Model calculation of electron-phonon couplings in a dimer with a non-degenerate orbital

We evaluate all the electron-phonon couplings derived from the one-body and two-body electronic interactions, in both the adiabatic and extreme non-ad iabatic limit, for a dimer with a non-degenerate orbital built from atomic wave functions of Gaussian shape. We find largely different values of the c oupling parameters in the two limits, as well as different expressions of t he corresponding terms in the Hamiltonian. Depending on the distance betwee n the dimer ions, some of the two-body couplings are comparable, or even la rger than the one-body ones.