Electronic structure of the A(8)Tr(11) (A = K, Rb, Cs; Tr = Ga, In, Tl) Zintl phases: possible chemical reasons behind their activated versus non activated conductivity.

The electronic structure of the A(8)Tr(11) (A = K, Cs; Tr = Ga, In, Tl) Zintl phases has been studied by means of first-principles density functional theory (DFT) calculations. It is shown that the hypoelectronic Tr(11) cluster in these phases must be considered as Tr(11)(8-) even if it would require just a 7- charge to maximize its bonding, filling all its bonding and nonbonding levels. Our calculations show that the lowest empty orbital of the isolated Tr(11)(7-) clusters is an a(1)-type orbital. However, a degenerate e-type set of orbitals is higher but quite close in the case of the Ga(11)(7-) clusters. Thus, for the isolated Tr(11)(8-) clusters, the extra electron occupies always an a(1)-type antibonding orbital that contains, however, some Tr-Tr bonding component thus leading to a weak global antibonding character. In the solid, cluster-alkali-metal bonding interactions occur and spread the cluster levels into bands, but the extra electron still fills the a(1)-type cluster level for most of the A(8)Tr(11) phases. The cluster-alkali-metal interactions have a minor role in stabilizing this orbital but they provide the necessary delocalization to lead to the metallic character of these phases. In contrast, the e-type antibonding levels of the Ga(11)(7-) isolated cluster are those which become filled by the extra electron in the Cs(8)Ga(11) solid. This phase should be metallic, but occupation of this degenerate pair of cluster levels would lead to a structural instability that may be avoided by reducing the interactions of the alkali-metal atoms with the cluster levels. In that way the occupation appropriate for the isolated cluster is restored (i.e., one electron fills the a(1) cluster orbital), but the extra electron now remains localized on the cluster, thus leading to the unexpected activated conductivity observed for the Cs(8)Ga(11) phase.