Exploring spin states by hybrid functional methods to define correct trends in electrocatalytic activity of SACs embedded in N-doped graphene

Embedding transition metal atoms in graphene is a promising strategy to make it an effective electrocatalyst for the oxygen evolution (OER) and reduction (ORR) reactions, which are crucial processes for the success of the energy transition. In this regard, theoretical investigations can be valuable complementary tools to experimental work, but only if they are able to adequately describe the system under examination. Transition metal atoms trapped in graphene pose serious challenges due to the presence of strongly correlated d-electrons, which can lead to complex spin configurations to be explored. In this work, by hybrid density functional theory (DFT) calculations we investigated several first-row transition metal atoms embedded in N-doped graphene as potential electrocatalysts for the OER and ORR. A detailed spin-dependent search has been performed to define the lowest energy spin state configurations for all intermediates along the associative path, finding Ni and Fe as the most promising systems for the OER and ORR, based on overpotential values (η) of 0.58 V and 0.52 V, respectively. Interestingly, if the study is limited to low-spin configurations, the resulting overpotential values differ within the range of 0.5 V, changing the order of activity between the various electrocatalytic systems. The most striking case is that of Fe, where according to the low-spin state reaction path it would suggest this to be the worst electrocatalyst for ORR. Thus, this work conveys a very important message and general warning to the community on trusting only data that come from a full spin optimization.