Tl(I) to Po(IV) 6s2 lone pairs in tetrahedral, triangular bipyramidal, square pyramidal, octahedral and hexahedral geometries: Crystal chemistry and ab initio visualizations and analyses

The stereochemistry of 6s2 (E) lone pair LP characterizing TlI, PbII, BiIII, and PoIV (M∗) in fluorides and oxides as well as in mixed valence compounds is examined within a coherent crystal chemistry and ab initio visualizations and analyses. Besides square planar environments, large coverage of tetrahedral, triangular bipyramidal, square pyramidal, octahedral and hexahedral geometries is presented and addressed. In our formal image ns2 lone pair is considered as a free electron doublet concentrated in a centroïd, called Ec, which generates around it an electronic cloud, detected in the crystal network as an empty volume, attached to M∗, opposite to bonding coordination and where physical condensation (pressure) can eventually distort but not compress. Finally the lone pair E is defined by a sphere of influence found to occupy a volume close to oxygen or fluorine anions. Only crystal network by its architecture more or less dense can really modify M∗–E eventually to m*–E = 0 coalescence of the center of volume of influence E with the cation center transforming M∗ in a large cation [M∗E]n+ comparable to K+, Cs+ or Ba2+. The crystal chemistry analyses combined with electron localization function ELF from density functional theory DFT based calculations allow defining E volume and plasticity, M∗–E directions and distances of the different extended case studies. Original features highlighted with ELF and electronic densities of states and chemical bonding plots characterize the mixed valence compounds containing both LP-bearing (ex. TlI, PbII, BiIII) and non LP bearing (TlIII, PbIV, BiV) ions.