Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Revisiting the universal principle for the rational design of single-atom electrocatalysts

Abstract

The notion of descriptors has been widely used for assessing structure–activity relationships for many types of heterogenous catalytic reaction, as well as in searching for highly active single-atom catalysts (SACs). Here, with the aid of a machine-learning model for identifying key intrinsic properties of SACs, we revisit our previous descriptor φ [Nat. Catal. 1, 339–348 (2018)] and present φ′ to correlate the activity of graphene-based SACs for the oxygen reduction reaction, oxygen evolution reaction and hydrogen evolution reaction. The descriptor φ′ not only captures the activity trend among experimentally reported SACs, but can also help with the search for SACs to replace precious-metal-based commercial catalysts (for example Pt/C and IrO2), including Fe-pyridine/pyrrole-4N for the oxygen reduction reaction and Co-pyridine/pyrrole-4N for the oxygen evolution reaction (discovered in previous experimental studies). More importantly, we show that the descriptor φ′ can be broadly applicable to correlate SACs embedded in small-, mid- and large-sized macrocyclic complexes, so long as the active metal centre has the same local coordination environment.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Schematic of graphene-supported SACs.
Fig. 2: Machine-learning model to correlate ΔGOH*GH*.
Fig. 3: ΔGOH* and ΔGH* versus structural descriptors φOH and φH, respectively.
Fig. 4: Electrocatalytic activity versus structural descriptor φ′.
Fig. 5: Schematic of SACs embedded in small-, mid- and large-sized macrocyclic complexes.
Fig. 6: Extension of structural descriptor φ' to SACs embedded in macrocycle complexes.

Similar content being viewed by others

Data availability

The optimized structures of graphene-supported SACs and SACs embedded in small-/mid-/large-sized macrocycles are provided in https://github.com/LEDlamar/chem. The data reported in this article are available in the paper and Supplementary Information. Additional data related to this study may be requested from the corresponding authors. Source data are provided with this paper.

References

  1. Qiao, B. et al. Single-atom catalysis of CO oxidation using Pt1/FeOx. Nat. Chem. 3, 634–641 (2011).

    Article  CAS  PubMed  Google Scholar 

  2. Zhang, F. et al. Noble metal single-atoms in thermocatalysis, electrocatalysis, and photocatalysis. Energy Environ. Sci. 14, 2954–3009 (2021).

    Article  CAS  Google Scholar 

  3. Zhao, C.-X., Li, B.-Q., Liu, J.-N. & Zhang, Q. Intrinsic electrocatalytic activity regulation of M–N–C single-atom catalysts for the oxygen reduction reaction. Angew. Chem. Int. Ed. 60, 4448–4463 (2021).

    Article  CAS  Google Scholar 

  4. Zhuo, H.-Y. et al. Theoretical understandings of graphene-based metal single-atom catalysts: stability and catalytic performance. Chem. Rev. 120, 12315–12341 (2020).

    Article  CAS  PubMed  Google Scholar 

  5. Nørskov, J. K., Bligaard, T., Rossmeisl, J. & Christensen, C. H. Towards the computational design of solid catalysts. Nat. Chem. 1, 37–46 (2009).

    Article  PubMed  Google Scholar 

  6. Zhao, Z.-J. et al. Theory-guided design of catalytic materials using scaling relationships and reactivity descriptors. Nat. Rev. Mater. 4, 792–804 (2019).

    Article  ADS  Google Scholar 

  7. Wang, Y. et al. Adsorption-energy-based activity descriptors for electrocatalysts in energy storage applications. Natl Sci. Rev. 5, 327–341 (2017).

    Article  Google Scholar 

  8. Xu, H., Cheng, D., Cao, D. & Zeng, X. C. A universal principle for a rational design of single-atom electrocatalysts. Nat. Catal. 1, 339–348 (2018).

    Article  CAS  Google Scholar 

  9. Xiao, B. B. et al. Design of effective graphene with the TM/O moiety for the oxygen electrode reaction. ACS Appl. Energy Mater. 3, 260–267 (2020).

    Article  CAS  Google Scholar 

  10. Li, X. et al. Single Ir atom anchored in pyrrolic-N4 doped graphene as a promising bifunctional electrocatalyst for the ORR/OER: a computational study. J. Colloid Interface Sci. 607, 1005–1013 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  11. Yan, T., Li, X., Li, Z. & Zhao, J. Rationally designed metal–N–C/MoS2 heterostructures as bifunctional oxygen electrocatalysts: a computational study. Appl. Surf. Sci. 606, 154969 (2022).

    Article  CAS  Google Scholar 

  12. Dong, K. et al. Electrochemical two-electron O2 reduction reaction toward H2O2 production: using cobalt porphyrin decorated carbon nanotubes as a nanohybrid catalyst. J. Mater. Chem. A 9, 26019–26027 (2021).

    Article  CAS  Google Scholar 

  13. Liu, S. S., Huang, Q. Y., Wang, L. L., Song, E. H. & Xiao, B. B. Boosting hydrogen evolution activity of transition metal-nitrogen embedded graphene through introducing secondary transition metal. Surf. Interfaces 29, 101714 (2022).

    Article  CAS  Google Scholar 

  14. Xu, X., Xu, H. & Cheng, D. Design of high-performance MoS2 edge supported single-metal atom bifunctional catalysts for overall water splitting via a simple equation. Nanoscale 11, 20228–20237 (2019).

    Article  CAS  PubMed  Google Scholar 

  15. Li, X., Jiao, D., Liang, Y. & Zhao, J. A NiN3-embedded MoS2 monolayer as a promising electrocatalyst with high activity for the oxygen evolution reaction: a computational study. Sustain. Energy Fuels 5, 3330–3339 (2021).

    Article  CAS  Google Scholar 

  16. Qin, Z., Wang, Z. & Zhao, J. Computational screening of single-atom catalysts supported by VS2 monolayers for electrocatalytic oxygen reduction/evolution reactions. Nanoscale 14, 6902–6911 (2022).

    Article  CAS  PubMed  Google Scholar 

  17. Qin, Z. & Zhao, J. 1 T-MoSe2 monolayer supported single Pd atom as a highly-efficient bifunctional catalyst for ORR/OER. J. Colloid Interface Sci. 605, 155–162 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  18. Niu, H. et al. Single-atom rhodium on defective g-C3N4: a promising bifunctional oxygen electrocatalyst. ACS Sustain. Chem. Eng. 9, 3590–3599 (2021).

    Article  CAS  Google Scholar 

  19. Sun, C. et al. Atomic-level design of active site on two-dimensional MoS2 toward efficient hydrogen evolution: experiment, theory, and artificial intelligence modelling. Adv. Funct. Mater. 32, 2206163 (2022).

    Article  MathSciNet  CAS  Google Scholar 

  20. Li, S.-L., Kan, X., Gan, L.-Y., Fan, J. & Zhao, Y. Designing efficient single-atomic catalysts for bifunctional oxygen electrocatalysis via a general two-step strategy. Appl. Surf. Sci. 556, 149779 (2021).

    Article  CAS  Google Scholar 

  21. Zeng, H. et al. Single atoms on a nitrogen-doped boron phosphide monolayer: a new promising bifunctional electrocatalyst for ORR and OER. ACS Appl. Mater. Interfaces 12, 52549–52559 (2020).

    Article  CAS  PubMed  Google Scholar 

  22. Wang, Y., Zhou, N. & Li, Y. Electrochemical catalytic mechanism of single transition metal atom-embedded BC3 monolayer for oxygen reduction and evolution reactions. Chem. Eng. J. 425, 130631 (2021).

    Article  CAS  Google Scholar 

  23. Zhang, P., Tan, H., Wang, Z., Lyu, L. & Hu, C. Efficient H2O2 dissociation and formation on zinc chalcogenides: a density functional theory study. Appl. Surf. Sci. 616, 156495 (2023).

    Article  CAS  Google Scholar 

  24. Yue, Y. et al. The OER/ORR activities of copper oxyhydroxide series electrocatalysts. Mol. Catal. 537, 112942 (2023).

    Article  CAS  Google Scholar 

  25. Zhang, R. et al. COF-C4N Nanosheets with uniformly anchored single metal sites for electrocatalytic OER: from theoretical screening to target synthesis. Appl. Catal. B 325, 122366 (2023).

    Article  CAS  Google Scholar 

  26. Long, J., Fu, X. & Xiao, J. The rational design of single-atom catalysts for electrochemical ammonia synthesis via a descriptor-based approach. J. Mater. Chem. A 8, 17078–17088 (2020).

    Article  CAS  Google Scholar 

  27. Wang, Y. et al. Theoretical insights into the electroreduction of nitrate to ammonia on graphene-based single-atom catalysts. Nanoscale 14, 10862–10872 (2022).

    Article  CAS  PubMed  Google Scholar 

  28. Guo, H. et al. Theoretical investigation on the single transition metal atom-decorated defective MoS2 for electrocatalytic ammonia synthesis. ACS Appl. Mater. Interfaces 11, 36506–36514 (2019).

    Article  CAS  PubMed  Google Scholar 

  29. Chen, Y., Zhang, X., Qin, J. & Liu, R. Taming the challenges of activity and selectivity in catalysts for electrochemical N2 fixation via single metal atom supported on WS2. Appl. Surf. Sci. 571, 151357 (2022).

    Article  CAS  Google Scholar 

  30. Nong, W. et al. Designing C3N-supported single atom catalysts for efficient nitrogen reduction based on descriptor of catalytic activity. Carbon 182, 297–306 (2021).

    Article  CAS  Google Scholar 

  31. Hou, P. et al. Computational screening and catalytic origin of transition metal supported on g-t-C3N4 as single-atom catalysts for nitrogen reduction reaction. Appl. Surf. Sci. 599, 153880 (2022).

    Article  CAS  Google Scholar 

  32. Liu, J., Wang, Z., Kou, L. & Gu, Y. Mechanism exploration and catalyst design for hydrogen evolution reaction accelerated by density functional theory simulations. ACS Sustain. Chem. Eng. 11, 467–481 (2023).

    Article  CAS  Google Scholar 

  33. Tong, Y., Wang, L., Hou, F., Dou, S. X. & Liang, J. Electrocatalytic oxygen reduction to produce hydrogen peroxide: rational design from single-atom catalysts to devices. Electrochem. Energy Rev. 5, 7 (2022).

    Article  CAS  Google Scholar 

  34. Liu, X. et al. Transition metal atoms anchored on nitrogen-doped α-arsenene as efficient electrocatalysts for nitrogen electroreduction reaction. Int. J. Hydrogen Energy 47, 29781–29793 (2022).

    Article  CAS  Google Scholar 

  35. Dong, S. et al. MgH2/single-atom heterojunctions: effective hydrogen storage materials with facile dehydrogenation. J. Mater. Chem. A 10, 19839–19851 (2022).

    Article  CAS  Google Scholar 

  36. Dong, J., Gao, Z., Yang, W., Li, A. & Ding, X. Adsorption characteristics of Co-anchored different graphene substrates toward O2 and NO molecules. Appl. Surf. Sci. 480, 779–791 (2019).

    Article  ADS  CAS  Google Scholar 

  37. Gao, Z. et al. On the adsorption of elemental mercury on single-atom TM (TM = V, Cr, Mn, Co) decorated graphene substrates. Appl. Surf. Sci. 516, 146037 (2020).

    Article  CAS  Google Scholar 

  38. Ge, B., Wei, F., Wan, Q., Yuan, P. & Lin, S. Design of catalysts for selective hydrogenation of acrylonitrile via confining single metal atoms within a C2N framework. J. Phys. Chem. C 126, 10053–10060 (2022).

    Article  CAS  Google Scholar 

  39. Wang, J. et al. Screening of transition-metal single-atom catalysts anchored on covalent–organic frameworks for efficient nitrogen fixation. ACS Appl. Mater. Interfaces 14, 1024–1033 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  40. Guo, M., Ji, M. & Cui, W. Theoretical investigation of HER/OER/ORR catalytic activity of single atom-decorated graphyne by DFT and comparative DOS analyses. Appl. Surf. Sci. 592, 153237 (2022).

    Article  CAS  Google Scholar 

  41. Wang, X., Zhang, Q. & Zhou, J. Computational screening of highly selective and active electrocatalytic nitrogen reduction on single-atom-embedded artificial holey SnN3 monolayers. J. Colloid Interface Sci. 610, 546–556 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  42. Xu, R. et al. High-throughput screening of transition metal doping and defect engineering on single layer SnS2 for the water splitting hydrogen evolution reaction. J. Mater. Chem. A 10, 21315–21326 (2022).

    Article  CAS  Google Scholar 

  43. Fu, Z., Wu, M., Li, Q., Ling, C. & Wang, J. A simple descriptor for the nitrogen reduction reaction over single atom catalysts. Mater. Horiz. 10, 852–858 (2023).

    Article  CAS  PubMed  Google Scholar 

  44. Peng, Q., Zhou, J., Chen, J., Zhang, T. & Sun, Z. Cu single atoms on Ti2CO2 as a highly efficient oxygen reduction catalyst in a proton exchange membrane fuel cell. J. Mater. Chem. A 7, 26062–26070 (2019).

    Article  CAS  Google Scholar 

  45. Qi, L., Gao, W. & Jiang, Q. Effective descriptor for designing high-performance catalysts for the hydrogen evolution reaction. J. Phys. Chem. C 124, 23134–23142 (2020).

    Article  CAS  Google Scholar 

  46. Zhao, C., Gao, W. & Jiang, Q. Scheme for screening O2 reduction electrocatalysts: from pure metals and alloys to single-atom catalysts. J. Phys. Chem. C 124, 25412–25420 (2020).

    Article  CAS  Google Scholar 

  47. Xiao, Y. et al. Electrocatalytic biomass upgrading of furfural using transition-metal borides via density functional theory investigation. Small 19, 2205876 (2023).

    Article  CAS  Google Scholar 

  48. Chen, D. et al. Transition metal–N4 embedded black phosphorus carbide as a high-performance bifunctional electrocatalyst for ORR/OER. Nanoscale 12, 18721–18732 (2020).

    Article  CAS  PubMed  Google Scholar 

  49. Huang, H.-C. et al. Rational design of an efficient descriptor for single-atom catalysts in the hydrogen evolution reaction. J. Mater. Chem. A 8, 9202–9208 (2020).

    Article  CAS  Google Scholar 

  50. Ran, N. et al. Bond electronegativity as hydrogen evolution reaction catalyst descriptor for transition metal (TM = Mo, W) dichalcogenides. Chem. Mater. 32, 1224–1234 (2020).

    Article  CAS  Google Scholar 

  51. Xi, C. et al. A bond-energy-integrated-based descriptor for high-throughput screening of transition metal catalysts. J. Phys. Chem. C 124, 5241–5247 (2020).

    Article  CAS  Google Scholar 

  52. Wu, L., Guo, T. & Li, T. Rational design of transition metal single-atom electrocatalysts: a simulation-based, machine learning-accelerated study. J. Mater. Chem. A 8, 19290–19299 (2020).

    Article  CAS  Google Scholar 

  53. Wang, J., Zheng, M., Zhao, X. & Fan, W. Structure-performance descriptors and the role of the axial oxygen atom on M–N4–C single-atom catalysts for electrochemical CO2 reduction. ACS Catal. 12, 5441–5454 (2022).

    Article  CAS  Google Scholar 

  54. Zheng, T., Han, X., Wang, J. & Xia, Z. Role of heteroatom-doping in enhancing catalytic activities and the stability of single-atom catalysts for oxygen reduction and oxygen evolution reactions. Nanoscale 14, 16286–16294 (2022).

    Article  CAS  PubMed  Google Scholar 

  55. Wang, J., Xu, H., Che, C., Zhu, J. & Cheng, D. Rational design of PdAg catalysts for acetylene selective hydrogenation via structural descriptor-based screening strategy. ACS Catal. 13, 433–444 (2023).

    Article  CAS  Google Scholar 

  56. Zhou, X. et al. Curvature effects on the bifunctional oxygen catalytic performance of single atom metal–N–C. Nanoscale 15, 2276–2284 (2023).

    Article  CAS  PubMed  Google Scholar 

  57. Gong, L. et al. Catalytic mechanisms and design principles for single-atom catalysts in highly efficient CO2 conversion. Adv. Energy Mater. 9, 1902625 (2019).

    Article  CAS  Google Scholar 

  58. Ren, C. et al. A universal descriptor for complicated interfacial effects on electrochemical reduction reactions. J. Am. Chem. Soc. 144, 12874–12883 (2022).

    Article  CAS  PubMed  Google Scholar 

  59. Wu, L., Guo, T. & Li, T. Data-driven high-throughput rational design of double-atom catalysts for oxygen evolution and reduction. Adv. Funct. Mater. 32, 2203439 (2022).

    Article  CAS  Google Scholar 

  60. Di Liberto, G., Cipriano, L. A. & Pacchioni, G. Universal principles for the rational design of single atom electrocatalysts? Handle with care. ACS Catal. 12, 5846–5856 (2022).

    Article  Google Scholar 

  61. Chen, Y. et al. Atomic Fe dispersed on N-doped carbon hollow nanospheres for high-efficiency electrocatalytic oxygen reduction. Adv. Mater. 31, 1806312 (2019).

    Article  Google Scholar 

  62. Liu, Q. et al. Sequential synthesis and active-site coordination principle of precious metal single-atom catalysts for oxygen reduction reaction and PEM fuel cells. Adv. Energy Mater. 10, 2000689 (2020).

    Article  CAS  Google Scholar 

  63. Cui, X. et al. Pyridinic-nitrogen-dominated graphene aerogels with Fe–N–C coordination for highly efficient oxygen reduction reaction. Adv. Funct. Mater. 26, 5708–5717 (2016).

    Article  CAS  Google Scholar 

  64. Wang, J. et al. Turning on Zn 4s electrons in a N2-Zn-B2 configuration to stimulate remarkable ORR performance. Angew. Chem. Int. Ed. 133, 183–187 (2021).

    Article  ADS  Google Scholar 

  65. Jia, Y. et al. Tailoring the electronic structure of an atomically dispersed zinc electrocatalyst: coordination environment regulation for high selectivity oxygen reduction. Angew. Chem. Int. Ed. 134, e202110838 (2022).

    Article  ADS  Google Scholar 

  66. Luo, E. et al. Single-atom Cr−N4 sites designed for durable oxygen reduction catalysis in acid media. Angew. Chem. Int. Ed. 58, 12469–12475 (2019).

    Article  CAS  Google Scholar 

  67. Yi, J. D. et al. Atomically dispersed iron–nitrogen active sites within porphyrinic triazine-based frameworks for oxygen reduction reaction in both alkaline and acidic media. ACS Energy Lett. 3, 883–889 (2018).

    Article  CAS  Google Scholar 

  68. Yang, L. et al. Unveiling the high-activity origin of single-atom iron catalysts for oxygen reduction reaction. Proc. Natl Acad. Sci. USA 115, 6626–6631 (2018).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  69. Peng, H. et al. Effect of transition metals on the structure and performance of the doped carbon catalysts derived from polyaniline and melamine for ORR application. ACS Catal. 4, 3797–3805 (2014).

    Article  CAS  Google Scholar 

  70. Zheng, Y. et al. Rational design of common transition metal-nitrogen-carbon catalysts for oxygen reduction reaction in fuel cells. Nano Energy 30, 443–449 (2016).

    Article  CAS  Google Scholar 

  71. Liu, X., Amiinu, I. S., Liu, S., Cheng, K. & Mu, S. Transition metal/nitrogen dual-doped mesoporous graphene-like carbon nanosheets for the oxygen reduction and evolution reactions. Nanoscale 8, 13311–13320 (2016).

    Article  ADS  CAS  PubMed  Google Scholar 

  72. Du, C., Gao, Y., Wang, J. & Chen, W. A new strategy for engineering a hierarchical porous carbon-anchored Fe single-atom electrocatalyst and the insights into its bifunctional catalysis for flexible rechargeable Zn–air batteries. J. Mater. Chem. A 8, 9981–9990 (2020).

    Article  CAS  Google Scholar 

  73. Li, J. et al. A general strategy for preparing pyrrolic-N4 type single-atom catalysts via pre-located isolated atoms. Nat. Commun. 12, 6806 (2021).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  74. Wang, K. et al. Modulation of ligand fields in a single-atom site by the molten salt strategy for enhanced oxygen bifunctional activity for zinc–air batteries. ACS Nano 16, 11944–11956 (2022).

    Article  CAS  PubMed  Google Scholar 

  75. Li, T. et al. Cobalt single atom anchored on N-doped carbon nanoboxes as typical single-atom catalysts (SACs) for boosting the overall water splitting. Chem. Eng. J. 458, 141435 (2023).

    Article  ADS  CAS  Google Scholar 

  76. Friedman, J. H. Greedy function approximation: a gradient boosting machine. Ann. Stat. 29, 1189–1232 (2001).

    Article  MathSciNet  Google Scholar 

  77. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    Article  ADS  CAS  Google Scholar 

  78. Kresse, G. & Furthmüller, J. Efficiency of ab initio total-energy calculations for metals and semiconductors using a plane-wave basis set. Comp. Mater. Sci. 6, 15–50 (1996).

    Article  CAS  Google Scholar 

  79. Lin, C.-Y., Zhang, L., Zhao, Z. & Xia, Z. Design principles for covalent organic frameworks as efficient electrocatalysts in clean energy conversion and green oxidizer production. Adv. Mater. 29, 1606635 (2017).

    Article  Google Scholar 

  80. Noerskov, J. K. et al. Trends in the exchange current for hydrogen evolution. J. Electrochem. Soc. 152, J23–J26 (2005).

    Article  Google Scholar 

  81. Nørskov, J. K. et al. Origin of the overpotential for oxygen reduction at a fuel-cell cathode. J. Phys. Chem. B 108, 17886–17892 (2004).

    Article  Google Scholar 

  82. Rossmeisl, J., Qu, Z. W., Zhu, H., Kroes, G. J. & Nørskov, J. K. Electrolysis of water on oxide surfaces. J. Electroanal. Chem. 607, 83–89 (2007).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The Beijing University of Chemical Technology group was supported by the National Key Research and Development Program of China (2019YFA0210300 and 2021YFA1500501).

Author information

Authors and Affiliations

Authors

Contributions

D. Cheng and X.C.Z. conceived the original idea and designed the DFT calculations. H.X. contributed to the DFT calculations. D. Cao analysed the results. All authors wrote the paper and have reviewed, discussed and approved the results and conclusions of this Article.

Corresponding authors

Correspondence to Daojian Cheng, Dapeng Cao or Xiao Cheng Zeng.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Catalysis thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Note 1, Tables 1–75 and Figs. 1–12.

Supplementary Data 1

The atomic coordinates of the optimized structural models.

Source data

Source Data Fig. 2

Statistical Source Data.

Source Data Fig. 3

Statistical Source Data.

Source Data Fig. 4

Statistical Source Data.

Source Data Fig. 6

Statistical Source Data.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, H., Cheng, D., Cao, D. et al. Revisiting the universal principle for the rational design of single-atom electrocatalysts. Nat Catal 7, 207–218 (2024). https://doi.org/10.1038/s41929-023-01106-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41929-023-01106-z

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing