\frac{1}{2} + \frac{1}{2} \cos \Big[ \pi (r_{ij} - R_{ij})/(S_{ij} - R_{ij}) \Big], & R_{ij} < r_{ij} < S_{ij} \\
0, & r_{ij} > S_{ij}
\end{array} \right.
+\label{eq:basics:fc}
\end{equation}
The function $b_{ij}$ represents a measure of the bond order, monotonically decreasing with the coordination of atoms $i$ and $j$.
\section{Denstiy functional theory}
\label{section:dft}
+\subsection{Hohenberg-Kohn theorem}
+
\subsection{Born-Oppenheimer (adiabatic) approximation}
-\subsection{Hohenberg-Kohn theorem}
+\subsection{Effective potential}
-\subsection{Exchange correlation}
+\subsection{Kohn-Sham system}
+
+\subsection{Approximations for exchange and correlation}
\subsection{Pseudopotentials}
+\section{Modeling of defects}
+\label{section:basics:defects}
+
+\section{Migration paths and diffusion barriers}
+\label{section:basics:migration}
+