Unbiased fuzzy global optimization of Lennard-Jones clusters for N ≤ 1000

We propose a fuzzy global optimization (FGO) algorithm to identify the lowest-energy structure of nanoclusters. In contrast to traditional methods implemented in the real space, FGO utilizes mostly the discrete space in a fuzzy search framework. Starting from random initial configurations, we carry out directed Monte Carlo and surface Monte Carlo in the discrete space to obtain low-energy candidate clusters and make real-space local optimizations finally to get the real global minimum structure. The performance of FGO is demonstrated in a large set of standard Lennard-Jones (LJ) clusters with up to 1000 atoms. All the putative global minima reported in the literature are successfully obtained with a low scaling of CPU time with cluster size, and new global minimum structures for LJ clusters with 894, 974, and 991 atoms are identified. Due to the unbiased nature, FGO can potentially deal with the global optimization of other nanomaterials with high efficiency and reliability. Published under license by AIP Publishing.