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 (t
7
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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