On the Structure of a Thiolated Gold Cluster: Au44(SR)282− - The

Feb 19, 2010 - University of Jyväskylä. , ⊥. Tampere University of Technology. This article is part of the C: Protected Metallic Clusters, Quantum Wel...
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J. Phys. Chem. C 2010, 114, 15883–15889

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On the Structure of a Thiolated Gold Cluster: Au44(SR)282-† De-en Jiang,*,‡ Michael Walter,*,§ and Jaakko Akola*,|,⊥ Chemical Sciences DiVision, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, Freiburg Materials Research Center and Department of Physics, UniVersity of Freiburg, Germany, Nanoscience Center, Department of Physics, UniVersity of JyVa¨skyla¨, FI-40014 JyVa¨skyla¨, Finland, and Department of Physics, Tampere UniVersity of Technology, FI-33101 Tampere, Finland, ReceiVed: October 11, 2009; ReVised Manuscript ReceiVed: December 3, 2009

Many thiolate-protected gold clusters prepared by wet-chemistry show abundances of certain compositions which can be explained by the shell-closing of the superatom orbitals 1S, 1P, 1D, ..., leading to magicnumber series 2, 8, 18, 20, 34, 58, etc. One recently isolated such cluster, Au44(SPh)282-, is a potential candidate for the magic number 18, although its structure has not been determined. Applying the “divide-and-protect” concept and recent knowledge obtained from the structures of Au25(SR)18- and Au102(SR)44 (-SR being a thiolate group), we compare two structural models for the Au44(SR)282- cluster. We have optimized their structures, computed powder X-ray diffraction patterns and optical absorption spectra, and performed the superatom analysis on them. The model featuring the -RS-Au-SR- and -RS-Au-SR-Au-SR- motifs in the protective layer shows better energetic stability and agreement with the experimental XRD pattern than the other model which has a protective layer including longer, polymeric RS(AuSR)x motifs. However, the computed optical spectra for both models are quite different from the experimental one. Our models here can serve as benchmarks for further proposals of Au44(SR)282- cluster structures. 1. Introduction Great advances have been made in the past two years regarding thiolated gold nanoclusters. The first major breakthrough came when the single-crystal structure of the Au102(SR)44 cluster was determined.1,2 This structure features a high-symmetry Au79 core protected by 19 monomer (-RS-AuSR-) and 2 dimer (-RS-Au-SR-Au-SR-) motifs. Walter et al.3 explained the cluster’s stability in terms of the superatom concept, where the 58 delocalized valence electrons of the cluster correspond to a shell-closing electron count. Jiang et al.4 hypothesized that the monomer motifs dominate the gold-thiolate interface for all thiolated gold clusters and demonstrated the formation of monomer and dimer motifs on a gold cluster surface from isolated thiolates with density functional theory based molecular dynamics simulations. The second major breakthrough came when Akola et al.5 correctly predicted the structure of Au25(SR)18- which was confirmed by two independent single-crystal structure determinations.6,7 This smaller cluster has a centered-icosahedron Au13 core protected exclusively by six dimer motifs. The Au25(SR)18- cluster’s stability is explained by the shell-closing electron count of 8.3,5 On the basis of the structures of Au102(SR)44 and Au25(SR)18-, Tsukuda and co-workers8 proposed three structural principles to construct models for thiolated gold clusters: (1) highsymmetry core, (2) more dimer motifs than monomers for the smaller clusters, and (3) the surface atoms of the core have to be fully protected by the terminal thiolates of the motifs. Using these principles, Tsukuda and co-workers8 proposed a bi† Part of the “Protected Metallic Clusters, Quantum Wells and MetalNanocrystal Molecules Symposium” special issue. * To whom correspondence should be addressed. E-mail: jiangd@ ornl.gov; [email protected]; [email protected]. ‡ Oak Ridge National Laboratory. § University of Freiburg. | University of Jyva¨skyla¨. ⊥ Tampere University of Technology.

icosahedral core protected by a combination of monomer and dimer motifs for the structurally unknown Au38(SR)24 cluster, and Pei et al.9 demonstrated computationally that a face-sharing bi-icosahedral core protected by six dimer motifs and three monomer motifs is more stable than all the previously proposed models for Au38(SR)24.4,10-12 The structural feature at the interface between the Au core and the protective layer of thiolated gold clusters reflects the “divide-and-protect” concept which was originally proposed by Ha¨kkinen et al.11 The basic idea is that not all of the gold atoms are in the core but some gold atoms are in the protective layer forming gold-thiolate complexes which then protect the pure Au core. Recent developments in both experiments and computational studies show the evolution of the viewpoint regarding the gold-thiolate complexes in the protective layer. Originally, (AuSR)4 cyclomers were proposed, but they were found to bind weakly to the core.11 Longer AuSR polymers were also proposed.13 However, the subsequent single crystal structures of Au102(SR)44 and Au25(SR)18- clearly displayed the -RS-AuSR- (monomer) and -RS-Au-SR-Au-SR- (dimer) motifs.1,6,7 Walter et al.3 further highlighted that the protective complexes are of the form RS(AuSR)x, where the oligomeric units -RSAu-SR- and -RS-Au-SR-Au-SR- correspond to x ) 1 and 2, respectively. Most recently, in their efforts to predict structures for high thiolate/Au ratio clusters such as Au20(SR)16 and Au10(SR)8, Zeng et al.14 and Jiang et al.15 demonstrated that the trimer motif (-RS-Au-SR-Au-SR-Au-SR- or x ) 3) is indeed needed. The existence of protective complexes with x > 3 remains to be seen, but as the thiolate/gold ratio approaches unity, the boundary between the core and the protective layer will become indistinguishable. Apart from geometric robustness, the detailed electronic structure of thiolated gold clusters plays a decisive role for stability. The magic-number series of the electron shell-closings goes as 2, 8, 18, 20, 34, 58, ... for a spherical square-well

10.1021/jp9097342  2010 American Chemical Society Published on Web 02/19/2010

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potential.16 The Au102(SR)44 and Au25(SR)18- clusters correspond to the electron counts of 58 and 8, respectively. Lopez-Acevedo et al.17 proposed a structure for the Au144(SR)60 cluster which has an electron count of 84, eight electrons short of the magic number 92. This is in agreement with the experimental observation that the 29 kDa cluster (140-150 Au atoms) has several available oxidation states in electrochemistry18,19 and sets an upper record for the superatom electron count. Furthermore, the most recent mass-spectrometry measurements for the 29 kDa cluster20,21 pinpoint the specific Au144(SR)60 composition as suggested by theory.17 Based on Tsukuda’s principles, Jiang et al.15,22 recently proposed several candidates for the magic number 2, the smallest thiolated-gold superatom. The best candidate they considered is Au12(SR)9+ which features an octahedral core protected by three dimer motifs each binding to two diagonal vertices.22 Here, further comparison of computed properties with measured ones is needed to elucidate the structure of the isolated and mass-spectroscopically identified Au12(SR)9 cluster.23 Recently, Dass24 identified Au68(SR)34 by mass spectrometry which corresponds to the magic number 34. Price and Whetten25 isolated and characterized the Au44(SPh)282- cluster which has a formal valence electron count of 18 according to the superatom complex (SAC) model.3 Therefore, it is a candidate for the magic number 18, corresponding to the delocalized electron configuration 1S21P61D10, where S, P, and D denote the global angular momentum shells. However, its structure has not been determined experimentally, and no models have been proposed. In this work, we seek structural models for the Au44(SR)282- cluster, based on the advances accumulated in the past several years about thiolated gold clusters. Two competing models will be addressed in the divide-and-protect framework: one based on monomer and dimer motifs using Tsukuda’s structural principles8 and the other based on the longer oligomeric Au-SR motifs; we call the former the monomer-dimer model and the latter the polymer model. We have computed their total energies, optical absorption spectra, and X-ray diffraction patterns and compared with experiments. We have also analyzed their valence electron distributions to see whether they show the SAC features of the 18 shell-closing electron count. 2. Methods Several methods and program packages which are based on the density functional theory (DFT) of electronic structure were used to study the Au44(SR)282- cluster with -SCH3 side groups representing -SR. The initial geometry optimization for the polymer model was performed with the Car-Parrinello molecular dynamics (CPMD) package.26 The exchange and correlation part of the total energy functional is calculated by using the general gradient-corrected approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE),27 and the interaction between the valence electrons and the ionic cores is described by the scalarrelativistic pseudopotentials of Troullier and Martins.28 The explicit Au valence is 5d106s1, and the valence electron density is represented in a plane wave basis with a kinetic energy cutoff of 70 Ry (952 eV). The periodic boundary conditions of the cubic unit cell of side length 25 Å have been switched off by using the method of Hockney.29 The initial geometry optimization for the monomer-dimer model was optimized with Vienna ab initio simulation package (VASP)30,31 with planewave basis set, periodic boundary conditions, and GGA-PBE functional. Blo¨chl’s all-electron projector augmented wave (PAW) method,32 as implemented by Kresse and Joubert33 within the frozen core approximation, was

Jiang et al. TABLE 1: Different Combinations of Monomer (SR-Au-SR-) and Dimer (-RS-Au-SR-Au-SR-) Motifs for Au44(SR)282scenario

number of monomer

number of dimer

Au core

number of terminal thiolates

1 2 3 4 5

2 5 8 11 14

8 6 4 2 0

26 27 28 29 30

20 22 24 26 28

employed to describe the electron-core interaction. Scalarrelativistic PAW potentials and a converged 450 eV kinetic energy cutoff were used. The Au44(SR)282- cluster was placed in a cubic box of a ) 25 Å and a uniform compensating background charge was assumed. The force tolerance for structural optimization was set at 0.05 eV/Å. Both the polymer and monomer-dimer models were further optimized with the same set of parameters by using parallel resolution-of-identity density functional theory (RI-DFT) calculations34 and GGA-PBE in Turbomole V5.10. The def2-SVP orbital and auxiliary basis sets35 were used for all atoms for structural optimization, and the calculations did not include periodic boundary conditions which require additional corrections for charged systems. This was a decisive factor for choosing this method for the final structural optimization of Au44(SR)282- isomers. An effective core potential which has 19 valence electrons and includes scalarrelativistic corrections was used for Au.36 The force convergence criterion was set at 0.05 eV/Å. The global angular momentum analysis of the Kohn-Sham orbitals and the optical spectra were performed with the realspace grid code GPAW,37,38 using GGA-PBE. The Kohn-Sham states were represented via the PAW method,32 where the smooth wave functions are represented on a real space grid using 0.25 Å grid spacing. A frozen core approximation was used for the core electron states. For the superatom analysis of the valence electrons, we have expanded the Kohn-Sham orbitals φn(r) in spherical harmonics Ylm(r) centered at the clusters center of mass to obtain the radial weights

φnlm(r) )

∫ dr Y*lm(r)φn(r)

The orbitals weight for a particular global angular momentum l is then calculated as

cnl(R0) )

∑ ∫0

R0

dr r2 |φnlm (r)| 2

m

where R0 ) 5 Å has been used for representing a cutoff between the Au core and the RS(AuSR)x ligand units (R ) CH3). The global angular momenta will be denoted by capital letters (l ) S, P, D, ...) in order to distinguish them from the atom-centered local angular momenta. X-ray diffraction patterns were simulated using the Debye formula, following a previous example.13 3. Results and Discussion We discuss first the construction of the monomer-dimer model and then the polymer model. After this, we compare the properties of the two models. 3.1. Monomer-Dimer Model. Two strategies were employed to construct an initial model for the Au44(SR)282- cluster. First, we used Tsukuda’s three principles.8 According to them, there are five possible scenarios of different combinations of monomer and dimer motifs, as shown in Table 1. Au44(SR)282-

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Figure 1. Constructing the initial monomer-dimer model for Au44(SR)282- based on 8 monomer and 4 dimer motifs protecting an fcc Au28 core. Au, green; S, blue; R-, not shown.

Figure 2. Optimized structure (a) of the monomer-dimer model for Au44(SR)282- and its Au28 core (b) with the inner Au4 shell highlighted in yellow. Au, green and yellow; S, blue; R-, not shown.

should be similar in size to Au38(SR)24 for which the most stable structural candidate features a combination of 3 monomers (-RSAu-SR-) and 6 dimers (-RS-Au-SR-Au-SR-).9 Therefore, we think that Au44(SR)282- should have roughly equal numbers of monomers and dimers, which points to the combinations of scenarios 2 and 3. Scenario 3 has a core of Au28 and 24 terminal thiolates, so that the Au28 core should consist of an inner shell of Au4 and an outer shell of Au24. There are several structural models for this Au28 core, including an fcc construction, an Au4 surrounded by a snub cube, and a C3 construction.39 We tried all these three cores (as well as a quad-icosahedral core, see the Supporting Information) and found that the fcc construction offers the most stable model for scenario 3 in Table 1. Figure 1 shows the fcc construction of scenario 3. The tetrahedral Au28 core is taken out of the bulk Au fcc lattice. Its inner core is the Au4 tetrahedron, and its outer Au24 shell consists of 4 supertriangle faces, 6 double-square edges, and 4 triangle corners. In the initial structure, the four dimer motifs wrap around the four high-curvature corners, whereas four monomers protect the 4 faces and the rest four protects 4 of the 6 edges. After geometry optimization, however, the initial structure underwent dramatic changes. Figure 2 shows the final structure and its Au28 core. One can see that the core becomes less ordered (Au-Au distances 2.95 ( 0.12 Å), although the inner Au4 shell stays inside and the four monomer and eight dimer motifs remain intact after optimization. The Au28 core has an approximate C2 symmetry (within 0.2 Å tolerance), in contrast with its initial Td symmetry. We call this structure the monomer-dimer model. Figure 3 shows the model with the core highlighted and the methyl groups displayed. The Au-Au

Figure 3. Optimized structure of the monomer-dimer model for Au44(SCH3)282- with the 28 core Au atoms represented in large spheres and the 16 Au atoms in the ligand-shell shown in orange. S, yellow; C, gray; H, white.

distances at the interface between the core and ligand-shell are 3.21 ( 0.13 Å. 3.2. Polymer Model. The other strategy to create models for thiolated-gold clusters is based on the original “divide-and-

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Figure 4. Two Au44(SCH3)282- isomers which are based on the Au16 cage (fcc symmetry, large spheres) in the core. (a) Isomer with six cyclic oligomers has got two tetramers and four pentamers placed octahedrally around the core. (b) Isomer with a chain-like ligand-shell comprises two capping (AuSCH3)14 rings (constrained Au16 cage, final geometry in Figure 5). The latter has been obtained from the former by breaking/forming Au-S bond in the ligand-shell.

Figure 5. Final optimized structure (a) of the polymer model for Au44(SR)282- from Figure 4b and its Au24 core (b) with the inner Au12 shell highlighted in yellow. Au, green and yellow; S, blue; R-, not shown.

protect” scheme reported by Ha¨kkinen et al. in 2006.11 In this study, DFT optimization of the Au38(SCH3)24 cluster with an initial fcc-symmetry (truncated octahedron of 38 atoms) resulted in a formation of 6 cyclic (AuSCH3)4 units protecting the 14 atom core. This illustrated that Au atoms can participate both in the core and ligand-shell, a phenomenon that was later confirmed by the experimental structure characterization (Xray diffraction) of the Au102(SR)44 and Au25(SR)18- nanoparticles.1,6,7 Based on the original finding of cyclic oligomers, we have built a model for Au44(SR)282- where a 16 atom cage with fcc symmetry (this is actually a stable isomer for Au16)40 is surrounded by six cyclic oligomers which have been placed octahedrally around the core. The geometry is shown in Figure

4a together with the highlighted Au-S oligomer conformation. In order to match with the composition, i.e., 28 thiolate side groups, there are two (AuSCH3)4 tetramers and four (AuSCH3)5 pentamers (note that two of the pentamers are significantly bent). The DFT-optimized geometry has retained the symmetry of the Au16 cage, and the interaction with the cyclic oligomers and the core is rather weak (Au-Au distances 2.98 ( 0.11 Å, no Au-S bonds in between). This may be partially related to the negative charge state of the cluster. Starting from the structure in Figure 4a we have built other geometries with cyclic oligomers by swapping Au-S bond in the ligand-shell. In other words, we have formed larger rings by breaking the initial tetramers and pentamers gradually while

On the Structure of Au44(SR)282enforcing new Au-S bonds in a concerted fashion. This has been performed in practice by running short sequences of constrained molecular dynamics in the Car-Parrinello mode26 for the whole nanoparticle, where selected Au-S distances elongate/shrink by a constant value for each time step while the other degrees of freedom remain at low temperature. The used time step is 0.121 fs (5 au), and the fictitious electron mass has been set to 800 me in the Car-Parrinello MD. One such (metastable) geometry is displayed in Figure 4b with two intertwined (AuSCH3)14 rings (“polymers”) which enclose the core in a manner similar to two leather pieces in a tennis ball. We call the structure of Figure 4b as the polymer model. The fcc-like Au16 cage in the core is, again, visible, but it twists upon further structural optimization, and 8 Au atoms from the ligand-shell become part of the core. Furthermore, the Au-SR polymer rings break down during the structural optimization, and the final relaxed structure comprises an Au24 core with an Au20(SR)28 protective layer (Figure 5a). The new Au24 core has an Au12 cage as the inner shell (Figure 5b), with the rest 12 Au atoms scattered around the cage. The final protective layer of the polymer model consists of two monomers (RS(AuSR)x, x ) 1), three dimers (x ) 2), two trimers (x ) 3), and one hexamer (x ) 6). This isomer has 1.6 eV lower total energy than its parent (Figure 4a) which correlates with the more effective protection of the modified core, and with the new anchoring Au-S bonds (2.59 Å) as the Au-SR rings break at the interface. A similar isomer with only one folded (AuSCH3)28 ring initially results in a comparable total energy and geometry (not shown). 3.3. Comparison of the Monomer-Dimer Model and the Polymer Model. We found that the monomer-dimer model is 2.0 eV more stable than the polymer model. They both have similar HOMO-LUMO gaps of 0.64 eV. This gap can be compared with the 0.9-eV gap found for the bi-icosahedral Au38(SR)24 cluster9 and the 1.2-eV gap for the icosahedral Au25(SR)18- cluster,5 all based on the PBE functional. The 0.64eV gap is a bit lower than what we expected for the Au44(SR)282cluster, because we originally estimated a gap of ∼0.77 eV, based on the extrapolation of the PBE gaps of Au25(SR)18- and Au38(SR)24 against the number of gold atoms to 44. Although the polymer model with a constrained Au16 fcc-cage in the core (Figure 4a) resulted in a gap of 0.90 eV, this was an early stage of the structural optimization and the core changed significantly, as discussed above. The higher energetic stability of the monomer-dimer model compared to the polymer model is expected, as have been demonstrated for the Au38(SR)24 cluster;4,9-12 namely, the shorter RS(AuSR)x oligomers (x ) 1 and 2) are favored as the dominant structures for the protective layer. This is presumably related to the reduced role of the terminal thiolates in longer oligomers.12 Figure 6 compares computed powder XRD patterns of the two models, in comparison with the experiment.25 The experimental pattern shows a dominant peak at 4.2 with a broad hump around 8.0. The dominant experimental peak is reproduced in both monomer-dimer and polymer models, although the computed peak positions are slightly smaller (by 0.1 nm-1). The polymer model displays a shoulder peak at 2.7, which is absent from the experiment and not pronounced in the monomer-dimer model. This shoulder peak in the polymer model is caused by the inner cage, which contributes a larger spacing. Overall, the XRD pattern of the monomer-dimer model shows a better agreement with the experiment. Figure 7 shows the computed optical absorption spectra for the two models in comparison with the experiment.25 The experimental absorption measured from ∼1.1 eV up shows an

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Figure 6. Computed powder X-ray diffraction patterns for (a) the monomer-dimer model and (b) polymer model, in comparison with experiment.25

Figure 7. Computed optical absorption spectra for (a) the monomer-dimer model and (b) polymer model, in comparison with experiment.25

on-set of absorption at ∼1.6 eV and two broad peaks at 2.1 and 3.0 eV. Both proposed models show weak absorption below 2.0 eV, while the monomer-dimer model displays two strong adsorption maxima at 2.4 and 2.7 eV and the polymer model has a strong absorption maximum around 2.9 eV. However, both computed spectra are rather different from the experimental one, indicating that better models should exist. Figure 8 shows the electronic-structure analysis of delocalized valence electrons in both models. The 44 delocalized Au 6s electrons, 28 electron-localizing SR units and the overall charge of -2 lead to a free electron count of 18. This electron count matches the shell closing of a hollow spherical symmetric structure with 1S21P61D10 configuration, and it is responsible for the increased stability of a hollow Au162- cage.40 The central Au16 cage in the polymer model is considerably distorted (see Figure 5) but still provides the expected state symmetry around the Fermi level as can be seen in Figure 8b: The states below the gap (occupied) show mainly D symmetry and the states above the gap mainly F symmetry. The 2S state can be found in the 1F manifold as a consequence of the distortion from spherical symmetry. Nevertheless we can still assign superatom properties to the polymer model.

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Figure 8. Superatom analysis of the delocalized valence electrons for (a) the monomer-dimer model and (b) polymer model. The colors denote global angular momentum components with respect to the center of mass.

The lower-energy monomer-dimer model (Figure 8a) does not show clear delocalized symmetries of the states near to Fermi energy as seen in Figure 8b. The states below the gap do not show a clear D character anymore, and only the LUMO has a pronounced F symmetry. The next higher energy state is of D symmetry, however; hence the HOMO-LUMO gap does not reflect a spherical shell closing. The strong splitting and mixture of the spherical D and F shells is a consequence of the strong distortion from spherical symmetry found in the core (Figure 2) and crystal-field (fcc) effects. The monomer-dimer model built from the Tsukuda’s three structural principles is energetically superior compared to the polymer model, which is expected based on the recent progress in elucidating and understanding the geometry and structure of thiolate-protected gold nanoclusters. Certainly, the powder-XRD pattern also indicates that the monomer-dimer model is a better approximation to the reality. However, the valence-electron analysis indicates that the monomer-dimer model is not a good superatom and the computed optical spectrum indicates that better models may exist. Nevertheless, it is currently the best model in terms of energetic stability and could serve as a benchmark for searching for better structures. We consider that the combinations of monomer and dimer motifs shown in Table 1 can still serve as a guideline for constructing new models; but the key is to look for better models for the core. We have tried four Au28 cores within the monomer-dimer model, which is only a tiny sampling of the configuration space (one also needs to consider the other scenarios in Table 1). We hope that the global minimum search methods41 can help one to find lower-energy isomers for the Au44(SR)282- cluster which will show electron shell-closing and better agreement with the experimental optical spectrum, before the cluster yields to totalstructure determination. 4. Summary and Conclusions We proposed two structural models for the Au44(SR)282nanocluster based on the divide-and-protect concept: the

monomer-dimer model based on the Tsukuda’s three structural principles8 and the polymer model based on the original “divideand-protect” scheme.11 The monomer-dimer model consists of an Au28 core covered with 8 monomer (-RS-Au-RS-) and 4 dimer (-RS-Au-SR-Au-SR-) motifs, while the polymer model consists of an Au24 core and a more diverse set of thiolate-gold oligomers. We found that the monomer-dimer model is more stable by 2.0 eV and has a better agreement with experiment in terms of the powder-XRD pattern. However, superatom analysis shows that this structure has split 1D and 1F electron shells while the polymer model does have a good shell-closing of the 1D orbital. Computed optical spectra for both models are rather different from the experimental one. We consider that the present work is the first attempt toward elucidating the structure for the Au44(SR)282- nanocluster, and better models can be predicted by benchmarking to the present geometries. Acknowledgment. This work was supported by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy. We thank CSC (Espoo, Finland) and JSC (Forschungszentrum Ju¨lich, Germany) for providing computational resources. This research also used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0205CH11231. The authors thank H. Ha¨kkinen and R. L. Whetten for their enthusiasm, encouragement, and discussion during the course of this collaborative project. Supporting Information Available: Coordinates for the two structures in Figures 3 and 5a and two quad-icosahedral models. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Jadzinsky, P. D.; Calero, G.; Ackerson, C. J.; Bushnell, D. A.; Kornberg, R. D. Science 2007, 318, 430. (2) Whetten, R. L.; Price, R. C. Science 2007, 318, 407.

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