  We calculate the lattice phonons and the electron-phonon coupling of the
organic superconductor \kappa-(BEDT-TTF)_2 I_3, reproducing all available
experimental data connected to phonon dynamics. Low-frequency intra-molecular
vibrations are strongly mixed to lattice phonons. Both acoustic and optical
phonons are appreciably coupled to electrons through the modulation of the
hopping integrals (e-LP coupling). By comparing the results relevant to
superconducting \kappa- and \beta-(BEDT-TTF)_2 I_3, we show that
electron-phonon coupling is fundamental to the pairing mechanism. Both e-LP and
electron-molecular vibration (e-MV) coupling are essential to reproduce the
critical temperatures. The e-LP coupling is stronger, but e-MV is instrumental
to increase the average phonon frequency.
