Abstract
Catalytic characteristics of metal nanoparticles heavily depend on their global shapes and sizes as well as on the structure and environment of catalytic sites. On the computational chemistry side, calculations of thermodynamic and kinetic data involve a high calculation cost which can be significantly lowered by the use of a trained machine learning model. This paper outlines a preliminary approach that aims at classifying the shape of the metal core of nanoparticles. Four different supervised artificial neural networks were trained, tested and submitted to a challenging dataset. They are based on two different structural descriptors, Coulomb matrices and radial distribution functions (RDFs). Each model is trained with hundreds of 3D models of nanoparticles that belong to eleven structural classes. The best model classifies a NP according to its discretized RDF profile and its first derivative. 100% accuracy is reached on the test stage, and up to 70% accuracy is obtained on the challenging dataset. It is mainly made of compounds that have global shapes significantly different from the training set. But some nonobvious structural patterns make then related to the eleven classes learned by the ANNs. Such strategy could easily be adapted to the recognition of NPs based on experimental neutron or X-ray diffraction data.
Similar content being viewed by others
References
Schmid G (ed.), Nanoparticles. From theory to application, 2nd edn. (Wiley-VCH, Weinheim, Germany, 2010)
Burda C, Chen XB, Narayanan R, El-Sayed MA (2005) Chem Rev 105(4):1025
Wilcoxon JP, Abrams BL (2006) Chem Soc Rev 35(11):1162
Mori T, Hegmann T (2016) J Nanopart Res 18:10
Kaatz FH, Bultheel A (2019) Nanoscale Res Lett 14:1
Shi Y, Lyu Z, Zhao M, Chen R, Nguyen QN, Xia Y (2020) Chem Rev 121(2):649
Niu W, Zhang W, Firdoz S, Lu X (2014) J Am Chem Soc 136(8):3010
Serp P, Philippot K (eds) (2013) Nanomaterials in Catalysis. Wiley-VCH, Weinheim
Polshettiwar V, Varma RS (2010) Green Chem 12(5):743
Martínez-Prieto LM, Chaudret B (2018) Acc Chem Res 51:376
del Rosal I, Poteau R Nanoparticles in Catalysis: Advances in Synthesis and Applications (Wiley-VCH, 2021), chap. Sabatier principle and surface properties of small Ruthenium nanoparticles and clusters. Case studies., pp. 331–348
Chorkendorff I, Niemantsverdriet JW (2003) Concepts Of modern catalysis and kinetics. Wiley-VCH
Nørskov JK, Bligaard T, Rossmeisl J, Christensen CH (2009) Nat Chem 1(1):37
Nørskov JK, Abild-Pedersen F, Studt F, Bligaard T (2011) Proc Natl Acad Sci USA 108(3):937
Abild-Pedersen F, Greeley J, Studt F, Rossmeisl J, Munter TR, Moses PG, Skúlason E, Bligaard T, Nørskov JK (2007) Phys Rev Lett 99:016105
Nørskov JK, Bligaard T, Logadottir A, Kitchin JR, Chen JG, Pandelov S, Stimming U (2005) J Electrochem Soc 152(3):J23
Schlexer Lamoureux P, Winther KT, Garrido Torres JA, Streibel V, Zhao M, Bajdich M, Abild-Pedersen F, Bligaard T (2019) Chem Cat Chem 11(16):3581
Jäger MOJ, Morooka EV, Federici Canova F, Himanen L, Foster AS (2018) npj Comput Mater 4(1):1
Rupp M, Tkatchenko A, Müller KR, von Lilienfeld OA (2012) Phys Rev Lett 108(5):058301
Huo H, Rupp M arXiv:1704.06439 [cond-mat, physics:physics] (2018). http://arxiv.org/abs/1704.06439. ArXiv: 1704.06439
Behler J (2011) J Chem Phys 134(7):074106
Bartók AP, Kondor R, Csányi G (2013) Phys Rev B 87(18):184115
Himanen L, Jäger MO, Morooka EV, Canova FF, Ranawat YS, Gao DZ, Rinke P, Foster AS (2020) Comput Phys Commun 247:106949
Cusinato L, del Rosal I, Poteau R (2017) Dalton Trans 46:378
Vargas JA, Petkov V, Nouh ESA, Ramaamorthy RK, Lacroix LM, Poteau R, Viau G, Lecante P, Arenal R (2018) ACS Nano 12:9521
von Lilienfeld OA, Ramakrishnan R, Rupp M, Knoll A (2015) Int J Quant Chem 115(16):1084
Timoshenko J, Lu D, Lin Y, Frenkel AI (2017) J Phys Chem Lett 8(20):5091
Silver D, Huang A, Maddison CJ, Guez A, Sifre L, van den Driessche G, Schrittwieser J, Antonoglou I, Panneershelvam V, Lanctot M, Dieleman S, Grewe D, Nham J, Kalchbrenner N, Sutskever I, Lillicrap T, Leach M, Kavukcuoglu K, Graepel T, Hassabis D (2016) Nature 529(7587):484
Krizhevsky A, Sutskever I, Hinton GE (2017) Commun ACM 60(6):84
Cascianelli S, Molineris I, Isella C, Masseroli M, Medico E (2020) Sci Rep 10(1):14071
Sutton AP, Chen J (1990) Philos Mag Lett 61(3):139
Huang R, Wen YH, Shao GF, Sun SG (2013) J Phys Chem C 117(8):4278
Hewage JW, Rupika WL, Amar FG (2012) Eur Phys J D 66(11):282
Hansen K, Montavon G, Biegler F, Fazli S, Rupp M, Scheffler M, von Lilienfeld OA, Tkatchenko A, Müller KR (2013) J Chem Theor Comput 9(8):3404
Proffen T, Billinge S (1999) J Appl Crystallogr 32(3):572
Korsunsky V (2000) Coord Chem Rev 199(1):55
Hardeveld RV, Hartog F (1969) Surf Sci 15(2):189
Teo BK, Sloane NJA (1985) Inorg Chem 24(26):4545
Martin TP (1996) Phys Rep 273:199
Mackay AL (1962) Acta Crystallogr 15(9):916
Dassenoy F, Casanove MJ, Lecante P, Verelst M, Snoeck E, Mosset A, Ely TO, Amiens C, Chaudret B (2000) J Chem Phys 112(18):8137
Margeat O, Respaud M, Amiens C, Lecante P, Chaudret B (2010) Beilstein J Nanotechnol 1:108
Frank FC, Kasper JS (1958) Acta Crystallogr 11(3):184
Frank FC, Kasper JS (1959) Acta Crystallogr 12(7):483
Rapps T, Ahlrichs R, Waldt E, Kappes MM, Schooss D (2013) Angew Chem Int Ed 52(23):6102
Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V, Vanderplas J, Passos A, Cournapeau D, Brucher M, Perrot M, Duchesnay E (2011) J Mach Learn Res 12:2825
Kingma DP, Ba J Adam: A method for stochastic optimization (2014). http://arxiv.org/abs/1412.6980. Cite arxiv:1412.6980Comment: Published as a conference paper at the 3rd International Conference for Learning Representations, San Diego, (2015)
Kohavi R In Intl Jnt Conf AI (Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 1995), IJCAI 95, pp. 1137–1143
Hofmeister H In Encyclopedia of Nanoscience and Nanotechnology, vol. 3, ed. by H.S. Nalwa (American Scientific Publishers, Stevenson Ranch, 2004), pp. 431–452
Ino S (1969) J Phys Soc Jpn 27(4):941
Marks LD (1983) J Cryst Growth 61(3):556
Boerdijk A (1952) Philips Res Rep 7:303
Coxeter HSM (1991) Regular Complex Polytopes, 2nd edn. Cambridge University Press
Bernal JD (1960) Nature 185(4706):68
Velaźquez-Salazar JJ, Esparza R, Mejiá-Rosales SJ, Estrada-Salas R, Ponce A, Deepak FL, Castro-Guerrero C, José-Yacamań M (2011) ACS Nano 5(8):6272
Goodfellow I, Bengio Y, Courville A Deep Learning (MIT Press, 2016). http://www.deeplearningbook.org
Acknowledgements
We acknowledge the CALcul en MIdi-Pyrénées HPC (CALMIP-Olympe, grant P0611) for generous allocations of computer time. Université Paul Sabatier-Toulouse, INSAT and CNRS are also thanked for financial support. FJ and RP also thank Béatrice Laurent-Bonneau and Olivier Roustant for helpful and stimulating discussions. This article is dedicated to Fernand Spiegelmann on the occasion of his retirement. Short private message from RP: “Fernand, je ne te remercierai jamais assez de m’avoir donné la passion de ce métier, d’avoir su aiguiser ma curiosité scientifique, d’avoir contribué à ma formation large en chimie physique et théorique, et de m’avoir appris que développer à bon escient ses propres outils est une démarche féconde”.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Published as part of the special collection of articles “Festschrift in honor of Fernand Spiegelmann”.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Fages, T., Jolibois, F. & Poteau, R. Recognition of the three-dimensional structure of small metal nanoparticles by a supervised artificial neural network . Theor Chem Acc 140, 98 (2021). https://doi.org/10.1007/s00214-021-02795-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00214-021-02795-0