Counteranion-induced structural isomerization of phosphine-protected PdAu8 and PtAu8 clusters

Controlling the geometric structures of metal clusters through structural isomerization allows for tuning of their electronic state. In this study, we successfully synthesized butterfly-motif [PdAu8(PPh3)8]2+ (PdAu8-B, B means butterfly-motif) and [PtAu8(PPh3)8]2+ (PtAu8-B) by the structural isomerization from crown-motif [PdAu8(PPh3)8]2+ (PdAu8-C, C means crown-motif) and [PtAu8(PPh3)8]2+ (PtAu8-C), induced by association with anionic polyoxometalate, [Mo6O19]2– (Mo6) respectively, whereas their structural isomerization was suppressed by the use of [NO3]– and [PMo12O40]3– as counter anions. DR-UV-vis-NIR and XAFS analyses and density functional theory calculations revealed that the synthesized [PdAu8(PPh3)8][Mo6O19] (PdAu8-Mo6) and [PtAu8(PPh3)8][Mo6O19] (PtAu8-Mo6) had PdAu8-B and PtAu8-B respectively because PdAu8-Mo6 and PtAu8-Mo6 had bands in optical absorption at the longer wavelength region and different structural parameters characteristic of the butterfly-motif structure obtained by XAFS analysis. Single-crystal and powder X-ray diffraction analyses revealed that PdAu8-B and PtAu8-B were surrounded by six Mo6 with rock salt-type packing, which stabilizes the semi-stable butterfly-motif structure to overcome high activation energy for structural isomerization.

M etal clusters of less than 100 atoms have attracted substantial interest because they have quantized electronic structures and unique geometric structures that cannot be predicted from the bulk metals and metal nanoparticles 1 . Since their electronic structures crucially depend on the cluster sizes, compositions, and geometric structures at the atomic level, atomically precise synthesis is required to understand the chemical and physical properties of the clusters. Recent progress in precise synthesis techniques has enabled the synthesis of a variety of gold, silver, copper, and alloy clusters protected by organic ligands such as thiolate, phosphine, alkynyl, carbene, and polyoxometalate ligands, with atomic precision [2][3][4][5][6][7][8][9] . Their unique catalytic, optical, magnetic, and redox properties related to geometric and core-ligand interfacial structures have been reported.
Structural control of ligand-protected metal clusters is one of the key factors in tuning the electronic state of these clusters. Numerous structural isomers have been reported using the structural flexibility of the metal cluster core and core-ligand interface. The structural isomers of metal clusters were found in [Au 9 (PR 8 ) 9 ] 3+6 , [Au 9 Ag 12 (SR) 4 (dppm) 6 X 6 ] 3+10 , and [Au 4 Cu 4 (L) 7 ] +11 . The protecting ligands with different steric structures gave us structural isomers with different core structures such as [Au 11 (PR) n ] 3+12 , [Au 18 (SR) 14 ] 13 , Au 24 (L) 20 14 , Au 25 (SR) 18 13 , Au 30 (SR) 18 13,15 , Au 52 (SR) 32 16 , and Au 144 (SR) 60 17 . The control of geometric structures by using external stimuli has been demonstrated. Ligand exchange induced the reversible isomerization of Au 28 clusters 18 . Thermal-induced isomerization has been reported for Au 38 (SR) 24 19 , Pd 2 Au 36 (SR) 24 20 , and Cu 15 (C ≡ CR) 10 (L) 5 21 . The coupling/decoupling of cationic surfactants provided the reversible isomerization of [Au 25 (p-MBA) 18 ]and collective rotation of the Au 13 core in the cluster has been proposed in the conversion process 22 . Structural isomerization by electrochemical redox has been found in the phosphine-protected Au 8 cluster 23 . Using high-resolution transmission electron microscopy, it was observed that the core structure of Au 144 (SR) 60 was isomerized between icosahedral and facecentered cubic structures 24 . The [Au 9 (PR) 8 ] 3+ , [PdAu 8 (PR) 8 ] 2+ , and [Au 25 (SR) 18 ]have been reported to be isomerized by gas phase collision 25,26 . The structural isomerization from unstable Au 38 to stable Au 38 clusters was induced by heating, and their optical absorption, fluorescence properties, and catalytic activities depended on their structures 27 .
It was previously reported that the core structure of [Au 9 (PPh 3 ) 8 ] 3+ could be controlled by counteranion [28][29][30][31][32] . The crown motif [Au 9 (PPh 3 ) 8 ] 3+ (Au9-C) in solution was maintained by the formation of salt with [PMo 12 O 40 ] 3-, whereas the butterfly-motif [Au 9 (PPh 3 ) 8 ] 3+ (Au9-B) was formed by the association with [NO 3 ]or Clas counteranions because of the soft Au-Au bonds in the Au 9 core 32 . The structural isomerization of [Au 9 (PPh 3 ) 8 ] 3+ was also induced by pressure 33 and gas phase collision 26 . The central Au atom of Au9-C can be substituted by Pd and Pt to synthesize bimetallic [PdAu 8 (PPh 3 ) 8 ] 2+ (PdAu8-C) and [PtAu 8 (PPh 3 ) 8 ] 2+ (PtAu8-C) with a crown-motif structure. In the cases of PdAu8-C and PtAu8-C, structural isomerization has yet to be reported despite them having the same geometric structure as Au9-C. One possible reason for the suppression of structural isomerization is the formation of stiff metal bonds by hetero metal atom doping 32 . Recently, it has been proposed that the isomerization of PdAu8-C occurs via gas phase collision 26 . This interesting possibility prompted us to hypothesize that the isomerization of PdAu8-C and PtAu8-C can be induced by applying strong external stimuli.
The as counteranions with different sizes and charges. We successfully synthesized isomers from the crown motif of PdAu8-C and PtAu8-C by using [Mo 6 O 19 ] 2-. The isomers showed different optical properties from PdAu8-C and PtAu8-C and had an absorption band in the longer-wavelength region. X-ray absorption fine structure (XAFS) analysis, which is a powerful tool to determine the local structure (coordination number, bonding distance) for each element, and density functional theory (DFT) calculations revealed that the isomers were butterfly-motif [PdAu 8 (PPh 3 ) 8 ] 2+ (PdAu8-B) and [PtAu 8 (PPh 3 ) 8 ] 2+ (PtAu8-B). Here, we also discuss the structural isomerization of PdAu8-C and PtAu8-C from the perspective of the activation energy for isomerization and crystal packing of clusters.  Fig. 1 and Supplementary Figs. S1-S3. The UV-Vis-NIR spectra of Au9-NO3, PdAu8-NO3, and PtAu8-NO3 in ethanol solution in Fig. 1 and Supplementary  Fig. S1 showed the characteristic optical properties of crownmotif Au9-C, PdAu8-C and PtAu8-C, respectively 34 . ESI-MS and NMR spectra in Fig. 1 O 40 ] (PtAu8-PMo12) with a crown-motif structure showed optical absorption similar to that of crown-motif PtAu8-NO3 in ethanol solution. In the case of non-doped [Au 9 (PPh 3 ) 8 ] 3+ , butterfly-motif Au9-B was formed in Au9-NO3 composite, which was formed from Au9-C ethanol solution by isomerization 32 . DR-UV-Vis-NIR spectrum of Au9-NO3 with a butterfly-motif structure showed a characteristic absorption peak at 687 nm, which differed from those of Au9-C solution (Au9-NO3 in ethanol) and crown-motif [Au 9 (PPh 3 ) 8 ] [PMo 12 O 40 ] (Au9-PMo12) 34 . Since the optical property of [Au 9 (PPh 3 ) 8 ][Mo 6 O 19 ] composite (Au9-Mo6) was in accordance with that of Au9-NO3 composite as shown in Supplementary Fig.  S1, the Au9-C in Au9-NO 3 ethanol solution was isomerized to Au9-B by the association with Mo6. The formation of Au9-B isomer and the appearance of an absorption peak in the longerwavelength region in Au9-Mo6 gave us the idea that the structural isomerization from crown-motif to butterfly-motif also occurs in the case of PdAu8 and PtAu8 by the association with Mo6, and an absorption peak appears at longer-wavelength (703 nm for PdAu8-Mo6, 600-700 nm for PtAu8-Mo6), as shown in Fig. 1.

Results
Stable structures and optical properties of PdAu8 and PtAu8. The stable structures of PtAu8-C and PtAu8-B were calculated in this study (Fig. 2). Au9-C, PdAu8-C, Au9-B, and PdAu8-B were also optimized at the same calculation level (see Supplementary  Fig. S6) although we had calculated them previously 32 . The optimized structure of PtAu8-C in Fig. 2 agrees with that determined by single-crystal XRD 34 . In addition, PtAu8-B can be generated as a stable entity like PdAu8-B as shown in Fig. 2. In all cases, the crown-motif structure was more stable than the butterfly-motif in Fig. 2 and Supplementary Fig. S6. Note that the energy difference between the crown-motif and butterfly-motif in PtAu8 (0.30 eV) was greater than those in Au9 (0.23 eV) and PdAu8 (0.20 eV).
Supplementary Fig. S7 shows the energy diagram and superatomic orbitals for all clusters. The electronic states near the frontier orbitals of Au9-C, PdAu8-C, and PtAu8-C were very similar. The highest occupied molecular orbitals (HOMOs) of the crown-motif structure are composed of degenerate superatomic 1P x and 1P y orbitals and an unoccupied 1P z orbital is located at the lowest unoccupied molecular orbital (LUMO) level. The superatomic 1D levels are shown at higher energy levels than LUMO. Au9-C, PdAu8-C, and PtAu8-C have the electronic configurations of 1S 2 1P 4 , which are consistent with those for oblate superatoms 36 . The isomerization from crown-motif to butterfly-motif induces the splitting of degenerated 1P x and 1P y in HOMO and 1D xy and 1D x2-y2 in LUMO + 1, stabilization of 1D x2-y2 , and destabilization of 1P z in all clusters. As a result, LUMO in Au9-B and PdAu8-B becomes 1D x2-y2 . Meanwhile, the LUMO in PtAu8-B is still a 1P z superatomic orbital because the energy gap between LUMO (1P z ) and LUMO + 1 (1D xy and 1D x2-y2 ) in PtAu8-C is larger than those in Au9-C and PdAu8-C. These electronic changes in frontier orbitals by isomerization affect the optical properties. The optical absorptions of all clusters were calculated by time-dependent (TD)-DFT as shown in Fig. 1 and Supplementary Fig. S1. Previously, we reported that the PtAu8-NO3/PtAu8-PMo12 with crown-motif (482, 432, 404, 358 nm) in Fig. 1 were reproduced by TD-DFT calculations, as shown in Fig. 1Cf (456, 421, 394, 352 nm) and Fig. 1Df (475, 416, 386, 362 nm). Interestingly, the simulated optical absorptions of PdAu8-B and PtAu8-B have peaks at a longer wavelength (648 nm for PdAu8-B and 568 nm for PtAu8-B), assigned to electron transition from HOMO(1P y ) to 1D x2-y2 , than PdAu8-C and PtAu8-C. Therefore, the absorptions at 703 nm in PdAu8-Mo6 (Fig. 1Cd) and at 600-700 nm in PtAu8-Mo6 (Fig. 1Dd), which appeared by the formation of a composite of PdAu8/PtAu8 with Mo6, are strongly suggested to be the optical gap of PdAu8-B and PtAu8-B.
Local structures of PdAu8-Mo6 and PtAu8-Mo6. The structural difference between crown-motif and butterfly-motif can be characterized by X-ray absorption fine structure (XAFS) because the coordination number (CN) of lateral Au-Au bonds (CN = 3) in the core of PdAu8-B and PtAu8-B is larger than that (CN = 2) in PdAu8-C and PtAu8-C, whereas the CNs of radial Au-Pd(Pt) bonds and Au-P bonds are 1.0 and 1.0, respectively from the Au site and the CN of radial Pd(Pt)-Au are 8.0 from Pd(Pt) site. Figure 3 shows the Au L 3 -edge FT-EXAFS spectra of PdAu8-PMo12, PdAu8-Mo6, PtAu8-PMo12, and PtAu8-Mo6 measured at 10 K, obtained from the EXAFS oscillations as shown in Supplementary Fig. S8. The Pd K-edge and Pt L 3 -edge EXAFS and FT-EXAFS spectra are also shown in Supplementary Fig. S9. Table 1 and Supplementary Table S1 show the results of curve fitting analysis. First, Pd K-and Pt L 3 -edges FT-EXAFS analysis revealed that the Pd in PdAu8-PMo12 and PdAu8-Mo6, and Pt in PtAu8-PMo12 and PtAu8-Mo6 were located at the center of the core because the Pd-P and Pt-P bonds did not observe and the CNs of Pd-Au and Pt-Au were ca 8.0, as shown in Supplementary Fig. S9 and Supplementary Table S1. The CN and bond distance (r) for all bonds obtained by the curve fitting analysis of PdAu8-PMo12 in Table 1 and Supplementary Table S1 agreed with those determined by single-crystal XRD as shown in Supplementary Table S2, and the CN of Au-Au in PdAu8-PMo12 with a crown-motif was 2.0 ± 0.2. A similar result was obtained for PtAu8-PMo12 (CN of Au-Au: 2.0 ± 0.2). Meanwhile, the CNs of Au-Au in PdAu8-Mo6 and PtAu8-Mo6 were 3.1 ± 0.2 and 2.9 ± 0.2, respectively, which are characteristic CNs of Au-Au (CN = 3) for butterfly-motif PdAu8-B and PtAu8-B in Supplementary Table S2. We also analyzed the local structures of Au9-NO3, Au9-PMo12, Au9-Mo6, PdAu8-NO3, and PtAu8-NO3 by XAFS. The Au L 3 -, Pd-, and Pt L 3 -edges EXAFS and FT-EXAFS spectra are shown in Supplementary Figs. S8-S10. The results of curve fitting analysis for Au9-NO3, Au9-PMo12, Au9-Mo6, PdAu8-NO3, and PtAu8-NO3 are listed in Supplementary Tables S1 and S3. The structural parameters indicate that Au9-NO3 has a butterfly-motif structure and the others have a crownmotif one, which is in agreement with the structures determined by single-crystal XRD analysis 31,34,37 .

Discussion
Structures of PdAu8-Mo6 and PtAu8-Mo6. It is known that crown-motif Au9-C can be isomerized to butterfly-motif Au9-B by the association of [NO 3 ]and Clanions 31,32 . In contrast, to the best of our knowledge, the structural isomers of PdAu8-C and PtAu8-C have not been reported to date because the formation of stiff M-Au (M = Pd, Pt) bonds by the hetero metal doping into Au9-C suppresses the isomerization 32 . In this study, we found that the composites of PdAu8-Mo6 and PtAu8-Mo6 showed different optical absorption properties from PdAu8-PMo12 and PtAu8-PMo12, which had crown-motif structures (see Fig. 1) 34 . Under the same condition, Au9-C in Au9-NO3 solution was isomerized to form butterfly-motif Au9-Mo6 composite by the association with Mo6, as shown in Supplementary Fig. S1. DFT calculation revealed that both PdAu8-B and PtAu8-B structures are stable entities and the optical absorptions of PdAu8-Mo6 and PtAu8-Mo6 are explained by TD-DFT analysis of PdAu8-B and PtAu8-B, respectively. XAFS analysis suggested that the local structures of PdAu8-Mo6 and PtAu8-Mo6 were in good accordance with those of PdAu8-B and PtAu8-B, respectively. From the above results, we concluded that the butterfly-motif PdAu8-B and PtAu8-B were successfully synthesized by the isomerization of crown-motif PdAu8-C and PtAu8-C using Mo6 as a counteranion.
Discussion on structural isomerization in PdAu8 and PtAu8. We previously reported that the structural isomerization from PdAu8-C to PdAu8-B is suppressed in PdAu8 because the activation energy for structural isomerization in PdAu8 becomes larger than that in Au9 by the presence of stiff Pd-Au bonds 32 .  Table 1. Since PtAu8-NO3 had a crown-motif structure like PdAu8-NO3, it was expected that radial Pt-Au bonds in PtAu8 are also stiffer than radial Au-Au bonds in Au9. The Pt-Au bond stiffness in PtAu8-PMo12 with a crown-motif structure was evaluated using the Einstein temperature (θ E ), which was determined by the temperature dependence of Debye-Waller (DW) factors 32 . The θ E for each bond was obtained from curve fitting analysis of Au L 3 -and Pt L 3 -edges FT-EXAFS measured at 10-300 K. Supplementary Fig. S11 shows the temperature dependence of DW factors for Au-P, Au-Pt, and Au-Au from Au L 3 -edge, and Pt-Au from the Pt L 3 -edge. The large temperature dependence of DW factors of Au-Pt and Au-Au bonds represented the thermalinduced fluctuation of PtAu8-PMo12. The θ E values of Au-P, Au-Pt, Au-Au, and Pt-Au bonds are shown in Table 1 and Supplementary Table S1. In the same way, we evaluated the θ E values of Au-P, Au-Pd, Au-Au, and Pd-Au bonds in PdAu8-PMo12 with a crown-motif structure using the temperature dependence of DW factors ( Supplementary Fig. S11), as shown in Table 1 and Supplementary Table S1. The obtained θ E values in PdAu8-PMo12 were comparable to those in crown-motif [PdAu 8 (PPh 3 ) 8 ]Cl 2 reported previously 32 . The θ E values (218 K from the Au L 3 -edge, 207 K from the Pt L 3 -edge) of Au-Pt in crown-motif PtAu8-PMo12 were similar to those (210 K from the Au L 3 -edge and 212 K from the Pd K-edge) of Au-Pd in a crown-motif PdAu8-PMo12. Since the θ E of radial Au-Au in Au9-PMo12 with a crown-motif was reported to be 181 K 32 , the radial M-Au (M = Pd, and Pt) bonds in PdAu8-C and PtAu8-C were stiffer than radial Au-Au in Au9-C. In addition, the energy difference between the crown-motif and the butterfly-motif in PtAu8 was largest among all clusters, as shown in Fig. 2 and Supplementary Fig. S6. From these results, the activation energy of structural isomerization is predicted, as shown in Fig. 4. The stiffness of the bond is related to the steepness of the potential curve along the reaction coordinate. Thus, the activation energy is estimated to be in the order of PtAu8 > PdAu8 > Au9. It was assumed that the electrostatic interaction of cationic metal clusters with compact anions such as Cland [NO 3 ]induces the structural isomerization from butterfly-motif to crown-motif in Au9 32 , but the structural isomerization of PdAu8 is suppressed by the stiffer Pd-Au bonds, which enhances the activation energy shown in Fig. 4. Therefore, PdAu8-NO3 and PtAu8-NO3 had a crown-motif structure. In this study, we demonstrated that Mo6 could induce the structural isomerization from crown-motif to butterfly-motif for not only Au9 but also PdAu8 and PtAu8, which have stiff M-Au bonds in the cluster core.
This isomerization was not explained by the electrostatic interaction of metal clusters with Mo6. Schulz-Dobrick and Jansen reported that butterfly-motif Au9-B was synthesized using keggin-type [PW 12 O 40 ] 3by controlling the packing of clusters in the crystal 37 . The rock salt-type structure (six anions are coordinated to Au9-B octahedrally, see Supplementary Fig. S12a) is a key to the isomerization of Au9-C to Au9-B because Au9-B is oriented in such a way that the eight PPh 3 ligands, which surround the Au 9 core in an almost cubic fashion, point towards the eight faces to the coordination octahedron with [PW 12 O 40 ] 3-. In fact, Au9-PMo12, PdAu8-PMo12, and PtAu8-PMo12, which have cesium chloride-type structure (eight PMo12 are coordinated to cluster, see Supplementary Fig. S12b) had crown-motif structures 34 . The diameter of butterfly-motif PdAu8-B, and PtAu8-B was estimated to be ca. 1.7 nm (1.60-1.80 nm). If the clusters have the cubic closed packing (ccp) geometry, octahedral site (space) in ccp has 0.66-0.74 nm diameter. Since the diameter of Mo6 is ca. 0.80 nm which is close to the size of octahedral site, Mo6 can occupy the octahedral site in the ccp of Au9-B, PdAu8-B, and PtAu8-B. Single-crystal X-ray diffraction analysis revealed that PdAu8-Mo6 had a rock salt-type structure, as shown in Supplementary Fig. S13, although the PPh 3 ligands and Mo6 were disordered. The power X-ray diffraction patterns also demonstrated that Au9-Mo6 and PtAu8-Mo6 had same rock salt-type    Supplementary Fig. S15. In addition, the PdAu8-B (PtAu8-B) in PdAu8-Mo6 (PtAu8-Mo6) was reversibly isomerized to PdAu8-C (PtAu8-C) by the dissolution into DMSO, as shown in Supplementary Fig. S16. Therefore, the reason why the isomerization of PdAu8-C (PtAu8-C) to PdAu8-B (PtAu8-B) was induced by association with Mo6 is that PdAu8-B (PtAu8-B) becomes more stable by the formation of a rock salt-type structure, which adds strong steric stress to the clusters to overcome the large activation energy for isomerization.

Conclusions
In this study, the composites between PdAu8/PtAu8 cations and Mo6 anions have been synthesized to control the structures of PdAu8/PtAu8. It was found that the optical properties of PdAu8-Mo6 and PtAu8-Mo6 composites differed from those of crown-motif structures, respectively. DFT calculations and XAFS analysis revealed that the PdAu8-C and PtAu8-C in the solution were isomerized to butterfly-motif structures by the association with Mo6 although it was predicted that the structural isomerization from crown-motif to butterfly-motif structure was suppressed in PdAu8 and PtAu8 by the higher activation energy and stiffer radial M-Au (M = Pd, Pt) than Au9. Single-crystal and powder X-ray diffraction analyses suggested that the PdAu8-Mo6 and PtAu8-Mo6 had a rock salt-type packing, which differed from crown-motif PdAu8-PMo12 and PtAu8-PMo12 having a cesium chloride-type packing (eight Mo6 are coordinated to PdAu8 and PtAu8). Six coordination of Mo6 to PdAu8 and PtAu8 stabilizes the semi-stable butterfly-motif structure to overcome high activation energy for structural isomerization.

Methods
Chemicals. All reagents were used as received, without further purification.  32 . NaBH 4 (0.2 mmol) ethanolic solution (14 mL) was added dropwise to the suspension of AuPPh 3 NO 3 (0.6 mmol) in ethanol (24 mL). After stirring for 2 h at room temperature, the solution was filtrated by a membrane filter (pore diameter = 0.20 μm). The filtrate was evaporated, and the precipitate was dissolved in dichloromethane (5 mL). After filtration and evaporation, the precipitate was washed with tetrahydrofuran and hexane. The green powder was obtained by vacuum drying.
[PdAu 8 (PPh 3 ) 8 ](NO 3 ) 2 (PdAu8-NO3) was synthesized by previously reported procedures 34,38 . Solid-form NaBH 4 (0.4 mmol) was slowly added into the suspension of AuPPh 3 NO 3 (0.3 mmol) and Pd(PPh 3 ) 4 (0.1 mmol) in ethanol (12 mL). After stirring for 1 h at room temperature, the solution was added to hexane (200 mL). The precipitated brown solid was washed with hexane and, then with pure water at least three times. After extraction of the residue with ethanol, a dark brown solid was obtained by evaporation of the solvent.
After stirring for 24 h at room temperature, the solution was evaporated. The residual solid was recrystallized with diethyl ether three times. Finally, brown solid was obtained after vacuum drying.
Synthesis of polyoxometalates. (TBA) 2 [Mo 6 O 19 ] (TBA-Mo6) was prepared by a slightly modified version of a previously reported process 40,41 . Na 2 MoO 4 ·2H 2 O (10.3 mmol) in pure water (10 mL) was acidified with 6 M HCl (2.9 mL) at room temperature. In addition to TBABr (4.0 mmol) aqueous solution (2 mL), white precipitate immediately formed. After stirring for 1 h at 348 K, a yellow precipitate formed and was collected by centrifugation (3500 rpm, 5 min) and washed with water and methanol three times each. The product was dissolved in acetone and recrystallized by freezing at 213 K.
(TBA) 3 (50 mL). After stirring for 0.5 h at room temperature, the precipitate was collected by centrifugation and washed with pure water. The precipitate was recrystallized from acetone (5 mL) and hexane (45 mL). Yellow powder was obtained by vacuum drying.
(TBA) 2 [W 6 O 19 ] (TBA-W6) was also prepared according to a reported procedure with a slight modification 40,44 . A mixture of Na 2 WO 4 ·2H 2 O (10.0 mmol) and acetic anhydride (4 mL) in N,N-dimethylformamide (DMF, 3 mL) was stirred at 373 K for 3 h. Then, a mixed acid of acetic anhydride (2 mL) and 12 M HCl (1.8 mL) in DMF (5 mL) was slowly added dropwise to the dispersion. The undissolved solid was removed by centrifugation and was washed with methanol (5 mL). After cooling the filtrate to room temperature, TBABr (5.2 mmol) methanolic solution was added dropwise with rapid stirring. The resulting precipitate was centrifugated and washed with methanol and diethyl ether. The white solid was obtained by vacuum drying.
Characterizations. The fabrication of gold clusters and polyoxometalates, and their composites was confirmed using the following techniques. The UV-Vis-NIR spectra of Au9/MAu8-NO3 in ethanol were recorded in transmittance mode (V-770; Jasco). The UV-Vis-NIR spectra of Au9/MAu8-Mo6, Au9/MAu8-PMo12, and Au9/MAu8-Mo6 were measured in diffuse reflectance (DR) mode. Electrospray ionization (ESI) mass spectra of Au9/MAu8-NO3 in acetonitrile were measured in positive-ion mode using a time-of-flight (TOF) mass spectrometer (micrOTOF-II; Bruker). The ligation of PPh 3 to gold clusters was confirmed using a 31 P NMR spectrometer (AV500; Bruker). The crystal structures of gold clusters were determined using a powder X-ray diffractometer (MiniFlex600; Rigaku). Crystal structure of PdAu8-Mo6 was analyzed by a single-crystal x-ray diffractometer (sc-XRD) equipped at the BL40XU beamline in SPring-8. The crystal packing was solved by a direct method and refined by the full-matrix least-squares method using the Yadokari-XG crystallographic software 45 . The thermal properties of TBA-Mo6 and TBA-PMo12 were measured using thermal gravity-differential thermal analyzer (TG-DTA, STA 2500 Regulus; Netzsch).
The X-ray absorption fine structure (XAFS) spectra of Au9/MAu8-Mo6 and Au9/MAu8-PMo12 were measured at the BL01B1 beamline of the SPring-8 facility of the Japan Synchrotron Radiation Research Institute, where Si(111) doublecrystal monochrometers were used to obtain the incident X-ray beam for Au L 3edge XAFS measurements. All samples were pressed into a pellet and mounted on a copper holder attached to the cryostat. Au L 3 -edge XAFS spectra were measured in the transmission mode using ionization chambers at 10-300 K. In the case of Pd Kand Pt L 3 -edges XAFS measurements, spectra were collected in fluorescence mode using ionization chamber and 19-element Ge solid state detector. The data reduction was conducted using the xTunes software 46 for extended X-ray absorption fine structure (EXAFS), Fourier transform (FT)-EXAFS, and curve fitting analyses and the REX2000 Ver. 2.5.9 program (Rigaku Co.) for the analysis of temperature-dependence of DW factors. The k 3 -weighted χ spectra in the k range of 3.0-18.5 Å -1 for Au L 3 -edge, 3.0-17.0 Å -1 for Pd K-edge, and 3.0-9.0 Å -1 for Pt L 3 -edge were Fourier transformed into r space to obtain FT-EXAFS spectra. The curve fitting analysis was conducted in the r range of 1.7-2.9 Å for Au L 3 -edge, 2.2-2.8 Å for Pd K-edge, and 1.7-3.2 Å for Pt L 3 -edge. Au9-C, Au9-B, MAu8-C, and MAu8-B have Au-P, radial (short) Au-Au (Au9-C, Au9-B) and Au-M (MAu8-C, MAu8-B), and lateral (long) Au-Au bonds in the clusters, as shown in Supplementary Table S2. Thus, the phase shifts and backscattering amplitude functions for Au-P, Au-Au, Au-Pd, Au-Pt, Pd-Au, and Pt-Au were extracted from Au 2 P 3 (ICSD#8058), Au metal (ICSD#44362), and PdAu 24 (SCH 3 ) 18 47 and PtAu 24 (SCH 3 ) 18 , whose structure was constracted by the substitution of Pd with Pt in PtAu 24 (SCH 3 ) 18 , using the FEFF8.5 L program 48 . The Au L 3 -edge FT-EXAFS data were fitted using the calculated phase shifts and backscattering amplitude functions of Au-P, short Au-M (M = Au, Pd, Pt), and long Au-Au bonds according to the previous report 32 and model structures, whose structual parameters are shown in Supplementary Table S2. In the case of Pd K-and Pt L 3edges FT-EXAFS, Pd-Au and Pt-Au bonds were applied for curve fitting analysis, respectively because the Pd-P and Pt-P bonds did not appear in the Pd K-and Pt L 3 -edges FT-EXAFS spectra. Amplitude reduction factor, S 0 , of 1.0 was used for the curve fitting analysis. The DW values were evaluated from the FT-EXAFS at each temperature obtained from EXAFS data (3.0 ≤ k ≤ 16.0 for Au L 3 -and Pd K-edges, 3.0 ≤ k ≤ 9.0 for Pt L 3 -edge) according to the previous work 32 . The values of r and DW at each temperature were determined by least-squares fit analysis while keeping the CN values the same as those obtained from the curve fitting analysis at 10 K 49 using the analytical EXAFS range of 3.0-18.5 Å −1 for the Au L 3 -edge, 3.0-17.0 Å −1 for the Pd K-edge, and 3.0-9.0 Å −1 for the Pt L 3 -edge, respectively.
The Debye-Waller factor (σ 2 ) consists of static (σ S 2 ) and dynamic (σ D 2 ) components, which arise from temperature-independent structural disorder and temperature-dependent atomic oscillation, respectively 31 . According to the Einstein model that assumes three independent harmonic oscillator with different Einstein temperatures (θ E ) for Au-M (M = central Au, Pd, and Pt), Au-Au, and Au-P bonds. σ 2 is expressed as follows: where h, k B , μ, and T represent the Planck constant, Boltzmann constant, reduced mass of adjacent atoms, and temperature, respectively. The θ E values were determined by fitting the temperature dependence of the DW factors for each bond. Density functional theory (DFT) calculations were conducted using the Gaussian 09 program 50

Data availability
All data generated or analyzed during this study are included in this article (and its Supplementary Information files).