ABSTRACT
Density functional theory (DFT) has extended not only to crystalline solids but also to glasses and minerals such as zeolites, polymers, DNAs, ice, and chemical solutions. Our main concern is, of course, solids. In this chapter, we will introduce electrons into a vast terrain of varying potentials in a solid and try to identify the consequences. At the end, we will have a new formulation of the KS equations in terms of Fourier coefficients and witness the formation of band structures, a very important property of solids. To reach that end, however, two obvious issues have to be resolved: the number of electrons becomes infinite, and so does the number of atoms in solids.
