The influence of soft vibrational modes on our understanding of oxide surface structure

We examine the reasons for the poor quantitative agreement between the stru ctures predicted from the minimum energy configuration of first principles calculations and those deduced from surface X-ray diffraction experiments f or the structure properties of the TiO2(110) surface. In order to confine a ll numerical approximations very large scale all-electron first principles calculations are used. We find a very soft, anisotropic and anharmonic surf ace rigid-unit vibrational mode which involves displacements of the surface ions of approximately 0.15 Angstrom for thermal vibrations corresponding t o room temperature. It is concluded that in order to perform an accurate co mparison between theory and experiment for this and perhaps other oxide sur faces it will be necessary to take account of such anisotropic vibrations i n models used to interpret experimental data. In addition the contribution of the vibrational entropy to the surface free energy is likely to be signi ficant and must be taken into account when computing surface energies and s tructures.