The key idea in this paper is to establish a simple system-bath model described by an effective spectral density function without explicitly taking the photon DOF, qc , into the description of the quantum subsystem (such as through Fock states). This can be achieved by regarding the cavity photon mode as the primary bath mode with the "coordinate" qc that directly couples to the reaction coordinate R, and cavity loss as the secondary bath that couples to qc . This multi-layer bath model has been extensively discussed in the literature, including the seminal work from Garg , as well as many others. By performing a harmonic analysis of the equations of motion it is shown that the model Hamiltonian of Eq. 8 has a one-to-one map (through a normal mode transformation) to the effective Hamiltonian as below,