Structure and energetics of two- and three-dimensional neutral, cationic, and anionic gold clusters Au5⩽n⩽9Z (Z=0,±1)

Computing gold cluster energies with density functional theory: the importance of correlation

Energies calculated with density functional theory depend critically on the choice of the exchange-correlation functional. In this work, we use measured dissociation energies of Aun+ (n = 5-17) clusters as benchmark data to test two very different functionals for calculating total energies in these clusters; the simpler (and fast) PBE and the evolved (and expensive) B2PLYP double-hybrid functionals. PBE consistently gives poor agreement with the experimental results. In contrast, the B2PLYP functional, which implicitly includes electron correlation by performing a perturbative second-order correction, significantly improves the agreement of the calculations, at the cost of much more demanding computations. The better performance of the double-hybrid functional is ascribed to the longer range of the interatomic potential.

Superatomic and adsorption properties of Ni atom doped Au clusters

Due to their strong relativistic effects, Au clusters exhibit many unusual geometric structures. Among them, Au7-, Au8 and Au9+ have 18 valence electrons satisfying the magic numbers in the jellium model, respectively, but these three non-spherical clusters are not superatoms. In general, a single dopant atom can drastically change the structural and electronic properties of Au clusters. Here, we searched structures of NiAu7-, NiAu8 and NiAu9+ clusters using the genetic algorithm program (GA) combined with density functional theory (DFT). It was found that the alloy clusters are all 3D spherical structures. The molecular orbitals and density of states analysis indicate that they have completely filled superatomic shells (1S21P6), in which the electronic structure of the Ni atom is d10. Then, the electrostatic potential surfaces of the alloy clusters are analyzed, and the calculated results show that the NiAu8 superatom has remarkable σ-holes with positive potential regions. Moreover, these electron-deficient regions can be considered as interaction sites with some electron donors. After a Lewis base CO gas molecule is adsorbed on the Au-based superatom, we found that the C-O bond distance becomes slightly elongated and its stretching frequency presents a significant red-shift. This is due to the fact that 5d electrons of the Au atom of the NiAu8 transfer towards the anti-bond π orbitals of the CO molecule. Hence, this is an effective strategy for finding new types of superatoms and potential catalysts for covalent bond activation.

Neutral gold clusters studied by the isothermal Brownian-type molecular dynamics and metadynamics molecular dynamics simulations

The DFTB theory was combined with the isothermal Brownian-type molecular dynamics (MD) and metadynamics molecular dynamics (MMD) algorithms to perform simulation studies for Au clusters. Two representative DFTB parametrizations were investigated. In one parametrization, the DFTB-A, the Slater-Koster parameters in the DFTB energy function were determined focusing on the ionic repulsive energy part, E_rep and the other, the DFTB-B, due attention was paid to the electronic band-structure energy part, E_band . Minimized structures of these two parametrizations were separately applied in MD and MMD simulations to generate unbiased and biased trajectories in collective variable (CV) space, respectively. Here, we found the MD simulations monitored at 300 K manifest fluxional characteristics in planar cluster Au₉ /DFTB-A, but give no discernible tracts of fluxionality for planar Au₈ /DFTB-A and Au₈ /DFTB-B, for nonplanar Au₁₀ /DFTB-A and, to some extent, for nonplanar Au₉ /DFTB-B; they are plausibly being hindered by higher-than k_B T energy barriers. Very recent FIR-MPD spectroscopy measurements, however, were reported to have detected at 300 K both the planar and nonplanar neutral Au_n clusters in the size range 5 ≤ n ≤ 13. The failure of MD simulations has prompted us to apply the MMD simulation and construct the free energy landscape (FEL) in CV space. Through scrutinizing the FELs of these clusters and their associated structures, we examine the relative importance of E_rep /DFTB-A and E_band /DFTB-B in unraveling the covalent-like behavior of valence electrons in Au_n . Most important of all, we shall evaluate the DFTB parametrization in MMD strategy through comparing extensively the simulation data recorded with the gas-phase experimental data.

The structures of cationic gold clusters probed by far-infrared spectroscopy

Determining the precise structures of small gold clusters is an essential step towards understanding their chemical and physical properties. Due to the relativistic nature of gold, its clusters remain planar (2D) up to appreciable sizes. Ion mobility experiments have suggested that positively charged gold clusters adopt three-dimensional (3D) structures from n = 8 onward. Computations predict, depending on the level of theory, 2D or 3D structures as putative energy-minimum for n = 8. In this work, far-infrared multiple photon dissociation spectroscopy, using Ar as tagging element, is combined with density-functional theory calculations to determine the structures of Au_n⁺ (n≤ 9) clusters formed by laser ablation. While the Au frameworks in Au₆Ar_m⁺ and Au₇Ar_m⁺ complexes are confirmed to be planar and that in Au₉Ar_m⁺ three-dimensional, we demonstrate the coexistence of 3D and planar Au₈Ar_m⁺ (m = 1-3) isomers. Thus, it is revealed that at finite temperatures, the formal 2D to 3D transition takes place at n = 8 but is not sharp.

The influence of support materials on the structural and electronic properties of gold nanoparticles – a DFT study

This study investigates the effect of commonly used support materials (MgO, C, CeO₂) on small gold particles using dispersion corrected density functional theory (DFT-D).

Optimum Particle Size for Gold-Catalyzed CO Oxidation

The structure sensitivity of gold-catalyzed CO oxidation is presented by analyzing in detail the dependence of CO oxidation rate on particle size. Clusters with less than 14 gold atoms adopt a planar structure, whereas larger ones adopt a three-dimensional structure. The CO and O₂ adsorption properties depend strongly on particle structure and size. All of the reaction barriers relevant to CO oxidation display linear scaling relationships with CO and O₂ binding strengths as main reactivity descriptors. Planar and three-dimensional gold clusters exhibit different linear scaling relationship due to different surface topologies and different coordination numbers of the surface atoms. On the basis of these linear scaling relationships, first-principles microkinetics simulations were conducted to determine CO oxidation rates and possible rate-determining step of Au particles. Planar Au₉ and three-dimensional Au₇₉ clusters present the highest CO oxidation rates for planar and three-dimensional clusters, respectively. The planar Au₉ cluster is much more active than the optimum Au₇₉ cluster. A common feature of optimum CO oxidation performance is the intermediate binding strengths of CO and O₂, resulting in intermediate coverages of CO, O₂, and O. Both these optimum particles present lower performance than maximum Sabatier performance, indicating that there is sufficient room for improvement of gold catalysts for CO oxidation.

The adsorption of helium atoms on small cationic gold clusters

Adducts formed between small gold cluster cations and helium atoms are reported for the first time. These binary ions, Aun+Hem, were produced by electron ionization of helium nanodroplets doped with neutral gold clusters and were detected using mass spectrometry. For a given value of n, the distribution of ions as a function of the number of added helium atoms, m, has been recorded. Peaks with anomalously high intensities, corresponding to so-called magic number ions, are identified and interpreted in terms of the geometric structures of the underlying Aun+ ions. These features can be accounted for by planar structures for Aun+ ions with n ≤ 7, with the addition of helium having no significant effect on the structures of the underlying gold cluster ions. According to ion mobility studies and some theoretical predictions, a 3-D structure is expected for Au8+. However, the findings for Au8+ in this work are more consistent with a planar structure.

DNA-stabilized Ag-Au bimetallic clusters: the effects of alloying and embedding on optical properties

Global geometry optimization and time-dependent density functional theory calculations have been used to study the structural evolution and optical properties of AgnAun (n = 2-6) nanoalloys both as individual clusters and as clusters stabilized with the fragments of DNA of different size. We show that alloying can be used to control and tune the level of interaction between the metal atoms of the cluster and the organic fragments of the DNA ligands. For instance, gold and silver atoms are shown to exhibit synergistic effects in the process of charge transfer from the nucleobase to the cluster, with the silver atoms directly connected to the nitrogen atoms of cytosine increasing their positive partial charge, while their more electronegative neighbouring gold atoms host the excess negative charge. This allows the geometrical structures and optical absorption spectra of small bimetallic clusters to retain many of their main features upon aggregation with relatively large DNA fragments, such as a cytosine-based 9-nucleotide hairpin loop, which suggests a potential synthetic route to such hybrid metal-organic compounds, and opens up the possibility of bringing the unique tunable properties of bimetallic nanoalloys to biological applications.

Geometric and electronic properties of gold clusters doped with a single oxygen atom

A systematic theoretical study on single oxygen atom doped gold clusters showed that a single oxygen atom can be adsorbed on various sites of gold surfaces, and obtain nearly one electron from gold atoms.

Neutral and Anionic Gold Decamers: Planar Structure with Unusual Spatial Charge-Spin Separation

We have investigated the issue of two-dimensional (2D) versus three-dimensional (3D) structures for neutral-state Au10 and clarified the lowest-energy structure among a few 2D Au10(-) isomers. Though almost all previous works were based on density functional theory (DFT), we here carried out not only extensive DFT calculations but also high levels of ab initio calculations of Möller-Plesset second order perturbation theory (MP2), and coupled cluster theory with single and double excitations (CCSD) including perturbative triple excitations [CCSD(T)]. While DFT favors 2D structures, MP2 and CCSD(T) favor 3D structures for moderate-sized basis sets. However, we note that the basis-set superposition error (BSSE) corrections make the ab intio results favor 2D structures too. The near-degeneracy (driven by relativistic effects) of 5d and 6s orbitals of gold helps stabilize acute apex gold atoms, resulting in 2D structures. The planar triangular structures of a local minimum Au10 (triplet) and the global minimum Au10(-) show remarkable spatial charge-spin separation due to their singly occupied molecular orbital(s). By the same reason, Au10(-) shows much larger vertical detachment energy than other even-numbered gold cluster anions.

Ab initio and anion photoelectron study of AunRhm (n = 1–7, m = 1–2) clusters

Anion photoelectron spectroscopy and DFT calculations study on Au_nRh_m (n = 1–7 and m = 1–2). PES spectra, vertical and adiabatic detachment energies, are compared. The characteristic planarity for gold clusters is preserved for many of the bimetallic clusters.

Probing the structural and electronic properties of bimetallic chromium-gold clusters CrmAun(m+n≤6): comparison with pure chromium and gold clusters

Bimetallic chromium-gold CrmAun(m+n≤6) clusters are systematically investigated using the density functional theory at PW91P86 level with LanL2TZ basis set to understand the evolution of various structural, electronic, magnetic, and energetic properties as a function of size (m+n) and composition (m/n) of the system. Theoretical results show a logical evolution of the properties depending on the size and the composition of the system. Cr m clusters clearly prefer 3D structures while Au n clusters favor planar configurations. The geometry of the bimetallic Cr m Au n clusters mainly depends on their composition, i.e., clusters enriched in Cr atoms prefer 3D structures while increasing Au contents promotes planar configurations. The stability is maximized when the composition of binary Cr m Au n clusters is nearly balanced. Meanwhile, the number of hetero Cr-Au bonds and charge transfer from Cr to Au are maximized for clusters with m≈n. The most probable dissociation channels of the Cr m Au n clusters are calculated and analyzed. Natural population analysis reveals that Au atoms tend to be negatively charged while Cr atoms tend to be positively charged. Combined with the trend that Au atoms favor the surface/edges/vertices and Cr atoms tend to be inside, the outer part of the cluster tends to be negatively charged, and the inner part tends to be positively charged.

The shape of Au8: gold leaf or gold nugget?

The size at which nonplanar isomers of neutral, pristine gold nanoclusters become energetically favored over planar ones is still debated amongst theoreticians and experimentalists. Spectroscopy confirms planarity is preferred at sizes up to Au7, however, starting with Au8, the uncertainty remains for larger nanoclusters. Au8 computational studies have had different outcomes: the planar D4h "cloverleaf" isomer competes with the nonplanar Td, C2v and D2d "nugget" isomers for greatest energetic stability. We here examine the 2D vs. 3D preference in Au8 by presenting our own B2PLYP, MP2 and CCSD(T) calculations on these isomers: these methods afford a better treatment of long-range correlation, which is at the root of gold's characteristic aurophilicity. We then use findings from these high-accuracy computations to evaluate two less expensive DFT approaches, applicable to much larger nanoclusters: alongside the standard functional PBE, we consider M06-L (highly parametrized to incorporate long-range dispersive interactions). We find that increasing basis set size within the B2PLYP framework has a greater destabilizing effect on the nuggets than it has on the Au8 cloverleaf. Our CCSD(T) and B2PLYP predictions, replicated by DFT-PBE, all identify the cloverleaf as the most stable isomer; MP2 and DFT-M06-L show overestimation of aurophilicity, and favor, respectively, the nonplanar D2d and Td nuggets in its stead. We conclude that PBE, which more closely reproduces CCSD(T) findings, may be a better candidate density functional for the simulation of gold nanoclusters in this context.

Diffusion of adatoms and small clusters on magnesium oxide surfaces

The diffusion of isolated adatoms and small clusters is reviewed for transition and noble metals adsorbed on the (001) surface of magnesium oxide. While isolated adatoms diffuse by hopping among adsorption sites, small clusters such as dimers, trimers and tetramers already display a variety of diffusion mechanisms, from cluster hopping to rotation, sliding, leapfrog, walking, concertina, flipping, twisting, rolling and rocking. Since most of the available results are computational, the review is mostly related to theoretical work. Connection to experiments is discussed where possible, mostly by dealing with the consequences that adatom and small cluster mobility may have on the growth of larger aggregates on the MgO(001) surface.

Structures and relative stability of neutral gold clusters: Aun (n=15-19)

We performed a global-minimum search for low-lying neutral clusters (Au(n)) in the size range of n=15-19 by means of basin-hopping method coupled with density functional theory calculation. Leading candidates for the lowest-energy clusters are identified, including four for Au(15), two for Au(16), three for Au(17), five for Au(18), and one for Au(19). For Au(15) and Au(16) we find that the shell-like flat-cage structures dominate the population of low-lying clusters, while for Au(17) and Au(18) spherical-like hollow-cage structures dominate the low-lying population. The transition from flat-cage to hollow-cage structure is at Au(17) for neutral gold clusters, in contrast to the anion counterparts for which the structural transition is at Au(16) (-) [S. Bulusu et al., Proc. Natl. Acad. Sci. U.S.A. 103, 8362 (2006)]. Moreover, the structural transition from hollow-cage to pyramidal structure occurs at Au(19). The lowest-energy hollow-cage structure of Au(17) (with C(2v) point-group symmetry) shows distinct stability, either in neutral or in anionic form. The distinct stability of the hollow-cage Au(17) calls for the possibility of synthesizing highly stable core/shell bimetallic clusters M@Au(17) (M=group I metal elements).

Complexes of DNA bases and Watson-Crick base pairs with small neutral gold clusters

The nature of the DNA-gold interaction determines and differentiates the affinity of the nucleobases (adenine, thymine, guanine, and cytosine) to gold. Our preliminary computational study [Kryachko, E. S.; Remacle, F. Nano Lett. 2005, 5, 735] demonstrates that two major bonding factors govern this interaction: the anchoring, either of the Au-N or Au-O type, and the nonconventional N-H...Au hydrogen bonding. In this paper, we offer insight into the nature of nucleobase-gold interactions and provide a detailed characterization of their different facets, i.e., geometrical, energetic, and spectroscopic aspects; the gold cluster size and gold coordination effects; proton affinity; and deprotonation energy. We then investigate how the Watson-Crick DNA pairing patterns are modulated by the nucleobase-gold interaction. We do so in terms of the proton affinities and deprotonation energies of those proton acceptors and proton donors which are involved in the interbase hydrogen bondings. A variety of properties of the most stable Watson-Crick [A x T]-Au3 and [G x C]-Au3 hybridized complexes are described and compared with the isolated Watson-Crick A x T and G x C ones. It is shown that enlarging the gold cluster size to Au6 results in a rather short gold-gold bond in the Watson-Crick interbase region of the [G x C]-Au6 complex that bridges the G x C pair and thus leads to a significant strengthening of G x C pairing.

Adsorption of molecular hydrogen and hydrogen sulfide on Au clusters

The authors present theoretical results describing the adsorption of H2 and H2S molecules on small neutral and cationic gold clusters (Au(n)((0/+1)), n=1-8) using density functional theory with the generalized gradient approximation. Lowest energy structures of the gold clusters along with their isomers are considered in the optimization process for molecular adsorption. The adsorption energies of H2S molecule on the cationic clusters are generally greater than those on the corresponding neutral clusters. These are also greater than the H2 adsorption energies on the corresponding cationic and neutral clusters. The adsorption energies for cationic clusters decrease with increasing cluster size. This fact is reflected in the elongations of the Au-S and Au-H bonds indicating weak adsorption as the cluster grows. In most cases, the geometry of the lowest energy gold cluster remains planar even after the adsorption. In addition, the adsorbed molecule gets adjusted such that its center of mass lies on the plane of the gold cluster. Study of the orbital charge density of the gold adsorbed H2S molecule reveals that conduction is possible through molecular orbitals other than the lowest unoccupied molecular orbital level. The dissociation of the cationic Au(n)SH2+ cluster into Au(n)S+ and H2 is preferred over the dissociation into Au(m)SH2+ and Au(n-m), where n=2-8 and m=1-(n-1). H2S adsorbed clusters with odd number of gold atoms are more stable than neighboring even n clusters.

Nonconventional hydrogen bonding between clusters of gold and hydrogen fluoride

The bonding patterns between small neutral gold Au(3 < or = n < or = 7) and hydrogen fluoride (HF)(1 < or = m < or = 4) clusters are discussed using a high-level density functional approach. Two types of interactions, anchoring Au-F and F-H...Au, govern the complexation of these clusters. The F-H...Au interaction exhibits all the characteristics of nonconventional hydrogen bonding and plays a leading role in stabilizing the lowest-energy complexes. The anchor bonding mainly activates the conventional F-H...F hydrogen bonds within HF clusters and reinforces the nonconventional F-H...Au one. The strength of the F-H...Au bonding, formed between the terminal conventional proton donor group FH and an unanchored gold atom, depends on the coordination of the involved gold atom: the less it is coordinated, the stronger its nonconventional proton acceptor ability. The strongest F-H...Au bond is formed between a HF dimer and the singly coordinated gold atom of a T-shape Au4 cluster and is accompanied by a very large red shift (1023 cm(-1)) of the nu(F-H) stretch. Estimations of the energies of formation of the F-H...Au bonds for the entire series of the studied complexes are provided.