Accelerated global optimization of metal cluster structures via the deep neural network complemented with transfer learning and genetic algorithm^†

Searching the global minimum (GM) structures of metal clusters is of great importance in cluster science. Very recently, the global optimization method based on deep neural network combined with transfer learning (DNN-TL) was developed to improve the efficiency of optimizing the GM structures of metal clusters by greatly reducing the number of samples to train the DNN. Aiming to further enhance the sampling efficiency of the potential energy surface and the global search ability of the DNN-TL method, herein, an advanced global optimization method by embedding genetic algorithm (GA) into the DNN-TL method (DNN-TL-GA) is proposed. In the case of the global optimization of Pt_n (n=9–15) clusters, the DNN-TL-GA method requires only a half number of samples at most with respect to the DNN-TL method to find the GM structures. Meanwhile, the DNN-TL-GA method saves about 70%-80% of computational costs, suggesting the significant improved efficiency of global search ability. There are much more samples distributed in the area of the potential energy surface with low energies for DNN-TL-GA (25% for Pt₁₄) than for DNN-TL (<1% for Pt₁₄). The success of the DNNTL-GA method for global optimization is evidenced by finding unprecedented GM structures of Pt₁₆ and Pt₁₇ clusters.