-%\subsubsection{The Lennard-Jones potential}
-%
-%The L-J potential is a realistic two body pair potential and is of the form
-%\begin{equation}
-%U^{LJ}(r) = 4 \epsilon \Big[ \Big( \frac{\sigma}{r} \Big)^{12} - \Big( \frac{\sigma}{r} \Big)^6 \Big] \, \textrm{,}
-%\label{eq:lj-p}
-%\end{equation}
-%where $r$ denotes the distance between the two atoms.
-%
-%The attractive tail for large separations $(\sim r^{-6})$ is essentially due to correlations between electron clouds surrounding the atoms. The attractive part is also known as {\em van der Waals} or {\em London} interaction.
-%It can be derived classically by considering how two charged spheres induce dipol-dipol interactions into each other, or by considering the interaction between two oscillators in a quantum mechanical way.
-%
-%The repulsive term $(\sim r^{-12})$ captures the non-bonded overlap of the electron clouds.
-%It does not have a true physical motivation, other than the exponent being larger than $6$ to get a steep rising repulsive potential wall at short distances.
-%Chosing $12$ as the exponent of the repulsive term it is just the square of the attractive term which makes the potential evaluable in a very efficient way.
-%
-%The constants $\epsilon$ and $\sigma$ are usually determined by fitting to experimental data.
-%$\epsilon$ accounts to the depth of the potential well, where $\sigma$ is regarded as the radius of the particle, also known as the van der Waals radius.
-%
-%Writing down the derivative of the Lennard-Jones potential in respect to $x_i$ (the $i$th component of the distance vector ${\bf r}$)
-%\begin{equation}
-%\frac{\partial}{\partial x_i} U^{LJ}(r) = 4 \epsilon x_i \Big( -12 \frac{\sigma^{12}}{r^{14}} + 6 \frac{\sigma^6}{r^8} \Big)
-%\label{eq:lj-d}
-%\end{equation}
-%one can easily identify $\sigma$ by the equilibrium distance of the atoms $r_e=\sqrt[6]{2} \sigma$.
-%Applying the equilibrium distance into \eqref{eq:lj-p} $\epsilon$ turns out to be the negative well depth.
-%The $i$th component of the force is given by
-%\begin{equation}
-%F_i = - \frac{\partial}{\partial x_i} U^{LJ}(r) \, \textrm{.}
-%\label{eq:lj-f}
-%\end{equation}
-%
-%\subsubsection{The Stillinger Weber potential}
-%
-%The Stillinger Weber potential \cite{stillinger_weber} \ldots
-%
-%\begin{equation}
-%U = \sum_{i,j} U_2({\bf r}_i,{\bf r}_j) + \sum_{i,j,k} U_3({\bf r}_i,{\bf r}_j,{\bf r}_k)
-%\end{equation}
-%
-%\begin{equation}
-%U_2(r_{ij}) = \left\{
-% \begin{array}{ll}
-% \epsilon A \Big( B (r_{ij} / \sigma)^{-p} - 1\Big) \exp \Big[ (r_{ij} / \sigma - 1)^{-1} \Big] & r_{ij} < a \sigma \\
-% 0 & r_{ij} \ge a \sigma
-% \end{array} \right.
-%\end{equation}
-%
-%\begin{equation}
-%U_3({\bf r}_i,{\bf r}_j,{\bf r}_k) =
-%\epsilon \Big[ h(r_{ij},r_{ik},\theta_{jik}) + h(r_{ji},r_{jk},\theta_{ijk}) + h(r_{ki},r_{kj},\theta_{ikj}) \Big]
-%\end{equation}
-%
-%\begin{equation}
-%h(r_{ij},r_{ik},\theta_{jik}) =
-%\lambda \exp \Big[ \gamma (r_{ij}/\sigma -a)^{-1} + \gamma (r_{ik}/\sigma - a)^{-1} \Big] \Big( \cos \theta_{jik} + \frac{1}{3} \Big)^2
-%\end{equation}
-
-\subsubsection{The Tersoff potential}
-
-Tersoff proposed an empirical interatomic potential for covalent systems.
-The Tersoff potential explicitly incorporates the dependence of bond order on local envirenments, permitting an improved description of covalent materials.
-Tersoff applied the potential to silicon \cite{tersoff_si1,tersoff_si2,tersoff_si3}, carbon \cite{tersoff_c} and also to multicomponent systems like $SiC$ \cite{tersoff_m}.
+\subsubsection{The Tersoff bond order potential}
+
+Tersoff proposed an empirical interatomic potential for covalent systems \cite{tersoff_si1,tersoff_si2}.
+The Tersoff potential explicitly incorporates the dependence of bond order on local environments, permitting an improved description of covalent materials.
+Due to the covalent character Tersoff restricted the interaction to nearest neighbor atoms accompanied by an increases in computational efficiency for the evaluation of forces and energy based on the short-range potential.
+Tersoff applied the potential to silicon \cite{tersoff_si1,tersoff_si2,tersoff_si3}, carbon \cite{tersoff_c} and also to multicomponent systems like silicon carbide \cite{tersoff_m}.
+...