To quantitatively express 𝑘 VSC , we analyze the overall effect of the cavity and the photon loss environment on molecular systems by performing a normal mode transformation to the Hamiltonian in Eq. 1 and obtaining an effective Hamiltonian, where now the cavity modes {q k } and the photon loss bath modes {x k,𝜁 } (described by Ĥloss ) are transformed into effective photonic normal mode coordinates { xk,𝜁 }, which are collectively coupled to the system DOF through the following term,