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Rapidly finding low-energy structures on high-dimensional potential energy surfaces remains a challenging problem for cluster science. We present a fast optimization method for structure prediction named mirror-rotation searching, which is inspired by the idea of symmetry and conservation. Our search algorithm can quickly converge to the minima of energy valley by continuously performing mirror-rotation transformation on the cluster, and we introduce the term vaminima to describe these minima. For the selected Lennard-Jones cluster of size N≤150, convergence to a vaminima on average takes 413 relaxations, and finding fullerene C_{60} from a random initial structure is 49-fold faster than the traditional genetic algorithm. The approach is general and flexible and can greatly improve the search efficiency of unbiased global optimization algorithms and be applied to different kinds of problems, such as molecular structure search, crystal structure prediction, and protein folding.