The dynamics of the isomerization reaction LiNCreversible arrowLiCN is considered at a quantum level. This study is performed with the aid of dynamically localized wave packets, which provide a wealth of information about the relevant parts of the molecular phase space. Three cases are considered, corresponding to energies close to the threshold for isomerization. The initial position of the packet is always localized in the LiNC well (which is the most stable), and different energies and distributions among the vibrational modes of the molecule are used. The packet will then explore phase space and, as a result of these dynamics, different time scales (including those from intramolecular energy transfer processes) exist, which appear in the low resolution features of the corresponding spectra. The characteristics of these spectra are discussed and analyzed using a variety of techniques, making extensive use of the ideas of nonlinear dynamics, and the conditions for the applicability of statistical theories to evaluate reaction rates in this case are considered.