Band structure of the 3d-t_2g sub-shell of V₂O₃ and Ti₂O₃ in the tight-binding approximation

Previous two-dimensional calculations of the band structure of V₂O₃ were extended to three dimensions. The band scheme was made to include the a1 band consisting of c-axis oriented functions, and the band width was estimated to be of order 2-4 ev. It was found that the α₁, band is nearly one-dimensional and its bonding part is almost completely full for Ti₂O₃; while the e_π band has a large effective mass in the c-axis direction in spite of a large transfer integral between c-axis neighbours. It is almost empty for Ti₂O₃, and partly filled for V₂O₃. This calculation neglects covalency with the oxygens and therefore cannot be regarded as quantitative, but rather as an order-of-magnitude evaluation, and as an illustration of certain features of the E_k versus k dispersion within the bands that result from symmetry considerations. In the sesquioxides, in contrast for example with ReO₃, interaction between metal ions is direct, and not only through the oxygen ions, and this is why we think the approximation presented here should give the broad outlines of the band structure.