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A data-science approach to predict the heat capacity of nanoporous materials


The heat capacity of a material is a fundamental property of great practical importance. For example, in a carbon capture process, the heat required to regenerate a solid sorbent is directly related to the heat capacity of the material. However, for most materials suitable for carbon capture applications, the heat capacity is not known, and thus the standard procedure is to assume the same value for all materials. In this work, we developed a machine learning approach, trained on density functional theory simulations, to accurately predict the heat capacity of these materials, that is, zeolites, metal–organic frameworks and covalent–organic frameworks. The accuracy of our prediction is confirmed with experimental data. Finally, for a temperature swing adsorption process that captures carbon from the flue gas of a coal-fired power plant, we show that for some materials, the heat requirement is reduced by as much as a factor of two using the correct heat capacity.

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Fig. 1: Temperature dependence of the heat capacity of MOF-74.
Fig. 2: Structure/heat-capacity relationships.
Fig. 3: DFT and machine learning predictions of the heat capacity.
Fig. 4: Mapping the heat capacity of nanoporous materials.
Fig. 5: The role of heat capacity in the performance and ranking of porous materials in carbon capture.

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Data availability

Supplementary Information, containing details of the theoretical aspects, machine learning methodology, experimental measurements and process modelling, is available for this paper. In addition, the crystal structures of the training set together with the DFT-optimized geometries and the corresponding calculated thermal properties; tabulated heat capacity of the MOFs in the CoRE-MOF34 and QMOF38 databases, zeolites in IZA36 and COFs in CURATED-COF35 at different temperatures; the data that were used and are needed to reproduce the results of this study, the thermogravimetric analysis, the synthesis protocols, and the powder X-ray diffraction, exported from electronic lab notebooks; and the codes to generate the figures of the paper are deposited on the Materials Cloud51 archive and can be accessed at Correspondence and requests for additional materials should be addressed to the corresponding authors.

Code availability

The featurization, prediction and trained models are available from


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We acknowledge support from the Accelerating Carbon Capture and Sequestration Technologies PrISMa Project (no. 299659), which has received funding through the Accelerating Carbon Capture and Storage Technologies programme (Horizon2020 project no. 294766). We gratefully acknowledge financial contributions made from the Department for Business, Energy & Industrial Strategy together with extra funding from the Natural Environment Research Council and Engineering and Physical Sciences Research Council, United Kingdom; The Research Council of Norway; Swiss Federal Office of Energy; and the United States Department of Energy. We also gratefully acknowledge additional financial support from Total and Equinor. S.M.M. was supported by the Swiss National Science Foundation under grant no. P2ELP2_195155. M.A. was supported by the Swiss National Science Foundation under grant no. P2ELP2_195134. C.C. was supported by the Industrial Strategy Challenge Fund from UK Research and Innovation Industrial Challenge within the UK Industrial Decarbonisation Research and Innovation Centre award no. EP/V027050/1. F.N. acknowledges funding from the European Commission (ERC CoG 772230), the Bundesministerium für Bildung und Forschung (research centre Berlin’s AI competence centre the Berlin Institute for the Foundations of Learning and Data), and the Berlin Mathematics Center MATH+ (AA2-8). The calculations of this work were enabled by the Swiss National Supercomputing Centre under project no. s1019. S.M.M. and B.A.N. thank M. J. Pougin for making the experimental MOF structures computation ready. S.M.M. thanks L. Talirz and M. Sadeghi for fruitful discussions.

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S.M.M., A.H.F., C.C., L.S., S.G. and B.S. formulated the scientific problem and the engineering context. S.M.M. developed the machine learning framework with the help of F.N.; S.M.M., D.O., Ö.K. and A.O.-G. performed the heat capacity calculations. E.M., C.C. and S.G. performed the process modelling. B.A.N. and M.A. synthesized the MOFs and measured the heat capacities. All authors contributed to the analysis and discussion of the results. S.M.M. and B.S. wrote the paper with the contribution of all authors.

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Correspondence to Seyed Mohamad Moosavi or Berend Smit.

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Supplementary Figs. 1–13, Tables 1–3, Discussion and refs. 1–46.

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Moosavi, S.M., Novotny, B.Á., Ongari, D. et al. A data-science approach to predict the heat capacity of nanoporous materials. Nat. Mater. 21, 1419–1425 (2022).

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