The influence of soft vibrational modes on our understanding of oxide surface structure
We examine the reasons for the poor quantitative agreement between the structures predicted from the minimum energy configuration of first principles calculations and those deduced from surface X-ray diffraction experiments for the structure properties of the TiO2(110) surface. In order to confine all numerical approximations very large scale all-electron first principles calculations are used. We find a very soft, anisotropic and anharmonic surface rigid-unit vibrational mode which involves displacements of the surface ions of approximately 0.15 Å for thermal vibrations corresponding to room temperature. It is concluded that in order to perform an accurate comparison between theory and experiment for this and perhaps other oxide surfaces it will be necessary to take account of such anisotropic vibrations in models used to interpret experimental data. In addition the contribution of the vibrational entropy to the surface free energy is likely to be significant and must be taken into account when computing surface energies and structures.