A density functional theory study of structural

J Nanopart Res (2013) 15:1809 DOI 10.1007/s11051-013-1809-9

RESEARCH PAPER

A density functional theory study of structural, electronic, optical and magnetic properties of small Ag–Cu nanoalloys Weiyin Li • Fuyi Chen

Received: 21 May 2013 / Accepted: 19 June 2013 Springer Science+Business Media Dordrecht 2013

Abstract The structures and properties of 13-atom silver and copper bimetallic clusters are systematically investigated by density functional theory (DFT) in the theoretical frame of the generalised gradient approximation (GGA) exchange-collection function. Optical absorption, Raman spectra, vibrational spectra, as well as electronic and magnetic properties are calculated by DFT/GGA and semi-core pseudopotentials. The following lowest-energy structures in the 13-atom Ag– Cu clusters are obtained: cuboctahedron for pure Ag13, icosahedrons for pure Cu13, Ag1Cu12, Ag6Cu7 and Ag12Cu1; and amorphous motifs for AgmCu13-m when m = 2–5 and 7–11. Ag2Cu11, Ag7Cu6 and Ag11Cu2 are magic clusters. The Ag2Cu11 cluster exhibits high energetic stability, strong electronic stability, multipole surface plasmon resonance (SPR) mode and small dipole moment. The Ag6Cu7 cluster is a Janusseparated cluster that possesses the strongest electronic stability with a band gap of 0.424 eV and a vertical ionisation potential of 5.8417 eV. The amorphous Ag7Cu6 cluster shows an Ag–Cu alloyed motif. The blue shift of the maximum SPR peak becomes increasingly evident as silver atoms are added. All Raman and vibrational spectra exhibit many significant vibration modes within the wavenumber ranges

W. Li F. Chen (&) State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, China e-mail: [email protected]

of 0–270 and 0–306.55 cm-1, respectively. Ferroelectric and ferromagnetic behaviours are observed in the 13-atom Ag–Cu nanoalloys, indicating their new potential applications in nonlinear optical devices. Keywords Nanoalloy Surface plasmon resonance Stability Optics

Introduction Nanoalloys are nanometer-sized clusters consisting of two or more metallic elements. The physical and chemical properties of these clusters depend on the size, structure, and chemical ordering of their components (Ferrando et al. 2008a, b; Jellinek 2008), and these properties often differ from those of the bulk form (Chen and Johnston 2007, 2008; Nunez and Johnston 2010). Bi- and multimetallic alloy clusters are gaining increased interest because of their widespread applications in catalysis (Lewis 1993), electronics (Darbha et al. 2007; Mirkin et al. 1996), optics (Brongersma et al. 2000; Quinten et al. 1998) and biomedicine (Dreaden et al. 2011; Nicewarner-Pena et al. 2001; Rosi et al. 2001). In particular, coinage metal (Au, Ag and Cu) nanoalloys have wide-ranging applications in plasmonic technologies. Many theoretical and experimental studies have been conducted on Ag–Cu nanoalloys. Jiang et al. (2006) reported on the structural and vibrational properties of

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small Cu1–7Ag clusters for both cationic and neutral systems. They found that Ag atoms tend to occupy peripheral positions, and the formation of three-dimensional geometries is observed in Cu7Ag for neutral clusters; for cationic ones, this formation occurs in Cu6,7Ag clusters. Kilimis and Papageorgiou (2010) investigated the structural and electronic properties of small gas-phase AgmCun cluster (m ? n = 2–5) atoms. They found that silver atoms have a clear tendency to occupy edge positions for tetramers and pentamers. Nunez and Johnston (2010), Ferrando et al. (2005, 2008a, b), Rapallo et al. (2005), Rossi et al. (2004), Barcaro et al. (2006), Molayem et al. (2011) and Yildirim et al. (2012) studied the structures of a family of bimetallic Ag–Cu clusters. They found that the minimum structures are Ag27Cu7, Ag27Cu13, Ag30Cu8, Ag32Cu6, Ag32Cu13 and Cu9Ag29 nanoalloys. Bochicchio and Ferrando (2010, 2012) recently proposed some selected large-sized Cu–Ag clusters: anti-Mackay icosahedra for Cu55Ag72 and Cu147Ag132, as well a chiral icosahedra for Cu309Ag200 and Cu561Ag312. They also found that the shells of Ag107Cu85, Ag132Cu147 and Ag212Cu309 nanoalloys are the most favourable for various numbers of Ag atoms and that the structures present notable thermal stability. Nanoclusters show both electronic and geometric magic number, where 13 (atoms) is the first geometric magic number because a 13-atom cluster forms stable, completely closed structure (Binns 2001; Knickelbein 1999). Many researchers have theoretically investigated the structural stability of 13-atom nanoparticles for a variety of silver and copper clusters. Chen and Johnston (2007, 2008), Michaelian et al. (1999), Pereiro et al. (2007) and Yang et al. (2007) found that Ag13 have a icosahedron (Ih) structure. Darby et al. (2002) indicated that the Cu13 cluster is Ih. Oviedo and Palmer (2002) found that Cu13, Ag13 and Au13 prefer amorphous structures. Longo and Gallego (2006), Chang and Chou (2004) reported Cu13, Ag13 and Au13 show that a buckled biplanar structure is more stable than an Ih configuration. Yang et al. (2006a, b) thought that the optimal structure of the Cu13 cluster is plateletlike and consists of two layers. Zeng et al. (2010) proposed that both the neutral and anionic Ih Cu13 clusters are less than their layered isomers. Baishya et al. (2011) found that the Cu13 cluster is triaxial with a layered structure and no interior atom. Recently, Weissker and Mottet (2011) determined that the most

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stable structures of Cu13 and Ag13 clusters are cuboctahedron (COh). Shin et al. (2012) and Rao et al. (2013) found that the stability of the COh structure exceeds that of the Ih structure for the Ag13 nanocluster, whereas the stability of the Ih structure exceeds that of the COh structure for the Cu13 nanocluster. The optical property response of Ag and Cu nanoparticles is dominated by a large surface plasmon resonance (SPR), which corresponds to the collective resonances of conduction electrons. Recently, quantum plasmonics in small metal clusters has been explored as a new aspect of plasmonics (Horiuchi 2012). The optical or plasmonic properties of bimetallic Ag–Cu clusters may be tuned by varying their composition and shape, as shown in the following examples. Ogut et al. (2006) examined the optical absorption spectra of Agn (n = 2–8) and Aun (n = 2– 3) clusters using the static and time-dependent density functional theory (TDDFT). Chen and Johnston (2007, 2008) calculated the optical and electronic properties of pure Ag13, Au13 and 13-atom Ag–Au clusters by DFT/local density approximation (LDA). Baishya et al. (2011) investigated the optical absorption spectra for the computed ground-state structures of pure copper clusters (Cun, n = 2–20) using TDDFT in adiabatic LDA (TDLDA). Weissker and Mottet (2011) investigated the optical absorption spectra of magic number noble-metal nanoparticles including Cu–Ag clusters by TDDFT (Delley 1990, 2000) calculations. They reported that the bimetallic Ag32Au6 core–shell cluster displays an intense peak corresponding to the SPR in the Ag cluster. However, the spectrum does not lie between the spectra of pure Ag38 and Au38 clusters. The copper core in the Ag38Cu6 cluster leads to a strong damping of this peak. Yan et al. (2012) performed a systematic study on the lowest-energy structures of medium-sized silver clusters Ag1 n (n = 21–29) using DFT calculations. They revealed that the experimental spectra well-fitted the optical absorption spectra obtained with the calculated structures. Bae and Aikens (2012) studied the evolution of the spectra of charged clusters (i.e. a closed shell) with octahedron, truncated octahedron and Ih shapes and sizes using TDDFT. Ma and Chen (2012) investigated the optical properties of [Ag13]?, [Ag12Cu1]? and [Cu13]? clusters with Ih symmetry using TDDFT methods. Although Ag–Cu nanoalloys have been extensively studied, some fundamental problems still need to be


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investigated. First, silver and copper are immiscible in their bulk forms, but their miscibility in the nanoscale is unknown. Second, Ih and COh are two basic structures, but the more stable structure for Ag13 and Cu13 clusters is still unclear. Moreover, the structural stability of a family of 13-atom Ag–Cu nanoclusters has not yet been determined. Third, reports on the Raman spectra of Ag–Cu nanoclusters are limited. Fourth and last, the optical property of neutral 13-atom Ag–Cu nanoclusters as open-shell systems has not been studied using TDDFT. The optical spectra prediction of nanoclusters is commonly based on the spin-unrestricted state for 13-atom neutral clusters. Previous optical calculations focus on pure Ag13 or Cu13 charged clusters, and few reports exist on the properties of Ag–Cu alloyed or mixed nanoclusters. In view of the prior art and its limitations, this study aims to determine the most stable structures for 13-atom Ag–Cu clusters, where the original structures have Ih shapes with different point groups. These structures are further optimised and the optical spectra of neutral clusters found with the lowest energy level are calculated. The electronic and magnetic properties of these stable nanoparticles are also investigated.

Model and computational method Atomistic potential In our computation, the atomistic potential employed is derived within the second-moment approximation to the tight-binding model and will be denoted in the following as Gupta potential. The Gupta potential is based on the semi-empirical many-body potential (Cleri and Rosato 1993; Gupta 1981; Rosato et al. 1989). The clusters have been modelled by a realistic many-body atom–atom potential for searching for the global energy minimum by genetic algorithm optimisation (Johnston 2003). The functional form contains a many-body attractive potential and a two-body repulsive potential. Cluster potential energy E is thus given by the sum over all the atoms of their bonding and repulsive energy: X E¼ Ejb þ Ejr ;

ð1Þ

j b

where the bonding term E is expressed as

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX 2 b n e2qðrij =r0 1Þ : Ej ¼ t

ð2Þ

i6¼j

The repulsive Born–Mayer term Er is Ejr ¼

N X

Aepðrij =r0 1Þ ;

ð3Þ

i6¼j

where N is the number of atoms, rij is the distance between atoms i and j in the cluster and r0 is the nearest-neighbour distance. The parameters A, r0, n, p and q for the pure species are fitted to several bulk experimental values, such as the cohesive energy, the lattice parameter, the elastic constants. The heteroatomic interactions are fitted to the solubility energy of an impurity A into a B bulk. The Gupta potential parameters used in this study are listed in Table 1 (Baletto et al. 2002). Global optimisation was performed using the Birmingham cluster genetic algorithm code, which has been described elsewhere (Johnston 2003), to find the GM of 13-atom Ag–Cu clusters. Simulation methods The above obtained Ag–Cu nanoclusters with the global energy minimum are selected as original configurations and optimised using DFT calculations, which are performed using the Dmol3 package included in the software Materials Studio (Delley 1990, 2000). Spinpolarised calculations are performed in real space within the framework of DFT-based semi-core pseudopotentials (DSPPs) (Delley 2002) with the double numerical plus polarisation (DNP) function. The Perdew–Burke– Ernzerhof and generalised gradient approximation (PBE/GGA) (1996) is used for the exchange–correlation function during geometry optimisation. The geometry of the cluster is fully optimised without symmetry and geometry constraints. Property calculations such as the binding energy, Mulliken atomic charges and molecular Table 1 Gupta potential parameters used for Ag–Ag, Ag–Cu and Cu–Cu interactions Parameters

A (eV)

n (eV)

p

q

˚) r0 (A

Ag–Ag

0.1031

1.1895

10.85

3.18

2.8921

Ag–Cu

0.0980

1.2274

10.70

2.8050

2.72405

Cu–Cu

0.0894

1.2799

10.55

2.43

2.556

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electric dipole moments and the Raman and vibration spectra of the clusters are performed using the PBE/ GGA. The optical spectra of the clusters are also calculated using the PBE/GGA with improved TDDFT (Delley 2010), i.e. spin-unrestricted calculations. The Raman spectra of the clusters are simulated by the wavelength of incident light at 514.5 nm and 10 K. A ˚ is used for grid integration. The global cutoff of 5.0 A self-consistent field procedures are performed with a convergence criterion of 10-6 Ha on the total energy. The PBE potential and DSPP/DNP basis set were used to calculate the lowest excited states of Ag dimer. Results show that the lowest excited state is 3.11 eV with an oscillation intensity of f = 0.36 au. These values agree well with the experimental value of 3.20 eV (Bechthold et al. 1985; Fedrigo et al. 1993) and earlier TDLDA result of 3.20 eV with f = 0.32 (Ogut et al. 2006; Idrobo et al. 2005), 3.11 eV with f = 0.33 (Tiago et al. 2009), and 3.2 eV (Yabana and Bertsch 1999; Yan and Gao 2008). Therefore, the selected potential and basis set are reasonably well used in calculating the lowest excited state of Ag clusters.


Figure 1 exhibits the lowest-energy structures for 13-atom Ag–Cu nanoclusters optimised using DFT from the pristine Ih clusters obtained by global

optimisation. Pure Cu13 and Ag13 lowest-energy structures after optimisation are marked as 0 and 13, at the end compositions of the cluster sequence. The pure Cu13 and Ag13 clusters have different lowestenergy motifs, Cu13 cluster is Ih, which coincides with the report of Shin et al. (2012), but differs from other reports (Darby et al. 2002; Oviedo and Palmer 2002; Longo and Gallego 2006; Chang and Chou 2004; Yang et al. 2006a, b; Zeng et al. 2010; Baishya et al. 2011; Weissker and Mottet 2011). No relative total energy difference is observed between the original and post-optimisation Cu Ih. Meanwhile, the COh Ag13 cluster coincides with some previous results (Weissker and Mottet 2011; Shin et al. 2012) but differs from others (Michaelian et al. 1999; Pereiro et al. 2007; Yang et al. 2007; Oviedo and Palmer 2002; Longo and Gallego 2006; Chang and Chou 2004; Yang et al. 2006a, b). The relative total energy difference of the original Ih and COh is 0.3272 eV. However, the COh pure Ag13 with D4h point group symmetry differs from a previous Ag13 which shows Oh point group symmetry (Chen and Johnston 2008). We classify the AgmCu13-m (m = 1–12) into two distinct groups: (1) core–shell structures, AgmCu13-m (m = 1, 6, 12) clusters; (2) amorphous, AgmCu13-m (m = 2–5, 7–11) clusters. The lowest-energy clusters for AgmCu13-m (m = 1, 6, 12) clusters (structures 1, 6 and 12, respectively) have CucoreAgshell structures that are favoured by the low energy of surface Ag atoms (surface energy ˚ 2, cohesive energy 2.95 eV/atom) as well as 78 meV/A

Fig. 1 Lowest-energy structures for 13-atom Ag–Cu nanoalloys. The number of Ag atoms, point group symmetry, relative total energy differences of original structures and lowest-energy

structures (number of square brackets, in electronvolts) are displayed. Copper atoms are shown in brown. The asterisks indicate hollow clusters. (Color figure online)

Results and discussion Lowest-energy geometric structures

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the small size and high cohesive energy of the interior ˚ 2, cohesive Cu atoms (surface energy: 113.9 meV/A energy: 3.49 eV/atom) (Ferrando et al. 2008a, b). This finding is similar to 34- and 38-atom Ag–Cu (Nunez and Johnston 2010).The Ag12Cu1, Ag1Cu12 and Ag6Cu7 clusters have the same shape as pure Cu13 clusters with Ih structures because the relative total energy differences of the original and lowest-energy structures are nearly neglected, however, they have different point group symmetries, namely, Ih, C5v and C5v, respectively. The lowest-energy structures for AgmCu13-m (m = 3, 4, 10) clusters (structures 3, 4 and 10, respectively) are hollow structures with both Ag and Cu atoms on the outer shell. The structures of AgmCu13-m (m = 2, 5, 7–9, 11) clusters (structures 2, 5, 7–9 and 11, respectively) are amorphous but not hollow; they have Cu–Cu or Ag–Cu bonds inside, and these amorphous clusters with different point group symmetries, i.e. C2, C1, C1, C1, Cs and C1, respectively. The original Ih and new amorphous structures for AgmCu13-m (m = 2–5, 7–11) clusters have large relative total energy differences, thereinto, the amorphous Ag2Cu11 cluster has the largest energy difference up to 1.2649 eV after optimised from the original Ih cluster. It is noteworthy that although the Ag6Cu7 and Ag7Cu6 clusters have similar compositions, their lowest-energy structures are significantly different.

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The Ag6Cu7 cluster is a Janus-separated CucoreAgshell cluster and the Ag7Cu6 cluster is amorphous alloyed motif. Energetic and electronic stability In the nanoscale, the energetic stability among a family of clusters is determined by calculating the excess energy with respect to the bulk alloy (D) and the second difference in energy (D2), both the minima in D and the maxima in D2 of a cluster indicate that this cluster is more stable than neighbour cluster. At the DFT level, D can be similarly defined as: D ¼ EðAgm Cun Þ m

EðAgÞ EðCuÞ n ; 13 13

ð4Þ

where E(AgmCun) is the DFT total energy for a Ag–Cu cluster, and E(Ag) and E(Cu) are the DFT energies calculated for pure Ag13 and Cu13 clusters, respectively. Clearly, D is the most reliable when the GM of pure clusters is correctly identified. Meanwhile, D2 (AgmCun) is defined as: D2 ¼ E Agmþ1 Cunþ1 þ EðAgm1 Cun1 Þ 2EðAgm Cun Þ; ð5Þ where E(AgmCun) is also the DFT total energy for a given cluster. Figure 2 compares with D, D2, energy gap Egap between the highest occupied molecular orbital

Fig. 2 Structural and electronic stability of the lowest-energy state for 13-atom Ag–Cu clusters

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(HOMO) and the lowest unoccupied molecular orbital (LUMO), and vertical ionisation potential (IPV) of the lowest-energy clusters with different Ag atom numbers. We can identify the stable compositions at 2, 7 and 11 Ag atoms because both the minima in D and the maxima in D2 concur in these clusters. Thus, the Ag2Cu11, Ag7Cu6 and Ag11Cu2 clusters are more stable than the other clusters. The Ag2Cu11 cluster with C2 is an amorphous motif with a smaller band gap (0.194 eV) but a larger IPV (5.7817 eV). Therefore, the Ag2Cu11 cluster has the highest energetic stability and high electronic stability. The Ag7Cu6 and Ag11Cu2 clusters are amorphous motifs, possess small band gaps (0.191 and 0.170 eV, respectively) and small IPVs (5.6161 and 5.3349 eV, respectively). At the same time, the Ag6Cu7 cluster with Ih has low energy stability, but the strongest electronic stability (the band gap of 0.424 eV and the IPV of 5.8417 eV). Thus, Ag2Cu11 with C2 symmetry, Ag7Cu6 with C1 symmetry and Ag11Cu2 with C1 symmetry clusters are the geometric magic clusters for 13-atom Ag–Cu nanoalloys. The Ag6Cu7 cluster with C5v symmetry is an electronic magic cluster for 13-atom Ag–Cu nanoalloys. Previously, magic clusters are reported as Ag8Au5 clusters bimetallic 13-atom Ag–Au cluster (Chen and Johnston 2008) and Ag27Cu7, Ag30Cu8, Ag27Cu13, Au34Cu6, Au17Cu23 for bimetallic Ag–Cu clusters (Ferrando et al. 2005, 2008a, b; Rapallo et al. 2005; Rossi et al. 2004; Barcaro et al. 2006; Molayem et al. 2011). We notice that Cu13, Ag1Cu12, Ag6Cu7, and Ag12Cu1 clusters with completely closed shell have large HOMO–LUMO gaps. This may be understood by the fact that high symmetry increases hybridization by way of strong overlapping of the wave functions. Bond length, bond order and charge–transfer effect on stability of Ag–Cu nanoalloys


Fig. 3 Bond order parameter and average bond length as functions of the composition for the lowest-energy structures of 13-atom Ag–Cu clusters

segregation of silver atoms. Therefore, AgmCu13-m (m = 1–12) clusters have some distortions caused by the different bond lengths, which is consistent with previous studies (Ferrando et al. 2008a, b; Nunez and Johnston 2010; Molayem et al. 2011). As expected, the average bond lengths of Cu–Cu in Ih Cu13, Ag1Cu12, Ag6Cu7 and Ag12Cu1 are closer to the bulk value of ˚ (Ferrando et al. 2008a, b), which may be 2.53 A another reason for forming core–shell structures of Ag1Cu12, Ag6Cu7 and Ag12Cu1 clusters. Calculation of the bond order parameter r is very helpful to give a quantitative measure for segregation. Positive values of r indicate the segregation of atoms in the cluster, whereas a value of zero indicates disorderly mixed clusters. Mixed and onion-like phases of clusters result in negative values of r (Molayem et al. 2011). The bond order parameter of an AgmCun cluster is defined as: r¼

Figure 3 shows the Ag–Ag, Ag–Cu and Cu–Cu average bond lengths of cluster. All results indicate that the metal–metal bond lengths follow the order Ag–Ag [ Ag–Cu [ Cu–Cu. The shorter and stronger Cu–Cu bonding facilitates the aggregation of Cu atoms at low Ag concentrations or linkage at low Cu concentrations. Observably, with the continuous replacement of Cu atoms by Ag, the additional Ag atoms occupy the surface sites of the cluster, leading to different degree distortions, even to the surface

123

NAgAg þ NCuCu NAgCu ; NAgAg þ NCuCu þ NAgCu

ð6Þ

where NAg–Ag, NAg–Cu and NCu–Cu are the number of nearest-neighbour bonds between Ag–Ag, Ag–Cu and Cu–Cu atoms, respectively. Figure 3 also shows bond order parameter r as functions of the composition for the lowest-energy structures of 13-atom Ag–Cu clusters. The r parameter is positive in all cases except the Ag7Cu6 cluster, suggesting some degree of segregation of Ag atom towards the surface or the formation of core–shell


structures. It is unexpected that the r in the Ag7Cu6 cluster is zero, indicating that the Ag7Cu6 cluster is disorderly mixed or alloyed cluster. Our previous work has shown that the structural order in 13-atom clusters induced the charge–transfer from the central atom to the peripheral ones or from peripheral atoms to other peripheral ones (Chen and Johnston 2008). Owing to the electronegativity difference between unlike Ag and Cu atoms, the directional charge–transfer is expected to happen in Ag–Cu nanoalloys. Induced charge–transfer may form highstability Ag–Cu clusters. Figure 4 shows the Mulliken atom charges in pure Cu13 and Ag13 clusters, and the lowest-energy structures of single atom-doped Ag13 and Cu13 clusters. In the pure Cu13 Ih cluster, charges– transfer are ?0.207 for the central Cu atom and 0.018 for a peripheral Cu atom. However, in the pure

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Ag13 COh cluster, the Mulliken charge–transfers are ?0.237 for the central Ag atom, ?0.039 for a fringe Ag atom and -0.049 for another fringe Ag atom. For the bimetal Ag–Cu clusters, a degree of charge– transfer from Cu to Ag atoms exists, because the Pauling electronegativity of Cu (1.90) is smaller than that of Ag (1.93). The less electronegative atom (Cu) lying at the Ih centre in Ag–Cu nanoalloys can attain maximum charge–transfer, namely, the charge–transfer from central atoms to the peripheral ones. For the Ag1Cu12 cluster, the charge–transfer of central Cu atom is only ?0.206 and those of peripheral Cu atoms and a peripheral Ag atom are -0.021 and -0.004, respectively, the transfers of Ag–Cu atom charges from the central Cu atom to peripheral Cu atoms and a peripheral Ag atom achieve maximum charge–transfer. Therefore, the Ag1Cu12 cluster with a surface Ag

Fig. 4 Mulliken atom charges (in units of electron charge) in pure Ag13 and Cu13 clusters (top), and the lowest-energy structures of single atom-doped Ag13 and Cu13 clusters (bottom)

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atom is more stable. For the case of the lowest energy cluster Ag12Cu1, the charge–transfer of central Cu atom is only ?0.232 and those of the fringe atom are 0.020 or -0.019, which arrive to maximum charge– transfer, thus the Ag12Cu1 cluster with a central Cu atom has the lower energy. Figure 5 shows the total net charges of Mulliken atoms in 13-atom Ag–Cu nanoclusters. The charges flow through the Cu–Cu, Ag–Cu and Ag–Ag bonds. For clusters with no Ag–Ag bond, the positive charges of clusters increase as Ag atoms are added. However, the appearance of Ag–Ag bonds allows the positive charges of clusters to decrease compared with the Ag4Cu9 and Ag5Cu8 clusters because the Pauling electronegativity of Cu is smaller than that of Ag. The positive charges of Ag7Cu6 (0.275) and Ag11Cu2 (0.331) clusters with Ag–Ag bonds are greater than those of neighbouring clusters, namely, Ag7Cu6 and Ag11Cu2, which have the maximum charge–transfers. Therefore, the Ag7Cu6 and Ag11Cu2 clusters are more stable than the others (including Ag6Cu7). For clusters with hollow structures, no bond exists inside and only 33 bonds are found in their structures, which are less than that in other structures. Thus, clusters with hollow structures only maximise the charge–transfers to form stable clusters, resulting in the appearance of more positive charges, unlike most clusters. Compared with the Ag2Cu11 cluster with a more stable structure and

Fig. 5 Net Mulliken charges of 13-atom Ag–Cu nanoclusters. The black up-triangle denotes positive charge and black downtriangle denotes negative charge. The hollow circle denotes the total net charges of Mulliken atoms in the 13-atom Ag–Cu nanoclusters. The black square with a value denotes clusters with an existing Ag–Ag bond. Otherwise, no Ag–Ag bond exists in the clusters. The hollow diamond denotes the total number of bonds in the clusters

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Ag3Cu10 clusters with a hollow structure, Ag2Cu11 cluster is more stable than the Ag3Cu10 cluster since the total number of bonds of the former cluster (37) is more than that of the latter cluster (33). Therefore, maximised charges transfer and more charges flow through bonds to form the most stable clusters in Ag– Cu nanoalloys. Optical absorption, Raman and vibration spectra of Ag–Cu clusters Figure 6 compares the calculated optical absorption spectra of pure Ag13, pure Cu13, Ag2Cu11 and Ag7Cu6 clusters with the PBE/GGA by improved TDDFT (with spin-unrestricted calculations). The blue shift of the maximum SPR peak becomes increasingly evident with increasing Ag atoms or decreasing Cu atoms, which has the same tendency as the reported charged 1þ Cu1þ and Ag1þ 13 ; Ag12 Cu1 13 clusters (Ma and Chen 2012). Pure Cu13 cluster has no intense band above 2.0 9 10-3 au from 1.3 to 2.2 eV. The intensity of the maximum SPR peak (1.55 eV and strength f = 0.0003 au) can be assigned to a linear combination of HOMO - 11 ? LUMO ? 6 and HOMO 10 ? LUMO ? 6 transitions, which are contributed by the up and down movement of the spin electron in the same decadency. Four distinct intense bands exist

Fig. 6 Absorption spectra of pure Ag13 (bottom), pure Cu13 (top), Ag2Cu11 (second), Ag7Cu6 (third) and Ag11Cu2 (fourth) clusters


in the Ag2Cu11 cluster at 1.60, 1.72, 1.90 and 1.92 eV with transition intensities above 2.0 9 10-3 au. The intensity of the maximum SPR peak (1.72 eV and f = 0.0033 au) can be assigned to a linear combination of HOMO - 1 ? LUMO ? 10 and HOMO ? LUMO ? 10 transitions. The Ag7Cu6 cluster has six intense bands at 1.33, 1.74, 1.95, 2.02, 2.13 and 2.15 eV with intensities above 2.0 9 10-3 au. The intensity of the maximum SPR peak (1.74 eV and f = 0.0058 au) can be assigned to a linear combination of HOMO - 5 ? LUMO ? 5 and HOMO 4 ? LUMO ? 5 transitions. The Ag11Cu2 cluster has ten intense bands at 1.08, 1.59, 1.74, 1.87, 1.97, 2.26, 2.31, 2.40, 2.45 and 2.49 eV with intensities above 2.0 9 10-3 au. The intensity of the maximum SPR peak (2.49 eV and f = 0.0079 au) can be assigned to a linear combination of HOMO 3 ? LUMO ? 12 and HOMO - 2 ? LUMO ? 12 transitions. The pure Ag13 cluster has only five intense bands at 2.44, 2.44, 2.46, 2.66 and 2.66 eV, and the intensity of its maximum SPR peak (2.46 eV and f = 0.0321 au) can be assigned to a linear combination of HOMO - 11 ? LUMO and HOMO 10 ? LUMO transitions. Although the energy of the maximum SPR peak of COh Ag13 is close to that of Ih Ag13 (2.50), the intensity of the maximum SPR peak of COh Ag13 is smaller than that of Ih Ag13 (above 8 au) (Chen and Johnston 2007). The intensity of the maximum SPR peak strengthens with increased Ag atoms and decreased Cu atoms. Pure Ag13 cluster with the COh structure shows the strongest SPR peak. As expected, in Ag–Cu nanoclusters, the dispersion behaviour of the surface plasmon polariton is highly sensitive to the electronic structure on the surface and the structural motif, but not to the internal structure of the cluster. Figure 7 compares the Raman spectra simulated by the wavelength of incident light at 514.5 nm and 10 K, as well as the vibration spectra for pure Ag13, pure Cu13, Ag2Cu11, Ag6Cu7, Ag7Cu6 and Ag11Cu2 clusters. All Raman and vibrational spectra exhibit many significant vibration modes. Altogether, the intensities of the maximum peak of the Raman spectra of these nanoalloys strengthen with increasing Ag atoms and decreasing Cu atoms. The maximum peak of the Raman spectrum of pure Cu13 cluster is at a wavenumber of 96.26 cm-1 and an oscillator strength f = 0.7167 au by the wavelength of incident light at 514.5 nm and 10 K; for Ag2Cu11,

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wavenumber = 105.99 cm-1 and f = 0.7370 au; for Ag6Cu7, wavenumber = 61.70 cm-1 and f = 1.7128 au; for Ag7Cu6, wavenumber = 82.11 cm-1 and f = 1.0741 au; for Ag11Cu2, wavenum-1 ber = 66.22 cm and f = 1.7171 au; for Ag13, wavenumber = 58.87 cm-1 and f = 2.0338 au. The calculated vibrational spectra of the clusters have no imaginary frequency using the GGA exchange–correlation function. In general, the ranges of the vibrational spectra decrease with increasing Ag atoms and decreasing Cu atoms. Vibration of pure Cu13 cluster with Ih symmetry point group ranges within 0–300 cm-1 with the maximum oscillator strength f = 1.7383 au at 110.55 cm-1. Vibration of the Ag2Cu11 cluster with C2 symmetry point group ranges within 0–253.42 cm-1 with the maximum oscillator strength f = 0.3160 au at 123.42 cm-1. Vibration of the Ag6Cu7 cluster with C5v symmetry point group ranges within 0–249.60 cm-1 with the maximum oscillator strength f = 1.4257 au at 106.91 cm-1. Vibration of the Ag7Cu6 cluster with C1 symmetry point group ranges within 0–252.66 cm-1 with the maximum oscillator strength f = 0.2425 au at 128.66 cm-1. Vibration of the Ag11Cu2 cluster with C1 symmetry point group ranges within 0–217.22 cm-1 with the maximum oscillator strength f = 0.3555 au at 161.22 cm-1. Vibration of the Ag13 cluster with D4h symmetry point group ranges within 0–199.40 cm-1 with the maximum oscillator strength f = 1.3718 au at 77.40 cm-1. The Ag13 and Cu13 clusters exhibit more significant vibrational modes than the Ag2Cu11, Ag7Cu6 and Ag11Cu2 clusters. These vibrational spectra indicate that the maximum oscillator strength is related to the cluster symmetry. Ferroelectric and ferromagnetic properties Figure 8 exhibits the ferroelectric properties of the lowest-energy structures of 13-atom Ag–Cu nanoalloys. The Ag12Cu1, pure metal Ag13 and Cu13 clusters have no dipole moment because of the high-symmetry distribution of Ag atoms on the surface. The AgmCu13m (m = 5–8) and Ag11Cu2 clusters have large dipole moments above 0.79 Debye, whereas the Ag1Cu12, Ag2Cu11 and Ag9Cu4 clusters have medium-sized moments. Among the hollow clusters, Ag3Cu10 has a large dipole moment, whereas Ag4Cu9 and Ag10Cu3 have medium-sized moments resulting from their structural asymmetry. The dipole moments of pure

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Fig. 7 Raman (left) and vibrational (right) spectra of pure Ag13 (bottom row), pure Cu13 (top row), Ag2Cu11 (second row), Ag6Cu7 (third row), Ag7Cu6 (fourth row) and Ag11Cu2 (fifth row) clusters. The Raman spectra of the clusters are simulated by the wavelength of incident light at 514.5 nm and 10 K

Ag13 metal clusters with D4h symmetry point group coincide with the previous calculations (Chen and Johnston 2008). These results indicate that no dipole moment exists regardless of the structure of pure Ag13 cluster (i.e. Ih or COh). As expected, the ferroelectric properties of 13-atom Ag–Cu nanoalloys are highly sensitive to structural symmetry or asymmetry. During the spin-polarised DFT calculation, first of all, we investigate the magnetic natures of bulk Ag and Cu, the results show that they have no magnetic properties. The magnetic moments of Ag–Cu nanoalloys are further calculated using the PBE functional, and DSPPs with DNP function. The calculated results of 13-atom Ag–Cu clusters are listed in Table 2. The

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Cu13, Ag1Cu12, Ag6Cu7 and Ag12Cu1 clusters have a small energy differences after optimisation from their original Ih, exhibit large magnetic moments (Sz) of 4.997–5.002 lB, and also exhibit large HOMO– LUMO gaps (D) of 0.397–0.469 eV. The Ag13 and AgmCu13-m (m = 2–5, 7–11) clusters have a large energy differences during optimisation, exhibit small magnetic moments (Sz) of 0.998–1.004 lB, and also exhibit small HOMO–LUMO gaps D of 0.147–0.234 eV. The magnetic moment of pure Ag13 with a COh is similar to a previous result (1.001 lB) (Chen and Johnston 2008) and differs from that of pure Ag13 with an Ih structure (4.998 lB; Chen and Johnston 2008 and 5.07 lB; Pereiro et al. 2007).


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Fig. 8 Dipole moment of the lowest energy structures of 13-atom Ag–Cu nanoalloys

Table 2 Symmetry point group (PG), HOMO–LUMO gap (D), vertical ionisation potential (IPV), bond order parameter (r), total positive charge (TPC) and total magnetic moment (Sz)

Figure 9 shows the atomic self-spin moments in pure Cu13, Ag7Cu6, Ag13 clusters. Pure Cu13 cluster with an Ih structure has a large total Sz of 5.000 lB; its core Cu atom has a small local moment of 0.224 lB and its surface Cu atom has a large local moment of 0.398 lB. However, pure Ag13 cluster with a COh structure has a small total Sz of 1.004 lB, the core Ag atom has a local moment of only 0.020 lB and surface Ag atoms also have local moments of only 0.019 and 0.208 lB. The lowest-energy Ag7Cu6 cluster has distorted structures with a total Sz of 1.000 lB. The magnetic moments of single-doped nanoalloys are close to the values of pure Cu13 cluster with similar geometry and much larger than that of pure Ag13 cluster (Table 2). Alloying also retains the

PG

Eb (eV)

D (eV)

IPV (eV)

TPC

r

Sz (lB)

Cu13

Ih

-27.81903

0.469

6.0602

1.000

0.207

5.000

Ag1Cu12

C5v

-27.11929

0.397

5.9881

0.714

0.206

4.999

Ag2Cu11

C2

-27.72398

0.194

5.7817

0.568

0.214

1.002

Ag3Cu10

Cs

-26.42797

0.231

5.6003

0.393

0.265

0.999

Ag4Cu9

C2v

-25.93562

0.152

5.3022

0.273

0.414

1.001

Ag5Cu8

C1

-25.20146

0.225

5.5803

0.143

0.197

0.998

Ag6Cu7

C5v

-23.89153

0.424

5.8417

0.238

0.216

4.997

Ag7Cu6 Ag8Cu5

C1 C1

-24.33580 -23.48574

0.191 0.185

5.6161 5.6116

0.000 0.029

0.275 0.254

1.000 1.000

Ag9Cu4

Cs

-22.57790

0.226

5.4524

0.353

0.237

1.001

Ag10Cu3

C1

-21.92471

0.234

5.4337

0.091

0.260

0.999

Ag11Cu2

C1

-21.36027

0.170

5.3349

0.222

0.331

1.001

Ag12Cu1

Ih

-19.93398

0.425

5.6850

0.429

0.232

5.002

Ag13

D4h

-19.00924

0.147

5.7047

1.000

0.393

1.004

Fig. 9 Local atomic magnetic moment (in Bohr magneton) of the lowest-energy clusters for pure Cu13 (left), Ag7Cu6 (middle) and Ag13 (right) clusters. The total magnetic moments of the Ag7Cu6 nanoalloys are 1.000 lB

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ferromagnetic arrangement found in pure clusters. These results show that the magnetic moment and HOMO–LUMO gap are related to the cluster structure and structural symmetry.

Conclusions The lowest-energy stable motifs for 13-atom Ag–Cu bimetallic nanoalloys have been identified, and reveal that these motifs originate from stronger Cu–Cu, Ag– Cu or Ag–Ag bonds and charge–transfers. The Ag2Cu11 with C2 symmetry, Ag7Cu6 with C1 symmetry and Ag11Cu2 with C1 symmetry clusters and the Ag6Cu7 cluster with C5v symmetry are the magic clusters for the 13-atom Ag–Cu nanoalloys. The Ag2Cu11 cluster exhibits high energy stability and strong electronic stability, as well as a multipole SPR mode and a small dipole moment. The Ag6Cu7 cluster has the strongest electronic stability (band gap 0.424 eV, IPV 5.8417 eV). The Ag7Cu6 cluster with a mixed, distorted motif indicates that silver and copper may be miscible on the nanoscale but not in bulk. The blue shift of the maximum SPR peak becomes more evident with increased Ag atoms and decreased Cu atoms. All Raman and vibrational spectra exhibit many significant vibration modes. The Raman spectra of the nanoalloys have wavenumbers ranging within 0–270 cm-1, and the vibrational spectra have wavenumbers ranging within 0–306.55 cm-1. Acknowledgments This study was supported by the National Natural Science Foundation of China (Grant Nos. 51271148 and 50971100), the Research Fund of State Key Laboratory of Solidification Processing in China (Grant No. 30-TP-2009), and the Aeronautic Science Foundation Program of China (Grant No. 2012ZF53073).

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