Magnetic Supramolecular Spherical Arrays: Direct Formation of Micellar Cubic Mesophase by Lanthanide Metallomesogens with 7‐Coordination Geometry

Abstract Here, an unprecedented phenomenon in which 7‐coordinate lanthanide metallomesogens, which align via hydrogen bonds mediated by coordinated H2O molecules, form micellar cubic mesophases at room temperature, creating body‐centered cubic (BCC)‐type supramolecular spherical arrays, is reported. The results of experiments and molecular dynamics simulations reveal that spherical assemblies of three complexes surrounded by an amorphous alkyl domain spontaneously align in an energetically stable orientation to form the BCC structure. This phenomenon differs greatly from the conventional self‐assembling behavior of 6‐coordinated metallomesogens, which form columnar assemblies due to strong intermolecular interactions. Since the magnetic and luminescent properties of different lanthanides vary, adding arbitrary functions to spherical arrays is possible by selecting suitable lanthanides to be used. The method developed in this study using 7‐coordinate lanthanide metallomesogens as building blocks is expected to lead to the rational development of micellar cubic mesophases.


Introduction
Constructing highly ordered supramolecular structures through the self-assembly of simple molecules is a promising approach for creating functional materials. [1]n particular, 3D ordered structures consisting of spontaneously formed spherical assemblies of molecules, i.e., supramolecular spherical arrays, have recently attracted considerable attention in various fields, from drug delivery to the food industry. [2]Originating from element-scale spherical motif arrays such as metals and salts, the construction of ordered structures consisting of nanosized spherical assemblies using a variety of building blocks, such as surfactants, block copolymers, dendrons, tetrahedral molecules, and rod-coil molecules, has been actively investigated. [3]he supramolecular approach is an attractive alternative for the generation of spherical arrays.For example, a phase transition from supramolecular columns of stacked disk-shaped molecules to supramolecular spheres has been reported. [4]Although such a phase transition usually requires high temperatures, supramolecular spherical arrays such as Im3̅ m (bodycentered cubic; BCC), P4 2 /mnm (Frank-Kasper ), and Pm3̅ n (Frank-Kasper A15) have been created. [5]Examples of direct synthesis of desired supramolecular spherical arrays at room temperature are limited, and the protocol is not yet well developed. [6]urthermore, the functionalization of spherical arrays is an attractive challenge with many possibilities for separation, luminescence imaging, sensors, and actuators. [7].
Metallomesogens, metal complexes that exhibit mesomorphic characteristics, can form various assembled structures depending on the type of metal and the design of the ligands and thus exhibit element-derived optical, magnetic, electrical, and redox properties. [8]Control of the higher-order structure of metallomesogens requires a balance between a rigid core moiety consisting of a metal and ligand and a flexible moiety on the ligand side chain.Metallomesogens can be designed by adapting the rules related to tuning the phase structures formed by liquid crystals based on organic molecules.Metallomesogens with rod-shaped rigid cores and a linear coordination geometry tend to form nematic or smectic mesophases. [9]On the other hand, metallomesogens with rigid disk-shaped cores generally form columnar mesophases.For example, metallomesogens prepared by introducing metal ions into the central region of rigid cyclic compounds such as porphyrins and phthalocyanines have been observed to form columnar mesophases. [10]Columnar metal complexes consisting of a quasi-disk-like core containing trivalent transition metals such as chromium (Cr 3+ ), ruthenium (Ru 3+ ), rhodium (Rh 3+ ), and iron (Fe 3+ ) and multiple ligands have also been studied. [11]This columnar structure is formed by stacking highly symmetric octahedral coordination structures, i.e., 6coordinate geometries.Since metal-metal and ligand-derived - interactions between cores are universally present in metallomesogens with symmetrical molecular structures, disk-shaped metallomesogens generally form a columnar mesophase due to the interaction between rigid core complexes. [12]The formation of a bicontinuous cubic mesophase is promoted by shifting the stack of the disk-shaped metallomesogens. [13]On the other hand, there have been only a few reports on the formation of micellar cubic mesophases, that is, supramolecular spherical arrays composed of disk-shaped metallomesogens, and the detailed internal structure of these structures is unclear. [14]Micellar cubic mesophases in solvent-free systems were first discovered for spherical supramolecular assemblies of carbohydrate-based compounds. [15]A series of detailed analyses of formation mechanisms based on molecular design have revealed the involvement of hydrogen bonds in the formation of micellar cubic mesophases. [16]6a] Design-ing metallomesogens with control of the spatial self-assembly requires following structural rules, and discovering spherical packing phases in metallomesogen-based materials remains challenging.
Lanthanide metals, which prefer high coordination numbers, show no marked stereochemical preference, and lanthanidomesogens form various assembled structures. [17]In this context, we investigate the design of higher-order structures based on lanthanide complexes.Holmium (Ho) is the lanthanide element with the highest magnetic moment, and magnetic materials such as single-molecule magnets have been fabricated with Ho as the metallic species. [18]We have developed Ho-doped soft magnetic materials by incorporating carboxyl and -diketone groups with high complexation efficiency with lanthanides into the material design. [19]Recently, we prepared a Ho complex (HoC0) consisting of Ho 3+ and a -diketone-type ligand, 1,3-diphenyl-1,3propanedione (C0) (Figure 1a).While HoC0 has been reported previously, [20] the crystal structure of the newly synthesized sample was obtained for confirmation: single-crystal X-ray diffraction (SC-XRD) measurements of HoC0 showed that three C0 ligands and one H 2 O molecule were coordinated around the central Ho atom. [21]The H 2 O molecule formed hydrogen bonds with the carbonyl oxygen of the ligand of an adjacent Ho complex, thereby forming a linearly aligned structure of Ho complexes in the crystalline state (Figure 1b).Incorporating hydrogen bonds, where bonding and dissociation are reversible at room temperature, into the design of materials has proven useful in many fields. [22]The unique nature of this self-organization process of a 7-coordinate lanthanide complex motivated us to further investigate the organization of Ho complexes into other assembled patterns.
Here, we present the discovery of a supramolecular spherical array based on a micellar cubic mesophase using lanthanide metallomesogens with 7-coordinate geometry (Figure 1a).We assumed that appropriate control of the spatial extent of the peripheral side chains, combined with the reversible hydrogen bonding behavior at room temperature, promotes the selfassembly of Ho complexes into the micellar mesophase.We thus prepared a HoC8 complex composed of ligand C8 with an 8-carbon alkoxy chain as a side chain.Synchrotron X-ray scattering experiments have revealed an unprecedented phenomenon: supramolecular spheres constructed by self-assembly of three HoC8 complexes directly form BCC-type micellar cubic mesophases at room temperature without the formation of a columnar mesophase in which disk-shaped molecules are generally formed.Using the molecular force field of Ho that we previously constructed, [21] we verified the construction of a BCC structure consisting of HoC8 complexes by molecular dynamics (MD) simulations.More importantly, this design concept was adapted to another lanthanide, europium (Eu), where EuC8 directly formed BCC-type micellar cubic mesophases at room temperature, similar to HoC8.Different lanthanides have different magnetic and luminescent properties, [23] leading to the formation of arbitrary functional supramolecular spherical arrays.The results presented here highlight this innovative strategy to develop new supramolecular morphologies based on the conformational asymmetry of lanthanide complexes with high coordination geometry.

Results and Discussion
The Ho complex HoC8 was prepared by combining the C8 ligand possessing a flexible alkyl group on the side chain with holmium chloride hexahydrate (HoCl 3 •6H 2 O).The detailed experimental procedure is provided in the Supporting Information (Scheme S1 and Figure S1, Supporting Information).The coordination of the -diketone group to the Ho cation was investigated by infrared (IR) spectroscopy (Figure 1c).In the IR spectrum of C8, a strong absorption peak was observed at 1574 cm −1 , which was attributed to the C═O stretching vibration of the -diketone moiety; in the spectrum of HoC8, this 1574 cm −1 peak redshifted to 1551 cm −1 , indicating that the carbonyl group was coordinated to the Ho cation. [24]19b] In the EuC8 spectrum shown in Figure S2 (Supporting Information), as in that of HoC8, the peaks attributed to the C═O and C═C (enol isomer) stretching vibrations of the -diketone group of C8 were redshifted after ligand coordination.Peaks attributed to C═C vibrations associated with the deprotonation of the enol hydroxyl group were also observed, indicating that the C8 ligand was coordinated to Eu.The coordination state of Ho in HoC8 was confirmed by X-ray absorption fine structure (XAFS) spectroscopy.The extended Xray absorption fine structure (EXAFS) and X-ray absorption near edge structure (XANES) spectra of the Ho L 3 -edge of HoC0 and HoC8 shown in Figure S3a,b (Supporting Information) are almost identical, suggesting that the coordination state of Ho in both complexes was the same.The Fourier-transformed (FT) k 3weighted Ho L 3 -edge EXAFS functions, that is, the radial distribution functions of HoC0 and HoC8, are shown in Figure 1d.For the strong peak at ≈2 Å attributed to Ho-O coordination, curvefitting analysis was performed based on the crystal structure of Ho(III) oxide: the fitting result and graph are shown in Table S1 and Figure S3c,d (Supporting Information), respectively.There was no difference between the Debye-Waller factors of HoC8 and HoC0, indicating that the coordination environment for oxygen was nearly identical (Table S1, Supporting Information).Notably, the coordination numbers of Ho in HoC0 and HoC8 were equal.Thus, HoC8 was a 7-coordinate complex with three ligands and one H 2 O molecule coordinated to the central Ho, similar to HoC0. [21]Synchrotron small-angle X-ray scattering (SAXS) measurements were performed to clarify the detailed phase structures.As shown in Figure 2a, the SAXS data for HoC8 at room temperature (25 °C) showed a considerable number of well-resolved reflections with q-spacing ratios of √ 16, and √ 18.By fitting the results to a cubic lattice, these peaks were indexed to the (110), ( 200), ( 211), ( 220), ( 310), ( 222), (321), (400), and (330/411) planes of a structure in the Im3̅ m space group (Table S2, Supporting Information).There was a broad peak at ≈1.4 Å −1 (2 = 13.2°, = 1.03 Å) attributed to the alkyl side chain of HoC8, indicating the mesomorphic nature of the sample. [25]Whether the Im3̅ m cubic mesophase was bicontinuous or micellar will be discussed later.The optical microscopy image of HoC8 showed a hard texture (Figure 2b right).The dark-field image obtained by polarized optical microscopy (POM) between crossed polarizers of the same field of view supported the presence of the cubic mesophase that was isotropic in three dimensions and showed no birefringence (Figure 2b left). [26]Equilibrium crystal habits obtained by extremely slow cooling of cubic mesophase droplets from the isotropic phase are known to form polyhedral structures with crystallographic facets. [27]Optical microscopy of the equilibrium crystal habits of the HoC8 droplet revealed a faceted polyhedral structure, indicating that HoC8 formed cubic mesophases at room temperature (Figure 2c).The SAXS profile for EuC8 also showed that this material formed a cubic mesophase in the Im3̅ m space group (Figure S4 and Table S3, Supporting Information).From the dimensions of the (110) reflections, the cubic lattice sizes of HoC8 and EuC8 at room temperature were estimated to be 31.34and 30.87 Å, indicating a nearly constant size regardless of the size of the lanthanide elements.Cubic mesophases can be classified into two types: bicontinuous types, which are formed by a continuous arrangement of molecules, and discontinuous micellar types, which are formed by spherical assemblies. [28]From the SAXS measurements, only the symmetry (space group) of the cubic mesophase was determined.Thus, to determine whether the cubic mesophase was bicontinuous or discontinuous, the number of HoC8 complexes in the lattice (Z value) was calculated using the following Equation ( 1): where Z is the number of molecules (complexes) in the lattice, a is the lattice constant,  is the density, N A is Avogadro's number, and M is the molar mass.Using the density of HoC8 (1.03 g cm −3 ) measured by means of a gas displacement pycnometer system with helium gas, the Z value was calculated to be 6.04.
It is difficult for approximately six complexes to form a bicontinuous cubic mesophase, which requires the self-assembly of many molecules, [28] suggesting that HoC8 forms a discontinuous micellar cubic mesophase.These results confirmed the formation of BCC-type supramolecular spherical arrays in which spherical assemblies consisting of three HoC8 complexes occupy two sites of the lattice (Figure 2d).6b,15,16] The three alkyl chains introduced into the side chain of each benzene ring of C8 contribute to the increase of the interfacial curvature, which probably led to the formation of the micellar cubic mesophase consisting of HoC8.The Z value of EuC8 was also ≈6, indicating that BCC-type supramolecular spherical arrays formed spontaneously at room temperature regardless of the lanthanide type.
Figure 3a shows the SAXS profiles of HoC8 at various temperatures.All the profiles maintained the Im3̅ m micellar cubic mesophase structure, although the peaks shifted slightly from 25 to 150 °C.At 175 °C, a change to an isotropic phase was observed.As shown in Figure S5 (Supporting Information), a peak near q = 1.4 Å −1 (d = 4.5 Å), which was attributed to the alkyl chain, was also observed at temperatures up to 150 °C, indicating that the mesomorphic properties were maintained up to this temperature range.Figure 3b shows the temperature dependence of the lattice size calculated from the peak corresponding to the (110) reflection at 50-150 °C.The lattice size of HoC8 was 31.76Å (50 °C), which decreased slightly to 31.30Å (150 °C) upon heating.The change in the lattice size of EuC8 showed a similar trend, with a slight decrease from 31.04 Å (50 °C) to 30.63 Å (150 °C) with increasing temperature.Compared to phase transitions, which result in significant changes in the ordered structure and mobility of materials, enthalpy changes due to changes in the lattice size are negligible.Thus, the lack of a distinct phase transition-derived peak in the differential scanning calorimetry (DSC) curve for HoC8 and EuC8 also suggested that the peak shift in the SAXS profile was due solely to a change in lattice size (Figure S6, Supporting Information).The thermogravimetric (TG) curves of HoC8 and EuC8 showed that the decomposition temperatures were above 300 °C (Figure S7, Supporting Information).The fluidity of HoC8 and EuC8 was visually investigated using an optical microscope because no clear peaks were observed in the DSC curves for the prepared complexes, as described above.While HoC8 and EuC8 exhibited a hard texture at room temperature (25 °C), their fluidity increased with increasing temperature (Figure S8, Supporting Information); the isotropization temperatures of HoC8 and EuC8 were estimated to be ≈170 and 165 °C, respectively.Note that the dark field of view of the cubic mesophase was maintained in the POM images of HoC8 and EuC8 in all temperature regions (Figure S8, Supporting Information).While the lattice size varied slightly with temperature, both HoC8 and EuC8 were shown to form BCC-type supramolecular spherical arrays over a wide temperature range, including room temperature.
To determine whether HoC8 forms an ordered structure inside a supramolecular sphere, the short-range ordered structure inside the material, i.e., the interatomic distance, was visualized by reduced pair distribution function (PDF) analysis based on synchrotron X-ray total scattering measurements. [29]Several distinct peaks were observed in the PDF of HoC8 shown in Figure 3c.Referring to the interatomic distances in the SC-XRD data for HoC0, the peaks below 3 Å were mainly correlated to atomic pairs within a single Ho complex.On the other hand, the distance between adjacent Ho complexes was ≈6.3 Å (Figure S9, Supporting Information).Therefore, the long-range correlations longer than 6 Å observed in Figure 3c indicated that Ho complexes may be adjacent to each other.Heavier elements with larger atomic numbers have more significant scattering coefficients and correlations. [30]Thus, the long-range observed correlations were mainly related to Ho and correlated with the Ho-O(H 2 O) (3.99 Å), Ho-O(C═O) (5.00 Å), and Ho-Ho pairs (6.39 Å) between adjacent HoC8 complexes.These data indicate that the three HoC8 complexes in the supramolecular sphere are not arranged randomly, but the complexes form a linearly aligned structure.Notably, the peaks at 25 °C were also observed at 150 °C, albeit with a slight shift due to thermal motion, indicating that the 7-coordinate structure of HoC8 and the linearly aligned complexes it forms were maintained after heating because of the stability of the H 2 O molecules coordinated to the lanthanides. [31]While the aligned complex structure inside the sphere center was maintained upon heating, the increased mobility of the alkyl side chains suggested that the supramolecu- lar spheres converged to a more stable structure, and the lattice size was reduced (Figure 3b).The assembly mechanism of the 7coordinate HoC8 was distinct from that of conventional symmetric transition metallomesogens.The Ho-Ho distances between neighboring complexes were too great, presumably suppressing columnar assembly due to the lack of metal-metal interactions. [32]n the other hand, the presence of Ho-O(H 2 O) pair signals corresponding to hydrogen bonding intercomplexes suggests that the self-assembly of HoC8 was due to hydrogen bond through H 2 O molecules within the complex, quite similar to the internal structure of HoC0 revealed by SC-XRD measurements.
Since Ho exhibits the highest magnetic moment among the lanthanide elements, [23a] HoC8 was floated on the water's surface in a petri dish to evaluate the sample's magnetic properties (Figure 4a,b).Although the density of HoC8 is 1.03 g cm −3 , the sample floated on the water surface, probably due to the presence of tiny bubbles.When a neodymium magnet (1 T) approached from below the petri dish, the HoC8 on the water surface moved with the movement of the magnet and showed excellent magnetic properties (Movie S1, Supporting Information).The mass magnetization was measured by superconducting quantum interference device (SQUID) measurements.Figure 4c shows the magnetization plots of HoC8 and EuC8 at 27 °C.Both passed through the origin at magnetic fields up to 5 T, indicating that both HoC8 and EuC8 are paramagnetic.The volume mass susceptibilities () of HoC8 and EuC8 calculated from the slope of the graph were 1.61 × 10 2 and 1.06 × 10 J T −2 m −3 , respectively, indicating that the magnetic properties can be controlled by the lanthanide elements used.Since Curie's law applies to paramagnetic behaviors, Curie's constant was determined from the following Equation ( 2): [33] where  is the volume magnetic susceptibility, T is the absolute temperature, and C is Curie's constant of the material.Using the calculated Curie's constant, the magnetic moment per complex was calculated from the following Langevin function (3): [33]  = where μ is the magnetic moment, V is the volume of the unit lattice, k B is Boltzmann's constant, and N is the number of complexes in a cubic lattice volume (Z value).The obtained magnetic properties of HoC8 and EuC8 are listed in Table 1, along with each element's previously reported magnetic moment values.The experimental values of the magnetic moments (μ) of HoC8 and EuC8 were 10.9 μ B and 2.8 μ B , respectively.These magnetic moments were calculated using the experimentally determined number of complexes in the unit lattice and the Z value.The obtained values are similar to the previously reported value of the effective paramagnetic moment of trivalent lanthanide ions, [23a] supporting the formation of a supramolecular sphere from three complexes.These results also indicated that cubic metallomesogens were constructed using the prepared lanthanide complexes as building blocks.Since Eu is known to have luminescence properties, although its magnetic prop- Sample HoC8 1.61 × 10 2 4.84 × 10 4 10.9 10.4-10.7
As shown in Figure 4d, a sharp peak was observed at a wavelength corresponding to the red color characteristic of Eu, indicating that the material inherited the properties of the element used.
We performed MD simulations to evaluate the validity of the BCC structure, which was experimentally shown to form by spontaneous assembly of supramolecular spheres composed of three HoC8 complexes (Movie S2, Supporting Information).The atomic structure derived from the MD simulation at the final step was visualized using VMD software, [34] as shown in Figure 5a.The left and middle images in Figure 5a were drawn with different colors for each assembly.The middle image was drawn without alkyl chains to identify its orientation.The right image shows a single assembly with three HoC8 complexes.The white straight lines in Figure 5a indicate the central axis through three Ho and two H 2 O molecules.The central lines for each assembly were determined from the coordination of Ho and O of H 2 O by solving the optimization problem described later.The time evolution of the structures from the initial structure is illustrated with a time sequence in Figures S10 and S11 (Supporting Information).An assembly including alkyl chains in the initial structure formed a spheroid centered around the central axis.Due to interactions between assemblies, the spheroid was transformed into an elongated shape with a major axis (Figure 5b).Visual inspection of the snapshots revealed that tilting and rotational motions occurred over time.The orientation of each assembly was defined within a spherical coordinate system, as shown in the right image of Figure 5a.The polar and azimuthal angles ( (0°≤  ≤ 180°) and ϕ (0°≤ ϕ ≤ 360°), respectively) were calculated from the central axis of each assembly.The perpendicular distance from the central axis to three Ho atoms and two O atoms of H 2 O molecules was estimated to determine the central axis vector.The centroid position, o i , and the central axis vector were calculated by the following expression (4) involving rotational and translational operations: arg min where dist [p,q] is the distance function used to calculate the distance between p and q in the xy-plane.(Supporting Information).As the MD simulation progressed, all assemblies tilted from  = 0 in the initial alignment to a range of 10 to 70°.Tilt angles exceeding 90°, which correspond to a complete inversion of an assembly with the head and tail swapped, were not observed.The mean and standard error of  for all assemblies after 0.6 μs were 28.9°± 12.3°.The time-dependent order parameter, denoted as S, was also calculated from (t) from Equation (5): where ⟨ ⟩ represents the ensemble average for all assemblies (Figure 5d).The time-dependent mean distance, denoted as ⟨d⟩ for the central axis, was also computed to assess the degree to which the three complexes and two H 2 O molecules aligned along a straight line (Figure 5e).S and ⟨d⟩ in the initial structure were 0, indicating that the central axes of all assemblies were perfectly aligned with the z-axis.Although slight disordering with ⟨d⟩ ≈ 0.3 was observed, the three arrays of HoC8 complexes along the central axis were maintained throughout the MD simulation.The distribution of ϕ for each assembly labeled as m in Figure S12 (Supporting Information) was visualized using a polar plot in Figure S14 (Supporting Information).The radial distance in Figure S14 (Supporting Information) indicates the distance between the head-Ho and the tail-Ho.The mean and stan-dard error of this distance for all assemblies were 12.5 ± 0.3 Å, corresponding to a nearest Ho-Ho distance of 6.25 Å (Figure 5f).From these results, the peak at ≈6.39 Å in Figure 3c was assigned to the distance between the nearest HoC8 complexes.The small standard error of the head-Ho-to-tail-Ho length implies tight binding of three HoC8 complexes along the central axis in the assembly.Some assemblies (m = 1,3 and m = 4) exhibited a ϕ distribution ranging from 0°to 360°, and other assemblies had a ϕ ranging from 45°to 180°centered in a specific direction.These observations indicated both rotational and librational motion around the z-axis, meaning that the motion of the central axis was precessional. [35]Such precessional motion is expected when an assembly is represented as a pseudospherical shape.As a result, the diffraction pattern of the crystal composed of HoC8 complexes indicated the BCC structure.
A proposed mechanism for forming HoC8-based supramolecular spherical arrays is summarized in Figure 6.HoC8 directly forms spherical assemblies consisting of three complexes.Inside the supramolecular sphere is the array structure of Ho complexes, surrounded by amorphous alkyl domains.These supramolecular spheres spontaneously align in an energetically stable orientation to form the BCC structure.HoC8 does not form columnar assemblies, which disk-shaped molecules tend to form, due to the unique 7-coordinate geometry of the lanthanide complex.The asymmetry of the complexes and the presence of H 2 O molecules coordinated to Ho promote the formation of the aligned structure of the complexes driven by hydrogen bonds.The formation of a single supramolecular sphere with three HoC8 complexes may be due to appropriate control of the spatial extent of the amorphous alkyl domains of the complex side chains.Nevertheless, the detailed formation mechanism of spherical assemblies still needs to be clarified.To elucidate the mechanism, it is necessary to comprehensively analyze the effects of side chains on the formation of higher-order structures, and this research is currently underway.Importantly, all micellar cubic mesophase formation self-assembly processes proceeded spontaneously at room temperature, indicating that complex structure formation was achieved via a low-energy process.

Conclusion
In conclusion, experiments and MD simulations have shown that supramolecular spherical arrays composed of three 7-coordinate lanthanide complexes form spontaneously at room temperature and create micellar mesophases directly without forming the columnar mesophases that conventional metal complexes tend to form.While there are limited examples of the preparation of Im3̅ m micellar cubic mesophases, [36] especially those obtained with metallomesogens as building blocks, [37] we experimentally and computationally demonstrated the formation of Im3̅ m micellar cubic mesophases based on lanthanide metallomesogens and the existence of ordered structures of metal complexes formed inside them.The supramolecular spherical arrays prepared with Ho possessed a high magnetic moment, as the central metal exhibited excellent magnetic properties that responded quickly to the movement of a bulk magnet.On the other hand, when Eu with a weak magnetic moment was used, the resulting supramolecular spherical arrays showed inferior magnetic properties, but red emission was observed.Since the magnetic and luminescence properties varied depending on the type of lanthanide element, it was possible to add any desired functionality by selecting the appropriate central metal.The newly developed method using 7-coordinate lanthanide complexes as building blocks is expected to lead to the rational development of micellar mesophases other than the BCC type.

Figure 1 .
Figure 1.a) Structures of 7-coordinate lanthanide complexes obtained by complexation with -diketone-type ligands (C0 and C8).b) Linearly aligned structure of the HoC0 complex along the c-axis in the crystal, based on HoC0 single-crystal data.The blue dotted lines indicate the predicted hydrogen bonds: the O…O interatomic distance is 2.957 Å, the O…O-Ho angle is 143.77°, and hydrogen atoms are omitted.This figure is based on data from the Cambridge Crystallographic Data Center (No. 2270020).c) IR spectra of C8 and HoC8.d) The radial distribution function of k 3 -weighted Ho L 3 -edge EXAFS for HoC0 and HoC8.

Figure 2 .
Figure 2. a) SAXS profile of HoC8 at 25 °C.b) POM image (left) and optical microscopy image (right) of HoC8 coated on a glass substrate at 25 °C.c) Optical micrograph at 25 °C of the equilibrium crystal habits of HoC8 droplets prepared by slowly cooling (0.01 °C min −1 ) the isotropic liquid (200 °C).d) Schematic of a BCC structure.

Figure 3 .
Figure 3. a) Temperature dependence of the SAXS profile of HoC8.b) Temperature dependence of the HoC8 and EuC8 lattice sizes.The lattice sizes were calculated from the peaks corresponding to the (110) reflections.c) PDF of HoC8 X-ray total scattering measurement data.

Figure 4 .
Figure 4. a) Photograph and b) schematic image of the magnetic responsive behavior of HoC8.See Movie S1 (Supporting Information) for the video.c) Magnetization plots of HoC8 and EuC8 in magnetic fields up to 5 T at 27 °C.d) The emission spectrum of EuC8. ex = 370 nm.
of effective paramagnetic moment of trivalent lanthanide ions.

Figure 5 .
Figure 5. a) The snapshot at the final MD step is displayed with and without alkyl chains (left and middle images).Each assembly is colored with different colors to facilitate the orientation.An assembly is shown in the right image, where the pink, brown, and white spheres represent Ho, C, and H atoms, respectively.Gray lines indicate the alkyl chains.Cyan-colored molecules correspond to water molecules.Dark gray lines denote the periodic boundaries of the unit cell.b) Time sequence of MD-derived structures: the white enclosure represents the assembly spread.c) Centroid trajectory for each assembly: the pink sphere in the unit cell represents the centroid position at each time.d) The time-dependent order parameter and e) the mean distance for three Ho and two O water molecules from the central axis of the assembly.f) Magnified image of the three HoC8 complexes inside the assembly.The numbers in the figure indicate the nearest Ho-Ho distance.

Figure 6 .
Figure 6.Schematic diagram of the mechanism of direct formation of a BCC-type supramolecular spherical array at room temperature.*Measured by PDF analysis of X-ray total scattering measurements.**Assuming that the supramolecular spheres are densely packed, we defined the diameter of the spheres as 1/2 the length of the diagonal of the lattice obtained from SAXS measurements.
r i and o i are the coordinates of the i-th atoms (three Ho atoms and two O atoms of H 2 O molecules) and the centroid of the central axis vector.R x () and R z (ϕ) are the rotation matrices around the x-and z-axes.Consequently, R x () • R z (ϕ) • (r i − o i ) denotes the coordinates of the i-th atoms after translational and rotational operations.All i-th atoms after these operations were coordinated around the z-axis when the argmin optimization problem in Equation (4) was solved.The central axis vector represented by , ϕ, and o i was determined at this point.The centroid displacements for each assembly were visualized by drawing the trajectory of o i (Figure5c).The trajectories of o i encircled the lattice points in the BCC structure; thus, the centroid of the assemblies was positioned within the BCC structure.The time-dependent  of each assembly is displayed in FigureS13(Supporting Information), where m in the panel corresponds to the label for each assembly shown in FigureS12