  The electronic structure of the $(2\sqrt{2}\times\sqrt{2})R45^{\circ}$
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
$(2\sqrt{2}\times\sqrt{2})R45^{\circ}$ phase. The main driving force for the
0.5ML 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.
