Tri-Base Synergy in Sulfuric Acid-Base Clusters

Round 1

Reviewer 1 Report

The manuscript shows the results of theoretical research on sulfuric acid clusters with different bases. As the authors admit, several systems have been studied before, but most of the clusters are presented for the first time. I appreciate the work put into this research.
My main consideration concerns the conditions with which the calculations relate. In the Thermochemistry section, the results only apply to the temperature and pressure conditions of 298.15 K and 1 atm. The stability and energy of the clusters as well as the synergy factors are shown and discussed for these conditions. Also conclusions are drawn after analyzing these results. As I understand in the chapter Concentrations, the binding free energy, whether the temperature also applies to 298 K and 1 atm. How does this relate to the conditions of the atmosphere, especially the troposphere, which contains the vast majority of gas molecules, including those under study? Should the authors not supplement their thermochemical results with calculations at lower temperature and pressure, e.g. for a height of 10 or 12 km above the ground (they can choose one point from the upper tropospheric layers)? Such calculations can be made for already optimized structures. Even a brief comparison of such data could significantly enrich the work. I encourage the authors to make this effort.
Another suggestion is from the Introduction to describe exactly what is meant by atmospheric conditions (line 48)? Which atmospheric conditions were included in the work?   In the caption of Fig. 1 add that in each structure three molecules of sulfuric acid are present. 
I noticed a few grammatical and stylistic errors.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

In this investigation, Xie et al. extended the synergy concept to three bases by performing the quantum chemical computations on atmospherically relevant (sulfuric acid)₃(base)₃ clusters where the bases are ammonia (A), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA) and ethylenediamine (EDA). It is claimed that the main findings of this investigation are

1. The cluster stability, in general, depends on the basicity of the constituent bases.
2. DMA enhances the cluster stability and TMA decrease the cluster stability
3. There is a high synergy between DMA and EDA.
4. It is highly likely that three, or potentially more different bases are involved in the growth pathways of sulfuric acid-base clusters.

The quantum chemical calculations were performed quite extensively, therefore, the results seem quite valuable to the wide range of gas-phase communities.

However, this manuscript is required to address the following comments and suggestions before publication

1. Page -2, line 51, Can the authors introduce the physical significance of the “synergistic effect “ in brief.
2. Page -2, line 62-63, It is not clear why the authors need to apply the Gaussian 09 default convergence criteria while working with Gaussian 16.
3. Page -2, line 92-93, Did the authors confirmed that there was no imaginary frequency from ωB97X-D/6-31++G(d,p) calculation? And was it because of the poor initial geometry of the clusters, the DFT calculations were restarted three times?
4. Page -3, Equation (2), There are three terms inside the parenthesis. Why the authors neglecting the free energy of clusters consists of j,j,k, j,k,k,   j,k,l etc?
5. Page-4, Figure 1, (SA)₃ prefix should be given before name of the individual cluster, e.g. (SA)₃ (A)₃ not (A)₃.
6. Page -4, line-156, How this cut-off of “100 cm^-1” was chosen? It is important to cite the relevant reference here.
7. Page 5-6, Please stick to either ‘stability’ or ‘free energy’ while comparing among the complexes. Then it will be easier to follow, otherwise, it is sometimes confusing.
8. Page 5, line 184, The authors started to discuss ‘mixed clusters’. Then page 6, line – 191, again started to discuss ‘remaining mixed clusters’. It is not very clear how the mixed clusters were divided into these two sets (‘mixed clusters’, ‘remaining mixed clusters’) for the discussion?
9. Page 6-7, line 227-229, The discussion is very convoluted. Therefore, it will be nice if the authors reiterate the most relevant key sentences under each of the three “fundamental additional guidelines”.
10. It will be nice to provide a correlation plot between the cluster stability and basicity of the constituent bases.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Sulfuric acid-base clusters play important roles in atmospheric new particle formation especially under urban environments. This manuscript performed quantum chemical calculations to investigate the synergistic effects by including three base molecules in a cluster containing three sulfuric acid molecules. It then draws conclusions based on the structures, thermochemistry, and concentration distributions of the clusters. The paper presents interesting results and is within the scope of the Journal. It is quite well written and can be publishable after the authors fully address the following issues.

 

Major comments:

1. L103-114 on p3, the description of the synergistic effects. How are the effects related to the values of those parameters? Are they stronger if the values are more positive or vice versa? Please give some detailed description.
2. L166-169 on p5, obviously it is opposite, isn’t it? The binding energy of (SA)1(TMA)1 is bigger than that of (SA)1(DMA)1 according the given numbers.
3. The authors attribute the stabilities of the clusters partly to the basicity of the clustering bases. Can the authors take one more step to present quantitively how the basicity works for the stabilization? Why EDA produce more synergistic effects? Is it because it is a diamine?
4. As shown in Table 3, the relative concentrations are as high as 10^8 and this is a quite large range. What is the estimated absolute concentration if the authors made some reasonable assumptions and based on the current knowledge? Then the authors may find that some estimates in Table 3 might be physically nonsense. Please corroborate the results.

 

Minor:

1. Affiliation 2, confirm?
2. Please keep the number format consistent throughout the manuscript.
3. L27 on p1, know here should be “known”.
4. L103-114 on p3, please give references.

 

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I recommend the manuscript for publication in its present form.