Ab initio hybrid DFT calculations of BaTiO3, PbTiO3, SrZrO3 and PbZrO3 (111) surfaces

The results of ab initio calculations for polar BaTiO3, PbTiO3, SrZrO3 and PbZrO3 (111) surfaces using the CRYSTAL code are presented. By means of the hybrid B3LYP approach, the surface relaxation has been calculated for two possible B (B = Ti or Zr) or AO3 (A = Ba, Pb or Sr) BaTiO3, PbTiO3, SrZrO3 and PbZrO3 (111) surface terminations. According to performed B3LYP calculations, all atoms of the first surface layer, for both terminations, relax inwards. The only exception is a small outward relaxation of the PbO3-terminated PbTiO3 (111) surface upper layer Pb atom. B3LYP calculated surface energies for BaO3, PbO3, SrO3 and PbO3-terminated BaTiO3, PbTiO3, SrZrO3 and PbZrO3 (111) surfaces are considerably larger than the surface energies for Ti (Zr)-terminated (111) surfaces. Performed B3LYP calculations indicate a considerable increase of TiO (ZrO) chemical bond covalency near the BaTiO3, PbTiO3, SrZrO3 and PbZrO3 (111) surface relative to the BaTiO3, PbTiO3, SrZrO3 and PbZrO3 bulk. Calculated band gaps at the Γ-point near the PbTiO3, SrZrO3 and PbZrO3 (111) surfaces are reduced, but near BaTiO3 (111) surfaces increased, with respect to the BaTiO3, PbTiO3, SrZrO3 and PbZrO3 bulk band gap at the Γ-point values.