In this example, we were able to effectively manipulate the CT 1 state in the bare molecular system by coupling to a higher-energy transition with non-zero oscillator strength. The character, including the optical activity, of the second polaritonic state was changed to allow experimental tunability of this CT system that can be utilized in realistic light-harvesting or light-emitting systems to achieve a high degree of exciton splitting or radiative recombination, respectively, after photoexcitation processes. In conclusion of this example, the procedure of utilizing common electronic structure analysis techniques to examine coupled electron-photon systems is largely unchanged and requires little-tono conceptual extension when one is interested in modifications to the electronic sub-system as a result of the photonic DOFs. Thereby, we propose to utilize the framework already established by the electronic structure community to analyze polaritonic properties of light-matter hybrid systems with the pQED procedure (using Eq. 6 to compute Fig. in the Supporting Information presents a slightly abstract extension of the real-space transition density matrix (Fig. ) by now examining the coherence between a single electronic coordinate and a photonic one. The mixed electronicphotonic transition density ρ 0j (r e , q c ) (Eq. S10) for the H 2 molecule is shown for three choices of coupling strengths. Due to the simplicity of the electronic system, the electron and photonic transition densities look very similar and yield conceptually simple results (see Supporting Information for discussion) regarding the mixed coordinate spatial coherence. This analysis tool will have direct application to multi-mode cavities where one is interested in examining the coherence between cavity modes or between electron and photon DOFs for low-frequency cavities where the electron and photon coordinates may, together, provide extremely meaningful insight into the complex interplay between these DOFs.