Nonadiabatic Trajectories at an Exhibition

The present article reviews two classes of semiclassical (mixed quantum mechanical/classical) methods for investigating multielectronic-state dynamics: the trajectory surface-hopping (TSH) method and the time-dependent self-consistent field (TDSCF) method. The recent availability of accurate quantum mechanical dynamics calculations for a variety of realistic three-body two-state potential energy matrices has allowed an assessment of the validity of semiclassical multisurface dynamics methods that are applicable to larger systems. These studies indicate that Tully's fewest switches algorithm is the best available TSH method and that the Ehrenfest method is the best previously available TDSCF method. The fewest switches surface-hopping method has relatively small errors even when it is not the best method while the Ehrenfest TDSCF method tends to have larger errors when it is not the best. However, the fewest switches algorithm involves unphysical discontinuities in momenta, and the results may depend on the choice of representation. Furthermore, the surface-hopping algorithm is frequently frustrated in its attempt to maintain ensemble-average self-consistency. The Ehrenfest method removes all these troublesome aspects but at the cost of producing unphysical mixed states, which are responsible for its larger errors in observables. A recently introduced TDSCF method, the continuous surface-switching method, removes the unphysical mixed states of the Ehrenfest method, and in initial tests it produces results that are systematically better than those calculated by the Ehrenfest method. The present article illustrates several of these aspects of nonadiabatic trajectory methods pictorially.