goes a nonadiabatic population transfer at around R = 4 a 0 , and evolves as well partially in the excited state and partially in the ground state since the TDPES develops a characteristic step that bridges between the cavity-adiabatic shapes of the (static) PESs. The geometric component of the TDPES, namely ε geo (q, R,t) represented in cyan and in red in Fig. , develops a strongly oscillatory behavior only in the Franck-Condon region, that is partially responsible for the oscillations observed as well in the density. The oscillations in ε geo (q, R,t) as function of R for fixed q, however, do not strongly affect the overall shape of the density, only its fine interference patterns. Interestingly, as also previously discussed by Maitra and coworkers , the TDPES as a function of q for two different values of the nuclear coordinate, namely R = 2 a 0 (dark-green circles) and R = 4 a 0 (blue circles), can become strongly anharmonic. At all times reported in Fig. , for R = 2 a 0 , the component ε V PEN (q, R,t) of TDPES develops a barrier around q = 0 whose maximum value reaches the corresponding electronic excited state. In addition, the geometric component ε geo that is summed to ε V PEN to obtain the full TDPES, presents as well a high broad barrier centered in q = 0 for R = 2 a 0 (note that for R = 4 a 0 , ε geo is a nearly constant function of q with a small negative value that is not reported in Fig. ). The analysis of the cuts of the TDPES allows us to conclude that as function of q the TDPES is strongly anharmonic, despite the fact that the cavity-adiabatic electronic PESs are seemingly harmonic, and that its shape is strongly dominated by ε geo .