A unified view of ligand-protected gold clusters as superatom complexes Michael Walter†, Jaakko Akola†‡, Olga Lopez-Acevedo†, Pablo D. Jadzinsky§¶, Guillermo Calero§, Christopher J. Ackerson§ʈ, Robert L. Whetten††, Henrik Gro¨ nbeck‡‡, and Hannu Ha¨ kkinen†§§¶¶ Departments of †Physics and §§Chemistry, Nanoscience Center, University of Jyva¨skyla¨, FI-40014 Jyva¨skyla¨, Finland; ‡Institut fu¨r Festko¨rperforschung, Forschungszentrum Ju¨lich, D-52425 Ju¨lich, Germany; §Department of Structural Biology, Stanford University School of Medicine, Stanford, CA 94305; ¶Department of Applied Physics, Stanford University, Stanford, CA 94305; ††School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA 30332; and ‡‡Competence Centre for Catalysis and Department of Applied Physics, Chalmers University of Technology, SE-41296, Go¨teborg, Sweden Edited by Royce W. Murray, University of North Carolina, Chapel Hill, NC, and approved April 10, 2008 (received for review January 31, 2008) Synthesis, characterization, and functionalization of self-assembled, 6s orbitals (10, 11), representing a finite-system analogy to the ligand-stabilized gold nanoparticles are long-standing issues in the bulk conduction electron states, which have 6s-character close to chemistry of nanomaterials. Factors driving the thermodynamic the Fermi surface. Exceptional stability is associated with a total stability of well documented discrete sizes are largely unknown. count of Herein, we provide a unified view of principles that underlie the stability of particles protected by thiolate (SR) or phosphine and n* ϭ 2, 8, 18, 34, 58, 92, 138, . [1] halide (PR , X) ligands. The picture has emerged from analysis of 3 electrons, corresponding to strong electron shell closures in an large-scale density functional theory calculations of structurally ؊ anharmonic mean-field potential (depending on the details of characterized compounds, namely Au (SR) ,Au (PR ) X , 102 44 39 3 14 6 the mean-field potential, 20 and 40 electrons can also account for Au (PR ) X , and Au (PR ) X 3؉, where X is either a halogen or 11 3 7 3 13 3 10 2 a stable cluster; see ref. 4). a thiolate. Attributable to a compact, symmetric core and complete Similarly to atom–ligand complexes, superatoms may be elec- steric protection, each compound has a filled spherical electronic tronically stabilized by adsorption of ligands. These ligands X shell and a major energy gap to unoccupied states. Consequently, may either withdraw electrons (or localize electrons into cova- the exceptional stability is best described by a ‘‘noble-gas supera- lent bonds) from the metal core or be attached as weak Lewis tom’’ analogy. The explanatory power of this concept is shown by base (L) ligands that coordinate to the core surface by dative its application to many monomeric and oligomeric compounds of bonds that do not withdraw electrons from the core metal atoms precisely known composition and structure, and its predictive A. The requirement for an electronically closed shell superatom power is indicated through suggestions offered for a series of complex, therefore, formulated as (L ⅐ A X )z,is anomalously stable cluster compositions which are still awaiting a s N M precise structure determination. ϭ Ϫ Ϫ n* NvA M z, [2] CHEMISTRY density functional theory ͉ monolayer-protected cluster where the shell-closing electron count (n*) of the metallic core has to satisfy one of the shell-closing numbers given in Eq. 1. n* n Mendeleev’s periodic table of elements, atoms are arranged is deduced from the superatomic number (i.e., the product of the Iaccording to their chemical nature. The periodic arrangement number (N) of core metal atoms, A, and the atomic valence, vA), and properties are fully explained by the electronic theory of from the number M of electron-localizing (or electron- atoms and the universal aufbau sequence of electrons in a withdrawing) ligands (assuming here a withdrawal of one elec- centrosymmetric Coulomb potential. Closed electronic shells tron per each X), and from the overall charge on the complex (z). appear for the noble gases, which are chemically inert. The The weak ligands Ls may be needed for completion of the steric electronic configuration of any other atom with atomic number protection of the core surface. Z in the periodic table can be expressed in terms of the maximum The predictive value of the simple arithmetic embodied in Eq. 2 has been demonstrated in the case of gas-phase metallic valence Z Ϫ nrg*, where nrg* is the shell-closing number of the underlying noble-gas configuration. Considering metals, all of clusters coordinated with small numbers of simple ligands (5–7) and for Ga-based metalloid clusters (8). However, it has been the Z Ϫ nrg* valence electrons can be transferred to suitable ligands, opening the possibility to restore the noble-gas elec- challenging to adapt the similar arithmetic for ‘‘solution’’-phase tronic configuration in formation of stable maximum-valence clusters, which besides satisfying expressions 1 and 2 must also complexes (1). have a sterically complete protective ligand shell compatible with Analogously to the atomic theory, the ‘‘superatom electronic a compact atomic shell structure for the metallic core. It has not been at all obvious how the three requirements of compact theory’’ predicts the stability and chemical nature of simple geometry, electron shell closing in the metal core, and complete metal clusters and nanoparticles (2, 3). This theory has been successful explaining the mass abundances of uncoordinated gas-phase metallic clusters (4), gas-phase metallic clusters co- Author contributions: H.H. designed research; M.W., J.A., O.L.-A., and H.G. performed ordinated with a small number of simple ligands (5–7), and research; M.W., J.A., O.L.-A., and H.G. analyzed data; and M.W., J.A., O.L.-A., P.D.J., G.C., Ga-based ‘‘metalloid’’ clusters (8). It has also been speculatively C.J.A., R.L.W., H.G., and H.H. wrote the paper. proposed (9) as a possible explanation for the compositions of The authors declare no conflict of interest. the distinct thermodynamically stable cluster sizes of various This article is a PNAS Direct Submission. monolayer-protected metal clusters that form by a self- Freely available online through the PNAS open access option. organized process in solution. ʈPresent address: Department of Chemistry and Biochemistry, University of Colorado, The appropriate aufbau rule of delocalized ‘‘superatomic Boulder, CO 80309. 2 6 10 2 14 6 18 orbitals’’ of metal clusters is 1S ͉ 1P ͉ 1D ͉ 2S 1F ͉ 2P 1G ¶¶To whom correspondence should be addressed. E-mail: [email protected].fi. 10 2 22 ͉ 2D 3S 1H ͉ . ., wherein S–P–D–F–G–H– denote the This article contains supporting information online at www.pnas.org/cgi/content/full/ angular-momentum characters. In the case of medium-size gold 0801001105/DCSupplemental. clusters, the delocalized orbitals are derived mainly from atomic © 2008 by The National Academy of Sciences of the USA www.pnas.org͞cgi͞doi͞10.1073͞pnas.0801001105 PNAS ͉ July 8, 2008 ͉ vol. 105 ͉ no. 27 ͉ 9157–9162 Downloaded by guest on September 30, 2021 steric shielding can be simultaneously achieved. Even worse, the ill defined nature of the surface chemical bond in some of the most important cases (e.g., the metal-rich gold- and silver- thiolate cluster compounds) leaves even the identity of the actual X groups uncertain. The recent breakthrough in total-structure determination of an all-thiolate-protected 102-atom gold cluster 1,Au102(p-MBA)44 (p-MBA, para-mercaptobenzoic acid, SC7O2H5), (12) presents an opportunity to rectify this problem. We present here large-scale density-functional calculations that solve the electronic structure of the 102-atom cluster starting from the experimentally determined coordinates, including the relevant p-MBA ligand. Analysis of the results and comparisons to the homologous compound 2, Au102(SMe)44 (Me, methyl), to the experimentally characterized phosphine-halide-protected Au39 cluster (13), formulated here as 3, Ϫ Au39(PR3)14Cl6 , to the undecagold compounds 4,Au11(PR3)7Cl3, and 5,Au11(PR3)7(SMe)3, and to the tridecagold compound 6, 3ϩ Au13(PR3)10Cl2 (refs. 14–17) unambiguously show that the su- peratom concept is valid irrespective of the chemical differences in the protection in 1–6. Compounds 4–6 correspond to n* ϭ 8, compound 3 to n* ϭ 34, and 1 and 2 to n* ϭ 58; in all cases vA ϭ 1 for gold. We discuss the relevance of our findings with respect to identification of the precise compositions of other known all- thiolate-protected gold clusters, as well as the importance of the atomic structure of the interface of the gold core and the gold- thiolate shell in compounds 1 and 2 regarding the structure of the interface of the bulk Au(111) and the self-assembled monolayer (SAM). The theoretical concepts laid out here provide a solid Fig. 1. Core-shell structure of the Au102(p-MBA)44 cluster. (a and b) Space- filling (a) and ball-and-stick (b) representations of the Au102(p-MBA)44 nano- background for further understanding of the distinct electrical, particle. Au, orange; S, yellow; C, gray; O, red; H, white. (c and d) Two views optical, and chemical properties of the stable monolayer-protected of the 40-atom surface of the Au79 core, together with the passivating Au nanoclusters (MPCs) (18–30), which eventually can parallel the Au23(p-MBA)44 mantle. The cationic Au atoms in the mantle are depicted by wealth of information gained from investigations of nanosized gold the smaller orange spheres. The ‘‘structure defects’’ at the core–mantle inter- clusters in the gas phase (10, 11, 31–35) and should facilitate face [two Au atoms with two Au–S bonds, and a long RS–(AuSR)2 unit] are engineering of nano-applications, made out of MPC building highlighted by the ellipse.