Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme

Abstract

The numerical behavior of the symplectic, implicit midpoint method with a wide range of integration timesteps is examined through an application to a diatomic molecule governed by a Morse potential. Our oscillator with a 12.6 fs period exhibits notable, integrator induced, timestep- (Δt) dependent resonances and we predict approximate values of Δt where they will occur. The particular case of a third-order resonance (Δt ≈ 7 fs here) leads to instability, and higher-order resonances (n = 4, 5) to large energetic fluctuations and/or corrupted phase diagrams. Significantly, for Δt > 10 fs the energy errors remain bound.