Dynamics of proton migration in free base porphines

We investigated the proton tautomerization in free base porphines by considering the dynamical coupling between the proton migration and the skeletal motion. We estimated the conformation change of the skeleton due to the tautomerization. The estimated geometry of the skeleton in the linear proton configuration indicated that the large skeletal deformation from D4h symmetry is mainly caused by the change in the valence structure due to the proton configuration change. The strong vibrational coupling indicates that the deformation motion of skeleton will destroy the coherence of the proton migration. Thus, the proton migration should be considered as an incoherent hopping process. A quantum mechanical model which incorporates the effect of skeletal vibrations was described, and the temperature dependence of the proton migration was discussed in detail. The result was in agreement with the previous suggestions [A. Sarai, Chem. Phys. Lett. 83, 50 (1981)] that a considerable part of the activation energy is contributed by the skeletal vibrations, and that the proton migration should include the bending motion as well as the stretching of N–H. The quantum mechanical study also indicated that the synchronous proton migration, in which the central two protons migrate simultaneously, is a dominant process at low temperatures, but the asynchronous process, in which the protons migrate in a successive way, can make considerable contribution to the proton migration at high temperatures.