Structure and apparent topography of ${\mathrm{TiO}}_2\mathrm{}\left(110\right)\mathrm{}$ surfaces

We present self-consistent ab initio total-energy and electronic-structure calculations on stoichiometric and nonstoichiometric ${\mathrm{TiO}}_2\mathrm{}\left(110\right)\mathrm{}$ surfaces. Scanning tunneling microscopy (STM) topographs are simulated by calculating the local electronic density of states over an energy window appropriate for the experimental positive-bias conditions. We find that under these conditions the STM tends to image the undercoordinated Ti atoms, in spite of the physical protrusion of the O atoms, giving an apparent reversal of topographic contrast on the stoichiometric $1\times 1$ or missing-row $2\times 1$ surface. We also show that both the interpretation of STM images and the direct comparison of surface energies favor an added-row structure over the missing-row structure for the oxygen-deficient $2\times 1$ surface.