A density functional theory study on the Ag<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>H (<Emphasis Type="Italic">n</Emphasis> = 1–10) clusters

Density functional GGA-PW91 method with DNP basis set is applied to optimize the geometries of Ag _n H (n = 1–10) clusters. For the lowest energy geometries of Ag _n H (n = 1–10) clusters, the hydrogen atom prefers to occupy the two-fold coordination bridge site except the occupation of single-fold coordination site in AgH cluster. After adsorption of hydrogen atom, most Ag _n structures are slightly perturbed and only the Ag₆ structure in Ag₆H cluster is distorted obviously. The Ag–Ag bond is strengthened and the strength of Ag–H bond exhibits a clear odd–even oscillation like the strength of Au–H bond in Au _n H clusters, indicating that the hydrogen atom is more favorable to be adsorbed by odd-numbered pure silver clusters. The adsorption strength of small silver cluster toward H atom is obviously weaker than that of small gold cluster toward H atom due to the strong scalar relativistic effect in small gold cluster. The pronounced odd–even alternation of the magnetic moments is observed in Ag _n H systems, indicating that the Ag _n H clusters possess tunable magnetic properties by adsorbing hydrogen atom onto odd-numbered or even-numbered small silver cluster.     

Structural Growth Sequences and Electronic Properties of Lanthanum-Doped-Gold Clusters

The geometries, stabilities, and electronic properties of Au _n La (n = 2–8) clusters have been systematically investigated by using density-functional theory. The results show that the doped La atom prefers to locate at the center site with the number of Au atom increasing from 2 to 8. Furthermore, the Au _n La clusters are more stable than the Au _n+1 clusters. The charges transfer from La atom to Au atoms at n = 2–4, but charge-transferring is reversed at n = 5.     

All-electron relativistic calculations on hydrogen atom adsorption onto small copper clusters

An all-electron scalar relativistic calculation on Cu _n H (n = 1–13) clusters has been performed by using density functional theory with the generalized gradient approximation at the PW91 level. Our results reveal that the hydrogen atom prefers to occupy the two fold coordination site for Cu _n H (n = 2, 4–6, 8, 10–13) clusters, the single fold coordination site for Cu _n H (n = 1, 3, 7) and the three fold coordination site for Cu₉H cluster. For all Cu _n H clusters, only the Cu₁₁ structure in Cu₁₁H is distorted obviously. After adsorption, the Cu–Cu bond is strengthened and the Cu–H bond of odd-numbered Cu _n H clusters is relatively stronger than that of adjacent even-numbered Cu _n H clusters. The Cu–Cu bond-length and Cu–H bond-length for all Cu _n H clusters of our work are significantly shorter than those of previous work. This discrepancy can be explained in terms of the scalar relativistic effect. The most favorable adsorption between small copper clusters and hydrogen atom takes place in the case that hydrogen atom is adsorbed onto an odd-numbered pure Cu _n cluster and becomes Cu _n H cluster with even number of valence electrons. The odd–even alteration of magnetic moments is observed in Cu _n H clusters and may provide the material with tunable code capacity of “0” and “1” by adsorbing a hydrogen atom onto odd- or even-numbered copper clusters.     

A Density Functional Investigation on C2Aun+ (n?=?1, 3, 5) and C2Aun (n?=?2, 4, 6): from Gold Terminals, Gold Bridges, to Gold Triangles

A systematic density functional theory investigation on C₂Au _n ⁺ (n = 1,3,5) and C₂Au _n (n = 2,4,6) indicates that gold atoms serve as terminals (–Au) in the chain-like C_s C₂Au⁺ (C=C–Au⁺) and D_∞h C₂Au₂ (Au–C≡C–Au) and as bridges (–Au–) in the side-on coordinated C_2v C₂Au₃ ⁺ ([Au–C≡C–Au]Au⁺) and C_s C₂HAu₂ ⁺([H–C≡C–Au]Au⁺). However, when the number of gold atoms reaches four, they form stable gold triangles (–Au₃) in the head-on coordinated C_2v C₂Au₄ (Au–C≡C–Au₃) and the side-on coordinated C_2v C₂Au₅ ⁺ ([Au–C≡C–Au]Au₃ ⁺). Similar –Au₃ triangular units exist in the head-on coordinated C_2v C₂HAu₃ (H–C≡C–Au₃) and D_2d C₂Au₆ (Au₃–C≡C–Au₃). The existence of stable –Au₃ triangular units in small dicarbon aurides is significant and intriguing. The high stability of Au₃ triangles originates from the fact that an equilateral D_3h Au₃ ⁺ cation possesses a completely delocalized three-center-two-electron (3c–2e) σ bond and therefore is σ-aromatic in nature. The extension from H/Au analogy to H/Au₃ analogy established in this work may have important implications in designing new gold-containing catalysts and nano-materials.     

The adsorptions of silver-doped small gold clusters toward carbon monoxide molecule

An all-electron scalar relativistic calculation on Au _n AgCO (n = 1–12) clusters has been performed using density functional theory with the generalized gradient approximation at PW91 level. The introduction of impurity silver weakens the adsorption, and, however, promotes the reactivity enhancement of CO molecule. The CO molecule is relatively more favorable to be adsorbed by the odd-numbered Au _n Ag clusters with closed-shell electronic structure. The values of chemical hardness indicate that the Au _n AgCO cluster is less stable than the corresponding Au _n+1CO cluster chemically. This picture of the influence of impurity silver on the adsorption behavior of Au _n Ag (n = 1–12) clusters toward CO molecule is consistent with previous experimental work (Haeck et al. in J Phys Chem A 115:2103, 2011), in which the cluster’s reaction probability toward CO molecule is reduced upon substitution of gold atoms for silver and the clusters with closed electronic shell are the most reactive toward CO molecule.     

Optimization of bimetallic Cu–Au and Ag–Au clusters by using a modified adaptive immune optimization algorithm

A modified adaptive immune optimization algorithm (AIOA) is designed for optimization of Cu–Au and Ag–Au bimetallic clusters with Gupta potential. Compared with homoatom clusters, there are homotopic isomers in bimetallic cluster, so atom exchange operation is presented in the modified AIOA. The efficiency of the algorithm is tested by optimization of Cu_nAu_38‐n (0 ≤ n ≤ 38). Results show that all the structures with the putative global minimal energies are successfully located. In the optimization of Ag_nAu_55‐n (0 ≤ n ≤ 55) bimetallic clusters, all the structures with the reported minimal energies are obtained, and 36 structures with even lower potential energies are found. On the other hand, with the optimized structures of Cu_nAu_55‐n, it is shown that all 55‐atom Cu–Au bimetallic clusters are Mackay icosahedra except for Au₅₅, which is a face‐centered cubic (fcc)‐like structure; Cu₅₅, Cu₁₂Au₄₃, and Cu₁Au₅₄ have two‐shell Mackay icosahedral geometries with I_h point group symmetry. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

Density functional study of structural and electronic properties of maximum‐spin n+1Aun−1Ag clusters

The structures and relative stabilities of high‐spin ⁿ⁺¹Au_n?1Ag and ⁿAu_n?1Ag⁺ (n = 2–8) clusters have been studied with density functional calculation. We predicted the existence of a number of previously unknown isomers. Our results revealed that all structures of high‐spin neutral or cationic Au_n?1Ag clusters can be understood as a substitution of an Au atom by an Ag atom in the high‐spin neutral or cationic Au_n clusters. The properties of mixed gold–silver clusters are strongly sized and structural dependence. The high‐spin bimetallic clusters tend to be holding three‐dimensional geometry rather than planar form represented in their low‐spin situations. Silver atom prefers to occupy those peripheral positions until to n = 8 for high‐spin clusters, which is different from its position occupied by light atom in the low‐spin situations. Our theoretical calculations indicated that in various high‐spin Au_n?1Ag neutral and cationic species, ⁵Au₃Ag, ³AuAg and ⁵Au₄Ag⁺ hold high stability, which can be explained by valence bond theory. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Structural, Electronic, and Optical Properties of Noble Metal Clusters from First Principles

We examine low-energy isomeric forms, static polarizabilities, and optical absorption spectra of Ag _n , n = 2–8, and Au _n , n = 2–3, clusters using first principles computations within the static and time-dependent versions of the density functional theory. The noticeable decrease in the static polarizabilities of Ag₇ and Ag₈ compared to the values characteristic of Ag _n , n = 2–6, is correlated with the transition from two-dimensional to three-dimensional structures at n = 7. The optical spectra computed within the time-dependent local density approximation for the most stable structures are in good agreement with the available experimental data and the results of earlier theoretical studies. Optical spectra of higher-energy isomers typically present features that are not observed in the experimental spectra. The d electrons affect the spectra of noble metal clusters by quenching the oscillator strengths through screening of the s electrons and by getting directly involved in the excitations. Due to the larger s–d hybridization in Au compared to Ag, these effects are more pronounced in Au _n clusters.     

First-principle Study of AunSc (n=2～13) Clusters

The geometries, stabilities, electronic, and magnetic properties of Au_nSc clusters have been systematically investigated by density functional theory. The lowest energy structures of Au_nSc favor planar structure and the doped Sc atom does not disturb the frame of Au_nclusters with n≤11. For n≥12, Sc atom is fully encapsulated by the Au cages. From theanalysis of the second-order energy difference, the fragmentation energies, vertical ionizationpotential, vertical electron affinity, and HOMO-LUMO gap, the clusters with odd Au atoms possess relatively higher stabilities than their neighbor size. The doping of Sc atom can greatly improve the stability and change the sequence of chemical activity for Au_n. For n≤11, the total magnetic moments of Au_nSc appear the alternation between 0.00 and 1.00 μB. The total magnetic moments are quenched when Sc is trapped into the Au cages with n≥12.     

Molecular orbital analysis of the bonding in high nuclearity gold cluster compounds

Extended Hückel molecular orbital calculations on high nuclearity gold clusters of the general type [Au(AuPH₃)_n]^x+ have demonstrated that they can be classified into two broad topological classes according to the three-dimensional disposition of the peripheral gold atoms. If they lie approximately on a sphere they are characterised by a total of 12n + 18 valence electrons, but if they adopt a toroidal or eliptical arrangement the total electron count is 12n + 16. The computed energy differences between alternative polyhedral geometries is generally small and accounts for the stereochemical non-rigidity of the gold cluster compounds in solution. Detailed aspects of the structures of the high nuclearity gold cluster compounds have been interpreted in terms of molecular orbital calculations on clusters derived from the centred chair [Au₇(PH₃)₆]⁺ by edge- and face-capping with Au(PH₃)⁺ fragments.     

Adsorption of carbon oxide on tetrahedral bimetallic gold–copper clusters

The interaction between carbon oxide and [Au_20–nCu_n]_q clusters (n = 0, 1, 19, 20 and q = 0, ±1) is studied by means of DFT/PBE in the scalar relativistic approximation. To establish the composition and structure of an adsorption site, isomers of bimetallic Au₁₉Cu and AuCu₁₉ particles with different positions of the heteroatom at an apex, edge, and face of the tetrahedral framework are considered. The optimized structures are used as the basis to determine the electronic properties of clusters (average bond energy per atom, difference of energies between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), ionization potential, electron affinity energy). The calculated parameters shrink as the copper content in clusters grows. Among the uncharged models, the highest CO adsorption energy is typical of Au₁₉Cu, the heteroatom of which lies at a cluster’s apex. The CO adsorption energy for cationic and anionic clusters grows in comparison to neutral clusters.     

Argon Adsorption on Cationic Gold Clusters Aun+ (n ≤ 20)

The interaction of Au_n⁺ (n ≤ 20) clusters with Ar is investigated by combining mass spectrometric experiments and density functional theory calculations. We show that the inert Ar atom forms relatively strong bonds with Au_n⁺. The strength of the bond strongly varies with the cluster size and is governed by a fine interplay between geometry and electronic structure. The chemical bond between Au_n⁺ and Ar involves electron transfer from Ar to Au, and a stronger interaction is found when the Au adsorption site has a higher positive partial charge, which depends on the cluster geometry. Au₁₅⁺ is a peculiar cluster size, which stands out for its much stronger interaction with Ar than its neighbors, signaled by a higher abundance in mass spectra and a larger Ar adsorption energy. This is shown to be a consequence of a low-coordinated Au adsorption site in Au₁₅⁺, which possesses a large positive partial charge.     

Hydrocarbon adsorption on gold clusters: Experiment and quantum chemical modeling

Heats of adsorption Q of n-alkanes C₆–C₉ on ZrO₂ modified with gold and nickel nanoparticles were determined experimentally. The Q values were found to be higher on average by 7 kJ/mol on the modified samples as compared to the pure support. Density functional theory with the PBE functional and the pseudopotential for gold effectively allowing for relativistic corrections was used to model the adsorption of saturated hydrocarbons on Au and Au + Ni, as exemplified by the interaction of alkanes C₁–C₃ with Au _m , Au _{m − 1}Ni (m = 3, 4, 5) clusters as well as the interaction of C₁–C₈ with Au₂₀. Based on the calculation results, the probable coordination centers of alkanes on nanoparticle surfaces were found to be vertices and edges, whereas face localization was less probable.     

X-ray crystal structure of a distorted tetrahedral cluster in the salt [(Ph3P)4Au4N]+ BF4−. Geometrical indication of stable electronic configurations in post-transition metal complexes and the magic number 18-e in centred gold clusters

According to an X-ray investigation (?120°C, λ(Mo-K_α), 6815 reflections, space group P2₁/c, Z = 4, R = 0.068), the cation of the tetraaurated ammonium salt [(Ph₃PAu)₄N]⁺ BF₄^? can be considered as a distorted tetrahedral Au₄(N) cluster built up of four linearly coordinated Au atoms with an interstitial N atom (AuAu 3.012–3.504 Å, AuN 1.93–2.10 Å). On the basis of the structural data on 14-, 16- and 18-electron mononuclear post-transition metal complexes, the magic number of 18 skeletal electrons can be suggested for [Au_nL_{n ? 1}]^m+ clusters with an interstitial Au atom and a quasi-spherical peripheral Au_{n ? 1} polyhedron.     

Bare Clusters Derived from Protein Templates: Au25+, Au38+ and Au102+

A discrete sequence of bare gold clusters of well‐defined nuclearity, namely Au₂₅⁺, Au₃₈⁺ and Au₁₀₂⁺, formed in a process that starts from gold‐bound adducts of the protein lysozyme, were detected in the gas phase. It is proposed that subsequent to laser desorption ionization, gold clusters form in the gas phase, with the protein serving as a confining growth environment that provides an effective reservoir for dissipation of the cluster aggregation and stabilization energy. First‐principles calculations reveal that the growing gold clusters can be electronically stabilized in the protein environment, achieving electronic closed‐shell structures as a result of bonding interactions with the protein. Calculations for a cluster with 38 gold atoms reveal that gold interaction with the protein results in breaking of the disulfide bonds of the cystine units, and that the binding of the cysteine residues to the cluster depletes the number of delocalized electrons in the cluster, resulting in opening of a super‐atom electronic gap. This shell‐closure stabilization mechanism confers enhanced stability to the gold clusters. Once formed as stable magic number aggregates in the protein growth medium, the gold clusters become detached from the protein template and are observed as bare Au_n⁺ (n=25, 38, and 102) clusters.     

Interaction of copernicium with gold: Assessment of applicability of simple density functional theories

Interactions of Cn (element 112) atom with small Au clusters are studied using accurate ab initio scalar relativistic coupled cluster method for correlation treatment and two‐component relativistic density functional theory (RDFT) to take account of spin‐dependent relativistic effects. The results demonstrate the failure of RDFT with simple generalized‐gradient and hybrid functionals in describing Cn–Au bonds in complex systems. © 2013 Wiley Periodicals, Inc.     

A density functional theory study of the Au7Hn (n = 1–10) clusters

The geometries, electronic, and magnetic properties of the Au₇H_n (n = 1–10) clusters have been systematically investigated by using relativistic all-electron density functional theory with generalized gradient approximation. It is found that the Au₇ on the whole retains its triangle structure after hydrogen atoms adsorption and adsorbing hydrogen atoms can stabilize the Au₇ structure. The Au₇H₇ cluster is much higher stability than the neighboring clusters. The pronounced even–odd alternation of the magnetic moments is observed in the Au₇H_n systems indicating Au₇H_n clusters possess tunable magnetic properties by adding even or odd number of H atoms.     

One-Electron Pseudo-Potential Determination of Stable Isomers of the Li*Ar n Excited Clusters: Absorption Spectra

We present pseudo-potential calculations of geometrical structures of stable isomers of LiAr _n clusters with both an electronic ground state and excited states of the lithium atom. The Li atom is perturbed by argon atoms in LiAr _n clusters. Its electronic structure obtained as the eigenfunctions of a single-electron operator describing the electron in the field of a Li⁺Ar _n core, the Li⁺ and Ar atoms are replaced by pseudo-potentials. These pseudo-potentials include core-polarization operators to account for the polarization and correlation of the inert core with the valence Lithium electron [J Chem Phys 116, 1839 1]. The geometry optimization of the ground and excited states of LiAr _n (n = 1–12) clusters is carried out via the Basin-Hopping method of Wales et al. [J Phys Chem 101, 5111 2; J Chem Phys 285, 1368 3]. The geometries of the ground and ionic states of LiAr _n clusters were used to determine the energy of the high excited states of the neutral LiAr _n clusters. The variation of the excited state energies of LiAr _n clusters as a function of the number of argon atoms shows an approximate Rydberg character, corresponding to the picture of an excited electron surrounding an ionic cluster core, is already reached for the 3s state. The result of optical transitions calculations shows that the absorption spectral features are sensitive to isomer structure. It is clearly the case for transitions close to the 2p levels of Li which are distorted by the cluster environment.     

Theoretical study of Aun clusters (n = 1–5) deposited on a rutile TiO2 (110) slab,concerning structure and stability

The initial nucleation of gold clusters Au_n (n = 1–5) on TiO₂ rutile (110) reduced surface is studied using density functional theory and a full-potential augmented-plane-wave method implemented in the WIEN2k code. The first two gold atoms remained tied to the surface with a bond length similar to those belonging to other well-known related materials, while the other gold atoms do not spread over the surface; they preferred to form a new layer. The occurrence of relativistic effects produced a preferential triangle geometry for Au₃ and a combination of triangular units for Au₄ and Au₅. The Au–Au average distance increased from n = 2 to n = 5, indicating an expansion with a tendency to the bond distance found in the bulk. We are reporting an early 2D→3D transition of small folding, from Au₃→Au₄, followed by an Au₄→Au₅ transition of evident 3D character.     

Evaluation of Electron Donation as a Mechanism for the Stabilisation of Chalcogenate‐Protected Gold Nanoclusters

Models based on Au(111) face have been extensively used to describe self‐assembled monolayers, as well nanoparticles and nanoclusters. However, for very small clusters (<2 nm), the chemisorption of ligands leads to surface reconstruction, making necessary the use of a more reliable model that is able to simulate the main electronic and geometrical features of these small systems. In this work, a simple model to describe the geometries and the metal–ligand bonding in chalcogenate‐protected gold nanoclusters is proposed. Three different models with Au_n⁺ and [XCH₃]^? (n=10, 15, 19, 22 and X=S, Se, Te) are used in this work. The obtained structures are in close agreement not only with the available crystallographic data, but also with much more expensive computational procedures, confirming that the proposed models are robust enough to describe the metal–ligand bonding. The results reveal that the Au–X distances are dependent on both the nature of the chalcogen and the coordination mode. The shortest Au–X distances are observed in the face‐centred cubic mode, indicating that the central gold atom seems to play a role in determining the adsorption strength. The proposed models show unambiguously chalcogen→cluster σ‐donation, as supported by energy decomposition analysis coupled with the natural orbitals for chemical valence and natural bond orbital analyses. In all cases, the metal–ligand interactions are characterised as being more covalent than electrostatic.