Where Does the Planar-to-Nonplanar Turnover Occur in Small Gold Clusters?

Going for Gold(-Standard): Attaining Coupled Cluster Accuracy in Oxide-Supported Nanoclusters

The structure of oxide-supported metal nanoclusters plays an essential role in their sharply enhanced catalytic activity over that of bulk metals. Simulations provide the atomic-scale resolution needed to understand these systems. However, the sensitive mix of metal-metal and metal-support interactions, which govern their structure, puts stringent requirements on the method used, requiring calculations beyond standard density functional theory (DFT). The method of choice is coupled cluster theory [specifically CCSD(T)], but its computational cost has so far prevented its application to these systems. In this work, we showcase two approaches to make CCSD(T) accuracy readily achievable in oxide-supported nanoclusters. First, we leverage the SKZCAM protocol to provide the first benchmarks of oxide-supported nanoclusters, revealing that it is specifically metal-metal interactions that are challenging to capture with DFT. Second, we propose a CCSD(T) correction (ΔCC) to the metal-metal interaction errors in DFT, reaching accuracy comparable to that of the SKZCAM protocol at significantly lower cost. This approach forges a path toward studying larger systems at reliable accuracy, which we highlight by identifying a ground-state structure in agreement with experiments for Au20 on MgO, a challenging system where DFT models have yielded conflicting predictions.

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.

{Nano-gold, iron(III)-1,3,5-benzene tricarboxylate metal organic framework (MOF)} nano-composite as precursor for laser ablation generation of gold-iron Aum Fen +/- (m = 1-35, n = 1-5) clusters. Mass spectrometric study

RATIONALE

Gold-iron bimetallic materials have applications in many fields, especially in nanotechnology and biomedicine. The chemistry of iron-doped gold clusters is still not fully understood but opens up the possibility of developing new materials, e.g. of gold cages doped with iron atoms. There have been several theoretical studies on these clusters but only a few experimental studies.

METHODS

Laser desorption ionisation (LDI) was used for the generation of Au-Fe bimetallic clusters via laser ablation (337 nm nitrogen laser) of the synthesised nano-composite {nano-gold; Fe(III) 1,3,5-benzene tricarboxylate}, i.e. {AuNPs, Fe-MOF}, while a quadrupole ion trap time-of-flight mass spectrometer, equipped with a reflectron, was used to acquire mass spectra.

RESULTS

A {AuNPs, Fe-MOF} nano-composite was prepared and found suitable for the LDI generation of Au_m Fe_n clusters. In addition to Au_m ^+/- (m = 1-35) clusters, a series of positively and negatively charged gold-iron Au_m Fe_n ^+/- clusters were generated. The mass spectra exhibited evidence for the clusters containing up to five iron atoms. In total, 113 binary Au_m Fe_n ^+/- clusters (m = 1-35, n = 1-5) were identified in the gas phase.

CONCLUSIONS

A synthesised {AuNPs, iron(III)-1,3,5-benzene tricarboxylate MOF} nano-composite was found suitable for the generation of many new gold-iron clusters and mass spectrometry was shown to be an efficient technique for the determination of the cluster stoichiometry. A broad series of over 100 bimetallic Au_m Fe_n clusters, some of them suggested to be gold cages doped with iron atoms (for m = 12 and higher), not only demonstrate a rich and complex chemistry, but also open wide possibilities of biomedical applications.

Electronic shells of a tubular Au26 cluster: a cage-cage superatomic molecule based on spherical aromaticity

Gold clusters, which display a variety of unusual geometric structures due to their strong relativistic effects, have attracted much attention. Among them, Au₂₆ has a high-symmetry tubular structure (D_6d) with a large HOMO-LUMO energy gap, but its electronic stability still remains unclear. In this paper, the electronic nature of the Au₂₆ cluster is investigated using the density functional theory method. Depending on the super valence bond model, the tubular Au₂₆ cluster with 26 valence electrons could be viewed as a superatomic molecule composed of two open cages based on spherical aromaticity, and its molecule-like electronic shell closure is achieved via a super triple bond (σ, 2π) between the two cages. Based on this new cage-cage superatomic structural model, a series of similar tubular clusters are predicted from the Au₂₆ skeleton. The two capped Au atoms are replaced by Cu, Ag and In atoms, respectively, to form tubular D_6d Au₂₄Cu₂ and Au₂₄Ag₂ (26e) and Au₂₄In₂ (30e) clusters, where the super triple bonds also exist. Moreover, tubular D_5d Au₂₀In₂ (26e) is obtained by replacing hexatomic Au₆ rings in the bulk of Au₂₄In₂ with pentagonal Au₅ rings. Chemical bonding analysis reveals that there is a super quintuple bond (σ, 2π, 2δ) between two open (Au₁₀In) cages, in accordance with the 26e Li₂₀Mg₃ superatomic molecule composed of two icosahedral superatoms. Our study proposes the new cage-cage structural model of superatomic molecules based on spherical aromaticity, which extends the range of the super valence bonding pattern and gives inferences for further study of superatomic clusters.

Effect of Charge and Phosphine Ligands on the Electronic Structure of the Au8 Cluster

In this work, we use density functional theory calculations with a hybrid exchange-correlation functional and effective core pseudopotentials to determine the geometry of bare and phosphine-protected Au₈ nanoclusters and characterize their electronic structure. Au₈ clusters were bonded to four and eight PH₃ ligands in order to evaluate the effect of ligand concentration on the electronic structure, while different positional configurations were also tried for four ligands attached to the cluster. We show that the neutral clusters become more nucleophilic as the ligands bind to the clusters at stable sites. The ground-state planar configuration of Au₈ is maintained depending on the concentration and position of ligands. The effect of ionizing to the +2 charge state results in disruption of planar geometry in some cases because of inoccupation of a molecular orbital with the Au-Au bonding character. Natural bond order charge analyses showed that Au atoms oxidize upon ionization, instead of phosphine. The net positive charge makes the clusters more electrophilic with a capacity to absorb electrons from nucleophiles depending on the concentration and position of ligands and on the concentration of low-coordinated gold atoms. Besides, ionization energies and electron affinities were calculated through different mechanisms, finding that both variables are much higher for charged systems and change inversely with the concentration of ligands.

Two-Dimensional Gold Quantum Dots with Tunable Bandgaps

Metallic gold nanoparticles (Au NPs) with multilayer Au atoms are useful for plasmonic, chemical, medical, and metamaterial application. In this article, we report the opening of the bandgap in substrate-supported two-dimensional (2D) gold quantum dots (Au QDs) with monolayer Au atoms. Calculations based on density functional theory suggest that 2D Au QDs are energetically favorable over 3D Au clusters when coated on hexagonal boron nitride (BN) surfaces. Experimentally, we find that BN nanotubes (BNNTs) can be used to stabilize 2D Au QDs on their cylindrical surfaces as well as Au atoms, dimers, and trimers. The electrically insulating and optically transparent BNNTs enable the detection of the optical bandgaps of the Au QDs in the visible spectrum. We further demonstrate that the size and shapes of 2D Au QDs could be atomically trimmed and restructured by electron beam irradiation. Our results may stimulate further exploration of energetically stable, metal-based 2D semiconductors, with properties tunable atom by atom.

Remarkable Structural Effect on the Gold-Hydrogen Analogy in Hydrogen-Doped Gold Cluster

In accordance with the well established gold-hydrogen analogy, a hydrogen atom mimics the properties of a gold atom in gold clusters. In a recent study it has been demonstrated that the properties of a hydrogen atom doped small gold cluster (Au₇H) are not in conformity with the aforementioned analogy. In this paper we study the properties of the Au₇H cluster exhaustively to re-examine the validity of the gold-hydrogen analogy in the context of adsorption of CO and O₂ molecules on pristine gold and hydrogen atom doped gold clusters. For this purpose we first determine the most stable structure of the Au₇H cluster by using an ab initio density functional theory based method with generalized gradient approximation (GGA) and Meta-GGA exchange-correlation functionals. We carry out geometry optimization by considering various planar and three-dimensional isomers of the Au₇H cluster as initial geometries. We find that the lowest energy structure of Au₇H is a planar one with C_{2 v} symmetry, and it is very close to the structure of the Au₈ cluster with D_{4 h} symmetry. Furthermore, to examine the validity of the gold-hydrogen analogy we carry out a detailed investigation of the adsorption of CO and O₂ molecules on the most stable as well as various other low energy isomers of the Au₇H cluster. We find that the adsorption energies and the extent of activation of CO and O₂ molecules on the most stable planar isomer of Au₇H are almost the same as those on the parent Au₈ cluster with D_{4 h} symmetry proving the validity of the gold-hydrogen analogy. On the other hand, for the high energy three-dimensional isomers of the Au₇H cluster obtained from the pristine Au₈ cluster with T _d symmetry, we find a significant enhancement in adsorption energy as well as the extent of activation of CO and O₂ molecules as compared to those for the corresponding pristine cluster. Therefore, the high reactivity of the 3D isomer of the Au₇H cluster may be attributed to its existence in a state which is higher in energy than its most stable planar isomer.

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).

Density-functional tight-binding approach for metal clusters, nanoparticles, surfaces and bulk: application to silver and gold

Density-functional based tight-binding (DFTB) is an efficient quantum mechanical method that can describe a variety of systems, going from organic and inorganic compounds to metallic and hybrid materials. The present topical review addresses the ability and performance of DFTB to investigate energetic, structural, spectroscopic and dynamical properties of gold and silver materials. After a brief overview of the theoretical basis of DFTB, its parametrization and its transferability, we report its past and recent applications to gold and silver systems, including small clusters, nanoparticles, bulk and surfaces, bare and interacting with various organic and inorganic compounds. The range of applications covered by those studies goes from plasmonics and molecular electronics, to energy conversion and surface chemistry. Finally, perspectives of DFTB in the field of gold and silver surfaces and NPs are outlined.

Au19M (M=Cr, Mn, and Fe) as magnetic copies of the golden pyramid

An investigation on structure, stability, and magnetic properties of singly doped Au19M (M=Cr, Mn, and Fe) clusters is carried out by means of density functional theory calculations. The studied clusters prefer forming magnetic versions of the unique tetrahedral Au20. Stable sextet Au19Cr is identified as the least reactive species and can be qualified as a magnetic superatom. Analysis on cluster electronic structures shows that the competition between localized and delocalized electronic states governs the stability and magnetic properties of Au19M clusters.

Evolution of the Spin Magnetic Moments and Atomic Valence of Vanadium in VCux+, VAgx+, and VAux+ Clusters (x = 3-14)

The atomic structures, bonding characteristics, spin magnetic moments, and stability of VCu_x⁺, VAg_x⁺, and VAu_x⁺ (x = 3-14) clusters were examined using density functional theory. Our studies indicate that the effective valence of vanadium is size-dependent and that at small sizes some of the valence electrons of vanadium are localized on vanadium, while at larger sizes the 3d orbitals of the vanadium participate in metallic bonding eventually quenching the spin magnetic moment. The electronic stability of the clusters may be understood through a split-shell model that partitions the valence electrons in either a delocalized shell or localized on the vanadium atom. A molecular orbital analysis reveals that in planar clusters the delocalization of the 3d orbital of vanadium is enhanced when surrounded by gold due to enhanced 6s-5d hybridization. Once the clusters become three-dimensional, this hybridization is reduced, and copper most readily delocalizes the vanadium's valence electrons. By understanding these unique features, greater insight is offered into the role of a host material's electronic structure in determining the bonding characteristics and stability of localized spin magnetic moments in quantum confined systems.

Benchmark Study of Density Functional Theory for Neutral Gold Clusters, Aun (n = 2-8)

Neutral gold clusters, Au_n (n = 2-8), were optimized using coupled cluster singles and doubles with perturbative triples (CCSD(T)) with a triple-ζ-level basis set to develop reliable reference values for their structural and energy parameters in order to assess the performance of density functionals. The performance of 44 density functional theory (DFT) methods for calculating molecular structures and relative energies is assessed with respect to CCSD(T). In addition, their performance when calculating vertical ionization potentials (vIPs) of Au_n (n = 2-8) is also assessed by comparison with experimental values. The revTPSS functional shows good performance for calculating both the structural and energy properties of Au_n (n = 2-8), whereas B3P86 shows a remarkable performance in calculating the vIPs. The quadruple-ζ-level valence basis set is necessary for obtaining accurate energy values in CCSD(T) calculations.

Vibrational anharmonicity of small gold and silver clusters using the VSCF method

We study the vibrational spectra of small neutral gold (Au₂–Au₁₀) and silver (Ag₂–Au₅) clusters using the vibrational self-consistent field method (VSCF) in order to account for anharmonicity.

DFT insights into the cycloisomerization of ω-alkynylfuran catalyzed by planar gold clusters: mechanism and selectivity, as compared to Au(i)-catalysis

A detailed reaction mechanism of Au_3–10-catalyzed cycloisomerization of ω-alkynylfuran was systemically investigated at the TPSSh/def2-TZVP levels.

Theoretical investigation of an ultrastable one dimensional infinite monatomic mixed valent gold wire with excellent electronic properties

A one-dimensional monatomic gold wire with mixed-valent Au³⁺ and Au⁰ exhibits excellent conductivity and strong visible absorption.

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.

A 2D-3D structure transition of gold clusters on CeO2-X(111) surfaces and its influence on CO and O2 adsorption: a comprehensive DFT + U investigation

Detailed knowledge of the structures of gold nanoparticles on ceria surfaces is of fundamental importance to understand their extraordinary activities in catalysis. In this work, we employ density functional theory with the inclusion of the on-site Coulomb interaction (DFT + U) to investigate the structure evolution of small-sized gold (Au, Au4, Au8 and Au12) clusters on four types of reduced CeO2-X(111) surfaces: SSV (single surface oxygen vacancy), LSVT (linear surface oxygen vacancy trimer), dLSVC (double linear surface oxygen vacancy with a surface vacancy dimer and a subsurface vacancy), and TSVT (triangular surface oxygen vacancy trimer). Our results indicate that the relative stabilities of multilayer (3D) structures are strengthened gradually compared with the monolayer (2D) structures with increasing the number of gold atoms. In addition, the 2D-3D structure transition occurs on the size order of Au(2D → 3D)@TSVT > Au(2D → 3D)@dLSVC ∼ Au(2D → 3D)@LSVT > Au(2D → 3D)@SSV, which is determined by the charge transfer magnitude between the CeO2 surfaces and gold clusters. Meanwhile, two competitive nucleation patterns are observed, fcc-like nucleation and hcp-like nucleation, which highly affect the morphology of supported gold clusters. Further site-by-site investigations indicate that the coordination number and the charges of Au atoms are the dominant factors to influence the adsorption strength of CO and O2, and the interface plays a relatively minor role. These findings not only enrich our knowledge of the relationship between surface defects, gold cluster structures and small molecule adsorptions, but also provide a theoretical perspective to help design the optimal Au/CeO2 systems possessing high catalytic efficiency.

Raman modes, dipole moment and chirality in periodically positioned Au8clusters

The solution-based assembly of h-Au₈clusters into a local periodic structure (LPS) of periodicity 1.47 nm with negative chirality as confirmed by experimental and theoretical analyses exhibits excitonic couplet state.

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.

Superatom-atom super-bonding in metallic clusters: a new look to the mystery of an Au20 pyramid

Using the super valence bond model, a generalized chemical picture for the electronic shells of an Au20 pyramid is given. It is found that Au20 can be viewed to be a superatomic molecule, of which its superatomic 16c-16e core (T) is in D(3)S hybridization bonded with four vertical Au atoms for the molecule-like (TAu4) electronic shell-closure. Based on such a superatom-atom bonding model, TX4 (X = F, Cl, or Br) are predicted to be very stable. Such a superatom-atom T-Au/T-X bonding enriches the scope of chemistry.

Communication: Determining the lowest-energy isomer of Au8: 2D, or not 2D

A parallel numerical derivative code, combined with parallel implementation of the coupled-cluster method with singles, doubles, and non-iterative triples (CCSD(T)), is used to optimize the geometries of the low-energy structures of the Au8 particle. The effects of geometry relaxation at the CCSD(T) level and the combined effects of the basis set and core-valence correlations are examined and the results are compared with the corresponding second-order Møller-Plesset perturbation theory calculations. The highest-level computations, in which the single-point CCSD(T) calculations employing the correlation-consistent basis set of the cc-pVTZ quality and the associated relativistic effective core potential (ECP), both optimized for gold, and correlating the 5d(10)6s(1) valence and 5s(2)5p(6) semi-core electrons, are combined with the geometrical information obtained with the corresponding CCSD(T)/cc-pVDZ/ECP approach, favor the planar configuration, with the next three non-planar structures separated by 4-6 kcal/mol. In agreement with the earlier work, smaller-basis set CCSD(T) computations provide unreliable results for the relative energetics, even when the geometries are optimized at the CCSD(T) level.

Fuel mediated solution combustion synthesis of ZnO supported gold clusters and nanoparticles and their catalytic activity and in vitro cytotoxicity

Well characterized atomic gold clusters and nanoparticles on the surface of ZnO are found to be effective against cancer cells.

Aerobic oxidation of methanol to formic acid on Au8-: benchmark analysis based on completely renormalized coupled-cluster and density functional theory calculations

The left-eigenstate completely renormalized coupled-cluster (CC) method with singles, doubles, and noniterative triples [CR-CC(2,3)] and a few representative density functional theory (DFT) approaches have been applied to methanol oxidation to formic acid on a Au8(-) cluster, which is a model for aerobic oxidations on gold nanoparticles. It is demonstrated that CR-CC(2,3) supports the previous exothermic reaction mechanism, placing the initial rate-determining transition state, which corresponds to hydrogen transfer from the methoxy species to the molecular oxygen, at about 20 kcal/mol above the reactants, less than 40 kcal/mol above the O2 and CH3O(-) species coadsorbed on Au8(-), and considerably above the remaining two transition states along the reaction pathway. The DFT calculations using the previously exploited M06 hybrid functional show reasonable agreement with CR-CC(2,3), but B3LYP offers additional improvements in the description of the relevant activation energies. Pure functionals, including M06-L, BP86, and TPSS, do not work well, significantly underestimating the activation barriers, but dispersion corrections, as in B97-D, bring the results closer to the M06 accuracy level.

Structure and properties of small aurocarbons: a selective study

Gold clusters are versatile catalysts, and adding nonmetal dopants can allow tuning of their electronic properties via both shape and composition alteration. In the present work, mixed clusters of carbon and gold atoms are studied in terms of structure, stability, and the correlation between the shape and electronic properties by using a density functional theory approach. Four series of isomers (hydrocarbon analogues, carbon chains and cycles on gold surface, and carbon cores encapsulated by gold atoms) are investigated, exhibiting variation of the relative stability with the system size. Calculated vertical ionization energies, vertical electron affinities, and HOMO-LUMO energy gaps of the mixed clusters show a considerable change relative to the values for the pure gold clusters, the properties generally altering more strongly for the gold-encapsulated-carbon isomers. Also discussed are the structure, stability, and properties of larger clusters with a few such encapsulated-carbon units, with pronounced effects due to aggregation.

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.

Direct atomic imaging and dynamical fluctuations of the tetrahedral Au(20) cluster

We report real-space, atomic-resolution images of Au(20) clusters obtained with the aberration-corrected Scanning Transmission Electron Microscopy. The proposed tetrahedral (FCC segment) pyramid structure is confirmed. The clusters cycle between isomers under the electron beam in the time-lapse images acquired. Disordered variants on the high symmetry forms are commonly observed. We believe that the direct experimental identification of these kinds of atomic structure, and the fluctuations between them, is fundamental to our understanding of nanoparticle structures, as well as applications such as heterogeneous catalysis.

Method and Basis Set Analysis of Oxorhenium(V) Complexes for Theoretical Calculations

A variety of method and basis set combinations has been evaluated for monooxorhenium(V) complexes with N, O, P, S, Cl, and Se donor atoms. The geometries and energies obtained are compared to both high-level computations and literature structures. These calculations show that the PBE0 method outperforms the B3LYP method with respect to both structure and energetics. The combination of 6-31G** basis set on the nonmetal atoms and LANL2TZ effective core potential on the rhenium center gives reliable equilibrium structures with minimal computational resources for both model and literature compounds. Single-point energy calculations at the PBE0/LANL2TZ,6-311+G* level of theory are recommended for energetics.

Low-energy isomer identification, structural evolution, and magnetic properties in manganese-doped gold clusters MnAu(n) (n = 1-16)

The size-dependent electronic, structural, and magnetic properties of Mn-doped gold clusters have been systematically investigated by using relativistic all-electron density functional theory with generalized gradient approximation. A number of new isomers are obtained for neutral MnAu(n) (n = 1-16) clusters to probe the structural evolution. The two-dimensional (2D) to three-dimensional (3D) transition occurs in the size range n = 7-10 with manifest structure competitions. From size n = 13 to n = 16, the MnAu(n) prefers a gold cage structure with Mn atom locating at the center. The relative stabilities of the ground-state MnAu(n) clusters show a pronounced odd-even oscillation with the number of Au atoms. The magnetic moments of MnAu(n) clusters vary from 3 μ(B) to 6 μ(B) with the different cluster size, suggesting that nonmagnetic Au(n) clusters can serve as a flexible host to tailor the dopant's magnetism, which has potential applications in new nanomaterials with tunable magnetic properties.

REEXAMINATION OF LOW ENERGY STRUCTURES OF ${\rm Au}_{4}^{-}$ AND Au4

Low energy isomers of [Formula: see text] and Au4 were reexamined using the hybrid density functional B3LYP method and the couple-cluster method with the aug-cc-pVDZ-PP and aug-cc-pVTZ-PP basis sets. For [Formula: see text], the B3LYP method favors the zigzag isomer and the second order Moller–Plesset perturbation (MP2) total energy calculation favors the D2h rhombus isomer, whereas the couple-cluster singles and doubles with perturbative triples [CCSD(T)] level of theory favors the Y-shaped C2v isomer. The pyramid isomer is much higher in energy and could be easily excluded. The Gibbs free energy correction based on harmonic approximation suggests that the zigzag isomer is lower in free energy than the D2h rhombus isomer at 298.15 K. These results confirm that the Y-shaped C2v isomer is the global minimum at both 0 K and room temperature and is thus the major isomer to account for the experimental photoelectron spectrum. The zigzag isomer is suggested, as a minor isomer, to account for the weak second peak at 3.40 eV in the experimental photoelectron spectrum. For neutral Au4 , the zigzag isomer is more stable than D2h rhombus isomer at the B3LYP level and the D2h rhombus isomer is the global minimum on basis of all post Hartree–Fock levels of theory.