the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Mar 2025
Growth of Atmospheric Freshly Nucleated Particles: A Semi-Empirical Molecular Dynamics Study
Abstract. When simulating new particle formation rates, collisions in the system are approximated as hard spheres without long-range interactions. This simplification may lead to an underestimation of the actual formation rate. In this study, we employ semi-empirical molecular dynamics (SEMD) at the GFN1-xTB level of theory to probe the sticking process of the monomers sulfuric acid (SA), methanesulfonic acid (MSA), nitric acid (NA), formic acid (FA), ammonia (AM), methylamine (MA), dimethylamine (DMA), and trimethylamine (TMA) onto freshly nucleated particles (FNPs). The FNPs considered are (SA)10 (AM)10, (SA)10 (MA)10, (SA)10 (DMA)10, and (SA)10 (TMA)10.
In general, we find that the hard-sphere kinetic approximation, which neglects long-range interactions, significantly underestimates the number of collisions leading to sticking. By calculating the sticking coefficient from SEMD simulations, we obtain enhancement factors of 2.3 and 1.5 for the SA+(SA)10 (AM)10 and AM+(SA)10 (AM)10 collisions, respectively. A comparison with OPLS all-atom force field simulations shows similar enhancement factors of 2.4 and 1.6 for the SA+(SA)10(AM)10 and AM+(SA)10(AM)10 collision, respectively
Compared to the force field simulations, SEMD exhibits a more isotropic sticking behavior, with the probability remaining near unity for small offsets before rapidly dropping to 0 % beyond a certain offset. In contrast, the force field simulations show a more gradual decline in sticking probability due to certain orientations still leading to sticking. The largest discrepancy between the two methods occur at lower collision velocities—below 200 m/s for SA and below 400 m/s for AM—where force field simulations, even for head-on collisions, predict low or zero sticking probability. This has previously been attributed to periodic repulsions between the rotating collision partners caused by fluctuations in their charge distributions. In contrast, SEMD simulations do not exhibit this behavior. Since these low velocities are not significantly populated in our simulations, both methods yield similar enhancement factors. However, for systems with larger effective masses, where such velocities are more prevalent, we would expect the two methods to diverge.
Competing interests: Jonas Elm is a member of the editorial board of Aerosol Research.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.- Preprint
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RC1: 'Comment on ar-2025-9', Anonymous Referee #1, 23 Mar 2025
The authors studied the collision and sticking processes of multiple acid and base molecules onto acid-base clusters with 10 acid-base pairs, using the semi-empirical GFN1-xTB method. The results were compared with those from the classical force field methods. The results are of interest, especially most previous studies on atmospheric cluster collision and sticking were performed using non-reactive force fields, while very few report results with a method that is reactive. The study is comprehensive and well carried out. I support its publication in Aerosol Research, with only a few minor comments:
Many readers might be interested to see more discussions/details on how proton transfer reactions happen at the molecule-cluster interface upon collision, and how that could vary the evaporation tendency of the newly captured molecule. I would encourage the authors to provide more details on this point. Maybe some statistics and visualizations could be helpful.
Line 74: To my knowledge, Yang et al (Yang H, Goudeli E, Hogan C J. Condensation and dissociation rates for gas phase metal clusters from molecular dynamics trajectory calculations[J]. The Journal of chemical physics, 2018, 148(16).) employed the same simulation setup and method to calculate the sticking rates. It is also earlier than the other papers, which used the same method, cited here. It might not be bad to also cite this paper.
Line 134: The form of the intermolecular potential might not be a good approximation for molecule-cluster interactions. Maybe the authors could consider to check the acceleration of the molecule instead, in order to make sure if the initial COM distance is large enough?
Citation: https://doi.org/10.5194/ar-2025-9-RC1 -
RC2: 'Comment on ar-2025-9', Mária Lbadaoui-Darvas, 10 Apr 2025
The authors present a comprehensive study of collisional growth of freshly nucleated particles using semi-empirical molecular dynamic at the GFN2-xTB level and characterise the new method as an alternative to hard sphere model approximations or classical molecular dynamics simulations. They investigate the uptake (sticking) of acidic and basic molecules on a freshly nucleated particle consisting of 10 sulfuric acid and 10 trimethylamine molecules. They estimate collision enhancement factors and sticking probabilities and compare the newly presented method with standard forcefield simulations as well with calculations based on the kinetic gas theory.
They conclude that the kinetic gas theory underestimates the sticking probability and find similar results as using classical molecular dynamics simulation. They highligh that the two latter methods might diverge for particles with larger masses and in case of proton transfer reactions which are neglected in standard forcefield simulations. The method presented in the manuscript has clear advantages over traditional methods used to estimate sticking probabilities which are essential for performing cluster dynamics models.
The publication is well written, and results represent an important contribution to the field, therefore I warmly recommend the paper to be published after the following minor comments are addressed:
Comments on content:
- The results and the context are very well presented and explained in details, however the description of the molecular simulations used to produce the data could be extended. In the current format many technical concepts, such as SEMD and the level of theory used in the calculation, remain only fully understandable to experts of MD simulations, while the journal targets a more general audience. Keeping this latter consideration in mind, I think that the paper would benefit from adding short description of SEMD and highlighting main differences with classical MD.
- I would appreciate a comparison of computational cost of the SEMD and the corresponding classical MD simulations.
Minor editorial comments
- Line 65 (Furthermore, it is not clear if the unit accommodation factor is a reasonable approximation for all clusters of interest in NPF) would fit better as the first sentence of the following paragraph
- In Figure 3, the total cumulative mean temperature is hardly visible, it would be perhaps meaningful to use a different linestyle that allows overlapping lines to show up.
Citation: https://doi.org/10.5194/ar-2025-9-RC2 - AC1: 'Comment on ar-2025-9', Yosef Knattrup, 29 Apr 2025
Status: closed
-
RC1: 'Comment on ar-2025-9', Anonymous Referee #1, 23 Mar 2025
The authors studied the collision and sticking processes of multiple acid and base molecules onto acid-base clusters with 10 acid-base pairs, using the semi-empirical GFN1-xTB method. The results were compared with those from the classical force field methods. The results are of interest, especially most previous studies on atmospheric cluster collision and sticking were performed using non-reactive force fields, while very few report results with a method that is reactive. The study is comprehensive and well carried out. I support its publication in Aerosol Research, with only a few minor comments:
Many readers might be interested to see more discussions/details on how proton transfer reactions happen at the molecule-cluster interface upon collision, and how that could vary the evaporation tendency of the newly captured molecule. I would encourage the authors to provide more details on this point. Maybe some statistics and visualizations could be helpful.
Line 74: To my knowledge, Yang et al (Yang H, Goudeli E, Hogan C J. Condensation and dissociation rates for gas phase metal clusters from molecular dynamics trajectory calculations[J]. The Journal of chemical physics, 2018, 148(16).) employed the same simulation setup and method to calculate the sticking rates. It is also earlier than the other papers, which used the same method, cited here. It might not be bad to also cite this paper.
Line 134: The form of the intermolecular potential might not be a good approximation for molecule-cluster interactions. Maybe the authors could consider to check the acceleration of the molecule instead, in order to make sure if the initial COM distance is large enough?
Citation: https://doi.org/10.5194/ar-2025-9-RC1 -
RC2: 'Comment on ar-2025-9', Mária Lbadaoui-Darvas, 10 Apr 2025
The authors present a comprehensive study of collisional growth of freshly nucleated particles using semi-empirical molecular dynamic at the GFN2-xTB level and characterise the new method as an alternative to hard sphere model approximations or classical molecular dynamics simulations. They investigate the uptake (sticking) of acidic and basic molecules on a freshly nucleated particle consisting of 10 sulfuric acid and 10 trimethylamine molecules. They estimate collision enhancement factors and sticking probabilities and compare the newly presented method with standard forcefield simulations as well with calculations based on the kinetic gas theory.
They conclude that the kinetic gas theory underestimates the sticking probability and find similar results as using classical molecular dynamics simulation. They highligh that the two latter methods might diverge for particles with larger masses and in case of proton transfer reactions which are neglected in standard forcefield simulations. The method presented in the manuscript has clear advantages over traditional methods used to estimate sticking probabilities which are essential for performing cluster dynamics models.
The publication is well written, and results represent an important contribution to the field, therefore I warmly recommend the paper to be published after the following minor comments are addressed:
Comments on content:
- The results and the context are very well presented and explained in details, however the description of the molecular simulations used to produce the data could be extended. In the current format many technical concepts, such as SEMD and the level of theory used in the calculation, remain only fully understandable to experts of MD simulations, while the journal targets a more general audience. Keeping this latter consideration in mind, I think that the paper would benefit from adding short description of SEMD and highlighting main differences with classical MD.
- I would appreciate a comparison of computational cost of the SEMD and the corresponding classical MD simulations.
Minor editorial comments
- Line 65 (Furthermore, it is not clear if the unit accommodation factor is a reasonable approximation for all clusters of interest in NPF) would fit better as the first sentence of the following paragraph
- In Figure 3, the total cumulative mean temperature is hardly visible, it would be perhaps meaningful to use a different linestyle that allows overlapping lines to show up.
Citation: https://doi.org/10.5194/ar-2025-9-RC2 - AC1: 'Comment on ar-2025-9', Yosef Knattrup, 29 Apr 2025
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