The basic ideas of MD in general and the adopted techniques as implemented in \textsc{posic} in particular are outlined in section~\ref{section:md} while the functional form and derivative of the employed classical potential is presented in appendix~\ref{app:d_tersoff}.
An overview of the most important tools within the MD package is given in appendix~\ref{app:code}.
Although classical potentials are often most successful and at the same time computationally efficient in calculating some physical properties of a particular system, not all of its properties might be described correctly due to the lack of quantum-mechanical effects.
-Thus, in order to obtain more accurate results quantum-mechanical calculations from first principles based on density functional theory (DFT) were performed.
+Thus, in order to obtain more accurate results, quantum-mechanical calculations from first principles based on density functional theory (DFT) were performed.
The Vienna {\em ab initio} simulation package (\textsc{vasp})~\cite{kresse96} is used for this purpose.
The relevant basics of DFT are described in section~\ref{section:dft} while an overview of utilities mainly used to create input or parse output data of \textsc{vasp} is given in appendix~\ref{app:code}.
The gain in accuracy achieved by this method, however, is accompanied by an increase in computational effort constraining the simulated system to be much smaller in size.
\end{quotation}
\noindent
-Pierre Simon de Laplace phrased this vision in terms of a controlling, omniscient instance --- the {\em Laplace demon} --- which would be able to look into the future as well as into the past due to the deterministic nature of processes, governed by the solution of differential equations.
-Although Laplace's vision is nowadays corrected by chaos theory and quantum mechanics, it expresses two main features of classical mechanics, the determinism of processes and time reversibility of the fundamental equations.
+Pierre Simon de Laplace phrased this vision in terms of a controlling, omniscient instance --- the {\em Laplace demon} --- which would be able to look into the future as well as into the past due to the deterministic nature of processes, which is governed by the solution of differential equations.
+Although Laplace's vision is nowadays corrected by chaos theory and quantum mechanics, it expresses two main features of classical mechanics, i.e.\ the determinism of processes and time reversibility of the fundamental equations.
This understanding may be regarded as the basic principle of molecular dynamics, considering an isolated system of particles, the behavior of which is fully determined by the solution of the classical equations of motion.
\subsection{Introduction to molecular dynamics simulations}
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 increase in computational efficiency for the evaluation of forces and energy based on the short-range potential.
+Due to the covalent character, Tersoff restricted the interaction to nearest neighbor atoms accompanied by an increase 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}.
The basic idea is that, in real systems, the bond order, i.e.\ the strength of the bond, depends upon the local environment~\cite{abell85}.
Atoms with many neighbors form weaker bonds than atoms with only a few neighbors.
This is illustrated in Fig.~\ref{img:tersoff_angle}.
\begin{figure}[t]
\begin{center}
-\includegraphics[width=8cm]{tersoff_angle.eps}
+\includegraphics[width=6cm]{tersoff_angle.eps}
\end{center}
\caption{Angle between bonds of atoms $i,j$ and $i,k$.}
\label{img:tersoff_angle}
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