First, a caveat. As I collaborate quite a lot with professor Elm, this comment should really be considered a “community comment” rather than a reviewer comment. I.e. the authors should feel free to disregard my comment, and the editors should place a low weight on my review (either way) when deciding on what to do with the paper.

This is a nice paper introducing a useful new concept, but I have a suggestion on how to take it further (either in this manuscript, or in future work). Specifically, it might be useful to discuss and treat the proposed additivity in terms of the two components of the binding/formation free energy: the enthalpy and the entropy. 

In the absence of steric constraints (e.g. all three groups of a tricarboxylic acid being prevented from binding optimally, compared to three separate HCOOH), and ignoring intermolecular H-binding in the reactant organics, the binding energy should indeed be roughly additive (and thus also the enthalpy, apart from the rather minor pV-term, which I’d like to thank Lauri Franzon in my group for pointing out). So far so good. 

However for the clustering entropy, the major contribution comes from the loss of translational and rotational degrees of freedom (and their conversion into lower-entropy vibrational degrees of freedom). Three of each (i.e. six in total) are lost per clustering molecule, so e.g. for 3 x HCOOH the total loss is 18 high-entropy degrees of freedom, while for a tricarboxylic only 6 would be lost. The entropy loss upon clustering is thus very probably NOT additive, or at least it could/should be split into two components:

-a definitely non-additive term coming from the above-mentioned loss (this should be counted only once per condensing molecule)

-another, possibly additive, term originating from some of the flexible internal rotations (especially important in large OOMs), becoming more constrained during clustering. 

As the translational entropy loss is determined directly from the molecular mass, and the rotational entropies can be estimated from very crude (e.g. molecular mechanics - level) simulations, or alternatively fitted to the datasets the authors already have, perhaps some parametrisation of the clustering entropy along the lines proposed above could be envisioned, in order to improve the model?

Having said that, the current admirably simple model probably benefits from some degree of cancellation of error. As discussed above, the entropy penalty of clustering one tricarboxylic (with say a SA-DMA “core”) is considerably smaller than that of clustering three HCOOH. So based on that, the delta-G for adding the tricarboxylic might be much more negative than the -15 kcal/mol value quoted here. At the same time, it’s unlikely that all three carboxylic acids groups of any real tricarboxylic can simultaneously reach the ideal bonding geometries shown in e.g. figure 8. So also the enthalpy gain will be less than in the “perfect additivity” assumption. Furthermore, the model (if I understand it correctly) completely neglects possible intramolecular H-bonds inside the reactant OOM, which tend to decrease the favourability of their clustering reactions (as some of the H-bonding capacity is already used up, so to speak). Almost certainly any real tricarboxylic will tend to have at least some interactions between some of the groups already in the organic monomer. 

This leads me to a suggestion (that I only realised after writing the above text): perhaps most or all of this (with the possible exception of more complex steric effects in huge OOMs) could be modelled by using e.g. (HCOOH)2 or (HCOOH)3 (or the corresponding clusters of other model organics) as the model reactants? I.e. take the enthalpy gain from a comparison of X + (HCOOH)n => X(HCOOH)n, and then split the entropy as suggested above, counting the “loss-of-translation-and-rotation” penalty only once? (X stands for the inorganic “core” here, e.g. SA*DMA).

Or - even simpler and better - the second entropy term, i.e. the constraining of flexible internal rotations, would actually already be partly taken into account in the (HCOOH)2 and (HCOOH)3 clusters… so actually just straightforwardly computing the delta-G for the reaction  X + (HCOOH)n => X(HCOOH)n would provide a decent proxy for the delta-G of the addition of a tricaboxylic without steric constraints, BUT making perfect internal H-bonds. (Thus providing some cancellation of errors also for this somewhat more nuanced additivity approach.) 

As the authors should have most of the data already (they certainly have at least (HCOOH)2, and (HCOOH)3 should be easy enough to generate), maybe quickly check what type of numbers this approach gives (at least for the carboxylics), and compare with what they have in the present paper?

Best regards,

Theo Kurtén

Elm et al. utilize a novel approach called the "cluster-of-functional-groups" to investigate the involvement of oxygenated organic molecules (OOMs) in atmospheric cluster formation. By examining these interactions, they aim to identify the structural characteristics of OOMs contributing to particle formation. Their study shows that clusters with multiple carboxyl groups are notably stable. Through simulations, they explore how OOMs with multiple carboxyl groups can stabilize sulfuric acid - base clusters, suggesting potential tracer compounds for future research. The presented “cluster-of-functional-groups" approach is novel and applicable in the study of atmospheric aerosols. The most part of this manuscript is well written and of broad interest to the readership of Aerosol Research. I recommend publication in Aerosol Research after the following comments have been addressed.

Specific Comments:

Comment 1: Page 4 lines 91-92: “For each protonation state in the cluster, 1000 local minima were saved.” The meaning of "each protonation state in the cluster" may be confused. Did the author investigate all possibilities of acid-base reactions within the same cluster? Please provide more detailed information on this aspect.

Comment 2: Page 4 lines 100-103: “Small organic molecules were chosen to represent the functional groups that act as hydrogen bond donors (alcohol (CH₃OH) and peroxide (CH₃OOH)), as well as functional groups that act as hydrogen bond acceptors (ether (CH₃OCH₃), epoxide (C₂H₄O), aldehyde (CH₃CHO), ketone (CH₃COCH₃), acid anhydride (CH₃C(=O)OC(=O)CH₃) and ester (COOCH₃). Besides these groups, carboxylic acid, (HCOOH), which is both an acceptor and a donor, was also included.” This method is innovative, however, I still have a concern. Earlier, the authors mentioned that "not a single OOM has definitively been proven to participate in nucleation in the planetary boundary layer (Elm et al, 2023). The lack of progress could be ascribed to the fact that previous work have been looking at the wrong compounds. All studies have been performed on the organic monomers, while recent evidence from the CLOUD chamber has shown that it is in fact the covalently bound organic dimers". This implies that monomers and dimers with similar functional groups may exhibit completely different nucleation capabilities. Can the "cluster-of-functional-groups" method adequately consider the difference between monomers and dimers? I hope the authors can provide a brief discussion on this concern.

Comment 3: Page 5 lines 127-130: “For our systems, we chose the clusters with one additional acid compared to the cluster sizes we have data for [(SA)₃(base)₂, (SA)₂(OOM)₂(base)₂ and (SA)₃(OOM)₁(base)₂]. These outgrowing cluster sizes are quite small and therefore artificially stabilize the systems as the critical cluster size is not necessarily captured well.” Why were different sizes of outgrowing clusters used for the SA-base and SA-base-OOM system? For the ACDC simulations, setting different sizes of outgrowing clusters may directly affect the simulated cluster formation rates of SA-base and SA-base-OOM system, thereby overestimating or underestimating the impact of OOM. Please provide more information about these settings.

Comment 4: Page 12 lines 222-227: “Hence, if these are treated as individual molecules it is unlikely that they form stable clusters at realistic atmospheric conditions. However, if all three functional groups are treated as single OOM, the free energy for adding a hypothetical idealized tricarboxylic to the (SA)₁(DMA)₁ cluster is ∆G = −15.71 kcal mol⁻¹. This is a very strong binding and would correspond to a quite stable cluster. Hence, by employing the “cluster-of-functional-groups" approach we have identified that tricarboxylic acids are likely candidates for forming stable clusters with SA and bases.” I have doubts about the hypothesis that the binding free energies of the individual functional groups are additive:

1. As shown in Figure 8, the introduction of three CAs into SA-DMA can saturate the cluster. However, these three CAs are positioned on the outer side of SA-DMA in three different directions, implying that a single tricarboxylic acid may have difficulty achieving the same effect. Would such a possibility affect the author's predictions?
2. Compared to three CAs, a tricarboxylic acid is likely to introduce some parts with minimal contributions to the nucleation process. Will these parts inhibit nucleation?
3. The author's hypothesis and conclusion demonstrate great innovation and foresight. If feasible, I suggest supplementing some data of the binding free energies of SA-DMA-tricarboxylic acid clusters to validate this conclusion.

Comment 5: Page 12 lines 231-233: “Letting the three carboxyl groups represent a single OOM we simulated the cluster formation potential (J_potential) of the (SA)₁₋₂(base)₁₋₂(OOM)₁ systems, with base = AM, MA, DMA and TMA.” To let the three carboxyl groups represent a single OOM, did the author treat the binding free energy of OOM as the sum of three carboxylic acid groups? If so, then I would like to know how parameters such as the radius and mass of the OOM are set during ACDC simulations, as these directly affect the simulation results.

Minor Comments:

Comment 1: Page 2 line 37: “The puzzle of the role of organics in aerosol nucleation originate from the fact that there exist a myriad of OOMs in the atmosphere.” “exist” → “exists”.

Comment 2: Page 2 line 50: “The lack of progress could be ascribed to the fact that previous work have been looking at the wrong compounds”. “have”→“has”.

Comment 3: Page 3 line 83: “The simulations were done at 278.15 K with a constant coagulation sink of − 1.6 × 10⁻³ s^−1”. The format of the value "1.6 × 10⁻³ s⁻¹" is inconsistent with the format of the main text. Similar problems occur repeatedly in the main text. Please correct it.

Comment 4: Page 5 line 131: “These rates illustrates the potential of the cluster to grow to larger sizes and corresponds to an upper-bound on the formation rate.” “illustrates”→“illustrate”.

Comment 5: Page 6 line 142: “However, this value correspond to a high evaporation rate of the formic acid dimer” “correspond”→“corresponds”.

Comment 6: Page 7 line 153: “... where there is two carboxylic acid groups in total as this fully saturates the SA molecule.” “is”→“are”.

Comment 7: Page 14 line 268: “Such a large compound has newer been studied in atmospheric cluster formation and would be worth investigating in the future.” “newer”→“never”.