where e is the electronic charge, ⃗ R is the unit vector of the optical transition dipole moment, e pp,q is the q th photonic mode polarisation, and Z q is the nuclear charge. The vibronic component is the usual nuclear-electronic coupling, while the vibrational-photon component describes the alignment between each normal mode and the light polarisation. The vibrational energy E vib corresponds to the energy difference between the initial and final vibrational states for all normal modes . It is worth highlighting that when both initial and final states are resonating in the absence of light (W cavity ), the atomic system component is off-resonance (W system ). In other words, both components are out of phase with respect to each other. Therefore, vibrational energy difference part of the density of states is different between both components of Equation .