Alloying Effects on the Optical Properties of Ag–Au Nanoclusters from

ARTICLE pubs.acs.org/JPCC

Alloying Effects on the Optical Properties of Ag
Au Nanoclusters from TDDFT Calculations Giovanni Barcaro,† Michel Broyer,‡ Nicola Durante,† Alessandro Fortunelli,† and Mauro Stener*,§,|| †

CNR-IPCF, Istituto per i Processi Chimico-Fisici del Consiglio Nazionale delle Ricerche, via G. Moruzzi 1, 56124, Pisa, Italy CNRS, Universit
e de Lyon 1, LASIM UMR 5579, F-69622 Villeurbanne, France § Dipartimento di Scienze Chimiche e Farmaceutiche, Universita di Trieste, via L. Giorgieri 1, I-34127, Trieste, Italy Consorzio Interuniversitario Nazionale per la Scienza e Tecnologia dei Materiali, INSTM, Unita di Trieste, Trieste, Italy

)

‡

bS Supporting Information ABSTRACT: The optical properties of alloyed Ag
Au 147-atom cuboctahedral nanoclusters are theoretically investigated as a function of composition and chemical ordering via a time-dependent density functional theory (TDDFT) approach. Compositions 37
63%, 46
54%, and 63
37%, in Ag
Au, and three types of chemical ordering, core
shell, multishell and maximum mixing, are considered. Additionally, the optical spectra of pure Ag clusters with several structural motifs are also studied. It is found that (a) pure Ag clusters exhibit a neater dependence of the absorption peak on the shape of the cluster than Au clusters, (b) the absorption spectrum of alloyed clusters is not strongly affected by changes in chemical ordering, possibly because of their limited size, and (c) the optical absorption peak smoothly shifts to higher energies, gets narrower, and substantially gains in intensity by increasing Ag concentration, in excellent agreement with available experimental data. An analysis of the character of the electronic transitions mostly contributing to the absorption peak allows us to rationalize the notable difference between Ag and Au in terms of optical properties and the effect of alloying.

1. INTRODUCTION The physics of nanoscale metal clusters has strongly developed in recent years, following the continuous advances in synthetic and characterization tools that allow one to prepare and measure the properties of these systems with increasing precision1,2 and the developments of theoretical methods able to rationalize and predict experimental behavior.3 This triggers the promising applications of metal nanoclusters in several fields such as opto-electronic devices, thermal treatment of cancer, and “cell imaging”, i.e., colorimetric probes for DNA detection, catalysis, and magnetism.4 For optical applications, nanoclusters are very attractive5 because their electronic structure and consequently their optical response are sensitive to structural parameters such as size, shape, and—for multicomponent systems— composition and chemical ordering, i.e., the distribution of the different atomic species in the structural framework. For simple or noble metal nanoclusters, the main feature of the optical response to excitation by light is an absorption band in the UV
vis range related to the surface plasmonic resonance (SPR), i.e., a coherent and collective oscillations of the electrons involved in the metallic bond subjected to electromagnetic radiation of proper wavelength. Although this effect has been employed by humanity since thousands of years and despite numerous research studies,6,7 rigorous data on this topic are partly lacking and are thus strongly needed, especially for the smaller and the alloyed particles. Mie theory,5 which is appropriate for bulk systems, can be extended to nanoparticles via mesoscopic empirical models such as the DDA (discrete dipole approximation)8 or electrodynamical models,9 but the validity of r 2011 American Chemical Society

these models is questioned for metal nanoparticles of few nanometers in size and especially for more complicated cases such as multicomponent metallic nanoparticles or nanoalloys.10 In addition to structural morphology and chemical composition, in fact, the chemical ordering or compositional structure plays a fundamental role in determining the optical properties of nanoalloys, being one of the reasons why they display distinctive properties as compared to their constituents, but the exact extent of the interplay between local and collective electronic states in interatomic metallic bonding as a function of the distribution of the atomic species within the particle is still scarcely known, despite the substantial amount of experimental work devoted to the optical properties of bimetallic particles, especially on the Ag
Au system (see e.g. ref 11 and references therein) or systems involving silver or gold.12 The size effects in mixed silver
gold clusters with different proportions of gold have also been studied.13 To answer this need for rigorous information and respond to some of the basic questions still existing in this field (e.g., the exact dependence of the shape and peak of SPR upon nanoparticle size, shape, composition, chemical ordering, and environmental effects), first-principles approaches, in particular those based on time-dependent density functional theory (TDDFT),14 can make a decisive contribution. The computational effort of TDDFT, however, increases so rapidly with the size of the Received: September 9, 2011 Revised: October 31, 2011 Published: November 04, 2011 24085

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The Journal of Physical Chemistry C system that one needs to push this approach to its present limits to produce results on clusters of experimentally and physically interesting size. An effective tool, employed in recent work15
17 to enlarge as much as possible the size of computationally affordable systems, is to consider high-symmetry “magic” clusters, which are obtained when the number of atoms in the clusters is such that a structural shell is completed, such as icosahedral, decahedral, or octahedral.18 The exploitation of symmetry (with highorder point groups such as Oh or Ih) allows one to drastically reduce the computational effort by 1
2 orders of magnitude and to treat clusters of 150
200 atoms, large enough to start observing a resonance peak that will lead to the SPR. Using this approach, the optical properties of Au nanoclusters in the size range around 150
170 atoms were recently studied as a function of the approximation used for the DFT exchangecorrelation (xc-) functional and the shape or morphology of the nanocluster.17 From this study, it was found that the position of the peak in the absorption spectrum was weakly dependent on the shape of the Au cluster but was essentially related to its size and to the DFT methodology (xc-functional) used in the calculations. Similarly, the optical properties of tetrahedral Ag nanoclusters in the size range from 10 up to 120 atoms were also investigated,16 and it was found that the spectra evolve from molecular-like to plasmon-like behavior as the size increases, in agreement with classical electrodynamics models. Moreover, a linear dependence with respect to the inverse size of the cluster was also observed.16 For nanoalloys, the high symmetry assured by magic structures is particularly convenient as it can be exploited not only to reduce the computational effort but also to partition the atoms into “symmetry orbits”, i.e., groups of symmetry-equivalent species which are converted into one another by the operations of the symmetry group19,20 (these geometric “orbits”, as they are named in group theory terminology, should not be confused with electronic orbits). This exponentially reduces the configurational degrees of freedom of the system, making sampling of the nanoalloy configurational phase space feasible via first-principles simulations even for medium-sized particles.21 In the present article, we apply this magic-cluster approach to pure Ag and mixed Ag
Au nanoclusters of size around 150 atom, focusing on the effect of alloying on the optical response of these systems. We find that the absorption spectrum of Ag clusters is slightly more sensitive to the particle shape than that of Au clusters, that configurations with rather different chemical ordering (such as core
shell vs intermixed ones) present spectra with similar position and intensity but different shape, and that the plasmonic peak shifts to higher energies, gets relatively narrower, and gains in intensity by increasing the Ag concentration in the cluster. All these data are in excellent agreement with and allow one to rationalize available experimental information. This opens promising perspectives for applications also in view of the possibility of investigating more complicated systems such as those presenting chiral and magneto-optical effects.22 The article is organized as follows. In section 2, the theoretical approach is described in some detail. Results and discussion are presented in section 3, while conclusions are summarized in section 4.

2. THEORETICAL METHOD A scalar relativistic (SR) self-consistent field (SCF) Kohn
Sham (KS) formalism has been employed to describe the cluster

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Figure 1. Structures of the cube-octahedral bimetallic clusters [Ag55Au92]5+ and [Ag68Au79]5+. For [Ag55Au92]5+ the three different chemical ordering are shown as well: core
shell (CS), multishell (MS), and maximum mixing (MM).

electronic structure at the density functional theory (DFT) level. Relativistic effects have been included at the SR zeroth-order regular approximation (ZORA) level23 using the ADF suite of programs.24,25 Optical spectra have been calculated at the TDDFT level, which involves solving the following eigenvalue equation:14 ΩFI ¼ ωI 2 FI

ð1Þ

where Ω is a four index matrix with elements Ωiaσ,jbτ, the indices consisting of products of occupied-virtual (ia and jb) KS orbitals, while σ and τ refer to the spin variable. The eigenvalues ωI2 correspond to squared excitation energies while the oscillator strengths are extracted from the eigenvectors FI. The Ω-matrix elements can be formulated in terms of KS eigenvalues (ε) and the coupling matrix K (built employing the KS orbitals); in the present work the adiabatic local density approximation (ALDA)26 for the xc-kernel has been employed. Magic metal clusters are metal aggregates which present electronic and/or structural shell closure, often associated with a peculiar energetic stability. The high symmetry of structurally magic clusters is here exploited in two ways. First, the ADF code efficiently exploits the point group symmetry to reduce the computational effort. The computational effort is typically reduced by a factor of the order of the dimension of the symmetry group in some parts of the code (for example, the calculation of the numerical integrals) or even greater in some other parts (e.g., the dimension of the matrices to be diagonalized can be reduced by a factor roughly proportional to the order of the symmetry group, so that the computational effort to diagonalize them is reduced by a power of the symmetry group of at least 2) as well as the exploitation of Wigner
Eckart theorem in the TDDFT part. Moreover, as noted above by partitioning the atoms into “symmetry orbits”19,20 and by restricting their occupation to like atomic species, one can circumvent the chemical ordering problem, i.e., the combinatorial increase in the number of possible “homotops” (isomers sharing the same skeletal structure and composition but differing in the mixing pattern)10 and reduce the configurational degrees of freedom of the system from the number of atoms to the number of symmetry orbits. This exponentially decreases the number of distinct homotops, making first-principles simulations feasible even for medium-sized 24086

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The Journal of Physical Chemistry C particles (see e.g. the study of segregation patterns of PdPt nanoparticles in ref 21). In the present work, we focus on a specific size and shape (a 147-atom cuboctahedral configuration, see Figure 1). Five different compositions were considered, ranging from pure Au (already studied in ref 17), Au147, and increasing the Ag content to ≈37%, Ag55Au92; ≈46%, Ag68Au79; ≈54%, Ag79Au68; ≈63%, Ag92Au55, until pure Ag, Ag147. The symmetry orbit structure of these configurations can be described as follows. Starting from regular octahedra, cuboctahedra are obtained by truncating symmetrically their six vertices, obtaining square and triangular facets (see Figure 1). In cuboctahedra atoms are arranged in concentric layers. In detail, the 147-atom cuboctahedron is generated by truncating a 231-atom octahedron and is formed by four layers: the first one corresponds to the central atom, the second one to an internal 12-atom layer, and the third one to an internal 42-atom layer, while the fourth one is composed of 92 surface atoms. The number of symmetry orbits is 9: one symmetry orbit each in the first two layers (with 1 and 12 atoms, respectively), three symmetry orbits in the third layer [12 atoms on vertexes, 24 on edges, and 6 on (100) facets], and 4 symmetry orbits in the fourth layer [12 atoms on vertexes, 48 on edges, 24 on (100) facets, and 8 on (111) facets]. At composition 55:92, three different chemical orderings are selected with a rather diverse amount of mixing and are shown in Figure 1. A core
shell (CS) configuration is obtained by populating all the core atoms with one species and all the surface atoms with the other one; multishell (MS) is similar to core
shell but now the 12 atoms in the second layer are exchanged with atoms on the surface vertexes, thus producing an A/B/A/B multishell arrangement, whereas maximum mixing (MM) presents a more thorough intermixing of the two species. By defining the number of bonds in the cluster as the number of atom
atom contacts with distance less than 3 Å, the percent of mixed (i.e., Ag
Au) bonds in the clusters reads 33.9% for CS, 54.6% for MS, and 59.2% for MM. CS realizes the minimum mixing compatible with Oh symmetry, MM the maximum mixing, and MS represents an intermediate degree of mixing. At composition 68:79 (which is closer to equimolar) the arrangement depicted in Figure 1d is selected which realizes a very thorough intermixing (the maximum compatible even with a lower D2h symmetry) and is not reminiscent of a multishell structure: the percent of mixed bonds for this chemical ordering is 64.0%, which is close to the maximum obtainable in a 147-atom cuboctahedron. Gold, silver, and mixed Ag
Au bimetallic nanoclusters with optimized geometries have been considered. For geometry optimization, the scalar relativistic ZORA formalism was used, with the double zeta (DZ) ZORA basis set of Slater type orbitals (STO) included in the ADF database, with frozen core (FC) up to 4f and 4p shells for Au and Ag, respectively. The basis set for Au contains two STO functions for each of the 5s, 6s, 5d, and 5p shells as well as one STO function for the 6p shell, while for Ag the basis set consists of two STO functions for each of the 5s and 4d shells as well as one STO function for the 5p shell. The local density approximation (LDA) was employed as the exchangecorrelation (xc-) functional in the geometry optimizations, with the VWN parametrization.27 The TDDFT calculations were performed at the optimized geometries, using the same DZ 4f/ 4p frozen core ZORA basis sets. In the TDDFT calculations, the LB94 xc-functional28 has been employed, which has proven to be more accurate than LDA from comparison with experiment.17 The calculated TDDFT spectra have been obtained extracting at

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Figure 2. Calculated TDDFT LB94 photoabsorption spectra of pure gold and silver clusters. In boxes (a) and (b) Td (green line) and CO (red line) shapes are compared.

least 300 roots. Limiting the number of roots (which is necessary to obtain a stable numerical algorithm17) entails that the highenergy component of the spectrum is truncated. However, the number of roots we use is sufficient to cover and focus on the most interesting part of the spectrum, i.e., the optical region, and allows us to disentangle from the high-energy, less interesting part. As already found before, the stability of Davidson algorithm is improved if tighter SCF convergence criteria are employed. The numerical stability of the DZ TDDFT spectra calculations up to 300 roots for Oh [Au146]2+ is demonstrated by the analysis reported in Figure S1 of the Supporting Information. In the upper panel of Figure S1 the low energy part of the spectrum is enlarged, and it can be observed that if 400 roots are requested, the spectrum starts to show some numerical instabilities, which almost disappear if 350 roots are requested. Therefore, we assume that 300 roots can be safely extracted. For an easier comparison, all the calculated discrete spectra have been broadened with Gaussian functions of fwhm = 0.12 eV. Calculations (geometry optimization as well as TDDFT optical spectra) have been performed employing Oh point group symmetry for octahedral, cubic, and cuboctahedral clusters, while the icosahedral clusters have been calculated using the D5d point group symmetry as the complete Ih point group is not supported by ADF.

3. RESULTS AND DISCUSSION The first issue when dealing with nanoalloys is how to model the chemical ordering or compositional structure.29,30 Several mixing patterns are known in the literature,31 such as core
shell or in general multishell ordering (in which concentric shells of different elements alternate), random solutions, ordered arrangements (more or less related to the known ordered phases of 24087

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The Journal of Physical Chemistry C bulk alloys), and Janus-like segregation typical of immiscible components. As discussed in section 2, in the present work we focus on 147-atom cuboctahedra of composition ranging between pure Au and pure Ag: Ag55Au92, Ag68Au79, Ag79Au68, Ag92Au55. At compositions 55
92 three different chemical orderings were considered: CS, MS, and MM, whereas at 68
79 only MM was considered. In Figure 2, we report the calculated spectra of various pure silver and gold clusters. In the first panel (a) a comparison is done between the tetrahedral Au120 and the cube-octahedral [Au147]5+ clusters, in order to identify shape effects on the optical spectra and provide comparison with previous work. In ref 17 we considered various shapes which were all ascribed to octahedral or icosahedral point groups, giving rather “spherical” structures. The tetrahedral shape, which has been thoroughly investigated in ref 16, is rather different, with sharper vertexes which could strongly affect the plasmon resonance as a consequence of the deviation from the spherical model assumed in the classical Mie theory. The shape effect is quite evident: going from cuboctahedron to tetrahedron the peak maximum is red-shifted by several tenths of an electronvolt, and the intensity is enhanced by more than a factor of 2. The same comparison for silver is shown in panel b: the effect is now much larger, with a red shift of 0.9 eV and a doubled intensity; moreover, also a peak narrowing is evident which halves the peak width in Ag120 Td. It is worth noting that the calculated optical spectra of silver clusters with respect to gold ones are characterized by a much more intense (by more than an order of magnitude) and narrow peak followed by very weak structures at higher energy, whereas in gold clusters the intensity is not focused on a very narrow peak but is distributed over a wider energy range. This effect can be ascribed to the different electronic structures of the two metals: for the silver atom the calculated 4d/5s gap (eigenvalue difference) is ≈3.2 eV, while for gold atom the calculated 5d/6s gap is only ≈1.5 eV, meaning that for silver the 4d shell is too deep to participate in the valence states involved in the excitation, while for gold the 5d and the 6s shells interact appreciably and the relevant valence states are hybrids between s and d bands.32 The absence of 4d contribution for silver clusters and the role of 5d orbitals for gold clusters can be verified in the tables reported in the Supporting Information, where the most intense transitions are analyzed in terms of leading configurations and the nature of the occupied-virtual orbitals involved. For this reason electrons in silver clusters behave more like a free electron gas, giving rise to well-defined intense and sharp plasmonic features, while gold electrons are more localized as 5d functions are less diffuse than 6s ones, and therefore the plasmonic response is strongly damped. The absolute excitation energies are much larger in silver than in gold clusters; in fact, the maximum of the tetrahedral clusters goes from 2.82 eV for Au120 to 3.66 eV for Ag120, while for the cuboctahedral ones the maximum falls at 3.28 and 4.54 eV for [Au147]5+ and [Ag147]5+, respectively. The stronger sensitivity of the plasmon peak on sharp-vertex structure for silver clusters as compared to gold clusters (Figure 2b versus Figure 2a) is similar to the sensitivity of the plasmon peak to small geometry changes observed experimentally on quasispherical clusters in single particle spectroscopy.33 Indeed, an ellipsoidal silver cluster with an aspect ratio of 0.97 (still close to 1 corresponding to the sphere) has a noticeable shift as compared to a sphere with light polarization along one of the symmetry axis.33 For gold clusters this effect is smaller due the interaction with interband transition that limits and damps this dependence.

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Figure 3. Calculated TDDFT LB94 photoabsorption spectra of cubeoctahedral bimetallic clusters. Upper line: [Ag55Au92]5+ and [Au55Ag92]5+ with CS, MS, and MM chemical ordering. Lower line: [Au68Ag79]5+ and [Ag68Au79]5+.

For a complete comparison, in panels c
f we have also reported the calculated spectra of silver clusters with the same structures as those considered in our previous work on gold clusters: octahedral [Ag146]4+ (c), cuboctahedral [Ag147]5+ (d), icosahedral [Ag147]
(e), and cubic [Ag172]4+ (f). The cluster charges have been chosen so as to achieve closed-shell electronic structures, and interestingly they are the same as in gold clusters, with the exception of the octahedral cluster whose gold counterpart is [Au146]2+. Inspecting Figure 2c
f, we observe little differences along the series, all the spectra being characterized by a strong peak contributed by few close transitions and the peak maximum not shifting much in energy: 4.37 eV (c), 4.54 eV (d), 4.50 eV (e), and 4.37 eV (f), so changing by 0.17 eV along the series. Apart from the values of the peak position and width, the behavior of the optical absorption of silver clusters is hence similar to that of gold clusters.17 As for gold clusters the theoretical spectra are also slightly blue-shifted as compared to experiment. For example, Meives-Broer et al. find 3.82 eV for Ag21+ and 4.02 eV for Ag9+,34 while Bonaci
c-Koutecky et al. find about 4 eV for Ag9+.35 For clusters Agn of 1.5 nm in diameter (n ∼ 104) in an alumina matrix, Cottancin et al.36 find the plasmon peak at 2.95 eV which corresponds to 3.8 eV in vacuum after correcting for the dielectric constant of the matrix. This slight blue shift is due to limitations in the Slater basis set16,37 and should not qualitatively affect the results (note that the quality of the basis set is the same for Ag and Au). In Figure 3, the spectra of the bimetallic clusters are reported: in the first row [Au55Ag92]5+ and [Ag55Au92]5+ are considered with different chemical ordering, namely CS, MS, and MM, as described above. The first difference that is immediately apparent between the two compositions is relative to the position in energy of the spectral features: for the [Au55Ag92]5+ clusters the intensity starts to rise around 3.5 eV, whereas for [Ag55Au92]5+ this occurs at 3.2 eV and is less sharp and intense than in the former case. These effects are of general significance: as the concentration of gold increases, the absorption peak is redshifted and becomes less intense and broader, in tune with the difference between the spectra of pure silver and gold clusters. The spectra are less sensitive to chemical ordering than composition, as apparent from an inspection of Figure 3. However, some differences can be mentioning in comparing the 24088

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Figure 4. Photoabsorption spectra of cube-octahedral bimetallic clusters with increasing silver concentration. Left box: calculated TDDFT LB94 spectra; right box: experimental spectra.13

Figure 5. Analysis of the calculated electron transitions of the photoabsorption spectra of [Ag55Au92]5+ and [Au55Ag92]5+ with CS chemical ordering.

optical response of clusters with different chemical orderings. In particular, the spectra of [Au55Ag92]5+ are characterized by a double feature, with a first peak around 3.7
3.8 eV and a second one around 4.0
4.2 eV, but the relative intensity of these peaks changes appreciably for CS, MS, and MM cluster. A similar effect is observed for [Ag55Au92]5+, but less evident due to peak broadening. It would be interesting to ascertain whether the “double peak” spectral feature observed at 55:92 composition is due to chemical ordering or composition effects. From electrodynamical models one expects a splitting of the absorption peak as a result of a core
shell arrangement.13 It is not easy to answer this question from the present calculations, due to the limited size of the clusters here investigated, composed of only four layers, so that even MM clusters are still slightly reminiscent of a multishell structure. The clusters [Au68Ag79]5+ and [Ag68Au79]5+ at a different composition were then selected because they represent

a situation with a very effective mixing and can be compared with the MM structures at 55:92 composition. Their spectra are shown in the bottom row of Figure 3. We find some resemblance between these spectra and the MM ones, but it should also be noted that for [Ag68Au79]5+ the broadening is such that a double peak profile is hardly discernible. The picture which emerges from this analysis is that for bimetallic gold
silver clusters of this size a double peak spectral feature is present for valence photoabsorption which is more clear-cut when the clusters have higher silver concentration and that chemical ordering influences the intensity distribution between the two peaks. However, it should be recalled that at such small sizes, even for pure clusters, a fragmentation of the SPR can in principle be expected, due to quantum size effects,38 so that the doublepeak structure is likely to be associated with these. It is of paramount importance to compare the present calculations with available experimental data, in order to validate the computational approach for bimetallic gold
silver nanoalloys and therefore to have a predictive tool for future applications. The experimental photoabsorption trend with respect to gold concentration in Ag
Au nanoclusters13 is reported in Figure 4 together with the present calculated spectra for the CS chemical ordering. As can be seen from an inspection of Figure 4, the agreement between theory and experiment is qualitatively very good. In particular, theory is able to reproduce accurately two effects found in the experiment, namely the increase in both energy and intensity of plasmon resonance with increasing silver concentration. It can be added that an increase in the energy and intensity of the plasmon resonance with increasing Ag concentration has also been recently observed in coated 144-atom systems (note however that only 84 delocalized electrons are present in the neutral species), together with a peculiar double-peak feature.39 A decrease in the ratio between peak width and height (relative narrowing) with increasing Ag concentration can also be observed in the theoretical spectra, again in excellent agreement with experiment. From a more quantitative point of view, since the experimental profile is rather smooth, it is convenient to discuss the trend in terms of the energy shift of the peak center. Gold concentration in [Au55Ag92]5+ and [Ag55Au92]5+ is 37% and 63%, respectively, i.e., lies in between the concentration of the experimentally measured clusters, which are 25%, 50%, and 75%. In the experiment for silver clusters of 2.3 nm (∼370 atoms) embedded in alumina matrix, the plasmon peak shifts roughly linearly with the silver concentration from 2.45 eV for pure gold to 2.93 eV for pure silver. By accounting for the influence 24089

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The Journal of Physical Chemistry C of the matrix,35 this corresponds to a linear shift from 2.75 to 3.75 eV in vacuum. This is in very good qualitative agreement with theoretical calculations (from 3.2 to 4.4 eV), except for a global blue shift as discussed above. Indeed, this agreement can be only qualitative. First, the size of the clusters was somewhat larger in the experiment (∼370 atoms as compared to 147). More importantly, in the experiment the clusters did not possess a welldefined geometry:13 the measurements were performed on an ensemble with a finite size distribution and a shape fluctuating around the spherical one, which broadened the experimental plasmon resonance. Taking into account these provisos the agreement between theory and experiment can be considered as qualitatively very good. Finally, we have analyzed in detail the electronic states giving rise to the most intense absorption features, in order to identify the nature of the photoabsorption transitions in terms of the electronic structure. To this end we have focused for simplicity on clusters with CS chemical ordering and selected, behind each peak in the absorption spectrum, the most intense transitions which are representative of the peak. For these transitions we have analyzed their nature in terms of the leading excited oneelectron configurations and, for each excited configuration, the molecular orbitals involved, characterized by the contribution of Ag and Au atomic functions. This analysis—reported in full for all the clusters in Tables 1
11 of the Supporting Information— is shown in Figure 5 in representative cases to summarize the most relevant findings. For the [Ag55Au92]5+ cluster the transition labeled A (excitation 159 in Table 2 of the Supporting Information) is the most intense within the first peak and corresponds essentially to a transition from occupied gold Au 6s band to an unoccupied band with a mixed nature of Au 6p and Ag 5p. The other intense transitions behind the second peak labeled B and C (excitations 241 and 287, respectively, in Table 2 of the Supporting Information) involve only 6s and 5d gold functions, the silver participation being very low. Therefore, we can give the following assignment of the spectrum: the main transitions start from gold occupied bands, and the two peaks are characterized by different silver involvement in the final state: the first peak corresponds to a transition to mixed Au 6p/Ag 5p states, while the second peak has contributions from only Au 6s/ 6p atomic functions. This picture is somehow surprising, since it could be expected that the higher energy peak should have a greater contribution from silver since pure silver clusters display a plasmon resonance at higher energy with respect to gold clusters of the same size. The same analysis on the [Au55Ag92]5+ cluster (features D, E, and F correspond to excitations 161, 212, and 243 of Table 3 of the Supporting Information) indicates that the first peak has a prominent Ag 5p nature in the final state and a mixed Au 6s/Ag 5s in the initial state, while the second peak (contributed by E and F) shows only silver contribution in the final states, the initial ones being essentially Au 5d. Also in this case we find that the silver contribution is higher in the first peak. From the analysis of both clusters it is evident that although Ag
Au bimetallic clusters give rise to a double peak structure, it is not possible to attribute the two peaks to the separate metals, but they are rather the result of a complex remixing of atomic contributions in the cluster bands. It can thus be concluded that simplified computational models based on compositionweighted averages of individual gold or silver dielectric functions can be better replaced by the present scheme, in which the photoabsorption of the bimetallic systems is calculated ab initio without any assumption on the individual Au or Ag dielectric

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function. Similarly, in the semiquantal model used by Gaudry et al.,13 a better agreement is obtained when the dielectric constants of AuAg alloy thin films are used to extract the contribution of d electrons εd, necessary to implement this model.

4. CONCLUSIONS The reasons of the interest arisen by metal alloy nanoparticles (or “nanoalloys”) lies in the fact that their structural, chemical, and physical properties can be tuned by varying the composition and the arrangement and the degree of atomic mixing. In the present work, we have focused on the optical properties of Ag
Au nanoalloys of size around 150 atoms via TDDFT calculations and studied their dependence on composition and chemical ordering. The aim was to provide rigorous data against which the experimentally prepared materials can be tested, going beyond electrodynamical mesoscopic models based on averaged properties of the component species. Several intriguing results emerged from this study: (a) pure Ag clusters exhibit a more definite dependence of the absorption peak on the shape of the cluster with respect to Au clusters; (b) the absorption spectrum of the alloyed nanoclusters is not strongly affected by changes in chemical ordering, possibly because of the limited size of the clusters, but a fragmentation of the absorption peak can be observed depending on intermixing and composition; (c) the optical absorption peak smoothly shifts to higher energies, gets relatively narrower, and substantially gains in intensity by increasing Ag concentration, in excellent agreement with the available experimental data. An analysis of the absorption spectra aimed at understanding the electronic origin of the fundamental electronic transitions and their dependence upon the constituent elements and the selected variables also allows us to rationalize the notable difference between Ag and Au in terms of optical properties and the effect of alloying. To the best of our knowledge, this is the first time that a first-principles TDDFT approach is employed to investigate the optical properties of nanoalloys and of a size large enough to allow a significant comparison with experiment. We hope that this work will contribute to set up a theoretical framework in the field of the optical response of nanoalloys and thus provide insights in the search of novel systems with specific properties (such as chiral and magnetooptical effects) and/or to the use of the optical signature as a tool to characterize the particle structure. ’ ASSOCIATED CONTENT

bS

Supporting Information. Tables reporting the calculated most intense transitions and Figure S1 with an analysis of the TDDFT numerical stability. This material is available free of charge via the Internet at http://pubs.acs.org.

’ ACKNOWLEDGMENT Computational support from CINECA supercomputing centre within the AuMixSPR ISCRA project is gratefully acknowledged. A.F. acknowledges financial support from the SEPON project within the ERC Advanced Grants. This work has been supported by MIUR (Programmi di Ricerca di Interesse Nazionale PRIN 2006 and 2008) of Italy. Networking from the MP0903 COST Action is also acknowledged. 24090

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’ REFERENCES (1) Ma, Y. Y.; Li, W. Y.; Cho, E. C.; Li, Z. Y.; Yu, T. K.; Zeng, J.; Xie, Z. X.; Xia, Y. N. ACS Nano 2010, 4, 6725. (2) Del Fatti, N.; Christofilos, D.; Vall
ee, F. Gold Bull. 2008, 41, 147–158. (3) Chen, H.; McMahon, J. M.; Ratner, M. A.; Schatz, G. C. J. Phys. Chem. C 2010, 114, 14384. (4) Burda, C.; Chen, X.; Narayanan, R.; El-Sayed, M. A. Chem. Rev. 2005, 105, 1025. (5) Kreibig, K.; Vollmer, M. Optical Properties of Metal Clusters; Springer: New York, 1995. (6) Halas, N. J.; Lal, S.; Chang, W.-S.; Link, S.; Nordlander, P. Chem. Rev. 2011, 111, 3913. (7) Morton, S. M.; Silverstein, D. W.; Jensen, L. Chem. Rev. 2011, 111, 3962. (8) Ye, E.; Win, K. Y.; Tan, H. R.; Lin, M.; Teng, C. P.; Mlayah, A.; Han, M.-Y. J. Am. Chem. Soc. 2011, 133, 8506. (9) Murray, W. A.; Suckling, J. R.; Barnes, W. L. Nano Lett. 2006, 6, 1772. (10) Jellinek, J.; Krissinel, E. B. Chem. Phys. Lett. 1996, 258, 283. (11) Cottancin, E.; Lerm
e, J.; Gaudry, M.; Pellarin, M.; Vialle, J. L.; Broyer, M.; Pr
evel, B.; Treilleux, M.; Melinon, P. Phys. Rev. B 2000, 62, 5179. (12) Broyer, M.; Cottancin, E.; Lerm
e, J.; Pellarin, M.; Del Fatti, N.; Vall
ee, F.; Burgin, J.; Guillon, C.; Langot, P. Faraday Discuss. 2008, 138, 137. (13) Gaudry, M.; Lerm
e, J.; Cottancin, E.; Pellarin, M.; Vialle, J. L.; Broyer, M.; Pr
evel, B.; Treilleux, M.; P. M
elinon, P. Phys. Rev. B 2001, 64, 085407. (14) Casida, M. E. In Recent Advances in Density-Functional Methods; Chong, D. P., Ed.; World Scientific: Singapore, 1995; p 155. (15) Stener, M.; Nardelli, A.; De Francesco, R.; Fronzoni, G. J. Phys. Chem. C 2007, 111, 11862. (16) Aikens, C. M.; Li, S.; Schatz, G. C. J. Phys. Chem. C 2008, 112, 11272. (17) Durante, N.; Fortunelli, A.; Broyer, M.; Stener, M. J. Phys. Chem. C 2011, 115, 6277. (18) Marks, L. D. Philos. Mag. A 1984, 49, 813. (19) Fortunelli, A.; Velasco, A. M. J. Mol. Struct. (THEOCHEM) 1999, 487, 251. (20) Wales, D. J. Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge University Press: Cambridge, 2004. (21) Barcaro, G.; Fortunelli, A.; Polak, M.; Rubinovich, L. Nano Lett. 2011, 11, 1766. (22) Ebert, H. Rep. Prog. Phys. 1996, 59, 1665. (23) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993, 99, 4597. (24) Baerends, E. J.; Ellis, D. E.; Ros, P. Chem. Phys. 1973, 2, 41. (25) Fonseca Guerra, C.; Snijders, J. G.; te Velde, G.; Baerends, E. J. Theor. Chem. Acc. 1998, 99, 391. (26) Gross, E. K. U.; Kohn, W. Adv. Quantum Chem. 1990, 21, 255. (27) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (28) Van Leeuwen, R.; Baerends, E. J. Phys. Rev. A 1994, 49, 2421. (29) Calvo, F.; Cottancin, E.; Broyer, M. Phys. Rev. B 2008, 77, 121406. (30) Cerbelaud, M.; Ferrando, R.; Barcaro, G.; Fortunelli, A. Phys. Chem. Chem. Phys. 2011, 13, 10232. (31) Ferrando, R.; Jellinek, J.; Johnston, R. L. Chem. Rev. 2008, 108, 845. (32) Desclaux, J. P.; Pyykko, P. Chem. Phys. Lett. 1976, 39, 300. (33) Baida, H.; Billaud, P.; Marhaba, S.; Christofilos, D.; Cottancin, E.; Crut, A.; Lerm, J.; Maioli, P.; Pellarin, M.; Broyer, M.; Del Fatti, N.; Vallee, F.; Sanchez-Iglesias, A.; Pastoriza-Santos, I.; Liz-Marzan, L. M. Nano Lett. 2009, 9, 3463. (34) Tiggesb€aumker, J.; K€oller, L.; Lutz, H. O.; Meiwes-Broer, K. H. Chem. Phys. Lett. 1992, 190, 42. (35) Mitri
c, R.; Petersen, J.; Kulesza, A.; Bonaci
c-Kouteck
y, V.; Tabarin, T.; Compagnon, I.; Antoine, R.; Broyer, M.; Dugourd, P. J. Chem. Phys. 2007, 127, 134301.

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(36) Cottancin, E.; Celep, G.; Lerm
e, J.; Pellarin, M.; Huntzinger, J. R.; Vialle, J. L.; Broyer, M. Theor. Chem. Acc. 2006, 116, 514. (37) Harb, M.; Rabilloud, F.; Simon, D. Phys. Chem. Chem. Phys. 2010, 12, 4246. (38) Lerm
e, J.; Baida, H.; Bonnet, C.; Broyer, M.; Cottancin, E.; Crut, A.; Maioli, P.; Del Fatti, N.; Vall
ee, F.; Pellarin, M. J. Phys. Chem. Lett. 2010, 1, 2922. (39) Kumara, C.; Dass, A. Nanoscale 2011, DOI: 10.1039/c1nr10429b.

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dx.doi.org/10.1021/jp2087219 |J. Phys. Chem. C 2011, 115, 24085–24091