which is the Wigner transformation of the nuclear wavefunction χ(R) = ⟨R|χ⟩ in the initial state. Here, R and P are the nuclear coordinate and momentum, respectively. The nuclear time step used in all the trajectory-based simulations is dt = 3.0 a.u., with 200 equally spaced time steps for the mapping variables' integration during each nuclear time step. The equation of motion in Eq. 24-Eq. 25 are integrated using a second-order symplectic integrator for the MMST variables . The population dynamics using all trajectory-based methods were averaged over 10000 trajectories.