Nonadiabatic dynamics with classical trajectories: The problem of an initial coherent superposition of electronic states.

Advances in coherent light sources and development of pump-probe techniques in recent decades have opened the way to study electronic motion in its natural time-scale. When an ultrashort laser pulse interacts with a molecular target a coherent superposition of electronic states is created and the triggered electron dynamics is coupled to the nuclear motion. A natural and computationally efficient choice to simulate this correlated dynamics are trajectory-based methods where the quantum-mechanical electronic evolution is coupled to a classical-like nuclear dynamics. These methods must approximate the initial correlated electron-nuclear state by associating an initial electronic wavefunction to each classical trajectory in the ensemble. Different possibilities exist that reproduce the initial populations of the exact molecular wavefunction when represented in a basis. We show that different choices yield different dynamics, and explore the effect of this choice in Ehrenfest, surface-hopping, and exact-factorization-based coupled-trajectory schemes in a model system.