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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 P 9 and P 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 P 9 and P 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.

journal of chemical theory and computation

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