GAUSSIAN APPROXIMATION POTENTIALS FOR FUNCTIONALIZED Pt–Cu NANOPARTICLES

Year 2026, Volume: 27 Issue: 1 , 166 - 177 , 27.03.2026

İlker Demiroğlu , Tuğbey Kocabaş

https://doi.org/10.18038/estubtda.1821872

https://izlik.org/JA52AD56ZA

Abstract

Bimetallic Pt–Cu nanoparticles are promising catalysts for oxidation and hydrogenation reactions due to their tunable electronic and geometric properties. However, first-principles simulations of realistic nanoparticle sizes remain computationally prohibitive. In this study, Gaussian Approximation Potential (GAP) models were developed for Pt–Cu nanoparticles functionalized with a single O2 or CO molecule, achieving near-DFT accuracy in energies and forces while drastically reducing computational cost. The training dataset, derived from ab initio molecular dynamics (AIMD) trajectories at 300–1000 K, spans various morphologies (pure, core–shell, Janus, and ordered alloys) and particle sizes (38–260 atoms), capturing both thermal and structural fluctuations representative of realistic catalytic conditions. The resulting GAP models successfully reproduce DFT-level energetics and atomic forces with root-mean-square errors below 0.4 meV atom-1 for energies and 70 meV Å-1 for forces, without overfitting to any specific morphology. AIMD simulations reveal that alloying Pt with Cu enhances thermal and mechanical stability, with core–shell and Janus configurations maintaining ordered atomic coordination up to 1000 K. Radial distribution function (RDF) analysis confirms that short-range order persists at elevated temperatures, ensuring structural integrity under reactive conditions. These results demonstrate that machine-learning-based interatomic potentials provide a robust and transferable framework for exploring adsorption-driven restructuring, morphology evolution, and catalytic stability of Pt–Cu nanoparticles beyond the accessible limits of conventional DFT.

Keywords

PtCu nanoparticles , Bimetallic alloys , Machine learning , Gaussian Approximation Potential , Molecular dynamics

Project Number

122Z736

Thanks

The authors acknowledges support by Scientific and Technological Research Council of Turkey (TUBITAK 122Z736) and by Eskisehir Technical University (BAP 25ADP121, 23ADP151, 22ADP111 and 25ADP027).

References

• [1] Ferrando R, Jellinek J, Johnston RL. Nanoalloys: From theory to applications of alloy clusters and nanoparticles. Vol. 108, Chemical Reviews. American Chemical Society; 2008. p. 845–910.
• [2] Zaleska-Medynska A, Marchelek M, Diak M, Grabowska E. Noble metal-based bimetallic nanoparticles: The effect of the structure on the optical, catalytic and photocatalytic properties. Adv Colloid Interface Sci. 2016 Mar 1;229:80–107.
• [3] Haruta M, Kobayashi T, Sano H, Yamada N. Novel Gold Catalysts for the Oxidation of Carbon Monoxide at a Temperature far Below 0 °C. Chem Lett [Internet]. 1987 Feb 5;16(2):405–8. Available from: https://doi.org/10.1246/cl.1987.405
• [4] Yan N, Xiao C, Kou Y. Transition metal nanoparticle catalysis in green solvents. Vol. 254, Coordination Chemistry Reviews. 2010. p. 1179–218.
• [5] Luneau M, Lim JS, Patel DA, Sykes ECH, Friend CM, Sautet P. Guidelines to Achieving High Selectivity for the Hydrogenation of α,β-Unsaturated Aldehydes with Bimetallic and Dilute Alloy Catalysts: A Review. Vol. 120, Chemical Reviews. American Chemical Society; 2020. p. 12834–72.
• [6] Demiroglu I, Li ZY, Piccolo L, Johnston RL. A DFT study of molecular adsorption on Au-Rh nanoalloys. Catal Sci Technol. 2016;6(18):6916–31.
• [7] Demiroglu I, Li ZY, Piccolo L, Johnston RL. A DFT study of molecular adsorption on titania-supported AuRh nanoalloys. Comput Theor Chem. 2017 May 1;1107:142–51.
• [8] Piccolo L, Li ZY, Demiroglu I, Moyon F, Konuspayeva Z, Berhault G, et al. Understanding and controlling the structure and segregation behaviour of AuRh nanocatalysts. Sci Rep. 2016 Oct 14;6.
• [9] Reuter Karsten and Stampf C and SM. AB Initio Atomistic Thermodynamics and Statistical Mechanics of Surface Properties and Functions. In: Yip S, editor. Handbook of Materials Modeling: Methods [Internet]. Dordrecht: Springer Netherlands; 2005. p. 149–94. Available from: https://doi.org/10.1007/978-1-4020-3286-8_10
• [10] Konuspayeva Z, Berhault G, Afanasiev P, Nguyen TS, Giorgio S, Piccolo L. Monitoring: In situ the colloidal synthesis of AuRh/TiO2 selective-hydrogenation nanocatalysts. J Mater Chem A Mater. 2017;5(33):17360–7.
• [11] Baletto F, Ferrando R. Structural properties of nanoclusters: Energetic, thermodynamic, and kinetic effects. 2005.
• [12] Jortner J. Atoms, Molecules and Clusters Cluster size effects. Vol. 24, Z. Phys. D-Atoms, Molecules and Clusters. 1992.
• [13] Hammer B, Norskov JK. Why gold is the noblest of all the metals. Nature [Internet]. 1995;376(6537):238–40. Available from: https://doi.org/10.1038/376238a0
• [14] Deringer VL, Caro MA, Csányi G. Machine Learning Interatomic Potentials as Emerging Tools for Materials Science. Advanced Materials [Internet]. 2019;31(46):1902765. Available from: https://advanced.onlinelibrary.wiley.com/doi/abs/10.1002/adma.201902765
• [15] Behler J. Perspective: Machine learning potentials for atomistic simulations. J Chem Phys [Internet]. 2016 Nov 1;145(17):170901. Available from: https://doi.org/10.1063/1.4966192
• [16] Zhang L, Han J, Wang H, Car R, E W. Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics. Phys Rev Lett [Internet]. 2018 Apr 4;120(14):143001. Available from: https://link.aps.org/doi/10.1103/PhysRevLett.120.143001
• [17] Demiroğlu İ, Karaaslan Y, Kocabaş T, Keçeli M, Vázquez-Mayagoitia Á, Sevik C. Computation of the Thermal Expansion Coefficient of Graphene with Gaussian Approximation Potentials. Journal of Physical Chemistry C. 2021 Jul 8;125(26):14409–15.
• [18] Dragoni D, Daff TD, Csányi G, Marzari N. Achieving DFT accuracy with a machine-learning interatomic potential: Thermomechanics and defects in bcc ferromagnetic iron. Phys Rev Mater [Internet]. 2018 Jan 30;2(1):13808. Available from: https://link.aps.org/doi/10.1103/PhysRevMaterials.2.013808
• [19] Szlachta WJ, Bartók AP, Csányi G. Accuracy and transferability of Gaussian approximation potential models for tungsten. Phys Rev B Condens Matter Mater Phys. 2014 Sep 24;90(10).
• [20] Kaya D, Demiroglu I, Isik IB, Isik HH, Çetin SK, Sevik C, et al. Highly active bimetallic Pt–Cu nanoparticles for the electrocatalysis of hydrogen evolution reactions: Experimental and theoretical insight. Int J Hydrogen Energy [Internet]. 2023;48(95):37209–23. Available from: https://www.sciencedirect.com/science/article/pii/S0360319923029592
• [21] Perdew JP, Burke K, Ernzerhof M. Generalized Gradient Approximation Made Simple. 1996.
• [22] Kresse G, Hafner J. Ab initio molecular dynamics for liquid metals. Phys Rev B [Internet]. 1993 Jan 1;47(1):558–61. Available from: https://link.aps.org/doi/10.1103/PhysRevB.47.558
• [23] Kresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B [Internet]. 1999 Jan 15;59(3):1758–75. Available from: https://link.aps.org/doi/10.1103/PhysRevB.59.1758
• [24] Bartõk AP, Csányi G. Gaussian approximation potentials: A brief tutorial introduction. Int J Quantum Chem [Internet]. 2015 Aug 15 [cited 2025 Oct 27];115(16):1051–7. Available from: /doi/pdf/10.1002/qua.24927
• [25] Thiemann FL, Rowe P, Müller EA, Michaelides A. Machine Learning Potential for Hexagonal Boron Nitride Applied to Thermally and Mechanically Induced Rippling. Journal of Physical Chemistry C. 2020;124(40):22278–90.
• [26] Tovey S, Narayanan Krishnamoorthy A, Sivaraman G, Guo J, Benmore C, Heuer A, et al. DFT Accurate Interatomic Potential for Molten NaCl from Machine Learning. Journal of Physical Chemistry C. 2020 Nov 25;124(47):25760–8.
• [27] Deringer VL, Bartók AP, Bernstein N, Wilkins DM, Ceriotti M, Csányi G. Gaussian Process Regression for Materials and Molecules. Vol. 121, Chemical Reviews. American Chemical Society; 2021. p. 10073–141.
• [28] Li CH, Li MC, Liu SP, Jamison AC, Lee D, Lee TR, et al. Plasmonically Enhanced Photocatalytic Hydrogen Production from Water: The Critical Role of Tunable Surface Plasmon Resonance from Gold-Silver Nanoshells. ACS Appl Mater Interfaces. 2016 Apr 27;8(14):9152–61.
• [29] Rosenbrock CW, Gubaev K, Shapeev A V., Pártay LB, Bernstein N, Csányi G, et al. Machine-learned interatomic potentials for alloys and alloy phase diagrams. NPJ Comput Mater. 2021 Dec 1;7(1).
• [30] Rowe P, Deringer VL, Gasparotto P, Csányi G, Michaelides A. An accurate and transferable machine learning potential for carbon. Journal of Chemical Physics. 2020 Jul 21;153(3).