A multi-populations multi-strategies differential evolution algorithm for structural optimization of metal nanoclusters

Theoretically, the determination of the structure of a cluster is to search the global minimum on its potential energy surface. The global minimization problem is often nondeterministic-polynomial-time (NP) hard and the number of local minima grows exponentially with the cluster size. In this article, a multi-populations multi-strategies differential evolution algorithm has been proposed to search the globally stable structure of Fe and Cr nanoclusters. The algorithm combines a multi-populations differential evolution with an elite pool scheme to keep the diversity of the solutions and avoid prematurely trapping into local optima. Moreover, multi-strategies such as growing method in initialization and three differential strategies in mutation are introduced to improve the convergence speed and lower the computational cost. The accuracy and effectiveness of our algorithm have been verified by comparing the results of Fe clusters with Cambridge Cluster Database. Meanwhile, the performance of our algorithm has been analyzed by comparing the convergence rate and energy evaluations with the classical DE algorithm. The multi-populations, multi-strategies mutation and growing method in initialization in our algorithm have been considered respectively. Furthermore, the structural growth pattern of Cr clusters has been predicted by this algorithm. The results show that the lowest-energy structure of Cr clusters contains many icosahedra, and the number of the icosahedral rings rises with increasing size.