Geometry optimization of bimetallic clusters using an efficient heuristic method

In this paper, an efficient heuristic algorithm for geometry optimization of bimetallic clusters is proposed. The algorithm is mainly composed of three ingredients: the monotonic basin-hopping method with guided perturbation (MBH-GP), surface optimization method, and iterated local search (ILS) method, where MBH-GP and surface optimization method are used to optimize the geometric structure of a cluster, and the ILS method is used to search the optimal homotop for a fixed geometric structure. The proposed method is applied to Cu(38-n)Au(n) (0 ≤ n ≤ 38), Ag(55-n)Au(n) (0 ≤ n ≤ 55), and Cu(55-n)Au(n) (0 ≤ n ≤ 55) clusters modeled by the many-body Gupta potential. Comparison with the results reported in the literature indicates that the present method is highly efficient and a number of new putative global minima missed in the previous papers are found. The present method should be a promising tool for the theoretical determination of ground-state structure of bimetallic clusters. Additionally, some key elements and properties of the present method are also analyzed.     

Structural optimization of Cu-Ag-Au trimetallic clusters by adaptive immune optimization algorithm

The putative global minimum structures of Cu-Ag-Au trimetallic clusters with 19 and 55 atoms are obtained by adaptive immune optimization algorithm (AIOA) with the Gupta potential. For the 19-atom trimetallic clusters, the results indicate that all of them have double-icosahedral motifs. For the optimized structures of Cu(13)Ag(n)Au(42-n) (n = 1-41), the clusters can be categorized into 19 Mackay icosahedral structures, 1 6-fold pancake structure, and 21 ring-like structures linked by three face-sharing double-icosahedra. Furthermore, the segregation phenomena of the Cu, Ag, and Au atoms in the Cu-Ag-Au trimetallic clusters are studied to provide useful information for geometric character. Results show that Cu and Ag atoms prefer to locate in the inner-shell and on the surface, respectively, whereas Au atoms mainly locate in the middle-shell and tend to solve into Cu and Ag atoms.     

Structural and energetic properties of Ni-Cu bimetallic clusters

The lowest-energy structures for all compositions of Ni n Cu m bimetallic clusters with N = n + m up to 20 atoms, N = 23, and N = 38 atoms have been determined using a genetic algorithm for unbiased structure optimization in combination with an embedded-atom method for the calculation of the total energy for a given structure. Comparing bimetallic clusters with homoatomic clusters of the same size, it is shown that the most stable structures for each cluster size are composed entirely of Ni atoms. Among the bimetallic clusters in the size range N = 2-20, the Ni N-1 Cu 1 clusters possess the highest stability. Further, it has been established that most of the bimetallic cluster structures have geometries similar to those of pure Ni clusters. The size N = 38 presents a special case, as the bimetallic clusters undergo a dramatic structural change with increasing atom fraction of Cu. Moreover, we have identified an icosahedron, a double, and a triple icosahedron with one, two, and three Ni atoms at the centers, respectively, as particularly stable structures. We show that in all global-minimum structures Ni atoms tend to occupy mainly high-coordination inner sites, and we confirm the segregation of Cu on the surface of Ni-Cu bimetallic clusters predicted in previous studies. Finally, it is observed that, in contrast to the bulk, the ground-state structures of the 15-, 16-, and 17-atom bimetallic clusters do not experience a smooth transition between the structures of the pure copper and the pure nickel clusters as a function of the relative number of the two types of atoms. For these sizes, the concentration effect on energy is more important than the geometric one.     

Temperature-dependent structuring of Au-Pt bimetallic nanoclusters on a thin film of Al2O3/NiAl(100)

Au-Pt bimetallic nanoclusters on a thin film of Al(2)O(3)/NiAl(100) undergo significant structural evolution on variation of the temperature. Au and Pt deposited sequentially from the vapor onto thin-film Al(2)O(3)/NiAl(100) at 300 K form preferentially bimetallic nanoclusters (diameter ≦ 6.0 nm and height ≦ 0.8 nm) with both Au and Pt coexisting at the cluster surface, despite the order of metal deposition. These bimetallic clusters are structurally ordered, have a fcc phase and grow with their facets either (111) or (001) parallel to the θ-Al(2)O(3)(100) surface. Upon annealing the clusters to 400-500 K, the Au atoms inside the clusters migrate toward the surface, resulting in formation of a structure with a Pt core and an Au shell. Annealing the sample to 500-650 K reorients the bimetallic clusters--all clusters have their (001) facets parallel to the oxide surface--and induces oxidation of Pt. Such annealed bimetallic clusters become encapsulated with the aluminium-oxide materials and a few Au remain on the surface.     

Global optimization of bimetallic cluster structures. I. Size-mismatched Ag-Cu, Ag-Ni, and Au-Cu systems

A genetic algorithm approach is applied to the optimization of the potential energy of a wide range of binary metallic nanoclusters, Ag-Cu, Ag-Ni, Au-Cu, Ag-Pd, Ag-Au, and Pd-Pt, modeled by a semiempirical potential. The aim of this work is to single out the driving forces that make different structural motifs the most favorable at different sizes and chemical compositions. Paper I is devoted to the analysis of size-mismatched systems, namely, Ag-Cu, Ag-Ni, and Au-Cu clusters. In Ag-Cu and Ag-Ni clusters, the large size mismatch and the tendency of Ag to segregate at the surface of Cu and Ni lead to the location of core-shell polyicosahedral minimum structures. Particularly stable polyicosahedral clusters are located at size N = 34 (at the composition with 27 Ag atoms) and N = 38 (at the composition with 32 and 30 Ag atoms). In Ag-Ni clusters, Ag32Ni13 is also shown to be a good energetic configuration. For Au-Cu clusters, these core-shell polyicosahedra are less common, because size mismatch is not reinforced by a strong tendency to segregation of Au at the surface of Cu, and Au atoms are not well accommodated upon the strained polyicosahedral surface.     

Equilibrium geometries, stabilities, and electronic properties of the bimetallic M2-doped Au(n) (M = Ag, Cu; n = 1-10) clusters: comparison with pure gold clusters

The density functional method with relativistic effective core potential has been employed to investigate systematically the geometrical structures, relative stabilities, growth-pattern behaviors, and electronic properties of small bimetallic M(2)Au(n) (M = Ag, Cu; n = 1-10) and pure gold Au(n) (n ≤ 12) clusters. The optimized geometries reveal that M(2) substituted Au(n+2) clusters and one Au atom capped M(2)Au(n-1) structures are dominant growth patterns of the stable alloyed M(2)Au(n) clusters. The calculated averaged atomic binding energies, fragmentation energies, and the second-order difference of energies as a function of the cluster size exhibit a pronounced even-odd alternation phenomenon. The analytic results exhibit that the planar structure Ag(2)Au(4) and Cu(2)Au(2) isomers are the most stable geometries of Ag(2)Au(n) and Cu(2)Au(n) clusters, respectively. In addition, the HOMO-LUMO gaps, charge transfers, chemical hardnesses and polarizabilities have been analyzed and compared further.     

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     

Geometrical and electronic structures of Au(m)Ag(n) (2 < or = m + n < or = 8)

The structural and electronic properties of Au(m)Ag(n) binary clusters (2 < or = m + n < or = 8) have been investigated by density functional theory with relativistic effective core potentials. The results indicate that Au atoms tend to occupy the surface of Au(m)Ag(n) clusters (n > or = 2 and m > or = 2). As a result, segregation of small or big bimetallic clusters can be explained according to the atomic mass. The binding energies of the most stable Au(m)Ag(n) clusters increase with increasing m+n. The vertical ionization potentials of the most stable Au(m)Ag(n) clusters show odd-even oscillations with changing m+n. The possible dissociation channels of the clusters considered are also discussed.     

Structure and energetics of equiatomic K-Cs and Rb-Cs binary clusters

The basin-hopping algorithm combined with the Gupta many-body potential is used to study the structural and energetic properties of (KCs)(n) and (RbCs)(n) bimetallic clusters with N=2n up to 50 atoms. Each binary structure is compared to those of the pure clusters of the same size. For the cluster size N=28 and for the size range of N=34-50, the introduction of K and Rb atoms in the Cs alkali metal cluster results in new ground state structures different from those of the pure elements. In the size range N>/=38 the binary and pure clusters show not only structural differences, but they also display different magic numbers. Most of the magic Rb-Cs and K-Cs clusters possess highly symmetric structures. They belong to a family of pIh structures, where a fivefold pancake is a dominant structural motif. Such geometries have not been reported for alkali binary clusters so far, but have been found for series of binary transition metal clusters with large size mismatch. Moreover, tendency to phase separation (shell-like segregation) is predicted for both K-Cs and Rb-Cs clusters with up to 1000 atoms. Our finding of a surface segregation in Rb-Cs clusters is different from that of theoretical and experimental studies on bulk Rb-Cs alloys where phase separation does not occur.     

单原子分散的Au/Cu(111)表面合金的表面结构与吸附性质

Au-Cu双金属合金纳米颗粒对包括CO氧化和CO2还原等在内的多个反应有较好的催化活性,然而关于其表面性质的研究却相当匮乏。在此工作中,我们通过对低覆盖度的Au/Cu(111)和Cu/Au(111)双金属薄膜退火,制备出了单原子级分散的Au/Cu(111)和Cu/Au(111)合金化表面,并利用高分辨扫描隧道显微镜(STM)和扫描隧道谱(STS)进一步研究了掺杂原子的电子性质及其对CO吸附行为的影响。研究发现,分散在Cu(111)表面的表层和次表层Au单原子在STM上表现出不同衬度。在-0.5 e V附近,前者表现出相较于Cu(111)明显增强的电子态密度,而后者则明显减弱。吸附实验表明表层Au单原子对CO的吸附能力并没有得到增强,甚至会减弱其周围Cu原子的吸附能力。与Au在Cu(111)表面较好的分散相反,Cu原子倾向于钻入Au(111)的次表层,并且形成多原子聚集体。且Cu原子受Au(111)衬底吸电子作用的影响,其对CO的吸附能力明显减弱。这个研究结果揭示了合金表面的微观结构与性质的关联,为进一步阐明Au-Cu双金属催化剂的表面反应机理提供参考。     

Structures of mixed gold-silver cluster cations (Ag(m)Au(n)+, m+n<6): ion mobility measurements and density-functional calculations

The collision cross sections of Ag(m)Au(n)+ (m+n)<6 cluster ions were determined. For bimetallic clusters, we observe a significant intracluster charge transfer leaving most of the ions positive charge on the silver atoms. The mixed trimeric ions Ag2Au+ and AgAu2+ are triangular like the pure gold and silver trimers. Most of the tetrameric clusters are rhombus shaped, with the exception of Ag3Au+, which has a Y structure with the gold atom in the center. Among the pentamers we find distorted X structures for all systems. For Ag2Au3+ we find an additional isomer which is a trigonal bipyramid. These findings are in line with predictions based on density-functional theory calculations, i.e., all these structures either represent the global minima or are within less than 0.1 eV of the predicted global minimum.     

Growth format, electronic architecture, magnetic, and optical properties of aromatic cyclo-Cu3Au3 homotops

Bimetallic Cu(3)Au(3) clusters have been investigated using electronic structure calculation techniques (DFT) to understand their electronic, magnetic, and optical properties as well as the geometrical structures. The most stable homotop is the planar cyclo-[Cu(3)(micro-Au)(3)] form consisting of a triangular positively charged Cu(3) structural core with negatively charged Au atoms occupying exposed positions. This structure is characterized by the maximum number of heterobonds and peripheral positions of Au atoms. Possible growth formats of the cyclo-[Cu(3)(micro-Au)(3)] homotops have been explored following both the edge-capping and the stepwise metal atom substitution mechanism. The bonding pattern along with the density of states (DOS) plots of the cyclo-[Cu(3)(micro-Au)(3)] homotop are thoroughly analyzed and compared with those of the pure cyclo-[Cu(3)(micro-Cu)(3)] and cyclo-[Au(3)(micro-Au)(3)] clusters. Particular attention was paid on the stability of these bimetallic clusters in relation with the ring-shaped electron density distribution (aromaticity). It was found that all 3-membered metal rings exhibit significant aromatic character, which was verified by a number of established criteria of aromaticity, such as structural, energetic, magnetic (NICS profiles), and out-of-plane ring deformability criteria. The NICS (1) values correlate well with the out-of-plane ring deformation energy. Finally, a comprehensive analysis of the optical spectra of the CuAu, Cu(2), and Au(2) diatomics and the cyclo-[Cu(3)(micro-Au)(3)], cyclo-[Cu(3)(micro-Cu)(3)], and cyclo-[Au(3)(micro-Au)(3)] clusters placed the electronic assignments of the optical transitions on a firm footing.     

Low energy structures of gold nanoclusters in the size range 3–38 atoms

Using a combination of first principles calculations and empirical potentials we have undertaken a systematic study of the low energy structures of gold nanoclusters containing from 3 to 38 atoms. A Lennard-Jones and many-body potential have been used in the empirical calculations, while the first principles calculations employ an atomic orbital, density functional technique. For the smaller clusters (n=3–5) the potential energy surface has been mapped at the ab initio level and for larger clusters an empirical potential was first used to identify low energy candidates which were then optimised with full ab initio calculations. At the DFT-LDA level, planar structures persist up to six atoms and are considerably more stable than the cage structures by more than 0.1 eV/atom. The difference in ab initio energy between the most stable planar and cage structures for seven atoms is only 0.04 eV/atom. For larger clusters there are generally a number of minima in the potential energy surface lying very close in energy. Furthermore our calculations do not predict ordered structures for the magic numbers n=13 and 38. They do predict the ordered tetrahedral structure for n=20. The results of the calculations show that gold nanoclusters in this size range are mainly disordered and will likely exist in a range of structures at room temperature.     

How cationic gold clusters respond to a single sulfur atom

Results describing the interaction of a single sulfur atom with cationic gold clusters (Au(n) (+), n=1-8) using density functional theory are described. Stability of these clusters is studied through their binding energies, second order differences in the total energies, fragmentation behavior, and atom attachment energies. The lowest energy structures for these clusters appear to be three dimensional right from n=3. In most cases the sulfur atom in the structure of Au(n)S(+) is observed to displace the gold atom siting at the peripheral site of the Au(n) (+) cluster. The dissociation channels of Au(n)S(+) clusters follow the same trend as Au(n) (+) cluster, based on the even/odd number of gold atoms in the cluster, with the exception of Au(3)S(+). This cluster dissociates into Au and Au(2)S(+), signifying the relative stability of Au(2)S(+) cluster regardless of having an odd number of valence electrons. Clusters with an even number of gold atoms dissociate into Au and Au(n-1)(S)(+) and clusters with an odd number of gold atoms dissociate into Au(2) and Au(n-2)(S)(+) clusters. An empirical relation is found between the conduction molecular orbital and the number of atoms in the Au(n)S(+) cluster.     

Geometries, stabilities, and electronic properties of Pt-group-doped gold clusters, their relationship to cluster size, and comparison with pure gold clusters

A systematic study of bimetallic Au(n)M(2) (n = 1-6, M = Ni, Pd, and Pt) clusters is performed by using density functional theory at the B3LYP level. The geometric structures, relative stabilities, HOMO-LUMO gaps, natural charges and electronic magnetic moments of these clusters are investigated, and compared with pure gold clusters. The results indicate that the properties of Au(n)M(2) clusters for n = 1-3 diverge more from pure gold clusters, while those for n = 4-6 show good agreement with Au(n) clusters. The dissociation energies, the second-order difference of energies, and HOMO-LUMO energy gaps, exhibiting an odd-even alternation, indicate that the Au(4)M(2) clusters are the most stable structures for Au(n)M(2) (n = 1-6, M = Ni, Pd, and Pt) clusters. Moreover, we predict that the average atomic binding energies of these clusters should tend to a limit in the range 1.56-2.00 eV.     

Au130−xAgx Nanoclusters with Non‐Metallicity: A Drum of Silver‐Rich Sites Enclosed in a Marks‐Decahedral Cage of Gold‐Rich Sites

The synthesis and structure of atomically precise Au_130?xAg_x (average x=98) alloy nanoclusters protected by 55 ligands of 4‐tert‐butylbenzenethiolate are reported. This large alloy structure has a decahedral M₅₄ (M=Au/Ag) core. The Au atoms are localized in the truncated Marks decahedron. In the core, a drum of Ag‐rich sites is found, which is enclosed by a Marks decahedral cage of Au‐rich sites. The surface is exclusively Ag?SR; X‐ray absorption fine structure analysis supports the absence of Au?S bonds. The optical absorption spectrum shows a strong peak at 523 nm, seemingly a plasmon peak, but fs spectroscopic analysis indicates its non‐plasmon nature. The non‐metallicity of the Au_130?xAg_x nanocluster has set up a benchmark to study the transition to metallic state in the size evolution of bimetallic nanoclusters. The localized Au/Ag binary architecture in such a large alloy nanocluster provides atomic‐level insights into the Au?Ag bonds in bimetallic nanoclusters.     

Formation of bimetallic Ag-Pd nanoclusters via the reaction between Ag nanoclusters and Pd2+ ions

We have investigated systematically the mechanistic aspects of the Ag-Pd bimetallic cluster formation within sodium bis(2-ethylhexyl)sulfosuccinate (AOT) reverse micelles by using in-situ X-ray absorption spectroscopy (XAS). A two-step sequential reduction method is employed for the synthesis of Ag-Pd bimetallic clusters. The first step involves preparation of Ag nanoclusters, by mixing the Ag+ ions containing the AOT microemulsion system with a reducing agent hydrazine (N2H4) containing the AOT microemulsion system. In the second step, the addition of Pd2+ ions to Ag nanoclusters led to the formation of Ag-Pd bimetallic clusters via the reaction between Ag nanoclusters and Pd2+ ions in AOT reverse micelles. The reduction of silver ions and the formation of corresponding Ag nanoclusters are monitored as a function of the dosage of the reducing agent, hydrazine. In-situ XAS allowed probing of the reaction between Ag nanoclusters and Pd2+ ions during the formation of Ag-Pd bimetallic clusters. Analysis of Ag and Pd K-edge XAS spectra reveals that in the final stage Ag-Pd clusters, in which "Ag" atoms prefer to be surrounded by "Pd" and "Pd" atoms prefer to be surrounded by "Pd", were formed. On the basis of XAS results presented here, we are able to propose a structural model for each step so that this work provides a detailed insight into the mechanism of nucleation and growth of Ag-Pd bimetallic clusters. We also discussed the atomic distribution of Ag and Pd atoms in Ag-Pd bimetallic clusters based on the calculated XAS structural parameters.     

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

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

Effect of Ni and Pd on the geometry, electronic properties, and active sites of copper clusters

The geometry, electronic properties, and active sites of copper clusters doped with Ni or Pd atoms, Cu(n)()(-)(1)M (n = 2-6; M = Ni, Pd) have been investigated using first-principles methods. Planar structures are energetically favorable in Cu(n)()(-)(1)Ni (n = 2-6). However, for Pd-doped clusters, three-dimensional structures are competitive in energy, and for n = 6, the most stable structure is not planar. Several properties of doped copper clusters present odd-even oscillations as the number of copper atoms grow. The different atomic ground-state configuration of Ni and Pd determines the bonding and electronic properties of doped copper clusters. The interaction between impurities and copper atoms can modify the chemical hardness and active sites of doped copper clusters markedly inducing directionality in the reactivity. This effect is relevant to the behavior of catalysts as well as in the growth of metallic films.     

Structure and shape variations in intermediate-size copper clusters

Using extensive, unbiased searches based on density-functional theory, we explore the structural evolution of Cu(n) clusters over the size range n=8-20. For n=8-16, the optimal structures are plateletlike, consisting of two layers, with the atoms in each layer forming a trigonal bonding network similar to that found in smaller, planar clusters (n相似文献