HYDROGEN-TRANSFER IN THE PORPHIN ANION - A QUANTUM DYNAMICAL STUDY OFVIBRATIONAL EFFECTS

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