Global geometry optimization of silicon clusters using the space-fixed genetic algorithm

The space-fixed genetic algorithm originally proposed by Niesse and Mayne [ J. Chem. Phys. 105, 4700 (1996)] is modified and used to study the lowest e nergy structure of small silicon clusters by employing empirical interatomi c potentials. In this new space-fixed genetic algorithm, a gradient-free si mplex method, rather than the conventional gradient-driven conjugate gradie nt minimization employed by Niesse and Mayne, is selected by virtue of its flexibility and applicability to any form of interatomic potentials for whi ch the calculation of derivatives is difficult. Using two empirical three-b ody potentials, we calculated the ground state structure up to Si-15 succes sfully using this new genetic algorithm based on the simplex method. The ef fect of angular dependent three-body potentials on the cluster structures i s examined and compared with the experimental results. (C) 2000 American In stitute of Physics. [S0021-9606(00)51324-5].