Hydrogen transfer in the porphin anion : A quantum dynamical study of vibrational effects

The observed temperature-dependent hydrogen transfer rate constants for the H, D, and T isotopic species of the porphin anion have been reproduced by two different quantum dynamical models. The approach is based on the master equation for the system-state populations. The models involve adapted localization properties and a simplified interaction with a quantum mechanical heat bath. A one-dimensional model describes a hindered circular transfer motion of the hydrogen atom between its four stable sites in the plane of the porphin ring framework. With five parameters that are common to the three isotopic species it yields agreement with the observed data. One of the parameters, the height of the fourfold potential encrgy barrier, predicts an acceptable estimate for the in-plane N-H wagging frequency. Interactions of the transfer motion with individual vibrations have been studied for a series of two-dimensional model systems. There the circular transfer motion is combined with ring framework modes having properties similar to those obtained for porphin by Li and Zgierski [J. Phys. Chem. 95, 4268 (1991)]. For vibrational modes near or above 960 cm -1 , strong interactions are found to be unlikely, as they would yield kinetic isotope effects and/or apparent activation energies in disagreement with the experimental data. For low frequency modes of the ring framework, however, sizeable couplings with the transfer cannot be ruled out. An interaction of the type suggested by quantum chemical results reported by Vangberg and Ghosh [J. Phys. Chem. B. 101, 1496 (1997)] has been included in a two-dimensional model involving a rectangular displacement of the pyrrole rings. With low vibrational frequency, a very large coupling strength, and a barrier close to the predicted one, this model has also been found to be compatible with experiment.