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1 DOI: /NCHEM.2507 Quasicrystallinity expressed in two-dimensional coordination networks Authors: José I. Urgel 1, David Écija 2,*, Guoqing Lyu 3, Ran Zhang 3, Carlos-Andres Palma 1, Willi Auwärter 1, Nian Lin 3,* and Johannes V. Barth 1,* Affiliations: 1 Physik Department E20, Technische Universität München, D Garching, Germany 2 IMDEA Nanoscience, Madrid, Spain 3 Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China *Correspondence to: david.ecija@imdea.org, phnlin@ust.hk, jvb@tum.de NATURE CHEMISTRY 1

2 Supplementary Fig. 1 Distinct europium-directed assemblies fabricated on Au(111) by regulating the Eu to linker stoichiometry. a-e, High-resolution STM images. a, Random string network based on threefold coordination, b, Reticular fourfold assembly and c, Random-tiling quasicrystal (V bias = -1.2 V, measured at 300 K). Scale bars: 10 nm. d, Irregular nanoarchitecture including simultaneous expression of threefold and fourfold nodes. e, Mixture of the reticular phase and an elongated triangle tiling tessellation, based on coexisting fourfold and fivefold coordination nodes, respectively. Scale bars: 5 nm. NATURE CHEMISTRY 2

3 Supplementary Fig. 2 Random-tiling quasicrystal. a, Long-range STM image of a dodecagonal randomtiling quasicrystal achieved on Au(111) by depositing qdc species and europium at a 5:2 stoichiometric ratio (V bias = -1.2 V, measured at 300 K). b, Geometrical model of a. The different colors of squares and triangles point out the distinct orientations with respect to the surface of the triangle and square tiles. In white three types of defective nodes are observed. c, Percentage of square and triangular tiling given by their orientation. NATURE CHEMISTRY 3

4 Supplementary Fig. 3 Structural defects in the 2D random-tiling quasicrystal. a, High resolution STM image of a dodecagonal random-tiling quasicrystal (V bias = -1.2 V, measured at 300 K). Scale bar: 4 nm. b, Stick model where typical defects are depicted. D 1, D 2 and D 3, illustrated in green, blue and orange respectively, show the structural imperfections presented in the 2D random-tiling QC. NATURE CHEMISTRY 4

5 Supplementary Fig. 4 Mesoscopic substrate patterning due to the persistence of the reconstruction of Au(111) leading to a mesoscopic chevron pattern. a, High-resolution STM image of qdc species diffusing on Au(111). c, e, g, High-resolution STM images after Eu deposition of fourfold, fivefold and ddqc phases respectively. b, d, f, h, Bluish-black color-code to enhance the presence of the chevron reconstruction. Scanning conditions: V bias = -1.2 V, measured at 300 K. NATURE CHEMISTRY 5

6 Supplementary Fig. 5 Formation of semi-regular tiling domains. a, c, High-resolution STM images of the elongated triangular tiling ( ) and the snub square tiling ( ) domains. b, d, Zoom-in models of the elongated triangular tiling and the snub square tiling respectively. Colored squares and triangles represent the and the unit cells. Scanning conditions: V bias = -1.2 V, measured at 300 K. NATURE CHEMISTRY 6

7 DOI: /NCHEM Supplementary Fig. 6 Dodecagonal symmetry of a nanoporous 2D metal-organic coordination network with random-tiling quasicrystal characteristics. a, Large scale STM image of the quasicrystalline MOCN engineered on Au(111) by depositing qdc and europium at a 5:2 stoichiometric ratio (Vbias = -1.2 V, measured at 300 K). b, Ball-and-stick model of a. c, FFT of b, revealing spots on four rings, where the third ring (yellow circles) is a contribution of the molecular linkers. d, Ball model of a. e, FFT of d, presenting three rings attributed to the presence of the atomic europium nodes (balls). f, Stick model of a. g, FFT of f, exhibiting three rings, assigned to the contribution of the molecular linkers (sticks). Red, green, yellow and blue circles represent the first, second, third and fourth ring. Scale bar = 0.84 nm NATURE CHEMISTRY 7

8 Supplementary Fig. 7 Bond orientational order radial distribution function G bond (r), defined as the sum of exp(i( θ)) normalized by the number of molecules within the radius r (see ref. 45, Nature 506, , 2014). θ is the linker s difference in angles respect to an arbitrary vector. G bond (r) is finite as expected for a quasicrystalline system featuring orientational order. NATURE CHEMISTRY 8

9 Supplementary Fig. 8 Metal-organic nanoarchitectures obtained by depositing qdc and Eu on Ag(111) at specific stoichiometric ratios. a, High-resolution STM image showing a fourfold reticular assembly. b, Highresolution STM image showing a fivefold snub-square tiling assembly. a-b, Scanning conditions: V bias = -1.2 V, measured at 300 K. Scale bar: 6 nm. NATURE CHEMISTRY 9