oxidation state as a function of pH. It especially simulates the chemistry of three selected OPs (methyl hydroperoxide (MHP), peracetic acid (PAA) and benzoyl peroxide (BZP)) with dissolved SO₂. This is certainly an important topic as organic peroxides and SO₂ are key components of aerosols and hydrometeors, that fits the scope of the journal.

Nevertheless, I would recommend that authors comments (and eventually modify their manuscript) to address the following comments, in addition to polishing the use of the English language.

While this reviewer is not an expert in the theoretical calculations reported here, the experimental section seems nevertheless short and not necessarily providing the level of information required to really assess the quality of the calculations.

The core content of this study concerns the effect of pH on the chemistry between the selected Ops and dissolved SO₂. This seems to be mainly (or even uniquely) simulated through the change of S(IV) species in presence at the selected pH. However, pH is known to catalyze the chemistry, and even the degradation, of Ops. This would certainly also affect the nature of reported transition states. But this not mention and corresponding papers not cited. Enami reported several studies, on different OPs, describing their acid catalyzed degradation (https://doi.org/10.1002/ejoc.202100343) or their overall fate in the condensed phase (https://doi.org/10.1021/acs.jpca.1c01513); while Krapf et al discussed their overall stability (https://doi.org/10.1016/j.chempr.2016.09.007).

In the opinion of this reviewer, it would be important to explore the effect of available protons on the actual structure of the transition state and not just on the distribution of S(IV) species.

The atmospheric implication is explored over a wide range of temperatures, corresponding even to ice conditions (at 240 K). It does not seem obvious that the temperature dependence of all parameters (such as acid-base equilibrium constants, etc.) have been considered to derive the temperature dependent rate constant. Could this be clarified? Also, this atmospheric significance needs to be compared to the lifetimes of the OPs which is also pH dependent (if the OP self-degrades faster that would limit the reported significance).

Minor points

The sentence starting line 30 (i.e., “In aqueous  media, OPs are produced by the reduction of ROx radicals and from fluorescent dissolved organic matter (DOM) by photogeneration, while other sources include partitioning from gas-phase to particle-phase (O'sullivan et al., 2005; Sun et al., 2021).”) does not provide a sound description of the formation of OPs.

Line 33: “ uptake on water surfaces”, this is not a sink but rather a source.

Line 59, change lowly to poorly

Line 122: the mention to uptake coefficients is unclear as bulk processes are described here.