The electronic structure of the (2root2xroot2)R45degrees O/Cu(001) system has been calculated using locally self-consistent, real space multiple scattering technique based on first principles. Oxygen atoms are found to perturb differentially the long-range Madelung potentials, and hence the local electronic subbands at neighboring Cu sites. As a result the hybridization of the oxygen electronic states with those of its neighbors leads to bonding of varying ionic and covalent mix. Comparison of results with those for the c(2x2) overlayer shows that the perturbation is much stronger and the Coulomb lattice energy much higher for it than for the (2root2xroot2)R45degrees phase. The main driving force for the 0.5 ML oxygen surface structure formation on Cu(001) is thus the long-range Coulomb interaction which also controls the charge transfer and chemical binding in the system.