Artificial neural network potential for Au₂₀ clusters based on the first-principles

Abstract

The search of ground-state structures (GSS) of gold (Au) clusters is a formidable challenge due to the complexity of potential energy surface (PES). In this work, we have built a high-dimensional artificial neural network (ANN) potential to describe the PES of Au20 clusters. The ANN potential is trained through learning the GSS search process of Au20 by the combination of density functional theory (DFT) method and genetic algorithm (GA). The root mean square errors (RMSE) of energy and force are 7.72 meV/atom and 217.02 meV/Å, respectively. As a result, it can find the lowest-energy structure (LES) of Au20 clusters that is consistent with previous results. Furthermore, the scalability test shows that it can predict the energy of smaller size Au16-19 clusters with errors less than 22.85 meV/atom, and for larger size Au21-25 clusters, the errors are below 36.94 meV/atom. Extra attention should be paid to its accuracy for Au21-25 clusters. Applying the ANN to search the GSS of Au16-25, we discover two new structures of Au16 and Au21 that are not reported before and several candidate LESs of Au16-18. In summary, this work proves that an ANN potential trained for specific size clusters could reproduce the GSS search process by DFT and be applied in the GSS search of smaller size clusters nearby. Therefore, we claim that building ANN potential based on DFT data is one of the most promising ways to effectively accelerate the GSS pre-screening of clusters.

Evaluation of Machine Learning Interatomic Potentials for the Properties of Gold Nanoparticles

“…These results were all obtained with a potential derived using data from all structures simultaneously, i.e the one whose statistics are shown in Figure 4 . Cao et al [ 23 ] studied structures of several small gold clusters including Au , and found a local minimum which resembles the one shown here. Ford et al [ 15 ] also found a similar structure at approximately the same energy above the global minimum.…”

“…The other two structures have a cage-like form and a more open flatter form, respectively. Note that related studies have mostly looked at larger clusters [ 20 , 21 , 22 , 23 ], primarily at structures only, but as we wanted to benchmark against an ab-initio MD run we chose this cluster as being computationally manageable but still able to cover the properties of interest.…”

“…There are now a few works in the literature looking at ML potentials for gold clusters it e.g., Refs. [ 19 , 20 , 21 , 22 , 23 ]. However, they all differ in a variety of ways, such as investigating different properties or using different ML-IP programs and models or slightly different methodology so part of this study is to compare our approach with these others to evaluate the best approach.…”

Revisiting the stable structures of gold clusters: Au n (n = 16–25) by artificial neural network potential

“…They also reported that Au n (n = 16-25) prefer the pyramid-based bulk fragment structures related to Au 20 [14]. However, many researchers have proposed different candidate structures, for example, hollow cage Au 16 given out by Cao et al [15], flat cage Au 16 by Bulusu and Zeng [16], hollow cage Au 17 and Au 18 [16], flat cage Au 24 [17] and Au 25 [18]. Obviously, there is controversy about the stable structures in the range of medium-sized Au clusters, and considerable work remains to be done.…”

“…In order to find the stable structures of Au clusters, enormous work has been carried out experimentally and theoretically so far [13][14][15][16][17][18]. Li et al proposed a tetrahedral structure of Au 20 which has been proved to be the most stable structure of Au 20 in experiment [13].…”