Using a non-empirical ionic model, we find harmonically unstable, double well potential surfaces for both La2CuO4 and YBa2Cu3O7 which may be related to the high temperature superconductivity. We have applied the Potential Induced Breathing (PIB) Model to La2CuO4 and YBa2Cu3O7 and find that the ionic description gives semiquantitative agreement with structural and vibrational observations. Furthermore, comparison with self-consistent linearized augmented plane wave  (LAPW) calculations shows that ionic contributions to the bonding and lattice dynamics of oxide superconductors are large. For La2CuO4 we find that an ionic description predicts the observed tetragonal to orthorhombic distortion, predicts a lower symmetry ground state, and predicts a stable oxygen breathing mode. We find harmonically unstable phonon branches that we relate to phase transitions. Unstable (anharmonic) modes will couple via ionic forces to the charge density in the metallic planes. This ionic coupling has not been included in previous lattice dynamics calculations. For YBa2Cu3O7 we find similar unstable phonon branches that involve oxygen motions perpendicular to the Cu-O bonds. We find the crystalline charge density is best approximated by overlapping ions if Cu and O ions of charge +1.6 and -1.8, respectively, are used.