Please wait a minute...
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
Abstract  

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: fujie@nbu.edu.cn Corresponding author. E-mail: duanxiangmei@nbu.edu.cn   

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.

[1]
Daniel M C Astruc D 2004 Chem. Rev. 104 293 DOI: 10.1021/cr030698+
[2]
Ahmed S Annu Ikram S Yudha S S 2016 J. Photochem. Photobiol. B 161 141 DOI: 10.1016/j.jphotobiol.2016.04.034
[3]
Turkevich J Stevenson P C Hillier J 1951 Discuss. Faraday Soc. 11 55 DOI: 10.1039/df9511100055
[4]
Mingos D M 2015 Dalton Trans. 44 6680 DOI: 10.1039/C5DT00253B
[5]
Wang J Wang G Zhao J 2002 Phys Rev B 66 035418 DOI: 10.1103/PhysRevB.66.035418
[6]
Thorn A Rojas-Nunez J Hajinazar S Baltazar S E Kolmogorov A N 2019 J. Phys. Chem. C 123 30088 DOI: 10.1021/acs.jpcc.9b08517
[7]
Yang D Pei W Zhou S Zhao J Ding W Zhu Y 2020 Angew. Chem. Int. Ed. 59 1919 DOI: 10.1002/anie.v59.5
[8]
Zhou S Pei W Du Q Zhao J 2019 Phys. Chem. Chem. Phys. 21 10587 DOI: 10.1039/C9CP01517E
[9]
Hu Y L Zhu H R Wei S H 2019 Chin. Phys. B 28 113101 DOI: 10.1088/1674-1056/ab4cdd
[10]
Du Q Wu X Wang P Wu D Sai L King R B Park S J Zhao J 2020 J. Phys. Chem. C 124 7449 DOI: 10.1021/acs.jpcc.9b11588
[11]
Chen D D Kuang X Y Zhao Y R Shao P Li Y F 2011 Chin. Phys. B 20 063601 DOI: 10.1088/1674-1056/20/6/063601
[12]
Haruta M Yamada N Kobayashi T Iijima S 1989 J. Catal. 115 301 DOI: 10.1016/0021-9517(89)90034-1
[13]
Brust M Walker M Bethell D Schiffrin D J Whyman R 1994 J. Chem. Soc., Chem. Commun. 1994 801 DOI: 10.1039/C39940000801
[14]
Mingos D M P 1996 J. Chem. Soc., Dalton Trans. 5 561 DOI: 10.1039/DT9960000561
[15]
Häberlen O D Chung S C Stener M Rösch N 1997 J. Chem. Phys. 106 5189 DOI: 10.1063/1.473518
[16]
Oliveira L F L Tarrat N Cuny J Morillo J Lemoine D Spiegelman F Rapacioli M 2016 J. Phys. Chem. A. 120 8469 DOI: 10.1021/acs.jpca.6b09292
[17]
Dong Y Springborg M 2007 J. Phys. Chem. C 111 12528 DOI: 10.1021/jp071120x
[18]
Tarrat N Rapacioli M Cuny J Morillo J Heully J L Spiegelman F 2017 Comput. Theor. Chem. 1107 102 DOI: 10.1016/j.comptc.2017.01.022
[19]
Koskinen P Häkkinen H Seifert G Sanna S Frauenheim T Moseler M 2006 New. J. Phys. 8 9 DOI: 10.1088/1367-2630/8/1/009
[20]
Pyykko P 2004 Angew. Chem. Int. Ed. 43 4412 DOI: 10.1002/(ISSN)1521-3773
[21]
Pyykko P 2008 Chem. Soc. Rev. 37 1967 DOI: 10.1039/b708613j
[22]
Xiao L Tollberg B Hu X Wang L 2006 J. Chem. Phys. 124 114309 DOI: 10.1063/1.2179419
[23]
Sutton A P Chen J 1990 Phil. Mag. Lett. 61 139 DOI: 10.1080/09500839008206493
[24]
Cleri F Rosato V V 1993 Phys Rev B 48 22 DOI: 10.1103/PhysRevB.48.22
[25]
Artrith N Kolpak A M 2015 Comp. Mater. Sci. 110 20 DOI: 10.1016/j.commatsci.2015.07.046
[26]
Lee K Yoo D Jeong W Han S 2019 Comput. Phys. Commun. 242 95 DOI: 10.1016/j.cpc.2019.04.014
[27]
Sumpter B G Noid D W 1992 Chem. Phys. Lett. 192 455 DOI: 10.1016/0009-2614(92)85498-Y
[28]
Tai No K Ha Chang B Yeon Kim S Shik Jhon M Scheraga H A 1997 Chem. Phys. Lett. 271 152 DOI: 10.1016/S0009-2614(97)00448-X
[29]
Lorenz S Groß A Scheffler M 2004 Chem. Phys. Lett. 395 210 DOI: 10.1016/j.cplett.2004.07.076
[30]
Handley C M Popelier P L 2010 J. Phys. Chem. A. 114 3371 DOI: 10.1021/jp9105585
[31]
Guo P Zheng J M Zhao P Zheng L L Ren Z Y 2010 Chin. Phys. B 19 083601 DOI: 10.1088/1674-1056/19/8/083601
[32]
Artrith N Urban A 2016 Comp. Mater. Sci. 114 135 DOI: 10.1016/j.commatsci.2015.11.047
[33]
Artrith N Urban A Ceder G 2017 Phys Rev B 96 014112 DOI: 10.1103/PhysRevB.96.014112
[34]
Broyden C G 1970 IMA J. Appl. Math. 6 76 DOI: 10.1093/imamat/6.1.76
[35]
Fletcher R 1970 The Computer Journal 13 317 DOI: 10.1093/comjnl/13.3.317
[36]
Goldfarb D 1970 Math. Comput. 24 23 DOI: 10.1090/S0025-5718-1970-0258249-6
[37]
Shanno D F 1970 Math. Comput. 24 647 DOI: 10.1090/S0025-5718-1970-0274029-X
[38]
Byrd R H Lu P Nocedal J Zhu C 1995 SIAM. J. Sci. Comput. 16 1190 DOI: 10.1137/0916069
[39]
Behler J 2011 Phys. Chem. Chem. Phys 13 17930 DOI: 10.1039/c1cp21668f
[40]
Behler J Parrinello M 2007 Phys. Rev. Lett. 98 146401 DOI: 10.1103/PhysRevLett.98.146401
[41]
Artrith N Kolpak A M 2014 Nano. Lett. 14 2670 DOI: 10.1021/nl5005674
[42]
Khaliullin R Z Eshet H Kühne T D Behler J Parrinello M 2010 Phys Rev B 81 100103 DOI: 10.1103/PhysRevB.81.100103
[43]
Artrith N Morawietz T Behler J 2011 Phys Rev B 83 153101 DOI: 10.1103/PhysRevB.83.153101
[44]
Morawietz T Behler J 2013 J. Phys. Chem. A. 117 7356 DOI: 10.1021/jp401225b
[45]
Artrith N Behler J 2012 Phys Rev B 85 045439 DOI: 10.1103/PhysRevB.85.045439
[46]
Artrith N Hiller B Behler J 2013 Phys Status Solidi B 250 1191 DOI: 10.1002/pssb.v250.6
[47]
Delley B 1990 J. Chem. Phys. 92 508 DOI: 10.1063/1.458452
[48]
Delley B 2000 J. Chem. Phys. 113 7756 DOI: 10.1063/1.1316015
[49]
Hohenberg P Kohn W 1964 Phys. Rev. 136 B864 DOI: 10.1103/PhysRev.136.B864
[50]
Kohn W Sham L J 1965 Phys. Rev. 140 A1133 DOI: 10.1103/PhysRev.140.A1133
[51]
Perdew J P Burke K Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 DOI: 10.1103/PhysRevLett.77.3865
[52]
Perdew J P Burke K Ernzerhof M 1997 Phys. Rev. Lett. 78 1396 DOI: 10.1103/PhysRevLett.78.1396
[53]
Behler J 2011 J. Chem. Phys. 134 074106 DOI: 10.1063/1.3553717
[54]
Doye J P K Wales D J 1998 New. J. Chem. 22 733 DOI: 10.1039/A709249K
[55]
[56]
Nhat P V Si N T Nguyen M T 2020 J. Phys. Chem. A. 124 1289 DOI: 10.1021/acs.jpca.9b09287
[57]
Plimpton S 1995 J. Comput. Phys. 117 1 DOI: 10.1006/jcph.1995.1039
[58]
G W Rodrigue G 1989 Math. Comput. 53 775 DOI: 10.2307/2008751
[59]
[1] First-principles study on β-GeS monolayer as high performance electrode material for alkali metal ion batteries
Meiqian Wan(万美茜), Zhongyong Zhang(张忠勇), Shangquan Zhao(赵尚泉), and Naigen Zhou(周耐根). Chin. Phys. B, 2022, 31(9): 096301.
[2] Effects of oxygen concentration and irradiation defects on the oxidation corrosion of body-centered-cubic iron surfaces: A first-principles study
Zhiqiang Ye(叶志强), Yawei Lei(雷亚威), Jingdan Zhang(张静丹), Yange Zhang(张艳革), Xiangyan Li(李祥艳), Yichun Xu(许依春), Xuebang Wu(吴学邦), C. S. Liu(刘长松), Ting Hao(郝汀), and Zhiguang Wang(王志光). Chin. Phys. B, 2022, 31(8): 086802.
[3] Machine learning potential aided structure search for low-lying candidates of Au clusters
Tonghe Ying(应通和), Jianbao Zhu(朱健保), and Wenguang Zhu(朱文光). Chin. Phys. B, 2022, 31(7): 078402.
[4] Pulse coding off-chip learning algorithm for memristive artificial neural network
Ming-Jian Guo(郭明健), Shu-Kai Duan(段书凯), and Li-Dan Wang(王丽丹). Chin. Phys. B, 2022, 31(7): 078702.
[5] Bandgap evolution of Mg3N2 under pressure: Experimental and theoretical studies
Gang Wu(吴刚), Lu Wang(王璐), Kuo Bao(包括), Xianli Li(李贤丽), Sheng Wang(王升), and Chunhong Xu(徐春红). Chin. Phys. B, 2022, 31(6): 066205.
[6] Alloying and magnetic disordering effects on phase stability of Co2 YGa (Y=Cr, V, and Ni) alloys: A first-principles study
Chun-Mei Li(李春梅), Shun-Jie Yang(杨顺杰), and Jin-Ping Zhou(周金萍). Chin. Phys. B, 2022, 31(5): 056105.
[7] Evaluation of performance of machine learning methods in mining structure—property data of halide perovskite materials
Ruoting Zhao(赵若廷), Bangyu Xing(邢邦昱), Huimin Mu(穆慧敏), Yuhao Fu(付钰豪), and Lijun Zhang(张立军). Chin. Phys. B, 2022, 31(5): 056302.
[8] First-principles calculations of the hole-induced depassivation of SiO2/Si interface defects
Zhuo-Cheng Hong(洪卓呈), Pei Yao(姚佩), Yang Liu(刘杨), and Xu Zuo(左旭). Chin. Phys. B, 2022, 31(5): 057101.
[9] Topological properties of Sb(111) surface: A first-principles study
Shuangxi Wang(王双喜) and Ping Zhang(张平). Chin. Phys. B, 2022, 31(4): 047105.
[10] Magnetic proximity effect induced spin splitting in two-dimensional antimonene/Fe3GeTe2 van der Waals heterostructures
Xiuya Su(苏秀崖), Helin Qin(秦河林), Zhongbo Yan(严忠波), Dingyong Zhong(钟定永), and Donghui Guo(郭东辉). Chin. Phys. B, 2022, 31(3): 037301.
[11] First-principles study of stability of point defects and their effects on electronic properties of GaAs/AlGaAs superlattice
Shan Feng(冯山), Ming Jiang(姜明), Qi-Hang Qiu(邱启航), Xiang-Hua Peng(彭祥花), Hai-Yan Xiao(肖海燕), Zi-Jiang Liu(刘子江), Xiao-Tao Zu(祖小涛), and Liang Qiao(乔梁). Chin. Phys. B, 2022, 31(3): 036104.
[12] A new direct band gap silicon allotrope o-Si32
Xin-Chao Yang(杨鑫超), Qun Wei(魏群), Mei-Guang Zhang(张美光), Ming-Wei Hu(胡明玮), Lin-Qian Li(李林茜), and Xuan-Min Zhu(朱轩民). Chin. Phys. B, 2022, 31(2): 026104.
[13] Parameter estimation of continuous variable quantum key distribution system via artificial neural networks
Hao Luo(罗浩), Yi-Jun Wang(王一军), Wei Ye(叶炜), Hai Zhong(钟海), Yi-Yu Mao(毛宜钰), and Ying Guo(郭迎). Chin. Phys. B, 2022, 31(2): 020306.
[14] First-principles study of two new boron nitride structures: C12-BN and O16-BN
Hao Wang(王皓), Yaru Yin(殷亚茹), Xiong Yang(杨雄), Yanrui Guo(郭艳蕊), Ying Zhang(张颖), Huiyu Yan(严慧羽), Ying Wang(王莹), and Ping Huai(怀平). Chin. Phys. B, 2022, 31(2): 026102.
[15] High-temperature nodal ring semimetal in two-dimensional honeycomb-kagome Mn2N3 lattice
Xin-Ke Liu(刘鑫柯), Xin-Yang Li(李欣阳), Miao-Juan Ren(任妙娟),Pei-Ji Wang(王培吉), and Chang-Wen Zhang(张昌文). Chin. Phys. B, 2022, 31(12): 127203.
No Suggested Reading articles found!