The polaritonic PESs E j (R) can then be calculated by using the values of V i (R) and V ij (R) calculated from the pure matter system (through the above DVR method) and the PFS overlaps (Eq. 33), m j |n i , and directly diagonalizing the matrix of Ĥpl . Note that identical results are obtained by solving Eq. 8 using the adiabatic-Fock basis |Φ α (R) ⊗ |n , where |Φ α (R) is the adiabatic states (see Eq. 6) and |n is the Fock state for the un-shifted field â † â + 1 2 hω c . As expected from our theoretical analysis in Eq. 16, the polariton state approaches the tensor product of the Mulliken-Hush (MH) diabatic states and the PFS states as the light-matter coupling increases. The curvature of the polariton potential energy surface will also approach the MH diabatic states, as indicated in Eq. 17. In particular, for the three-level Shin-Metiu model system studied here, we consider three MH diabatic states, a donor state |D where the electron is localized on the donor atom, an acceptor state |A where the electron is localized on the acceptor atom, and an atomic state |C where the electron is localized on the transferring charged ion (proton). With a strong light-matter coupling strength, at a particular nuclear configuration R, the ground state of the light-matter hybrid will approach one of these diabatic states depending on which of the diabatic energies