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Self-assembly of tetravalent Goldberg polyhedra from 144 small components

Nature volume 540, pages 563566 (22 December 2016) | Download Citation

Abstract

Rational control of the self-assembly of large structures is one of the key challenges in chemistry1,2,3,4,5,6,7,8,9, and is believed to become increasingly difficult and ultimately impossible as the number of components involved increases. So far, it has not been possible to design a self-assembled discrete molecule made up of more than 100 components. Such molecules—for example, spherical virus capsids10—are prevalent in nature, which suggests that the difficulty in designing these very large self-assembled molecules is due to a lack of understanding of the underlying design principles. For example, the targeted assembly of a series of large spherical structures containing up to 30 palladium ions coordinated by up to 60 bent organic ligands11,12,13,14,15,16 was achieved by considering their topologies17. Here we report the self-assembly of a spherical structure that also contains 30 palladium ions and 60 bent ligands, but belongs to a shape family that has not previously been observed experimentally17. The new structure consists of a combination of 8 triangles and 24 squares, and has the symmetry of a tetravalent Goldberg polyhedron18,19. Platonic and Archimedean solids have previously been prepared through self-assembly, as have trivalent Goldberg polyhedra, which occur naturally in the form of virus capsids20 and fullerenes21. But tetravalent Goldberg polyhedra have not previously been reported at the molecular level, although their topologies have been predicted using graph theory. We use graph theory to predict the self-assembly of even larger tetravalent Goldberg polyhedra, which should be more stable, enabling another member of this polyhedron family to be assembled from 144 components: 48 palladium ions and 96 bent ligands.

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Acknowledgements

This work was supported by the JST–PRESTO programme and the ACCEL programme, and partly supported by KAKENHI (25102007). The synchrotron X-ray crystallography was performed at the BL38B1 and BL41XU beamlines at SPring-8 (2014A0042 and 2015B0120); preliminarily experiments were performed at the BL-1A beamline at KEK PF (2015G097). We thank M. Kotani and M. Tagami for providing us with mathematical discussion (see Methods) and references (refs 26, 27, 28).

Author information

Affiliations

  1. Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

    • Daishi Fujita
    • , Yoshihiro Ueda
    •  & Makoto Fujita
  2. PRESTO (Precursory Research for Embryonic Science and Technology), Japan Science and Technology Agency, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

    • Daishi Fujita
  3. ACCEL, Japan Science and Technology Agency, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

    • Daishi Fujita
    • , Yoshihiro Ueda
    •  & Makoto Fujita
  4. Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan

    • Sota Sato
  5. ERATO, Japan Science and Technology Agency, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan

    • Sota Sato
  6. Japan Synchrotron Radiation Research Institute (JASRI), SPring-8, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan

    • Nobuhiro Mizuno
    •  & Takashi Kumasaka

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Contributions

D.F. and Y.U. performed and analysed the experiments. D.F. and S.S. worked on the preliminary X-ray diffraction analysis. N.M. and T.K. finalized the X-ray data. D.F. built the mathematical discussion. D.F. and M.F. wrote the paper. D.F. and M.F. designed and supervised the research project.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Daishi Fujita or Makoto Fujita.

Reviewer Information Nature thanks F. Beuerle, P. Schwerdtfeger and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Extended data

Supplementary information

Crystallographic information files

  1. 1.

    Supplementary Data 1

    X-ray data of M30L60.

  2. 2.

    Supplementary Data 2

    X-ray data of M48L96.

Videos

  1. 1.

    MEM electron density map of M30L6.

    360° rotating movie of the electron density map.

  2. 2.

    MEM electron density map of M48L96.

    360° rotating movie of the electron density map.

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DOI

https://doi.org/10.1038/nature20771

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