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

   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- (t) dependent  resonances and we predict approximate values of t where they will occur. The particular case of a third order resonance (t7 fs here) leads to instability, and higher-order resonances (n = 4, 5) to large energetic fluctuations and/or corrupted phase diagrams. Significantly for t > 10 fs the energy errors remain bound.

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