ensuring the initial forces (at t = 0) are simply F = -∇V aa (R). Previously, without any adjustments to γ b , the chosen values for γ b were only dependent on the windowing function itself, i.e., γ b = 0.366 for the square windows and γ b = 1/3 for the triangle windows. With the above γ-correction method, 80 each individual trajectory will have its own state-specific γ b for state |b⟩ that is completely independent of the choice of window function. This method has been proven to provide very accurate non-adiabatic dynamics in model photo-dissociation problems (coupled Morse potential), and has outperformed fewest-switches surface hopping (FSSH) with decoherence correction in ab initio on-thefly simulations. The Spin-LSC method.