Of the most prominent properties of Nanoparticles is the high ratio of surface to volume which causes the domination of the surface properties and results in novel properties comparing with the corresponding bulk material. One of the consequences of surface properties is the enhancement in the chemical activity of the system that may improve the efficiency of the chemical catalyses in an effective manner. Copper nanoparticles have various applications in catalyses and industries; therefore, in this thesis, the properties of pure and alloyed copper nanoclusters are studied via ab-initio calculations by using the computational packet of ' Frite Habber Institue-ab initio molecular simulation' (FHI-aims). This all electron and full potential calculation packet is used to explain the molecules and materials properties efficiently and precisely. In the software FHI-aims, one may obtain almost the precise position of the Highest Occupied Molecular Orbital( HOMO) and Lowest Uno ccupied Molecular Orbital ( LUMO) and consequently the electronic properties of the system via implying the many body GW correction . At first, in order to verify validity of the FHI-aims calculations, C opper dimer were calculated by using FHI-aims and Wien2k packets . The correspondence of the two sets of results ensured us in continuing the calculation by the FHI-aims software. Then, the input parameter optimization and choosing the proper exchange-correlation functional were performed and the structural, magnetic, vibrational and electronic properties of the pure nanoclusters of copper including dimer through nine atomic clusters were studied. A structural transition from two dimension to three dimension was observed between the six and seven atomic nanoclusters and accordingly a peak is seen in the values of average coordination number of atoms and the average bond length. N anoclusters with even number of atoms are more stable because of their closed electronic shell and among even clusters, two and eight atomic systems were found as magic numbers of pure Cu Copper . On the other hand, Although bulk Copper is a non-magnetic material, we observe that clusters with odd number of atoms have a finite magnetic moment. It is a kind of atomic like magnetism which is originated from the uncompensated spin moment of a single unpaired electron of Copper . T he calcaluted electronic properties including ionization potential, electron affinities and chemical hardness confirm the more stability of the even nanoclusters. In order to improve the catalyses properties of the Copper nanoclusters, these nanoclusters are alloyed with palladium. Hence, the effect of substituting one or two Palladium atoms in the two through nine atomic pure nanoclusters, and then the structural, electronic, vibrational and magnetic properties of the alloy nanoclusters were studied. It was observed that average bond length of nanoclusters of Cu n- 1 Pd and Cu n- 2 Pd 2 are more than the corresponding values in the pure copper nanoclusters .The theoretical magic numbers of Cu n- 1 Pd and Cu n- 2 Pd 2 were found to be (3,7) and (3,4,8). , more over, we observ ed that s table Cu n- 2Pd 2 clusters are made of Cu 2Pd 2 pyramid and consequently Pd atoms in Cu n- 2 Pd 2 tends to bond together . Keywords: Density functional theory, Cu cluster, Cu n- 1 Pd and Cun- 2 Pd 2 clusters , N umerical atom centred orbitals, FHI- aims