Natural transition orbital (NTO) analysis is another, maybe even more common, method to understand the electron and hole distributions in real space, which can be readily evaluated by electronic structure packages through diagonalization (or rather singular value decomposition, in general) of the transition density matrix, ξ M βα (r e , r h ) (see Eq. ) M αβ followed by inserting into Eq. 6 with Bph = 1ph , where 1ph is the identity matrix for the photonic DOFs. This will give a similar result as that of Eq.13 where the photonic DOFs have been traced out, and the examination of the cavity-induced effects on the local electronic structure can be examined. The inclusion of such an analysis of the photonic DOFs are not required due to the simplicity of the single quantized cavity mode harmonic oscillator structure.