An Iterative Global Optimization Algorithm for Potential Energy Minimization

In this paper we propose an algorithm for the minimization of potential energy functions. The new algorithm is based on the differential evolution algorithm of Storn and Price (Journal of Global Optimization, vol. 11, pp. 341–359, 1997). The algorithm is tested on two different potential energy functions. The first function is the Lennard Jones energy function and the second function is the many-body potential energy function of Tersoff (Physics Review B, vol. 37, pp. 6991–7000, 1988; vol. 38, pp. 9902–9905, 1988). The first problem is a pair potential and the second problem is a semi-empirical many-body potential energy function considered for silicon-silicon atomic interactions. The minimum binding energies of up to 30 atoms are reported.