Systematic trends in (0 0 1) surface ab initio calculations of ABO₃ perovskites

By means of the hybrid exchange–correlation functionals, as it is implemented in the CRYSTAL computer code, ab initio calculations for main ABO₃ perovskite (0 0 1) surfaces, namely SrTiO₃, BaTiO₃, PbTiO₃, CaTiO₃, SrZrO₃, BaZrO₃, PbZrO₃ and CaZrO₃, were performed. For ABO₃ perovskite (0 0 1) surfaces, with a few exceptions, all atoms of the upper surface layer relax inward, all atoms of the second surface layer relax outward, and all third layer atoms, again, inward. The relaxation of (0 0 1) surface metal atoms for ABO₃ perovskite upper two surface layers for both AO and BO₂-terminations, in most cases, are considerably larger than that of oxygen atoms, what leads to a considerable rumpling of the outermost plane. The ABO₃ perovskite (0 0 1) surface energies always are smaller than the (0 1 1) and especially (1 1 1) surface energies. The ABO₃ perovskite AO and BO₂-terminated (0 0 1) surface band gaps always are reduced with respect to the bulk values. The B–O chemical bond population in ABO₃ perovskite bulk always are smaller than near the (0 0 1) and especially (0 1 1) surfaces.