  The locally self-consistent real space multiple scattering technique has been
applied to calculate the electronic structure and chemical binding for the
c(2x2)O/Cu(001) system, as a function of $d_{O-Cu1}$ -- the height of oxygen
above the fourfold hollow sites. It is found that the chemical binding between
oxygen and copper has a mixed ionic-covalent character for all plausible values
of $d_{O-Cu1}$. Furthermore, the electron charge transfer from Cu to O depends
strongly on $d_{O-Cu1}$ and is traced to the variation of the long-range
electrostatic part of the potential. A competition between the hybridization of
Cu1-$d_{xz}$ with O-$p_x,p_y$ and Cu1-$d_{x^2-y^2}$ with O-$p_z$ states
controls modification of the electronic structure when oxygen atoms approach
the Cu(001) surface. The anisotropy of the oxygen valence electron charge
density is found to be strongly and non-monotonically dependent on $d_{O-Cu1}$.
