Large orbital magnetic moment in Pt₁₃ clusters

Enhancing the Performance of Global Optimization of Platinum Cluster Structures by Transfer Learning in a Deep Neural Network

The global optimization of metal cluster structures is an important research field. The traditional deep neural network (T-DNN) global optimization method is a good way to find out the global minimum (GM) of metal cluster structures, but a large number of samples are required. We developed a new global optimization method which is the combination of the DNN and transfer learning (DNN-TL). The DNN-TL method transfers the DNN parameters of the small-sized cluster to the DNN of the large-sized cluster to greatly reduce the number of samples. For the global optimization of Pt₉ and Pt₁₃ clusters in this research, the T-DNN method requires about 3-10 times more samples than the DNN-TL method, and the DNN-TL method saves about 70-80% of time. We also found that the average amplitude of parameter changes in the T-DNN training is about 2 times larger than that in the DNN-TL training, which rationalizes the effectiveness of transfer learning. The average fitting errors of the DNN trained by the DNN-TL method can be even smaller than those by the T-DNN method because of the reliability of transfer learning. Finally, we successfully obtained the GM structures of Pt_n (n = 8-14) clusters by the DNN-TL method.

Metastable Structures in Cluster Catalysis from First-Principles: Structural Ensemble in Reaction Conditions and Metastability Triggered Reactivity

Reactivity studies on catalytic transition metal clusters are usually performed on a single global minimum structure. With the example of a Pt₁₃ cluster under a pressure of hydrogen, we show from first-principle calculations that low energy metastable structures of the cluster can play a major role for catalytic reactivity and that hence consideration of the global minimum structure alone can severely underestimate the activity. The catalyst is fluxional with an ensemble of metastable structures energetically accessible at reaction conditions. A modified genetic algorithm is proposed to comprehensively search for the low energy metastable ensemble (LEME) structures instead of merely the global minimum structure. In order to reduce the computational cost of density functional calculations, a high dimensional neural network potential is employed to accelerate the exploration. The presence and influence of LEME structures during catalysis is discussed by the example of H covered Pt₁₃ clusters for two reactions of major importance: hydrogen evolution reaction and methane activation. The results demonstrate that although the number of accessible metastable structures is reduced under reaction condition for Pt₁₃ clusters, these metastable structures can exhibit high activity and dominate the observed activity due to their unique electronic or structural properties. This underlines the necessity of thoroughly exploring the LEME structures in catalysis simulations. The approach enables one to systematically address the impact of isomers in catalysis studies, taking into account the high adsorbate coverage induced by reaction conditions.