  The crystal structure and lattice phonons of (BEDT-TTF)_2I_3 superconducting
\beta-phase are computed and analyzed by the Quasi Harmonic Lattice Dynamics
(QHLD) method. Whereas the crystal structure and its temperature and pressure
dependence are properly reproduced within a rigid molecule approximation, this
has to be removed to account for the specific heat data. Such a mixing between
lattice and low-frequency intramolecular vibrations also yields good agreement
with the observed Raman and infrared frequencies. From the eigenvectors of the
low-frequency phonons we calculate the electron-phonon coupling constants due
to the modulation of charge transfer (hopping) integrals. The hopping integrals
are evaluated by the extended Hueckel method applied to all nearest-neighbor
BEDT-TTF pairs in the ab crystal plane. From the averaged electron-phonon
coupling constants and the QHLD phonon density of states we derive the
Eliashberg coupling function, which compares well with that experimentally
obtained from point-contact spectroscopy. The corresponding dimensionless
coupling constant \lambda is found to be around 0.4 .
