BEDT-TTF organic superconductors: the entangled role of phonons

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.