Tangential ligand-induced strain in icosahedral Au13.

Metal nanoclusters1 (and gold nanoclusters in particular2) can exhibit structures that differ significantly from that corresponding to the bulk, ones that depend strongly on cluster size. Detailed knowledge of these structures is crucial for understanding and predicting nanocluster properties, including chemical, electrical, magnetic, and optical ones. The experimental determination of atomistic structural information is a very difficult task: analyses by imaging or scattering methods are presently limited by insufficient spatial resolution or by the coherent scattering size of these techniques. As a result, most structural determinations proceed indirectly by comparing experimentally accessible properties (e.g., ion mobility, photoemission spectra, polarizability, optical absorption, etc.) with those computed theoretically for candidate structures. A more direct approach to the determination of nanocluster structure is afforded by the extended X-ray absorption fine structure (EXAFS) technique.3,4 By careful analysis of oscillations on the high photon energy side of the X-ray absorption edge in sufficiently monodisperse clusters, one can extract accurate information as to the identity, average distance, and coordination of the neighbors to the X-ray absorbing atom. Even so, EXAFS only yields ensemble-averaged information. If applied to size-controlled nanoclusters, however, it yields a more detailed understanding of the structure, size, and shape of the nanoclusters because it drastically reduces the number of candidate structures that are a priori potentially consistent with it. A recent combination of EXAFS and atom counting methods of transmission electron microscopy (TEM) on such specially synthesized nanoclusters (Au13[PPh3]4[S(CH2)11CH3]4) has found them to be highly monodisperse, with their overall structure possessing, on average, 13 gold atoms, with Au-Au coordination number of 6.7 ( 0.7, an average a Au-Au bond length of 2.85 ( 0.02 Å, and an average Au-ligand distance of 2.324 ( 0.007 Å.5 The presence of eight ligands per cluster was deduced from X-ray photoelectron spectroscopy data.6 While the combination of the experimental results points toward an icosahedral shape of the Au13 core, theoretical verification and a detailed interpretation of such a model was lacking. In particular, two central questionssligand placement and anomalously high AuAu bond length disorderswere left unanswered by the experimental results. First, EXAFS is not capable of discriminating between Au-S and Au-P neighbors, treating them cumulatively as Au-L (L ) S/P) pairs and obtaining the oVerall Au-L coordination number as the total number of Au-S and Au-P bonds divided by the total number of Au atoms. However, the phosphines and the thiolates may have distinctly different bonding motifs: on-top for phosphines7 and bridge sites for thiolates.8 Thus, the preferred ligand placement remains ambiguous. Second, the experimental distribution of Au-Au bond lengths was σ2 ) 0.017 ( 0.005 Å2, which is much larger than that in bulk gold (0.008 Å2) at the same temperature (300 K).5 Such enhanced σ2 must be configurational in nature because the temperature-dependent, dynamic component in nanoparticles has previously exhibited only weak, if any, size dependence.4 However, neither EXAFS nor TEM provide enough information to uncover its origin. The gaps left in our understanding of the three-dimensional structure of ligand-stabilized gold nanoparticles are filled here using first principles calculations based on density functional theory (DFT)9 that provide a consistent interpretation of the experiments. In this Communication, we use the EXAFS and TEM results as a starting point for a theoretical analysis of the mixed-ligand Au13 nanocluster, Au13[PPh3]4[S(CH2)11CH3]4. All calculations were performed using the GAUSSIAN03 code10 using the local density approximation for the exchange correlation. The LANL2DZ basis set was used for Au, and the 6-31G(d,p) basis set was used for all other elements. The robustness of the results was ascertained via comparison of select results to those obtained with a hybrid functional and with larger basis sets. As a further test, for the Au dimer, we found a bond length of 2.48 Å, in good agreement with previous theoretical studies11,12 and with experiment (2.47 Å).13 For bare Au13 nanoclusters, many structures, including icosahedral,14 cuboctahedral,15 biplanar,16 and amorphous17 ones, have been predicted theoretically as comprising the lowest energy configuration. Both ordered and disordered structures were predicted theoretically for ligated Au38 structures,18-20 and experimental verification was limited to scattering methods (e.g., X-ray diffraction) which are less than ideal for clusters of this size. This may reflect the existence of several energetically close isomers.20 Nevertheless, the high order determined from the EXAFS data allowed us to focus on high-symmetry metal cores. We hypothesized that all four phosphine ligands and two of the thiolates are bonded on-top a Au atom and that the two other thiolates bridge two Au atoms, leaving two Au atoms uncapped. This model is supported by the experimentally observed Au-L coordination number, NAu-L ) 0.76 ( 0.05. This coordination number is consistent with 9-10 of the surface atoms being bonded to a ligand.5 However, it is inconsistent with alternative models where all eight ligands are bound to on-top sites (NAu-L ) 0.615) or all four thiolates are bound to bridge sites (NAu-L ) 0.92). In the calculations, the long-chain thiolates were replaced with methylthiol groups and the triphenylphosphines were replaced by phosphine groups for numerical expediency. While an icosahedral metallic core is potentially consistent with the experimental data, we also tested the possibility of a cuboctahedral core. Starting from a ligand configuration as explained above, upon relaxation, all S atoms reverted to a bridging configuration, increasing the Au-L coordination number to 0.92, in contrast with the EXAFS experiment. In addition, the average Au-Au bond † Weizmann Institute of Science. ‡ Yeshiva University. § University of Illinois. Published on Web 08/18/2007