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Distance-depending electron-phonon interactions from one- and two-body electronic terms in a dimer

For a dimer with a non-degenerate orbital built from atomic wave functions of Gaussian shape we evaluate all the electron-phonon couplings derived from the one-body and two-body electronic interactions, considering both the adiabatic and extreme non-adiabatic limit. Not only the values of the coupling parameters in the two limits, but also the expressions of the corresponding terms in the Hamiltonian differ. Depending on the distance between the dimer ions, some of the two-body couplings are comparable, or even larger than the one-body ones.