Pseudopotentials in Action

Summary

In this chapter we shall illustrate how the plane wave/pseudopotential degenerate case can be used to produce the band structure E_n(k) from the unperturbed free-electron relation ${E_{k}^{(o)}} = {\hbar^2} {k^2}/2m$. We shall present first the simplest 1D case, and then we shall examine a model 2D case that incorporates the basic concepts and the main graphical constructions without burdening, at this stage, the presentations with 3D plots. The latter will be examined in connection with real 3D solids in the next chapter after the readers become familiar with the general features of the plane wave/pseudopotential approach. The latter also provides corrections to the ground state energy and to the electron-phonon interactions; it also allows realistic calculations of the phononic dispersion relations ω_qs at least for simple metals.