Fuzzy Global Optimization Study Of Lennard-Jones Clusters

Global optimization(GO)plays an important role in the field of structure prediction.The basin-hopping(BH)method is a traditional GO algorithm,which has been widely applied in the structure optimization of metal,ionic,and biomolecular clusters.However,this method generally has a high computational cost,and thus cannot be efficiently employed in systems with a large number of atoms.This has restricted its wide application to complex systems.We propose a fuzzy global optimization(FGO)method based on BH,which can efficiently explore the low-energy structures in the high-dimensional configuration space.In contrast to the traditional approaches implemented in the real space,FGO utilizes the discrete space for global optimization.Starting from a completely random initial structure,we use atomic BH to search the configuration space for a best cluster and carry out surface Monte Carlo to polish this best cluster in the surface configuration space for lowest-energy cluster candidates.Because of the energy difference between the structures in discrete and real spaces,we finally optimize these candidates in the real space and get the real lowest-energy cluster.The Lennard-Jones(LJ)potential is an empirical potential,which has been widely used to describe the Van der Waals interaction between pairs of neutral atoms or molecules.LJ clusters also usually serve as a class of model systems to benchmark the efficiency of different GO algorithms.We apply FGO to all the LJ clusters with up to 1000 atoms.All the global minimum structures reported in the literature have been obtained with a relatively small scaling of computational time.Especially,better global minima for LJ clusters with 894,974,and 991 atoms have been found out.Because restriction of the cluster optimization has not been utilized,FGO is an unbiased GO algorithm.Besides LJ clusters,FGO can potentially deal with the GO of general nanomaterials with a high efficiency.