Polymorphism in magic-sized Au144(SR)60 clusters

Ultra-small, magic-sized metal nanoclusters represent an important new class of materials with properties between molecules and particles. However, their small size challenges the conventional methods for structure characterization. Here we present the structure of ultra-stable Au144(SR)60 magic-sized nanoclusters obtained from atomic pair distribution function analysis of X-ray powder diffraction data. The study reveals structural polymorphism in these archetypal nanoclusters. In addition to confirming the theoretically predicted icosahedral-cored cluster, we also find samples with a truncated decahedral core structure, with some samples exhibiting a coexistence of both cluster structures. Although the clusters are monodisperse in size, structural diversity is apparent. The discovery of polymorphism may open up a new dimension in nanoscale engineering.


Supplementary Note 1: The PDF method
The PDF method is here briefly described, while more information can be found elsewhere. 1,2 The experimental PDFs are obtained from raw total scattering data using the program PDFgetX3 3 by subtracting background scattering as well as Compton and fluorescent intensities that do not carry structural information. The remaining coherent scattering intensity I(Q) is then normalized by the atomic scattering factors to yield the total scattering structure function S(Q): Here, the average values of the scattering factor f(Q) are calculated over all chemical species in the specimen. The structure function can then be expressed in the form of reduced scattering structure function = ( − 1) which can be evaluated from an atomic structure by the Debye scattering equation: Here f i is the scattering power of atom i and r ij is the distance between atoms i and j. By applying a Fourier transformation, the sine-terms in the Debye equation transform to Dirac delta functions and thus yield real-space probabilities of interatomic distances in the material.
The integration limits Q min , Q max in the Fourier integral are the Q-limits of the data measured in the X-ray experiment.
Given a specific structure model, the expected PDF can be simulated from atom coordinates by evaluating F(Q) with an extra term for pair distance uncertainty arising from atom displacements due to thermal motion or static disorder: The scattering factors are here omitted for simplicity. The static and thermal atom displacements cause a spread in pair distances and thus broadening of PDF peaks, but at a short distance the peaks are sharper due to correlated motion of tightly bound atoms. 4 The U ij term for the mean square deviation of the atom distance r is therefore adjusted according to the correlated motion model by Jeong et al as: 5 !" For a given structure model, the agreement of its simulated PDF with the measured data is evaluated as a least-squares residuum R w : The parameters of a structure model, such as atom positions or displacement parameters can be refined to minimize the difference between experimental and simulated PDFs.
Here, we do this using the program suite DiffPy-CMI.

Supplementary Note 2: Cluster refinement procedures
All cluster modeling was done using the same procedure. All atomic positions in the cluster model were given as xyz coordinates, taken either from published models, closed packed derived models, or Mark decahedrons models. For all refinements, these positions were kept fixed which ensured that the basic structure did not change. However, the atomic displacement parameters (ADP) were refined, along with the δ 2 value taking into account the correlated motion described above. An expansion coefficient allowing the whole structure to expand isotropically was also refined, which served as a way to fit the interatomic distances without changing the structural model. For certain refinements (noted in the main text) separate ADPs and expansion factors were refined for the shell and core atoms, where the shell atoms were considered as those with 9 or fewer Au neighbors. The atoms were considered neighbors if their distance was smaller than the midpoint between the first and the second neighbor separations in a bulk fcc lattice. A scale factor was furthermore refined to match the PDF intensities. The PDFs were refined in the r-range 1-20 Å. The Q-range used in the Fourier transform of the calculated Debye intensities was 1.3 to 28 Å -1 , i.e. the same range used when obtaining the experimental PDFs from total scattering data from 11-ID-B, APS and ID11, ESRF.

Supplementary Note 3: Scattering power
The experimental PDF pattern contains contributions from the gold core as well as from the thiolate ligand molecules (SR) 60 that passivate the surface. In a PDF measurement the signal from each atom is scaled by its scattering strength, which is proportional to the number of electrons, or atomic number, therefore we can estimate the relative ratio of the gold core signal to the total PDF. The total scattered intensity is proportional to: For the Au 144 (p-MBA) 60 cluster (containing 144 gold atoms, 60 sulfur atoms, 420 carbon atoms, 120 oxygen atoms and 300 hydrogen atoms), this implies that 50% of the diffracted radiation originates from the 144 gold atoms and is independent of thiolate arrangement. If including the 60 sulfur atoms, the model will account for 60% of the scattered radiation. Furthermore, the organic carbon chains are not rigid units and not well ordered at r-distances larger than ca. 3 Å, meaning that they would not give rise to significant features in the final PDF. These two factors show that the contribution of the ligands to the signal in the measured PDF will be small. For the fcc lattice, the closest size was 141 atoms at the 8-th neighbor distance and for the hcp lattice the nearest structure had 147 atoms within the 14-th neighbor separation.
Although these sizes are slightly different from the expected size of 144 atoms, the PDF simulation is quite insensitive with respect to the addition or removal of a few surface atoms and we wished to preserve the close-packed spherical particle. The next attempted model was a two-phase fit of the PDFs from cutouts from fcc and hcp. Mixing the PDFs from fcc and hcp models is a strategy to mimic stacking faults in close-packed structures. 6 The expansion coefficients in both phases were tied to the same value in the refinement, as were the ADPs of their core and shell atoms.
As an approximate measure of the surface energy we also include the number of free bonds per atom BPA, which was evaluated as the per-atom average ⟨12 -Z i 〉 with Z i being the coordination number of atom i. The atoms were considered neighbors if their distance was smaller than the midpoint between the first and the second neighbor separations in a bulk fcc lattice.
The fcc/hcp mixture fits the data well, with the main features reproduced well and no significant missing peaks. R w is also approaching a value what would be considered a good fit especially in the PDF literature, especially for nanoparticles. 7,8 However, issues are seen at larger r-values and the refined ADPs are very large, indicating deficiencies in the model. The expansion coefficient of the surface layer is negative, which seem unphysical. As well as the issues with the fit, these close-packed models do not explain the extreme stability and magic number of the 144 gold atom cluster.

Supplementary Note 5: Marks decahedra
The Marks decahedron size and shape are controlled by 4 integral coefficients N, M, K and T. Coefficient N is the number of atoms along the central 5-fold axis, M is the number of (002) shells, K is the number of atomic columns along the twin boundary, and T is a number of planes perpendicular to the central axis truncated from top and bottom of the decahedron. 9,10 Variations of these coefficients produced 20 clusters in the size range from 134 to 154 atoms, all of which were fitted to the data. Out of this group the 9 clusters generated with N = 6 showed remarkably better fit than the remaining structures.

Supplementary note 6: MD6341 with staples
The MD6341 structure has 10 facets with fcc (111) structure exposed (top and bottom) as well as 5 facets with fcc (100) structure (sides). Various configurations of 30 -SR-Au-RS-staples on the MD6341 were considered. Firstly, a model was created were the staples were only attached to the (111)-facets of the clusters, as this is the bonding motif that is most studied in gold-thiol structures. To get physical S-Au distances that fit to the experimental PDF, the staples were twisted: The Au atoms was kept fixed centrally between the two gold anchors, but the sulfur atoms were displaced from the anchors. This same motif is seen in the DFT structures, and is allowed within the degrees of freedom in the staple structure. While an acceptable fit was obtained, the proximity of the staples gives rise to some unphysical short atom-atom distances (e.g. Au-S distances of 1.44 Å).
The structure also seems unlikely due to naked (100) surfaces. Models with different rearrangements of the staples were then constructed, where thiolate bonding on the (100) surfaces was included. We assumed the same staple structure, where the -SR-Au-SRstaples were anchored on the (100) surface, although this has not yet been reported on Au (100) surfaces. Several different models were constructed, of which some are presented in supplementary Figure 12. All of the models give acceptable fits to the data, with R w values of ca. 15-16%. The PDF is somewhat sensitive to the staple attachment, as subtle differences between the features in the fitted PDF can be observed.

Supplementary note 7: Synthesis of Au 144 (SR) 60
Chemicals: The polymer solution was initially a slightly opaque canary yellow color, which turned clear and colorless the following day. Au 144 (pMBA) 60 was then synthesized by reducing 25 mL aliquots of polymer with freshly prepared aqueous NaBH 4 (25 mL, 150 mM) in 50 mL conical vials over a period of 2 hours while shaking vigorously on a vortexing mixer.
The particles were then precipitated with the addition of 1 mL 5 M NH 4 OAc and 24 mL methanol, followed by centrifugation at 4,000 rpm for 10 min. The supernatant was discarded, the particles (which appeared dark brown/black) were washed twice with approximately 5 mL of nanopure water and precipitated again as described above. The resulting supernatant was decanted and the pellet was allowed to air dry. The particles were redispersed in water and analyzed by polyacrylamide gel electrophoresis (16% PAGE run at 110 V for 1 hour in 1X TBE). Polyacrylamide gel electrophoresis is well established for validating thiol protected nanocluster preparations. 12 After fractional precipitation with first 37.5% aqueous methanol and subsequenty 41% aqueous methanol, both in 100mM mM NH 4 OAc the product was indistinguishable from known ml of ice-cold water was prepared. The solutions were than combined rapidly and stirred.
After 5 hours the stirring was stopped and a black oil settled out of the solution. The supernatant was discarded and the product was precipitated out of the oil by adding methanol. The precipitate was then centrifuged and the supernatant discarded. In order to remove any remaining thiol, the precipitate was washed with methanol. Au 25 (SR) 18 -1 was removed by washing the precipitate with acetone. Au 144 (SR) 60 was extracted from the precipitate with dichloromethane and then dried. Au 144 (SR) 60 protected by alkanethiols was further purified by size exclusion chromatography.
The synthetic products were validated by ESI-MS and voltammetry for organosoluble products, by TEM, and by polyacrylamide gel electrophoresis for watersoluble products. Supplementary Figure 1 shows the results of Electrospray Ionization Mass Spectrometry. Electrospray mass spectra were acquired on an Agilent 6220 TOF-MS using 2µl injection volumes with a flow rate of 0.3 ml/min The sheath gas temperature was set at 120 ºC and a drying gas with a flow rate of 5 L/min was used. The pressure of the nebulizer was 45 psig. A potential of 4000 V was applied for the V cap .
The potential applied to the fragmentor and skimmer were 75 V and 60 V, respectively. . Cs + , Na + , and K + ions were present in all samples, contributing to the appearance of multiple ion peaks. The raw data were smoothed using a moving average alorithm.
In the ESI-MS, we observe that Au 144 (SR) 60 is the dominant product, with Au 137 (SR) 56 detectable as a minor product. Table S5 shows the assignments of the numbered major peaks. In addition, any of the un-numbered minor peaks we examined (40 additional peaks) we examined could also be assigned as either Au 144 (SR) 60 or Au 137 (SR) 56 .
Differential pulse voltammetry is previously established as a means for identifying nanoclusters after purification, for instance as a column chromatographic detector. 14,15 As prepared here, Au 144 (SR) 60 exhibits at least 14 reversible oxidation/reductions waves and the potential between each peak is almost equal for each charging event, indicating purity of material. It has been shown that the potential at which these charging events occur is related to size of the dielectric layer, solvent, and supporting electrolyte in solution. 14 The peak spacings, peak shape, and electrochemical reversibility of the system correlate to previous reports for all four of the organic soluble Au 144 (SR) 60 compounds. 14