Direct evidence for mode-specific vibrational energy relaxation from quantum time-dependent perturbation theory. III. The nu(4) and nu(7) modes of nonplanar nickel porphyrin models.

The time scales and pathways of vibrational energy relaxation (VER) of the nu(4) and nu(7) modes of three nickel porphyrin models, nickel porphine (NiP), nickel protoporphyrin IX (Ni-heme), and nickel octaethylporphyrin (NiOEP), were studied using a non-Markovian time-dependent perturbation theory at the B3LYP/6-31G(d) level. When NiP is calculated with D(4h) symmetry, it has the planar structure and the same VER properties as ferrous iron porphine (FeP). The porphine cores of both Ni-heme and NiOEP were distorted from a planar geometry, assuming a nonplanar structure, similar to that of the heme structure in cytochrome c. The VER time scales of Ni-heme are found to be similar to those predicted for a planar iron heme, but the derived pathways have distinctly different features. In particular, the strong coupling between the nu(7) mode and the overtone of the approximately 350 cm(-1) gamma(7) mode, observed for planar porphyrins, is absent in both nonplanar nickel porphyrins. Direct energy exchange between the nu(4) and nu(7) modes is not observed in NiOEP, but is found to play an essential role in the VER of the nu(4) mode in Ni-heme. The Ni-heme isopropionate groups are involved in the dominant VER pathways of both the nu(4) and nu(7) modes of Ni-heme. However, in contrast with VER pathways derived in planar iron heme, the isopropionate groups are not observed to play an essential role relative to other side chains in spatially directing the vibrational energy flow.