At t = 0, the TDPES reproduces the shape of the cavityadiabatic S 1 PES, where the photoexcited wavepacket is initially prepared: its slope in the R direction induces the density to move towards the right, while it confines the density in the q direction being essentially a parabola. While the dynamics of the photon-nuclear density is quite simple, as it mainly moves in R towards the right, we can observe that an interesting behavior develops in time along q. Around t = 500 a.t.u., the TDPES modulates its shape between R = 2 a 0 and R = 2.5 a 0 , causing the density to separate in two portions, one that moves to the right and one that remains in the Franck-Condon region all along the dynamics. In the Franck-Condon region, we observe the formation of a localized peak extending in the R direction up to (slightly less than) R = 2.5 a 0 at q = 0, which enforces the splitting of the photon-nuclear density along q. There, the shape of the density along q is reminiscent of the first excited state of the harmonic potential, thus it coincides with the photon formation. The formation of the two portions of the density along R is complete already at t = 750 a.t.u., and at later times, i.e., t = 1000 a.t.u. in the figure, while the S 1 component continues its evolution towards the avoided crossing, the component associated to the Franck-Condon region remains fairly well localilzed on the left. At the final snapshot reported, namely at t = 1250 a.t.u., a very small portion of density moving towards the right remains in the excited state after the passage through the avoided crossing, and is reflected back (not visible in the panel), while the main portion keeps travelling in the ground state towards the right. TDPES for model A at times: t = 0, 250, 500, 750, 1000, 1250 a.t.u., as indicated in the panels. The color bar is given in hartree. The nuclear density is superimposed at the same times as black contour lines.