In this study, we perform a systematic search to find the possible lowest energy structure of silicon nanoclusters Sin (n = 8-80) by means of an evolutionary algorithm. The fitness function for this search is the total energy of density functional tight binding (DFTB). To be on firm ground, we take several low energy structures of DFTB and perform further geometrical optimization by density functional theory (DFT). Then we choose structures with the lowest DFT total energy and compare them with the reported lowest energy structures in the literature. In our search, we found several lowest energy structures that were previously unreported. We further observe a geometrical transition at n = 27 from elongated to globular structures. In addition, the optical gap of the lowest energy structures is investigated by time-dependent DFTB (TD-DFTB) and time-dependent DFT (TD-DFT). The results show the same trend in TD-DFTB and TD-DFT for the optical gap. We also find a sudden drop in the optical gap at n = 27, precisely where the geometrical transition occurs.
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For the first search, USPEX/DFTB+ provides 70 structures at each generation. We selected the top 20 lowest DFTB energy structures plus 10 randomly selected structures among the rest, and then we re-optimized the structures at the DFT level. For our second search, using the top 10 lowest energy structures of the first search as seeds, USPEX/DFTB+ provides 140 structures at each generation. We selected the top 20 lowest DFTB energy structures and re-optimized them within the DFT framework.