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

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.