In the left panels of Fig. , the one-dimensional TDPES is plotted for q = 0 (orange circles) and for q = 1.5 a 0 (green circles) as function of the nuclear coordinate R. Note that the orange and green circles represent only the component ε V PEN (q, R,t) of the full TDPES. For the same values of q, we report cuts of the photon-nuclear density as functions of R (thin orange and green lines). In agreement with the above discussion, we observe that at the times reported in the figure, the density develops two main portions. The portion that remains in the Franck-Condon region (at around R = 2 a 0 ) is partially associated to the electronic ground states and partially to the excited state. Specifically, the shape of the TD-PES in orange (for q = 0) follows at all times reported in the figure the shape of the excited state (dashed lines), while the shape of the TDPES in green (for q = 1.5 a 0 ) at t = 1250 a.t.u. follows the ground state (continuous lines). The portion of the density that moves towards the avoided crossing under- , decomposed in ε V PEN (q, R,t) (orange circles at q = 0 and green circles at q = 1.5 a 0 ) and in ε geo (q, R,t) (cyan lines at q = 0 and red lines at q = 1.5 a 0 ) and superimposed at the cavityadiabatic PESs (purple and light-blue as in Fig. ). Thin orange and green lines are the corresponding cuts of the photon-nuclear density as functions of R along the same values of q. Right: Cuts of the TDPES as function of q, decomposed in ε V PEN (q, R,t) (dark-green circles at R = 2 a 0 and blue circles at R = 4 a 0 ) and in ε geo (q, R,t) (cyan at R = 2 a 0 ) and superimposed at the cavity-adiabatic PESs (fuchsia and light-green as in Fig. ). Thin dark-green and blue lines are the corresponding cuts of the photon-nuclear density as functions of q along the same values of R. Note that in the top panel the thin blue line is not visible because at R = 4 a 0 at t = 250 a.t.u. the density is nearly zero.