An alternative approach is to solve the same problem in two steps. This procedure involves obtaining the electronic adiabatic states (eigenstates of the adiabatic molecular Hamiltonian, see Eq. 2) using any of the previously mentioned traditional electronic structure methods and then constructing the total polariton wavefunction using these adiabatic states for the molecule -and Fock states for the photonic modes -through diagonalization of the total light-matter Hamiltonian. For this procedure, only the molecular energies and dipole operator matrix elements are required as input in the dipole-gauge Pauli-Fierz Hamiltonian (see Eq. 1 in Theoretical and Computational Methods section). In this work, this procedure is referred to as the parameterized QED (pQED) scheme.