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In this work, the transition metal copper (Cu) doped Zn1-xCuxO nanoparticles were synthesized by different doping concentration of Cu (x=1, 3, 5 and 7 M%) through surfactant free benzyl alcohol route method in which zinc acetate and copper acetate were selected as precursors. We have carried out the spin polarized density functional calculations based on the plane wave (PW) and projector augmented wave (PAW) methods using the generalized gradient approximation (GGA) by Perdew and Wang (PBE), as implemented in the QUANTUM ESPRESSO package within the framework of density functional theory (DFT). The following electronic states are treated, as valence electrons of Cu(3d104s1), Zn(3d104s2) and O(2s22p4) for atoms. The wave functions and charge densities are expressed as plane waves up to a kinetic energy cutoff of 60 and 300 Ry, respectively. We have done calculations on the hexagonal wurtzite ZnO unit cell and ZnO (3×3×2) supercell including the 36 Zn and 36 O atoms. For the Cu-doped ZnO nanoparticles 2 coppers are placed in the crystal structure at 3 different distances: short, medium, and long. We used the tetrahedral method when we evaluate the electronic total and projected density of state (DOS). For the self-consistent field (SCF) iterations, the total energy convergence is 10- 5 eV. The occupation numbers of electrons are expressed Gaussian distribution function with an electronic temperature of kT = 0.02 Ry. To express the strong correlated effect of electrons in the Cu(3d) and Zn(3d) states, we have chosen to be U = 3.5 and 8.5 eV respectively, using the simplified rotational-invariant formulation based on the linear response method. The numerical error in the magnetic energy gain was 3 meV. The ionic positions are relaxed at the fixed lattice parameters until the residual forces are less than 0.05eV/Å. An experimental result was validated theoretically by performing DFT calculations. Our predicted values of lattice parameters were agreed with our experimental values of crystal structure, in which the errors of the lattice parameter a are 1.14% and 1.01% by the PW and PAW methods, respectively. Our results of magnetism are shown that the hole-mediated ferromagnetism of Cu-doped ZnO is created by the double exchange mechanism, as created localized empty holes on the localized t2g state of Cu ions due to the bound magnetic polarons. These results agree with our experimental results
