Quantum dynamics (QD) simulations are performed in the diabatic basis using the split-operator technique on a grid of 500×500 points in the range q ∈ [-10, 10] a 0 and R ∈ [0, 8] a 0 . We used a time step dt = 0.05 a.t.u. These calculations provide the full PEN wavefunction in the electronic diabatic basis with corresponding photon-nuclear amplitudes. The marginal photon-nuclear density of the EF is then calculated as well as the electronic conditional amplitude in the diabatic basis. The TDPES and the TDVP can be calculated using the electronic amplitude as illustrated in detail in Ref. [ 7]. The initial state of the system for both models studied here is defined with full occupation of the S 1 state and with a Gaussian in q and in R centered at q = 0 and R = 2 a 0 . The widths of the Gaussians are σ q = 2.425 a 0 and σ R = 0.223 a 0 .