Chemical engineering of quasicrystal approximants in lanthanide-based coordination solids

Tessellation of self-assembling molecular building blocks is a promising strategy to design metal-organic materials exhibiting geometrical frustration and ensuing frustrated physical properties. Appearing in two-dimensional quasiperiodic phases, tilings consisting of five-vertex nodes are regarded as approximants for quasicrystals. Unfortunately, these structural motifs are exceedingly rare due to the complications of acquiring five-fold coordination confined to the plane. Lanthanide ions display the sufficient coordinative plasticity, and large ionic radii, to allow their incorporation into irregular molecule-based arrays. We herein present the use of ytterbium(II) as a five-vertex node in a two-dimensional coordination solid, YbI2(4,4′-bipyridine)2.5. The semi-regular Archimedean tessellation structure verges on quasicrystallinity and paves the way for lanthanide-based metal-organic materials with interesting photonic and magnetic properties.

Q uasicrystals are ordered materials lacking translational symmetry 1 , which leads to unique physical properties 2 , including novel magnetic and photonic phenomena [3][4][5] . They exhibit symmetries that are forbidden for any periodic structure, such as the 5-fold rotational symmetry first discovered in an Al-Mn alloy by Shechtman et al. 6 or the 12-fold symmetry in dodecagonal quasicrystals 7 . Dodecagonal symmetry is achieved in a maximally random assembly of squares and triangles linked through four-, five-, and six-vertex nodes 8,9 . Dodecagonal quasicrystallinity has been observed in a plethora of materials including alloys 10,11 , mesoporous silica 12 , nanoparticle superlattices 13 , and copolymers 14 . Notably, all of these quasicrystalline phases have motifs of, or coexist with, domains of periodic tilings of squares and triangles, whose existence was hypothesized by Frank and Kasper 15 , and whose topologies were first introduced by Kepler in Harmonices Mundi in 1619 16 . The tilings of squares and triangles belong to the uniform tessellations of the twodimensional (2D) (Euclidian) plane 17 , where all vertices are identical and the tilings are labeled by the sequence of their surrounding polygons. For instance, six-vertex nodes are found only in the regular triangular tiling (3 6 ; Fig. 1a) containing a single equilateral polygon, whereas five-vertex nodes are part of the snub hexagonal (3 4 .6), elongated triangular (3 3 .4 2 ), and snub square tilings (3 2 .4.3.4; cf. Fig. 1b, e, f). Due to their similarities with the local structure of dodecagonal quasicrystals, crystalline phases with structure motifs of five-vertex semi-regular Archimedean tessellations (ATs) are referred to as quasicrystal approximants 9,12,[18][19][20] . The appearance of approximants suggests the possibility of designing quasicrystallinity by chemical means. The realization of regular tilings in chemistry and nature is ubiquitous. However, of the ATs only the trihexagonal tiling ((3.6) 2 ; cf. Fig. 1c), the kagomé lattice, appears frequently 21 . Notably, ATs in materials have been hailed as a key component for exploring novel photonics applications [22][23][24] and to host peculiar magnetic phenomena, such as frustration [25][26][27][28] , which call for novel synthetic strategies to their authentication. Whereas for intermetallics 29 numerous quasicrystalline approximants have been isolated, ATs have remained almost elusive in metal-organic materials. Reticular coordination chemistry harbors the synthetic handles on controlling dimensionality and topology of metalorganic coordination solids, suitable for targeting complex tessellations. Indeed, applying this strategy resulted in a singular example of a metal-organic quasicrystal consisting of a surface self-assembled array of Eu atom nodes linked by ditopic carbonitrile bridging ligands 7 . This network is reminiscent of a random tiling containing nanoscale motifs of the semi-regular ATs. The flexibility and the large atomic radii of Eu allowed for coordinating up to six ligands in the equatorial plane allowing the formation of local dodecagonal symmetry 7 . Notably, small differences in the preparation conditions led to the formation of prevailing 3 3 .4 2 or 3 2 .4.3.4 tilings, which underlines the close relationship of the periodic approximants with the dodecagonal phase. Accordingly, the assembly of atomic Ce and the same ditopic ligand on a Ag(111) surface lead to the formation of a  20 . Herein, however, the presence of a net charge of the 2D layer could impede the possibilities for further processing of this material for nanostructuring and the nonmagnetic uranyl nodes hinder the exploration of magnetic properties. Similar to uranium, the lanthanide ion series distinguishes itself by a strong propensity to high coordination numbers. In addition, the lanthanide ions exhibit paramount plasticity in their chemical bonding and unique optical and magnetic properties, of immense technological importance, which are not paralleled by any other elements 31 . Motivated by the possibilities to extend these properties to ATs and quasiperiodic materials, we, herein, report a coordination-assembly strategy and the crystallographic characterization of the first example of a lanthanide-based AT in a bulk, molecule-based material.

Results
Structural characterization and description. Numerous examples of first-row transition element-based 2D coordination solids pillared on 4,4′-bipyridine (bipy) and related ditopic, organic ligands are known 32 . Therein, the limiting, prevailing coordination number of six imposes a square (4 4 ; cf. Fig. 1d) tessellation of the 2D plane calling for employment of significantly larger metal ions for the generation of ATs. The tendency to high coordination numbers in di-and trivalent lanthanide (Ln(II/III)) compounds offers the possibility of generating, for instance, [LnI 2 (pyridine) 5 ] +/0 (Ln = Lu 33 , Sm 34 ). Notably, these systems closely resemble a local D 5h coordination geometry of the Ln(II/ III) with the organic ligands placed in the equatorial plane, presumably directed by the space-filling, axial iodide ligands. Translating this structure-directing motif to 2D coordination solids seems key for tailoring metal-organic ATs and quasicrystals. Indeed, the self-assembly reaction of ytterbium(II) iodide with bipy in acetonitrile at room temperature under strictly anaerobic conditions yielded dark blue, block-shaped crystals of YbI 2 (bipy) 2.5 ·1.5 CH 3 CN (1) suitable for single-crystal X-ray diffraction analysis. Compound 1 crystallizes in the triclinic space group P 1 hosting a single Yb in the asymmetric unit ( Fig. 2 and Supplementary Fig. 1). The {YbN 5 } moiety deviates marginally from planarity with a maximal distortion from ideality of ∼5% for I2-Yb-N3 and approximates closely a D 5h coordination environment with N-Yb-N angles in the range from 69°to 77°, close to the ideal angle of 72° (Fig. 2b). Within the 2D plane, the linking of bipy and Yb(II) forms both square and triangular tiles with the bipy linkers spanning the edges. The squares and triangles closely approximate equilateral geometries with edge lengths of 12.14 Å and 12.25 Å for the squares and 12.32 Å, 12.14 Å, and 12.34 Å for the triangles. Despite the local D 5h symmetry, a slight bending of the bipy linkers leads to the formation of an ideal 3 3 .4 2 tessellation (Fig. 2a). The 2D layers are stacked with an inter-plane separation of ∼6 Å imposed by the axial iodide ligands (Fig. 3). The packing motif of the 2D layers leads to the formation of solvent-accessible pore channels of distorted 3 3 .4 2 topology along both the crystallographic a and b directions and of distorted 3 6 topology along the c direction ( Supplementary  Fig. 2). To our knowledge, 1 is the first example of any coordination solid constructed from divalent lanthanide ions. The presence of potentially reducible bipy and strongly reducing Yb(II) (E ⦵ Yb 3+ /Yb 2+ = -1.1 V) could be expected to lead to the occurrence of redox events, similar to what is found in the reaction between elemental sodium and bipy 35  The structural data thus echo the presence of Yb(II) and the absence of any Yb(III)-bipy •valence tautomer formation, which has been observed in related, molecular Yb(II) complexes of 2,2′-bipyridine 39,40 . Changing the solvent of the synthesis to tetrahydrofuran (THF) resulted in a slightly different compound, YbI 2 (bipy) 2 (THF)·1.5 THF (2). The dark green 2 is structurally related to 1 but lacks the square tiles due to coordination of a THF solvent molecule and can be considered to be composed of isolated strands of a bisected 3 6 tessellation (Figs. 1a and 4, and Supplementary Fig. 3). Notably, the crystal packing enforces a supramolecular distorted 3 3 (4). Yb···Yb separations (Å) amount to 12.14 and 12.25 for the squares, and 12.32, 12.14, and 12.34 for the triangles (Yb light blue; I dark red; N blue; C gray; hydrogen atoms and co-crystallized CH 3 CN have been omitted for clarity).   Fig. 4). Interestingly, considering only the Yb sites, the structure can be described as resting at an intermediate position between the 3 3 .4 2 (with quadratic tiles: ∠Yb···Yb···Yb = 90°) and the 3 6 (∠Yb···Yb···Yb = 60°) tessellations. The Yb-I (3.1311(8), 3.1038(8) Å) and Yb-N (2.585(5)-2.666(5) Å) bond lengths are all close to those of 1, indicating the presence of divalent Yb in 2. The oxidation state assignment of Yb(II) and the absence of any valence-tautomerism in 1 and 2 were further corroborated by bulk magnetometry. Yb (II), having a closed-shell [Xe]4f 14 electronic configuration, is expected to be fully diamagnetic. Indeed, the magnetic susceptibility-temperature products, χT, of both 1 and 2 at 273 K were typically vanishing at ∼0.06 cm 3 K mol -1 ( Supplementary  Fig. 4). Assuming the identity of a paramagnetic impurity as Yb (III) (2.57 cm 3 K mol -1 calculated for 2 F 7/2 and g J = 8/7), its concentration is estimated to be <2%.

Discussion
A quasicrystalline tiling consisting solely of squares and triangles has an optimal square-to-triangle ratio of √3/4 ≈ 0.43 8,41 . Hence, to approach a dodecagonal quasicrystalline tiling with the 3 3 .4 2 tessellation structure at hand, triangle-rich motifs need to be introduced into the tiling. The lanthanide ions here stand out as ideal materials modules due to their exceptional structural versatility that is inimitable amongst the inner and outer transition metal elements of the periodic table. This allows their accommodation into the in-plane tetra-, penta-, and hexa-coordinated nodes that coexist in dodecagonal quasicrystals 7,12 . It is here particularly important that the strategy is not reserved for divalent lanthanide ions. Indeed, several molecular complexes of the trivalent lanthanide ions possess an approximate D 5h (e.g., [LnI 2 (THF) 5 ] + 42-47 and [LuI 2 (pyridine) 5 ] + 33,38 ) coordination environment necessary for their incorporation into such materials. Notably, contrasting the intermetallics, the typical optical transparency of lanthanide-based coordination solids provides for exploitation of optical properties of complex tilings. For instance, ATs offer the potential of photonic band gap opening 23,48 , which in conjunction with the unique luminescence characteristics of the lanthanide ions 31 , lays the foundation for materials with novel optical properties. In addition, the field of molecular magnetism has recently seen a blossoming of approximate C 5 symmetric single-ion magnets with exceedingly high magnetization reversal barriers [49][50][51] . Linking of single-ion magnets or lanthanide-based qubits 52 into ATs and quasicrystals to yield spin-frustrated arrays would be an attractive extension of this work 53 . This approach also comprises controlling metal-ligand redox events with the aim of introducing electronic conductivity and increasing the strength of inter-ion magnetic interactions in ATs and derived network structures as has been developed for regular tessellations with lighter first-row transition element analogs 54 .
In conclusion, we have reported a chemical strategy to tailor AT topologies in coordination solids by employing the propensity for high coordination numbers intrinsic to the lanthanide series ions. The appearance of five-vertex tilings suggests the possibility for the occurrence of metal-organic quasicrystalline phases in a bulk material. Exemplified by the structure of 2, our approach opens up a novel route to design supramolecular metal-organic AT analogs, which is currently pursued for fully organic materials [55][56][57] . In addition, the 2D nature hosts potential for nanostructuring and exfoliation of complex tilings, as is now intensively practiced for the 3d congeners with regular tessellation structures 58 . Although nanoscale arrays of lanthanide-based ATs have previously been observed on surfaces using scanning tunneling microscopy 30 , the isolation of 1 demonstrates the possibilities to design lanthanide-based ATs in bulk, crystalline materials. This result paves the way for next-generation materials with complex and non-periodic tiling structures hosting novel photonic and magnetic phenomena originating from the unique physical properties of the lanthanide ions.
Crystallography. Single crystals of 1 and 2 were covered with polybutene oil (Aldrich, >90%) and mounted onto a nylon loop, which was attached to a SuperNova Dual Source CCD diffractometer. Data were collected using Mo Kα radiation at T = 120(1) K. Using Olex2 59 , the structure was solved with the ShelXT 60 structure solution program and refined with the SHELXS 61 refinement package using least squares minimization. All non-hydrogen atoms were refined anisotropically (cf. Supplementary Table 1). The crystal structure of 1 consists of one additional, highly disordered solvent molecule in the unit cell, i.e., half a solvent molecule per formula unit, which could not be modeled accurately and was treated by solvent mask method implemented in Olex2 62 . Twenty-three electrons were found in a volume of 282 Å 3 in one void per unit cell. This indicates the presence of one acetonitrile molecule per unit cell, which accounts for 22 electrons. Similarly, a solvent mask was calculated for 2 and 38 electrons were found in a volume of 177 Å 3 in one void per unit cell. This is consistent with the presence of one molecule of THF per unit cell, which accounts for 40 electrons. Powder X-ray diffraction patterns ( Supplementary Fig. 5) were measured at room temperature in transmission mode with a Huber G670 powder diffractometer using Cu Kα 1 (λ = 1.5406 Å, quartz monochromator) radiation. The powder samples were measured in sealed bags and the powder of 1 was additionally immersed in polybutene oil (Aldrich, >90%) to suppress loss of co-crystallized CH 3 CN molecules. The resulting powder patterns were background corrected.
Magnetization measurements. The isofield dc magnetization measurements were performed using the VSM option on a QuantumDesign Dynacool Physical Property Measurement System equipped with a 9T dc magnet in the temperature range from 1.7 K to 273 K in a magnetic field of 0.1 T. The polycrystalline samples were loaded into standard QuantumDesign powder capsules inside an Ar-filled glovebox. The experimental data were corrected for diamagnetic contributions from the sample holder and the intrinsic sample diamagnetism.

Data availability
The X-ray crystallographic coordinates for structures reported in this Article have been deposited at the Cambridge Crystallographic Data Centre (CCDC), under the deposition numbers CCDC 1988173-1988174. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif. All other relevant data are available from the authors on request.