A reaction surface Hamiltonian is calculated for a gas phase model system mimicking CO-ligated heme complexes, such as hemoglobin or myoglobin. The reaction coordinates comprise the CO bond distance as well as its centre of mass motion with respect to the heme iron. Two low-frequency vibrational modes are identified which couple most strongly to these reaction coordinates. The quantum dynamics of this four-dimensional reduced system is investigated using the multi-configuration time-dependent Hartree approach. It is shown that the anharmonic coupling between the C-O and the Fe-CO coordinates is insufficient to trigger ultrafast Fe-CO bond breaking by virtue of intramolecular energy redistribution even after excitation of the CO bond above the dissociation limit. The results are discussed in the light of recent experiments on laser-driven vibrational ladder climbing. (C) 2004 Elsevier B.V. All rights reserved.