10000 HD ● 1000 100 BD 10 MD QS fs ps ns us ms time Figure 1.Schematic comparison of time-and length-scales,accessible to different types of simulation techniques(quantum simulations(QM),molecular dynamics (MD),Brow- nian dynamics (BD)and hydrodynamics/fluid dynamics(HD)).The black dots mark the longest(≈1s)and the biggest(N>5×109,L≈0.4 m molecular dynamics simulations by Duan Kollman'and Roth2 respectively.) scales are of order of A and ps.Classical molecular dynamics approximates electronic distributions in a rather coarse-grained fashion by putting either fixed partial charges on interaction sites or by adding an approximate model for polarization effects.In both cases, the time scale of the system is not dominated by the motion of electrons,but the time of intermolecular collision events.rotational motions or intramolecular vibrations,which are orders of magnitude slower than those of electron motions.Consequently,the time step of integration is larger and trajectory lengths are of order ns and accessible lengths of order 10-100 A.If one considers tracer particles in a solvent medium,where one is not inter- ested in a detailed description of the solvent,one can apply Brownian dynamics,where the effect of the solvent is hidden in average quantities.Since collision times between tracer particles is very long,one may apply larger timesteps.Furthermore,since the solvent is not simulated explicitly,the lengthscales may be increased considerably.Finally,if one is in- terested not in a microscopic picture of the simulated system but in macroscopic quantities the concepts of hydrodynamics may be applied,where the system properties are hidden in effective numbers,e.g.density,viscosity,sound velocity. It is clear that the performance of particle dynamics simulations strongly depends on the computer facilities at hand.The first studies using MD simulation techniques were performed in 1957 by B.J.Alder and T.E.Wainright3 who simulated the phase transition 213fs ps ns µs ms 1 10 100 1000 10000 QS MD BD QS MD BD HD length [ Å] time Figure 1. Schematic comparison of time- and length-scales, accessible to different types of simulation techniques (quantum simulations (QM), molecular dynamics (MD), Brow￾nian dynamics (BD) and hydrodynamics/fluid dynamics (HD)). The black dots mark the longest (≈ 1 µs) and the biggest (N > 5 × 109 , L ≈ 0.4µm molecular dynamics simulations by Duan & Kollman1 and Roth2 respectively.) scales are of order of A˚ and ps. Classical molecular dynamics approximates electronic distributions in a rather coarse-grained fashion by putting either fixed partial charges on interaction sites or by adding an approximate model for polarization effects. In both cases, the time scale of the system is not dominated by the motion of electrons, but the time of intermolecular collision events, rotational motions or intramolecular vibrations, which are orders of magnitude slower than those of electron motions. Consequently, the time step of integration is larger and trajectory lengths are of order ns and accessible lengths of order 10 − 100 A. ˚ If one considers tracer particles in a solvent medium, where one is not inter￾ested in a detailed description of the solvent, one can apply Brownian dynamics, where the effect of the solvent is hidden in average quantities. Since collision times between tracer particles is very long, one may apply larger timesteps. Furthermore,since the solvent is not simulated explicitly, the lengthscales may be increased considerably. Finally, if one is in￾terested not in a microscopic picture of the simulated system but in macroscopic quantities, the concepts of hydrodynamics may be applied, where the system properties are hidden in effective numbers, e.g. density, viscosity, sound velocity. It is clear that the performance of particle dynamics simulations strongly depends on the computer facilities at hand. The first studies using MD simulation techniques were performed in 1957 by B. J. Alder and T. E. Wainright3 who simulated the phase transition 213