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.