Ensemble-Average Representation of Pt Clusters in Conditions of Catalysis Accessed through GPU Accelerated Deep Neural Network Fitting Global Optimization

Abstract

We first report a global optimization approach based on GPU accelerated Deep Neural Network (DNN) fitting, for modeling metal clusters at realistic temperatures. The seven-layer multidimensional and locally connected DNN is combined with limited-step Density Functional Theory (DFT) geometry optimization to reduce the time cost of full DFT local optimization, which is considered to be the most time-consuming step in global optimization. An algorithm based on bond length distribution analysis is used to efficiently sample the configuration space and generate random initial structures. A structure similarity measurement method based on depth-first search is used to identify duplicates. The performance of the new approach is examined by the application to the global minimum searching for Pt 9 and Pt 13 . The ensemble-average representations of the two clusters are constructed based on all geometrically different isomers, on which the structure transition is predicted at low and high temperatures, for Pt 9 and Pt 13 clusters, respectively. Finally, the ensemble-averaged vertical ionization potential changes when temperature increases, and the property in conditions of catalysis can be different from that evaluated at the global minimum structure.

Origin of high oxygen reduction reaction activity of Pt12 and strategy to obtain better catalyst using sub-nanosized Pt-alloy clusters

“…The energetically most probable geometries for Pt 12 and Pt 13 are (a) and (j), respectively. These geometries are consistent with previous global optimizations based on density functional theory (DFT) by Zhang23, Da Silva24, Wei25, and Zhai26 et al ., which focused on obtaining a static global minimum geometry in each cluster size. Although it is difficult to obtain a global minimum with a single simulated annealing (SA) run, we can increase the precision when obtaining a global minimum geometry by performing multiple independent AIMD-SA runs.…”

Fluxionality of Catalytic Clusters: When It Matters and How to Address It

“…In Figure 4A, we show the application of this approach to the equilibrium properties of the Pt 9 and Pt 13 clusters. 16 It has been demonstrated that not only the zero-point energies (from vibrational degrees of freedom) but also different spin multiplicities and point-group symmetries can make significant contributions to entropy and change the probability of isomer occurrence. This indicates that electronic, vibrational, and rotational degrees of freedom are all important in this description…”

“…16 The calculated heat capacity, which is sensitive to the isomer structure, can be different if fewer isomers are included.…”

Application of Artificial Neural Networks for Catalysis: A Review

“…Similar studies on varying Au configurations were also reported by Boes et al [99]. With a similar method, Zhai and Alexandrova developed a GPU-accelerated deep neural network (DNN) [32] for the global optimization of Pt 13 clusters [100]. To provide a general package for PES fitting, Khorshidi and Peterson developed an atomistic machine-learning package (Amp) combined with the new neural network representation shown above [101].…”

“…(2) Similarly, with the rapid development of big data analysis and deep learning techniques [32], it is expected that they could be widely applied for catalytic activity predictions and global structural optimizations of catalytic systems. Though, so far, only a few relevant studies have focused on deep learning techniques (e.g., Zhai et al [100]), more applicable studies should emerge in the near future. It is also expected that some of the current challenges, such as CO 2 electroreduction selectivity and machine learning-assisted MD simulations, could be well-addressed and understood by state-of-the-art data-mining analysis and deep learning techniques.…”