Multiple timescale molecular dynamics with very large time steps: avoidance of resonances

Reversible multiple timescale (MTS) integration algorithms have long been recognized as a straightforward way to increase efficiency and extend accessible timescales in molecular dynamics simulations without altering the ensemble distribution sampled. MTS methods are based on the idea that interatomic forces in a system drive motion on numerous timescales, and by decomposing force components according to these timescales and assigning an individual time step to each one, fast, computationally cheaper forces are evaluated more frequently than the slow, expensive forces. As it happens, the largest time step that can be employed in standard MTS methods is fundamentally limited by so-called resonance artifacts that originate in the fastest timescales. Thus, while it should be possible to assign the slowest timescales very large time steps approaching 100 fs in, for example, fully atomistic simulations, resonances impose a practical limit on this step size to around 5–10 fs, which allows for useful but only modest savings in computational overhead. This article will review the basic MTS approach and the origin of resonances and then will provide a perspective on how to solve the resonance problem for molecular dynamics simulations in different ensembles, showing how both statistical and dynamical properties can be generated with very large time steps.