In a typical surface hopping simulation, the initial nuclear coordinates and velocities are sampled in the ground state (state 1), and the trajectory propagation starts in the excited state L. Thus, after creating the initial geometries and momenta with one of the techniques discussed in Section 4.2, we must decide on which state for each trajectory will start. The most straightforward procedure is to assign a specific initial state. Nevertheless, such an approach does not consider that the character of the adiabatic state can be different in the different geometries. For instance, S2 may be the bright state at the ground state minimum (see Figure ). However, S2 may be dark in many geometries of the initial ensemble. where the oscillator strength is large and n* character (brown), with feeble oscillator strength. To decide the initial state for a set of initial geometries (blue Gaussian distribution), Newton-X checks each geometry's excitation energies and oscillator strengths in each excited state. The algorithm picks initial states falling within a predefined excitation-energy window and favors those transitions with large excitation probabilities (black arrows over gray ones). The excitation probabilities are assumed to be proportional to the oscillator strength, and a stochastic selection is applied. The scheme is 1D, but actual cases are worked out on multidimensional potential energy surfaces.