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. 2020 Feb 18;11:938. doi: 10.1038/s41467-020-14565-w

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — a The geometric configurations of Mg embedded in graphene framework predominantly existing as single atoms coordinated with different numbers (from 1 to 4) of nitrogen atoms. The green, blue, and gray balls represent metal, N and C atoms, respectively. b Adsorption free energies of OOH as a function of that of OH for models of Mg, Al, and Ca coordinated with different numbers of pyridine nitrogen atoms embedded in graphene matrix. c Adsorption free energies of O versus that of OH for all models. d The two-dimensional volcano map about theoretical onset potential versus adsorption free energies ΔG_OH* and ΔG_OOH* on main group metal cofactors (M–N–C). e The zoomed-in view of the onset potential versus ΔG_OH* in the region close to the performance ceiling of models and transition metal cofactors (TM–N4–C).