  The oxygen evolution reaction (OER) plays an important role in evaluating a
photocatalyst and to understand its surface chemistry. In this work we present
a comparative study of the OER on the oxide NaTaO$_3$ (113) surface and the
oxynitride SrTaO$_2$N (001) surface. Oxynitrides are highly promising
photocatalysts due to their smaller band gap and resulting better visible light
absorption compared to oxides but our knowledge about their surface structure
and chemistry is still very limited. With the goal to compare the surface
chemistry of oxides and oxynitrides, we perform density functional theory
calculations to obtain the free energy changes associated with the OER reaction
steps. For the OER at the Ta site of the clean surfaces, our results predict
the rate-limiting step for both materials to be the formation of the *OOH
intermediate, with a larger overpotential for the oxide than the oxynitride
(1.30 V vs 1.01 V). The Na site is found to be more active than the Ta site on
the oxide surface with an OER overpotential of 0.88 V, whereas the OER at the
Sr site on the oxynitride has an overpotential of 1.14 V. For the A sites,
contrary to the Ta site, the deprotonation of *OH was found to be the
rate-limiting step. Computed Pourbaix diagrams show that at relevant
(photo)electrochemical conditions all surfaces are covered with oxygen
adsorbates. Oxygen adsorbates at A (Na, Sr) sites are however found to couple
and desorb as O$_2$, leaving these sites empty under typical operating
conditions. Following this desorption, we find the OER to proceed by the
conventional *OOH mechanism on the SrO termination of the oxynitride but by a
direct coupling of neighbouring *O at Na sites on the oxide surface. This
coupling mechanism on the oxide has the smallest overpotential of 0.79 V
compared to 0.88 V for the oxynitride, implying that the oxide is a better OER
catalyst.
