Simulation of materials in different conditions and obtaining the properties of these materials requires the stable structure of that material. There are several methods to obtain the stable structure of materials. Genetic Algorithm is one of these methods. In order to produce structures by the Genetic Algorithm, we have used computational package USPEX. Structures generated by USPEX, should be relaxed by another computational package. Considering that the process is of a high order time consuming job, a computational package that has a high speed and accuracy is desired. For this goal, semi-empirical methods has been used for structural relaxation. In this method parameters which are entered in the Hamiltonian are set by the experimental results. In this dissertation, we search for stable nano structures of (MoO 3 ) n . Two semi-empirical methods PM6 and PM7 are applied to obtain metastable structures of molybdenum trioxide nanoclusters by using computational package MOPAC. The results of semi-empirical methods are then studied by computational package FHI-aims which is a full-potential all-electron code. In the first chapter we have briefly explained physical properties of molybdenum trioxide. In the second chapter semi-empirical methods which have been used in this work, are explained. In the third chapter we have focused on genetic algorithm, computational package USPEX, computational package FHI-aims and its optimization of the parameters. Finally in chapter four, structures which are obtained for the molybdenum trioxide nanoclusters have been examined and the stability of these structures is discussed.