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. 2023 Feb 15;14:843. doi: 10.1038/s41467-023-36380-9

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© The Author(s) 2023

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. 2 — a Schematics of two OER pathway (AEM and LOM) on the surface of M_0.5Ru_0.5O₂ (110). b The variation of Ru charge in M_0.5Ru_0.5O₂ with an ionic electronegativity of different M. c Theoretical overpotential volcano plot under AEM pathway as a function of the Ru charge. d Projected DOS plots of Ru (d) and O (p) near the Fermi level for M_0.5Ru_0.5O₂. The light gray filling shows the overlap between Ru (d) and O (p). e Variation of O (p) contribution near Fermi level with Ru charge. f Theoretical overpotential plot under LOM pathway as a function of the Ru charge. g The Ru vacancy formation energy (ΔG_VRu) of M_0.5Ru_0.5O₂ is characterized by Ru charge. For RuO₂ and Cr_0.5Ru_0.5O₂, ΔG_VRu were calculated without (transparent dots in yellow and green) and with (opaque dots in yellow and green) the consideration of lattice oxygen vacancies. Source data are provided as a Source Data file.