\section{Denstiy functional theory}
\label{section:dft}
-In quantum-mechanical modeling the problem of describing a many-body problem is manifested in the high-dimensional Schr\"odinger equation for the wave function $\Psi({\vec{R}},{\vec{r}})$ that depends on the coordinates of the nuclei and electrons.
+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.
-In density functional theory (DFT) the problem is recasted to the charge density $n(\vec{r})$ instead of using the description by a wave function.
+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.
-
-Since {\textsc vasp} \cite{kresse96} is used in this work, theory and implementation of sophisticated algorithms of DFT codes is not subject of this work.
-Thus, the content of the following sections is restricted to the very basic idea of DFT.
+In the following sections the basic idea of DFT will be outlined.
\subsection{Born-Oppenheimer approximation}
-The first approximation ...
+The first approximation employed
\subsection{Hohenberg-Kohn theorem}
projects / lectures / latex.git / blobdiff