  We present a first principles investigation of the lattice dynamics and
electron-phonon coupling of the high-T_c superconductor YBa_2Cu_3O_7 within the
framework of density functional perturbation theory using a mixed-basis
pseudopotential method. The calculated phonon dispersion curves are in
excellent agreement with Raman, infrared and neutron data. Calculation of the
Eliashberg function alpha^2F leads to a small electron-phonon coupling
lambda=0.27 in disagreement with earlier approximate treatments. Our
calculations strongly support the view that conventional electron-phonon
coupling is not an important contribution to superconductivity in high-T_c
materials.
