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Extra info for Electronic Structure of Materials
Disordered systems do not have translational symmetry and as a result, Bloch’s theorem is not applicable. Therefore, all the above-mentioned methods cannot be used to obtain the electronic structure of disordered alloys. Substitutional disordered alloys are the simplest disordered systems that have only compositional disorder and there is an underlying periodic lattice. The simplest way to handle these systems is to use some approximation similar to the mean-field approximation. Essentially, one replaces a disordered alloy by an ordered alloy of effective atoms.
15 is a complicated equation for many-electron wave function ψ, which is a function of all electronic coordinates (position as well as 19 Quantum Description of Materials spin). 16) where y i (r , s ) denotes the wave function of a single electron i with spin σ 2 and is also called orbital. It has the usual interpretation that y i d 3r gives the probability of finding the electron with spin σ in volume element d3r. In this section, we shall be neglecting the spin of the electrons as it plays no role in the Hartree method.
2, which first used electronic density as the basic variable. We shall see that although the Thomas–Fermi theory is a very approximate theory, it contained the seeds for the development of the DFT (for definition of functional, see Appendix D). 3, we shall discuss an application of the Thomas–Fermi theory to the problem of screening. 4, we shall prove Hohenberg–Kohn theorems, which laid down the foundation of the DFT. 6, which has proved most useful in calculating the electronic structure of solids.