We performed B3PW and B3LYP computations for BaTiO₃ (BTO), CaTiO₃ (CTO), PbTiO₃ (PTO), SrTiO₃ (STO), BaZrO₃ (BZO), CaZrO₃ (CZO), PbZrO₃ (PZO) and SrZrO₃ (SZO) perovskite neutral (001) along with polar (011) as well as (111) surfaces. For the neutral AO- as well as BO₂-terminated (001) surfaces, in most cases, all upper-layer atoms relax inwards, although the second-layer atoms shift outwards. On the (001) BO₂-terminated surface, the second-layer metal atoms, as a rule, exhibit larger atomic relaxations than the second-layer O atoms. For most ABO₃ perovskites, the (001) surface rumpling s is bigger for the AO- than BO₂-terminated surfaces. In contrast, the surface energies, for both (001) terminations, are practically identical. Conversely, different (011) surface terminations exhibit quite different surface energies for the O-terminated, A-terminated and BO-terminated surfaces. Our computed ABO₃ perovskite (111) surface energies are always significantly larger than the neutral (001) as well as polar (011) surface energies. Our computed ABO₃ perovskite bulk B-O chemical bond covalency increases near their neutral (001) and especially polar (011) surfaces.

We performed, to the best of our knowledge, the world’s first first-principles calculations for the WO₂-terminated cubic WO₃ (001) surface and analyzed the systematic trends in the WO₃, SrTiO₃, BaTiO₃, PbTiO₃ and CaTiO₃ (001) surface ab initio calculations. According to our first principles calculations, all WO₂ or TiO₂-terminated WO₃, SrTiO₃, BaTiO₃, PbTiO₃ and CaZrO₃ (001) surface upper-layer atoms relax inwards towards the crystal bulk, while all second-layer atoms relax upwards. The only two exceptions are outward relaxations of first layer WO₂ and TiO₂-terminated WO₃ and PbTiO₃ (001) surface O atoms. The WO₂ or TiO₂-terminated WO₃, SrTiO₃, BaTiO₃, PbTiO₃ and CaTiO₃ (001) surface-band gaps at the Γ–Γ point are smaller than their respective bulk-band gaps. The Ti–O chemical bond populations in the SrTiO₃, BaTiO₃, PbTiO₃ and CaTiO₃ bulk are smaller than those near the TiO₂-terminated (001) surfaces. Conversely, the W–O chemical bond population in the WO₃ bulk is larger than near the WO₂-terminated WO₃ (001) surface.

We performed, for first time, ab initio calculations for the ReO₂-terminated ReO₃ (001) surface and analyzed systematic trends in the ReO₃, SrZrO₃, BaZrO₃, PbZrO₃ and CaZrO₃ (001) surfaces using first-principles calculations. According to the ab initio calculation results, all ReO₃, SrZrO₃, BaZrO₃, PbZrO₃ and CaZrO₃ (001) surface upper-layer atoms relax inwards towards the crystal bulk, all second-layer atoms relax upwards and all third-layer atoms, again, relax inwards. The ReO₂-terminated ReO₃ and ZrO₂-terminated SrZrO₃, BaZrO₃, PbZrO₃ and CaZrO₃ (001) surface band gaps at the Γ–Γ point are always reduced in comparison to their bulk band gap values. The Zr–O chemical bond populations in the SrZrO₃, BaZrO₃, PbZrO₃ and CaZrO₃ perovskite bulk are always smaller than those near the ZrO₂-terminated (001) surfaces. In contrast, the Re–O chemical bond population in the ReO₃ bulk (0.212e) is larger than that near the ReO₂-terminated ReO₃ (001) surface (0.170e). Nevertheless, the Re–O chemical bond population between the Re atom located on the ReO₂-terminated ReO₃ (001) surface upper layer and the O atom located on the ReO₂-terminated ReO₃ (001) surface second layer (0.262e) is the largest.