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 a numerical point of view. In this paper, we consider simplified models with two essential time scales and describe how these two time scales interact. 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 results on the averaging over fast degrees of motion will also shed new light on the appropriate implementation of multiple-time-stepping algorithms for CMD and QCMD.