Designing rules and probabilistic weighting for fast materials discovery in the Perovskite structure.

High-throughput electronic-structure calculations are becoming increasingly popular in materials science and in the design of new compounds. Electronic-structure theory, for example, in the form of density-functional theory, can be used to calculate stabilities and electronic properties as bandgaps of new compounds. However, in practice, the methods are often limited to rather small atomic-scale systems or periodic crystals with only a limited number of atoms in the unit cell. It is therefore of interest to be able to derive generally useful information from simple systems to be applied in other, more complex, crystals. Here, we consider a large database of calculated stabilities and bandgaps of oxides and oxynitrides in the perovskite structure. We use the database as a testing ground for existing ideas about the behavior of these types of compounds and we derive some new simple chemical-based rules which combine structural information, like the ionic radii of the chemical elements, with electronic data, like the number of electrons and the valences of the pure elements. The rules extracted from the ABO₃ cubic perovskite are then tested using the ABO₂N and A₂BO₄ stoichiometry in the cubic and layered perovskite structure, respectively. These rules allow a saving in computer time of around 80%.