5035
2009, 113, 5035–5038 Published on Web 01/16/2009
Structure and Bonding in the Ubiquitous Icosahedral Metallic Gold Cluster Au144(SR)60 Olga Lopez-Acevedo,† Jaakko Akola,† Robert L. Whetten,‡ Henrik Gro¨nbeck,§ and Hannu Ha¨kkinen*,†,| Department of Physics, Nanoscience Center, UniVersity of JyVa¨skyla¨, FI-40014 JyVa¨skyla¨, Finland, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, Competence Center for Catalysis and Department of Applied Physics, Chalmers UniVersity of Technology, SE-41296 Go¨teborg, Sweden, and Department of Chemistry, Nanoscience Center, UniVersity of JyVa¨skyla¨, FI-40014 JyVa¨skyla¨, Finland ReceiVed: December 31, 2008
Density-functional theory computations on a cluster Au144(SR)60 with an icosahedral Au114 core with 30 RS-Au-SR units protecting its surface yield an excellent fit of the structure factor to the experimental X-ray scattering structure factor measured earlier for 29 kDa thiolate-protected gold clusters. This cluster has a special combination of atomic and electronic structure that provides explanations for the observed stability and capacitive charging properties with several available oxidation states in electrochemistry and optical absorption extending well into the infrared region. The gold-sulfur interaction gives rise to the archetypal metal-molecule interfaces, ubiquitous as self-assembled monolayers (SAMs) on Au(111),1 as colloidal particles2 and nanocrystals3 stabilized by thiolate groups, and for linking molecules to metal electrodes in molecular electronics.4 Despite the wide presence of this interface in molecular nanoscience, atomic details of the junction have not yet been fully unravelled. Recent breakthroughs in understanding the structure of the protecting monolayer of thiolate-stabilized gold clusters5-10 have given new insight into the atomic details of the curved Au-S interface and are also having an impact on reconsideration of the planar (zero-curvature) Au(111)/SAM molecular junction,11-13 once thought as solved. Understanding the gold-sulfur interface, its atomic and electronic structure as well as its signal transmittance properties, such as electronic excitations and electron transport, is crucial for applications in such diverse fields as biolabeling, photonics, sensing, nanocatalysis and molecular electronics. Among the series of stable thiolate-stabilized clusters, each distinguished by its core mass, the 29 kDa gold particle has played a pivotal role as it has been abundantly synthesized for over a decade,3 and its electrochemical properties14-18 and optical absorption19-21 have been particularly well studied. The chemical derivatization of its protective thiolate layer yields bioconjugate forms, and most recently it has been demonstrated that this particle can be used as multivalent therapeutics when conjugated to a fragment of a potent HIV inhibitor.22 Despite the extensive characterization efforts, its total-structure determination has remained elusive. Various authors have suggested compositions in the range 140-150 gold atoms and 50-60 thiolates.19,21 A state-of-art evaluation of size and composition, * Corresponding author. E-mail:
[email protected]. † Department of Physics, Nanoscience Center, University of Jyva¨skyla¨. ‡ Georgia Institute of Technology. § Chalmers University of Technology. | Department of Chemistry, Nanoscience Center, University of Jyva¨skyla¨.
10.1021/jp8115098 CCC: $40.75
by electrospray ionization mass spectrometry, yielded recently a composition of Au144(SR)59z with an overall positive charge z > 0.21 We used density functional theory (DFT) methods to investigate geometric and electronic properties of methylthiolate (R ) Me) protected gold clusters of about 150 gold atoms (see Supporting Information, for computational details). Here we show that one special size and composition among the studied clusters, namely Au144(SR)60, provides an excellent structural model for the 29 kDa cluster, judged from the comparison of the computed X-ray diffraction (XRD) pattern to earlier experimental results.19 We analyze the electronic structure of Au144(SR)60 in terms of the “superatom-complex model” (SACM), recently elucidated for thiolate (and other “pseudohalide”) protected gold clusters9 and show that Au144(SR)60 accounts for the reported optical19-21 and electrochemical14-18 properties of the 29 kDa nanoparticle. The relaxed structure of Au144(SR)60, displaying icosahedral symmetry I, is shown in Figure 1. The cluster has a compact, metallic core of 114 Au atoms, arranged into three concentric shells of 12, (30 + 12), and 60 symmetry-equivalent atoms. These 60 atoms form the core’s surface layer and are protected by 30 equivalent RS-Au-SR units. The calculated binding energy of one RS-Au-SR unit to the core is 2.0 eV. The shellby-shell construction of the cluster is shown in Figure S1, Supporting Information. The polyhedral geometry of the 114-atom gold core (Figure 1) may be described as rhombicosidodecahedron, one of the 13 Archimedean solids, that has undergone a symmetry lowering (Ih to I). The two first shells of the core have 12 and 42 atoms, respectively, forming a familiar Mackay icosahedral packing structure (MI) containing 54 atoms (or 55 with a central atom) and 20 triangular faces. Alternatively, one can describe the MI by 20 face-sharing fcc elongated tetrahedra. Completion of the third shell is achieved by filling each of the 20 faces of the tetrahedra by three atoms in a bulk hcp packing order. In this manner, the third shell has 60 symmetry-equivalent atoms at 2009 American Chemical Society
5036 J. Phys. Chem. C, Vol. 113, No. 13, 2009
Letters
Figure 2. Theoretical structure-factor for the relaxed Au144(SR)60 and Au145(SR)60 clusters (R ) Me) and the experimental X-ray scattering function (R ) n-dodecyl) from ref 19. s is the length of the diffraction vector and I(s) is the intensity. Figure 1. (A), (B) Relaxed structure of Au144(SR)60 viewed down a 5-fold (A) and a 3-fold (B) symmetry axis. Key: yellow, Au in the Au114 core; orange, Au in the RS-Au-SR unit; bright yellow, S; gray, C; white, H. (C) highlights the chiral arrangement of the RS-Au-SR units covering the 60-atom surface of the Au114 core (blue). (D) shows all the 144 gold atoms, with different atom shells denoted by different colors.
vertices of 12 pentagons, 30 squares, and 20 equilateral triangles.23 The protective RS-Au-SR units each cap diagonally one square, causing a slight reconstruction of the core surface. This symmetry reduction becomes apparent when analyzing Au-Au distances at the surface of the core (see Figure S2, Supporting Information). Even with this coherent reconstruction, the nearest point group symmetry that can be assigned to the Au114 core is the icosahedral one. The Au-Au bond distances in the three atom shells are 2.845 ( 0.019, 3.010 ( 0.047, and 3.154 ( 0.187 Å, respectively. The distance between Au(I) in the RS-Au-SR unit and the nearest Au atom at the core surface is 3.205 ( 0.124 Å. We find several geometric features that are common for the gold cores of the Au144(SR)60 and the previously characterized Au102(SR)44 cluster.5,9 The 60-atom surface of the Au114 core of Au144(SR)60 is remarkably spherical: the standard deviation of the radius of 7.10 Å is only 0.04 Å; hence all these distances can be considered identical. This feature was also observed for the 40 surface atoms of the Au79 core of the Au102(SR)44 cluster.5,9 Similar to the Au102(SR)44, the Au144(SR)60 cluster can have two enantiomeric isomers as the arrangement of the RS-Au-SR units on its surface is chiral (Figure 1C). The cores of both clusters feature 5-fold symmetries (D5h and I); all 12 5-fold symmetry axes of Au144(SR)60 act also as axes of chirality. The two pentagons on the D5h symmetry axis of the Au79 core of Au102(SR)44 have vertices where (in an idealized geometry) a triangle, a square, a pentagon, and a square meet, just as is the case for the vertices of the 12 pentagons on the surface of the Au114 core of Au144(SR)60 (Figure 1C). Finally, as in Au102(SR)44, there are two distinct Au-S bond lengths at the Au/S interface of Au144(SR)60. The surface-chemical bond between sulfur and gold atom at the interface (2.463 ( 0.013 Å) is 5% longer than the ones within the RS-Au-SR unit (2.339 ( 0.004 Å). Interestingly, the same pattern was observed when RS-Au-SR units are adsorbed at the Au(111) surface.11,13 The innermost 12-atom shell of Au144(SR)60 could accommodate a central atom. However, on energetic grounds this hollow core seems to be preferred over that with a central atom included in Au145(SR)60: the central atom has a binding energy, which is only 60% of the calculated cohesive energy of fcc bulk gold. The hollow structure relieves significantly the intrinsic strain associated with MI packing: removal of the central atom
Figure 3. (A) Projected density of electron states (PDOS) within the Au114 core region of Au144(SR)60. The color-filled curves denote weights of various angular momenta up to L ) 6 (I symmetry). Note the manifold of states in the energy range below -7 and -1 eV to +1 eV, where each state can be described by a single major angular momentum component. These states are the Au(6s)-derived delocalized “metallic” states in the core. Gray denotes angular momenta L > 6. The energy range of -7 to -1 eV includes the Au(5d)-derived states. (B) shows the region around the HOMO (zero energy), with the lowest optically allowed transitions (from H to I symmetry) marked by arrows. The numbers denote subshell closing numbers in the spherical electron gas model for metal clusters in the 1H-2D-3S-1I manifold of states.24 (C) shows the calculated total energies for charge states -4 e z e 4 and a quadratic fit to E(Q) - E(Q)0).
induces radial inward relaxations by 0.12 (4%), 0.05, and 0.02 Å for the first three shells, respectively. Figure 2 displays the computed structure-factor (X-ray scattering pattern) for both the Au144(SR)60 and Au145(SR)60 clusters along with earlier experimental results from powder samples containing the 29 kDa gold cluster.19 The role of the central atom is minor; the relaxations in the gold core change the structure factor slightly only in the high-momentum transfer region of 7 e s e 11 nm-1. Both clusters yield a remarkably good fit to the experimental data: all the major peaks in the experimental diffraction function are accounted for, as well as the shoulder features at s ≈ 7, 9, and 10 nm-1. Oh, HCP, Dh, and Ih structures do not yield a fit,19 see also comparison of Ino-decahedral21 and icosahedral cores in Figure S3, Supporting Information. We have analyzed the electronic structure of neutral Au144(SR)60, and panels A and B of Figure 3 display its projected electronic density of states within the gold core region along with the angular momentum analysis (for technical details of this analysis, see the Supporting Information text). The energy
Letters gap between the highest occupied and lowest unoccupied states (HOMO and LUMO, respectively) is vanishingly small for the neutral cluster. Furthermore, in the range of (1 eV about that energy, each state can be assigned to one dominant “global” (within the volume of the Au114 core) angular momentum symmetry. The ordering of these subshells corresponds to the manifold of states between electron shell-closing numbers 58 and 92 in the spherical free-electron model for metal clusters.24 These states define the low-energy optical and electrochemical response of the protected particle. According to the “superatom complex model” (SACM, see ref 9), Au144(SR)60 has 144 - 60 ) 84 “metallic” electrons in the neutral state, meaning that it is deficient by 8 electrons from the shell closing of 92 electrons. The average density of single-electron states is high in the HOMO-LUMO region with an average state separation of only 0.02 eV. The gaps within the 3S2D1H manifold are typically small (
