Hierarchical structural complexity in atomically precise nanocluster frameworks

Abstract The supramolecular chemistry of nanoclusters is a flourishing area of nano-research; however, the controllable assembly of cluster nano-building blocks in different arrays remains challenging. In this work, we report the hierarchical structural complexity of atomically precise nanoclusters in micrometric linear chains (1D array), grid networks (2D array) and superstructures (3D array). In the crystal lattice, the Ag29(SSR)12(PPh3)4 nanoclusters can be viewed as unassembled cluster dots (Ag29–0D). In the presence of Cs+ cations, the Ag29(SSR)12 nano-building blocks are selectively assembled into distinct arrays with different oxygen-carrying solvent molecules―Cs@Ag29(SSR)12(DMF)x as 1D linear chains (Ag29–1D), Cs@Ag29(SSR)12(NMP)x as 2D grid networks (Ag29–2D), and Cs@Ag29(SSR)12(TMS)x as 3D superstructures (Ag29–3D). Such self-assemblies of these Ag29(SSR)12 units have not only been observed in their crystalline state, but also in their amorphous state. Due to the diverse surface structures and crystalline packing modes, these Ag29-based assemblies manifest distinguishable optical absorptions and emissions in both solutions and crystallized films. Furthermore, the surface areas of the nanocluster crystals are evaluated, the maximum value of which occurs when the cluster nano-building blocks are assembled into 2D arrays (i.e. Ag29–2D). Overall, this work presents an exciting example of the hierarchical assembly of atomically precise nanoclusters by simply controlling the adsorbed molecules on the cluster surface.

Most recently, we have proposed a novel clusterassembly pattern, namely, capturing Cs + cations and dimethylformamide (DMF) molecules onto the nanocluster surface [48]. Specifically, in the crystal lattice, the Cs + −DMF−cluster interactions assemble the Ag 29 (SSR) 12 nano-building blocks into 1D linear chains (SSR = 1,3-benzene dithiol) [48]. Considering that such an assembly largely relies on the Cs + −O interactions (the O junction site comes from the DMF), we perceive a good opportunity to control the assembly modes of Ag 29 (SSR) 12 simply altering the oxygen-carrying solvents in the crystallization.
Herein, the Ag 29 (SSR) 12 nanocluster building blocks are selectively assembled into micrometric linear chains (1D array), grid networks (2D array) and superstructures (3D array), and such hierarchical constructions are determined by the single crystal X-ray diffraction (SC-XRD). Specifically, the presence of PPh 3 (or the absence of Cs + ) yields unassembled cluster dots (Ag 29 (SSR) 12 (PPh 3 ) 4 , Ag 29 -0D). By comparison, when the Cs + cations are captured on the nanocluster surface with different oxygen-carrying solvent molecules, the Ag 29 (SSR) 12 nano-building blocks are selectively assembled into distinct arrays (Scheme 1)-the capture of Cs + -DMF on Ag 29 (SSR) 12 producing 1D linear chains (Cs@Ag 29 (SSR) 12 (DMF) x , Ag 29 -1D), the capture of Cs + -NMP on Ag 29 (SSR) 12 making up 2D grid networks (Cs@Ag 29 (SSR) 12 (NMP) x , Ag 29 -2D; NMP = N-methyl-2-pyrrolidone), and the capture of Cs + -TMS giving rise to 3D superstructures (Cs@Ag 29 (SSR) 12 (TMS) x , Ag 29 -3D; TMS = tetramethylene sulfone). Besides, the 1D-3D assemblies of these Ag 29 (SSR) 12 nano-building blocks have not only been observed in their crystalline state, but also in their amorphous state, with the help of the aberration-corrected high angle annular dark field scanning transmission electron microscope (HAADF-STEM). Furthermore, the optional assembly modes result from different cluster-Cs-solvent interactions. Because of the different surface structures and crystalline packing modes, these Ag 29 -based assemblies manifest distinguishable optical absorptions and emissions in both solutions and crystallized films. Moreover, the surface areas and pore size distributions of the crystals of these nanoclusters are evaluated, and the maximum value of the surface area is reached when the cluster nano-building blocks are assembled into 2D arrays (i.e. Ag 29 -2D). n [Cs 3 Ag 29 (SSR) 12 Nano-building block of Ag 29 -0D

Ag 29 -0D cluster dot and Ag 29 -1D linear chain
The Ag 29 (SSR) 12 framework is composed of an icosahedral Ag 13 kernel that is stabilized by an Ag 12 (SSR) 12 shell, and the obtained Ag 25 (SSR) 12 structure is further capped by four bare Ag atoms with a tetrahedral pattern ( Fig. S1) [49,50]. Although the Ag 29 (SSR) 12 compound could exist in isolation, its four Ag terminals have a strong disposition to be sealed by the introduced PPh 3 ligand, giving rise to the Ag 29 (SSR) 12 (PPh 3 ) 4 (Ag 29 -0D) nanocluster (Figs 1A and S2A). In the crystal lattice, all Ag 29 -0D entities are independent without any direct inter-cluster interactions in either direction ( Fig. 1B-D). Accordingly, the presence of PPh 3 with Ag 29 (SSR) 12 yields the unassembled cluster dots, representing the zero-dimensional arrangement of the Ag 29 cluster entities in the crystalline cell. The capture of Cs + cations with Ag 29 -0D dissociates the PPh 3 ligands from the nanocluster surface, giving rise to Cs@Ag 29 (SSR) 12 (DMF) x (Ag 29 -1D, as depicted in Figs 1E and S2B) [48]. Besides, the interactions among the cluster framework, the Cs + cations, and the DMF molecules assemble the Ag 29 (SSR) 12 nano-building blocks into cluster-based linear chains ( Fig. 1F and G). As shown in Figs 1G and S3, the Ag 29 -based, 1D linear chains extend along the y axis, and the inter-chain distance between two adjacent cluster lines along the z direction is 17.291Å [48]. Collectively, the introduction of Cs + cations and DMF molecules onto the Ag 29 nanocluster surface assembles the cluster dots into linear arrays, representing the 1D arrangement of the Ag 29 cluster entities in the crystalline cell.

Ag 29 -2D grid networks
Considering that the aforementioned 1D assembly largely relies upon the Cs + −O interactions where the oxygen junction site comes from the DMF, we perceive a good opportunity to tailor the assembled modes of Ag 29 (SSR) 12 nano-building blocks-altering the oxygen-carrying solvents in the crystallization. We first replaced DMF molecules in Ag 29 -1D into NMP to produce the Cs@Ag 29 (SSR) 12 (NMP) x (Ag 29 -2D; see the Methods Section for the detailed preparation). Significantly, the 2D-array assembly of Ag 29 cluster entities was accomplished in the crystal lattice (Fig. 2). Structurally, the nano-building block of Ag 29 -2D contains two Ag 29 (SSR) 12   are in different twisting angles, and are mutually connected by two Cs + cations (Cs1 and Cs1 ) through Cs-C and Cs-π interactions ( Fig. 2A and B). In addition, the inter-cluster assembly is induced by the outward interactions from four Cs + conjunction sites-Cs2, Cs2 , Cs4 and Cs4 . The Cs4 is bonded on the nanocluster surface through Cs4-NMP-Cs3-cluster interactions (the same to Cs4 ), whereas the Cs2 is directly anchored onto the nanocluster surface by Cs-C interactions (the same to Cs2 ). Of note, the Cs4 (or Cs4 ) on one cluster nano-building block also acts as the Cs2 (or Cs2 ) of the adjacent block. In this context, the number of Cs + cations in each nano-building block is six, and the ratio between [Ag 29 (SSR) 12 ] 3− and Cs + is exactly 1:3, for achieving the charge balance ( Fig. 2A and B).
For the 2D-array assembly, each [Cs@Ag 29 (SSR) 12 (NMP) x ] 2 unit is adjacent to four identical units through the four Cs + conjunction sites, making up an Ag 29 -based, two-dimensional grid network ( Fig. 3B and C). The grid network extends along the (001) plane, or both x and y axes ( Fig. 3C-G). Along the z direction, the two neighboring networks display no interaction, but are in a face-symmetric relationship (the two types of layers are labeled in blue and orange of Ag atoms in Fig. 3D-G). In this context, the assembly of Ag 29 -2D in the crystal lattice follows an ABAB layer-by-layer packing mode.
The inter-layer distance (from kernel Ag to kernel Ag, as shown in Fig. 2D and G) between two adjacent networks is 14.622Å. Overall, the capture of Cs + and NMP of the Ag 29 (SSR) 12 framework enables the self-assembly of cluster dots into grid networks, representing the two-dimensional arrangement of the Ag 29 nano-building blocks in the crystalline cell.

Ag 29 -3D superstructure
The further substitution of oxygen-carrying solvent molecules (DMF of Ag 29 -1D, or NMP of Ag 29 -2D) into TMS yields Cs@Ag 29 (SSR) 12 (TMS) x (Ag 29 -3D; see the Methods Section for the detailed preparation), which follows a 3D-array assembly in the crystal lattice (Figs 3 and S2D). To the nano-building block of Ag 29 -3D, all Cs + cations are directly anchored onto the nanocluster surface through Cs-C interactions (Fig. 3A). For each Ag 29 -3D nano-building block, there are six Cs + conjunction sites that are subordinate to two categories: inward Cs1, Cs1 and Cs1 that are simply bonded on the nanocluster surface, and outward Cs2, Cs2 and Cs2 that induce the inter-cluster assembly ( Fig. 3A and B).
For the 3D-array assembly (Fig. 3C), each Ag 29 -3D nano-building block is surrounded by six adjacent nanoclusters including three cluster1 (labeled in orange of Ag atoms) and three cluster2 (labeled in magenta of Ag atoms). More specifically, each outward Cs + cation connects one cluster1 and one cluster2, of which the cluster1 is arranged downwardly but the cluster2 is organized upwardly, constructing the Ag 29 -based, three-dimensional superstructures ( Fig. 3C and D). The Ag 29 -3D nanobuilding blocks are assembled with a cubic pattern in the crystal lattice (i.e. a = b = c, and α = β = γ for the cell parameter). In this context, the cluster packing modes are identical in all directions, making up a highly symmetrical superstructure (Fig. 3E-H). Taken together, the bonding of Cs + and TMS on Ag 29 (SSR) 12 triggers the self-assembly of cluster dots into superstructures, representing the threedimensional arrangement of the Ag 29 nano-building blocks in the crystalline cell.

Comparison of crystal structures and packing modes
Due to the different surfaces, these Ag 29 nanoclusters (Ag 29 -0D, Ag 29 -1D, Ag 29 -2D, and Ag 29 -3D) exhibited distinct crystal structures and crystalline packing modes (Figs S4 and S5, and Tables S1 and S2). Although the overall Ag 29 (SSR) 12 configuration retained from Ag 29 -0D to Ag 29 -1D, Ag 29 -2D and Ag 29 -3D, obvious changes have been observed by comparing the corresponding bond lengths. Specifically, all of the three types of Ag-Ag interactions (Ag(core)-Ag(icosahedral shell), Ag(icosahedral shell)-Ag(icosahedral shell), and prism-like Ag(icosahedral shell)-Ag(motif) bonds) in Cs@Ag 29 nanoclusters (Ag 29 -1D, Ag 29 -2D, and Ag 29 -3D) were much longer than those in the PPh 3 @Ag 29 nanocluster (Ag 29 -0D), demonstrating an expanding trend of the overall framework along with the PPh 3 dissociated process (Fig. S4A-C and  Table S1). For the pyramid-like interactions between the vertex Ag and the icosahedral Ag, the bond lengths were all close to 3.04Å for Cs@Ag 29 nanoclusters. However, no analogous interaction was observed in the PPh 3 @Ag 29 nanocluster since the corresponding distances ranged from 3.493 to 3.643Å (Fig. S4D and Table S1). In this context, the vertex Ag atoms became closer to the icosahedral kernel when the Ag 29 -0D nanocluster was transformed into Ag 29 -1D, Ag 29 -2D and Ag 29 -3D, and the newly generated Ag 4 pyramids were anticipated to make the Ag 29 (SSR) 12 framework more robust.
The chemical environments of Cs + ions in different Ag 29 -based assemblies have been compared. For Ag 29 -1D, three Cs + ions (Cs1, Cs2 and Cs3) stabilize the cluster surface and the other three Cs + ions (Cs4, Cs5 and Cs6) assemble Ag 29 nano-building blocks into 1D linear chains (Fig. 1). For Ag 29 -2D, all Cs + ions are used to activate the assembly of cluster nano-building blocks into 2D grid networks (Fig. 2). For Ag 29 -3D, the inward Cs + ions (Cs1, Cs1 and Cs1 ) stabilize the cluster surface, and the outward Cs + ions (Cs2, Cs2 and Cs2 ) induce the inter-cluster assembly of cluster nano-building blocks into 3D superstructures (Fig. 3). Of note, only the presence of Cs + can induce the assembly of Ag 29 nano-building blocks; by comparison, the Ag 29 -0D nanocluster maintains its structure in the presence of Li + , Na + or K + cations [48].
The crystalline packing modes of these Ag 29based assemblies were further compared ( Fig. S5 and Table S2). Of note, two types of crystallization patterns of Ag 29 -0D have been reported-Ag 29 -0D-cubic and Ag 29 -0D-trigonal-due to their different crystallization processes [49,50]. Because of the distinct interactions among Ag 29 clusters, Cs + cations and solvent molecules, Ag 29 -1D, Ag 29 -2D and Ag 29 -3D were also crystallized in different systems. Specifically, although both Ag 29 -1D and Ag 29 -2D follow an orthorhombic packing mode, their unit cell parameters (i.e. values of a, b, c) were totally different (Table S2). The Ag 29 -3D displayed a cubic packing mode, the same as that of Ag 29 -0Dcubic, whereas the unit size of Ag 29 -3D was remarkably smaller than the Ag 29 -0D-cubic (14375Å 3 versus 40006Å 3 ; see details in Table S2). Such differences reflected both the molecular effects of the Cs + capture and the solvent effects in affecting nanocluster geometric structures and crystalline packing patterns.
Notably, the hierarchically 1D-, 2D-and 3Darray assemblies of Ag 29 building blocks have not only been observed in their crystalline state, but also in their amorphous state. Specifically, the aberration-corrected HAADF-STEM images of Ag 29 -0D, Ag 29 -1D, Ag 29 -2D and Ag 29 -3D nanoclusters were obtained by recording the drying solutions of these nanoclusters on carbon films. The Ag 29 -0D cluster entities were still discrete under the microscope vision (Fig. S6A), whereas some linear assembled Ag 29 -1D clusters were discovered (Fig. S6B). Given that Ag 29 -0D and Ag 29 -1D were controlled to the same concentration in the aberration-corrected HAADF-STEM detection, the 1D-array assembly of Ag 29 -1D indeed existed in its non-crystalline state. Figure S6C and D exhibited the HAADF-STEM images of Ag 29 -2D and Ag 29 -3D. Of note, for promoting the 2D-array and 3D-array assemblies of these two nanoclusters, the concentrations of them were much higher than in Ag 29 -0D and Ag 29 -1D. Compared with Ag 29 -1D, which displayed the linear assembly, the Ag 29 -2D nano-building blocks were more inclined to be aggregated with a 2D-array reticular pattern (Fig. S6C). Furthermore, although most cluster entities were discrete in the HAADF-STEM image of Ag 29 -3D, several cluster-based, 3D aggregates have been observed (Fig. S6D), which unambiguously demonstrated the 3D-array assembly of some Ag 29 (SSR) 12 cluster entities. To sum up, the introduction of Cs + cations and oxygen-carrying solvents was also able to induce the self-assembly of Ag 29 (SSR) 12 nano-building blocks in the non-crystalline state.

Characterization of Ag 29 -based assemblies
The electrospray ionization mass spectrometry (ESI-MS) measurement was firstly performed to verify the specific composition of each nanocluster (Fig. S7). Mass spectra of Ag 29 -0D showed five peaks that corresponded to [Ag 29 (SSR) 12 (PPh 3 )

] 3− , [Ag 29 (SSR) 12 (PPh 3 ) 3 ] 3− , [Ag 29 (SSR) 12 (PPh 3 ) 2 ] 3− , [Ag 29 (SSR) 12 (PPh 3 ) 1 ] 3− and [Ag 29
(SSR) 12 ] 3− , respectively, in good agreement with the reported 'dissociation-aggregation pattern' of the PPh 3 ligands on the Ag 29 -0D surface (Fig. S7A) [51]. These PPh 3 -containing signals were absent in the spectra of Cs@Ag 29 nanoclusters because the PPh 3 ligands had been dissociated from the nanocluster surface induced by the Cs + capture. Two intense peaks, matching with the [Ag 29 (SSR) 12 ] 3− and [CsAg 29 (SSR) 12 ] 2− compounds, were observed for each mass spectrum of Ag 29 -1D, Ag 29 -2D or Ag 29 -3D (Fig. S7B-D), which verified the Cs + capture in these nanoclusters. However, as to the mass spectra of each Cs@Ag 29 nanocluster, only the single Cs + -adhered Ag 29 compound (i.e. CsAg 29 (SSR) 12 ) could be detected. The unattained mass signals of the complete Cs@Ag 29 molecules resulted from the weak interactions among the Ag 29 (SSR) 12 frameworks, the Cs + cations, and the solvent molecules when the nanoclusters were in solutions. 133 Cs and 31 P nuclear magnetic resonance (NMR) were then recorded to validate the capture of PPh 3 ligands or Cs + ions on the Ag 29 nanocluster surface. As depicted in Fig. S8A  intense 31 P NMR signal of Ag 29 -0D at 26.20 ppm disappeared after the PPh 3 ligands were dissociated from the nanocluster surface (Fig. S8B); that is, no phosphine signal was observed in the 31 P NMR of Cs@Ag 29 nanoclusters. The structures of nanoclusters are determinant of their physical-chemical properties. Due to their distinct surface structures and crystalline packing modes, these Ag 29 -based assemblies manifested distinguishable optical absorptions and emissions in both solutions and crystallized films. Of note, the solution-state UV-vis and photoluminescence (PL) spectra of Ag 29 -0D and Ag 29 -1D were monitored in DMF, whereas Ag 29 -2D was in NMP and Ag 29 -3D was in TMS. The optical absorptions of these Ag 29 nanoclusters in the solution state were very similar (Fig. 4A, solid lines)-an intense peak at 445 nm and a shoulder band at 365 nm. Such a similarity might result from the fact that the molecularly electronic transitions of these nanoclusters mainly originated in their almost identically inner Ag 29 (SSR) 12 framework. For the PL, all nanocluster solutions emitted when illuminated at 445 nm (Fig. 4A, dotted lines); however, remarkable differences took place. The DMF solutions of both Ag 29 -0D and Ag 29 -1D emitted at 640 nm, whereas the emission wavelengths of Ag 29 -2D (in NMP) and Ag 29 -3D (in TMS) exhibited obvious blue-shifts, of which Ag 29 -2D emitted at 625 nm and Ag 29 -3D luminesced at 622 nm. Furthermore, the PL intensities of Ag 29 -0D, Ag 29 -1D and Ag 29 -3D showed 1.7-, 2.1-and 2.3-fold enhancement, respectively, relative to that of Ag 29 -2D with the lowest PL intensity. These differences reflected both the structural effect and the solvent effect on nanocluster emissions.
The nanocluster crystallized films exhibited apparent differences in both optical absorptions and emissions (Fig. 4B). The UV-vis spectrum of each nanocluster presented an intense absorption at 455 nm; however, the features of these spectra varied greatly-the 455 nm signal of Ag 29 -2D was much more intense than those of other nanoclusters, and the UV-vis spectrum of Ag 29 -1D showed a broad shoulder band at 550 nm that was absent for other nanoclusters (Fig. 4B, solid lines). The normalized emissions of these Ag 29 nanoclusters in crystallized films were further compared. Both Ag 29 -0D and Ag 29 -1D films were singly emissive: the former emitted at 700 nm and the latter emitted at 670 nm. Of note, the Ag 29 -0D film emitted at 700 nm when crystallized in the cubic unit cell, or at 670 nm when crystallized in the trigonal unit cell [50]. By comparison, both Ag 29 -2D and Ag 29 -3D films were dualemissive: although the two of them luminesced at 680 and 725 nm, the shoulder emission (725 nm) of Ag 29 -3D was more distinguishable than that of the Ag 29 -2D (Fig. 4B, dotted lines). The conspicuous differences in emissions of these Ag 29 -based assemblies in different forms (crystal film and solution) arose from distinct combinations of the electronic coupling and the lattice-origin, non-radiative decay pathways occurring through electron-phonon interactions [49,52,53]. Besides, these differences can also be explained in terms of the diverse surface chemistry of these nanoclusters: the PPh 3 ligand surface of Ag 29 -0D, and the distinct cluster-Cs-solvents surfaces of Ag 29 -1D, Ag 29 -2D and Ag 29 -3D.
Because of their different crystalline packing modes, these Ag 29 -based assemblies should exhibit distinctive surface areas. Herein, the nitrogen adsorption-desorption tests were performed on the crystals of these Ag 29 nanoclusters for evaluating their specific surface area and pore size distribution (Figs 4C-F and S9). The values of the specific surface areas of Ag 29 -0D, Ag 29 -1D and Ag 29 -3D were all below 10 m 2 /g (about 6, 4 and 8 m 2 /g for Ag 29 -0D, Ag 29 -1D and Ag 29 -3D, respectively). By comparison, the Ag 29 -2D crystal generated a much bigger specific surface area of about 19 m 2 /g. In this context, as to this Ag 29 system, the nanocluster crystals would expose the maximum surface areas when the cluster nano-building blocks were assembled into 2D arrays. Indeed, compared with other cluster crystals, the Ag 29 -2D crystal presented larger pore sizes (Fig. 4C-F, insets).

CONCLUSION
The cluster-based 1D linear chains, 2D grid networks and 3D superstructures were selectively constructed by the self-assembly of Ag 29 (SSR) 12 nano-building blocks with different solventconjoining Cs + cations. In the absence of Cs + cations, the bare Ag atoms on Ag 29 (SSR) 12 were prone to be stabilized by PPh 3 ligands, producing the unassembled cluster dots in the crystal lattice.
In the presence of Cs + cations, the Ag 29 (SSR) 12 units could be selectively assembled into distinct arrays with different oxygen-carrying solvents: Cs@Ag 29 (SSR) 12 (DMF) x as 1D linear chains with the DMF solvent, Cs@Ag 29 (SSR) 12 (NMP) x as 2D grid networks with the NMP solvent, and Cs@Ag 29 (SSR) 12 (TMS) x as 3D superstructures with the TMS solvent. Besides, the 1D-3D selfassemblies of these Ag 29 (SSR) 12 nano-building blocks have not only been observed in their crystalline state, but also in their amorphous state, with the help of the aberration-corrected HAADF-STEM. Such Ag 29 -based assemblies manifested distinguishable optical absorptions and emissions in both solutions and crystallized films, and these differences originated from their different surface structures and crystalline packing modes. The surface areas of these Ag 29 crystals were evaluated, and the 2D-array assembled nanocluster (i.e. Ag 29 -based grid networks) displayed the maximum value of the surface area. Overall, this work presents the hierarchical assembly of atomically precise nanoclusters by simply controlling the adsorbed molecules on the cluster surface, which hopefully sheds light on more future works touching upon the supramolecular chemistry of metal nanoclusters.

Synthesis of Cs@Ag 29 (SSR) 12 (NMP) x (Ag 29 -2D)
The 50-mg Ag 29 -1D crystal was dissolved in 5 mL of NMP under vigorous stirring. This NMP solution was poured into 200 mL of CH 2 Cl 2 , and the precipitate was collected and further dissolved in 5 mL of NMP, producing the Ag 29 -2D nanocluster. The yield was 95% based on the Ag element (calculated from Ag 29 -1D). This NMP solution of Ag 29 -2D was directly used for the crystallization and the characterization.

Synthesis of Cs@Ag 29 (SSR) 12 (TMS) x (Ag 29 -3D)
The 50-mg Ag 29 -1D crystal was dissolved in 5 mL of TMS under vigorous stirring. This TMS solution was poured into 200 mL of CH 2 Cl 2 , and the precipitate was collected and further dissolved in 5 mL of TMS, producing the Ag 29 -3D nanocluster. The yield was 95% based on the Ag element (calculated from Ag 29 -1D). This TMS solution of Ag 29 -3D was directly used for the crystallization and the characterization.

Crystallization of Ag 29 -2D and Ag 29 -3D
Single crystals of Ag 29 -0D and Ag 29 -1D were cultivated based on the reported methods [48,49]. Single crystals of Ag 29 -2D and Ag 29 -3D were cultivated at room temperature by diffusing methanol into the NMP solution of Ag 29 -2D, or the TMS solution of Ag 29 -3D. After two weeks, red crystals were collected, and the structure of Ag 29 -2D or Ag 29 -3D was determined. The CCDC numbers of Ag 29 -2D and Ag 29 -3D are 1961389 and 1941329, respectively.

Characterization
All UV-vis absorption spectra of nanoclusters were recorded using an Agilent 8453 diode array spectrometer. PL spectra were measured on a FL-4500 spectrofluorometer with the same optical density of 0.1. ESI-MS measurements were performed by MicrOTOF-QIII highresolution mass spectrometer. The sample was directly infused into the chamber at 5 μL/min. For preparing the ESI samples, nanoclusters were dissolved in DMF/NMP/TMS (1 mg/mL) and diluted (v/v = 1:2) by methanol. 133 Cs and 31 P NMR spectra were acquired using a Bruker 600 Avance III spectrometer equipped with a Bruker BBO multinuclear probe (BrukerBioSpin, Rheinstetten, Germany). The Ag 29 -based assemblies were imaged with an aberration-corrected HAADF-STEM technique after the solvent that contained Ag 29 -based assemblies was dropped casting onto ultrathin carbon film TEM grids. The microscope employed was a FEI Themis Z. The electron beam energy was 200 kV. The collecting angle HAADF detector was used to collect signals scattered between 52 (inner angle) and 200 (outer angle) mrad (camera length of 146 mm). The aberration-corrected HAADF-STEM image was obtained by Thermo Scientific Velox software using 1024 * 1024 pixels and dwell time was set to 10 us.

Nitrogen adsorption-desorption test
The specific surface area and pore size distribution were calculated from each corresponding nitrogen adsorption-desorption isotherm by applying the Brunauer-Emmett-Teller (BET) equation on ASAP2020 M plus Physisorption. By using the quenched solid density functional theory (QS-DFT), the pore size distributions were derived from the sorption data. The BET surface areas of Ag 29 -0D, Ag 20 -1D, Ag 29 -2D and Ag 29 -3D samples are about 6, 4, 19 and 8 m 2 /g, respectively. Of note, the experimental errors of the nitrogen adsorption-desorption data might be 5%-10%; however, these errors have no effect on the conclusion that Ag 29 -2D displays the maximum value of the surface area because the BET surface area of Ag 29 -2D (19 m 2 /g) is remarkably higher than those of the Ag 29 -0D, Ag 20 -1D and Ag 29 -3D samples.

Single-crystal analysis
The data collection for single crystal X-ray diffraction was carried out on Stoe Stadivari diffractometer under nitrogen flow, using graphite-monochromatized Cu Kα radiation (λ = 1.54186Å). Data reductions and absorption corrections were performed using the SAINT and SADABS programs, respectively. The electron density was squeezed by Platon. The structure was solved by direct methods and refined with full-matrix least squares on F 2 using the SHELXTL software package. All non-hydrogen atoms were refined anisotropically, and all the hydrogen atoms were set in geometrically calculated positions and refined isotropically using a riding model.