What is the best semiclassical method for photochemical dynamics of systems with conical intersections?

We present a systematic test of four general semiclassical procedures for the theoretical treatment of multistate molecular processes such as electronically nonadiabatic photochemical reactions. The methods are tested by comparing their predictions to accurate quantal results for three two-state model reactions involving conical intersections. The four methods tested are Tully’s fewest-switches version of trajectory surface hopping (1990), the Blais–Truhlar trajectory surface hopping method (1983), the Ehrenfest scheme (1975–1979), and the Meyer–Miller method (1979). We test the ability of the classical path methods to predict both electronic probabilities and product rovibrational distributions. For each of the four basic approaches we test six options for extracting final-state information from the calculated dynamics. We find that, although in most cases there is qualitative agreement between average quantum mechanical and trajectory results, the overall average error is about 50% for Tully’s fewest-switches method, the Ehrenfest method, and the Meyer–Miller method, and even higher, about 60%, for the Blais–Truhlar method. These values do not include additional errors in the below-threshold regions, which are especially large for the Meyer–Miller method because of the electronic zero-point energy in the Meyer–Miller classical analog Hamiltonian.