Ligand and Solvation Effects on the Structural and Electronic

Article pubs.acs.org/JPCC

Ligand and Solvation Effects on the Structural and Electronic Properties of Small Gold Clusters F. Dufour,†,‡,§ B. Fresch,† O. Durupthy,‡,§ C. Chaneac,‡,§ and F. Remacle*,† †

Department of Chemistry, University of Liege, B6c, B4000 Liege, Belgium Sorbonne Universités, UPMC Univ Paris 06, CNRS, Collège de France, UMR 7574, Chimie de la Matière Condensée de Paris, F-75005 Paris, France

‡

S Supporting Information *

ABSTRACT: The catalytic, electrochemical, and optical properties of gold clusters and small nanoparticles depend on the cluster size, on the nature of the ligand shell and on the solvent environment. The structural and electronic properties of the neutral and trication bare cluster Au11 are investigated using density functional theory. We focus on the influence of the cluster charge, the solvent, and the nature and number of the ligands (thiol, thiolate, thiyl radical, phosphine, chloride, and chlorine) on the cluster electronic structure and its geometry, with special attention to the structural motifs present in the metallic core of the different conformers. Single bindings are systematically studied and a comparison with full ligand coverage is discussed. Pure thiyl and phosphine ligand shells as well as mixed thiyl/phosphine shells are considered. This study provides a better understanding of the ligand shell and cooperative effects that could be probed experimentally. of mass spectrometry,15 infrared spectroscopy,16,17 or nuclear magnetic resonance18 results. Ligand-protected gold clusters have been extensively studied theoretically both in gas phase and in solution. Early works focused on small bare gold clusters using solid state and quantum chemistry implementations of density functional theory (DFT).19,20 Special emphasis was put on the size dependence of the 2D−3D transition in small clusters.21−23 Because of the large relativistic effects in gold,24−26 the 2D−3D transition occurs at a larger size than for other coinage metals, but the precise nuclearity at which the transition occurs is still an open issue.27,28 Clusters of different sizes, that is, the tetrahedral Au20,17,29,30 Au25,31−33 Au55,34−36 Au102,6,37,38 or Au144,39−41 have been investigated in detail. The ligand shell protecting these clusters plays a major role in their structural, electronic, and optical properties, like the metallic or insulating character or the plasmonic properties.10,37,42,43 Here we aim to better understand the effects of different binders and of the solvent environment on small gold clusters through a computational study, mostly at the level of density functional theory (DFT). We focus on undecagold clusters in the neutral and 3+ charge states. Several complexes based on the Au11 metal core coordinated with phosphines, thiyl radicals, and pseudohalides have been experimentally obtained and characterized.44−47 The crystal structures of many phosphine-

1. INTRODUCTION Gold clusters and small nanoparticles are widely investigated for optical,1−3 catalytic,4−8 and electrochemical3 properties. Because these properties are highly correlated to the size of particles that must be adjusted for each application, size control is mandatory to obtain useful materials. The same holds true for the control of interfacial properties. For example, in diagnostic and therapeutic applications, gold nanoparticles used as radiosensitizers9 are harmless only if their size is small enough to allow elimination by the kidneys.10 Yet, the genotoxicity of the gold cluster Au55 has been proved, with a major influence from the ligand shell nature.11 In order to obtain active catalytic materials, the nanoparticles must be of a few nanometers at most.6,12 Recently, size controlled subnano metal clusters with a dozen atoms, smaller than 1 nm, have been employed in catalysis with promising results.4,13 Bare small gold clusters and nanoparticles are usually not stable. Functionalization is needed to stabilize and tune the size of gold clusters. Passivation by ligands is used not only as a way to prevent the aggregation of the gold nanoparticles but also to control the cluster formation.14 Most syntheses take place in a solvent, usually in alcohol or water. Since ligand binding and solvation both modify the structural and electronic properties of the nanoparticles, they can be used at an advantage to adjust them. Theoretical studies of functionalized small clusters provide understanding on the interplay between structural and electronic properties and can be used for the interpretation © 2014 American Chemical Society

Received: September 9, 2013 Revised: January 8, 2014 Published: January 21, 2014 4362

dx.doi.org/10.1021/jp409019z | J. Phys. Chem. C 2014, 118, 4362−4376

The Journal of Physical Chemistry C

Article

On the other hand, we find that thiolates and thiyl radicals strongly bind gold clusters in a bridge Au−S−Au pattern in the gas phase and in water. Their binding is accompanied by a significant distortion of the geometry of the bare Au cluster. Solvation does not change drastically the geometry of the ligated cluster but it does influence the energetics of the interaction, especially for the charged species. For example, compared to the thiyl radical, the binding strength of thiolates is disfavored by solvation effects. We draw the analogy between the thiyl and the thiolate anion on the one hand and the chlorine and chloride ligands on the other. Chlorine is a known poison for catalyst and a very common impurity on gold surfaces since many syntheses use HAuCl4 as precursor. Our computations show that the radical chlorine displays the same reactivity as the thiyl radical while the closed shell Cl− behaves more like the thiolate anion. A “full” coverage of eight ligands (thiyls, phosphines, or a mixed coverage of both) on Au11 clusters was also studied. The full coverage leads to metallic core geometries different from the bare or one ligand clusters, which allows describing new structural isomers of the metal core and different motifs of ligation. We analyze the effects of multiple ligation in terms of Au-ligand charge transfer, suggesting the possibility of cooperative effects in surface ligand adsorption.

coordinated undecagold clusters reported to date show centered structures, with the metal moiety forming a rather compact core around a central gold atom.44,46,47 In addition, synthetic routes have been designed to obtain subnanometer phosphine protected gold clusters with flake core geometries, containing edge-fused gold tetrahedron motifs. For example, in ref 45, Shichibu et al. report a structural isomer of [Au11(Ph2P(CH2)2PPh2]3+ with a flake metal core composed of a nine gold atom toroidal unit plus two exo gold atoms forming a triangular motif by sharing an edge of the Au9 core. The optical properties of this structure are completely different from those of the more common compact-core Au11 clusters, showing the importance of investigating theoretically different charge states and structural isomers of the same metal clusters in different environment where the crystallographic structures are not necessarily the most stable. We first report on the structural isomers of the bare Au11 gold clusters. The neutral Au11 cluster is a radical and found to be planar or 3D depending on whether or not the noncovalent interactions are taken into account in the electronic structure computation. On the other hand, the Au113+ cluster, which has a closed shell electronic structure and obeys the magic number of electron rule,48 is found to be 3D and particularly stable. For comparison, we also investigated the ligation binding patterns on the closed shell cluster Au10 and on the tetrahedral cage cluster Au20 whose exceptional stability arises both from its compact geometry and electronic structure, since its 20 valence electrons also correspond to a closed shell in the super atom model.29,30 The structures obtained for Au10 and Au20 are reported in the Supporting Information. For the Au11 bare clusters, the dependence of several properties (relative stability, HOMO−LUMO gap, charge distribution) on the chosen functional is investigated, with a special emphasis on the role of noncovalent interactions. We next investigate the adsorption of thiol, phosphine, and chlorine ligands on these clusters in the gas phase and in water. Like in previous computational studies,19,31,49,50 we model thiols by the small methanethiol molecule and phosphine with PH3, which allows a good description of the organic−metallic core interaction. For the thiol and chlorine ligands, we explore different charged species. The binding of each of these ligands on neutral and trication Au11 clusters is characterized in terms of stability order, cluster distortion compared to the stable bare clusters, ligand binding mode, and ligand-cluster charge transfer. Most of the previous theoretical studies on thiol ligand coverage focused on the adsorption of thiyl radical. However, the mechanism of the formation of the Au−S bond in solution and the nature of the adsorbed thiol species are not yet fully elucidated.51−53 The release of hydrogen during the reaction between gold clusters and thiols has been experimentally detected under certain conditions,54,55 while recent theoretical studies elucidated the mechanism of the S−H bond rupture on gold clusters.56,57 Moreover, the mobility of the thiol ligand on the surface is experimentally suspected, but is still a matter of debate.58,59 For these reasons, in addition to the thiyl species (R-S• with an odd number of electrons), we also investigated the bonding patterns of the thiols (R-SH) and thiolates (R-S−) that are closed shell species. The absorption of thiols is analogous but weaker than that of phosphines, another closed shell ligand commonly used for stabilizing the smallest size clusters. The Au−S bonding takes place in “on top” pattern and does not distort significantly the geometry of the metallic core.

2. COMPUTATIONAL METHODOLOGY The Gaussian 0960 quantum chemistry suite of codes was used for all DFT and MP2 (Moller−Plesset second order) calculations. Noncovalent interactions are expected to play a significant role both in the 2D−3D transition and in the binding of ligands, especially when they are weakly chemisorbed or physisorbed, that is, for the thiols and the phosphine. In order to improve the description of noncovalent interactions in DFT, different methods have been proposed: long-range corrected functionals, like CAM-B3LYP61 and wB97X,62 or the addition of an empirical dispersion term, the Grimme correction,63 to the functional. Here we use CAMB3LYP as our method of choice. For selected calculations, we compare the results with calculations performed with the B3LYP64 functional and with the long-range corrected functional wB97X. Ideally, the coupled cluster methodology is the best suited for describing noncovalent and dispersion interactions, see for example the recent work28 on Au8 but remains prohibitive for the systems investigated here. Geometry optimizations with the MP2 perturbative method that is expected to better describe the long-range forces have also been carried out for selected geometries and ligands. The relativistic pseudopotentials and corresponding basis sets LANL2DZ65,66 were used for gold atoms together with the 631+G(d,p) for the ligand atoms. The MP2 computations were carried out with the same basis sets for gold and the ligands. Atomic charges were computed using the Natural Population analysis and the Natural Bond Orbitals (NBO) methodology.67 Frequency calculations on optimized geometries showed no imaginary frequencies and give the thermochemical characterization of the optimized structures. The free energy differences, ΔG, are computed within the rigid rotor and the harmonic oscillator approximations at room temperature and at a pressure of 1 atm. The ligand adsorption free energy is defined according to the fully relaxed geometries of the ligated and bare clusters and of the ligand. The deformation energy of the metal core is defined at 0 K by Ed = (E*bare − Ebare). Ebare is the electronic energy of the optimized bare cluster and E*bare is the 4363



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Figure 1. Stable geometries of the Au11 bare neutral conformers computed with the CAM-B3LYP functional in gas phase. The relative free energies are reported in kJ·mol−1 and Dmax in Å.

Table 1. Relative Free Energies, ΔG, in kJ mol−1, and the HOMO−LUMO Gaps, ΔEHL in eV, Computed with the Functional Indicated in Vacuum for the Neutral (N1−N6) and Charged (P1−P4) Conformers of Au11a N1

N2

N3

ΔG ΔEHL

0.0 0.87

46.6 0.96

50.5 0.87

ΔG ΔEHL μ

0.0 2.53 0.61

28.7 2.75 0.47

35.9 2.56 1.16

ΔG ΔGsolvation ΔEHL μ

0.0 −41.1 2.55 2.29

39.2 −30.6 2.75 1.57

55.2 −21.8 2.59 4.19

ΔG ΔEHL

3.8 3.73

56.7 3.93

N4

N5

N6

B3LYP 21.7 52.9 1.14 1.02 CAM-B3LYP 40.7 7.7 36.3 2.98 3.11 3.19 1.80 1.49 1.13 CAM-B3LYP (Water) 36.0 11.1 45.3 −37.7 −32.1 −45.8 2.96 3.10 3.28 6.03 3.46 3.26 wB97X 28.6 0.0 22.8 4.27 4.36 4.52 55.7 1.05

P1

P2

P3

P4

0.0 3.07

22.5 2.49

55.9 3.09

0.0 5.30 1.23

25.0 4.66 2.09

56.8 5.18 0.00

110.4 4.71 1.39

4.5 −1630.6 4.88 3.59

0.0 −1660.1 4.80 4.37

12.7 −1679.2 4.97 0.03

67.0 −1678.5 4.64 0.78

0.0 6.93

25.7 6.27

53.9 6.55

110.8 6.14

ΔEHL refers to ΔEα−β in the case of neutral open shell clusters. For the CAM-B3LYP functional ΔGsolvation is computed as ΔGwater − ΔGvacuum and the permanent dipole moments in Debye. a

respectively. The long-range corrected functionals give slightly shorter average distances than B3LYP that better compare with the values obtained at the MP2 level. The conformers N3 and N6 derive from N1. N3 is a {111} plane containing eight Au atoms (3 + 2 + 3 in three rows in the plane of the sheet) with three additional atoms (the one in the middle of the top row and the two central atoms) being duplicated orthogonally to the plane. It is the most compact cluster with a Dmax (maximum distance between two gold atoms) of about 6.9 Å, while Dmax is 9.5 Å for N1. Similarly, the conformer N6 is a {111} plane of 9 atoms (4 + 3 + 2 in the plane of the sheet) with the two central atoms of the bottom row being duplicated behind the plane. Because of the structural analogies, some atoms in N3 and N6 should exhibit reactivity typical of edges or corners formed by {111} faces. N2 and N5 can both be seen as a {111} eight atom plane being folded, with a triangle added parallel to this plane (N2, Dmax = 7.2 Å) or in an orthogonal way (N5, Dmax = 7.5 Å).

electronic energy of the metal core at its geometry in the complex. Solvation effects were included implicitly by using the Polarizable Continuum Model (PCM) approach.68

3. PROPERTIES OF THE BARE CLUSTERS The equilibrium geometries of the six more stable conformers of the neutral Au11 cluster in the gas phase, labeled N1 to N6, are shown in Figure 1. Their energies, obtained with the different computational methodologies, are reported in Table 1. The equilibrium geometries are similar for the three functionals, except that of the N2 conformer that is not stable with the wB97X functional. The conformer N1 is a compact plane of 11 gold atoms that mimics a {111} surface (the most stable crystallographic face for fcc bulk gold).69 The cluster belongs to the Cs symmetry with out-of-plane distortions of less than 0.002 Å, which is planar enough to be a model for a {111} terrace. The average Au−Au lengths computed at the B3LYP, CAMB3LYP, wB97X, and MP2 level are 2.81, 2.78, 2.79, and 2.78 Å, 4364



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Figure 2. Computed NBO charges in |e| for N1, N5, P1, and P2 clusters using the CAM-B3LYP functional in vacuum. The permanent dipole moment vector is drawn as a blue arrow attached to the center of mass.

Figure 3. Conformations of 3+ clusters obtained with CAM-B3LYP (P1 to P4) in vacuum. P1-w is the solvated P1 conformer computed at the PCM level.

is reversed and the most stable 3D form (which is also N5) is more stable than the planar one by 73.7 kJ·mol−1. The N5 geometry is not the most packed structure and does not present a stacking of atoms corresponding to the face-centered cubic system as can be observed in larger size clusters. In the bulk solid, the electronic density (number of electrons per m3) is maximized for the most stable structures, but in molecular clusters like Au11, compact packing does not necessarily lead to the most stable cluster. The other more compact 3D conformers reported in Figure 1 and in Table 1 are higher in energy than N5 by at least 20 kJ·mol−1. The HOMO−LUMO (HL) gap, ΔEHL, is often considered as an indicator of the stability of the optimized geometry: the wider the gap, the more stable the structure. For all the DFT functionals used, the ΔEα−α, ΔEβ−β, and the ΔEα‑β gaps of the 3D N5 conformer are larger than those of the planar 2D N1. With the CAM-B3LYP functional, the computed ΔEα−β for N5

N4 derives from a Au10 tetrahedron structure, with three {111} six-atom faces sharing edges, and one duplicated atom. Noncovalent interactions play an important role in the cohesion energy of the cluster as appears from the comparison of the relative free energies of the structural isomers calculated with different functionals reported in Table 1. Au11 is in the range of sizes for which the 2D−3D transition is reported to occur.22,23,70 At the B3LYP level, the most stable conformer is planar (N1) while the next stable structure is a 3D geometry (N5) with a free energy difference, ΔG = 21.7 kJ·mol−1. The 2D (N1)−3D (N5) ΔG is reduced to 7.7 kJ·mol−1 at the CAMB3LYP level, while the 3D form is slightly more stable than the 2D one, by 3.8 kJ·mol−1, with wB97X. For the long-range corrected functionals, the 2D−3D forms coexist since we estimate the numerical error of the computational level used here to be of order of 8−10 kJ·mol−1. At the MP2 level, for which dispersion forces are better described, the stability order 4365



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contrast, the orbitals with major contributions from the d-type AOs are lower in energy and more localized around each gold atom. To illustrate this point we show the density of state (DOS) of the Au113+ cluster P3 in Figure 4, together with the

is 0.6 eV larger than for N1. However, we could not correlate directly the gaps with the relative stability here, especially because of the small energy differences. Solvation effects in water were investigated for both neutral and charged clusters using the PCM model for the CAMB3LYP functional and at the MP2 level. The equilibrium geometries are not noticeably modified. The solvated equilibrium geometry of N1 is not strictly planar and exhibits an out-of-plane deviation of 0.1 Å. This suggests that the solvation by a polar solvent favors the transition to a 3D form. This effect is also observed at the MP2 level for which the equilibrium geometry of the 2D form in water also exhibits out of plane deformation of about 0.1 Å. At the MP2 level, the solvated 3D N5 cluster remains more stable than solvated N1 (2D) by 73.6 kJ·mol−1, a value almost unchanged compared to the gas phase. The solvation of N1 computed with the CAMB3LYP is stabilizing the cluster by about 40 kJ·mol−1, in good agreement with the MP2 value of 44.8 kJ·mol−1. The MP2 solvation energy of the N5 form is computed to be −42.1 kJ· mol−1 and is very close to that of the N1 cluster. There is no significant effect of the solvation on the HL gaps. Other interesting properties are the distribution of the partial charges and the permanent dipole moment. There is no absolute definition of partial charges and we used the NBO methodology, which is recognized to be only slightly basis set dependent. The partial charges on the Au atoms in N1 and N5 computed with the CAM-B3LYP functional are shown in Figure 2. These charges are in good agreement with those obtained at the MP2 level. In both clusters, highly coordinated atoms are usually negatively charged, while the less coordinated atoms share a positive partial charge. In the planar N1 conformer we observe a more uniform charge distribution, which leads to a lower value of the dipole moment. The computed negative charges on the highly coordinated atoms are larger for the long-range corrected functionals. For instance, the most negative charge in N1 is −0.37, −0.43, −0.46, and −0.56 |e| for B3LYP, CAM-B3LYP, wB97X, and MP2 levels, respectively. Undecagold clusters are often produced as cations, especially trications,71−73 so we have also investigated the geometries of several Au113+ clusters (named P1−P4, see Figure 3). The equilibrium geometry of Au113+ was found to be 3D for all the DFT functionals used in this work, as well as at the MP2 level. It was not possible to obtain a stable 2D conformer. Indeed, electrons in a positively charged cluster are more tightly bound to the metallic core, which is expected to favor the 3D geometries.23 The most stable conformer at the CAM-B3LYP level, P1, is similar to the neutral N4 with the 2 exo atoms exhibiting large positive charges (+0.6 |e|). Even with an overall 3+ charge, the most coordinated atoms are almost neutral (see Figure 2). The solvated conformer, P1-w, is slightly more compact than the gas phase structure (Dmax reduced by 0.8 Å, see Figure 3). The geometry of the next lower in energy conformer, P2, is similar to P1 and can also be described as a Au10 tetrahedron with one exo atom. The P3 geometry is a rather compact cage pyramid-like structure of D3h symmetry. The C2v geometry of P4 is similar to that of P3 but with one central atom. For both neutral and cationic clusters the highest energy occupied orbitals, as well as the lowest energy virtual orbitals, are mainly built from the mixing of s-type gold atomic orbitals with d-type orbitals. These orbitals are “cluster orbitals” significantly delocalized over several atoms of the cluster. In

Figure 4. DOS and representative orbitals of bare 3+ Au11 bare cluster with D3h symmetry.

iso-surfaces of the two qualitatively different sets of orbitals. The Au113+ cluster is expected to be particularly stable because it possesses 8 valence electrons which corresponds to a closed shell in the aufbau filling of the super atom model.41 This model is based on the hypothesis that the geometry of the cluster is spherical enough for a hydrogenic model to be valid, with a spherical potential supporting delocalized hydrogenic super atom orbitals (SAO). P1 and P2 do not exhibit a “quasi spherical geometry” while P3 (D3h) and P4 (C2v) do. Their last three occupied orbitals present an evident overall p character in agreement with the SAO model, see Figure S1 of the SI. As expected for closed shell species, ΔEHL is much larger for the 3+ cation, of the order of 5 eV using CAM-B3LYP, see Table 1. Solvation of the 3+ species reduces the energy differences between the conformers. The P2 conformer becomes quasi isoenergetic with P1. The PCM model of solvation does not substantially influence the gaps and the electronic structure described above.

4. CHARACTERISTICS OF ONE LIGAND BINDING In view of the importance of including long-range corrections for the bare cluster, all calculations reported for ligand binding were performed with the CAM-B3LYP functional unless stated otherwise. The adsorption of one methylthiol (CH3SH), methylthiolate (CH3S−), methylthiyl radical (CH3S•), chlorine (Cl), chloride (Cl−), and phosphine (PH3) was systematically investigated on both planar and 3D Au11 clusters, for the neutral species (N1−N6) and the trications (P1−P4). The results are summarized in Table 2. The binding patterns of the thiol and the phosphine ligands exhibit similar trends in all the structural isomers and charge state of the Au11 cluster we considered. These trends are also recovered for selected computations at the MP2 level on 3D metallic cores, see Table S1. Thiols and phosphines are weakly adsorbed in the neutral clusters (see Table 2A, B, E, and F). For both ligands, only an on-top conformation is observed. Their binding does not lead to a significant geometry reorganization of the metallic core except when the ligands bind to the central gold atom of the planar cluster. In this case we observe a significant out of plane deformation which triggers a transition 4366



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Table 2. Equilibrium Geometries of One Ligand Complexes with 2D and 3D Conformers of the Neutral Au11 Cluster and of the Au113+ Cation and Selected Propertiesa

The binding free energies (kJ mol−1), ΔGb = ΔGcomplex − ΔGligand − ΔGAu11 are reported for gas phase and water. The free energy of Au11 is taken to be the free energy of the most similar bare structural isomer. L−Au bond lengths in vacuum and the computed NBO partial charge on the metallic gold cluster in the gas phase and in water are also reported. S is represented in blue, P in orange, Cl in green, Au in yellow, C in grey, and H in white. a

to a 3D metallic core (Figure S2-A of the SI). The deformation energy is of the order of 3−8 kJ·mol−1 for both the 2D (N1)

and the 3D (N5) neutral Au11 metallic core. The deformation energy of the metallic core needs to be at least compensated by 4367



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stable top conformation. Since the binding with a radical ligand leads to a closed shell complex, the interaction is expected to be very favorable. Indeed, the computed adsorption energy is large (of the order of −200 kJ·mol−1 for thiyls and more than −250 kJ·mol−1 for chlorine). For both thiyls and chlorine, the binding interaction is slightly stronger with the 3D gold core than with the planar structure. Solvation does not change significantly the binding energy of thiyls, while the binding of the chlorine increases (see Table 2J,K,R,S for the actual values of the binding energy). The Au-L-Au binding pattern causes a larger geometry distortion of the metallic core than the “on top” adsorption mode of a thiol and phosphine. The metallic core can still be considered 2D for Cl binding while the adsorption of a thiyl induces a deviation from a planar geometry of 0.1 Å. The gold core deformation energies with Cl and H3C−S• are of the order of 15 kJ·mol−1 for the N1 conformer and 30 kJ·mol−1 for N5. Contrary to the thiol and phosphine, the binding with thiyl radical and chlorine leads to a depletion of electronic charge in the metal core. Upon binding, the metallic core carries a positive partial charge of 0.25−0.30 |e| for thiyls and of 0.5−0.6 |e| for Cl. For the 2D Au10 cluster, the computed binding free energy is smaller than for the 2D Au11 (−117.0 kJ·mol−1, Figure S2-E) since the overall complex is a radical in this case. The adsorption of a thiyl on Au20 is a spontaneous process with a free energy gain of −54.0 kJ·mol−1 (Figure S2-F). The thiyl binds in a bridge configuration which leads to a distortion of the gold core geometry. Also in this case the binding is characterized by a charge transfer toward the ligand resulting in a positive metallic core with a partial charge of 0.20 |e|. The adsorption of a thiyl radical on Au113+ can lead to both an on top and a bridge conformation (Table 2L,M). The most stable pattern, namely, Au-L-Au, stabilizes the complex by only −174.5 kJ·mol−1, which is slightly less than the computed binding energy for a thiol. The NBO charges of the complex indicate a charge transfer from the thiyl radical to the metallic core, since this is a trication when it is considered isolated. The direction of the electronic charge transfer is thus reversed with respect to the binding with the neutral cluster, where the thiyl behaves as an electron acceptor. This is not the case for the chlorine radical, indicating its stronger electron affinity. The binding of a thiolate or a chloride anion on the neutral Au11 leads to negatively charged complexes with an odd number of electrons. The stable complexes obtained for both the N1 and N5 metallic core geometries exhibit the Au-L-Au bridge (Table 2N,U) and the on top Au-L bond (Table 2O,V) binding patterns. In the gas phase the computed adsorption free energy of the thiolate (about −300 kJ·mol−1) is larger than for the thiyl radical. This is not the case for the chloride anion, which binds more weakly than the chlorine radical, see Table 2. Water solvation considerably lowers the binding energies of both the anionic species (by about 150 kJ·mol−1). This is a consequence of the large solvation energy of the isolated thiolate or chloride ions. Because the chloride is better solvated than the thiol, the destabilization effect on the adsorption energy of the chloride complex is even more pronounced. In the case of the thiolate adsorption, the binding leads, in gas phase, to a negative charge on the gold metallic core of −0.50 to −0.70 |e|, which means that more than half of the total negative charge is on the metallic core. In the case of chloride, the charge on the metallic core is smaller, of the order of −0.30 |e|, because of the strong electron attractor character of Cl.

the bonding energy with the ligands to obtain a spontaneous adsorption. The use of different functionals highlights the role of noncovalent interactions in the calculation of the binding energy. For example, the adsorption free energy of a thiol on a peripheral Au atom of the 2D form (Table 2) is computed to be −15.0 kJ·mol−1 with CAM-B3LYP (with an Au−S bond length of 2.48 Å), while only half this value is obtained at the B3LYP level (with a longer Au−S bond equal to 2.58 Å). The difference is particularly significant for ligands interacting with the gold core through weak binding, as is the case of thiol and phosphine. Methanethiol is weakly chemisorbed in both the planar (A) and the 3D isomer (B) of the neutral Au11 cluster. The binding is stronger in the 3D structure (−23.8 kJ·mol−1 against −15.0 kJ·mol−1 in the planar geometry), while the bond lengths are almost the same in the two cases (2.49 and 2.48 Å for the 3D and 2D geometries, respectively). The binding is accompanied by a charge transfer from the thiol to the metallic core leading to an overall NBO charge of about −0.2 |e| on the gold core. The negative charge is mainly localized on the peripheral Au atoms and almost neutralizes them (Figure S3-B). The computed adsorption energies are even smaller in water (−5.8 and −11.9 kJ·mol−1 for 2D and 3D cluster, respectively). The charge transfer to the metallic core remains unchanged by solvation. The adsorption mode of a thiol on the planar closed shell Au10 is similar to Au11 but is energetically slightly less favorable (Figure S2-B). Binding a thiol on Au20 is not spontaneous: ΔGb is slightly positive, equal to 1.5 kJ·mol−1 (Figure S2-C). Phosphine binds somewhat stronger on the neutral Au11 than thiol with an adsorption free energy of −43.2 kJ·mol−1 for the 2D conformer N1 (Table 2E) and of −48.2 kJ·mol−1 for the 3D N5 one (Table 2F). The respective bond lengths are 2.37 and 2.38 Å. Another proof of the stronger binding of a phosphine is its ability to bind spontaneously on top of the pyramidal Au20 (Figure S2-D). Unlike in the case of thiols, solvation by water does not significantly decrease the binding energy of phosphines. The phosphine also behaves as an electron donor. The charge transfer is similar to that computed for thiols and not significantly affected by solvation. The binding energy of a thiol or a phosphine to Au113+ (P2 conformer) is much stronger than in the neutral cluster. The binding free energy is computed to be −184.7 kJ·mol−1 for CH3SH and −212.2 kJ·mol−1 for PH3. The fraction of charge transferred from the ligands to the cationic metal core is higher than in the neutral case. The overall NBO charge on the gold core is computed to be 2.54 |e| with the thiol (Table 2 C) and 2.51 |e| with the phosphine (Table 2 D), corresponding to a net transfer of about −0.5 |e| compared to the bare core Au113+. A bridge thiol binding pattern has been also obtained for Au113+, yet less stable than the top conformation (Table 2D). The binding energy of the ligand is large enough to trigger the Au core reorganization from the P3 to P2 conformation. Upon binding of a thiol or a phosphine, the P3 core relaxes to the P2 geometry which consists of a Au10 tetrahedron with an additional exo atom binding the ligand, optimizing the number of {111} undisturbed faces. To provide more understanding on the Au−S bond formation, we next characterize the binding mode of a thiyl radical and a thiolate and that of atomic chlorine and chloride anion, which exhibit similar trends. The preferential bonding pattern of a thiyl radical on a neutral Au11 gold cluster is found to be a bridge conformation (Table 2J,K). We did not obtain a 4368



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Figure 5. DOS and representative orbitals of the bare planar cluster and of the complexes with different forms of thiol: the neutral bare cluster (a), the complex with thiol (b), the complex in which the thiol is dissociated (c), the thiolate (d), and the radical species (e). The HOMOs of each complex are shown in each panel. The bonding orbitals of the thiol and the dissociated thiol are shown on the left-hand side.

The adsorption of a Cl− or of a thiolate on Au113+ leads to the hollow geometries shown in Table 2Q,W with a significant deformation of the cluster. Since it is the adsorption of anions on a trication, the binding energy is very large (−1316.6 kJ· mol−1 for a thiolate and −1130.2 kJ·mol−1 for a chloride). In addition to the hollow binding mode, a stable bridging mode of the thiolate is also observed (Table 2P), whereas it was not obtained with a chloride anion. The solvation of charged clusters shows, as expected, a dramatic effect. The binding energy of a thiol and a thiyl radical on the trication is reduced by half. The adsorption free energy of a thiolate is decreased from −1301.8 to −146.9 kJ·mol−1, because of the high solvation of both the 3+ cluster and the anion. This effect is even more pronounced for Cl. The adsorption of a chlorine atom on the charged cluster is barely affected by solvation whereas the chloride adsorption is decreased from −1130.2 to −50.7 kJ·mol−1. We did not observe the dissociation of the methanethiol upon binding on the metallic core in any of the cases investigated above. When starting from equilibrium geometries, the released binding energy is not large enough to trigger the dissociation of the S−H bond. In order to provide some

understanding on the mechanism of the Au−S bond formation, we used in some of the computations a “dissociated thiol” as a starting geometry, for which the H nucleus is close to the metallic core but not to the S of the thiol. This starting geometry can be rationalized taking into account the proton acceptor character of the Au atoms in the bare cluster.74 The overall complex is isoelectronic to the thiol-Au11 complex discussed above (Table 2A,B) and remains a radical, since CH3SH is a closed shell species and the metallic core is a radical. The computed stable geometries are shown in Table 2H,I, which differ by the position of the H nucleus, either on top or in a bridging position with respect to the gold atoms. When the H nucleus is in a bridge position on the 2D Au11, the metallic core is considerably distorted and adopts a 3D geometry. The Au−H bond lengths are 1.72 and 1.82 Å for complexes H and I, respectively, and much smaller than the sum of the van der Waals radius (2. 86 Å). An Au−S−Au bridge is formed that is similar to that of a thiyl radical. The charge transfer is directed from the metallic core to the ligand, unlike in the case of the nondissociated thiol complexes. Additionally, the NBO charge analysis gives a negative charge of −0.22 |e| on H, indicating a hydride character of the Au−H 4369



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Figure 6. Au11(PH3)8 neutral conformations obtained with the CAM-B3LYP functional. The charge on the metallic core and the stabilization energy are reported in vacuum, ΔGv, and in water, ΔGw.

complex with thiol (b), the complex in which the thiol is dissociated (c), the thiolate (d), and the radical species thiyl (e), together with iso-surface of the HOMO and other representative orbitals. The sulfur of the thiol (panel b) interacts mainly with the d-band of the gold cluster and the bonding orbitals (shown on the left-hand side of panel b) are located at an energy of about −13 eV. In the thiol complex, the HOMO is slightly destabilized with respect to the bare (+0.54 eV) with a contribution of less than 10% of the sulfur atomic orbitals (AO). Both thiol and phosphine do not significantly modify the frontier orbitals which remain those of the bare gold cluster. In the case of the thiolate, the thiyl, and the dissociated thiol, besides the interaction with the d-band of the cluster, the p-orbitals of the sulfur mix significantly with the metallic core orbitals near the HL frontier. The changes in the frontier orbital region are significant for the thiyl and thiolate ligands (panels e and d). In the closed shell thiyl radical complex (panel e), the HOMO is well delocalized on the sulfur (which contributes for 13% to its composition), while for the dissociated thiol (c) and the thiolate (d), the bonding MO are just below the frontier orbital (i.e., HOMO-1−3). The HOMO of the thiolate complex is mainly the LUMO of the bare Au11. In the anion complex (panel d), the bonding S−C orbitals that have energies around and under −14 eV in the neutral complex are shifted to lower energies. For the dissociated thiol on the gold cluster we found that the bonding orbital between gold and hydrogen is located at −15 eV. In the left-hand side of Figure 5 we show such orbital for the two different configurations of the bond: that reported in Table 2H for which the bonding orbital involved the three atoms S−Au−H and that reported in the Table 2I that involves only gold and hydrogen (Au−H−Au).

bonding. The stabilization free energy of these complexes is about four times stronger than that obtained with a stable thiol (it is of the order of 60 kJ·mol−1 and not significantly affected by solvation). However, the energetic cost of the thiol dissociation is not taken into account. We therefore suggest that a thiol is able to form a strong Au−S bond only if it is first activated as thiyl radical or a thiolate. It remains an open question to relate this needed activation with the experimental conditions of the syntheses. Two possible mechanisms are a heterolytic dissociation mediated by the aqueous solvent or a homolytic dissociation assisted by defects on the gold surface or the morphology of the cluster.75 These two cases could be discriminated against one another experimentally by varying pH, which should affect the thiolate route or detecting the formation of H2,75 which would point to the thiyl radical route. From a computational point of view, the calculation of the transition state56,57,69 and dynamics simulation76 may help to further elucidate the issue of the bond formation mechanism. Binding one ligand on a neutral cluster does not strongly modify the HL gap compared to that of the bare cluster, except for radical ligands for which going from an open to a closed shell electronic structure triggers an important opening of the gap (of about 1.5 eV for both thiyl radical and for the chlorine). From an experimental point of view, orbital energies and density of states can be determined by XPS-UPS photoemission spectroscopy.77,78 Since thiols can bind the gold cluster in different redox forms, we have investigated the characteristics of density of states and of the orbitals of the different complexes for the planar bare cluster. We report in Figure 5 the computed DOS of the neutral bare cluster (a), the 4370



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Figure 7. [Au11(PH3)8 ]3+ conformations obtained with the CAM-B3LYP functional. The NBO charge on the metallic core and the stabilization energy are reported in vacuum, ΔGv, and in water, ΔGw.

for comparison two isomers of the cluster Au11(PH3)7(SCH3)3, which is a well-known model for experimentally characterized clusters.46,47 The optimized isomers of the Au11(PH3)8 cluster, labeled CPN1−5, are reported in Figure 6. In all the structures, the phosphines are found in an “on top” conformation with Au−P bond lengths very similar to that observed for a single ligand (about 2.4 Å). The NBO charge analysis shows a charge of about −1.5 |e| on the gold cluster for both the planar and the 3D geometry of the Au11 core. This is in good agreement with the charge transfer of about −0.2 |e| for one phosphine on the cluster, indicating no cooperative effects in the charge transfer process. The metallic core geometries are different from those of the bare clusters. The 2D compact plane CPN1 or CPN4 is distorted to a 3D geometry but we can observe the {111} motif with duplicated atoms. The geometries of these clusters are not far from that of the cluster synthesized and characterized by Shichibu et al.45 On the other hand, the CPN2, 3, and 5 geometries cannot be directly related to the close packing {111} motif. The arrangement of tetrahedrons sharing faces or edges is reminiscent of the compact packing but accommodating eight ligands on top positions requires accessible gold atoms, promoting more “open” clusters. Consequently, CPN2, CPN1, and CPN4 that fulfill this pattern are more stable than the more isotropic CPN3 and CPN5 geometries.79 The energetic stabilization resulting from the adsorption of eight phosphines is much smaller than eight times that of a single phosphine on the Au11 cluster (see Table 2). This is not surprising since steric hindrance effects reduce the binding

There is therefore a clear signature of the possible binding ligand species in the DOS spectrum. The binding of the different forms of the thiol ligand to the cation 3+ leads to similar effects on the electronic structure as those described above for the neutral complexes (the DOS of the cationic complexes with thiol are reported in Figure S4). The only major difference arises in the case of the thiol which, when interacting with the cationic Au113+, is also contributing to the frontier orbital of the complex as the radical and the anionic ligand.

5. FULL LIGAND COVERAGE Synthesized clusters and nanoparticles are generally fully covered rather than interacting with one ligand. Our computational studies indicate that the neutral Au11 can accommodate a maximum of eight ligands of the same chemical nature. We report on neutral and 3+ clusters covered by 8 radical thiyls and 8 phosphines. Moreover, we optimized isomers for the mixed ligand cluster covered with five phosphines and three radical thiyls. The choice of this composition is motivated by two reasons: we maintain a total number of eight ligands in order to easily compare with the only thiol and only phosphine covered clusters and we consider clusters that are particularly stable according to the superatomic model of ligated gold cluster. In this model, a thiyl radical is assumed to localize one electron of the metallic core while phosphine does not influence the number of valence electron to be considered. The presence of three thiols on the neutral Au11 thus leaves eight electrons to close the P-shell of the superatom model.48 We also optimized 4371



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Figure 8. Neutral and trication stable geometries of Au11(SCH3)8 obtained with the CAM-B3LYP functional. The NBO charge on the metallic core and the stabilization energy are reported in vacuum, ΔGv, and in water, ΔGw.

the gold core is around 0.4 |e|. The charge transfer per phosphine with respect to the isolated Au113+ is, however, smaller (0.3 |e|) than in the case of a single PH3 ligand where it was computed to be 0.5 |e|. Compared to phosphine, we show above that the adsorption of one thiyl ligand on Au11 leads to a significant distortion of the metallic core due to the bridging binding mode of that ligand. In the case of the binding of eight thiyls the metallic core is indeed dramatically distorted. In some complexes the gold core looses its integrity and fragments: some gold atoms are separated from the nearest ones by distances up to 3.2 Å. In Figure 8 we report three isomers of the neutral Au11(SCH3)8, named CTN1−3, and two isomers obtained for the trication [Au11(SCH3)8]3+, labeled CTP1,2. In the most stable cluster, CTN3, the gold core is reduced to two tetrahedrons of gold atoms sharing a face and the six remaining gold atoms are localized on two exo rings of alternatively Au and S atoms. In this structure all the thiyl radicals are linked in a bridge mode and incorporated in the outer sphere of the metallic core. Such a large distortion is also observed for the other two stable structures where two thiyl radicals are adsorbed on top positions and the six others in bridging mode. The computed structures support the empirical fact that small gold clusters cannot be stabilized by thiyls because they interact too strongly with gold atoms. Moreover, the synergic action of two or more thiyls is able to isolate a gold atom from the rest of the cluster and may account for the gold atoms mobility on thiol protected nanoparticles.

energy per ligand and there is also a reorganization of the geometry of the metallic core. Modeling water solvation using the PCM model does not affect noticeably the geometry of the clusters. The CPN2 cluster remains the most stable one, actually more stabilized than the other clusters. The adsorption energy associated to the coverage for CPN3 becomes negative while it was not the case in vacuum. As we observed for one ligand, the charge transfer is more efficient in water and the adsorption of the phosphines is overall stronger. Due to steric hindrance, the stable structures obtained upon the adsorption of eight phosphines on the trication (labeled CPP1−4) can only be slightly different from the neutral ones. Indeed CPP1 shown in Figure 7 is similar to CPN5 and the geometry of the most stable cluster, CPP4, is close to that of CPN2. The CPP2 structure is surprisingly less close packed than the other structures and exhibits two three-atom rings and only two tetrahedrons sharing a corner. In this structure, the loss in cohesion energy of the gold core (the deformation energy of the core is about 80 kJ·mol−1) is balanced by a better Au−P binding on more isolated gold atoms. The CPP3 geometry is the most compact and similar to the reported geometry for the undecagold core44,46,47 but is less stable than CPP2 and CPP4. The adsorption of eight phosphines on a positively charged cluster is less favorable in water than in the vacuum, as was observed for the binding of one phosphine. The binding energies are four times smaller than the one computed in vacuum. As reported in Figure 7, the residual positive charge on 4372



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Figure 9. Neutral Au11(SCH3)3(PH3)5 conformations obtained with the CAM-B3LYP functional. The NBO charge on the metallic core and the stabilization energy are reported in vacuum, ΔGv, and in water, ΔGw.

properties, since all the species Au113+, Au11(SCH3)3(PH3)5, and [Au11(PH3)8]3+ can be considered closed P shell according to the counting rule of the superatom model. The total binding energy in the mixed ligand clusters is about −500 kJ·mol−1, so also in this case the effect of steric hindrance and the core reorganization is lowering the effective binding energy per ligand (on the basis of the computed adsorption energies of single ligands the total binding energy would be around −800 kJ·mol−1). If we look at the NBO charge of the mixed ligand clusters, we find only a small partial charge on the metallic core. From the analysis of single ligand effects discussed above, a phosphine gives about −0.3 |e| to the metallic core and a thiyl radical takes about 0.25 |e| from a neutral gold cluster. Moreover, we observe about the same charge transfer per ligand in the only phosphine and only thiol full covered cluster. In the case of the mixed ligand shell, the phosphines are still donating about the same amount of charge of −0.3 |e| per unit, but the charge is transferred to the thiols (which carry a more negative partial charge of −0.45 |e| per unit), leaving the metal core basically neutral. It therefore seems that, in the presence of phosphines, the thiyl molecules are a more efficient electro acceptor. This shows a possibly cooperative effect of the two ligands. For the Au11(PH3)7(SCH3)3, which is analogous to the characterized form,46,47 we obtained both a compact core isomer as CMN1 and a flake core structure analogous to CMN3, which is slightly more stable (ΔG = −15.3 kJ/mol). The distribution of partial charges in these species is similar to the one described above for Au11(PH3)5(SCH3)3, with a nearly neutral metal core and the three radical thiyl molecules carrying in this case a partial charge of −0.48 |e| per unit.

In CTN3 (Figure 8), the gold atoms between two bridging thiyls are bearing a 0.3 |e| positive charge, while the residual gold core is negatively charged. The geometries of CTN1 and CTN2 can also be described with the staple motifs (Au−S−Au units protecting a pure metallic core).48,76,80,81 Indeed, CTN1 can be described as a gold core of eight atoms with four atoms in the staple motif, bound with thiyls and protecting this core. The solvation, as for the single ligation, slightly decreases the adsorption energy. The integrity of a close packed trication gold core is also altered by the adsorption of eight thiyls. All the ligands are in a bridging mode in the two stable structures reported in Figure 8 and are separating the gold atoms in two or more subunits. The calculation of the total net charge carried by gold atoms with the NBO charge analysis gives 3.5−4 |e| charge, meaning the thiyl radicals still exhibit an electroacceptor behavior. In this case, the adsorption energy of each thiyl radical is similar to the energy obtained for a single thiyl on the planar Au11 cluster (of the order of 200 kJ·mol−1). However, this favorable binding is accompanied by a loss in the cluster cohesion energy, because of the observed fragmentation of the gold core. In order to mimic a ligand exchange on a Au11 cluster initially fully covered with phosphines, we have replaced three of them by thiyls with an on-top bridging mode. There are hundreds of possibilities for replacing three ligands out of eight on five different structures of Au11. We show in Figure 9 a few that are useful for drawing some trends about the effect of a mixed ligand coverage. We report on three complexes (CMN1−3) where the gold atoms carrying the thiyls are separated one from another by phosphine groups. We observe consequently that, in the relaxed systems, the thiyl ligands remain in an on top position instead of evolving to a bridging pattern. This is due to the steric hindrance caused by the PH3 groups and because the neighbors are already bound to a phosphine. Moreover, the cohesion of the gold core is preserved because Au−S−Au bridges are not formed, unlike in the full thiyl coverage case. The gold core geometries of the complexes reported in Figure 9 are close to those described for the trication clusters. The most stable complex, CMN3, exhibits the same core geometry as that of the Au113+ core in the most stable complex with eight phosphines, CPP4 of Figure 7, while the more compact core of CMN1 is close to P4 in Figure 3. This structural similarity can be understood in terms of electronic

6. SUMMARY AND CONCLUSIONS Bare small gold clusters are unstable and often passivated by a full coverage of ligands. Targeted cluster properties can be achieved through the tailoring of ligand shell by using different ligands. It is therefore of interest to study cooperative effects between different kinds of ligands. In order to achieve this goal, we begin with a systematic analysis of the adsorption of single ligands with different binding strength and charge transfer properties on the different conformers of the neutral and trication Au11 cluster. We have then considered multiple ligand clusters with thiols, phosphines, and a mixed ligand shell, gaining insights into cooperative effects of ligand binding. The 4373



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Present Address

nature of the ligands is found to strongly affect structural and electronic properties of the bare Au11 and Au113+ clusters. The binding of a single phosphine or thiol is rather weak on the neutral cluster and does not trigger a significant structural reorganization of the metal core. The same ligands interact strongly with the cationic metal cores, triggering in this case an important reorganization of their geometry. In both cases phosphines and thiols prefer an on-top binding configuration and the binding is accompanied by a charge transfer from the ligand to the metal core. Radical thiyl and chlorine, in contrast, bind more effectively to the neutral gold cluster than to the charged metal core and preferentially in a bridge position. The geometry of the metallic core undergoes considerable deformation upon binding and the direction of the charge transfer is from the gold cluster to the ligand shell. The chlorine atom exhibits an enhanced electron-attractor character with respect to the radical thiol binder. Negatively charged ligands, thiolates, and chlorides show binding energies and binding patterns similar to those of the radical chlorine and thiyl in the gas phase, but their binding properties are strongly influenced by solvation. Our study also sheds light on the still debated issue of the mechanism of thiol species adsorption. We systematically investigated the three species, thiol, thiyls, and thiolates, which lead to neutral radical, closed shell species, and radical anion complexes when they bind to a neutral Au11 cluster. We here show that the three species could be distinguished on the basis of the characteristics of their density of states by XUPS spectroscopy. In the second part of this paper we analyzed structures and energetics induced by the interaction of the metal core with multiple ligands. The presence of several molecules in the ligand shell favors flake structures where gold atoms are easily accessible to the ligands and the steric hindrance between different ligands is minimized. Multiple ligations thus trigger an important rearrangement of the metal core in most of the cases we considered. We find that the neutral Au11 can bind up to eight phosphines preferentially in an on-top conformation or eight thiyls forming in many cases staple motifs. For the only phosphine-covered clusters, we calculate that solvation enhances the ligand-core charge transfer and the binding energy for the neutral species, while ligation of the trication complexes is disfavored in water with respect to the gas phase. In the case of thiyl radicals, solvation slightly decreases the adsorption energy for both neutral and charged species. In the only phosphine clusters, Au11(PH3)8, and only thiyl clusters Au11(SCH3)8, the charge transfer properties of each ligand are the same as in the one-ligand case. In the mixed ligand species Au11(PH3)5(SCH3)3 and Au11(PH3)7(SCH3)3, on the other hand, the charge transfer between the ligands shell and the metallic core is not given by the sum of the effect computed at the level of single ligand binding, which is an indication of a cooperative effect.

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Sorbonne Universités, UPMC Univ Paris 06, CNRS, Collège de France, UMR 7574, Chimie de la Matière Condensée de Paris, F-75005, Paris, France. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS F.D. acknowledges support from the EC Ph.D. School IDS FunMat and a mobility fellowship from the University of Liège. B.F. is a postdoctoral fellow of the University of Liège. F.R., B.F., and F.D. acknowledge support of the Action de Recherche Concertée NANOFORCE. F.R. is a Director of Research with Fonds National de la Recherche Scientifique, Belgium.

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ASSOCIATED CONTENT

S Supporting Information *

The structures obtained for Au10 and Au20. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

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