4 - LCAO energy band model for cubic perovskites

Summary

In Chapter 1 a qualitative description of the energy bands of perovskites was developed starting from a simple ionic model. It was argued that the essential electronic structure of the perovskites is derived from the BO₃ ions of the ABO₃ compound. The A ion was shown to be important in determining the ionic state of the B ion. Also, the A ion contributes to the electrostatic potentials. However, the energy bands associated with the outer s orbitals of the A ion were found to be far removed in energy from the lowest empty d bands and were unoccupied. As a result of these considerations the electronic structure of the A ion can be neglected in discussing the principal features of perovskite energy bands.

The energy bands that are electronically and chemically active are derived from the d orbitals of the transition metal (B) cation and the 2p orbitals of the oxygen anions. The deep core states of the ions produce atomic-like levels at energies far below the valence bands and may also be omitted in our discussion.

One of the first energy band calculations for perovskites was carried out by Kahn and Leyendecker [1] for SrTiO₃. They employed a semiempirical approach based on the method of Slater and Koster [2] (described in Section 3.2). The model presented in this chapter follows closely the work of Kahn and Leyendecker.