  We study the effect of decoherence on the sub-Planck scale structures of the
vibrational wave packet of a molecule. The time evolution of these wave packets
is investigated under the influence of a photonic or phononic environment. We
determine the master equation describing the reduced dynamics of the
wave-packet and analyze the sensitivity of the sub-Planck structures against
decoherence in the case of a hydrogen iodide (HI) molecule.
