  Inter-site interactions between single atom catalysts (SACs) in the high
loading regime are critical to tuning the catalytic performance. However, the
understanding on such interactions and their distance dependent effects remains
elusive, especially for the heteronuclear SACs. In this study, we reveal the
effects of the distance-dependent inter-site interaction on the catalytic
performance of SACs. Using the density functional theory calculations, we
systematically investigate the heteronuclear iron and cobalt single atoms
co-supported on the nitrogen-doped graphene (FeN4-C and CoN4-C) for oxygen
reduction reaction (ORR). We find that as the distance between Fe and Co SACs
decreases, FeN4-C exhibits a reduced catalytic activity, which can be mitigated
by the presence of an axial hydroxyl ligand, whereas the activity of CoN4-C
shows a volcano-like evolution with the optimum reached at the intermediate
distance. We further unravel that the transition towards the high-spin state
upon adsorption of ORR intermediate adsorbates is responsible for the decreased
activity of both FeN4-C and CoN4-C at short inter-site distance. Such high-spin
state transition is also found to significantly shift the linear relation
between hydroxyl (*OH) and hydroperoxyl (*OOH) adsorbates. These findings not
only shed light on the SAC-specific effect of the distance-dependent inter-site
interaction between heteronuclear SACs, but also pave a way towards shifting
the long-standing linear relations observed in multiple-electron chemical
reactions.
