  In$_2$O$_3$-based catalysts have shown high activity and selectivity for
CO$_2$ hydrogenation to methanol, however the origin of the high performance of
In$_2$O$_3$ is still unclear. To elucidate the initial steps of CO$_2$
hydrogenation over In$_2$O$_3$, we have combined X-ray Photoelectron
Spectroscopy (XPS) and Density Functional Theory (DFT) calculations to study
the adsorption of CO$_2$ on the In$_2$O$_3$(111) crystalline surface with
different terminations, namely the stoichiometric, the reduced, and the
hydroxylated surface, respectively. The combined approach confirms that the
reduction of the surface results in the formation of In ad-atoms and that water
dissociates on the surface at room temperature. A comparison of the
experimental spectra and the computed core-level-shifts (using methanol and
formic acid as benchmark molecules) suggests that CO$_2$ adsorbs as a carbonate
on all surface terminations. We find that CO$_2$ adsorption is hindered by
hydroxyl groups on the hydroxylated surface.
