Conclusion

We have developed a hybrid competent genetic algorithm that utilizes Nelder-Mead simplex algorithm for optimizing small silicon clusters. We have successfully predicted optimal structures for clusters of size 4-11. These results agree with those in literature. Furthermore, we have empirical evidence that the number of function evaluations and the population size increase with the number of atoms in a cluster as O(n^4.2) and O(n^8.2) respectively. The results indicate that more efficient algorithms have to be designed that retain the high reliability of the proposed technique but would have a better scale-up behavior.