This paper discusses an analysis of the formation of accretion products from the cross-reactions of peroxy (RO₂) radicals formed in atmospheric reactions of several representative compounds using a modified version of the Gecko-A atmospheric chemical mechanism generation system. Previously it was thought that the major pathways for such cross-reactions was either dissociation forming alkoxy radicals or H-shifts (when possible) forming an alcohol and carbonyl, but addition forming peroxides + O₂ has also been considered. More recently, experimental and theoretical studies indicated that accretion reactions forming more stable (yet lower molecular weight) ethers and esters may also occur in some cases. This is investigated in this work, where the Gecko-A system is modified to include estimates of these accretion reactions for peroxy radicals formed from representative compounds. A number of the estimates are uncertain and approximations had to be used in this analysis because it is not possible in practice to represent all the possible peroxy + peroxy combinations in explicit mechanisms, and because the levels and distributions of peroxy radicals formed, depend significantly on the environment where they react. Therefore, as the authors admit, the results are largely qualitative, and do not necessarily represent any particular environment. However, this appears to be the first attempt to estimate the distributions formation of accretion products in reactions of organics in atmospheric systems, which are potentially important sources of secondary organic aerosol in the atmosphere that are not represented in current models. For this reason, I consider this work to be of high scientific significance and appropriate for publication in this journal.

Although the methods they used to estimate the branching ratios for the peroxy + peroxy reactions have uncertainties, especially for the larger radicals where accretion reactions may be more significant, I believe their chemical mechanism estimation methods represent the current state of the science and are probably as good as can reasonably be done given our current state of knowledge. Unfortunately, the Gecko-A tool that they used was not ideally suited for this study because it did not consider H-shift auto-oxidation isomerization reactions of peroxy radicals, which will affect predictions of distributions of peroxy radicals formed and which last long enough to react with other peroxy radicals. The authors recognize this limitation and attempts are made to deal with it by removing at least one type of radical where this is known to be fast from their analysis (acyl peroxy radicals with ‑OOH groups). However, this isomerization is either fast or at least non-negligible for radicals with -CHO groups or with allylic hydrogens, and these are formed from many compounds, including some examined in this study. Fortunately, structure and reactivity (SAR) methods now exist for H-shift reactions of a wide variety of peroxy radicals (e.g., Vereecken and Nozière, 2020, https://doi.org/10.5194/acp-20-7429-2020), and those could be incorporated in mechanism generation systems to account for this type of reaction. It would have been better, and certainly within our current state of knowledge, had they also modified Gecko-A to include these auto-oxidation reactions as well as the accretion reactions. As it is, a study like this would need to be repeated once this modification is made.

The greatest problem I have with this work is that it did not provide any indication of the overall importance of these peroxy + peroxy reactions in atmospheric systems, or how the estimated accretion product yields and distributions might depend on environmental conditions. Environmental conditions are important in affecting both the importance of peroxy + peroxy reactions compared to competing reactions with NO_x and HO₂, and also the distribution of peroxy radicals present. Peroxy + peroxy reactions can be important in laboratory systems in experiments with high concentrations and no NO_x, but are negligible at high or moderate NO_x levels characteristic of urban daytime scenarios, and tend to be much less important than reactions with HO₂ under lower NO_x conditions in the atmosphere. Therefore, the significance of these reactions as a source of low-volatility compounds in the real atmosphere is uncertain. Unfortunately, this work provided no useful information in this regard, which yields given only relative to the total amounts of peroxy + peroxy reactions.

A better approach for this study would be to define a set of standard environments where levels of NO_x, HO_x, O₃, peroxy radicals, light intensity and spectrum and reaction times are specified, so that total yields of accretion and all other products, relative to the amount of compound reacted, can be unambiguously determined. This gives information not only on product yields and distributions, but also how they depend on the environment if more than one standard environment is used. For the purpose of this study, it is also necessary to specify a distribution of peroxy radicals that serve as co-reactants for the peroxy radicals formed from the compound of interest, unless the scenario being simulated has only one organic reactant initially present. That may be a good representation of laboratory experiments carried out to determine product yields, but is a poor representation of the atmospheric environment where a wide variety of compounds are reacting, most being lower the molecular weight compounds than compounds of interest for SOA formation. However, if a peroxy radical distribution that is reasonably representative of the environment is specified as an input, with Gecko calculating only the peroxy radicals formed from individual compounds of interest, then the modified Gecko simulations could give quantitative predictions of types of accretion products formed from the compounds in various environments. It may not be practical to use Gecko to simulate complex atmospheric mixtures, but the MCM mechanism, which explicitly represents many of the most important types of radicals formed, should be sufficient for this purpose.

However, the use of scenarios with simple mixtures, as employed in two of the three sets of calculations presented in this study, is not a good representation of either the atmosphere or of the types of laboratory experiments generally used to study product formation from individual compounds. The other set of calculations used beta-caryophyllene alone, which may be a good representation of product yield experiments with that compound, but is a very poor representation of real atmospheres.

I found their discussion of how they estimated product yields in the approach they employed to be unclear and questionable. The discussion of how yields are determined for the purpose of determining which radical pairs can be neglected, and for the purpose of reporting relative yields in the various figures, is unclear and needs to be improved. On lines 110-115 they suggested that a maximum yield of 100% was used for competitive bimolecular reactions, while in Section 2.1.2 they discuss calculating relative yields based on rate constants and levels of co-reactants. I'm not sure the approach they discuss in Section 2.1.2 is valid for acyl peroxy radicals, since reaction with NO₂ is not a final sink for these radicals, since the PAN compounds formed in the acyl peroxy + NO₂ reaction can decompose and re-form these radicals. What is needed is presentation of simple examples in the SI for exactly what calculations are used to judge whether reactions of a peroxy pair should be neglected, and for how the relative yields that are presented in the figures are derived. However, if they used actual yields in calculations with standard environments, as suggested above, then all this complexity and questionable treatments regarding estimated yields can be eliminated.

I could not locate a discussion of how they handle cases where both of the reacting peroxy radicals form alkoxy radicals with rapid decompositions. If they both form alkoxys with rapid b-scission reactions that form alkyl radicals, could they react together and form accretion products with new C-C bonds, rather than ethers or esters?

There are several other concerns or issues I have with this paper. These are summarized below, in approximate order they appear in the manuscript and supplement.

Main Manuscript:

I do not understand why the fact that several reaction channels may form the same accretion products, mentioned in Section 2.2.3, is a problem. Certainly Gecko-A must have the code needed to tell whether a molecule formed in one reaction is the same as that formed in another. For the purpose of this paper, I think this should be sufficient for the code to compute the number of products formed without double counting. Or am misunderstanding something in this section?

In Table 3 in the "Statistics" section, it indicates that the first generation n-decane reactions could form an acyl peroxy radical in one generation. I don't understand how this could be the case. In addition, the column headers on Table 3 need to be improved. How are the numbers in the "yield" column computed and what are they relative to? It can't be relative to the amounts of compounds reacted because the yields of peroxy radicals on OH or NO₃ reactions should be close to 100%, or higher in cases where consecutive reactions are important. If they are relative to the amount of reactant present, then they would depend on the reaction time and the levels OH, O₃, or NO₃ present.

I am assuming that the yields shown plots shown on Figures 2-5 are relative to the total amount of accretion products formed from a given compound, since it looks like they may sum up to 100%. If so, this should be stated explicitly. If not, the meaning of yields in these figures, and what they are relative to, need to be clarified. Note that as mentioned above these relative yields give no useful information on how important these products may actually be in the atmospheric environment, which might be very low or negligible for many conditions.

Figures 2b, 2d, 5b, 5d, and perhaps others seem to have more colors on the bar graphs than there are in the legends. If lighter and darker shades of the same color on the bar graphs have significance, then this needs to be mentioned.

In figure 3, it is very difficult to determine which structures are being plotted because the font of the group designations on the X axis is so small it is unreadable without greatly expanding the screen. This figure needs to be redone so that the main information, the type of group, can be more clearly seen. In addition, the plot labels should have "terpene and beta-caryophyllene peroxy radicals", not "terpene peroxy radicals".

Line 424 in section 3.3 states that "the code insures that peroxy radicals with an NO₂ group in the alpha position never forms accretion products". This should be corrected to state that the NO₂ is in the beta position. It may be in the alpha position of the alkyl radical formed in the decomposition, but it is in the beta position in the peroxy radical.

Why are the product yields shown on the volatility distribution plots on Figures 9b and 9d be almost an order of magnitude lower than on the analogous plots of carbon or oxygen number distributions on Figures 2-5? Are they relative to a different quantity? Note that the volatility distributions seem to include compounds of all volatilities, so the total amounts should be the same as in the atom number plots on the earlier figures.

Supplement:

As indicated above, there needs to be a section giving a more complete description of the algorithm(s) used to derive yields for various purposes, and it should include examples of such calculations. The examples would need to as simple as possible while incorporating all the types of situations that may need to be considered. With an adequate discussion of yields in the supplement, some of the complexity in sections 2.1.2 and 2.1.5 could well be moved to the supplement, so the main paper focuses more on the chemistry.

Section S1 is useful, and is sufficiently important that it may be appropriate to include some of this discussion in the main text. This includes possibly Figure S3, which I found to be interesting. However, I think Figure S3 could be improved by using only one plot with different symbols for the complexes with multiple stereoisomers, and also include the 35 kJ/mole cutoff. The line fit should only consider the points below or near that cutoff.

I found the bubble plots on Figure S19 sufficiently interesting that maybe this figure should also be promoted to the main text. Similar bubble plots comparing C and O numbers would also be interesting.

This study analyzes to possible contribution of alkoxy radical chemistry in the triplet RO/RO complexes formed in RO2+RO2 bimolecular reactions, as a source of accretion products for atmospherically relevant molecules. They do this by generating a large number of RO2 intermediates potentially formed in the atmosphere and looking at the likelihood that such accretion reaction occur. The research topic is timely, as the formation of HOMs, accretion products, and other contributors to SOA formation are of high interest at the moment, and our understanding of the formation of these precursors and their chemistry is evolving rapidly. The methodology used to show the importance of these reactions is mostly good (see comments below), and shows that the title reactions are likely to play a role in RO2-driven atmospheric chemistry. The manuscript itself is well-written and clear, and of the appropriate length for the topics discussed. The results are relevant for modeling SOA formation, even if the manuscripts does not provide any direct information under which reactions conditions / regions the reactions are expected to be important.

I support publication of this work. The authors may wish to consider the comments below.

General comments:

The methodology used to generate the datasets of RO2 intermediates of interest is rather elaborate. Using a mechanism generator like Gecko-A is much better than just randomly generating substituted RO2, as the RO2 produced can be assumed to be formed in the atmosphere to some extent. However, using the Gecko-A generator without modeling does not yield any quantitative data; this is acknowledged by the authors not only in the title but explicitly in several places in the manuscript. In that respect, it is awkward that the authors provide statistics weighted by a theoretical maximum yield. This latter quantity is unrelated to atmospheric concentrations nor does it provide any sensible ranking, and should only be used for filtering out reactions. By using maximum yield in a weighting process, it is implied that there is quantitative meaning to both the number of distinct species as well as their theoretical maximum yield, facilitating erroneous interpretation as providing relative proportions that are atmospherically meaningful. This is even more so because several processes are not included in the generation process (autoxidation, CH3O2, RO2 ring closure, scrambling,...), and there is little guarantee that including them would not drastically change the RO2 dataset size and content, and/or the theoretical maximum yields.

I propose that the results weighted by maximum generated yield are removed from the paper as being more confusing/misleading than enlightening. If the authors wanted to provide (semi)quantitative information, they might have set the (lumped) concentrations of all co-reactants to a representative value relevant for a specific environment (HO2, RO2, NO, OH, NO3, O3, HV, ...), as then the reaction selection becomes based on fluxes even for bimolecular reactions, and a better estimate of the real RO2 concentrations can be made. I recognize that the Gecko-A software was not designed for such a selection process.

Section 2.1.2 feels like an overly complex presentation. Overall, it appears the authors just set the concentrations of the 5 co-reactants, and assume an autoxidation rate, which leads to a lumped pseudo-first-order loss rate that can be compared to the bimolecular rate of interest.

The use of the "effective H-bond number HBN = nDα * nAβ + nDβ * nAα" seems incorrect to me. That formula calculates the number of distinct H-bonds possible, e.g. with 1 donor and 16 acceptors you get HBN=16. What is needed conceptually in this context is the maximum number of H-bonds possible, i.e. "HBN = min(nDα, nAβ) + min(nDβ, nAα)", e.g. if only 1 donor is available only 1 H-bond can be present (HBN=1) irrespective of the number of acceptors (≥1). This then correlates to the best possible complex bonding strength and hence the complex lifetime. Overestimating HBN will result in selecting too many "viable" RO2 molecules, and thus artificially increasing the apparent impact of the title chemistry. The cut-off used by the authors is fairly low (1.75), so perhaps the impact of this is limited.

Minor comments :

MetC(O)O2 notation seems inconsistent as all other instances of the CH3 group which are written as "CH3".

p. 3, line 67: The Novelli et al. 2021 update to the RO decomposition SAR is mentioned later in the paper, but could already be mentioned here. In this work the update mostly affects nitrated intermediates.

p. 10, line 250: "In the Supplementary of Peräkylä et al. (2023) this assumption was tested for a small model system, where it turned out that this recombination required an ISC." Perhaps rephrase this, as one does not need a small model to know a triplet to singlet transition requires an ISC.

p,. 10, line 254: "in reality, it is reasonably to assume that dissociation of the product radical and the remaining RO is less competitive than dissociation of the two RO in the 3(RO. . .OR) complex". Mention the estimate of the ISC rate to show why this is reasonable. If the decomposition is exothermic, which is nearly always, the energy release will accelerate the dissociation, making this assumption perhaps not so obvious.

p. 11, line 270: "as we lack the ability to estimate them adequately.". add "... during the mechanism generation" (they can be estimated by modeling).

p. 12, line 309: "..., as the current paramerization in GECKO-A this reaction most often leads to formation of hydrotrioxides (ROOOH), chemistry includes several unknown details." Correct this sentence.

p. 15, line 388: "RO2 punch above their weight". This phrasing may not be understandable to non-native English speakers. I propose e.g. "contribute more than expected from their concentration"

Table 3: "". I'm a bit weary of using "yield", as that has a specific meaning in kinetics, and what is listed here is not a yield. Alternatives: Fraction, Contribution, Subset size,...

p. 27, upper paragraph. A cyclisation reaction that might be mentioned is the ring closure in unsaturated RO2, which has been theoretically predicted (e..g Vereecken et al., DOI 10.1039/d1cp02758a) and very recently been measured to be fast (work by Barbara Nozière and coworkers, submitted). These reactions represents another reaction class missing in the mechanism generation process.

p. 27, line 531: "How do the results for β-caryophyllene compare to the monoterpenes? In the end, not considerably." This Q&A style is better suited for a conference than a paper. I propose e.g. "the results for β-caryophyllene are [not] comparable to those of monoterpenes".