Ab initio study of small gold clusters

Geometric, Electronic, and Optoelectronic Properties of Carbon-Based Polynuclear C3O[C(CN)2]2M3 (where M = Li, Na, and K) Clusters: A DFT Study

Carbon-based polynuclear clusters are designed and investigated for geometric, electronic, and nonlinear optical (NLO) properties at the CAM-B3LYP/6-311++G(d,p) level of theory. Significant binding energies per atom (ranging from -162.4 to -160.0 kcal mol^-1) indicate excellent thermodynamic stabilities of these polynuclear clusters. The frontier molecular orbital (FMOs) analysis indicates excess electron nature of the clusters with low ionization potential, suggesting that they are alkali-like. The decreased energy gaps (E_H-L) with increased alkali metals size revael the improved electrical conductivity (σ). The total density of state (TDOS) study reveals the alkali metals' size-dependent electronic and conductive properties. The significant first and second hyperpolarizabilities are observed up to 5.78 × 10³ and 5.55 × 10⁶ au, respectively. The β_o response shows dependence on the size of alkali metals. Furthermore, the absorption study shows transparency of these clusters in the deep-UV, and absorptions are observed at longer wavelengths (redshifted). The optical gaps from TD-DFT are considerably smaller than those of HOMO-LUMO gaps. The significant scattering hyperpolarizability (β_HRS) value (1.62 × 10⁴) is calculated for the C3 cluster, where octupolar contribution to β_HRS is 92%. The dynamic first hyperpolarizability β(ω) is more pronounced for the EOPE effect at 532 nm, whereas SHG has notable values for second hyperpolarizability γ(ω).

Dynamic hetero-metallic bondings visualized by sequential atom imaging

Traditionally, chemistry has been developed to obtain thermodynamically stable and isolable compounds such as molecules and solids by chemical reactions. However, recent developments in computational chemistry have placed increased importance on studying the dynamic assembly and disassembly of atoms and molecules formed in situ. This study directly visualizes the formation and dissociation dynamics of labile dimers and trimers at atomic resolution with elemental identification. The video recordings of many homo- and hetero-metallic dimers are carried out by combining scanning transmission electron microscopy (STEM) with elemental identification based on the Z-contrast principle. Even short-lived molecules with low probability of existence such as AuAg, AgCu, and AuAgCu are directly visualized as a result of identifying moving atoms at low electron doses.

The dynamic assembly and disassembly of atoms and molecules is challenging to characterize in real time, with atomic resolution and elemental identification. Here, the authors report direct observation of more than twenty homo and hetero-metallic compounds, including labile Ag-Cu dimers and Au-Ag-Cu trimers.

Tempering of Au nanoclusters: capturing the temperature-dependent competition among structural motifs

A computational approach to determine the equilibrium structures of nanoclusters in the whole temperature range from 0 K to melting is developed. Our approach relies on Parallel Tempering Molecular Dynamics (PTMD) simulations complemented by Harmonic Superposition Approximation (HSA) calculations and global optimization searches, thus combining the accuracy of global optimization and HSA in describing the low-energy part of configuration space, together with the PTMD thorough sampling of high-energy configurations. This combined methodology is shown to be instrumental towards revealing the temperature-dependent structural motifs in Au nanoclusters of sizes 90, 147, and 201 atoms. The reported phenomenology is particularly rich, displaying a size- and temperature-dependent competition between the global energy minimum and other structural motifs. In the case of Au₉₀ and Au₁₄₇, the global minimum is also the dominant structure at finite temperatures. In contrast, the Au₂₀₁ cluster undergoes a solid-solid transformation at low temperature (<200 K). Results indicate that PTMD and HSA very well agree at intermediate temperatures, between 300 and 400 K. For higher temperatures, PTMD gives an accurate description of equilibrium, while HSA fails in describing the melting range. On the other hand, HSA is more efficient in catching low-temperature structural transitions. Finally, we describe the elusive structures close to the melting region which can present complex and defective geometries, that are otherwise difficult to characterize through experimental imaging.

Extremely large static and dynamic nonlinear optical response of small superalkali clusters NM3M' (M, M'=Li, Na, K)

Exploring novel nonlinear optical (NLO) materials with excess electron properties is essential for advancing the use of excess electron compounds in optics. The studied superalkali clusters NM₃M' (M, M' = Li, Na, K) are thermodynamically stable and their binding energies range from -27.10 to -53.84 kcal mol^-1. The observed significant values for VIPs suggest their electronic stabilities. Being excess electron candidate these clusters show significant β_o value (3.9 × 10⁷ au), which nicely correlates the hyperpolarizability reported by a two-level model (β_tl). Furthermore, these clusters exhibit a remarkable static second hyperpolarizability (γ_o) value of 1.1 × 10¹⁰ au for the NK₄ superalkali cluster. The hyper Rayleigh scattering (β_HRS) is also computed where the highest value of 2.9 × 10⁷ is recorded for NNa₃K superalkali. The obtained values of β_vec values (projection of hyperpolarizability on dipole moment vector) also signify the excellent nonlinearity of clusters. Besides, the calculated electro-optica pockel's effect β(-ω; ω,0) and second harmonic generation β(-2ω; ω, ω) values are much pronounced at larger dispersion frequency ω = 1064 nm. Moreover, the frequency-dependent second hyperpolarizability γ(ω) with dc-Kerr effect γ(-ω; ω,0,0) and electric field induced second harmonic generation γ(-2ω; ω,ω,0) show larger values at ω = 1064 nm. Thus the highest value of the dc-Kerr constant increases up to 1.0 × 10¹¹ au which also signifies the larger nonlinear refractive index of the studied cluster. We hope this work could open up new possibilities using superalkali clusters as NLO materials for optoelectronics, laser, second harmonic generation and as frequency doubler.

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).

Retracted Article: A highest stable cluster Au58 (C 1) re-optimized via a density-functional tight-binding (DFTB) approach

The vibrational spectrum ω i of a re-optimized neutral gold cluster Au58 has been calculated using a numerical finite-difference approach and the density-functional tight-binding (DFTB) method. We have exactly predicted the vibrational frequency ranging from 3.88 through to 304.49 cm-1 which depends on the size and the arrangement of the atoms in the nanoparticle morphology of the cluster at ΔE = 0. Our investigation has revealed that the vibrational spectrum is strongly influenced by size and structure. It is well known that gold atomic clusters can have planar or hollow cage-like structures due to their relativistic effect. However, in our study, by first principles calculations on a Au58 cluster we have proposed that gold clusters of medium size can form a shell-like structure (skeleton/helmet), this is demonstrated by the remarkable robustness of a double shell structure with a hollow inner shell of about ten atoms. Finally, the structure symmetry (C 1) is confirmed through the cluster size, vibrational spectroscopy, and by studying the effect of temperature on a neutral gold cluster for the first time.

The Lattice Kinetic Monte Carlo Simulation of Atomic Diffusion and Structural Transition for Gold

For the kinetic simulation of metal nanoparticles, we developed a self-consistent coordination-averaged energies for Au atoms based on energy properties of gold bulk phases. The energy barrier of the atom pairing change is proposed and holds for the microscopic reversibility principle. By applying the lattice kinetic Monte Carlo simulation on gold films, we found that the atomic diffusion of Au on the Au(111) surface undergoes a late transition state with an energy barrier of about 0.2 eV and a prefactor between 40~50 Ų/ps. This study also investigates the structural transition from spherical to faceted gold nanoparticles upon heating. The temperatures of structural transition are in agreement with the experimental melting temperatures of gold nanoparticles with diameters ranging from 2 nm to 8 nm.

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.

A comparative study of AumRhn (4 ≤ m + n ≤ 6) clusters in the gas phase versus those deposited on (100) MgO

The combined use of a genetic algorithm and Density Functional Theory (DFT) calculations allows us to explore the potential energy surface. Our results show interesting effects on the geometries of the clusters on deposition. Two-dimensional clusters in the gas phase become three-dimensional and vice versa.

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.

Isomerism and structural fluxionality in the Au26 and Au26(-) nanoclusters

Using the minima hopping global optimization method at the density functional level, we found low-energy nanostructures for neutral Au26 and its anion. The local-density and a generalized gradient approximation of the exchange–correlation functional predict different nanoscale motifs. We found a vast number of isomers within a small energy range above the respective putative global minima with each method. Photoelectron spectroscopy of Au26(-) under different experimental conditions revealed definitive evidence of the presence of multiple isomers, consistent with the theoretical predictions. Comparison between the experimental and simulated photoelectron spectra suggests that the photoelectron spectra of Au26(-) contain a mixture of three isomers, all of which are low-symmetry core–shell-type nanoclusters with a single internal Au atom. We present a disconnectivity graph for Au26(-) that has been computed completely at the density functional level. The transition states used to build this disconnectivity graph are complete enough to predict Au26(-) to have a possible fluxional shell, which facilitates the understanding of its catalytic activity.

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.

Determination of the structures of small gold clusters on stepped magnesia by density functional calculations

The structural modifications of small supported gold clusters caused by realistic surface defects (steps) in the MgO(001) support are investigated by computational methods. The most stable gold cluster structures on a stepped MgO(001) surface are searched for in the size range up to 24 Au atoms, and locally optimized by density-functional calculations. Several structural motifs are found within energy differences of 1 eV: inclined leaflets, arched leaflets, pyramidal hollow cages and compact structures. We show that the interaction with the step clearly modifies the structures with respect to adsorption on the flat defect-free surface. We find that leaflet structures clearly dominate for smaller sizes. These leaflets are either inclined and quasi-horizontal, or arched, at variance with the case of the flat surface in which vertical leaflets prevail. With increasing cluster size pyramidal hollow cages begin to compete against leaflet structures. Cage structures become more and more favourable as size increases. The only exception is size 20, at which the tetrahedron is found as the most stable isomer. This tetrahedron is however quite distorted. The comparison of two different exchange-correlation functionals (Perdew-Burke-Ernzerhof and local density approximation) show the same qualitative trends.

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.

Towards a scalable and accurate quantum approach for describing vibrations of molecule-metal interfaces

We present a theoretical framework for the computation of anharmonic vibrational frequencies for large systems, with a particular focus on determining adsorbate frequencies from first principles. We give a detailed account of our local implementation of the vibrational self-consistent field approach and its correlation corrections. We show that our approach is both robust, accurate and can be easily deployed on computational grids in order to provide an efficient computational tool. We also present results on the vibrational spectrum of hydrogen fluoride on pyrene, on the thiophene molecule in the gas phase, and on small neutral gold clusters.

Small gold clusters on graphene, their mobility and clustering: a DFT study

Motivated by the experimentally observed high mobility of gold atoms on graphene and their tendency to form nanometer-sized clusters, we present a density functional theory study of the ground state structures of small gold clusters on graphene, their mobility and clustering. Our detailed analysis of the electronic structures identifies the opportunity to form strong gold-gold bonds and the graphene-mediated interaction of the pre-adsorbed fragments as the driving forces behind gold's tendency to aggregate on graphene. While clusters containing up to three gold atoms have one unambiguous ground state structure, both gas phase isomers of a cluster with four gold atoms can be found on graphene. In the gas phase the diamond-shaped Au(4)(D) cluster is the ground state structure, whereas the Y-shaped Au(4)(Y) becomes the actual ground state when adsorbed on graphene. As we show, both clusters can be produced on graphene by two distinct clustering processes. We also studied in detail the stepwise formation of a gold dimer out of two pre-adsorbed adatoms, as well as the formation of Au(3). All reactions are exothermic and no further activation barriers, apart from the diffusion barriers, were found. The diffusion barriers of all studied clusters range from 4 to 36 meV only, and are substantially exceeded by the adsorption energies of - 0.1 to - 0.59 eV. This explains the high mobility of Au(1-4) on graphene along the C-C bonds.

Mononuclear, dinuclear, and hexanuclear goldI complexes with (aza-15-crown-5)dithiocarbamate

The reactions of sodium (aza-15-crown-5)dithiocarbamate with [AuClL] precursors lead to mono-, di-, or hexanuclear derivatives depending on L. The homoleptic hexanuclear gold(I) cluster [Au6(S2CNC10H20O4)6] is formed by displacement of the chloride and isocyanide ligands in [AuCl(CN(2,6-Me2C6H3))]. X-ray diffraction studies show a novel geometry in gold cluster chemistry where the six gold atoms display a cyclohexane-like geometry in a chair conformation with Au-Au-Au angles of 117.028(9) degrees, two short gold-gold distances of 2.9289(5) A, and bidentate bridging dithiocarbamate ligands. The molecular structure shows a crown of gold atoms surrounded by crown ethers. This derivative luminesces at 569 nm at room temperature in the solid state. A dinuclear isomer [Au2(S2CNC10H20O4)2] had been reported previously and was obtained by reaction with [AuCl(SMe2)]. The mechanism to obtain the hexanuclear derivative involves a mononuclear intermediate [Au(S2CNC10H20O4)(CNR)] for which the X-ray structure shows a short gold-gold distance of 3.565 A with the two molecules in an anti configuration. Phosphine gold(I) mononuclear derivatives [Au(S2CNC10H20O4)(PR3)] (R = Me, Ph, both characterized by X-ray diffraction) and dinuclear diphosphine derivatives [{Au(S2CNC10H20O4)}2(mu-P-P)] (P-P = dppm, bis(diphenylphosphinomethane); dppp, 1,3-bis(diphenylphosphinopropane); and dppf, 1,1'-bis(diphenylphosphinoferrocene)) are also reported. In the mononuclear complexes, the molecular structure confirms that the dithiocarbamato ligand is mainly acting as monodentate, with a second longer Au-S distance of 3.197 (PMe3), 2.944(4) (PPh3), and 2.968 A (CNR). Three phosphine complexes are emissive at 562 (PMe3), 528 (PPh3), and 605 nm (dppm), at 77 K. X-ray diffraction studies of the dppm derivative show gold-gold intramolecular contacts of 3.0972(9) A (3.2265(10) A for a second independent molecule) and basically monodentate coordination of the dithiocarbamato ligands. All the complexes extract sodium and potassium salts from aqueous solutions. The diphosphine derivatives are noticeably better extractors than the monophosphino derivatives, mainly for potassium salts.

Isomers of Au8

Using newly developed correlation consistent basis sets for gold, the relative energies for the neutral Au8 geometric isomers have been re-evaluated and the vertical ionization potentials calculated. The results using the correlation consistent basis sets show that second-order Moller-Plesset perturbation theory calculations strongly favor nonplanar Au8 structures for all basis sets that were employed. However, the general trend at the coupled cluster singles and doubles with perturbative triples level of theory is to increasingly favor planar structures as the basis set is improved. The effects of basis set and the effects of core-valence correlation are discussed.