where µ i is eigen-dipole value associated with the state |µ i . These |µ i states can be obtained from the direct diagonalization of the μ matrix in the adiabatic representation (with the matrix element expressed in Eq. 7). A good example of µ i could be the ionic and covalent dipole for a diatomic molecule, whereas the µ αβ are the transition and permanent dipoles (see Fig. of Ref. 38) Using the MH diabatic states, the matter Hamiltonian in Eq. 4 can be expressed as