Structural diversity and complexity of antiperovskites

The overview of more than 280 antiperovskites as compounds based upon the units formed by condensation of XA6 anion-centered octahedra (X = anion; A = cation) shows that there are forty-five topologically different types of antiperovskite structures, including eighteen frameworks, fourteen layers, six chains and seven finite clusters. The XA6 octahedra may polymerize by sharing common corners, edges and faces. One A atom may be shared by no more than six XA6 octahedra, whereas one A-A edge may be shared by no more than three octahedra. The average connectivity of an octahedron in the unit, , defined as the average number of octahedra linked to a single octahedron in the complex, correlates positively with the X:A ratio. The information-based analysis of topological complexity of antiperovskite units shows that most antiperovskites are rather simple from the structural point of view with the most complex units being the layers present in the crystal structures of A4[N8O3A47](A'N4)12 (A = Ca, Sr; A' = Mo, W). The information-based complexity parameters correlate with the number k' of symmetrically independent octahedra in the antiperovskite unit: the higher the value of k', the more complex is the unit. From the chemical point of view, the review covers oxides, suboxides, oxysalts, nitrides, subnitrides, and complex halogenides.