The bond valence model as a prospective approach: examination of the crystal structures of copper chalcogenides with Cu bond valence excess.

Bond valence analysis has been applied to various copper chalcogenides with copper valence excess, i.e. where the formal valence of copper exceeds 1. This approach always reveals a copper bond valence excess relative to the unit value, correlated to an equivalent ligand bond valence deficit. In stoichiometric chalcogenides, this corresponds to one ligand electron in excess per formula unit relative to the valence equilibrium considering only Cu. This ligand electron in excess is 50/50 shared between all or part of the Cu-atom positions, and all or part of the ligand-atom positions. In CuSe, only one of the two Cu positions is involved in this sharing. It would indicate a special type of multicentre bonding (`one-electron co-operative bonding'). Calculated and ideal structural formulae according to this bond valence distribution are presented. At the crystal structure scale, Cu-ligand bonds implying the single electron in excess form one-, two- or three-dimensional subnetworks. Bond valence distribution according to two two-dimensional subnets is detailed in covellite, CuS. This bond valence description is a formal crystal-chemical representation of the metallic conductivity of holes (mixing between Cu 3d bands and ligand p bands), according to published electronic band structures. Bond valence analysis is a useful and very simple prospective approach in the search for new compounds with targeted specific physical properties.