The photon-nuclear dynamics of Eq. ( ) will be solved via an ensemble of coupled trajectories representing both nuclei and photons, thus, they will be indicated as q I (t), R I (t) = X I (t). To simplify the notation below, we will indicate the dependence on the photon-nuclear trajectories only via the label I; each trajectory at every time thus becomes a collection of N N + 2N P coordinates, that will be collectively labeled with the index Γ ≡ α, ν. The evolution of positions and momenta of these trajectories adheres to Hamilton's equations of motion, guided by the TDPES, the R-TDVP, and the q-TDVP.