Abstract
Reticular frameworks are crystalline porous materials that form via the self-assembly of molecular building blocks in different topologies, with many having desirable properties for gas storage, separation, catalysis, biomedical applications and so on. The notable variety of building blocks makes reticular chemistry both promising and challenging for prospective materials design. Here we propose an automated nanoporous materials discovery platform powered by a supramolecular variational autoencoder for the generative design of reticular materials. We demonstrate the automated design process with a class of metal–organic framework (MOF) structures and the goal of separating carbon dioxide from natural gas or flue gas. Our model shows high fidelity in capturing MOF structural features. We show that the autoencoder has a promising optimization capability when jointly trained with multiple top adsorbent candidates identified for superior gas separation. MOFs discovered here are strongly competitive against some of the best-performing MOFs/zeolites ever reported.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 digital issues and online access to articles
$119.00 per year
only $9.92 per issue
Rent or buy this article
Prices vary by article type
from$1.95
to$39.95
Prices may be subject to local taxes which are calculated during checkout




Similar content being viewed by others
Data availability
Data for the training of the SmVAE including the augmented two million MOF set and the tabulated textural and gas-separation property data for the randomly selected MOF structures are available at https://github.com/zhenpengyao/Supramolecular_VAE/tree/master/data.
Code availability
Code for the SmVAE is available at https://doi.org/10.24433/CO.8185164.v1.
References
Yaghi, O. M. et al. Reticular synthesis and the design of new materials. Nature 423, 705–714 (2003).
Li, H., Eddaoudi, M., Groy, T. L. & Yaghi, O. M. Establishing microporosity in open metal–organic frameworks: gas sorption isotherms for Zn(BDC) (BDC = 1,4-benzenedicarboxylate). J. Am. Chem. Soc. 120, 8571–8572 (1998).
Mason, J. A. et al. Methane storage in flexible metal–organic frameworks with intrinsic thermal management. Nature 527, 357–361 (2015).
Chen, K.-J. et al. Synergistic sorbent separation for one-step ethylene purification from a four-component mixture. Science 366, 241–246 (2019).
Nugent, P. et al. Porous materials with optimal adsorption thermodynamics and kinetics for CO2 separation. Nature 495, 80–84 (2013).
Diercks, C. S., Liu, Y., Cordova, K. E. & Yaghi, O. M. The role of reticular chemistry in the design of CO2 reduction catalysts. Nat. Mater. 17, 301–307 (2018).
Hu, Z., Deibert, B. J. & Li, J. Luminescent metal–organic frameworks for chemical sensing and explosive detection. Chem. Soc. Rev. 43, 5815–5840 (2014).
Sheberla, D. et al. Conductive MOF electrodes for stable supercapacitors with high areal capacitance. Nat. Mater. 16, 220–224 (2017).
Tan, L. L. et al. Stimuli-responsive metal-organic frameworks gated by pillar[5]arene supramolecular switches. Chem. Sci. 6, 1640–1644 (2015).
Li, M., Li, D., O’Keeffe, M. & Yaghi, O. M. Topological analysis of metal-organic frameworks with polytopic linkers and/or multiple building units and the minimal transitivity principle. Chem. Rev. 114, 1343–1370 (2014).
Kirkpatrick, P. & Ellis, C. Chemical space. Nature 432, 823 (2004).
Wilmer, C. E. et al. Large-scale screening of hypothetical metal–organic frameworks. Nat. Chem. 4, 83–89 (2012).
Boyd, P. G. et al. Data-driven design of metal–organic frameworks for wet flue gas CO2 capture. Nature 576, 253–256 (2019).
Collins, S. P., Daff, T. D., Piotrkowski, S. S. & Woo, T. K. Materials design by evolutionary optimization of functional groups in metal-organic frameworks. Sci. Adv. 2, e1600954 (2016).
Chung, Y. G. et al. In silico discovery of metal–organic frameworks for precombustion CO2 capture using a genetic algorithm. Sci. Adv. 2, e1600909 (2016).
Fernandez, M., Boyd, P. G., Daff, T. D., Aghaji, M. Z. & Woo, T. K. Rapid and accurate machine learning recognition of high performing metal organic frameworks for CO2 capture. J. Phys. Chem. Lett. 5, 3056–3060 (2014).
Moghadam, P. Z. et al. Structure–mechanical stability relations of metal–organic frameworks via machine learning. Matter 1, 219–234 (2019).
Raccuglia, P. et al. Machine-learning-assisted materials discovery using failed experiments. Nature 533, 73–76 (2016).
Kingma, D. P. & Welling, M. Auto-encoding variational Bayes. In 2nd International Conference on Learning Representations, ICLR 2014—Conference Track Proceedings (International Conference on Learning Representations, 2014).
Goodfellow, I. J. et al. Generative adversarial networks. Preprint at https://arxiv.org/abs/1406.2661 (2014).
Sanchez-Lengeling, B. & Aspuru-Guzik, A. Inverse molecular design using machine learning: generative models for matter engineering. Science 361, 360–365 (2018).
Gómez-Bombarelli, R. et al. Automatic chemical design using a data-driven continuous representation of molecules. ACS Cent. Sci. 4, 268–276 (2018).
Jin, W., Barzilay, R. & Jaakkola, T. Junction tree variational autoencoder for molecular graph generation. In Proc. 35th International Conference on Machine Learning ICML 2018 Vol. 5 3632–3648 (IMLS, 2018).
Noh, J. et al. Inverse design of solid-state materials via a continuous representation. Matter 1, 1370–1384 (2019).
Kim, B., Lee, S. & Kim, J. Inverse design of porous materials using artificial neural networks. Sci. Adv. 6, eaax9324 (2020).
Chung, Y. G. et al. Advances, updates, and analytics for the computation-ready, experimental metal–organic framework database: CoRE MOF 2019. J. Chem. Eng. Data https://doi.org/10.1021/acs.jced.9b00835 (2019).
Duvenaud, D. et al. Convolutional networks on graphs for learning molecular fingerprints. Adv. Neural Inf. Process. Syst. 2, 2224–2232 (2015).
Krenn, M., Hase, F., Nigam, A., Friederich, P. & Aspuru-Guzik, A. Self-referencing embedded strings (SELFIES): a 100% robust molecular string representation. Mach. Learn. Sci. Technol. https://doi.org/10.1088/2632-2153/aba947 (2020).
Li, P. et al. Bottom-up construction of a superstructure in a porous uranium-organic crystal. Science 356, 624–627 (2017).
Jain, A. et al. Commentary: The materials project: a materials genome approach to accelerating materials innovation. APL Mater. 1, 011002 (2013).
Bartók, A. P., Kondor, R. & Csányi, G. On representing chemical environments. Phys. Rev. B 87, (2013).
Isayev, O. et al. Universal fragment descriptors for predicting properties of inorganic crystals. Nat. Commun. 8, 15679 (2017).
Ziletti, A., Kumar, D., Scheffler, M. & Ghiringhelli, L. M. Insightful classification of crystal structures using deep learning. Nat. Commun. 9, 2775 (2018).
Ryan, K., Lengyel, J. & Shatruk, M. Crystal structure prediction via deep learning. J. Am. Chem. Soc. 140, 10158–10168 (2018).
Xie, T. & Grossman, J. C. Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Phys. Rev. Lett. 120, 145301 (2018).
Park, C. W. & Wolverton, C. Developing an improved crystal graph convolutional neural network framework for accelerated materials discovery. Phys. Rev. Mater. 4, 063801 (2020).
Eon, J. G. Topological features in crystal structures: a quotient graph assisted analysis of underlying nets and their embeddings. Acta Crystallogr. A 72, 268–293 (2016).
Delgado-Friedrichs, O., Hyde, S. T., O’Keeffe, M. & Yaghi, O. M. Crystal structures as periodic graphs: the topological genome and graph databases. Struct. Chem. 28, 39–44 (2017).
O’Keeffe, M. & Yaghi, O. M. Deconstructing the crystal structures of metal–organic frameworks and related materials into their underlying nets. Chem. Rev. 112, 675–702 (2012).
Furukawa, H., Kim, J., Ockwig, N. W., O’Keeffe, M. & Yaghi, O. M. Control of vertex geometry, structure dimensionality, functionality, and pore metrics in the reticular synthesis of crystalline metal–organic frameworks and polyhedra. J. Am. Chem. Soc. 130, 11650–11661 (2008).
Bucior, B. J. et al. Identification schemes for metal–organic frameworks to enable rapid search and cheminformatics analysis. Cryst. Growth Des. 19, 6682–6697 (2019).
Anderson, R. & Gómez-Gualdrón, D. A. Increasing topological diversity during computational “synthesis” of porous crystals: how and why. CrystEngComm 21, 1653–1665 (2019).
Ghersi, D. & Singh, M. molBLOCKS: decomposing small molecule sets and uncovering enriched fragments. Bioinformatics 30, 2081–2083 (2014).
Colón, Y. J., Gómez-Gualdrón, D. A. & Snurr, R. Q. Topologically guided, automated construction of metal–organic frameworks and their evaluation for energy-related applications. Cryst. Growth Des. 17, 5801–5810 (2017).
Kingma, D. P. & Welling, M. An introduction to variational autoencoders. Found. Trends Mach. Learn. 12, 307–392 (2019).
Fu, H. et al. Cyclical annealing schedule: a simple approach to mitigating. In Proc. 2019 Conference of the North 240–250 (Association for Computational Linguistics, 2019); https://doi.org/10.18653/v1/N19-1021
Kingma, D. P., Rezende, D. J., Mohamed, S. & Welling, M. Semi-supervised learning with deep generative models. Adv. Neural Inf. Process. Syst. 4, 3581–3589 (2014).
Rasmussen, C. E. & Williams, C. K. I. Gaussian Processes for Machine Learning (MIT Press, 2005); https://doi.org/10.7551/mitpress/3206.001.0001
Deria, P. et al. Ultraporous, water stable, and breathing zirconium-based metal–organic frameworks with ftw topology. J. Am. Chem. Soc. 137, 13183–13190 (2015).
Mondloch, J. E. et al. Vapor-phase metalation by atomic layer deposition in a metal–organic framework. J. Am. Chem. Soc. 135, 10294–10297 (2013).
Li, H., Eddaoudi, M., O’Keeffe, M. & Yaghi, O. M. Design and synthesis of an exceptionally stable and highly porous metal–organic framework. Nature 402, 276–279 (1999).
Gu, Z. Y., Jiang, J. Q. & Yan, X. P. Fabrication of isoreticular metal–organic framework coated capillary columns for high-resolution gas chromatographic separation of persistent organic pollutants. Anal. Chem. 83, 5093–5100 (2011).
Coley, C. W., Rogers, L., Green, W. H. & Jensen, K. F. SCScore: synthetic complexity learned from a reaction corpus. J. Chem. Inf. Model. 58, 252–261 (2018).
Herm, Z. R., Krishna, R. & Long, J. R. CO2/CH4, CH4/H2 and CO2/CH4/H2 separations at high pressures using Mg2(dobdc). Micropor. Mesopor. Mater. 151, 481–487 (2012).
Xiang, S. et al. Microporous metal–organic framework with potential for carbon dioxide capture at ambient conditions. Nat. Commun. 3, 954 (2012).
Mason, J. A., Sumida, K., Herm, Z. R., Krishna, R. & Long, J. R. Evaluating metal–organic frameworks for post-combustion carbon dioxide capture via temperature swing adsorption. Energy Environ. Sci. 4, 3030–3040 (2011).
Cavenati, S., Grande, C. A. & Rodrigues, A. E. Adsorption equilibrium of methane, carbon dioxide, and nitrogen on zeolite 13X at high pressures. J. Chem. Eng. Data 49, 1095–1101 (2004).
Howarth, A. J. et al. Chemical, thermal and mechanical stabilities of metal–organic frameworks. Nat. Rev. Mater. 1, 15018 (2016).
Rieth, A. J., Wright, A. M. & Dincă, M. Kinetic stability of metal–organic frameworks for corrosive and coordinating gas capture. Nat. Rev. Mater. 4, 708–725 (2019).
Willems, T. F., Rycroft, C. H., Kazi, M., Meza, J. C. & Haranczyk, M. Algorithms and tools for high-throughput geometry-based analysis of crystalline porous materials. Micropor. Mesopor. Mater. 149, 134–141 (2012).
Bae, Y. S., Yazayd’n, A. Ö. & Snurr, R. Q. Evaluation of the BET method for determining surface areas of MOFs and zeolites that contain ultra-micropores. Langmuir 26, 5475–5483 (2010).
Biovia, D. S. Materials Studio (San Diego Dassault Systèmes, 2019).
Rappe, A. K., Casewit, C. J., Colwell, K. S., Goddard, W. A. & Skiff, W. M. UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J. Am. Chem. Soc. 114, 10024–10035 (1992).
Collins, S. P. & Woo, T. K. Split-charge equilibration parameters for generating rapid partial atomic charges in metal–organic frameworks and porous polymer networks for high-throughput screening. J. Phys. Chem. C 121, 903–910 (2017).
Campañá, C., Mussard, B. & Woo, T. K. Electrostatic potential derived atomic charges for periodic systems using a modified error functional. J. Chem. Theory Comput. 5, 2866–2878 (2009).
Dubbeldam, D., Calero, S., Ellis, D. E. & Snurr, R. Q. RASPA: molecular simulation software for adsorption and diffusion in flexible nanoporous materials. Mol. Simul. 42, 81–101 (2016).
Martin, M. G. & Siepmann, J. I. Transferable potentials for phase equilibria. 1. United-atom description of n-alkanes. J. Phys. Chem. B 102, 2569–2577 (1998).
Chung, J., Gulcehre, C., Cho, K. & Bengio, Y. Empirical evaluation of gated recurrent neural networks on sequence modeling. Preprint at https://arxiv.org/abs/1412.3555 (2014).
Paszke, A. et al. PyTorch: an imperative style, high-performance deep learning library. Preprint at https://arxiv.org/abs/1912.01703 (2019).
Landrum, G. RDKit: Open-source Cheminformatics Software (RDKit, 2006); http://www.rdkit.org
Hamon, L., Jolimaître, E. & Pirngruber, G. D. CO2 and CH4 separation by adsorption using Cu-BTC metal–organic framework. Ind. Eng. Chem. Res. 49, 7497–7503 (2010).
Liu, H. et al. A hybrid absorption–adsorption method to efficiently capture carbon. Nat. Commun. 5, 5147 (2014).
Millward, A. R. & Yaghi, O. M. Metal–organic frameworks with exceptionally high capacity for storage of carbon dioxide at room temperature. J. Am. Chem. Soc. 127, 17998–17999 (2005).
Li, J., Li, J., Yang, J. & Li, L. Separation of CO2/CH4 and CH4/N2 mixtures using MOF-5 and Cu3(BTC)2. J. Energy Chem. 23, 453–460 (2014).
Myers, A. L. & Prausnitz, J. M. Thermodynamics of mixed‐gas adsorption. AIChE J. 11, 121–127 (1965).
Simon, C. M., Smit, B. & Haranczyk, M. PyIAST: ideal adsorbed solution theory (IAST) Python package. Comp. Phys. Commun. 200, 364–380 (2016).
Acknowledgements
Z.Y., N.S.B., B.J.B., S.G.H.K., O.K.F., R.Q.S. and A.A.-G. were supported as part of the Nanoporous Materials Genome Center by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under award number DE-FG02-17ER16362. Funding for T.B., S.P.C. and T.K.W. were provided by NSERC. Computations were made on the supercomputer ‘beluga’ from École de technologie supérieure, managed by Calcul Québec and Compute Canada. The operation of this supercomputer is funded by the Canada Foundation for Innovation (CFI), the ministère de l’Économie, de la science et de l’innovation du Québec (MESI) and the Fonds de recherche du Québec - Nature et technologies (FRQ-NT). This research was supported in part through the computational resources and staff contributions provided for the Quest high-performance computing facility at Northwestern University, which is jointly supported by the Office of the Provost, the Office for Research, and Northwestern University Information Technology. A.A.-G. is a Canadian Institute for Advanced Research (CIFAR) Lebovic Fellow.
Author information
Authors and Affiliations
Contributions
Z.Y. conceived the overall project. Z.Y. B.J.B. and R.Q.S. designed the reticular framework representation approach. N.S.B. and R.Q.S. conducted the MOF property determination calculations. Z.Y. and B.S.-L. developed the deep learning variational autoencoder. S.P.C., T.B. and T.K.W. did the charge calculations for the framework charges for property simulations. A.A.-G. led the project and provided the overall directions. All authors participated in preparing the manuscript.
Corresponding authors
Ethics declarations
Competing interests
O.K.F. and R.Q.S. have a financial interest in NuMat Technologies, a startup company that is seeking to commercialize MOFs.
Additional information
Peer review information Nature Machine Intelligence thanks Jihan Kim, Joshua Schrier and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Supplementary Information
Supplementary Tables 1–3, Figs. 1–12, structures and reference.
Supplementary Data 1
Crystallographic information file: GMOF-1.cif.
Supplementary Data 2
Crystallographic information file: GMOF-2.cif.
Supplementary Data 3
Crystallographic information file: GMOF-3.cif.
Supplementary Data 4
Crystallographic information file: GMOF-4.cif.
Supplementary Data 5
Crystallographic information file: GMOF-5.cif.
Supplementary Data 6
Crystallographic information file: GMOF-4.cif.
Supplementary Data 7
Crystallographic information file: GMOF-4.cif.
Supplementary Data 8
Crystallographic information file: GMOF-4.cif.
Supplementary Data 9
Crystallographic information file: GMOF-4.cif.
Rights and permissions
About this article
Cite this article
Yao, Z., Sánchez-Lengeling, B., Bobbitt, N.S. et al. Inverse design of nanoporous crystalline reticular materials with deep generative models. Nat Mach Intell 3, 76–86 (2021). https://doi.org/10.1038/s42256-020-00271-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s42256-020-00271-1
This article is cited by
-
Inverse Hamiltonian design by automatic differentiation
Communications Physics (2023)
-
Direct prediction of gas adsorption via spatial atom interaction learning
Nature Communications (2023)
-
CRAFTED: An exploratory database of simulated adsorption isotherms of metal-organic frameworks
Scientific Data (2023)
-
Rapid design of top-performing metal-organic frameworks with qualitative representations of building blocks
npj Computational Materials (2023)
-
A multi-modal pre-training transformer for universal transfer learning in metal–organic frameworks
Nature Machine Intelligence (2023)