Validation study of the ability of density functionals to predict the planar-to-three-dimensional structural transition in anionic gold clusters

Creating Benchmarks for Lithium Clusters and Using Them for Testing and Validation

Metal clusters often have a variety of possible structures, and they are calculated by a wide range of methods; however, fully converged benchmarks on the energy differences of structures and spin states that could be used to test or validate these methods are rare or nonexistent. Small lithium clusters are good candidates for such benchmarks to test different methods against well-converged relative energetics for qualitatively different structures because they have a small number of electrons. The present study provides fully converged benchmarks for Li4 and Li5 clusters and uses them to test a diverse group of approximation methods. To create a dataset of well-converged single-point energies for Li4 and Li5, stationary structures were optimized by Kohn-Sham density functional theory (KS-DFT) and then single-point energy calculations at these structures were carried out by two quite different beyond-CCSD(T) methods. To test other methods single-point energy calculations at these structures were carried out by KS-DFT, Mo̷ller-Plesset (MP) theory, coupled cluster (CC) theory, five composite methods (Gaussian-4, the Wuhan-Minnesota (WM) composite method, and the W2X, W3X, and W3X-L composite methods of Radom and co-workers), multiconfiguration pair-density functional theory (MC-PDFT), complete active space second-order perturbation theory (CASPT2), and n-electron valence state second-order perturbation theory (NEVPT2). Our results show that rhomboid and trigonal bipyramid (TBP) geometries are the most stable structures for Li4 and Li5, respectively. Using the W3X-L method to obtain our best estimates, the mean unsigned deviations were calculated for other methods for several structures and spin states of both Li4 and Li5. Binding energies and M diagnostics were calculated for all structures. The data in this paper are valuable for assessing the reliability of current electronic structure theories and also developing new density functionals and machine learned models.

Suppressing the Conductance of Single-Molecule Junctions Fabricated by sp2 C-H Bond Metalation

High-conducting single-molecule junctions have attracted a great deal of attention, but insulating single-molecule junctions, which are critical in molecular circuits, have been less investigated due to the long-standing challenges. Herein, the in situ formation of a Au-C linker via electrical-potential-mediated sp2 C-H bond metalation of polyfluoroarenes with the assistance of scanning tunneling microscope-based break junction technique is reported. This metalation process is bias-dependent and occurs with an electropositive electrode, and the formed junction is highly oriented. Surprisingly, these polyfluoroarenes exhibit unexpected low conductance even under short molecular lengths and are superior molecular insulators. Flicker noise analysis and DFT calculations confirm that the insulating properties of polyfluoroarenes are ascribed to their multiple fluorine substituents. Our results pave a way for constructing oriented asymmetric molecular junctions and provide an efficient strategy to suppress the single-molecule conductance, which will aid in the design of molecular insulators and advance the development of self-integrating functional molecular circuits.

Nonmetal-to-Metal Transition of Magnesia Supported Au Clusters Affects the Ultrafast Dissociation Dynamics of Adsorbed CH3Br Molecules

The detection of intermediate species and the correlation of their ultrafast dynamics with the morphology and electronic structure of a surface is crucial to fully understand and control heterogeneous photoinduced and photocatalytic reactions. In this work, the ultrafast photodissociation dynamics of CH₃Br molecules adsorbed on variable-size Au clusters on MgO/Mo(100) is investigated by monitoring the CH₃⁺ transient evolution using a pump-probe technique in conjunction with surface mass spectrometry. Furthermore, extreme-UV photoemission spectroscopy in combination with theoretical calculations is employed to study the electronic structure of the Au clusters on MgO/Mo(100). Changes in the ultrafast dynamics of the CH₃⁺ fragment are correlated with the electronic structure of Au as it evolves from monomers to small nonmetallic clusters to larger nanoparticles with a metallic character. This work provides a new avenue to a detailed understanding of how surface-photoinduced chemical reactions are influenced by the composition and electronic structure of the surface.

C-H Bond Activation Mechanism by a Pd(II)-(μ-O)-Au(0) Structure Unique to Heterogeneous Catalysts

We focused on identifying a catalytic active site structure at the atomic level and elucidating the mechanism at the elementary reaction level of liquid-phase organic reactions with a heterogeneous catalyst. In this study, we experimentally and computationally investigated efficient C-H bond activation for the selective aerobic α,β-dehydrogenation of saturated ketones by using a Pd-Au bimetallic nanoparticle catalyst supported on CeO₂ (Pd/Au/CeO₂) as a case study. Detailed characterization of the catalyst with various observation methods revealed that bimetallic nanoparticles formed on the CeO₂ support with an average size of about 2.5 nm and comprised a Au nanoparticle core and PdO nanospecies dispersed on the core. The formation mechanism of the nanoparticles was clarified through using several CeO₂-supported controlled catalysts. Activity tests and detailed characterizations demonstrated that the dehydrogenation activity increased with the coordination numbers of Pd-O species in the presence of Au(0) species. Such experimental evidence suggests that a Pd(II)-(μ-O)-Au(0) structure is the true active site for this reaction. Based on density functional theory calculations using a suitable Pd₁O₂Au₁₂ cluster model with the Pd(II)-(μ-O)-Au(0) structure, we propose a C-H bond activation mechanism via concerted catalysis in which the Pd atom acts as a Lewis acid and the adjacent μ-oxo species acts as a Brønsted base simultaneously. The calculated results reproduced the experimental results for the selective formation of 2-cyclohexen-1-one from cyclohexanone without forming phenol, the regioselectivity of the reaction, the turnover-limiting step, and the activation energy.

Catalytic Oxidation of Benzyl Alcohol to Benzaldehyde on Au8 and Au6Pd2 Clusters: A DFT Study on the Reaction Mechanism

Density functional theory calculations were performed to investigate the reaction mechanism of the aerobic oxidation of benzyl alcohol to benzaldehyde catalyzed by Au and Au–Pd clusters. Two consecutive reaction mechanisms were examined with Au8 and Au6Pd2 clusters: (1) the oxidation of benzyl alcohol with dissociated O atoms on metal clusters generating benzaldehyde and H2O; and (2) oxidation with adsorbed oxygen molecules generating benzaldehyde and H2O2. The calculations show that the aerobic oxidation of benzyl alcohol energetically prefers to proceed in the former mechanism, which agrees with the experimental observation. We demonstrate that the role of Au centers around the activation of molecular oxygen to peroxide-like species, which are capable of the H–abstraction of benzyl alcohol. The roles of Pd in the Au6Pd2 cluster are: (1) increasing the electron distribution to neighboring Au atoms, which facilitates the activation of O2; and (2) stabilizing the adsorption complex and transition states by the interaction between positively charged Pd atoms and the π-bond of benzyl alcohol, both of which are the origin of the lower energy barriers than those of Au8.

Au60-: The Smallest Gold Cluster with the High-Symmetry Icosahedral Core Au13

Among coinage metal nanoclusters with 55 atoms, only Ag₅₅^- and Cu₅₅^- are the geometric magic-number clusters, as both exhibit icosahedral symmetry. Au₅₅^-, however, exhibits much lower symmetry due largely to the strong relativistic bonding effect. In this study, we collect a much larger population (>10,000 isomers) of low-energy isomers of Au₅₅^- to Au₆₀^- by using the combined density-functional theory and basin-hopping global optimization method. We also include the spin-orbit effect in the density-functional theory computation to achieve simulated photoelectron spectra in quantitative fashion. Remarkably, we uncover that the Au₁₃ core with the highest icosahedral ( I_h) symmetry emerges at the size of Au₆₀^-. Stability analysis suggests that Au₅₇^- with 58 valence electrons, an electronic magic number, is the relatively more stable cluster in the size range considered. Overall, in this size range we reveal a compromise between the trend toward having a perfect icosahedral 13-atom core and the strong relativistic bonding effect.

Structural Evolution of Core-Shell Gold Nanoclusters: Aun- (n = 42-50)

Gold nanoclusters have attracted great attention in the past decade due to their remarkable size-dependent electronic, optical, and catalytic properties. However, the structures of large gold clusters are still not well-known because of the challenges in global structural searches. Here we report a joint photoelectron spectroscopy (PES) and theoretical study of the structural evolution of negatively charged core-shell gold nanoclusters (Au_n^-) for n = 42-50. Photoelectron spectra of size-selected Au_n^- clusters are well resolved with distinct spectral features, suggesting a dominating structural type. The combined PES data and density functional calculations allow us to systematically identify the global minimum or candidates of the global minima of these relatively large gold nanoclusters, which are found to possess low-symmetry structures with gradually increasing core sizes. Remarkably, the four-atom tetrahedral core, observed first in Au₃₃^-, continues to be highly robust and is even present in clusters as large as Au₄₂^-. Starting from Au₄₃^-, a five-atom trigonal bipyramidal core appears and persists until Au₄₇^-. Au₄₈^- possesses a six-atom core, while Au₄₉^- and Au₅₀^- feature seven- and eight-atom cores, respectively. Notably, both Au₄₆^- and Au₄₇^- contain a pyramidal Au₂₀ motif, which is stacked with another truncated pyramid by sharing a common 10-atom triangular face. The present study sheds light on our understanding of the structural evolution of the medium-sized gold nanoclusters, the shells and core as well as how the core-shell structures may start to embrace the golden pyramid (bulk-like) fragment.

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.

Size evolution and ligand effects on the structures and stability of (AuL)n (L = Cl, SH, SCH3, PH2, P(CH3)2, n = 1–13) clusters

Size evolution on the global minimum structures of (AuCl)_n clusters at n = 1–13.

Mechanism of the Aerobic Homocoupling of Phenylboronic Acid on Au₂₀⁻: A DFT Study

The mechanism of the gold nanocluster-catalyzed aerobic homocoupling of arylboronic acids has been elucidated by means of DFT calculations with Au20(-) as a model cluster for the Au:[poly(N-vinylpyrrolidin-2-one)] catalyst. We found that oxygen affects the adsorption of phenylboronic acid and, by lowering the energy barrier, a water molecule enhances dissociation of the C-B bond, which is probably the rate-determining step. The key role of oxygen is in activating the surface of the gold cluster by generating Lewis acidic sites for adsorption and activation of the phenylboronic acid, leading to the formation of biphenyl through a superoxo-like species. Moreover, the oxygen adsorbed on the Au nanocluster can act as an oxidant for phenylboronic acid, giving phenol as a byproduct. As shown by NBO analysis, the basic aqueous reaction medium facilitates the reductive elimination process by weakening the Au-C bond, thereby enhancing the formation of biphenyl. The coupling of phenyl and reductive elimination of biphenyl occur at the top or facet site with low-energy-barrier through spillover of phenyl group on Au NC. The present findings are useful for the interpretation or design of other coupling reactions with Au NC.

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.

Modification of the catalytic properties of the Au4 nanocluster for the conversion of methane-to-methanol: synergistic effects of metallic adatoms and a defective graphene support

By means of the density functional theory calculations, enhanced catalytic activity of Au₄ cluster for the partial oxidation of methane with the N₂O oxidant is observed when the cluster is deposited on top of the Pd/graphene.

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.

Ligand-Mediated Ring → Cube Transformation in a Catalytic Subnanocluster: Co4O4(MeCN)n with n = 1-6

We studied the Co4O4 subnanocluster and its MeCN-coated species using density functional theory, and we found that the Co4O4 core presents distinctive structures in bare and ligand-coated species. We propose a possible ligand-mediated ring → cube transformation mechanism during the ligand-coating process of the Co4O4 core due to the stronger binding energies of the MeCN ligands to the 3D distorted cube structure than to the 2D ring and ladder structures; theory indicates that three ligands are sufficient to stabilize the cube structure. Both ring and cube structures are ferromagnetic. Our finding is potentially useful for understanding the catalysis mechanism of Co4O4 species, which have important applications in solar energy conversion and water splitting; these catalysis reactions usually involve frequent addition and subtraction of various ligands and thus possibly involve core rearrangement processes similar to our findings.

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.

Conversion of CO2 and C2H6 to propanoic acid over a Au-exchanged MCM-22 zeolite

Finding novel catalysts for the direct conversion of CO2 to fuels and chemicals is a primary goal in energy and environmental research. In this work, density functional theory (DFT) is used to study possible reaction mechanisms for the conversion of CO2 and C2H6 to propanoic acid over a gold-exchanged MCM-22 zeolite catalyst. The reaction begins with the activation of ethane to produce a gold ethyl hydride intermediate. Hydrogen transfers to the framework oxygen leads then to gold ethyl adsorbed on the Brønsted-acid site. The energy barriers for these steps of ethane activation are 9.3 and 16.3 kcal mol(-1), respectively. Two mechanisms of propanoic acid formation are investigated. In the first one, the insertion of CO2 into the Au-H bond of the first intermediate yields gold carboxyl ethyl as subsequent intermediate. This is then converted to propanoic acid by forming the relevant C-C bond. The activation energy of the rate-determining step of this pathway is 48.2 kcal mol(-1). In the second mechanism, CO2 interacts with gold ethyl adsorbed on the Brønsted-acid site. Propanoic acid is formed via protonation of CO2 by the Brønsted acid and the simultaneous formation of a bond between CO2 and the ethyl group. The activation energy there is 44.2 kcal mol(-1), favoring this second pathway at least at low temperatures. Gold-exchanged MCM-22 zeolite can therefore, at least in principle, be used as the catalyst for producing propanoic acid from CO2 and ethane.

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.

Oxidation of gold clusters by thiols

The formation of gold-thiolate nanoparticles via oxidation of gold clusters by thiols is examined in this work. Using the BP86 density functional with a triple ζ basis set, the adsorption of methylthiol onto various gold clusters Aun(Z) (n = 1-8, 12, 13, 20; Z = 0, -1, +1) and Au38(4+) is investigated. The rate-limiting step for the reaction of one thiol with the gold cluster is the dissociation of the thiol proton; the resulting hydrogen atom can move around the gold cluster relatively freely. The addition of a second thiol can lead to H2 formation and the generation of a gold-thiolate staple motif.

Improved CO Adsorption Energies, Site Preferences, and Surface Formation Energies from a Meta-Generalized Gradient Approximation Exchange-Correlation Functional, M06-L

A notorious failing of approximate exchange-correlation functionals when applied to problems involving catalysis has been the inability of most local functionals to predict the correct adsorption site for CO on metal surfaces or to simultaneously predict accurate surface formation energies and adsorption energies for transition metals. By adding the kinetic energy density τ to the density functional, the revTPSS density functional was shown recently to achieve a balanced description of surface energies and adsorption energies. Here, we show that the older M06-L density functional, also containing τ, provides improved surface formation energies and CO adsorption energies over revTPSS for five transition metals and correctly predicted the on-top/hollow site adsorption preferences for four of the five metals, which was not achieved by most other local functionals. Because M06-L was entirely designed on the basis of atomic and molecular energies, its very good performance is a confirmation of the reasonableness of its functional form. Two GGA functionals with an expansion in the reduced gradient that is correct through second order, namely, SOGGA and SOGGA11, were also tested and found to produce the best surface formation energies of all tested GGA functionals, although they significantly overestimate the adsorption energies.

DFT and Proton Transfer Reactions: A Benchmark Study on Structure and Kinetics

A significant number of different exchange correlation functionals, ranging from generalized gradient approximations to double hybrids, has been tested on a difficult playground represented by proton transfer reactions. In order to have a complete picture of their performances, both energetics and structural features have been compared and the obtained ranking compared with those issued from the standard test for kinetics (i.e., the DBH24/08 set). Among all of the functionals, the ωB97X, BMK, B1LYP, and PBE0-DH approaches are those providing a good error balance on all four trials. Beyond these figures, the obtained results allow for some general considerations, such as those on the role of Hartree-Fock exchange in reaction barriers or the relation between structure and energetics.

Probing the electronic properties and structural evolution of anionic gold clusters in the gas phase

Gold nanoparticles have been discovered to exhibit remarkable catalytic properties in contrast to the chemical inertness of bulk gold. A prerequisite to elucidate the molecular mechanisms of the catalytic effect of nanogold is a detailed understanding of the structural and electronic properties of gold clusters as a function of size. In this review, we describe joint experimental studies (mainly photoelectron spectroscopy) and theoretical calculations to probe the structural properties of anionic gold clusters. Electronic properties and structural evolutions of all known Au(n)(-) clusters as experimentally confirmed to date are summarized, covering the size ranges of n = 3-35 and 55-64. Recent experimental efforts in resolving the isomeric issues of small gold clusters using Ar-tagging, O(2)-titration and isoelectronic substitution are also discussed.

Dopant-induced 2D-3D transition in small Au-containing clusters: DFT-global optimisation of 8-atom Au-Ag nanoalloys

A genetic algorithm (GA) coupled with density functional theory (DFT) calculations is used to perform global optimisations for all compositions of 8-atom Au-Ag bimetallic clusters. The performance of this novel GA-DFT approach for bimetallic nanoparticles is tested for structures reported in the literature. New global minimum structures for various compositions are predicted and the 2D-3D transition is located. Results are explained with the aid of an analysis of the electronic density of states. The chemical ordering of the predicted lowest energy isomers are explained via a detailed analysis of the charge separation and mixing energies of the bimetallic clusters. Finally, dielectric properties are computed and the composition and dimensionality dependence of the electronic polarizability and dipole moment is discussed, enabling predictions to be made for future electric beam deflection experiments.

Icosahedral crown gold nanocluster au(43)cu(12) with high catalytic activity

Structural and catalytic properties of the gold alloy nanocluster Au(43)Cu(12) are investigated using a density-functional method. In contrast to the pure Au(55) nanocluster, which exhibits a low-symmetry C(1) structure, the 55-atom "crown gold" nanocluster exhibits a multishell structure, denoted by Au@Cu(12)@Au(42), with the highest icosahedral group-symmetry. In addition, density functional calculations suggest that this geometric magic-number nanocluster possesses comparable catalytic capability as a small-sized Au(10) cluster for the CO oxidation, due in part to their low-coordinated Au atoms on vertexes. The gold alloy nanocluster also shows higher selectivity for styrene oxidation than the bare Au(111) surface.

Density functional theory for transition metals and transition metal chemistry

We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.