The discussion of dynamics at interfaces is based on the motion of ion cores and electronic excitations that are mostly optically driven. Hence, the electronic structure is of fundamental importance here. In solids such as molecular or ionic crystals, the valence electron distribution is not considerably distorted from the respective isolated atoms, ions, or molecules. Hence, their cohesion is entirely given by the classical potential energy of negligibly deformed electron distributions of bare particles, and van der Waals or Coulomb interactions are responsible for the formation of solid materials. This ceases to be so in metals and covalent crystals because the valence electron distribution plays the decisive role in bonding the constituents to a solid. In turn, the valence electron distribution can be considerably modified from the isolated atom or ion. A general description of solids must, therefore, consider the electronic structure in the first place. Furthermore, the dynamical processes discussed in this book are mostly optically excited or electron mediated.
This chapter introduces the basic concepts widely used in the description of the electronic structure in solid materials. In Section 1.1, we present the description of the nearly free electron approximation that is motivated by optical excitations of a solid following the Drude model.We introduce the Fermi sphere and the dispersion of electronic bands in momentum space. In Section 1.2, the influence of the periodic potential in a crystal is considered, which leads to the description of the electronic band structure by Blochs theory for delocalized states. There is a considerable variety of materials that is not described by band theory, which originates from electron– electron interaction. In Section 1.3, we introduce Mott insulators that manifest deviations from the band picture. In Section 1.4, we introduce established concepts to describe the electronic structure of materials with strong electron correlations and give examples..
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