ReO3 Band Structure in the Tight-Binding Approximation

Using tight-binding, LCAO methodology, a formal band structure scheme has been specified for the ReO₃ structure based on the use of $\text{2s}$ and $\text{2p}$ orbitals for oxygen and of $\text{5d}$ , $\text{6s}$ , and $\text{6p}$ orbitals for rhenium. The scheme should also be useful in the characterization of band structures for perovskites in general. Two sets of sufficient conditions have been found under which the secular determinant reduces to two special cases: one corresponding to a model previously considered by Goodenough and the other to a model considered by Kahn and Leyendecker. The nature of the approximation schemes is discussed in some detail.