Graph attention network for global search of atomic clusters: A case study of Agn (n = 14−26) clusters

doi:10.1007/s11467-022-1219-5

Front. Phys.

2023, Vol. 18

Issue (1) : 13306 https://doi.org/10.1007/s11467-022-1219-5

RESEARCH ARTICLE

Graph attention network for global search of atomic clusters: A case study of Ag_n (n = 14−26) clusters

Linwei Sai¹, Li Fu², Qiuying Du^2,³, Jijun Zhao²(

)

¹. School of Science, Hohai University, Changzhou 213022, China
². Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University of Technology), Ministry of Education, Dalian 116024, China
³. College of Physics and Electronic Information, Inner Mongolia Normal University, Hohhot 010022, China

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Abstract

Due to coexistence of huge number of structural isomers, global search for the ground-state structures of atomic clusters is a challenging issue. The difficulty also originates from the computational cost of ab initio methods for describing the potential energy surface. Recently, machine learning techniques have been widely utilized to accelerate materials discovery and molecular simulation. Compared to the commonly used artificial neural network, graph network is naturally suitable for clusters with flexible geometric environment of each atom. Herein we develop a cluster graph attention network (CGANet) by aggregating information of neighboring vertices and edges using attention mechanism, which can precisely predict the binding energy and force of silver clusters with root mean square error of 5.4 meV/atom and mean absolute error of 42.3 meV/Å, respectively. As a proof-of-concept, we have performed global optimization of medium-sized Ag_n clusters (n = 14−26) by combining CGANet and genetic algorithm. The reported ground-state structures for n = 14−21, have been successfully reproduced, while entirely new lowest-energy structures are obtained for n = 22−26. In addition to the description of potential energy surface, the CGANet is also applied to predict the electronic properties of clusters, such as HOMO energy and HOMO-LUMO gap. With accuracy comparable to ab initio methods and acceleration by at least two orders of magnitude, CGANet holds great promise in global search of lowest-energy structures of large clusters and inverse design of functional clusters.

Keywords deep learning graph attention network potential surface fitting Ag clusters global search

Corresponding Author(s): Jijun Zhao

Issue Date: 03 November 2022

Cite this article:

Linwei Sai,Li Fu,Qiuying Du, et al. Graph attention network for global search of atomic clusters: A case study of Ag_n (n = 14−26) clusters[J]. Front. Phys. , 2023, 18(1): 13306.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1219-5
https://academic.hep.com.cn/fop/EN/Y2023/V18/I1/13306

Fig.1 Feature extraction and graph convolution operations.

Fig.2 (a) Energy prediction network and (b) force prediction network.

Fig.3 Root mean square error of energy (left) and mean absolute error of force (right) for Ag₁₆, Ag₂₀ and Ag₂₄.

Fig.4 Root mean square error (RMSE) of energy (upper) and mean absolute error (MAE) of force (lower) for mixed-size train of Ag₁₆, Ag₂₀ and Ag₂₄.

Fig.5 Lowest-energy structures of Ag_n clusters (14 ≤ n ≤ 26). The point group symmetry is given in parenthesis. Red color highlights the newly found lowest-energy structures, while black color denote those the same as in literature [21, 39-45].

Fig.6 Mean absolute error of HOMO energy (lower) and HOMO−LUMO gap (upper) trained for Ag₂₀.

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