From the molecular picture to the band structure of cubic and tetragonal barium titanate

A band structure of barium titanate crystal has been calculated with the WIEN2k program, using FP LAPW method. A broad dispersion of the valence band (about 5 eV) and a narrow forbidden energy gap (about 2 eV) confirm the crucial role of covalent interactions in this compound. The calculations have been performed for cubic and tetragonal structures of the crystal, which have allowed to determine the changes in the electronic structure due to the ferroelectric phase transition. It is found that the transition between cubic and tetragonal structures does not change significantly either the bands widths or their positions in relation to the Fermi level. The main difference concerns the character of the bands and is clearly related to the oxygen electronic states. This indicates that the ferroelectric behavior of the material may be explained by the crucial role of the pi bonds formed by the oxygen ions. The band structure obtained remains in direct relation to the molecular picture thus confirming ligand field theory.