Thomas-Fermi-Dirac method

Fia. 2-19.—Curves representing values of electron energies, as a function of atomic number. These curves were obtained by approximate solution of the wave equation by the Thomas-Fermi-Dirac method. 

The so-called Hartree-Fock-Slater method is much more widely utilized, and is a hybrid of the Hartree and Thomas-Fermi-Dirac methods. In this method the direct part of the potential is calculated using the Hartree-Fock approach, whereas the exchange part is approximated by some statistical expression of the model of free electrons. The Slater potential is given by ... 

Historically16 it is worthy of note that if one resorts in equation (51) to the TF approximation (18) for tr, then the Euler equation of the Thomas-Fermi-Dirac method results. We shall not go into the solutions of the Thomas-Fermi-Dirac equation in this review, though there has been recent interest in this area. Suffice it to say that in the full form of the Euler equation (51), we are working at the customary Hartree-Fock-Slater level. However, we shall content ourselves, until we come to Section 17 below, with understanding in a more intuitive, but inevitably less detailed, way how the corrections to the TF energy in equation (48) arise. 

Levy et al. [63] examine adiabatic scaling in the Thomas-Fermi-Dirac method set out earlier in this chapter, and also propose a formula for U c in Eq. (52). These two aspects will be taken in turn below. 

The exchange part in a uniform electron gas is nothing else that the exchange functional that we met in the Thomas-Fermi-Dirac method (2.27). Thus, the exchange energy Ex in this LDA approximation is also given by ... 

TFD ThomaS Fermi-Dirac method, a c+art-kHral treafmont nf plw trnn rifin itv ... 

---