Predicting core-level X-ray photoemission spectra of oxide surfaces from first principles -- a case study for SnO$_2$
X-ray photoemission spectroscopy (XPS) is a powerful technique to gain insight into the chemical properties of oxide surfaces. However, the interpretation of XPS spectra is notoriously difficult as realistic surfaces contain different terminations, reconstructions, adsorbates and defects all of which leave (potentially overlapping) spectroscopic fingerprints. To address this challenge, we present a first-principles approach based on the Z+1 method that allows us to predict XPS spectra of oxide surfaces which can directly be compared to experimental measurements. We present results for different SnO$_2$ (110) surfaces: the stoichiometric surface, surfaces with different types of vacancies (one of which is the fully reduced surface) and also the fully reduced surface with adsorbed OH and O$_2$ molecules. For these systems, we calculate the O 1s core-electron binding energies of all oxygen atoms and then use this to predict the XPS spectrum. We find that the fully reduced surface gives rise to a highly symmetric peak shape in agreement with recent XPS measurements. In contrast, the spectrum of the stoichiometric surface exhibits an additional feature at low binding energies caused by the bridging oxygen atoms at the surface. For the reduced surface with OH and O$_2$ adsorbates, the spectrum exhibits additional features at higher binding energies. The predicted spectra are in good agreement with experimental results obtained for reduced surfaces that have been exposed to oxygen gas. The presented method is general and can be straightforwardly applied to other surfaces.