Phonon dispersion and electron-phonon interaction for

We present a first-principles investigation of the lattice dynamics and electron-phonon coupling of the high-$T_{\ab{c}}$ superconductor $\chem{YBa_2Cu_3O_7}$ 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 $\alpha^2 F$ 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-$T_{\ab{c}}$ materials