+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.
+This understanding was one of the first ideas for doing molecular dynamics simulations, considering an isolated system of particles, the behaviour of which is fully determined by the solution of the classical equations of motion.
+
+\subsection{Introduction to molecular dynamics simulations}
+
+Basically, molecular dynamics (MD) simulation is a technique to compute a system of particles, referred to as molecules, with their positions, volocities and forces among each other evolving in time.
+The MD method was first introduced by Alder and Wainwright in 1957 \cite{alder1,alder2} to study the interactions of hard spheres.
+The basis of the approach are Newton's equations of motion to describe classicaly the many-body system.
+MD simulation is the numerical way of solving the $N$-body problem which cannot be solved analytically ($N>3$).
+Quantum mechanical effects are taken into account by an analytical interaction potential between the nuclei.
+
+By MD simulation techniques a complete description of the system in the sense of classical mechanics on the microscopic level is obtained.
+This microscopic information has to be translated to macroscopic observables by means of statistical mechanics.
+
+The basic idea is to integrate Newton's equations numerically.
+A system of $N$ particles of masses $m_i$ ($i=1,\ldots,N$) at positions ${\bf r}_i$ and velocities $\dot{{\bf r}}_i$ is given by
+\begin{equation}
+m_i \frac{d^2}{dt^2} {\bf r}_i = {\bf F}_i \, \textrm{.}
+\end{equation}
+The forces ${\bf F}_i$ are obtained from the potential energy $U(\{{\bf r}\})$:
+\begin{equation}
+{\bf F}_i = - \nabla_{{\bf r}_i} U({\{\bf r}\}) \, \textrm{.}
+\end{equation}
+Given the initial conditions ${\bf r}_i(t_0)$ and $\dot{{\bf r}}_i(t_0)$ the equations can be integrated by a certain integration algorithm.
+The solution of these equations provides the complete information of a system evolving in time.
+
+The following chapters cover the tools of the trade necessary for the MD simulation technique.
+Three ingredients are required for an MD simulation:
+\begin{enumerate}
+\item A model for the interaction between system constituents is needed.
+ Interaction potentials and their accuracy for describing certain systems of elements will be outlined in chapter \ref{subsection:interact_pot}.
+\item An integrator is needed, which propagtes the particle positions and velocities from time $t$ to $t+\delta t$, realised by a finite difference scheme which moves trajectories discretely in time.
+ In chapter \ref{subsection:integrate_algo} a detailed overview of the available integration algorithms is given, including their advantages and disadvantages.
+\item A statistical ensemble has to be chosen, which allows certain thermodynamic quantities to be controlled or to stay constant.
+ This is discussed in chapter \ref{subsection:statistical_ensembles}
+\end{enumerate}