Wu et al. present a definition of freshly nucleated particles based the determination of thermodynamic properties of large sulfuric acid-base clusters (where base = ammonia/methylamine/dimethylamine/trimethylamine). Their study allows to clearly distinguish the boundary between discrete cluster configurations and bulk particles. This study is of fundamental importance in understanding the cluster-to-particle transition process in sulfuric-based clusters. The manuscript is very well written and results are of substantial relevance to Aerosol science. Therefore, I recommend publication to Aerosol Research after the following minor comments have been addressed.

1. Introduction. It would be better to give a reference to the recent IPCC report.
2. Subsection 2.1.1. For each cluster type, the authors start from thousands randomly generated configurations, ending up with one assumed cluster structure lowest in free energy that is used in further thermochemical analysis and modeling. It is obvious that real life situations would involve multiple configurations. Although they report in Subsection 3.5 that two lowest energy configurations are enough when determining the clusters properties, the populations of two lowest energy configurations can rarely exceed 60% in some cases. Can’t the thermal averaging of multiple conformers be considered in this case?
3. Subsection 2.1.2. The authors used the convex hull approach to investigate when the first solvation shell appears. Don’t they think that molecular dynamics simulations could be a better approach since they provide the “real” dynamics of clusters evolution with time?
4. Subsection 3.5. What is the energy difference range between the global minimum and other three lowest free energy configurations?
5. Page 15, Line 312: “…to disentangle which bases that are important for nucleation and which that are important for the growth.” Remove “that” at the two places.
6. The authors should choose to use either the unit kcal mol^-1 or kcal/mol both in the text and in the figures/tables and not use both in a sporadic way.
7. Check the good spelling of the author named “Sipilä” used at line 25 and in the reference list.

The study by Wu et al. addresses the question of molecular-cluster-to-particle transition in aerosol nucleation. Resolving such transition sizes is important for being able to understand and represent secondary particle formation and growth in atmospheric models. Assessing transition processes has mostly been impossible due to the lack of reliable theoretical and computational approaches for describing the chemistry of growing molecular complexes of >1nm, and therefore this work makes an important contribution.

The study is relevant for the journal scope, and the methods and results are generally sound. I have a few comments that I ask the authors to address before I can recommend publication.

1. It needs to be clarified that the suggested criteria for a cluster becoming a particle address the structure and stability of the molecular complex, and not the actual chemical or thermodynamic properties as compared to liquid properties, as described e.g. by well-established ionic liquid models such as E-AIM and AIOMFAC.

Therefore, for clarity, I suggest to reformulate statements such as “…freshly nucleated particle (FNP) regime where the properties more resemble bulk particle-like properties”, as this is easily (mis)understood as bulk thermodynamic properties, e.g. protonation states, activity coefficients and Kelvin effect.

2. I’m not sure if I understand the meaning of the quantity that is used to define “FNP” in Figure 4, left panel. By looking at the values in Figure 4 and as stated in the text, this quantity seems to be the binding free energy divided by the number of molecules in the complex, i.e. DeltaG/m. As a result, the shape of the graphs mainly illustrates the reciprocal of the monomer number, i.e. 1/m, m = 2, 4, 6, …

Especially the definition in the Abstract is strange: “we define the onset of FNPs as (…) when the gradient of the change in free energy per monomer (m) approaches zero” since DeltaG/m is not a gradient nor does it approach zero in Figure 4.

I recommend to use instead the change in DeltaG upon addition of monomer pair, i.e. the actual gradient Delta(DeltaG); maybe this was also the original idea of the authors based on what is written in the Abstract?  Intuitively, the discrete “cluster-like” effects should gradually disappear with increasing molecular complex size as the effects of the positions, orientations and bonds of individual molecules become less important. The transition to a more “particle-like” phase can indeed be expected to be manifested by the gradient of the size-dependent thermochemical properties exhibiting a smoother behavior with increasing size, instead of larger and irregular changes.

3. (i) Even when the properties start to resemble those of liquid particles as the cluster size increases, the stability is still expected to exhibit a size dependence at nanometer sizes through the surface curvature effect, i.e. the Kelvin effect (e.g. Factorovich et al., Am. Chem. Soc. 136, 4508-4514, 2014). Can you comment on if and how such effect is present in the stability of the studied complexes?

(ii) Related to this, it must be noted that the stability can’t be studied solely based on additions of acid-base monomer pairs. The gradient Delta(DeltaG) determines the size- and composition-dependent exponential factor in the cluster evaporation rate, or equally in the saturation vapor pressure above the cluster/particle surface, and consequently the size-dependence becomes negligible when Delta(DeltaG) levels off. However, this behavior is not necessarily same for single monomers, as evaporation of molecule pairs is typically rare event compared to evaporation of molecules.

Can the results be expected to be similar when studying the energetics of single-molecule additions instead?

4. P15L291: A weight of >30 % for the lowest-energy structure in the ensemble is actually not that high. How would considering the ensemble affect the effective binding free energies (e.g. Partanen et al., J. Phys. Chem. A 120, 8613-8624, 2016)? Or why can it be assumed that the ensemble would not affect them?

5. P10L226: Is the use of self-consistent distribution necessary? Does this artificially change the differences between the binding free energies of different clusters, i.e. Delta(DeltaG)? I’m not convinced that the monomer free energies need to be forced to zero, as the important quantity of interest when studying the growth thermodynamics and nucleation barriers are the differences Delta(DeltaG), not the absolute energies DeltaG.

Minor comments:

P1L11 and other such occurrences: the cluster sizes are here denoted as the total number of monomers, i.e. including both acid and base molecules. For clarity and since only 1:1 acid:base compositions are studied, it could be better to use the number of acid-base pairs.

P1L14: Presumably the SA-AM and SA-MA clusters can grow also beyond 1.8 nm, even if it’s not addressed in the present study?

P1L16: SA-TMA clusters are here found to not grow to larger sizes, but could they do this by condensation by some other compounds?

P1L18: Should the statement “aerosol-cloud interactions remain the largest uncertainty in global climate modelling” be rather “aerosol-cloud interactions remain the largest uncertainty in global radiative forcing”?

P1L23: A “measurable” particle is said to be of approximately 2 nm in diameter: while this is true for many standard atmospheric measurement sites, it must be noted that particles and clusters down to ca. 1 nm sizes or even beyond can be measured by both mass spectrometer and condensation particle counter techniques.

P10L221-222: The statement about cluster thermochemistry being dependent on the concentration of the clustering monomers should be clarified. What does this exactly refer to? The relative distribution of different cluster compositions, as well as the driving force of condensation/clustering, are indeed dependent on vapor concentrations, but the thermochemical properties of given compositions are not.

P10L232: It can be noted that in non-polluted environments, the “low-concentration” limit of 1 ppt for amines can actually be somewhat high, and the concentrations are likely lower outside the vicinity of amine sources. 1 ppt is of the order of >1e7 cm^-3, which can be ca. an order of magnitude higher than the concentration of sulfuric acid in many environments (of the order of 1e6 cm^-3). Assuming that both SA and amines condense efficiently on aerosol, maintaining an amine concentration of >1e7 cm^-3 would require a constant amine source.

P12L237: It should be noted that in general, nucleation barriers can’t be determined based on only 1:1 compositions, as barriers might be involved in additions of single molecules.

Please review the citations as some are not written correctly, such as “IPC” and “Sipilää et al.” on P1.