The results of a simple local-density energy band model (XoO are used to carry through a calculation of the phonon dispersion relations in fcc Ne and At. Adiabatic phonons, calculated from the computed Xa total energy surface, are perturbed by the Fr6hlich Hamiltonian with electron-phonon matrix elements calculated from the Xa energy bands. The use of low-order perturbation theory gives results in fair comparison with observed values, but shows the general scheme to be feasible. Except for questions of the exact physical content of the Xa model itself, the calculation is entirely ab initio, and is believed to be the first such achieved in insulators.