Flexible Vertex Engineers the Controlled Assembly of Distorted Supramolecular Tetrahedral and Octahedral Cages

Designing and building unique cage assemblies attract increasing interest from supramolecular chemists but remain synthetically challenging. Herein, we propose the use of a flexible vertex with adjustable angles to selectively form highly distorted tetrahedral and octahedral cages, for the first time, in which the flexible vertex forms from the synergistic effect of coordination and covalent interactions. The inherent interligand angle of the vertex can be modulated by guest anions present, which allows for the fine-tuning of different cage geometries. Furthermore, the reversible structural transformation between tetrahedral and octahedral cages was achieved by anion exchange monitored by mass spectrometric technique, the smaller anions favoring tetrahedral cages, while the larger anions supporting octahedral cages. Additionally, the KBr-based cage thin films exhibited prominent enhancement of their third-order NLO responses in two or three orders of magnitude compared to those obtained for their corresponding solutions. This work not only provides a new methodology to build irregular polyhedral structures in a controlled and tunable way but also provides access to new kinds of promising functional optical materials.


Introduction
Over the past decades, designing and synthesizing unique supramolecular cages featuring intriguing polyhedral geometries and confined cavities have sparked great interest in supramolecular community [1][2][3][4][5][6]. In addition to their aesthetically pleasing structures, their unique physical and chemical properties resulting from specific shapes and functionalities endow them wide applications across various fields, ranging from biomedicine [7][8][9], catalysis [10][11][12][13][14], guest encapsulation [15][16][17], separation [18,19] to luminescent materials [20][21][22]. Recent progress allows the structures of supramolecular cages to be readily designed and synthesized using highly directional coordination bonds linking metal ions with specific coordination geometries with organic linkers of different symmetries, lengths, and steric bulk [1][2][3][4][5][6][23][24][25][26]. If the directionality of coordination bonds has critically contributed to spectacular developments in the field, access to only a limited number of interligand angles significantly hinders the development of higher structural diversity and complexity [27,28]. Typically, the most encountered interligand angles are centered around 60°, 90°, and 109°and cannot be easily modified because they are dictated by the nature of the metal center [28]. These angles favor the formation of regular cages with tetrahedral, octahedral, cubic, M n L 2n -type polyhedral, and adamantanoidal structures (Figure 1(a)) [1,29,30]. Consequently, being able to adjust the interligand angles at a vertex would represent a highly desirable and major step forward to efficiently expand the existing libraries of molecular cages.
However, the coordination interaction-based vertices used for the construction of supramolecular cage architectures are limited to single/double metal nodes [1,31] and metal cluster nodes (carboxylate-containing and polyoxometalate clusters) [32][33][34][35], which are quasirigid elementary bricks that significantly restrict angular changes on vertexes. Therefore, the introduction of additional interactions, such as covalent interactions, would provide vertexes with higher flexibility and distorted characteristic and thus access to unconventional supramolecular cages [36]. In particular, if the variable angles at a flexible vertex could be tuned by an external stimulus, such as a guest molecule, the controllable construction of diverse supramolecular cage architectures would be more readily accessible [5,[37][38][39][40].
We herein report a new strategy based on a type of flexible vertex with adjustable angles to selectively construct a series of severely distorted tetrahedral and octahedral cages. The synergistic effect of both coordination and covalent interactions gives the vertex flexible and low-symmetry merits. Consistent with the possibility of the associated anion to act as a template and guide the assembly of supramolecular structures [41][42][43][44][45], we have now observed that the size of guest anions allowed a controllable angular modulation of a flexible vertex, facilitating the selective formation of irregular polyhedral structures (Figure 1(b)). Remarkably, the transformation between the cages containing a smaller anion and the relatively larger anions was found to be reversible, thus highlighting the impact of vertex flexibility on the structural tuning of cage assemblies.  (Figure 2) to generate a tetracoordinated building block of low symmetry [36,46]. During this reaction, L undergoes a significant configuration change and forms the new linker L a [36,46]. The resulting 4coordinated building block binds with Cu(I) ions to form a new flexible vertex that can be used to construct unique supramolecular cages. In addition, the π-conjugated pyridyl moieties on ligand L can engender favorable H-bonding and anion-π interactions with guest anions [47][48][49]. Formation of these H-bonding interactions and anion-π interactions constitutes the driving force for regulating angular changes in the flexible vertex units.  (Figures 2 and 3), as established by single-crystal X-ray diffraction (SCXRD). Its stoichiometry was further confirmed by electrospray ionization mass spectrometry (ESI-MS), with a peak at m/z = 1239:9343 with the correct isotopic distribution pattern for { [1](BF 4 )} 3+ in MeCN, indicating that cage [1](BF 4 ) 4 was stable in solution ( Figure S1). Furthermore, diffusion-ordered NMR spectroscopy (DOSY) experiment on [1](BF 4 ) 4 showed the presence of a discrete tetrahedral cage structure, with the single diffusion coefficient (D = 4:84 × 10 −10 m 2 s −1 ) ( Figure S10). Taking advantage of a type of flexible coordination vertex capable of adapting angular changes in response to the changes of the size of guest anions, the controlled construction of distorted supramolecular tetrahedral and octahedral cages can be achieved.

Research
The SCXRD result reveals that [1](BF 4 ) 4 crystallizes in the triclinic space group P 1. As shown in Figure 3(a), one alkynyl group of L undergoes coupling with two S atoms on [Tp * WS 3 ] − to produce covalent interactions (S−C=C−S) in a 1,2-enedithiolato [Tp * WS 3 (L a )] − moiety, in which three coordination sites of the W (VI) center are occupied by the Tp * and the octahedral coordination sphere is completed by three S atoms. This addition reaction resulted in a significant change of the geometry of L from linear to "boat" in the newly formed linker L a . The remaining terminal S atom of A and two S (S−C=C−S) atoms are available for binding with two Cu(I) ions, thus forming the [Tp * WS 3 Cu 2 (L a )] + moiety that can be regarded as a single "vertex" (Figure 3 (Figure 3(b)). The four connections extend out of the [Tp * WS 3 Cu 2 (L a )] + unit, but it is clear that the two short connections, involving both a pyridyl donor and acceptor, are directed towards a single [Tp * WS 3 Cu 2 (L a )] + unit, which further links only three other chemically similar, but crystallographically distinct [Tp * WS 3 Cu 2 (L a )] + units. This results in a severely distorted, dissymmetrical tetrahedral cage (Figure 3(c) and 3(d)) possessing an unprecedented topology (Figure 3(e)). This dissymmetrical character results in a chiral tetrahedral structure ( Figure S22), but the enantiomeric cages crystallize in a 1 : 1 stoichiometry ( Figure S23) to form a racemic conglomerate.
The internal BF 4 − anion in the tetrahedral cage [1] fits snugly within the hollow (Figure 3(c)), which suggests that the internal anion plays an important templating role in the formation of the tetrahedral cage. It is found to associate with the tetrahedral host in which the F atoms interact with the close H atoms of adjacent pyridine rings on the L a linker, forming H-bonding interactions, with the primary C−H···F distances in the range of 2.61-2.87 Å ( Figure S24A). Furthermore, it is engaged in typical anion-π contacts in which the F atoms interact with the C atoms on the pyridine rings, establishing the directional F···C pyridine − or PF 6 − ) (2 equiv) led to the formation of the framework of cationic distorted tetrahedral cage [2]. The framework of cationic distorted octahedral cage [2] formed from the reaction of subcomponents A and L together with [Cu(MeCN) 4 ]SbF 6 in the same stoichiometry of 1 : 1 : 2.
3 Research contacts in the range of 3.07-3.45 Å ( Figure S24B). The above close-contact analysis of cage [1] (BF 4 ) 4 shows that the framework of tetrahedral host is well stabilized by H-bonding and F-π interactions between the pyridyl moieties and the encapsulated BF 4 − .

Impact of Guest Anions on the Angular Changes in a Flexible
Vertex. The host-guest interactions between the internal BF 4 − and the tetrahedral host [1] indicate that this guest anion acts as a competent template in the selfassembly process and the larger anions may generate similar interactions with the [Tp * WS 3 Cu 2 (L a )] + units and influence the angle α at the node, thereby possibly realizing a finetuning of supramolecular cage geometries. To verify this assumption, three other anions with increasing volume, oxyanion perchlorate (ClO 4 − ), hexafluorophosphate (PF 6 − ) and hexafluoroantimonate (SbF 6 − ) were adopted. Using similar reaction conditions as for [1](BF 4 ) 4 , two isostructural tetrahedral assemblies [1](ClO 4 ) 4 ( Figure S25A) and [1](PF 6 ) 4 ( Figure S25B) were obtained, respectively, with the value for the angle α in the vertex approximately equal to that in the counterpart in [1](BF 4 ) 4 ( Figure S26). Each tetrahedral cage encapsulates one ClO 4 − or one PF 6 − within its cavity, and similar host-guest interactions are also observed as described in [1](BF 4 ) 4 ( Figure S27 and Figure S28). Interestingly, when the larger anion SbF 6 − was employed, a cationic octahedral assembly [Tp * WS 3 Cu 2 (L a )] 6 (SbF 6 ) 6 ([2](SbF 6 ) 6 ) ( Figure 2 and Figure S30) was isolated, which crystallized in the trigonal space group R 3. The above solid compounds had good thermal stability ( Figure S31) confirmed by the thermogravimetric analyses (TGA), and the octahedral compound [2](SbF 6 ) 6 exhibited higher thermal stability than the tetrahedral compounds.
In the octahedral cage [2], although the [Tp * WS 3 Cu 2 (L a )] + unit serves as a 4-connector and as a structural vertex, the angle α is dramatically increased to 69.8°( Figure 4 and Figure S30C). This nicely validates our speculation that the [Tp * WS 3 Cu 2 (L a )] + unit functions as a versatile vertex that is able to stretch its interligand angles ranging from 42.5°to 69.8°in response to the large SbF 6 − anions. The vertexes containing the angle α being 69.8°a llow to be splayed apart from each other permitting connections to four rather than three equivalent units, thus leading to a low symmetry cage of distorted octahedral geometry ( Figure S30D). This exemplifies the real possibility of controlling the assembled structure through adjusting the angle at a flexible vertex.
Inspecting the cavity of the octahedral cage [2] shows that there is one pair of SbF 6 − anions ( Figure S30A). Each Sb(V) center is located just off a 3-fold axis that passes through the cage. In addition to the positional disorder, the internal anions exhibit considerable orientational disorder (only one orientation is shown in Figure S30A, Figure S32, and Figure S33). Despite this disorder, it is . (e) Topology of [1]. The angle of α marked here corresponds to the angle of vertex in Figure 3(b). The red balls and cyan balls, respectively, stand for the Tp * WS 3 unit and reacted alkynyl ligand L a units. Color codes: W (red), Cu (azure), S (yellow), N (blue), C (silver), B (light salmon), and F (green). In all views, all hydrogen atoms, the nonencapsulated anions, solvent molecules, and disorder are omitted for clarity. 4 Research apparent that the F atoms establish a rather close contact with the aromatic surfaces. Both encapsulated SbF 6 − anions develop hydrogen bonding contacts with the pyridyl H atoms, with the primary C−H···F distances being 2.08-2.97 Å ( Figure S33A). In addition, the C atoms of the linker L a also establish directional F···C pyridine contacts with the F atoms of the SbF 6 − anions with the primary distances being 3.12-3.60 Å ( Figure S33B). Interestingly, the pyridyl group of the linker L a in [2](SbF 6 ) 6 is oriented in such a way that the hydrogen atoms of the pyridyl group are pointing inwards in a configuration that results in the C −H···F contacts. Examination of each structure suggests that the angle at the vertex could be adjusted in a controlled manner, adapting to the changes of the size of guest anions. When the size of guest anions increases from , the angle in the metal vertex drastically expands from 42.5°to 69.8°, resulting in the structural transition from the tetrahedral cage [1] to the octahedral cage [2] (Figure 4). [2]. The anion-dependent formation of the tetrahedral and octahedral assemblies encouraged us to explore their interconversion starting from the respective pure entities. We speculated that a change of the anion might result in a unique reversible conversion between tetrahedral [1] and octahedral cages [2]. After dissolution of the octahedral cage compound [2](SbF 6 ) 6 in MeCN ( Figure 5(a)), an excess of ( n Bu 4 N)(BF 4 ) was added to the MeCN solution stirring for 8 h at ambient temperature. ESI-MS analysis revealed a new peak at m/z 1239.9617, assigned to the tetrahedral cage {[1](BF 4 )} 3+ with the correct isotopic distribution ( Figure 5(b)). This demon-strated that introduction of small BF 4 − anions to a solution of the octahedral cage compound [2] induces its transformation to the tetrahedral cage [1]. However, when we introduced excess (Et 4 N)(SbF 6 ) to the tetrahedral [1](BF 4 ) 4 system, no any octahedral cage [2] signal ( Figure S34) was observed, indicating no cage transformation took place. Intriguingly, upon addition of HSbF 6 and NEt 3 to a solution of [1](BF 4 ) 4 , we did observe the structural transformation of the tetrahedral cage [1] to the octahedral cage [2] by ESI-MS. One signal at m/z 1475.2583 can be assigned to be the octahedral cage {[2](SbF 6 )(Cl)·10H 2 O} 4+ (Figures 5(c) and 5(d)). The results demonstrate aniondirected reversible transformation between the tetrahedral cage [1] and the octahedral cage [2] and further validate the concept of flexible building block where the angle at the vertex is capable of adjusting to the nature of the anion present, to give the preferred cage structure.

Investigation of Third-Order Nonlinear Optical (NLO)
Properties. The rigid skeletons of the above cage assemblies hold multiple heavy metal atoms and highly π-conjugated organic linkers, which inspired us to explore their thirdorder nonlinear optical (NLO) properties [36,50]. The third-order NLO properties of KBr-based thin films of A,  (Table S2) and better than that of [(C 4 H 9 ) 4 ] 2 [Cu(C 3 S 5 ) 2 ]-doped polymethylmethacrylate (PMMA) thin film [53]. Similar Zscan results for [1](ClO 4 ) 4 ( Figure S41 and Table S2) and [1](PF 6 ) 4 ( Figure S42 and Table S2) were also obtained. Such an outstanding enhancement of the NLO performances could be due to doping concentrations in the KBr films being much larger than those of solution. The difference between the KBr-based tetrahedral and octahedral films may be ascribed to the increase of W/Cu/S cluster cores and the structural expansion from a tetrahedral cage to an octahedral cage. In addition, the third-order NLO response could be gradually improved by increasing the concentrations of [1](BF 4 ) 4 and [2](SbF 6 ) 6 in DMF by 1.5 times (2:07 × 10 −4 mol/L) and 2 times (2:76 × 10 −4 mol/L) ( Figure S43, Figure S44, and Table S2).

Discussion
We have demonstrated that taking advantage of a flexible vertex with adjustable angles represents a feasible and promising strategy for creating new cage assemblies. Using this  ) favor the formation of the small-angle vertex and trigger the generation of the highly distorted tetrahedral cages, whereas the larger SbF 6 − anions increase the angle of the vertex and thus lead to the formation of distorted octahedral cages. The structures of these two types of supramolecular cages with host-guest interactions were demonstrated by detailed X-ray crystallography studies. Furthermore, the reversible topological transformation between these cages induced by the presence of different anions was demonstrated by ESI-MS technique. Finally, a significant amplification of the third-order NLO responses of both types of cages was realized by engineering them in KBr-based thin films, when compared to those of their solutions. This work provides a readily accessible access to topologically irregular polyhedral edifices, demonstrates anion-triggered reversible conversion between tetrahedral and octahedral cages, and paves the way for the development of new optical components.

Physical Characterizations.
Elemental analyses (C, H, and N) were performed on a Carlo-Erba CHNO-S microan-alyzer. Fourier-transform infrared (IR) spectra of the solid samples (KBr tablets) in the range 400-4000 cm −1 were recorded on a Varian 1000 spectrometer. Thermogravimetric analyses (TGA) were performed on a Mettler Toledo Star System under a nitrogen atmosphere at a heating rate of 10°C min −1 . UV-Vis spectra were recorded on a Varian Cary-50 UV-Vis spectrophotometer. The solid samples used for elemental analysis and TGA analysis were dried overnight at 80°C in a vacuum oven for removing solvent molecules. 1 H NMR spectra and 13 C NMR spectra of the ligand L were recorded on BRUKER AVANCE III HD (400 MHz) at room temperature and referenced to the residual protonated solvent for NMR spectra. 1 6 were recorded on a Bruker micrOTOF-Q III mass spectrometer.

Structural Transformation from the Octahedral Cage
4.9. Structural Transformation from the Tetrahedral Cage [1] to the Octahedral Cage [2]. Upon dissolution of crystals of to the octahedral cage [2] has been triggered by the larger anion (SbF 6 − ).  Table S2.

Data Availability
All data that support the findings of this study are available from the corresponding author upon reasonable request.  4 showing the inclusion of one BF 4 with a space filling representation within the cavity as well as three external BF 4 anions.