Skip to main content
See More

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.

  • Perspective
  • Published:

System of sequences in multivariate reticular structures

Nature Reviews Materials volume 8, pages 331–340 (2023)Cite this article

Subjects

Abstract

When variance is encountered in reticular structures such as metal–organic frameworks, it occurs as multiple kinds of functionalities bound and distributed in aperiodic lattices. In these multivariate systems, unknown spatial arrangements of functionalities create properties that go beyond those of their simple sum. It is therefore essential that we learn how to recognize, study and use these arrangements, and for this purpose we propose using the concept of sequences. Accordingly, we propose a classification system, outline a method for characterizing sequences and describe the application to self-propelled reticular machines. On a fundamental level, this contribution transforms the chemist’s thinking from the usual ‘make, characterize, use’ protocol of doing chemistry to a discovery routine based on finding correlations between input synthesis parameters and output performance. This approach provides an alternative and widely accessible pathway for determining the properties that the system of sequences confers on multivariate reticular structures.

Access through your institution
Buy or subscribe

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

Access options

Access through your institution

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

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

Fig. 1: Atomic spatial arrangement and sequences in classifying molecules and extended molecular networks.
Fig. 2: Proposed classification of framework multivariation applied to a mixed-metal nanocrystal with a known structure.
Fig. 3: Molecular sorting performed on an N2/CO2/H2O gas mixture by a multivariate MOF-5 framework.
Fig. 4: Multivariate reticular machines at work in suitable conditions.

Similar content being viewed by others

References

  1. Freund, R. et al. 25 years of reticular chemistry. Angew. Chem. Int. Ed. 60, 23946–23974 (2021).

    Article  CAS  Google Scholar 

  2. Jiang, H., Alezi, D. & Eddaoudi, M. A reticular chemistry guide for the design of periodic solids. Nat. Rev. Mater. 6, 466–487 (2021).

    Article  CAS  Google Scholar 

  3. Xu, W. et al. Anisotropic reticular chemistry. Nat. Rev. Mater. 5, 764–779 (2020).

    Article  CAS  Google Scholar 

  4. Deng, H. et al. Multiple functional groups of varying ratios in metal–organic frameworks. Science 327, 846–850 (2010).

    Article  CAS  Google Scholar 

  5. Liu, Q., Cong, H. & Deng, H. Deciphering the spatial arrangement of metals and correlation to reactivity in multivariate metal–organic frameworks. J. Am. Chem. Soc. 138, 13822–13825 (2016).

    Article  CAS  Google Scholar 

  6. Meekel, E. G. & Goodwin, A. L. Correlated disorder in metal–organic frameworks. CrystEngComm 23, 2915–2922 (2021).

    Article  CAS  Google Scholar 

  7. Kong, X. et al. Mapping of functional groups in metal–organic frameworks. Science 341, 882–885 (2013).

    Article  CAS  Google Scholar 

  8. Sue, A. C.-H. et al. Heterogeneity of functional groups in a metal–organic framework displays magic number ratios. Proc. Natl Acad. Sci. USA 112, 5591–5596 (2015).

    Article  CAS  Google Scholar 

  9. Ji, Z., Li, T. & Yaghi, O. M. Sequencing of metals in multivariate metal–organic frameworks. Science 369, 674–780 (2020).

    Article  CAS  Google Scholar 

  10. Furukawa, H., Müller, U. & Yaghi, O. M. ‘Heterogeneity within order’ in metal–organic frameworks. Angew. Chem. Int. Ed. 54, 3417–3430 (2015).

    Article  CAS  Google Scholar 

  11. Xia, Q. et al. Multivariate metal–organic frameworks as multifunctional heterogeneous asymmetric catalysts for sequential reactions. J. Am. Chem. Soc. 139, 8259–8266 (2017).

    Article  CAS  Google Scholar 

  12. Zhai, Q.-G., Bu, X., Mao, C., Zhao, X. & Feng, P. Systematic and dramatic tuning on gas sorption performance in heterometallic metal–organic frameworks. J. Am. Chem. Soc. 138, 2524–2527 (2016).

    Article  CAS  Google Scholar 

  13. Feng, Y., Chen, Q., Jiang, M. & Yao, J. Tailoring the properties of UiO-66 through defect engineering: a review. Ind. Eng. Chem. Res. 58, 17646–17659 (2019).

    Article  CAS  Google Scholar 

  14. Taddei, M. When defects turn into virtues: the curious case of zirconium-based metal–organic frameworks. Coord. Chem. Rev. 343, 1–24 (2017).

    Article  CAS  Google Scholar 

  15. Cadman, L. K. et al. Compositional control of pore geometry in multivariate metal–organic frameworks: an experimental and computational study. Dalton Trans. 45, 4316–4326 (2016).

    Article  CAS  Google Scholar 

  16. Yuan, S. et al. Continuous variation of lattice dimensions and pore sizes in metal–organic frameworks. J. Am. Chem. Soc. 142, 4732–4738 (2020).

    Article  CAS  Google Scholar 

  17. Ehrling, S. et al. Adaptive response of a metal–organic framework through reversible disorder–disorder transitions. Nat. Chem. 13, 568–574 (2021).

    Article  CAS  Google Scholar 

  18. Bennett, T. D., Cheetham, A. K., Fuchs, A. H. & Coudert, F.-X. Interplay between defects, disorder and flexibility in metal–organic frameworks. Nat. Chem. 9, 11–16 (2016).

    Article  Google Scholar 

  19. Islamov, M., Babaei, H. & Wilmer, C. E. Influence of missing linker defects on the thermal conductivity of metal–organic framework HKUST-1. ACS Appl. Mater. Interfaces 12, 56172–56177 (2020).

    Article  CAS  Google Scholar 

  20. Krivovichev, S. V. Which inorganic structures are the most complex? Angew. Chem. Int. Ed. 53, 654–661 (2014).

    Article  CAS  Google Scholar 

  21. Krivovichev, S. V. Structural and topological complexity of zeolites: an information-theoretic analysis. Microporous Mesoporous Mater. 171, 223–229 (2013).

    Article  CAS  Google Scholar 

  22. Simonov, A. & Goodwin, A. L. Designing disorder into crystalline materials. Nat. Rev. Chem. 4, 657–673 (2020).

    Article  CAS  Google Scholar 

  23. Ejsmont, A. et al. Applications of reticular diversity in metal–organic frameworks: an ever-evolving state of the art. Coord. Chem. Rev. 430, 213655 (2021).

    Article  CAS  Google Scholar 

  24. Gándara, F. & Bennett, T. D. Crystallography of metal-organic frameworks. IUCrJ 1, 563–570 (2014).

    Article  Google Scholar 

  25. Ockwig, N. W., Delgado-Friedrichs, O., O’Keeffe, M. & Yaghi, O. M. Reticular chemistry: occurrence and taxonomy of nets and grammar for the design of frameworks. Acc. Chem. Res. 38, 176–182 (2005).

    Article  CAS  Google Scholar 

  26. Zhang, Y.-B. et al. Introduction of functionality, selection of topology, and enhancement of gas adsorption in multivariate metal-organic framework-177. J. Am. Chem. Soc. 137, 2641–2650 (2015).

    Article  CAS  Google Scholar 

  27. Li, S., Chung, Y. G., Simon, C. M. & Snurr, R. Q. High-throughput computational screening of multivariate metal-organic frameworks (MTV-MOFs) for CO2 capture. J. Phys. Chem. Lett. 8, 6135–6141 (2017).

    Article  CAS  Google Scholar 

  28. Drummond, M. L., Cundari, T. R. & Wilson, A. K. Cooperative carbon capture capabilities in multivariate MOFs decorated with amino acid side chains: a computational study. J. Phys. Chem. C 117, 14717–14722 (2013).

    Article  CAS  Google Scholar 

  29. Wu, Y., Duan, H. & Xi, H. Machine learning-driven insights into defects of zirconium metal–organic frameworks for enhanced ethane–ethylene separation. Chem. Mater. 32, 2986–2997 (2020).

    Article  CAS  Google Scholar 

  30. 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).

    Article  CAS  Google Scholar 

  31. Wang, L. J. et al. Synthesis and characterization of metal–organic framework-74 containing 2, 4, 6, 8, and 10 different metals. Inorg. Chem. 53, 5881–5883 (2014).

    Article  CAS  Google Scholar 

  32. Liu, Q., Cong, H. & Deng, H. Deciphering the spatial arrangement of metals and correlation to reactivity in multivariate metal–organic frameworks. J. Am. Chem. Soc. 138, 13822–13825 (2016).

    Article  CAS  Google Scholar 

  33. Feng, L. et al. Imprinted apportionment of functional groups in multivariate metal–organic frameworks. J. Am. Chem. Soc. 141, 14524–14529 (2019).

    Article  CAS  Google Scholar 

  34. Feng, L. et al. Creating hierarchical pores by controlled LinkerThermolysis in multivariate metal–organic frameworks. J. Am. Chem. Soc. 140, 2363–2372 (2018).

    Article  CAS  Google Scholar 

  35. Dodson, R. A., Kalenak, A. P. & Matzger, A. J. Solvent choice in metal–organic framework linker exchange permits microstructural control. J. Am. Chem. Soc. 142, 20806–20813 (2020).

    Article  CAS  Google Scholar 

  36. Schrimpf, W. et al. Chemical diversity in a metal–organic framework revealed by fluorescence lifetime imaging. Nat. Commun. 9:1647, 1–10 (2018).

    Google Scholar 

  37. Fracaroli, A. M. et al. Seven post-synthetic covalent reactions in tandem leading to enzyme-like complexity within metal–organic framework crystals. J. Am. Chem. Soc. 138, 8352–8355 (2016).

    Article  CAS  Google Scholar 

  38. Svane, K. L., Bristow, J. K., Gale, J. D. & Walsh, A. Vacancy defect configurations in the metal-organic framework UiO-66: energetics and electronic structure. J. Mater. Chem. A 6, 8507–8513 (2018).

    Article  CAS  Google Scholar 

  39. Trousselet, F., Archereau, A., Boutin, A. & Coudert, F. X. Heterometallic metal–organic frameworks of MOF-5 and UiO-66 families: insight from computational chemistry. J. Phys. Chem. C 120, 24885–24894 (2016).

    Article  CAS  Google Scholar 

  40. Taddei, M. et al. Mixed-linker UiO-66: structure–property relationships revealed by a combination of high-resolution powder X-ray diffraction and density functional theory calculations. Phys. Chem. Chem. Phys. 19, 1551–1559 (2017).

    Article  CAS  Google Scholar 

  41. Guo, W. et al. Kinetic-controlled formation of bimetallic metal–organic framework hybrid structures. Small 13, 1–8 (2017).

    Google Scholar 

  42. Fukushima, T. et al. Modular design of domain assembly in porous coordination polymer crystals via reactivity-directed crystallization process. J. Am. Chem. Soc. 134, 13341–13347 (2012).

    Article  CAS  Google Scholar 

  43. Shearer, G. C. et al. Tuned to perfection: Ironing out the defects in metal–organic framework UiO-66. Chem. Mater. 26, 4068–4071 (2014).

    Article  CAS  Google Scholar 

  44. Ye, G. et al. Boosting catalytic performance of metal–organic framework by increasing the defects via a facile and green approach. ACS Appl. Mater. Interfaces 9, 34937–34943 (2017).

    Article  CAS  Google Scholar 

  45. Lyu, H., Ji, Z., Wuttke, S. & Yaghi, O. M. Digital reticular chemistry. Chem 6, 2219–2241 (2020).

    Article  CAS  Google Scholar 

  46. Choi, K. M., Na, K., Somorjai, G. A. & Yaghi, O. M. Chemical environment control and enhanced catalytic performance of platinum nanoparticles embedded in nanocrystalline metal–organic frameworks. J. Am. Chem. Soc. 137, 7810–7816 (2015).

    Article  CAS  Google Scholar 

  47. Kotnala, A., Ding, H. & Zheng, Y. Enhancing single-molecule fluorescence spectroscopy with simple and robust hybrid nanoapertures. ACS Photonics 8, 1673–1682 (2021).

    Article  CAS  Google Scholar 

  48. Choi, H.-K. et al. Single-molecule surface-enhanced raman scattering as a probe of single-molecule surface reactions: promises and current challenges. Acc. Chem. Res. 52, 3008–3017 (2019).

    Article  CAS  Google Scholar 

  49. Banerjee, R. et al. High-throughput synthesis of zeolitic imidazolate frameworks and application to CO2 capture. Science 319, 939–943 (2008).

    Article  CAS  Google Scholar 

  50. Viola, R. et al. Operator-assisted harvesting of protein crystals using a universal micromanipulation robot. J. Appl. Crystallogr. 40, 539–545 (2007).

    Article  CAS  Google Scholar 

  51. Moosavi, S. M. et al. Capturing chemical intuition in synthesis of metal–organic frameworks. Nat. Commun. 10, 1–7 (2019).

    Article  Google Scholar 

  52. Raccuglia, P. et al. Machine-learning-assisted materials discovery using failed experiments. Nature 533, 73–76 (2016).

    Article  CAS  Google Scholar 

  53. Butler, K. T., Davies, D. W., Cartwright, H., Isayev, O. & Walsh, A. Machine learning for molecular and materials science. Nature 559, 547–555 (2018).

    Article  CAS  Google Scholar 

  54. Skoulidas, A. I. Molecular dynamics simulations of gas diffusion in metal–organic frameworks: argon in CuBTC. J. Am. Chem. Soc. 126, 1356–1357 (2004).

    Article  CAS  Google Scholar 

  55. Witherspoon, V. J. et al. Combined nuclear magnetic resonance and molecular dynamics study of methane adsorption in M2(dobdc) metal–organic frameworks. J. Phys. Chem. C 123, 12286–12295 (2019).

    Article  CAS  Google Scholar 

  56. Düren, T., Bae, Y. S. & Snurr, R. Q. Using molecular simulation to characterise metal–organic frameworks for adsorption applications. Chem. Soc. Rev. 38, 1237–1247 (2009).

    Article  Google Scholar 

  57. Karlen, S. D. & Garcia-Garibay, M. A. in Molecular Machines (ed. Kelly, T. R.) 179–227 (Springer, 2005).

  58. Gonzalez-Nelson, A., Coudert, F.-X. & van der Veen, M. A. Rotational dynamics of linkers in metal–organic frameworks. Nanomaterials 9, 330 (2019).

    Article  CAS  Google Scholar 

  59. Evans, J. D., Krause, S. & Feringa, B. L. Cooperative and synchronized rotation in motorized porous frameworks: impact on local and global transport properties of confined fluid. Faraday Discuss. 225, 286–300 (2021).

    Article  CAS  Google Scholar 

  60. Vogelsberg, C. S. et al. Ultrafast rotation in an amphidynamic crystalline metal organic framework. Proc. Natl Acad. Sci. USA 114, 13613–13618 (2017).

    Article  CAS  Google Scholar 

  61. Perego, J. et al. Fast motion of molecular rotors in metal–organic framework struts at very low temperatures. Nat. Chem. 12, 845–851 (2020).

    Article  CAS  Google Scholar 

  62. Danowski, W. et al. Unidirectional rotary motion in a metal–organic framework. Nat. Nanotechnol. 14, 488–494 (2019).

    Article  CAS  Google Scholar 

  63. Kistemaker, J. C. M., Štacko, P., Visser, J. & Feringa, B. L. Unidirectional rotary motion in achiral molecular motors. Nat. Chem. 7, 890–896 (2015).

    Article  CAS  Google Scholar 

  64. Koumura, N., Geertsema, E. M., Meetsma, A. & Feringa, B. L. Light-driven molecular rotor: unidirectional rotation controlled by a single stereogenic center. J. Am. Chem. Soc. 122, 12005–12006 (2000).

    Article  CAS  Google Scholar 

  65. Koumura, N., Zijlstra, R. W. J., van Delden, R. A., Harada, N. & Feringa, B. L. Light-driven monodirectional molecular rotor. Nature 401, 152–155 (1999).

    Article  CAS  Google Scholar 

  66. Krause, S. & Feringa, B. L. Towards artificial molecular factories from framework-embedded molecular machines. Nat. Rev. Chem. 4, 550–562 (2020).

    Article  CAS  Google Scholar 

  67. Kolodzeiski, E. & Amirjalayer, S. Collective structural properties of embedded molecular motors in functionalized metal–organic frameworks. Phys. Chem. Chem. Phys. 23, 4728–4735 (2021).

    Article  CAS  Google Scholar 

  68. Terzopoulou, A. et al. Metal−organic frameworks in motion. Chem. Rev. 120, 11175–11193 (2020).

    Article  CAS  Google Scholar 

  69. IUPAC. Compendium of Chemical Terminology 2nd edn (Blackwell, 1997).

  70. Kozak, R., Sologubenko, A. & Steurer, W. Single-phase high-entropy alloys — an overview. Z. Kristallogr. Cryst. Mater. 230, 55–68 (2015).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

S.C. acknowledges the Research Foundation Flanders (FWO) for financial support (grant ID: 12ZV120N), and thanks H.-B. Bürgi and R. Frison for introducing him to the crystallography of correlated disorder. O.M.Y. thanks current and former students whose experiments have helped to shape the ideas presented. C.G., Leopoldina postdoctoral fellow of the German National Academy of Science (LPDS 2019-02), acknowledges the receipt of a fellowship of the Swiss National Science Foundation (P2EZP2-184380). E.P. thanks the Center for NanoScience Munich (CeNS) and the Deutsche Forschungsgemeinschaft (PL 696/4-1) for financial support.

Author information

Author notes

  1. Stefano Canossa

    Present address: Max Planck Institute for Solid State Research, Stuttgart, Germany

Authors and Affiliations

  1. EMAT, Department of Physics, University of Antwerp, Antwerp, Belgium

    Stefano Canossa

  2. Department of Chemistry, Stanford University, Stanford, CA, USA

    Zhe Ji

  3. Department of Chemistry, University of California–Berkeley, Berkeley, CA, USA

    Cornelius Gropp, Zichao Rong & Omar M. Yaghi

  4. Bakar Institute of Digital Materials for the Planet (BIDMaP), Division of Computing, Data Science, and Society, University of California–Berkeley, Berkeley, CA, USA

    Zichao Rong & Omar M. Yaghi

  5. Department of Chemistry and Center for NanoScience, Ludwig-Maximilians-Universität München, Munich, Germany

    Evelyn Ploetz

  6. Ikerbasque, Basque Foundation for Science, Bilbao, Spain

    Stefan Wuttke

  7. Basque Center for Materials, University of the Basque Country, UPV/EHU Science Park, Leioa, Spain

    Stefan Wuttke

  8. Joint UAEU–UC Berkeley Laboratories for Materials Innovations, UAE University, Al Ain, United Arab Emirates

    Omar M. Yaghi

Authors
  1. Stefano Canossa
    View author publications

    Search author on:PubMed Google Scholar

  2. Zhe Ji
    View author publications

    Search author on:PubMed Google Scholar

  3. Cornelius Gropp
    View author publications

    Search author on:PubMed Google Scholar

  4. Zichao Rong
    View author publications

    Search author on:PubMed Google Scholar

  5. Evelyn Ploetz
    View author publications

    Search author on:PubMed Google Scholar

  6. Stefan Wuttke
    View author publications

    Search author on:PubMed Google Scholar

  7. Omar M. Yaghi
    View author publications

    Search author on:PubMed Google Scholar

Contributions

S.C. contributed to writing, supervision, review and editing, and graphics. Z.J., C.G. and Z.R. contributed to writing, review and editing. E.P. and S.W. contributed to review and editing. O.M.Y. contributed to writing, review and editing, and supervision.

Corresponding authors

Correspondence to Stefano Canossa or Omar M. Yaghi.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Reviews Materials thanks Vladislav Blatov, Dariusz Matoga 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.

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

Canossa, S., Ji, Z., Gropp, C. et al. System of sequences in multivariate reticular structures. Nat Rev Mater 8, 331–340 (2023). https://doi.org/10.1038/s41578-022-00482-5

Download citation

  • Accepted:

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1038/s41578-022-00482-5

This article is cited by

Search

Advanced 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