We have performed LCAO semi-empirical calculations for the Cu(110)-p(2 × 1)O surface. The Cu substrate has been described by means of a recently proposed set of parameters giving excellent results for the bulk bands as well as for the surfaces states of the clean surfaces. The O-Cu and the O-O interactions have been accounted for by parameters determined by fitting the available photoemission and inverse photoemission experimental data. The O-O interactions (which were neglected in preceding LCAO studies) have an important role and contribute to fix the position of the "third" antibonding oxygen induced band. Our calculations localize this band 0.2 eV under the Fermi level at the Ȳ point. The position of this band has not yet firmly established experimentally. However, some indications of its presence 0.18 eV under the Fermi level at the Ȳ point have been given by Courths et al. [Surf. Sci. 376 (1997) 43]. Other issues are also discussed, such as the displacement above the Fermi level of the surface state localized 0.4 eV below EF on the clean surface, or the relative position of the Cu and O atoms in the added chains. © 2004 Elsevier B.V. All rights reserved.