The calculations were performed with the ELVIBROT Fortran code . Trajectory-based calculations were performed using the G-CTMQC code. For Ehrenfest, CTMQC and CTMQC-E, we run N tr aj = 1000 trajectories, whereas for TSHED and CTTSH, we repeated n = 5 times the calculations with N tr aj = 1000 trajectories to sample over various hopping histories. The same initial conditions, i.e., positions and momenta, were used in all calculations, by sampling them from the harmonic Wigner distribution obtained from |χ(r, θ, 0)| 2 of Eq. (B1). G-CTMQC uses the velocity-Verlet algorithm and the Runge-Kutta-Gill scheme to integrate the nuclear and electronic evolution equations, respectively. The trajectories were propagated for 96 fs (4000 a.t.u.) using a time step of dt n = dt e = 0.0012 fs (0.05 a.t.u.) for both nuclear dt n and electronic dt e dynamics; however, tests were performed by changing the nuclear and the electronic time steps, to dt n = dt e = 0.0024 fs and to dt n = 0.0024 fs, dt e = 0.0012 fs, to assess the stability of the results.