Electrons

Abstract

Now turning to Equation (2.27) concerning the electrons:

$$\{ \sum\limits_i {\frac{{P_i^2}}{{2{m_o}}}} + \sum\limits_{i,j} {\frac{{{e^2}}}{{4\pi {e_0}{\text{|}}{{\text{r}}_{\text{i}}}{\text{ - }}{{\text{r}}_{\text{j}}}{\text{|}}}}} + {U_e}({r_i})\} {\psi _e} = {E_e}{\psi _e}$$

(3.1)

where the first term represents the kinetic energy, the second the mutual Coulombic repulsion between the electrons, and the last the potential energy in the electric field from the ions which, to a first approximation, is given by Equation (2.22) with r ⁰_Ib , the equilibrium position of the nucleus, instead of r_Ib . Part of the nuclear charge, Z _b , is screened off by the deeper lying core electrons. The periodicity of the crystal allows us, in analogy with the previous chapter, to write

$${U_e}({r_i}) = \sum\limits_{I,b} {{U_{e,Ib}}({r_i} - r_{Ib}^0)} $$

(3.2)