Quasiclassical calculations of one-dimensional potential parameters of the hydrogen migration in m e s o-tetraphenylporphine from experimental tunnel rates

The migration of the two inner hydrogen atoms of meso-tetraphenylporphine (TPP) between the four nitgrogen atoms proceeds by ground state tunneling and by tunneling between the first excited degenerate NH-stretching states separated by the barrier. The experimental tunnel rates, measured previously by dynamic NMR spectroscopy, are used to compute barrier heights, Ed, and hydrogen transport distances, Δr, in quasiclassical, one-dimensional WKB approximation. Two computation methods are compared: the transmission function (TR) method and the energy splitting (ES) method. Whereas Δr is not very sensitive to the barrier type, it depends very much on the degree of cooperativity of the two-particle motion and on the computation method. There was a close agreement between the transport distances calculated from the crystallographic data of TPP and those calculated for synchronous hydrogen tunneling using the ES method. Since the TR method neglects resonance tunneling effects the transport distances calculated are too small. The calculations provide a quantitative explanation why deuterium tunneling in the two lowest ND-stretching states is too slow to be detected in the experiments. Synchronous hydrogen tunneling in TPP is then a consequence of the synchronous hydrogen motion in the potential wells.