An evolutionary type global optimization method for the geometries of atomic clusters has been developed and used for finding stable structures of carbon clusters as a test application. Carbon clusters have been chosen because of large barriers in the potential energy function which makes the optimization procedure harder. Simple optimization methods fail for the carbon clusters because of this property. Genetic algorithms (GAs) are known to be very powerful since they provide an efficient search of the configuration space. However, their power is still not enough when relatively larger carbon clusters are the subject. Combining GAs with a local optimization method reduces the search over all configuration space to a search over local minima and hence improves the efficiency of the GA. In this study, classical Monte Carlo (MC) method has been used as the local optimization between GA steps. MC optimization jumps over most of the local minima and this reduces the search space even further. Single parent GA has been preferred and a fitness based selection mechanism has been applied. Total potential energy of the cluster has been used as the fitness function. A geometrical mutation operation which rotates half of the cluster by an arbitrary angle has been applied. A shrinking operation has also been applied by multiplying all the atomic coordinates by a coefficient less than one, causing the MC local optimization to be an inflationary motion and this increases the efficiency of the method for cage like carbon clusters. Results obtained by this GA - MC hybrid method have been compared with available results in the literature and reliability of the method has been justified for up to 38 atoms. This hybrid method has been parallelized by distributing individuals to the available computing nodes and a high efficiency has been observed for this parallel running version.

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1. On the Energetics and Structural Behavior of some Si_n Clusters: Molecular Dynamics Simulations