Periodic HF/6-31G and a hybrid density functional, B3LYP/6-31G. calculations have been carried out in order to determine the geometric and electronic structure of bulk ZnO. The lattice parameters, bulk modulus, charge distribution and band structure are reported. Surface energy and charge distribution of the ZnO (10(1) over bar 0) surface are obtained, while top site adsorption of Cu atoms on Zn or O atoms on the ZnO (10(1) over bar 0) surface are considered. Optimized distances, charge transfers. vibrational frequencies and binding energies associated with both types of adsorption processes are calculated. The theoretical results are compared with previous theoretical studies and available experimental data.