Statistical evaluation of the big bang search algorithm

We probe the statistical performance of the big bang search algorithm, a highly parallel method involving large numbers of gradient quenches from random, but highly compressed initial geometries. Using Lennard-Jones clusters as test systems, we find that the number of energy evaluations required to locate global minima follows an exponential distribution and that the width of the distribution is reduced by starting from compressed geometries. With a volume compression of about 1/100, the efficiency of the method is comparable to that of more sophisticated algorithms for clusters containing up to 40 atoms. We apply the algorithm to the problem of Si clusters, obtaining the ground state structures for Si_n and Sin+ for n = 20-27, a range that spans the well-known silicon cluster shape transition. The results provide a detailed accounting of the transition, including a simple explanation of the three structural families observed in this size range.