Multiple Time Scales in Classical and Quantum Classical Molecular Dynamics

The existence of multiple time scales in molecular dynamics poses interesting and challenging questions from an analytical as well as from a numerical point of view In this paper we consider simpli ed models with two essential time scales and describe how these two time scales inter act The discussion focuses on classical molecular dynamics CMD with fast bond stretching and bending modes and the so called quantum classical molecular dynamics QCMD model where the quantum part provides the highly oscillatory solution components The analytic res ults on the averaging over fast degrees of motion will also shed new light on the appropriate implementation of multiple time stepping MTS algorithms for CMD and QCMD