Analytical treatment of a generalized Hubbard Hamiltonian and of polarization in organic molecular aggregates

Starting with a Hamiltonian which comprises onsite, transfer and generalized Hubbard electron–electron plus a linear electron–phonon interaction, allowing in principle any number of sites i and excitations image, we derive a matrix equation for the dimer problem. Regarding the general electronic sub-Hamiltonian coupled to an electric field image, an expression for the polarization image is derived analytically.