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Chin. Phys. B, 2020, Vol. 29(11): 117304    DOI: 10.1088/1674-1056/abc15d
Special Issue: SPECIAL TOPIC — Machine learning in condensed matter physics
SPECIAL TOPIC—Machine learning in condensed matter physics Prev   Next  

Artificial neural network potential for gold clusters

Ling-Zhi Cao(曹凌志)1,2, Peng-Ju Wang(王鹏举)3, Lin-Wei Sai(赛琳伟)4, Jie Fu(付洁)1,2, †, and Xiang-Mei Duan(段香梅)1,2,, ‡
1 School of Physical Science and Technology, Ningbo University, Ningbo 315211, China
2 Laboratory of Clean Energy Storage and Conversion, Ningbo University, Ningbo 315211, China
3 Key Laboratory of Materials Modification by Laser, Ion and Electron Beams, Ministry of Education, Dalian University of Technology, Dalian 116024, China
4 College of Science, Hohai University, Changzhou 213022, China

In cluster science, it is challenging to identify the ground state structures (GSS) of gold (Au) clusters. Among different search approaches, first-principles method based on density functional theory (DFT) is the most reliable one with high precision. However, as the cluster size increases, it requires more expensive computational cost and becomes impracticable. In this paper, we have developed an artificial neural network (ANN) potential for Au clusters, which is trained to the DFT binding energies and forces of 9000 AuN clusters (11 ≤ N ≤ 100). The root mean square errors of energy and force are 13.4 meV/atom and 0.4 eV/Å, respectively. We demonstrate that the ANN potential has the capacity to differentiate the energy level of Au clusters and their isomers and highlight the need to further improve the accuracy. Given its excellent transferability, we emphasis that ANN potential is a promising tool to breakthrough computational bottleneck of DFT method and effectively accelerate the pre-screening of Au clusters’ GSS.

Keywords:  empirical potential      artificial neural network      gold cluster      first-principles  
Received:  10 August 2020      Revised:  14 September 2020      Accepted manuscript online:  15 October 2020
Fund: the National Natural Science Foundation of China (Grant Nos. 11804175, 11874033, 11804076, and 91961204) and the K.C. Wong Magna Foundation in Ningbo University.
Corresponding Authors:  Corresponding author. E-mail: Corresponding author. E-mail:   

Cite this article: 

Ling-Zhi Cao(曹凌志), Peng-Ju Wang(王鹏举), Lin-Wei Sai(赛琳伟), Jie Fu(付洁), and Xiang-Mei Duan(段香梅) Artificial neural network potential for gold clusters 2020 Chin. Phys. B 29 117304

Fig. 1.  

Schematic diagram of an ANN model (N0N1–⋯–Nn).

Network Number of weight RMSE/(meV/atom) MAE/(meV/atom)
architecture parameters Training set Test set Training set Test set
26–2–2–1 63 19.2 20.4 14.1 14.5
26–5–5–1 171 18.6 17.8 13.7 13.2
26–10–10–1 391 16.2 16.1 12.0 11.9
26–15–15–1 661 16.0 16.7 11.9 12.4
26–20–20–1 981 15.3 17.2 11.4 12.5
Table 1.  

ANN architecture complexity test. Root mean square error (RMSE) and mean absolute error (MAE) are the values after 1000 iterations.

Fig. 2.  

Comparison of binding energy and force calculated by ANN and DFT.

Fig. 3.  

Calculated binding energies of Au11 – 80 clusters by different approaches.

Fig. 4.  

Comparison of binding energies of Au20, Au40, Au60, and Au80 cluster isomers by ANN and DFT.

Fig. 5.  

Binding energies and relative binding energies of Au27 isomers by ANN and DFT.

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