Metal arrays in structural units based on anion-centered metal tetrahedra

Structural units based on anion-centered metal tetrahedra (XA(4); X = O, N; A = metal) are described as eutactic metal fragments with anions in tetrahedral interstices. In this respect these units may be subdivided into fluorite derivatives and units based on stellae quadrangulae (tetrahedral stars). To describe the geometry of the metal arrays a set of tetrahedrally packed metal radii, r(tp), is derived for A = Cu, Pb, Bi, and some rare-earth metals from the systematic analysis of the A...A distances within (XA(4)) tetrahedra. Analysis of these radii and of the structural geometry of the units shows that the insertion of anions into tetrahedral interstices of the metal fragment causes its expansion and distortions by nonbonded anion-anion repulsions. The main effect is owing to the linkage of (XA(4)) tetrahedra via edges, which leads to compression of the shared A...A edges and stretching of the unshared edges. The geometry of this effect is described by some empirical expressions. It is suggested that the eutactic arrangement of metal atoms in structural units based on anion-centered metal tetrahedra is caused by the closed-shell metal-metal bonding interactions.