In this work, we use the Fourier Grid Hamiltonian (FGH) approach to solve the eigenvalue problem of all matter and polariton Hamiltonians. In particular, we use a total of N = 2000 grid basis {|r i } to describe the electronic degrees of freedom r in the range [R D -10, R A + 10] (with ∆r = 0.01 a.u.), which allows us to solve the adiabatic states of the matter. The matrix elements of the elec-Table : Parameters used in the molecular Hamiltonian ĤM for both Model I (Fig. ) and Model II (Fig. ).