Skip to main content

Thank you for visiting 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.

Constructing and interpreting volcano plots and activity maps to navigate homogeneous catalyst landscapes


Volcano plots and activity maps are powerful tools for studying homogeneous catalysis. Once constructed, they can be used to estimate and predict the performance of a catalyst from one or more descriptor variables. The relevance and utility of these tools has been demonstrated in several areas of catalysis, with recent applications to homogeneous catalysts having been pioneered by our research group. Both volcano plots and activity maps are built from linear free energy scaling relationships that connect the value of a descriptor variable(s) with the relative energies of other catalytic cycle intermediates/transition states. These relationships must be both constructed and postprocessed appropriately to obtain the resulting plots/maps; this process requires careful execution to obtain meaningful results. In this protocol, we provide a step-by-step guide to building volcano plots and activity maps using curated reaction profile data. The reaction profile data are obtained using density functional theory computations to model the catalytic cycle. In addition, we provide volcanic, a Python code that automates the steps of the process following data acquisition. Unlike the computation of individual reaction energy profiles, our tools lead to a holistic view of homogeneous catalyst performance that can be broadly applied for both explanatory and screening purposes.

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

Access options

Rent or buy this article

Prices vary by article type



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

Fig. 1: General workflow of the procedure.
Fig. 2: Schematic outline of the volcano plot construction process.
Fig. 3: Examples of catalytic processes that have been studied using different variants of the volcano plots.
Fig. 4: Volcano plot study of CO2 hydrogenation with transition metal pincer complexes.
Fig. 5: Volcano plot and activity map study of C–C cross-coupling reactions.

Data availability

All data to reproduce all the figures of this work are available at, as well as instructions to generate such plots using the volcanic package.

Code availability

The volcanic package is available at Supplementary Methods detail the manual procedure for the application highlighted in Fig. 4.


  1. Nørskov, J. K. et al. The nature of the active site in heterogeneous metal catalysis. Chem. Soc. Rev. 37, 2163 (2008).

    PubMed  Google Scholar 

  2. Kulkarni, A., Siahrostami, S., Patel, A. & Nørskov, J. K. Understanding catalytic activity trends in the oxygen reduction reaction. Chem. Rev. 118, 2302–2312 (2018).

    CAS  PubMed  Google Scholar 

  3. Wodrich, M. D., Sawatlon, B., Busch, M. & Corminboeuf, C. The genesis of molecular volcano plots. Acc. Chem. Res. 54, 1107–1117 (2021).

    CAS  PubMed  Google Scholar 

  4. Sabatier, P. Hydrogénations et déshydrogénations par catalyse. Ber. Dtsch. Chem. Ges. 44, 1984–2001 (1911).

    CAS  Google Scholar 

  5. Calle-Vallejo, F., Martı́nez, J. I., Garcı́a-Lastra, J. M., Rossmeisl, J. & Koper, M. T. M. Physical and chemical nature of the scaling relations between adsorption energies of atoms on metal surfaces. Phys. Rev. Lett. 108, 116103 (2012).

    CAS  PubMed  Google Scholar 

  6. Busch, M., Wodrich, M. D. & Corminboeuf, C. Linear scaling relationships and volcano plots in homogeneous catalysis—revisiting the Suzuki reaction. Chem. Sci. 6, 6754–6761 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  7. Bligaard, T. et al. The Brønsted–Evans–Polanyi relation and the volcano curve in heterogeneous catalysis. J. Catal. 224, 206–217 (2004).

    CAS  Google Scholar 

  8. Gerischer, H. Mechanismus der elektrolytischen Wasserstoffabscheidung und Adsorptionsenergie von atomarem Wasserstoff. Bull. Soc. Chim. Belg. 67, 506–527 (2010).

    Google Scholar 

  9. Parsons, R. The rate of electrolytic hydrogen evolution and the heat of adsorption of hydrogen. Trans. Faraday Soc. 54, 1053 (1958).

    CAS  Google Scholar 

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

    PubMed  Google Scholar 

  11. Man, I. C. et al. Universality in oxygen evolution electrocatalysis on oxide surfaces. ChemCatChem 3, 1159–1165 (2011).

    CAS  Google Scholar 

  12. Medford, A. J. et al. From the Sabatier principle to a predictive theory of transition-metal heterogeneous catalysis. J. Catal. 328, 36–42 (2015).

    CAS  Google Scholar 

  13. Medford, A. J. et al. Activity and selectivity trends in synthesis gas conversion to higher alcohols. Top. Catal. 57, 135–142 (2014).

    CAS  Google Scholar 

  14. Andersen, M., Medford, A. J., Nørskov, J. K. & Reuter, K. Analyzing the case for bifunctional catalysis. Angew. Chem. Int. Ed. 55, 5210–5214 (2016).

    CAS  Google Scholar 

  15. Busch, M. et al. Beyond the top of the volcano? A unified approach to electrocatalytic oxygen reduction and oxygen evolution. Nano Energy 29, 126–135 (2016).

    CAS  Google Scholar 

  16. Exner, K. S. Recent advancements towards closing the gap between electrocatalysis and battery science communities: the computational lithium electrode and activity–stability volcano plots. ChemSusChem 12, 2330–2344 (2019).

    CAS  PubMed  Google Scholar 

  17. Anand, M., Rohr, B., Statt, M. J. & Nørskov, J. K. Scaling relationships and volcano plots in homogeneous catalysis. J. Phys. Chem. Lett. 11, 8518–8526 (2020).

    CAS  PubMed  Google Scholar 

  18. Swiegers, G. Mechanical catalysis: Methods of enzymatic, homogeneous, and heterogeneous catalysis. (John Wiley, 2008).

  19. Sues, P. E., Lough, A. J. & Morris, R. H. Stereoelectronic factors in iron catalysis: synthesis and characterization of aryl-substituted iron(II) carbonyl pnnp complexes and their use in the asymmetric transfer hydrogenation of ketones. Organometallics 30, 4418–4431 (2011).

    CAS  Google Scholar 

  20. Meek, S. J., Pitman, C. L. & Miller, A. J. M. Deducing reaction mechanism: a guide for students, researchers, and instructors. J. Chem. Educ. 2, 275–286 (2016).

    Google Scholar 

  21. Fey, N. & Lynam, J. M. Computational mechanistic study in organometallic catalysis: why prediction is still a challenge. WIREs Comput. Mol. Sci. 12, e1590 (2021).

    Google Scholar 

  22. Harvey, J. N., Himo, F., Maseras, F. & Perrin, L. Scope and challenge of computational methods for studying mechanism and reactivity in homogeneous catalysis. ACS Catal. 9, 6803–6813 (2019).

    CAS  Google Scholar 

  23. Ryu, H. et al. Pitfalls in computational modeling of chemical reactions and how to avoid them. Organometallics 37, 3228–3239 (2018).

    CAS  Google Scholar 

  24. Wodrich, M. D., Sawatlon, B., Busch, M. & Corminboeuf, C. On the generality of molecular volcano plots. ChemCatChem 10, 1586–1591 (2018).

    CAS  Google Scholar 

  25. Wodrich, M. D., Busch, M. & Corminboeuf, C. Accessing and predicting the kinetic profiles of homogeneous catalysts from volcano plots. Chem. Sci. 7, 5723–5735 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  26. Kozuch, S. & Shaik, S. How to conceptualize catalytic cycles? The energetic span model. Acc. Chem. Res. 44, 101–110 (2010).

    PubMed  Google Scholar 

  27. Wodrich, M. D., Sawatlon, B., Solel, E., Kozuch, S. & Corminboeuf, C. Activity-based screening of homogeneous catalysts through the rapid assessment of theoretically derived turnover frequencies. ACS Catal. 9, 5716–5725 (2019).

    CAS  Google Scholar 

  28. Wodrich, M. D., Busch, M. & Corminboeuf, C. Expedited screening of active and regioselective catalysts for the hydroformylation reaction. Helv. Chim. Acta 101, e1800107 (2018).

    Google Scholar 

  29. Sawatlon, B., Wodrich, M. D. & Corminboeuf, C. Probing substrate scope with molecular volcanoes. Org. Lett. 22, 7936–7941 (2020).

    CAS  PubMed  Google Scholar 

  30. Meyer, B., Sawatlon, B., Heinen, S., von Lilienfeld, O. A. & Corminboeuf, C. Machine learning meets volcano plots: computational discovery of cross-coupling catalysts. Chem. Sci. 9, 7069–7077 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  31. Sawatlon, B., Wodrich, M. D., Meyer, B., Fabrizio, A. & Corminboeuf, C. Data mining the C–C cross-coupling genome. ChemCatChem 11, 4096–4107 (2019).

    CAS  Google Scholar 

  32. Wodrich, M. D., Fabrizio, A., Meyer, B. & Corminboeuf, C. Data-powered augmented volcano plots for homogeneous catalysis. Chem. Sci. 11, 12070–12080 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  33. Busch, M., Wodrich, M. D. & Corminboeuf, C. A generalized picture of CC cross-coupling. ACS Catal. 7, 5643–5653 (2017).

    CAS  Google Scholar 

  34. Busch, M., Wodrich, M. D. & Corminboeuf, C. Improving the thermodynamic profiles of prospective Suzuki–Miyaura cross-coupling catalysts by altering the electrophilic coupling component. ChemCatChem 10, 1592–1597 (2018).

    CAS  Google Scholar 

  35. Sawatlon, B., Wodrich, M. D. & Corminboeuf, C. Unraveling metal/pincer ligand effects in the catalytic hydrogenation of carbon dioxide to formate. Organometallics 37, 4568–4575 (2018).

    CAS  Google Scholar 

  36. Anand, M. & Nørskov, J. K. Scaling relations in homogeneous catalysis: analyzing the Buchwald–Hartwig amination reaction. ACS Catal. 10, 336–345 (2019).

    Google Scholar 

  37. Das, S., Tobel, B. D., Alonso, M. & Corminboeuf, C. Uncovering the activity of alkaline earth metal hydrogenation catalysis through molecular volcano plots. Top. Catal. 65, 289–295 (2021).

    PubMed  PubMed Central  Google Scholar 

  38. Cordova, M., Wodrich, M. D., Meyer, B., Sawatlon, B. & Corminboeuf, C. Data-driven advancement of homogeneous nickel catalyst activity for aryl ether cleavage. ACS Catal. 10, 7021–7031 (2020).

    CAS  Google Scholar 

  39. Steinmann, S. N. & Corminboeuf, C. A system-dependent density-based dispersion correction. J. Chem. Theory Comput. 6, 1990–2001 (2010).

    CAS  PubMed  Google Scholar 

  40. Steinmann, S. N. & Corminboeuf, C. A density dependent dispersion correction. CHIMIA 65, 240–244 (2011).

    CAS  PubMed  Google Scholar 

  41. Steinmann, S. N. & Corminboeuf, C. Comprehensive benchmarking of a density-dependent dispersion correction. J. Chem. Theory Comput. 7, 3567–3577 (2011).

    CAS  PubMed  Google Scholar 

  42. Klamt, A. The COSMO and COSMO-RS solvation models. WIREs Comput Mol Sci. 8, (2017).

  43. Martin, R. L., Hay, P. J. & Pratt, L. R. Hydrolysis of ferric ion in water and conformational equilibrium. J. Phys. Chem. A 102, 3565–3573 (1998).

    CAS  Google Scholar 

  44. Gallarati, S., Dingwall, P., Fuentes, J. A., Bühl, M. & Clarke, M. L. Understanding catalyst structureselectivity relationships in pd-catalyzed enantioselective methoxycarbonylation of styrene. Organometallics 39, 4544–4556 (2020).

    CAS  Google Scholar 

  45. Frisch, M. J. et al. Gaussian16 Revision C.01. (2016).

  46. te Velde, G. et al. Chemistry with ADF. J. Comp. Chem. 22, 931–967 (2001).

    CAS  Google Scholar 

  47. Neese, F., Wennmohs, F., Becker, U. & Riplinger, C. The ORCA quantum chemistry program package. J. Chem. Phys. 152, 224108 (2020).

    CAS  PubMed  Google Scholar 

  48. Smith, D. G. A. et al. Psi4 1.4: open-source software for high-throughput quantum chemistry. J. Chem. Phys. 152, 184108 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  49. Dennington, R., Keith, T. A. & Millam, J. M. GaussView Version 6. (2019).

  50. Hanwell, M. D. et al. Avogadro: An advanced semantic chemical editor, visualization, and analysis platform. J. Cheminformatics 4, 17 (2012).

    CAS  Google Scholar 

  51. Hunter, J. D. Matplotlib: A 2D graphics environment. Comp. Sci. Eng. 9, 90–95 (2007).

    Google Scholar 

  52. Uhe, A., Kozuch, S. & Shaik, S. Automatic analysis of computed catalytic cycles. J. Comp. Chem. 32, 978–985 (2010).

    Google Scholar 

Download references


The authors are grateful to the EPFL for financial support and computational resources. This publication was created as part of NCCR Catalysis (grant number 180544), a National Centre for Competence in Research funded by the Swiss National Science Foundation (financial support of R.L.). The Swiss National Science Foundation (grant no. 200020-175496) is acknowledged for financial support of S.D. P. Steinbach is acknowledged for his contribution to one of the volcanic modules.

Author information

Authors and Affiliations



All authors contributed to the conceptualization, elaboration of the content and writing of the manuscript.

Corresponding author

Correspondence to Clémence Corminboeuf.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Protocols thanks Xin Hong and the other, anonymous, reviewer(s) 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.

Related Links

Key references using this protocol

Busch, M. et. al. Chem. Sci. 6, 6754–6761 (2015):

Wodrich, M. D. et. al. Chem. Sci. 7, 5723–5735 (2016):

Busch, M., et. al. ACS Catal. 7, 5643–5653 (2017):

Wodrich, M. D. et. al. ChemCatChem 10, 1586–1591 (2018):

Wodrich, M. D. et. al. ACS Catal. 9, 5716–5725 (2019):

Key data used in this protocol

Wodrich, M. D. et. al. Chem. Sci. 7, 5723–5735 (2016):

Busch, M., et. al. ACS Catal. 7, 5643–5653 (2017):

Cordova, M. et. al. ACS Catal. 10, 7021–7031 (2020):

Das, S. et. al. Top. Catal. 65, 289–295 (2022):

Supplementary information

Supplementary Information

Supplementary Methods, Supplementary Figs. 1–5 and Supplementary Table 1.

Rights and permissions

Springer Nature or its licensor 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

Laplaza, R., Das, S., Wodrich, M.D. et al. Constructing and interpreting volcano plots and activity maps to navigate homogeneous catalyst landscapes. Nat Protoc 17, 2550–2569 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


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