The electronic band structure of polar polymorph α/β-BaTeMo₂O₉ phases

Based on the reported experimental geometrical structure, a comprehensive theoretical calculations were performed to investigate the electronic band structure, the angular momentum projected density of states, the electronic charge density distribution and the chemical bonding characters of α-BaTeMo₂O₉ and β-BaTeMo₂O₉. Calculation reveals that in both phases the conduction band minimum (CBM) is located at Γ point of first Brillouin zone (BZ) whereas the valence band maximum (VBM) of β-BaTeMo₂O₉ phase is situated in the mid way between Z and Γ points of BZ, while it is located at Z point for α-BaTeMo₂O₉ phase, resulting in an indirect band gap of about 2.93 eV (β) and 3.12 eV (α) in good agreement with the measured values 2.95 eV (β) and 3.12 eV (α). It has been noticed that the VBM is mainly formed by O-p states while the CBM is controlled by Mo-d state. The valence band's electronic charge density distribution reveals that β-BaTeMo₂O₉ phase show there exists a strong covalent bonding between Mo and O also between Te and O atoms, while Ba atom forms mostly ionic and partially covalent bonding with O atom. The phase transition from β → α cause to perturb the interaction between Mo and O atoms, Te and O atoms and Ba and O atoms which is attributed to the different arrangement between the atoms of the two phases, where the asymmetric unit of β-phase have a formula BaTeMo₂O₉ while for α-phase the asymmetric unit have the formula Ba₂Te₂Mo₄O₁₈. Due to the electro-negativity difference between the atoms we can see a charge transfer towards O atoms as indicated by the blue color around O atoms. The calculated bond lengths and angles show good agreement with the experimental values. The good agreement with experimental data in the matter of lattice parameters, energy gap values, the bond lengths and angles reveals the accuracy of the selected exchange correlation potentials used here. - Highlights: • β-BaTeMo₂O₉ and α-BaTeMo₂O₉ phases show indirect band gap. • The valence band's electronic charge density distribution were calculated. • Asymmetric unit of β-phase have formula BaTeMo₂O₉ while α-phase it has Ba₂Te₂Mo₄O₁₈.