Nonadiabatic trajectories at an exhibition

The present article reviews two classes of semiclassical (mixed quantum mec hanical/classical) methods for investigating multielectronic-state dynamics : the trajectory surface-hopping (TSH) method and the time-dependent self-c onsistent 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 large r systems. These studies indicate that Tully's fewest switches algorithm is the best available TSH method and that the Ehrenfest method is the best pr eviously 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. Fu rthermore, the surface-hopping algorithm is frequently frustrated in its at tempt to maintain ensemble-average self-consistency. The Ehrenfest method r emoves all these troublesome aspects but at the cost of producing unphysica l mixed states, which are responsible for its larger errors in observables. A recently introduced TDSCF method, the continuous surface-switching metho d, removes the unphysical mixed states of the Ehrenfest method, and in init ial tests it produces results that are systematically bet;ter than those ca lculated by the Ehrenfest method. The present article illustrates several o f these aspects of nonadiabatic trajectory methods pictorially.