Preface VII tions.In the paper by BERNE,the r-RESPA multiple timestepping (MTS) method is described and applied in the context of Hybrid Monte Carlo meth- ods for sampling techniques such as J-Walking and S-Walking with the aim of a more rapid exploration of rugged energy landscapes.In the next pa- per,SKEEL IZAGUIRRE advocate the use of MTS in a mollified impulse method to overcome resonance instabilities that are inherent in the standard impulse method.Yet another MTS-like approach can be found in the paper by JANEZIC MERZEL,who suggest to split off a harmonic high frequency part of the motion and integrate that analytically.Finally,LEIMKUHLER demon- strates the stability of the recently proposed explicit symplectic integrators (with fixed timestep)in the numerical integration of rigid body motion over long time spans. The fourth chapter,on Quantum-Classical Simulations,deals with the integration of molecular systems,parts of which are modelled in terms of quantum mechanics,where a full quantum mechanical treatment would be impossible.In the first paper,JUNGWIRTH GERBER treat clusters of inert gases by calculating effective single-mode potentials from classical molecular dynamics which are then used in quantum calculations.An extension be- yond the separability approximation is also suggested.The quality of the quantum-classical molecular dynamics (QCMD)model compared with full quantum mechanics (QM)and the Born-Oppenheimer approximation(BO) is considered by SCHUTTE BORNEMANN in terms of approximation theory. They also suggest an extended QCMD model that may open new perspectives in the case of energy level crossings,where BO is known to break down.Re- cently developed structure-preserving numerical integrators for this QCMD model are given by NETTESHEIM SCHUTTE.Symplectic multiple timestep- ping variants of these integrators are derived in the paper by NETTESHEIM& REICH.An alternative scheme is presented by HOCHBRUCK LUBICH,who suggest that a type of mollified exponential integrators are especially well- suited for highly oscillatory systems such as QCMD and the Car-Parrinello approximation.The latter approximation is also used in the paper by MEIER ET AL.on ab-initio MD simulations of catalysis in a polymerization process. In the last paper of this chapter,IZVEKoV describes an algorithm for the calculation of absorption spectra based on exciton-phonon interactions. The fifth and final chapter,on Parallel Force Field Evaluation,takes account of the fact that the bulk of CPU time spent in MD simulations is required for evaluation of the force field.In the first paper,BoARD and his coworkers present a comparison of the performance of various parallel implementations of Ewald and multipole summations together with recommendations for their application.The second paper,by PHILLIPS ET AL.,addresses the special problems associated with the design of parallel MD programs.Conflicting issues that shape the design of such codes are identified and the use of features such as multiple threads and message-driven cxecution is described.The final paper,by OKUNBOR MURTY,compares three force decomposition techniques (the checkerboard partitioning method