Furthermore, the truncation of the electronic dipole matrix with the number of included adiabatic electronic states will drastically affect the results, since the transition dipole matrix appears directly in the light-matter coupling term and its square appears in the DSE term, thus possibly contributing a great deal of complication to the off-diagonal (and on-diagonal) couplings due to the shape and distribution of the transition dipole matrix itself. As an example, Fig. showcases the dipole matrix for four molecules: (a) formaldehyde, (b) LiF, (c) animopropenal, and (d) 35PPE, all of which under recent study in polaritonic schemes. In each case, the 20 lowest energy adiabatic electronic states are shown as the vector norm of the dipole matrix elements as computed at the TD-DFT level. In all four cases, although symmetry-based arguments regarding selection rules could be applied, it is hard to discern any pattern of the dipole matrix elements. The two small organic molecules (Fig. ) showcase the most scattered of the dipole matrices, the LiF (Fig. ) shows a blocklike structure (due to the reduced dimensionality), and the large organic species (Fig. ) shows an intermediate regime where the high-energy states are weakly coupled and have some structure while the low-energy states showcase a strong degree of coupling in a blocklike fashion. Using the pQED procedure, one needs to pay careful attention to the electronic dipole matrix and discern the distribution of strong coupling. At larger numbers of electronic states (i.e., ∼100 states), it is usually straightforward to see where the strong coupling away from the diagonal elements will decay to near zero. This effective "width" is expected to play a direct role in the convergence of the electronic basis states used for the pQED procedure. However, one also requires the square of this dipole matrix (which will change depending on the choice of electronic state truncation N ) for obtaining the DSE terms, which adds additional complexity to the situation.