<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Sr</mml:mi><mml:mi mathvariant="normal">Ti</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mn>001</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>reconstructions: First-principles calculations of surface energy and atomic structure compared with scanning tunneling microscopy images

$(1\ifmmode\times\else\texttimes\fi{}1)$ and $(2\ifmmode\times\else\texttimes\fi{}1)$ reconstructions of the (001) $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$ surface were studied using the first-principles full-potential linear muffin-tin orbital method. Surface energies were calculated as a function of $\mathrm{Ti}{\mathrm{O}}_{2}$ chemical potential, oxygen partial pressure ${p}_{{\mathrm{O}}_{}2}$and temperature. The $(1\ifmmode\times\else\texttimes\fi{}1)$ unreconstructed surfaces were found to be energetically stable for many of the conditions considered. Under conditions of very low oxygen partial pressure the $(2\ifmmode\times\else\texttimes\fi{}1)$ ${\mathrm{Ti}}_{2}{\mathrm{O}}_{3}$ reconstruction [Martin R. Castell, Surf. Sci. 505, 1 (2002)] is stable. The question as to why STM images of the $(1\ifmmode\times\else\texttimes\fi{}1)$ surfaces have not been obtained was addressed by calculating charge densities for each surface. These suggest that the $(2\ifmmode\times\else\texttimes\fi{}1)$ reconstructions would be easier to image than the $(1\ifmmode\times\else\texttimes\fi{}1)$ surfaces. The possibility that the presence of oxygen vacancies would destabilise the $(1\ifmmode\times\else\texttimes\fi{}1)$ surfaces was also investigated. If the $(1\ifmmode\times\else\texttimes\fi{}1)$ surfaces are unstable then there exists the further possibility that the $(2\ifmmode\times\else\texttimes\fi{}1)$ DL-$\mathrm{Ti}{\mathrm{O}}_{2}$ reconstruction [Natasha Erdman et al. Nature (London) 419, 55 (2002)] is stable in a $\mathrm{Ti}{\mathrm{O}}_{2}$-rich environment and for ${p}_{{\mathrm{O}}_{2}}&gt;{10}^{\ensuremath{-}18}$ atm.