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  • Perspective
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Current and future machine learning approaches for modeling atmospheric cluster formation

Nature Computational Science volume 3, pages 495–503 (2023)Cite this article

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Abstract

The formation of strongly bound atmospheric molecular clusters is the first step towards forming new aerosol particles. Recent advances in the application of machine learning models open an enormous opportunity for complementing expensive quantum chemical calculations with efficient machine learning predictions. In this Perspective, we present how data-driven approaches can be applied to accelerate cluster configurational sampling, thereby greatly increasing the number of chemically relevant systems that can be covered.

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Fig. 1: Overview of cluster sizes.
Fig. 2: ML step in cluster configurational sampling.
Fig. 3: Influence of database selection on ML accuracy.
Fig. 4: Extrapolation of ML models.
Fig. 5: ML prediction of energies for large clusters.

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References

  1. Haywood, J. & Boucher, O. Estimates of the direct and indirect radiative forcing due to tropospheric aerosols: a review. Rev. Geophys. 38, 513–543 (2000).

    Article  Google Scholar 

  2. Lohmann, U. & Feichter, J. Global indirect aerosol effects: a review. Atmos. Phys. Chem. 5, 715–737 (2005).

    Article  Google Scholar 

  3. Boucher, O. & Lohmann, U. The sulfate–CCN–cloud albedo effect. Tellus B 47, 281–300 (1995).

    Article  Google Scholar 

  4. Spracklen, D. V. et al. The contribution of boundary layer nucleation events to total particle concentrations on regional and global scales. Atmos. Phys. Chem. 6, 5631–5648 (2006).

    Article  Google Scholar 

  5. Kulmala, M. et al. Direct observations of atmospheric aerosol nucleation. Science 339, 943–946 (2013).

    Article  Google Scholar 

  6. Sipilä, M. et al. The role of sulfuric acid in atmospheric nucleation. Science 327, 1243–1246 (2010).

    Article  Google Scholar 

  7. Kirkby, J. et al. Role of sulphuric acid, ammonia and galactic cosmic rays in atmospheric aerosol nucleation. Nature 476, 429–433 (2011).

    Article  Google Scholar 

  8. Almeida, J. et al. Molecular understanding of sulphuric acid–amine particle nucleation in the atmosphere. Nature 502, 359–363 (2013).

    Article  Google Scholar 

  9. Merikanto, J., Spracklen, D. V., Mann, G. W., Pickering, S. J. & Carslaw, K. S. Impact of nucleation on global CCN. Atmos. Chem. Phys. 9, 8601–8616 (2009).

    Article  Google Scholar 

  10. IPCC Climate Change 2021: The Physical Science Basis (eds Masson-Delmotte, V. et al.) (Cambridge Univ. Press, 2021).

  11. Tröstl, J. et al. The role of low-volatility organic compounds in initial particle growth in the atmosphere. Nature 533, 527–531 (2016).

    Article  Google Scholar 

  12. Alfaouri, D. et al. A study on the fragmentation of sulfuric acid and dimethylamine clusters inside an atmospheric pressure interface time-of-flight mass spectrometer. Atmos. Meas. Tech. 15, 11–19 (2022).

    Article  Google Scholar 

  13. Kurtén, T. et al. The effect of H2SO4–amine clustering on chemical ionization mass spectrometry (CIMS) measurements of gas-phase sulfuric acid. Atmos. Meas. Tech. 11, 3007–3019 (2011).

    Google Scholar 

  14. Olenius, T. et al. Comparing simulated and experimental molecular cluster distributions. Faraday Discuss. 165, 75–89 (2013).

    Article  Google Scholar 

  15. Zapadinsky, E., Passananti, M., Myllys, N., Kurtén, T. & Vehkamäki, H. Modeling on FRagmentation of Clusters inside A Mass Spectrometer. J. Phys. Chem. A 123, 611–624 (2019).

    Article  Google Scholar 

  16. Passananti, M. et al. How well can we predict cluster fragmentation inside a mass spectrometer? Chem. Commun. 55, 5946–5949 (2019).

    Article  Google Scholar 

  17. Merikanto, J., Zapadinsky, E., Lauri, A. & Vehkamäki, H. Origin of the failure of classical nucleation theory: incorrect description of the smallest clusters. Phys. Rev. Lett. 98, 145702 (2007).

    Article  Google Scholar 

  18. McGrath, M. J. et al. Atmospheric cluster dynamics code: a flexible method for solution of the birth–death equations. Atmos. Chem. Phys. 12, 2345–2355 (2012).

    Article  Google Scholar 

  19. Olenius, T., Kupiainen-Määttä, O., Ortega, I. K., Kurtén, T. & Vehkamäki, H. Free energy barrier in the growth of sulfuric acid–ammonia and sulfuric acid–dimethylamine clusters. J. Chem. Phys. 139, 084312 (2013).

    Article  Google Scholar 

  20. Karl, M. et al. Description and evaluation of the community aerosol dynamics model MAFOR v2.0. Geosci. Model Dev. 15, 3969–4026 (2022).

    Article  Google Scholar 

  21. Clusius, P. et al. Atmospherically relevant chemistry and aerosol box model—ARCA box (version 1.2). Geosci. Model Dev. 15, 7257–7286 (2022).

    Article  Google Scholar 

  22. Roldin, P. et al. Development and evaluation of the aerosol dynamics and gas phase chemistry model ADCHEM. Atmos. Chem. Phys. 11, 5867–5896 (2011).

    Article  Google Scholar 

  23. Roldin, P. et al. The role of highly oxygenated organic molecules in the boreal aerosol–cloud–climate system. Nat. Commun. 10, 4370 (2019).

    Article  Google Scholar 

  24. Yu, F., Nadykto, A. B., Luo, G. & Herb, J. H2SO4–H2O binary and H2SO4–H2O–NH3 ternary homogeneous and ion-mediated nucleation: lookup tables version 1.0 for 3-D modeling application. Geosci. Model Dev. 13, 2663–2670 (2020).

    Article  Google Scholar 

  25. Elm, J. Towards a holistic understanding of the formation and growth of atmospheric molecular clusters: a quantum machine learning perspective. J. Phys. Chem. A 125, 895–902 (2021).

    Article  Google Scholar 

  26. Kubečka, J., Christensen, A. S., Rasmussen, F. R. & Elm, J. Quantum machine learning approach for studying atmospheric cluster formation. Environ. Sci. Technol. Lett. 9, 239–244 (2022).

    Article  Google Scholar 

  27. Elm, J. Clusteromics I: principles, protocols and applications to sulfuric acid–base cluster formation. ACS Omega 6, 7804–7814 (2021).

    Article  Google Scholar 

  28. Elm, J. Clusteromics II: methanesulfonic acid–base cluster formation. ACS Omega 7, 17035–17044 (2021).

    Article  Google Scholar 

  29. Elm, J. Clusteromics III: acid synergy in sulfuric acid–methanesulfonic acid–base cluster formation. ACS Omega 6, 15206–15214 (2022).

    Article  Google Scholar 

  30. Knattrup, Y. & Elm, J. Clusteromics IV: the role of nitric acid in atmospheric cluster formation. ACS Omega 7, 31551–31560 (2022).

    Article  Google Scholar 

  31. Ayoubi, D., Knattrup, Y. & Elm, J. Clusteromics V: organic enhanced atmospheric cluster formation. ACS Omega 8, 9621–9629 (2023).

  32. Elm, J. An atmospheric cluster database consisting of sulfuric acid, bases, organics, and water. ACS Omega 4, 10965–10974 (2019).

    Article  Google Scholar 

  33. Kubečka, J. Jammy Key for Configurational Sampling. JKCS (accessed 30March 2023); https://jkcs.readthedocs.io/en/latest/index.html

  34. Kubečka, J., Besel, V., Kurtén, T., Myllys, N. & Vehkamäki, H. Configurational sampling of noncovalent (atmospheric) molecular clusters: sulfuric acid and guanidine. J. Phys. Chem. A 123, 6022–6033 (2019).

    Article  Google Scholar 

  35. Dral, P. O. in Chemical Physics and Quantum Chemistry Advances in Quantum Chemistry Vol. 81 (eds Ruud, K. & Brändas, E. J.) 291–324 (Academic Press, 2020).

  36. Noé, F., Tkatchenko, A., Müller, K.-R. & Clementi, C. Machine learning for molecular simulation. Annu. Rev. Phys. Chem. 71, 361–390 (2020).

    Article  Google Scholar 

  37. Kulichenko, M. et al. The rise of neural networks for materials and chemical dynamics. J. Phys. Chem. Lett. 12, 6227–6243 (2021).

    Article  Google Scholar 

  38. Bender, A. et al. Evaluation guidelines for machine learning tools in the chemical sciences. Nat. Rev. Chem. 6, 428–442 (2022).

    Article  Google Scholar 

  39. Browning, N. J., Faber, F. A. & Anatole von Lilienfeld, O. GPU-accelerated approximate kernel method for quantum machine learning. J. Chem. Phys. 157, 214801 (2022).

    Article  Google Scholar 

  40. Pederson, R. et al. Large scale quantum chemistry with tensor processing units. J. Chem. Theory Comput. 19, 25–32 (2023).

    Article  Google Scholar 

  41. Lumiaro, E., Todorović, M., Kurten, T., Vehkamäki, H. & Rinke, P. Predicting gas–particle partitioning coefficients of atmospheric molecules with machine learning. Atmos. Chem. Phys. 21, 13227–13246 (2021).

    Article  Google Scholar 

  42. Hyttinen, N., Pihlajamäki, A. & Häkkinen, H. Machine learning for predicting chemical potentials of multifunctional organic compounds in atmospherically relevant solutions. J. Phys. Chem. Lett. 13, 9928–9933 (2022).

    Article  Google Scholar 

  43. Jiang, S. et al. Towards fully ab initio simulation of atmospheric aerosol nucleation. Nat. Commun. 13, 6067 (2022).

    Article  Google Scholar 

  44. Rupp, M., Tkatchenko, A., Müller, K.-R. & von Lilienfeld, O. A. Fast and accurate modeling of molecular atomization energies with machine learning. Phys. Rev. Lett. 108, 058301 (2012).

    Article  Google Scholar 

  45. Hansen, K. et al. Machine learning predictions of molecular properties: accurate many-body potentials and nonlocality in chemical space. J. Phys. Chem. Lett. 6, 2326–2331 (2015).

    Article  Google Scholar 

  46. Bartók, A. P., Kondor, R. & Csányi, G. On representing chemical environments. Phys. Rev. B 87, 184115 (2013).

    Article  Google Scholar 

  47. Huo, H. & Rupp, M. Unified representation of molecules and crystals for machine learning. Mach. Learn.: Sci. Technol. 3, 045017 (2022).

    Google Scholar 

  48. Christensen, A. S., Bratholm, L. A., Faber, F. A. & Anatole von Lilienfeld, O. FCHL revisited: faster and more accurate quantum machine learning. J. Chem. Phys. 152, 044107 (2020).

    Article  Google Scholar 

  49. Faber, F. A., Christensen, A. S., Huang, B. & von Lilienfeld, O. A. Alchemical and structural distribution based representation for universal quantum machine learning. J. Chem. Phys. 148, 241717 (2018).

    Article  Google Scholar 

  50. Christensen, A. S. et al. QML: a Python toolkit for quantum machine learning. GitHub https://github.com/qmlcode/qml (2017).

  51. Stewart, J. Optimization of parameters for semiempirical methods V: modification of NDDO approximations and application to 70 elements. J. Mol. Model. 13, 1173–1213 (2007).

    Article  Google Scholar 

  52. Karaboga, D. & Basturk, B. On the performance of artificial bee colony (ABC) algorithm. Appl. Soft Comput. 8, 687–697 (2008).

    Article  Google Scholar 

  53. Zhang, J. & Dolg, M. ABCluster: the artificial bee colony algorithm for cluster global optimization. Phys. Chem. Chem. Phys. 17, 24173–24181 (2015).

    Article  Google Scholar 

  54. Zhang, J. & Dolg, M. Global optimization of clusters of rigid molecules using the artificial bee colony algorithm. Phys. Chem. Chem. Phys. 18, 3003–3010 (2016).

    Article  Google Scholar 

  55. Dieterich, J. M. & Hartke, B. OGOLEM: global cluster structure optimisation for arbitrary mixtures of flexible molecules. a multiscaling, object-oriented approach. Mol. Phys. 108, 279–291 (2010).

    Article  Google Scholar 

  56. Hartke, B. Global optimization. Wiley Interdiscip. Rev. Comput. Mol. Sci. 1, 879–887 (2011).

    Article  Google Scholar 

  57. Wales, D. J. & Doye, J. P. K. Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. J. Phys. Chem. A 101, 5111–5116 (1997).

    Article  Google Scholar 

  58. Stewart, J. Optimization of parameters for semiempirical methods VI: more modifications to the NDDO approximations and re-optimization of parameters. J. Mol. Model. 19, 1–32 (2013).

    Article  Google Scholar 

  59. Grimme, S., Bannwarth, C. & Shushkov, P. A robust and accurate tight-binding quantum chemical method for structures, vibrational frequencies, and noncovalent interactions of large molecular systems parametrized for all spd-block elements (Z = 1–86). J. Chem. Theory Comput. 13, 1989–2009 (2017).

    Article  Google Scholar 

  60. Bannwarth, C., Ehlert, S. & Grimme, S. GFN2-xTB—an accurate and broadly parametrized self-consistent tight-binding quantum chemical method with multipole electrostatics and density-dependent dispersion contributions. J. Chem. Theory Comput. 15, 1652–1671 (2019).

    Article  Google Scholar 

  61. Riplinger, C. & Neese, F. An efficient and near linear scaling pair natural orbital based local coupled cluster method. J. Chem. Phys. 138, 034106 (2013).

    Article  Google Scholar 

  62. Riplinger, C., Sandhoefer, B., Hansen, A. & Neese, F. Natural triple excitations in local coupled cluster calculations with pair natural orbitals. J. Chem. Phys. 139, 134101 (2013).

    Article  Google Scholar 

  63. Grimme, S., Brandenburg, J. G., Bannwarth, C. & Hansen, A. Consistent structures and interactions by density functional theory with small atomic orbital basis sets. J. Chem. Phys. 143, 054107 (2015).

    Article  Google Scholar 

  64. Brandenburg, J. G., Bannwarth, C., Hansen, A. & Grimme, S. B97-3c: a revised low-cost variant of the B97-D density functional method. J. Chem. Phys. 148, 064104 (2018).

    Article  Google Scholar 

  65. Grimme, S., Hansen, A., Ehlert, S. & Mewes, J. r2SCAN-3c: a ‘Swiss army knife’ composite electronic-structure method. J. Chem. Phys. 154, 064103 (2021).

    Article  Google Scholar 

  66. Temelso, B. et al. Effect of mixing ammonia and alkylamines on sulfate aerosol formation. J. Phys. Chem. A 122, 1612–1622 (2018).

    Article  Google Scholar 

  67. Odbadrakh, T. T., Gale, A. G., Ball, B. T., Temelso, B. & Shields, G. C. Computation of atmospheric concentrations of molecular clusters from ab initio thermochemistry. J. Vis. Exp. 158, e60964 (2020).

    Google Scholar 

  68. Bready, C. J., Vanovac, S., Odbadrakh, T. T. & Shields, G. C. Amino acids compete with ammonia in sulfuric acid-based atmospheric aerosol prenucleation: the case of glycine and serine. J. Phys. Chem. A 126, 5195–5206 (2022).

    Article  Google Scholar 

  69. Kurfman, L. A., Odbadrakh, T. T. & Shields, G. C. Calculating reliable Gibbs free energies for formation of gas-phase clusters that are critical for atmospheric chemistry: (H2SO4)3. J. Phys. Chem. A 125, 3169–3176 (2021).

    Article  Google Scholar 

  70. Harold, S. E. et al. Hydrogen-bond topology is more important than acid/base strength in atmospheric prenucleation clusters. J. Phys. Chem. A 126, 1718–1728 (2022).

    Article  Google Scholar 

  71. Xu, W. & Zhang, R. A theoretical study of hydrated molecular clusters of amines and dicarboxylic acids. J. Chem. Phys. 139, 064312 (2013).

    Article  Google Scholar 

  72. Peng, X.-Q., Liu, Y.-R., Huang, T., Jiang, S. & Huang, W. Interaction of gas phase oxalic acid with ammonia and its atmospheric implications. Phys. Chem. Chem. Phys. 17, 9552–9563 (2015).

    Article  Google Scholar 

  73. Wang, Z.-Q. et al. The nucleation mechanism of succinic acid involved sulfuric acid–dimethylamine in new particle formation. Atmos. Environ. 263, 118683 (2021).

    Article  Google Scholar 

  74. Wang, Z.-Q. et al. Multicomponent nucleation of malonic acid involved in the sulfuric acid–dimethylamine system and its atmospheric implications. Atmos. Environ. 267, 118558 (2021).

    Article  Google Scholar 

  75. Ramakrishnan, R., Dral, P. O., Rupp, M. & von Lilienfeld, O. A. Big data meets quantum chemistry approximations: the Δ-machine learning approach. J. Chem. Theory Comput. 11, 2087–2096 (2015).

    Article  Google Scholar 

  76. Ruddigkeit, L., van Deursen, R., Blum, L. C. & Reymond, J.-L. Enumeration of 166 billion organic small molecules in the chemical universe database GDB-17. J. Chem. Inf. Model. 52, 2864–2875 (2012).

    Article  Google Scholar 

  77. Reymond, J.-L. The Chemical Space Project. Acc. Chem. Res. 48, 722–730 (2015).

    Article  Google Scholar 

  78. Ramakrishnan, R., Dral, P. O., Rupp, M. & von Lilienfeld, O. A. Quantum chemistry structures and properties of 134 kilo molecules. Sci. Data 1, 140022 (2014).

    Article  Google Scholar 

  79. Smith, J. S., Isayev, O. & Roitberg, A. E. ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost. Chem. Sci. 8, 3192–3203 (2017).

    Article  Google Scholar 

  80. Smith, J. S., Isayev, O. & Roitberg, A. E. ANI-1, a data set of 20 million calculated off-equilibrium conformations for organic molecules. Sci. Data 4, 170193 (2017).

    Article  Google Scholar 

  81. Smith, J. S. et al. The ANI-1ccx and ANI-1x data sets, coupled-cluster and density functional theory properties for molecules. Sci. Data 7, 134 (2020).

    Article  Google Scholar 

  82. Devereux, C. et al. Extending the applicability of the ANI deep learning molecular potential to sulfur and halogens. J. Chem. Theory Comput. 16, 4192–4202 (2020).

    Article  Google Scholar 

  83. Chmiela, S. et al. Machine learning of accurate energy-conserving molecular force fields. Sci. Adv. 3, e1603015 (2017).

    Article  Google Scholar 

  84. Schütt, K. T., Arbabzadah, F., Chmiela, S., Müller, K. R. & Tkatchenko, A. Quantum-chemical insights from deep tensor neural networks. Nat. Commun. 8, 13890 (2017).

    Article  Google Scholar 

  85. Thaler, D., Elezaj, L., Bamer, F. & Markert, B. Training data selection for machine learning-enhanced Monte Carlo simulations in structural dynamics. Appl. Sci. 12, 581 (2022).

    Article  Google Scholar 

  86. Wibbeke, J., Teimourzadeh Baboli, P. & Rohjans, S. Optimal data reduction of training data in machine learning-based modelling: a multidimensional bin packing approach. Energies 15, 3092 (2022).

    Article  Google Scholar 

  87. Jensen, A. B., Kubečka, J., Schmitz, G., Christiansen, O. & Elm, J. Massive assessment of the binding energies of atmospheric molecular clusters. J. Chem. Theory Comput. 18, 7373–7383 (2022).

    Article  Google Scholar 

  88. Chmiela, S., Sauceda, H. E., Müller, K.-R. & Tkatchenko, A. Towards exact molecular dynamics simulations with machine-learned force fields. Nat. Commun. 9, 3887 (2018).

    Article  Google Scholar 

  89. Chmiela, S., Sauceda, H. E., Poltavsky, I., Müller, K.-R. & Tkatchenko, A. sGDML: constructing accurate and data efficient molecular force fields using machine learning. Comput. Phys. Commun. 240, 38–45 (2019).

    Article  MATH  Google Scholar 

  90. Schmitz, G. & Christiansen, O. Gaussian process regression to accelerate geometry optimizations relying on numerical differentiation. J. Chem. Phys. 148, 241704 (2018).

    Article  Google Scholar 

  91. Born, D. & Kästner, J. Geometry optimization in internal coordinates based on gaussian process regression: comparison of two approaches. J. Chem. Theory Comput. 17, 5955–5967 (2021).

    Article  Google Scholar 

  92. Yang, Y., Jiménez-Negrón, O. A. & Kitchin, J. R. Machine-learning accelerated geometry optimization in molecular simulation. J. Chem. Phys. 154, 234704 (2021).

    Article  Google Scholar 

  93. Ha, M., Hajibabaei, A., Pourasad, S. & Kim, K. S. Sparse Gaussian process regression-based machine learned first-principles force-fields for saturated, olefinic, and aromatic hydrocarbons. ACS Phys. Chem. Au 2, 260–264 (2022).

    Article  Google Scholar 

  94. Deringer, V. L. et al. Gaussian process regression for materials and molecules. Chem. Rev. 121, 10073–10141 (2021).

    Article  Google Scholar 

  95. Venturi, S., Jaffe, R. L. & Panesi, M. Bayesian machine learning approach to the quantification of uncertainties on ab initio potential energy surfaces. J. Phys. Chem. A 124, 5129–5146 (2020).

    Article  Google Scholar 

  96. Mansimov, E., Mahmood, O., Kang, S. & Cho, K. Molecular geometry prediction using a deep generative graph neural network. Sci. Rep. 9, 20381 (2019).

    Article  Google Scholar 

  97. Ortega, I. K. et al. From quantum chemical formation free energies to evaporation rates. Atmos. Chem. Phys. 12, 225–235 (2012).

    Article  Google Scholar 

  98. Lim, H. & Jung, Y. Delfos: deep learning model for prediction of solvation free energies in generic organic solvents. Chem. Sci. 10, 8306–8315 (2019).

    Article  Google Scholar 

  99. Weinreich, J., Browning, N. J. & Anatole von Lilienfeld, O. Machine learning of free energies in chemical compound space using ensemble representations: reaching experimental uncertainty for solvation. J. Chem. Phys. 154, 134113 (2021).

    Article  Google Scholar 

  100. Alibakhshi, A. & Hartke, B. Improved prediction of solvation free energies by machine-learning polarizable continuum solvation model. Nat. Commun. 12, 3584 (2021).

    Article  Google Scholar 

  101. Martins-Costa, M. T. C., Anglada, J. M., Francisco, J. S. & Ruiz-Lopez, M. F. Reactivity of volatile organic compounds at the surface of a water droplet. J. Am. Chem. Soc. 134, 11821–11827 (2012).

    Article  Google Scholar 

  102. Zhu, C., Kais, S., Cheng Zeng, X., Francisco, J. S. & Gladich, I. Interfaces select specific stereochemical conformations: the isomerization of glyoxal at the liquid water interface. J. Am. Chem. Soc. 139, 27–30 (2017).

    Article  Google Scholar 

  103. Zhu, C. et al. New mechanistic pathways for criegee-water chemistry at the air/water interface. J. Am. Chem. Soc. 138, 11164–11169 (2016).

    Article  Google Scholar 

  104. Zhong, J., Kumar, M., Zhu, C. Q., Francisco, J. S. & Zeng, X. C. Surprising stability of larger criegee intermediates on aqueous interfaces. Angew. Chem. Int. Ed. 56, 7740–7744 (2017).

    Article  Google Scholar 

  105. Kumar, M., Zhong, J., Francisco, J. S. & Zeng, X. C. Criegee intermediate–hydrogen sulfide chemistry at the air/water interface. Chem. Sci. 8, 5385–5391 (2017).

    Article  Google Scholar 

  106. Kumar, M., Zhong, J., Cheng Zeng, X. & Francisco, J. S. Reaction of Criegee intermediate with nitric acid at the air–water interface. J. Am. Chem. Soc. 140, 4913–4921 (2018).

    Article  Google Scholar 

  107. Li, L. et al. Near-barrierless ammonium bisulfate formation via a loop-structure promoted proton-transfer mechanism on the surface of water. J. Am. Chem. Soc. 138, 1816–1819 (2016).

    Article  Google Scholar 

  108. Kumar, M. & Francisco, J. S. Ion pair particles at the air–water interface. Proc. Natl Acad. Sci. USA 114, 12401–12406 (2017).

    Article  Google Scholar 

  109. Kumar, M., Trabelsi, T. & Francisco, J. S. Can urea be a seed for aerosol particle formation in air? J. Phys. Chem. A 122, 3261–3269 (2018).

    Article  Google Scholar 

  110. Zhong, J., Kumar, M., Francisco, J. S. & Cheng Zeng, X. Insight into chemistry on cloud/aerosol water surfaces. Acc. Chem. Res. 51, 1229–1237 (2018).

    Article  Google Scholar 

  111. Zheng, P., Yang, W., Wu, W., Isayev, O. & Dral, P. O. Toward chemical accuracy in predicting enthalpies of formation with general-purpose data-driven methods. J. Phys. Chem. Lett. 13, 3479–3491 (2022).

    Article  Google Scholar 

  112. Gao, X., Ramezanghorbani, F., Isayev, O., Smith, J. S. & Roitberg, A. E. TorchANI: a free and open source PyTorch-based deep learning implementation of the ANI neural network potentials. J. Chem. Inf. Model. 60, 3408–3415 (2020).

    Article  Google Scholar 

  113. Unke, O. T. & Meuwly, M. PhysNet: a neural network for predicting energies, forces, dipole moments, and partial charges. J. Chem. Theory Comput. 15, 3678–3693 (2019).

    Article  Google Scholar 

  114. Li, Z., Meidani, K., Yadav, P. & Farimani, A. B. Graph neural networks accelerated molecular dynamics. J. Chem. Phys. 156, 144103 (2022).

    Article  Google Scholar 

  115. Doerr, S. et al. TorchMD: a deep learning framework for molecular simulations. J. Chem. Theory Comput. 17, 2355–2363 (2021).

    Article  Google Scholar 

  116. Xu, M., Zhu, T. & Zhang, J. Z. H. Automatically constructed neural network potentials for molecular dynamics simulation of zinc proteins. Front. Chem. 9, 692200 (2021).

    Article  Google Scholar 

  117. Degiacomi, M. T. Coupling molecular dynamics and deep learning to mine protein conformational space. Structure 27, 1034–1040 (2019).

    Article  Google Scholar 

  118. Döscher, R. et al. The EC-Earth3 Earth system model for the Coupled Model Intercomparison Project 6. Geosci. Model Dev. 15, 2973–3020 (2022).

    Article  Google Scholar 

  119. Stevens, B. et al. Atmospheric component of the MPI-M Earth system model: ECHAM6. J. Adv. Model. Earth Syst. 5, 146–172 (2013).

    Article  Google Scholar 

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Acknowledgements

J.E. thanks the Independent Research Fund Denmark grant number 9064-00001B for financial support. O.C. acknowledges support from the Independent Research Fund Denmark through grant number 1026-00122B. We gratefully acknowledge the contributions of Aarhus University Interdisciplinary Centre for Climate Change (iClimate, Aarhus University).

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Authors and Affiliations

  1. Department of Chemistry, Aarhus University, Aarhus, Denmark

    Jakub Kubečka, Yosef Knattrup, Morten Engsvang, Andreas Buchgraitz Jensen, Daniel Ayoubi, Haide Wu, Ove Christiansen & Jonas Elm

  2. iCLIMATE Aarhus University Interdisciplinary Centre for Climate Change, Aarhus, Denmark

    Jonas Elm

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Conceptualization, investigation: J.K., Y.K., M.E., A.B.J., D.A., H.W., O.C. and J.E.; writing—original draft: J.K. and J.E.; writing—review and editing: J.K., Y.K., M.E., A.B.J., D.A., H.W., O.C. and J.E.; visualization: J.K. and J.E.; project administration: J.E.; funding acquisition: O.C. and J.E; supervision: J.E.

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Correspondence to Jonas Elm.

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Kubečka, J., Knattrup, Y., Engsvang, M. et al. Current and future machine learning approaches for modeling atmospheric cluster formation. Nat Comput Sci 3, 495–503 (2023). https://doi.org/10.1038/s43588-023-00435-0

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