of a system of hard spheres.The general method,however,was presented two years later" In this early simulation.which was run an an IBM-704,up to 500 particles could be simu- lated,for which 500 collisions per hour could be calculated.Taking into account 200000 collisions for a production run,these simulations lasted for more than two weeks.The propagation of hard spheres in a simulation is determined by the collision events between two particles.Therefore,the propagation is not based on an integration of the equations of motion.but rather the calculation of the time of the next collision.which results in a variable time step in the calculations The first MD simulation which was applied to atoms interacting via a continuous po- tential was performed by A.Rahman in 1964.In this case,a model system for Argon was simulated and not only binary collisions were taken into account but the interactions were modeled by a Lennard-Jones potential and the equations of motion were integrated with a finite difference scheme.This work may be considered as seminal for dynamical calcula- tions.It was the first work where an exact method (within numerical precision)was used to calculate dynamical quantities like autocorrelation functions and transport coefficients like the diffusion coefficient for a realistic system.Also more involved topics like the dy- namic van Hove function and non-Gaussian corrections to diffusion were evaluated.The calculations were performed for 864 particles on a CDC 3600,where the propagation of all particles for one time step took 45 s.The calculation of 50000 timesteps then took more than three weeks!a With the development of faster and bigger massively parallel architectures the accessi- ble time and length scales are increasing.In the case of classical MD simulations it was demonstrated by J.Roth in 1999 on the CRAY T3E-1200 in Juilich that it is possible to simulate more than 5 x 109 particles,corresponding to a length scale of several 1000 A. This was possible with the highly memory optimised MD program IMD5.2,which used the 512 nodes with 256 MB memory each,quite efficiently.However,the limits of such a demonstration became rather obvious,since for a usual production run of 10000 time steps a simulation time of a quarter of a year would be required(given that the whole machine is dedicated to one user).In another demonstration run Y.Duan and P.A.Kollman extended the time scale of an all atom MD simulation to 1 us,where they simulated the folding process of the subdomain HP-36 from the villin headpiece.1.The protein was modelled with a 596 interaction site model dissolved in a system of 3000 water molecules.Using a timestep of integration of 2 x 10-15s,the program was run for 5 x 108 steps.In order to perform this type of calculation,it was necessary to run the program several months on a CRAY T3D and CRAY T3E with 256 processors.It is clear that such kind of simulation is exceptional due to the large amount of computer resources needed,but is nonetheless a kind of milestone pointing to future simulation practices. Classical molecular dynamics methods are nowadays applied to a huge class of prob- lems,e.g.properties of liquids,defects in solids,fracture,surface properties,friction, molecular clusters,polyelectrolytes and biomolecules.Due to the large area of applica- bility,simulation codes for molecular dynamics were developed by many groups.On the internet homepage of the Collaborative Computational Project No.5(CCP5)?a lot of com- puter codes are assembled for condensed phase dynamics.During the last years several programs were designed for parallel computers.Among them,which are partly avail- "On a standard PC this calculation may be done within one hour nowadays! 214of a system of hard spheres. The general method, however, was presented two years later4 . In this early simulation, which was run an an IBM-704, up to 500 particles could be simu￾lated, for which 500 collisions per hour could be calculated. Taking into account 200000 collisions for a production run, these simulations lasted for more than two weeks. The propagation of hard spheres in a simulation is determined by the collision events between two particles. Therefore, the propagation is not based on an integration of the equations of motion, but rather the calculation of the time of the next collision, which results in a variable time step in the calculations. The first MD simulation which was applied to atoms interacting via a continuous po￾tential was performed by A. Rahman in 1964. In this case, a model system for Argon was simulated and not only binary collisions were taken into account but the interactions were modeled by a Lennard-Jones potential and the equations of motion were integrated with a finite difference scheme. This work may be considered as seminal for dynamical calcula￾tions. It was the first work where an exact method (within numerical precision) was used to calculate dynamical quantities like autocorrelation functions and transport coefficients like the diffusion coefficient for a realistic system. Also more involved topics like the dy￾namic van Hove function and non-Gaussian corrections to diffusion were evaluated. The calculations were performed for 864 particles on a CDC 3600, where the propagation of all particles for one time step took ≈ 45 s. The calculation of 50000 timesteps then took more than three weeks! a With the development of faster and bigger massively parallel architectures the accessi￾ble time and length scales are increasing. In the case of classical MD simulations it was demonstrated by J. Roth in 1999 on the CRAY T3E-1200 in Julich ¨ that it is possible to simulate more than 5 × 109 particles, corresponding to a length scale of several 1000 A. ˚ This was possible with the highly memory optimised MD program IMD5, 2 , which used the 512 nodes with 256 MB memory each, quite efficiently. However, the limits of such a demonstration became rather obvious, since for a usual production run of 10000 time steps a simulation time of a quarter of a year would be required (given that the whole machine is dedicated to one user). In another demonstration run Y. Duan and P. A. Kollman extended the time scale of an all atom MD simulation to 1 µs, where they simulated the folding process of the subdomain HP-36 from the villin headpiece6, 1 . The protein was modelled with a 596 interaction site model dissolved in a system of 3000 water molecules. Using a timestep of integration of 2 × 10−15s, the program was run for 5 × 108 steps. In order to perform this type of calculation, it was necessary to run the program several months on a CRAY T3D and CRAY T3E with 256 processors. It is clear that such kind of simulation is exceptional due to the large amount of computer resources needed, but is nonetheless a kind of milestone pointing to future simulation practices. Classical molecular dynamics methods are nowadays applied to a huge class of prob￾lems, e.g. properties of liquids, defects in solids, fracture, surface properties, friction, molecular clusters, polyelectrolytes and biomolecules. Due to the large area of applica￾bility, simulation codes for molecular dynamics were developed by many groups. On the internet homepage of the Collaborative Computational Project No.5 (CCP5)7 a lot of com￾puter codes are assembled for condensed phase dynamics. During the last years several programs were designed for parallel computers. Among them, which are partly avail￾aOn a standard PC this calculation may be done within one hour nowadays! 214