+In quantum-mechanical modeling the problem of describing the many-body problem, i.e. a system of a large amount of interacting particles, is manifested in the high-dimensional Schr\"odinger equation for the wave function $\Psi({\vec{R}},{\vec{r}})$ that depends on the coordinates of all nuclei and electrons.
+The Schr\"odinger equation contains the kinetic energy of the ions and electrons as well as the electron-ion, ion-ion and electron-electron interaction.
+This cannot be solved exactly and there are several layers of approximations to reduce the number of parameters.
+The key point in density functional theory (DFT) is to recast the problem to a description using the charge density $n(\vec{r})$ that depends on only three spatial coordinates instead of the many-body wave function.
+Formally DFT can be regarded as an exactification of both, the Thomas Fermi and Hartree theory.
+In the following sections the basic idea of DFT will be outlined.
+
+\subsection{Born-Oppenheimer approximation}