Galib Hasan et al. have studied the formation of freshly nucleated particles from sulfuric acid and two bases, ammonia and dimethylamine, using quantum chemical methods. The manuscript shows the synergetic impact of these two bases on particle formation, and how, despite being a weaker base, larger clusters with addition of one to three ammonia monomers are more stable than clusters consisting purely of sulfuric acid and dimethylamine. The study also bring insight into the transition from clusters to particles, a question that has for long remained open. It is relatively well-written and easy to follow, and the analysis itself is well-made. Overall,, this study by Galib Hasan et al. furthers our understanding of the formation of freshly nucleated particles, and therefore I recommend it to be accepted for publication after the following comments have been addressed.

General comments

The transition of a cluster to a particle is a big part of the main conclusions and relevance of the paper. Therefore, it should be explained more than it is. Now it remains unclear for the reader how exactly the point of transition is defined, and what it is based on.

I am also missing some discussion on environmental impacts and the relation of these results to the real atmosphere. For example, conditions with two different temperatures and concentration regimes are studied, and these could be more clearly related to real atmospheric environments. In addition, the differences in the results for these different conditions and their impacts on atmospheric cluster formation could be discussed further.

There are some typos, formatting issues and minor grammatical issues, and I suggest the authors go over the text with care. Many of these issues are specified in the detailed comments.

Specific comments

Introduction

1. The first paragraph is half a page long, which makes it harder to read. It could be divided into at least two separate paragraphs.

2. L37: While this sentence does not really need a reference to begin with, referring to a study over 10 years old does not really fit the point it is trying to make.

3. L85: Would it be possible to explain a bit more in detail what this property-based criteria for determining the boundary between clusters and particles is?

Methods:

4. L134: Please define how this error is determined.

Results

5. Figure 3 and the respective text. The only clusters that are labeled are on the upper and lower edges. Therefore, on e.g., L194 (L197), where clusters (0,7) and (0,8) ( (0,9) and (0,10) ) are discussed, I cannot see what points refer to these clusters and where the free energy values referred to in the text are read from. This should be somehow clarified, the reader should also be able to see where the values come from.

6. L202: As this transition from cluster to particle is such a big part of the conclusions of the manuscript, the concept and why it is interpreted so should be explained a bit more. What is the threshold value of the averaged binding free energy change from cluster to cluster after which transition to particle is considered to have occurred? And why? In addition, I think a brief explanation on why the leveling out of the averaged binding free energy can be thought of as the cluster transitioning to a particle would also help in clarifying the concept and the relevancy of this paper for the readers who might be less familiar with the topic.

7. L219: “Hence, the cluster-to-particle transition point occurs at a cluster size of 14 monomers…” Please explain how this is determined from Figure 3. In addition, as such a large part of aerosol research is concerned with diameters of clusters/particles, could rough estimations of the diameter these clusters correspond to be given?

8. L229: In real world, sulfuric acid concentration also varies between environments. Would including that variation affect the results?

Technical comments

L46: Formatting issue with reference: “...base molecules Almeida et al. (2013).”

L59: “… in the stabilizing the initial SA clusters” → “… in stabilizing the initial SA clusters”

L155: “… the GFN1-xTB (Grimme et al., 2017) semi-empirical method.” → “… the GFN1-xTB semi-empirical method (Grimme et al., 2017).” When possible, placing the reference to the end of sentence, improves readability of the text.

L180: “We previously Wu et al. (2024) tested …” should be reformulated e.g., “In Wu et al. (2004), we previously tested …”

L185: “ … clusters are taken from (Wu et al., 2024),” → “… clusters are taken from Wu et al. (2024),”

L186: Figure 3a, not 2a, I presume.

Figure 3 caption:

“… ≤ n., under …” → “… ≤ n, under …”

“(298,15 k and 1 tm)” → “(298.15 k and 1 atm)”

Figure 4 caption: I would presume yellow is supposed to be sulfur, not nitrogen.

L210: “AM molecule, makes it”→ “AM molecule makes it”

L221: “single point refinement single point refinement.”

L236: “energies in Figure 5a, shows that” → “energies in Figure 5a show that”

L244: Please define MA and TMA.

L251: “around 4 monomers” Please clarify that this is for the SA-AM.

L235, L245, L257 and L265: “298,15 K” → “298.15 K” , “278,15 K” → “278.15 K”