Direct evidence for mode-specific vibrational energy relaxation from quantum time-dependent perturbation theory. I. Five-coordinate ferrous iron porphyrin model.

The time scales and mechanisms of mode-specific vibrational energy relaxation in imidazole ligated ferrous iron porphine were studied using a non-Markovian time-dependent perturbation theory and density functional theory calculation. Seven normal modes, including nu(4), nu(7), and five Fe out-of-plane modes (Fe-oop), were treated as the relaxing system mode coupled to all other modes forming the bath. The derived cooling time constants for the nu(4) and nu(7) modes agree well with the results of previous experimental studies. The pathways for energy transfer from each system mode were identified. The gamma(7) mode, associated with Fe-oop motion with frequency approximately 350 cm(-1), was observed to couple strongly through its overtone with the nu(7) porphine in-plane vibration. This suggests a possible mechanism for the excitation of the nu(7) mode, which is distinct from the direct excitation together with Fe-oop motion of the nu(4) mode. Four other Fe-oop motions were observed to couple to low frequency modes including those involving significant imidazole ligand motions. Through these couplings, excitation following ligand photodissociation may be efficiently transferred from the heme doming mode to the protein backbone motions essential to conformational changes associated with the protein's function.