Four clusters of ZnO, O-Zn-SR (-SR = ligand) and doping ZnO structures (with Cr, Cu, Al atoms) were investigated using density functional theory at theB3LYP/Lanl2dz level. The characteristics of Zn(3)O(3) and Zn(4)O(4) structures, which are the units of experimental wurtzite and zinc blende structures, were found to be similar to those of experimental ZnO nanocrystals. Moreover, the calculated Raman and IR spectra of ZnO clusters were almost consistent with experimental results. Raman spectra were observed to shift to higher frequencies with decreasing numbers of atoms. Both ligands and solvent make the wavelength of absorption peaks shift to blue. All transitions of absorption peaks for these pure clusters were from d to p orbitals. Finally, doping clusters and experimental doping nanocrystals were similar in character. The doping of metal changed the orbital of ZnO nanocrystals. The transitions in doping clusters (Cr-ZnO, Cu-ZnO) are from d to d orbitals, while Al-ZnO clusters have s-p transitions.