2-DIMENSIONAL TUNNELING - BIFURCATIONS AND COMPETING TRAJECTORIES

Different types of tunneling trajectories contribute to 2D vibrational ly assisted tunneling in semiclassical approximation. Two families of periodic trajectories compete on the potential energy surface (PES) wi th two symmetrically situated saddle points. Depending on the temperat ure, either 1D or 2D periodic orbits give the major contribution to th e rate constant K(T) for the incoherent transition. As a result, an ad ditional crossover temperature T(c2) appears that corresponds to the b ifurcation of the extremal tunneling trajectory. In the coherent case both periodic and aperiodic paths contribute to the spectroscopic spli tting DELTA of degenerate vibrational levels, and competition between these trajectories occurs even on simple PES with the only saddle Poin t. Contribution from aperiodic paths depends upon the quantum number o f the promoting vibration. Bifurcation diagram for the two-proton tran sfer in free-base porphyrin is constructed. Its analysis show that at PES parameters, chosen to fit the experimental rate constant, the tran sfer follows the asynchronous mechanism closely up to low temperatures . Tunneling splitting in cyclopentanone is evaluated. Dominating a per iodic paths make the transition configuration of vibrationally excited cyclopentanone strongly bent, rather than planar. These paths become ''switched of'' at a small coupling strength between two coordinates.