Crystal and electronic structures of ScAuGe, CeAuGe, and LuAuGe: A transition from two- to three-dimensional [AuGe] polyanions

New germanides ScAuGe, TmAuGe, and LuAuGe were prepared by melting mixtures of the elements in an are furnace and subsequent annealing at 1070 K. The structures of ScAuGe and LuAuGe were refined from X-ray single-crystal diffractometer data: P6(3)mc (No. 186), Z=2, a=430.82(5) pm, c=684.58(10) pm, V=0.1100(1) nm(3), wR2=0.0688, 275 F-o(2) values, ten variables for ScAuGe; P6(3)me (No. 186), Z=2, a=437.75(4) pm, c=711.38(6) pm, V=0.1181(1) nm(3), wR2=0.0340, 355 F-o(2) values, 11 variables, and a batch scale factor of 0.47(3) for LuAuGe. The lattice constants for TmAuGe are a=439.08(4) pm, c=716.59(7) pm, and V=0.1196(1) nm(3). The crystal structures of these germanides are derived from the CaIn2-type structure by an ordered arrangement of Au and Ge atoms at the indium position. The crystal chemistry of ScAuGe and LuAuGe is compared with that of the recently reported cerium compound. Although the Au-Ge intralayer distances at 259.6 pm in CeAuGe, 260.5 pm in LuAuGe, and 257.6 pm in ScAuGe are similar, the Au-Ge interlayer distances at 364.2 pm in CeAuGe, 292.7 pm in LuAuGe, and 275.2 pm in ScAuGe differ significantly. Thus, the [AuGe] polyanions are changed from two-dimensional layers in CeAuGe to a three-dimensional network of distorted tetrahedra in ScAuGe. Chemical bonding within the structures was investigated by TB-LMTO-ASA band structure calculations. The energy bands, the densities of states and the valence charge densities are discussed. Bonding is characterized by intralayer bonds between Au and Ge within the puckered AuGe hexagons. In addition, in the case of ScAuGe strong bonds are directed from the Au atoms of one layer to the Ge atoms of the neighbouring layer. Weaker interlayer bonding is observed in LuAuGe and no interlayer interaction in CeAuGe, as already indicated by the pronounced increase of the interlayer distances.