In this model, the photon-nuclear density remains localized around q = 0 and R = 2 a 0 . The dynamics does not manifest any peculiar behavior along the R direction, since the wavepacket is transferred from S 1 to S 0 and back without major geometrical modification in the nuclear direction. Nonetheless, the dynamics along q is quite interesting: the cavity switches from the zero photon state to the one photon state, and back, thus, the density along q needs to evolve from the ground state to the first excited state, and back, of the harmonic oscillator. This is exactly what we observe in the evolution of the photon-nuclear density, shown as black contour lines in Fig. at times t = 0, 270, 540, 810 a.t.u., that are, respectively, the initial time, one-quarter, half and three-quarters of the oscillation period of the average photon number. In order to produce the expected density in the q direction, the TDPES develops a very localized high barrier at q = 0 for all values of R. Upon closer inspection of the components of the TDPES (not reported), the main contribution to this barrier is ε geo . Thus, once again we observe that the dynamics of the TDPES along q is strongly dominated by this term, which is completely neglected in CTMQC. This observation explains the disagreement between CTMQC (in blue in Fig. ) and QD results in describing the dynamics of the average photon number and of the S 1 population. MTE and TSH do not perform better than CTMQC, actually TSH provides once again a poorer description of the dynamics than MTE and CTMQC.