Fig. 7: 2D map classifying chemical bonding in solids.

The map is spanned by the renormalized electron transfer (ET) obtained after division through the formal oxidation state (x-axis) and the sharing of electrons (ES) between adjacent atoms (y-axis). Different colors indicate different material properties and have been related to different chemical bonding mechanisms. Ionic bonding (black-shaded area) is characterized by a significant electron transfer with an ET value larger than 0.6. In covalent solids (red-shaded area), on the contrary, there is only modest ET between atoms, but up to one electron pair (i.e., two electrons) defined by Lewis⁸⁴ are shared between neighboring atoms. Metallic bonding (blue-shaded area) is recognized by the delocalization of electrons over several neighbors and, thereby, is characterized via a small or vanishing ET and the sharing of far less than one electron between atoms. MVB materials share about one electron between adjacent neighbors and are characterized via small or moderate ET. Therefore, they are all located in the well-defined (green-shaded) region between covalent and metallic bonding. The red−black solid line characterizes the transition from ideal covalent bonds to perfect ionic bonds. The green dashed line denotes MVB solids with the perfect octahedral arrangement, while all distorted octahedrally coordinated structures are situated above it, characterized by a larger number of ES. Figure replotted and updated upon data exhibited in refs. ^29,37. Here, β-As₂Te₃, Sb₂Te₃, and Bi₂Te₃ are marked with yellow circles; GeTe and SnTe are marked in light green circles; ZnTe and CdTe are tagged with light purple circles. This map can be employed to guide the rational design of high-efficiency Te thermoelectric composites.