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The vibrational bound and resonance state structure of highly excited DCO (X  ˜  2 A´) has been investigated using an effective Hamiltonian based on the polyad approximation. The model Hamiltonian takes advantage of the accidental 1:1:2 degeneracy of the three DCO (X  ˜ ) fundamental vibrational frequencies. Allowance was made for vibrational couplings by the 1:1 and 2:2 interaction terms between the DC and CO stretching modes and the 1:2 coupling terms of the two stretching vibrations with the DCO bending mode. A pleasing description of the experimentally observed vibrational term energies [2] was reached up to excitation energies of E v (X  ˜ )≈15000 cm -1 , far above the D-CO (X  ˜ ) bond dissociation limit. Moreover, a one-to-one state-to-state correspondence was established between the experimental energies, the effective Hamiltonian predictions, and exact quantum dynamics results [18]. The Hamiltonian was subsequently applied to explore the kinetics of the intramolecular vibrational energy redistribution (IVR) in the highly excited DCO (X  ˜ ). The vibrational eigenstate compositions were investigated in terms of the respective zero-order basis functions to analyze the extent of the state mixing. 2D and 3D vibrational wavefunctions predicted by the effective Hamiltonian were compared to the wavefunctions from the quantum dynamics studies. IVR rates and IVR pathways were evaluated as a function of the vibrational excitation. Eventually, an attempt was made to model the trends of the observed state-specific DCO (X  ˜ ) uni-molecular decay constants by a complex effective Hamiltonian. The results give a rationale for the two orders of magnitude difference between the experimental state-specific decay constants and statistical unimolecular rate theory predictions observed by Stöck  et al.  [2].

Analysis of Vibrationally Highly Excited Bound and Resonance States of DCO (X ˜ 2 A′) Using an Effective Polyad Hamiltonian