Theoretical Details In order to examine the excited state properties of the polaritonic systems, the computation of the individual properties of the isolated electronic and photonic systems must be first computed and then mixed through linear combinations by Eq. 6 to acquire the polaritonic properties. We will derive one example for clarity to outline the general procedure, but this can be simplified by using commercial electronic structure packages to obtain the final results for the bare electronic quantities. The one-particle transition density operator between the α th and β th molecular states ξM αβ is defined as