High proton mobility in perovskite-type oxides of composition ABO, strongly depends on the dynamics of the proton environment, especially on the fluctuations of the oxide ion separations. The dynamics of the oxide host lattices of the model materials BaTiO3, and BaZrO3 have been studied using quantum molecular dynamics simulations. The simulation method has already been shown to yield numerical results in agreement with experimental findings for the cubic phase of BaCeO3. At atoms in the plane perpendicular to the B-O-B axis is found. The free energy of the oxygen lattice vibrations is evaluated and the activation energy for proton transfer is estimated to be 0.450 eV for BaTiO3, 0.69 eV for BaZrO3, and 0.64 eV for BaCeO3.