Quantum mechanical and semiclassical dynamics at a conical intersection

We present simulations of wave-packet dynamics for a model of a conical intersection in two dimensions. The potential energy surfaces and couplings are functions of a total symmetrical coordinate and of a symmetry breaking one. The wave packet crosses the coupling region once, moving essentially in the direction of the symmetrical coordinate. The dynamics are determined by two methods, one quantum mechanical and the other semiclassical, based on trajectories and surface hopping. The semiclassical approximation is quite adequate for low coupling strengths in the diabatic representation, less so for larger couplings. Approximate analytic solutions for the two-dimensional problem and for one-dimensional analogs are provided, in order to generalize the numerical results and to analyze the reasons of the discrepancies between semiclassical and quantum mechanical results.