Computational and Theoretical Chemistry

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1 Computational and Theoretical Chemistry 993 (2012) Contents lists available at SciVerse ScienceDirect Computational and Theoretical Chemistry journal homepage: Atomic structures and electronic properties of small Au Ag binary clusters: Effects of size and composition Liang Hong a, Haoliang Wang a, Jingxin Cheng a, Xiaoming Huang a,b, Linwei Sai b,c, Jijun Zhao a,b, a School of Physics and Optoelectronic Engineering, Dalian University of Technology, Dalian , China b College of Advanced Science and Technology, Dalian University of Technology, Dalian , China c School of Mathematical Sciences, Dalian University of Technology, Dalian , China article info abstract Article history: Received 3 March 2012 Received in revised form 18 May 2012 Accepted 22 May 2012 Available online 6 June 2012 Keywords: Genetic algorithm Binary clusters Lowest-energy structure Genetic algorithm combined with first-principle calculations is used to globally search the potential energy surface of the most stable configurations of elementary Au m and Ag n clusters, as well as Au m Ag n (5 6 m + n 6 12) binary clusters. The effects of size and composition (i.e., Au:Ag ratio) on the atomic structures, coordination numbers and electronic properties including the binding energies and formation energies of Au Ag binary clusters are discussed. The critical Au:Ag ratios for the 2D 3D transition are obtained and it is found that Ag atoms sometimes play a more important role in determining the ground-state configuration of a Au Ag bimetallic cluster. The electron density of states is further analyzed to explore the influence of Au and Ag atoms. Stronger s d hybridization originated from relativistic effects of Au atom is observed in the planar structure with regard to the 3D structures. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction Owing to the increasing interests on the design of novel functional nanoscale materials, the study of nanoparticles or nanoclusters consisting of noble metals like copper, silver, and gold has become a hot research field for chemists, physicists, and materials scientists. Gold clusters have been widely investigated [1,2] due to their important role as building blocks in electronic, optical and medical diagnostic nanodevices [3]. In particular, small gold clusters have attracted a surge of interests for their applications as tips and contacts in molecular electronic circuits [4], as well as potential chemical catalysts [5]. Their electronic, chemical and optical properties have been explored theoretically using ab initio computational methods over the past two decades. The ground-state structures of Au m clusters were found to transform from planar to tetrahedral [6] and cage-like [7,8] ones as the cluster size increases, and the structural transition from two-dimensional (2D) to three-dimensional (3D) occurs in the size range of atoms [9 15]. The origin for a variety of novel geometry structures was attributed to the strong s d hybridization and the d d interaction enhanced by the relativistic effects, which is rather unique for Au element [1,9]. Silver clusters have also attracted considerable interests due to their practical importance in photography [16] and catalysis [17], Corresponding author at: School of Physics and Optoelectronic Engineering, Dalian University of Technology, Dalian , China. Tel.: ; fax: address: zhaojj@dlut.edu.cn (J. Zhao). as well as their potential use in new electronic materials [18]. Numbers of researches have been done both theoretically and experimentally, and the geometric structures of silver clusters are among the best known after those of carbon and silicon [19 24]. Compared with gold clusters, silver clusters start to adopt planar geometries at much smaller size. The transition of planar to 3D geometries in Ag n clusters was reported to occur at n = 5 7. Meanwhile, instead of the tetrahedral structure which was considered as the most stable one for Au 20, amorphous structure was found to be more favorable for Ag 20 [21]. In addition to the pure Au and Ag clusters, Au Ag binary clusters play an important role in catalysis, colloidal chemistry, and medical science [25]. New molecular nanocrystalline materials with gold and silver nanoclusters and nanowires, which would be considered as prototypes for electronic nanodevices and biosensors, have also been synthesized [26]. Compared with the exhaustive studies of pure gold and silver clusters, gold silver binary clusters have been less investigated, especially on their geometric and electronic structures. However, due to different relativistic effects and geometric structures of pure gold and silver clusters, the structural and electronic properties of gold silver binary clusters are expected to be strongly dependent on the cluster size and mixing ratio of gold and silver atoms. Previously, there have been several theoretical researches on the structures and electronic properties of gold silver binary clusters. Bonačić-Koutecký et al. [27] studied the neutral and charged Au m Ag n (3 6 m + n 6 5), Au n Ag n (n = 3, 4, 5, 10) and Au 8 Ag 12 clusters using the density functional theory (DFT) method with gener X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.

2 L. Hong et al. / Computational and Theoretical Chemistry 993 (2012) alized gradient approximation (GGA) and relativistic effective core potentials (RECP). Bimetallic tetramer and hexamer were found to share the same planar geometric shape with pure ones, while Au 4 Ag 4 and Au 5 Ag 5 adopt 3D configurations in contrast to the 2D structures of Au 8 and Au 10. Lee et al. [26] employed the gradient corrected DFT method and high-level coupled cluster theory with RECP to investigate the properties of pure gold and pure silver clusters up to 13 atoms, as well as neutral and anionic Au m Ag n clusters (2 6 m + n 6 7). They concluded that since the Ag-5s orbital is energetically much higher than the Au-6s orbital, partial charge transfer from Au to Ag takes place in Au Ag binary clusters. Consequently, Au atoms tend to be negatively charged and favor the surface, edges or vertices, while Ag atoms tend to be positively charged and favor the interior sites. Zhao and Zeng [28] performed relativistic DFT GGA calculations on Au m Ag n (2 6 m + n 6 8) clusters to determine the ground-state configurations and discuss the binding energies and vertical ionization potentials. Recently, medium-sized gold silver nanoalloys were investigated by several groups. Curley et al. [29] explored gold silver alloys with 38 atoms using a Gupta many-body potential combined with genetic algorithm (GA), and observed the changes in structures as a function of Ag/Au composition with a tendency for surface segregation of the Ag atoms. Chen and Jhonston studied (AuAg) n alloys with atoms [30,31], as well as Au m Ag 55 m [32], using DFT calculations also combined with GA global search. Very recently, Deng et al. [33] and Heiles et al. [34] explored the structural and electronic properties of 32-atom and 8-atom Au Ag systems, respectively. The 32-atom clusters were reported to assume hollow cage-like or space-filling configurations as the possible lowest-energy ones, while a transition from 2D to 3D was predicted between the ground-state structures of Au 6 Ag 2 and Au 5 Ag 3 in the 8-atom system. Despite these previous efforts, our theoretical knowledge on the gold silver binary clusters is still rather limited due to the following aspects: (1) so far only relatively smaller (up to 5 8 atoms), which prefer planar configurations, and relatively larger ones (more than 20 atoms), which prefer cage-like structures, were studied; but the clusters within the size range of 2D 3D structural transition have not been systematically studied yet; (2) the relationship between the structures and composition (Au:Ag ratio) as well as the correlation between atomic structures and electronic properties are unclear; (3) only limited number of cluster configurations were considered, which cannot be guaranteed to be the global minima owing to the complexity of potential energy surface (PES). In order to address these unsolved issues, in this paper we performed an unbiased global search using GA incorporated with DFT method to elucidate the relationship between pure gold, silver clusters and gold silver alloys with 5 12 atoms, as well as the structural growth pattern of gold silver binary clusters. 2. Computational method The unbiased global search of the most stable configurations of pure Au m and Ag n, as well as Au m Ag n (5 6 m + n 6 12) binary clusters was carried out using genetic algorithm [35 39], incorporated with all-electron relativistic DFT method as implemented in the DMol 3 package [40,41]. In the GA search, sixteen initial configurations were generated from scratch. Any two individuals in this population were then chosen as parents to produce a child cluster via a cut and splice crossover operation [35], followed by an optional mutation operation of 30% probability. Two types of mutations are used in this work: (1) give each atom a small random displacement and (2) exchange the atomic types between a pair of different atoms. The child cluster was then relaxed using DFT optimization. In order to keep the diversity of the populations, the locally stable child was selected to replace one of the individuals if they share the same value of inertia [39]; otherwise (the new structure has an inertia different from all existing isomer), replace the highest energy isomer by the new one. For each cluster size, we performed GA iterations to ensure that the global minimum on the PES is obtained. The number of GA iteration generally increases with cluster size, and relies on the specific chemical composition of the cluster (generally, gold-rich clusters need more GA iterations than silver-rich ones in the same cluster size). The details of GA procedure can be found in the review articles [35 37] and our recent publication [39]. Perdew Burke Ernzerholf (PBE) function within generalized gradient approximation (GGA) [42] was used for describing the exchange correlation interaction. Double numerical basis set including d-polarization function (DND) were adopted [40,41]. Geometry optimization was performed without symmetry constraint using a convergence criterion of Hartree on the maximum energy gradient and Å on the maximum displacement for each atom. Self-consistent field (SCF) electronic structure calculations were carried out with a convergence criterion of Hartree on the total energy. To assess the current computational method, we first performed calibration calculations on Au and Ag atoms, as well as Au 2,Ag 2, and AuAg dimers and compared with the available experimental data [28,43 51]. The results are listed in Table 1. A satisfactory agreement is found between our calculations and experiments for the bond lengths, with largest deviation of less than 0.1 Å. Compared to experiments, the binding energies and vertical ionization potentials from our DFT calculations are slightly higher by about 5% while electron affinities are systematically lower by about ev. Generally speaking, our method is suitable for investigating the structural and electronic properties of gold and silver clusters, as well as their binary clusters. 3. Results and discussion 3.1. Pure gold and silver clusters Before exploring the Au m Ag n binary systems, it is essential to know the structures of pure gold and silver clusters. The binding energies (E B ) per atom are defined as E B ¼ E Au mag n ðme Au-single þ ne Ag-single Þ ; m þ n where E AumAg n, E Au-single and E Ag-single are the energies of Au m Ag n alloy cluster, Au single atom and Ag single atom, respectively. E B per atom of Au m and Ag n (5 6 m, n 6 12) along with their lowest-energy structures are plotted in Fig. 1. For both Au and Ag clusters, E B generally increases with the increasing cluster size. With five or six atoms, Au m and Ag n clusters share the same planar configuration, i.e., trapezia for Au 5 and Ag 5, triangle for Au 6 and Ag 6. With up to seven atoms, Au m remains planar and the 2D structure lasts the entire size range (up to m = 12), while Ag n begins to prefer 3D configurations instead of 2D ones. The higher stability of the planar structures of neutral gold clusters is associated with a relativistically enhanced strong s d hybridization and d d interaction in Au atom [52]. On the contrary, neutral silver which is characterized by s-type bonding adopts 3D structures for larger size than hexamer [27]. The lowest-energy structures of Au m (5 6 m 6 12) consist of triangular subunits and can be derived by adding every single Au atom to the lowest-energy structure of Au m 1. The present results agree well with those previous DFT calculations [9 13,15,26]. Regarding to a recent study of Assadollahzadeh and Schwerdtfeger

3 38 L. Hong et al. / Computational and Theoretical Chemistry 993 (2012) Table 1 The bond length (r), binding energy (E B ), vertical ionization potentials (IP v ) and electron affinities (EA) of Au and Ag atom and dimers Au 2,Ag 2 and AuAg from our DFT calculations compared with experimental data. r (Å) E B (ev) IP v (ev) EA (ev) Theo. Expt. Theo. Expt. Theo. Expt. Theo. Expt. Au a b Ag a b Au c c ± 0.21 b b Ag b c b b AuAg b ± 0.1 d 8.66 <9.15 b b a Ref. [38]. b Refs. [39 44]. c Ref. [45]. d Ref. [46]. Fig. 1. The binding energies per atom (E B /atom) of Au m and Ag n (5 6 m,n 6 12) with their lowest-energy structures. Fig. 2. The second differences of energy (D 2 E) for Au m and Ag n (6 6 m,n 6 11), and HOMO LUMO gaps for Au m and Ag n (5 6 m,n 6 12). [15] on small gold clusters from DFT LSDA calculations, their results are consistent with ours except for Au 8 and Au 11. For Au 8,a D 4h configuration with a square in the center was considered as the global minimum in their work. However, the structure distorts into a D 2h configuration with a rhombus in the center after our DFT optimization. For Au 11, Assadollahzadeh and Schwerdtfeger probably did not succeed in locating the global minimum since a 3D structure for Au 11 was reported as the lowest-energy one, which violate the planar pattern of small gold clusters. The lowest-energy structures of Ag n (5 6 n 6 12) are also composed of triangular subunits. As the cluster size increases, Ag clusters generally grow up by adding atoms to layers, which leads to close-packed flat configurations. The ground-state structures of pure silver clusters obtained in this work are generally consistent with those in previous studies [19,20,22 24,26]. In particular, the energy order of the T d structure and the D 2d structure of Ag 8 seems to be very sensitive on the details of theoretical treatment [23]. The D 2d structure lies only ev lower in energy than the T d structure from our PBE/DND calculations. The T d structure was reported to be more stable than the D 2d isomer by Bonačić-Koutecký et al. [23] using CCSD method and Lecoultre et al. [24] using time dependent DFT (TD-DFT) method in their recent works; however, small energy differences (60.1 ev) were also found between the two isomers. The second-order differences of energy (D 2 E), defined as D 2 E n = E n 1 + E n+1 2 E n, and the gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO HUMO gap) of pure gold and silver are shown in Fig. 2 as function of cluster size. Both D 2 E and HOMO LUMO gaps exhibit pronounced even odd alternation which indicates higher stability of clusters with even number of electrons than those with odd number of electrons. The even odd oscillation behavior of gold and silver clusters coincides well with the previous experimental results [53 55]. 5.1 C 2v 4.2 C 2v 3.3 D 3h 3.3b C s (0.001 ev) 3.3c D 3h (0.043 ev) 2.4 C 2v 1.5 C 2v 1.5b C 2v (0.056 ev) Fig. 3. The lowest-energy structures and some metastable isomers of Au 6 n Ag n (n = 1 5), along with their point group symmetries and energy differences in the parentheses. Color scheme: yellow for gold, light blue for silver. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

4 L. Hong et al. / Computational and Theoretical Chemistry 993 (2012) Atomic structures of Au Ag binary clusters The lowest-energy configurations of binary Au m Ag n (6 6 m + n 6 12) are shown in Figs For convenience, the lowest-energy structure of Au m Ag n is signed as m.n ; its metastable isomers are signed as m.nb and m.nc, if presented. In the following, we discuss the details of these structures in the sequence of cluster size from 6 to C s 7.1b C 2v (0.048 ev) 6.2 C 2h 6.2b C 2v (0.052 ev) 6.2c D 2h (0.342 ev) Au 6 n Ag n (n = 1 5) All the 6-atom Au Ag binary clusters prefer 2D triangular configuration, which is consistent with the results in previous works [26 28,56]. In the most stable structure of Au 5 Ag 1, the four-coordinated Ag atom locates at the center of an edge, in agreement with that reported by Lee et al. [26] and Zhao and Zeng [28]. In previous studies [26 28,56], the ground state of Au 3 Ag 3 was considered as a triangle with three Au atoms at vertices (3.3c); however, the triangle configuration with three Ag atoms at vertices (3.3) is found to be ev energetically favorable from our DFT calculations. In addition, another isomer structure for Au 3 Ag 3 (3.3b) lies only ev above the ground state. The structure of Au 1 Ag 5 which contains a four-coordinated Au atom is found to be ev more stable than the structure with a two-coordinated Au atom (1.5b) reported by Lee. The different mixing pattern in the 6-atom system compared with the previous results by Lee and Zhao can be attributed to the difference in DFT methodology since the energetic separation between these isomers is very small. 5.3 C 3v 5.3b C s (0.022 ev) 3.5b C 3v (0.139 ev) 2.6 C 2v 2.6b C 2v (0.172 ev) 4.4 D 2d 4.4b T d (0.095 ev) 3.5 C s 1.7 C s 1.7b C 3v (0.081 ev) Fig. 5. The lowest-energy structures and some metastable isomers of Au 8 n Ag n (n = 1 7), along with their point group symmetries and energy differences in the parentheses. Color scheme: yellow for gold, light blue for silver. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Au 7 n Ag n (n = 1 6) The ground-state structure of Au 6 Ag 1 can be obtained by replacing one Au atom by Ag atom in the lowest-energy structure of Au 7. However, the most stable structures of Au 6 Ag 1 reported by Lee et al. (6.1b) [26] and Zhao and Zeng (6.1c) [28] are found to be ev and ev, respectively, higher than 6.1 in energy. Both Au 5 Ag 2 and Au 4 Ag 3 adopt the Au-centered hexagon as their lowest-energy structures, in which Ag atoms occupy separated sites at the fringe of the hexagon, thus the high symmetry of cluster structure is retained (D 2h for Au 5 Ag 2 and C 3v for Au 4 Ag 3 ). The 2Dto-3D structural transition occurs at Au 3 Ag 4 and the pentagonal bipyramid (PBP) configuration remains invariant until Ag 7. For Au 1 Ag 6, Lee reported a similar structure with a four-coordinated Au atom at the fringe of the PBP; but our results reveal that PBP configuration with Au atom on the top is more stable by ev. 8.1 C 2v 7.2 C s 6.3 C 2v 5.4 C s 5.4b C s (0.096 ev) 5.4c C 2 (0.098 ev) 4.5 C C C C 2v Fig. 6. The lowest-energy structures and some metastable isomers of Au 9 n Ag n (n = 1 8), along with their point group symmetries and energy differences in the parentheses. Color scheme: yellow for gold, light blue for silver. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Au 8 n Ag n (n = 1 7) The lowest-energy structure of Au 7 Ag 1 can be constructed by replacing an Au atom with Ag atom in the ground-state configuration of Au 8, or adding an Ag atom to the planar configuration of Au 7 ; while Au 6 Ag 2 can be obtained by substituting one Au atom by Ag atom in Au 7 Ag 1. The 2D 3D structural transition occurs at Au 5 Ag 3 which adopts a T d structure. Au 4 Ag 4 assumes PBP configuration and this configuration retains until Ag 8. Heiles et al. [34] 6.1 C s 6.1b C s (0.288 ev) 6.1c C s (0.129 ev) 5.2 D 2h 4.3 C 3v 3.4 C s 2.5 D 5h 1.6 C 5v Fig. 4. The lowest-energy structures and some metastable isomers of Au 7 n Ag n (n = 1 6), along with their point group symmetries and energy differences in the parentheses. Color scheme: yellow for gold, light blue for silver. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) recently reported their study on the 8-atom Au Ag alloys from GA DFT calculations. They also found a 2D 3D transition between the structures of Au 6 Ag 2 and Au 5 Ag 3. According to their calculations, however, the 3D structures in the 8-atom system share the skeleton of the T d configuration of Ag 8, which is different from the D 2d configuration in this work. The structures reported in their work are also shown in Fig. 5 (5.1b, 6.2b, 6.2c, 5.3, 4.4b, 3.5b, 2.6b and 1.7b), along with their energy differences in terms of our results. The highest energetic difference is ev between structures 2.6 and 2.6b, which is still very sensitive on the theoretical treatment. Thus we cannot make a clear identification of the global minima since the energy differences fall within the range of the accuracy of DFT methodology. Nevertheless, the 2D 3D transition can be clearly identified between Au 6 Ag 2 and Au 5 Ag 3.

5 40 L. Hong et al. / Computational and Theoretical Chemistry 993 (2012) C 2v 8.2 D 2h 7.3 C 2v 6.4 C 2 6.4b C 2v (0.005 ev) 5.5 C 1 5.5b C s (0.004 ev) 4.6 C 2v 4.6b C 2 (0.169 ev) 3.7 C s 2.8 D 4d 1.9 C 1 Fig. 7. The lowest-energy structures and some metastable isomers of Au 10 n Ag n (n = 1 9), along with their point group symmetries and energy differences in the parentheses. Color scheme: yellow for gold, light blue for silver. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 10.1 C s 9.2 C s 8.3 C s 7.4 C s 6.5 C s 6.5b C s (0.018 ev) 6.5c C 1 (0.125 ev) 5.6 C C C C C 1 Fig. 8. The lowest-energy structures and some metastable isomers of Au 11 n Ag n (n = 1 10), along with their point group symmetries and energy differences in the parentheses. Color scheme: yellow for gold, light blue for silver. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 11.1 C s 11.1b C 2v (0.083 ev) 11.1c C 2v (0.640 ev) 10.2 C s 9.2 C 3h 8.4 C s 7.5 C s 6.6 D 3h 6.6b C s (0.252 ev) 5.7 C s 4.8 C C C C s Fig. 9. The lowest-energy structures and some metastable isomers of Au 12 n Ag n (n = 1 11), along with their point group symmetries and energy differences in the parentheses. Color scheme: yellow for gold, light blue for silver. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Au 9 n Ag n (n = 1 8) The most stable configuration of Au 8 Ag 1 can be obtained either by adding an Ag atom to that of Au 8 or substituting an Au atom with Ag atom in the planar Au 9. Similarly, Au 7 Ag 2 and Au 6 Ag 3 clusters are constructed by orderly replacing the two two-coordinated Au atoms in Au 8 Ag 1. The 2D 3D structural transition occurs at Au 5 Ag 4 which can be constructed by adding an Au atom to the lowest-energy structure of Au 4 Ag 4. Another two isomers (5.4b and 5.4c) are also presented in Fig. 6. The frustum structure of 5.4b with C s symmetry is ev energetically higher than 5.4, while

6 L. Hong et al. / Computational and Theoretical Chemistry 993 (2012) c which can be viewed as replacing an Ag atom with an Au atom in structure 4.5, lies ev above the ground-state structure. The other four structures in the 9-atom binary systems share the same skeleton of Ag 9, i.e., a bicapped pentagonal bipyramid Au 10 n Ag n (n = 1 9) The structures of 10-atom binary Au Ag clusters are somehow more complicated with regard to the other systems. The first three structures (Au 9 Ag 1,Au 8 Ag 2 and Au 7 Ag 3 ) share the same 2D skeleton of Au 10 and can be constructed by replacing a three-coordinated Au atom by an Ag atom on the periphery. The most stable configuration of Au 6 Ag 4 and Au 5 Ag 5 is a deformed bicapped prism with a chain of Au atoms at the peripheral positions. It is noted that the planar isomer for Au 6 Ag 4 (6.4b) lies only ev above the most stable structure in energy. Thus, the preference for 3D configuration with regard to Au 6 Ag 4 cannot be clearly identified. A similar bicapped prism configuration without homo-bonds for Au 5 Ag 5 was reported by Bonačić-Koutecký et al. [27] and Mitrić et al. [56], but it transforms into the 5.5 configuration after our DFT optimization. Another isomer for Au 5 Ag 5, which can be obtained by replacing an Ag atom with an Au atom in structure 4.6, is found to be only ev above the ground-state one and has not been reported previously. From our GA search, the lowest-energy structure of Au 4 Ag 6 is found to be a spindle-shaped configuration with C 2v symmetry, which can be also viewed as a tricapped PBP. The bicapped square prism configuration (4.6b) is ev higher in energy. However, such bicapped square prism is favorable for Au 3 Ag 7 and Au 2 Ag 8 clusters. Au 1 Ag 9 can be considered as replacing a six-coordinated Ag atom by Au atom in the lowest-energy structure of Ag 10, which is also a deformed bicapped prism configuration Au 11 n Ag n (n = 1 10) In the 11-atom binary Au Ag clusters, the structures of Au 11 n Ag n (n = 1 5) share the same planar skeleton of Au 11, while those of Au 11 n Ag n (n = 6 10) share the same 3D skeleton of Ag 11, which is by two interpenetrating PBPs. Interestingly, in all these 2D and 3D ground-state configurations Ag atoms prefer peripheral positions with relatively low coordination numbers (CN = 2 4), while Au atoms prefer central positions with high coordination numbers (CN P 6). Two additional isomers (6.5b assumes planar configuration and 6.5c assumes non-planar configuration) at the 2D 3D transition point are also shown in Fig. 8. They lie ev and ev, respectively, higher than the lowest-energy structure, indicating that the planar structure is energetically favorable for Au 6 Ag 5. Previously, there was no theoretical study on 11-atom and 12-atom Au Ag binary clusters ev higher than structure 6.6, indicating its preference for planar structure Structural growth pattern of Au Ag binary clusters The average coordination number (ACN) of Au and Ag atoms in an Au Ag binary cluster is defined in Ref. [26] as: ACNðAuÞ ¼ 2 N Au Au þ N Au Ag m ACNðAgÞ ¼ 2 N Ag Ag þ N Au Ag n where N Au Au, N Au Ag and N Ag Ag are the numbers of Au Au, Au Ag and Ag Ag bonds, respectively. Fig. 10 displays the ACN of gold and silver atoms as a function of the number of Ag atoms in the Au Ag binary clusters. Obviously, Au atoms possess higher ACNs than Ag atoms, especially for those Au 1 Ag n clusters where the only one Au atom always possesses the highest CN in the cluster. For example, Au 1 Ag 10 consists of a seven-coordinated Au atom and Au 1 Ag 11 possess a nine-coordinated Au atom. Except for Au 5 Ag 1 which contains a four-coordinated Ag atom, the average CNs of Ag atoms are usually rather low (between 2 and 3) for Au m Ag n clusters with small value of n. The preference of lower CN for Ag and higher CN for Au can be easily understood by the sequence of bond strength: Au Au > Au Ag > Ag Ag, which is clearly shown in Table for the dimers. It is noteworthy that the tendency of average CN from our DFT GA search contradicts to the previously reported results [26 28], where the CNs of Au atoms were believed to be less than those of Ag atoms. This is probably due to the insufficient consideration of 3D structures in the previous works and the relatively smaller cluster sizes explored in those studies. In addition, there is a sudden increase of average CN for Ag atoms in the systems with 7 12 atoms. This feature is related to the 2D 3D transition of gold silver alloy clusters, which will be further discussed below. Generally, for each size, the planar 2D structures of Au Ag alloys share the same skeleton of pure gold clusters, while the 3D structures share the same skeleton of pure silver clusters. This phenomenon is pronounced in the 11-atom and 12-atom systems. For Au m Ag 1 (m = 6 11), the structures can be viewed as replacing one Au atom with an Ag atom in the planar Au m+1 structures. Moreover, the Ag atom prefers to stay at the peripheral sites with lower CN and Au atoms tend to occupy the central position with higher CN. Accordingly, the structures of Au m Ag 2 (m = 6 10) clusters evolve from replacing one Au atom with an Ag atom in the structures of Au m+1 Ag 1. The second Ag atom tends to occupy another peripheral position that is the remote from the first one. This phenomenon is well demonstrated in the ground-state structures of Au 12 n Ag n (n = 1 11) The structural pattern of the 12-atom binary clusters is similar to that of the 11-atom ones, that is, the structures of Au 12 n Ag n (n = 1 6) share the same planar skeleton of Au 12, while those of Au 12 n Ag n (n = 7 11) share the same 3D skeleton of Ag 12 (a flat configuration formed by twelve tetrahedrons). Except for Au 8 Ag 4, the ground-state configurations of Au 12 n Ag n (n = 1 5) can be obtained by adding an Au atom to the corresponding Au 11 n Ag n clusters. Like the 11-atom system, three-coordinated Ag atoms at peripheral positions are favored in the planar structures in the 12-atom system, which can be evidenced by the less stable isomers 11.1b (contains a four-coordinated Ag atom) and 11.1c (contains a six-coordinated Ag atom). The substitution of Au atoms by Ag atoms at the peripheral sites in the planar structures continues until all the three-coordinated positions are occupied, and then the cluster structure transforms from 2D to 3D. The 3D isomer of Au 6 Ag 6 (6.6b), which assume the configuration of Ag 12, lies Fig. 10. The ACN of gold and silver atoms as a function of the number of Ag atoms in binary Au m Ag n (6 6 m + n 6 12) for each cluster size.

7 42 L. Hong et al. / Computational and Theoretical Chemistry 993 (2012) Au 6 Ag 2 and Au 8 Ag 2, in which Ag atoms locate at the opposite positions far away from each other. The substitution of low coordinated (two- or three-coordinated) Ag atoms continues until most of the peripheral positions are occupied. Then the structural change from 2D to 3D takes place, resulting in a sudden increase in CNs of Ag atoms. In the 3D configurations, Au m Ag n still evolves from Au m+1 Ag n 1 by replacing Au atom with Ag atom without changing the geometry, unless the original configuration cannot stay stable any more, e.g., the transition from the bicapped square prism configuration of Au 2 Ag 8 to the deformed configuration of Au 1 Ag 9. Since Au m (m = 7 12) clusters prefer 2D configurations while Ag n (n = 7 12) adopt 3D one, the 2D 3D structural transition occurs in for Au Ag binary systems with 7 12 atoms. The critical Au:Ag ratios for the 2D 3D transition are summarized in Table 2. As discussed above, the 2D structures originate from the strong s d hybridization and relativistic effects of Au atoms, while the 3D structures are the results of s valence orbitals in Ag atom. For the binary clusters with 7, 11, and 12 atoms, the transition Au:Ag ratio is close to one, which means that the influences of Au and Ag atoms are nearly the same. As for the binary systems with 8, 9 and 10 atoms, the 2D 3D transition occurs at Au 5 Ag 3,Au 5 Ag 4 and Au 6 Ag 4, respectively, where the Au:Ag ratio is larger than 1. Thus the Ag atoms may play a more important role than Au atoms in these systems. Fig. 11. The size-dependent binding energies per atom (E B /atom) of Au m Ag n (6 6 m + n 6 12) with the same number of Ag atoms (n) in a series Size-dependent electronic properties of Au Ag binary clusters The size-dependent binding energy per atom (E B )ofau m Ag n (6 6 m + n 6 12) are plotted in Fig. 11. E B increases with the increasing number of Au atom; that is to say, the E B of Au Ag cluster increases with the increasing cluster size. The tendency is consistent with pure gold and silver clusters (see Fig. 1). In order to further explore the influence of Au:Ag ratio on E B, we plot the E B of Au m Ag n (6 6 m + n 6 12) as a function of the number of Ag atoms with each cluster size in a series in Fig. 12). For each cluster size, E B decreases with the increasing number of Ag atoms (or the decreasing ratio of Au:Ag), and such decrease trend is more pronounced as the number of Ag atoms increases. We also found that the curves in Fig. 12 fit quite well to quadratic curves, where standard error for each parameter is less than Roughly speaking, the binding energies are correlated with the numbers of Au Au, Ag Ag and Au Ag bonds, which is proportional to N 2 Au and N2 Ag (N Au, N Ag is the numbers of Au and Ag atoms, respectively). Thus the binding energies may contain a leading term proportional to the factor of N 2 Ag, resulting in the quadratic curves in Fig. 12. Compared with the curves plotted in Fig. 7 of Ref. [28], our results are smoother, which are capable of uncovering the structural pattern of gold silver alloy clusters. The size-dependent formation energies (E F ) per atom of Au m Ag n (6 6 m + n 6 12) can be defined as E F ¼ E Au mag n ðme Au-solid þ ne Ag-solid Þ m þ n Fig. 12. The binding energies per atom of Au m Ag n (6 6 m + n 6 12) as a function of the number of Ag atoms for each cluster size (6 12) in a series. Table 2 The critical Au:Ag ratios (m:n) at the 2D 3D transition for Au m Ag n binary clusters with 7 12 atoms. Cluster size 2D 3D 7 4:3 3:4 8 6:2 5:3 9 6:3 5:4 10 7:3 6:4 11 6:5 5:6 12 6:6 5:7 Fig. 13. The size-dependent formation energies per atom (E F /atom) of Au m Ag n (6 6 m + n 6 12) with the same number of Ag atoms (n) in a series. where E AumAg n, E Au-solid, and E Ag-solid are the energies of Au m Ag n alloy cluster, Au solid (per atom) and Ag solid (per atom), respectively. The theoretical formation energies are plotted in Fig. 13. One can

8 L. Hong et al. / Computational and Theoretical Chemistry 993 (2012) properties of Au Ag binary clusters, in particular, the interplay of relativistic effects by Au and s-type bonding of Ag. Acknowledgements This work was supported by the Undergraduate Innovative Research Training Program ( ) and the National Natural Science Foundation of China (No ). References Fig. 14. Partial density of states (PDOS) for s, p, d orbitals of the lowest-energy structures of Au 6 Ag 6 (above) and Au 5 Ag 7 (below) with 2D and 3D structures, respectively. see that E F increases with the increasing number of Au atom (or the increasing cluster size), and exhibits an even odd oscillation where even-sized clusters are more stable than odd-sized ones. In other words, from thermodynamic point of view, formation of Au Ag binary clusters with less Ag atoms is more favorable. As representatives of 2D and 3D configurations, the partial electron density of states (PDOS) of the lowest-energy structures of Au 6 Ag 6 and Au 5 Ag 7 are plotted in Fig. 14. As shown in Fig. 14, the PDOS of the d orbital in both Au 6 Ag 6 and Au 5 Ag 7 exhibit high peaks in the energy range of 1 6 ev below the Fermi level. The s band in Au 6 Ag 6 extends to lower energy regions (below 1 ev) than that in Au 5 Ag 7, resulting an enhanced s d hybridization due to the planar configuration of Au 6 Ag 6. In contrast, the PDOS of the s orbital in Au 5 Ag 7 exhibits higher peaks near the Fermi energy, which contributes its 3D configuration. 4. Conclusion To summarize, unbiased search using genetic algorithm incorporated with first-principles approach was performed to obtain the lowest-energy configurations of pure Au m, Ag n and Au m Ag n (5 6 m + n 6 12) binary clusters. The ground-state structures from our DFT GA search generally agree with previous first-principles results, especially for the pure Au and Ag clusters. With regard to Au Ag binary clusters, the distribution of Au and Ag is slightly different compared to previous work. The main reason should be the different DFT functionals and basis sets being used. Another possible reason is insufficient configurations being considered in previous work. The effects of size and Au:Ag ratio on the atomic structures and electronic properties of Au Ag binary clusters are discussed. For each cluster size, it is found that the planar structures of the Au Ag binary clusters retain the skeleton of pure gold clusters, while the 3D structures share the same skeleton of pure silver clusters. Ag atoms prefer peripheral positions with lower coordination number while Au atoms occupy central sites with higher coordination numbers. 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