Dielectric screening and self-consistent crystal fields

The construction of self-consistent Hartree crystal potentials is discussed in terms of screening of "external" ionic potentials by a nearly-free valence-electron gas. An essential preliminary is the introduction of a repulsive potential which replaces the requirement of orthogonality of one-electron valence and core wave functions. Because of the excellent cancellation of core and repulsive potentials, the resulting effective ionic potential Veff is weak. Using an approximate dielectric constant to screen Veff, we obtain a prescription for estimating a priori self-consistent Hartree potentials in metals and semiconductors. The dielectric screening can be extended to include exchange and correlation. Comparison with detailed band calculations for diamond, silicon, and cubic boron nitride reveals the accuracy and limitations of the method. The screening of the longest wavelength Fourier component of Veff is predicted quite satisfactorily. By studying bonding and charge transfer effects we find that nonlinear local field corrections (crystal hybridization) are important in screening of shorter wavelength Fourier components of Veff.