Bonding and crystal structures of average-valence- compounds: A spectroscopic approach

Abstract

A number of aspects of the Phillips-Van Vechten spectroscopic approach to covalent bonding are applied to average-valence- compounds. An average energy gap $E_g$ can be defined which is reasonably close to the energy of the single large peak that dominates the optical spectra of these compounds. The bond charge of As estimated from the dielectric constant as suggested by Phillips compares well with that determined from band-structure calculations. Covalent radii are determined and with these the Phillips electronegativities $C$ and ionicities $F_i$ are also found. Heats of formation are related to ionicities in the manner of Phillips and Van Vechten; however, their metallization factor is found not to be important here. A critical ionicity $f_i^c=0.62\mathrm{}\pm 0.03$ appears to be the limit above which the rhombohedral $\alpha -\mathrm{GeTe}$ and $\alpha -\mathrm{As}$ structures do not exist under any conditions. The stability of the orthorhombic black P, SnS, and TlI structures relative to the cubic or rhombohedral ones is not yet understood; however, trends in the orthorhombic structures with ionicity are evident. Complications of metallic contributions to the bonding are considered. The relation of the Phillips approach to pseudopotential theory is reviewed. The expressions for the gap $E_g$ in second-order pertubation theory show differences for average valences of and . An examination of these differences suggests one more reason for why the group-V semimetals occur in the rhombohedrally distorted simple-cubic structure rather than the true simple-cubic or diamond structures. At the same time, the critical ionicity $f_i^c$ of compounds seems not surprisingly to have the same underlying explanation as the critical ionicity which separates tetrahedral from octahedral compounds.