Insulating oxides in low dimensionality: A theoretical review

In the light of recent studies, we summarize our present theoretical unders tanding of insulating oxides in low dimensionality, including unsupported c lusters, planar or stepped surfaces and ultrathin films. We review the vari ous theoretical approaches, their efficiency in calculating ground and exci ted state properties, and their applications to the present systems. We dis cuss the forces at work which determine the atomic structure around under-c oordinated atoms (equilibrium geometries of very small clusters, bond lengt hs, relaxation and rumpling at surfaces), the energetics associated with lo w dimensionality (surface energies and mean cohesion energy in clusters), t he electronic properties, such as electron distribution, magnetic interacti ons and ordering, and electronic excitations (ionization potentials, electr on affinity, quasiparticle spectra, d --> d and charge transfer excitations ).