Covalent Bond in Crystals. I. Elements of a Structural Theory

An a posteriori theory is developed for the structural energy of covalent crystals. The microscopic theory is based on ionic pseudopotentials and valence dielectric screening. The theory explains the difference between empirical pseudopotential form factors derived from the optical spectra of semiconductors and the metallic form factors calculated from free-ion term values by Animalu and Heine. A byproduct of the theory, which utilizes Penn's model isotropic semiconductor dielectric function, is a relation between the covalent bonding charge and the macroscopic dielectric constant. In self-consistent form the theory is an example of the "bootstrap" approach, applied here to treat the effect of covalent bonding on the ground-state energy of the valence electron gas. It is argued that the axiomatic character of the covalent theory is to be expected on symmetry grounds, and it is shown that the theory is superior to a nonlinear multiple-scattering theory based on the free-electron dielectric function. The extension of the theory to III---V and II---VI semiconductors is described briefly. The theory may be used to calculate elastic and macroscopic dielectric properties of covalent crystals starting only from ionic pseudopotential form factors.