Restoring electronic coherence/decoherence for a trajectory-based nonadiabatic molecular dynamics

By utilizing the time-independent semiclassical phase integral, we obtained modified coupled time-dependent Schrodinger equations that restore coherences and induce decoherences within original simple trajectory-based nonadiabatic molecular dynamic algorithms. Nonadiabatic transition probabilities simulated from both Tully's fewest switches and semiclassical Ehrenfest algorithms follow exact quantum electronic oscillations and amplitudes for three out of the four well-known model systems. Within the present theory, nonadiabatic transitions estimated from statistical ensemble of trajectories accurately follow those of the modified electronic wave functions. The present theory can be immediately applied to the molecular dynamic simulations of photochemical and photophysical processes involving electronic excited states.