Electron state calculations

Abstract

In Chapter 3 we introduced the one-particle state representation of ∣χ _n 〉 and established the use of the H.F.- and other representations for our problems. In this chapter we shall discuss appropriate procedures for calculating them. It is clear that the state calculations for mosaicblocks with approximately 10¹⁵ electrons cannot be performed in the same way as state calculations for atoms with, for instance, 10² electrons. Thus, we have to develop appropriate methods which are adapted to the problem under consideration and which are more powerful than the usual atomic or molecular state calculation techniques. Generally, the calculations can be divided into two parts, namely the calculation of ∣χ _n 〉 with the full dependence on the lattice coordinates (dynamical electron-lattice coupling) and the calculation of ∣χ _n 〉 only for the lattice equilibrium positions (static electron-lattice coupling). The procedure is performed in such a way that the dynamical calculations depend on the successful solution of the static calculations.