Global Minimum Pt13M20 (M = Ag, Au, Cu, Pd) Dodecahedral Core

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Global Minimum Pt M (M=Ag, Au, Cu, Pd) Dodecahedral Core-Shell Clusters Dora Julia Borbon-Gonzalez, Alessandro Fortunelli, Giovanni Barcaro, Luca Sementa, Roy L. Johnston, and Alvaro Posada-Amarillas J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 04 Dec 2013 Downloaded from http://pubs.acs.org on December 10, 2013

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The Journal of Physical Chemistry

Global Minimum Pt13M20 (M=Ag, Au, Cu, Pd) Dodecahedral Core-Shell Clusters

Dora J. Borbón-González1, Alessandro Fortunelli2,*, Giovanni Barcaro2, Luca Sementa2, Roy L. Johnston3,*, Alvaro Posada-Amarillas4,*

1

Departamento de Matemáticas, Universidad de Sonora, Blvd. Luis Encinas & Rosales, 83000 Hermosillo, Sonora, México 2

3

CNR, Consiglio Nazionale delle Ricerche, v. G. Moruzzi 1, Pisa, 56124, Italy

School of Chemistry, University of Birmingham, Edgbaston, B15 2TT, Birmingham, UK

4

Departamento de Investigación en Física, Universidad de Sonora, Blvd. Luis Encinas & Rosales, 83000 Hermosillo, Sonora, México.

*

Authors for correspondence:

E-mail: [email protected], [email protected], [email protected]

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ABSTRACT In this work, we report finding dodecahedral core-shell structures as the putative global minima of Pt13M20 (M=Ag, Au, Cu, Pd) clusters by using the basin hopping method and the many-body Gupta model potential to model interatomic interactions. These nanoparticles consist of an icosahedral 13-atom platinum core encapsulated by a 20 metal-atom shell exhibiting a dodecahedral geometry (and Ih symmetry). The interaction between the icosahedral platinum core and the dodecahedral shell is analyzed in terms of the increase in volume of the icosahedral core, and the strength and stickiness of M-Pt and M-M interactions. Low-lying metastable isomers are also obtained. Local relaxations at the DFT level are performed to verify the energetic ordering and stability of the structures predicted by the Gupta potential finding that dodecahedral core-shell structures are indeed the putative global minima for Pt13Ag20 and Pt13Pd20, whereas decahedral structures are obtained as the minimum energy configurations for Pt13Au20 and Pt13Cu20 clusters.

Keywords: Nanoalloys, platonic solids, dodecahedral clusters, basin hopping method


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1. Introduction Chemical composition, size and atomic arrangement determine the structures and properties of metal nanoparticles.1 At the nanoscale level, a variety of structural motifs (morphologies) can be found, such as crystalline, amorphous, or morphologies with symmetries forbidden in a crystal but allowed in isolated systems, such as pentagonal axes.2 Indeed, complexity is the signature of nanoscale materials, and multiple morphologies can be obtained for a given atomic composition and nanoparticle size.3,4 In particular, bimetallic nanoparticles (nanoalloys) exhibit a vast number of structural families which, from an energy landscape perspective, represent local minima on a potential energy hypersurface,5 and the determination of their spatial atomic configuration is of crucial importance for practical applications. Such an increase in structural complexity in nanoalloys is connected with the existence of homotops,6 i.e., isomers with identical overall structures but having different chemical ordering. There is a growing interest in catalytic properties of nanoparticles, especially those composed of transition and noble metal atoms, aiming to provide practical solutions to intricate issues such as pollution control and renewable energy sources.7,8 The potential utility of nanoparticles and the availability of experimental fabrication approaches have placed morphological peculiarities at the forefront of current structural property investigations.9 Controlled synthesis methods have produced fascinating structures including cubes, rods, spirals, and multiply twinned faceted nanoparticles.10-12 Thus, the production of nanoparticles exhibiting different shapes has been stimulated, and nowadays there are several different preparation methods, such that multiply facetted polyhedra, resembling Platonic and Archimedean solids in the nanometer size range, have been



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repeatedly reported (see e.g. Ref.13). These high symmetry polyhedra are constructed from basic 3-D building blocks and, according to their symmetry elements, are characterized by their point groups. Nanoalloys are currently the subject of a very active research work worldwide. They are interesting because of the synergetic effect produced by combining different chemical elements,14 which allows tuning of their physical and chemical properties to develop new tailored nanomaterials. There has been significant effort to comprehend the detailed structures of bimetallic nanoparticles and experimental and computational studies have contributed equally to the unveiling of unusual, novel morphologies, adopted as a consequence of the synthesis conditions and inter-atomic interactions.4 Different geometrical shapes have been obtained by varying experimental conditions, and diverse computational models have provided several different morphologies which resemble those obtained by experimentalists. Thus, it is currently accepted that small sized clusters typically adopt Platonic solid shapes while intermediate and large sizes nanoparticles prefer more complex, polyhedral morphologies, such as Archimedean solids, before eventually becoming bulk-like.15 Polyhedral nanoparticles have been experimentally obtained for elemental clusters, including Ag cubes and octahedra,16 Au rhombic dodecahedra17 and Pt cubic nanoparticles.18 Polyhedral nanoalloys have also been fabricated, such as Pd-Rh concave nanocubes,19 Au-Pd cubes and other faceted structures.13,15,20 Theoretically, polyhedral nanoparticles have been studied by first-principles methods when the number of atoms is of the order of tens, and by semiempirical potentials (EP) for larger atomic clusters. The optical properties of polyhedral Al and Al-Pb clusters were analyzed by Time-Dependent 4 ACS Paragon Plus Environment

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Density Functional Theory (TD-DFT), showing that these properties can be tuned by controlling the size, shape and composition, making these clusters excellent candidates for tunable optical applications.21 Montejano-Carrizales et al.15 identified small dodecahedral bimetallic Au-Pd nanoparticles (~1-2 nm) in high-resolution electron microscopy images. They also reported DFT calculations on dodecahedral monometallic (Au) nanoparticles, generating model structures from geometrical considerations. Marville and Andreoni22 performed semiempirical studies on polyhedral clusters by minimizing the cohesive energy of transition-metal clusters for different geometry structures. Besley et al.23 predicted the stability order of polyhedral Fe clusters of selected geometries for diameters ~3 nm, using the Murrell-Mottram EP. They predict the existence of stable rhombic dodecahedral (bcc-like) structures for medium-sized iron clusters. Yang et al. performed molecular dynamics simulations to study the thermal stability of icosahedral Pt-Au nanoparticles.24 Monte Carlo simulations have also been reported for Ptbased alloy nanoparticles25 in the size range of 3-4 nm (approx. 1654 atoms). In this work, various truncated-octahedra (TO) configurations were chosen by varying the chemical ordering and using a hybrid optimization scheme on a hypersurface defined by the embedded atom method (EAM) model potential. Core-shell TO structures were predicted for Pt-Ag and Pt-Au clusters, while an onion-like TO structure was found for Pt-Cu clusters and a mixed TO nanoalloy was established as the minimum energy configuration of Pt-Pd clusters. Recently, X-ray experiments have provided evidence on the existence of a Ag32 dodecahedral core consisting of an inner 12-atom hollow icosahedron, encapsulated by a 20-atom dodecahedron, in silver thiolated clusters.26



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In contrast to the above mentioned previous theoretical studies, in the work reported here we have performed an extensive global search of the minimum energy structures of Ptbased clusters from initial randomly generated configurations. Small 33-atom cluster structures Pt13M20, where M is Ag, Au, Cu and Pd, are analyzed. The potential energy surface (PES) defined by the Gupta EP was explored using the Monte Carlo basin hopping algorithm. Quite unexpectedly, we find that in all cases the predicted global minimum (GM) structures have a Pt13 icosahedral core (Ih13) surrounded by an M20 dodecahedral shell. To the best of our knowledge, this is the first time that a dodecahedral structure has been predicted as the GM rather than enforced by a biased potential model. The reasons for the stability of dodecahedral configurations at this size and composition are discussed below. Low-lying metastable isomers are also obtained to provide information on competing structural families at higher energy values and are used as a basis for an exploration of these nanoalloys using a higher-level theoretical approach, i.e., Density Functional Theory (DFT). This combined approach has proven to be very effective in the elucidation of the energetics of different structural families.27 Indeed in the present case we find that only in the Ag-Pt and Pd-Pt case the dodecahedral structure is confirmed to be the putative global minimum of the system.

2. Methodology 2.1 Semiempiric Approach We modeled the interatomic interactions by the Gupta many-body potential,28 which describes the intermetallic bonding of transition and noble metal clusters reasonably well. This is a many-body potential based on Friedel's tight-binding model, and it consists 6 ACS Paragon Plus Environment

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of a two-body repulsive component and a many-body attractive term. In this interaction model, the configurational energy of a cluster is written as the sum over all the atoms of the attractive and repulsive energy components.29 Their analytic form contain a set of parameters, A, ξ, p, q and r0, fitted to experimental properties of bulk metals and alloys, such as the cohesive energy, lattice parameters, and independent elastic constants for the reference crystal structure at 0 K; r0 denotes the nearest neighbor distance of the pure bulk elements, often taken as the average of the pure distances but it can also be taken as the experimental nearest-neighbor distance in some specific ordered bulk alloy. Values of the Gupta potential parameters describing Pt-Pt and M-M interactions are taken from the work of Cleri and Rosato.29 The heteronuclear (Pt-M) parameters utilized in this work are the average parameters which have been successfully used previously in theoretical studies of bimetallic clusters.30-34 The potential parameters are reported in Table 1. The basin hopping algorithm (BH) to explore hypersurfaces was systematically investigated by Doye and Wales as a stochastic search strategy, and applied to atomic clusters with simple interaction models.35 Albeit simple, the BH method has proven to be an effective strategy to study a number of systems described by empirical potentials or force fields.36-38 This method is based on a mathematical transformation of the potential energy function, which is transformed into a collection of interpenetrating staircases.35 For each Pt13M20 cluster our optimizations started from 300 randomly generated configurations. Each search consists of 5000 variable size Monte Carlo steps, with an initial step size of 1.2 Å and a thermal energy of 0.086 eV (kBT). It is worth noting that different simulation conditions were used, obtaining in all cases identical final results.



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2.2 DFT Calculations DFT calculations were performed using the Quantum ESPRESSO package,39 employing a basis set of plane waves, ultrasoft pseudopotentials40 and the Perdew-BurkeErnzerhof (PBE) exchange-correlation (xc-) functional.41 The chosen pseudopotentials include relativistic effects for the Pt atom at the scalar relativistic level. Values of 40 and 240 Ry (1Ry = 13.606 eV) were used as the energy cut-off for the selection of the planewave basis set for the description of the wave function and the electron density, respectively. Eigenvalues and eigenstates of the Kohn–Sham Hamiltonian have been calculated at the Γ point only of a cubic cell of side of approximately 20 Å, applying a Gaussian smearing technique with a broadening of the one-particle levels of 0.03 eV. The DFT local relaxations were performed on the lowest-energy structures obtained from the empirical potential search, and carrying out a DFT re-optimization according to a combined DFT-EP procedure as discussed in Ref. 42. Metal atoms coordinates were fully relaxed until the forces were smaller than 0.05 eV Å−1, and have been checked with relaxations using a threshold of 0.01 eV Å−1 finding total energy values differing by few hundredths of an eV.

3. Results and Discussion Figure 1 shows the optimized Pt13M20 (M=Ag, Au, Cu, Pd) cluster structures predicted as putative global minima together with the lowest-energy isomers and the corresponding relative energy differences. The core-shell morphology is evident in these nanoalloys, as well as the Ih13 platinum core. Energetic factors favor surface segregation of the M atoms. The higher surface energy and higher cohesive energy of Pt compared to M 8 ACS Paragon Plus Environment

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(Ag, Au, Cu, and Pd), leads to segregation of the majority element to the outer dodecahedral shell. The superior stability of dodecahedra with respect to other possible isomers is due to the high symmetry exhibited by these structures and their chemical ordering, connected with the fact that 13-20 is a magic cluster and a magic composition for dodecahedra, achieving geometric shell closure for both elemental components. Bond counting is suggestive: one finds 132 nearest-neighbor bonds in Pt13M20 as compared to only 128 in the (larger) 34-atom truncated octahedron (TO) obtained from the perfect TO38 by removing one of the (100) facets. Even though some of the surface bonds are strained (see below), the perfect core-shell arrangement, combined with a high number of metalmetal contacts (especially the stronger Pt-Pt and M-Pt interactions) make dodecahedra prevail over other non- closed-shell competitors, such as fcc-like structures, icosahedra or decahedra. It should be noted that the 20 surface atoms (the dodecahedral shell) adopt antiMackay coverage (i.e. sitting over triangular faces) with respect to the icosahedral core.43 Finding a dodecahedral configuration as the GM is particularly surprising in the Pt13Cu20 case. In fact, whereas in the case of Ag-Pt44 and Au-Pt45 all energetic factors agree in favoring the Ptcore-Mshell arrangement, and this tendency is (albeit more weakly) also present in the Pd-Pt case,34 the smaller lattice parameter of Cu should favor an inverse Cucore-Ptshell segregation, and indeed preferential occupation of core sites by Cu is what is usually found in both theory and experiment for larger clusters and extended surfaces; however, the presence of ligands such as CO can drive Cu to the surface.46,47 The predicted Cu surface segregation is thus a peculiarity of the nanoscale character of these Pt13Cu20 clusters.



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These remarkable dodecahedral structures, previously reported on the basis of experiment, but so far never found as global minima in the theoretical literature, exhibit some peculiarities according to the shell atom types, i.e., the chemical nature and the symmetry of the dodecahedral cage modify some of the structural characteristics of the icosahedral Pt core, through a core-shell interaction that symmetrically changes the core's volume. Consider, for example, the central Pt atom distance to the neighboring Pt atoms (r0): Table 2 lists the nearest-neighbor distances for the clusters considered in this study (the bare Pt13 cluster distance values are presented here as a reference).48 As a result of the coreshell interaction, the Pt13 cluster in M20 slightly expands, depending on the M-Pt bond strength, which is larger for Pd-Pt and Au-Pt than for Ag-Pt and Cu-Pt. The other two geometrical parameters reported in Table 2 are the M-Pt and M-M distances which are clearly in competition: for a given radial distance of the M atoms, the shorter D(M-Pt) the larger D(M-M). This competition is realized in different ways in the systems here considered: in the Cu-Pt case, e.g., one finds very short D(Cu-Pt), but quite elongated D(Cu-Cu). The basic quantities which determine this behavior are the strength and the ‘stickiness’ of the various metal-metal interactions, i.e., the relative easiness with which a metal-metal bond is strained.49 The greater the strength and stickiness of M-Pt with respect to M-M, the shorter D(M-Pt) and the longer D(M-M). Stickiness in general increases going down a column of the periodic table, and it is large for 3rd-row transition and noble metals and in particular for Au and Pt, but it is small e.g. for Cu. Ag stickiness is intermediate between Cu and Pt whereas Pd stickiness is more or less similar to that of Pt depending on the empirical potential parametrization. Indeed we find strongly elongated Cu-Cu distances: D(Cu-Cu)=2.944 Å compared to 2.544 Å in the bulk. In contrast, D(Ag-Ag)=3.054 Å is much less elongated with respect to the bulk value of 2.889 Å. Similar behavior is observed 10 ACS Paragon Plus Environment

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for distances D(Pd-Pd) and D(Au-Au), whose relationship to bulk values are 2.964 Å with respect to 2.75 Å for D(Pd-Pd), and 3.028 Å with respect to 2.88 Å in the case of D(AuAu). In addition to global minima, our PES exploration also provides isomeric structures. This is relevant because two types of effects are found when the level of theory includes electronic interactions: energetic reordering or structural distortions. The lower symmetry of the chemical ordering of the isomeric structures obtained in this work, suggest structurally dissimilar configurations as possible competing motifs to be considered in, for example, DFT calculations. Indeed, the binding energy/atom (-Eclust/N) difference between the lowest energy and first isomer structures of, e.g., the Pt13Cu20 cluster is rather small at the empirical potential theory level, which emphasizes the importance of carrying out first principles calculations. A detailed study of Pt13M20 (M=Cu,Ag,Au,Pd) clusters by the DFT method was then conducted with the aim of clarifying the energetics of these nanoparticles at a higher theoretical level. As mentioned in Sec. 2.2, several structural motifs were singled out in the empirical potential global optimization search and were re-optimized at the DFT level. Results are shown in Figure 2, where we present only the lowest energy and first isomeric structures obtained after DFT optimization. Coordinates and the corresponding geometric characterization for these and other highest energy isomers are available in Supporting Information. By inspecting this figure, we observe that the dodecahedral structure is confirmed as the lowest-energy structure at the DFT level for Pt13Ag20 cluster, exhibiting a large energy difference of ~1 eV between this structure and the first higher-energy structure (first isomer), which makes the dodecahedral structure a very stable one. Dodecahedral 11 ACS Paragon Plus Environment


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geometry was also obtained as the putative global minimum for the Pt13Pd20 cluster, for which the energy difference between the dodecahedral structure and the first isomer is nevertheless smaller: 0.24 eV. In contrast, in the case of the Pt13Cu20 and Pt13Au20 systems, the putative global minimum structures are Marks decahedra (Dh-Mk) with an energy difference of 0.18 eV (Cu-Pt) and 0.10 eV (Au-Pt) with respect to the first isomer. In both cases, the dodecahedral structure is higher in energy. With reference to the ground state structure of Pt13Cu20 and Pt13Au20 clusters, the corresponding dodecahedral structures have an energy difference of 0.30 eV and 1.57 eV, respectively. The reasons of the disagreement between empirical potential and DFT predictions are different in the Au-Pt and Cu-Pt cases. In the former case, the strong directionality effects which play a decisive role in Au-Pt interactions are not well accounted for by the isotropic Gupta potential.28 In the latter case, instead, in addition to slightly stronger directionality effects DFT predicts a stickier Cu-Cu bonding which does not survive the large elongation imposed by the anti-Mackay arrangement of the surface shell (see Table 2), explaining the energy destabilization of 0.30 eV thus found. In any case, the present results suggest that in appropriate conditions of size and composition dodecahedral arrangements may be the thermodynamically favored global minima of the system (such as in the present Ag-Pt and Pd-Pt examples) or low-energy isomers (such as in the present Cu-Pt example), thus providing a possible rationalization of the direct identification of the bimetallic dodecahedral nanoparticles in, for example, HAADF-STEM experiments.15,50 An additional analysis of the Pt13M20 clusters' electronic properties revealed no electronic closure for any of the systems studied here.

4. Conclusions


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We obtain the lowest-energy structures and low-lying isomers of free Pt13M20 clusters (M=Ag, Au, Cu, Pd) through a thorough global optimization approach using the basin hopping method. We find that highly symmetrical structures are energetically favored as putative global minima at the empirical potential level for this cluster size, consisting of a M20 dodecahedral cage encapsulating an Ih13 platinum core. Because of the symmetry, the core-shell interaction is isotropic and causes an expansion of the Ih13 Pt core depending on the nature of the monolayer shell, in the order: Pt-Ag ≈ Pt-Cu < Pt-Pd ≈ Pt-Au. The radial position of the surface shell is determined by the competition between M-Pt and M-M bonds. The magic character of these dodecahedral motifs in terms of both structural and compositional shell closure, with the more cohesive element (Pt) segregating into an Ih core, explains the superior stability of dodecahedra with respect to other competing motifs. To the best of our knowledge, this is the first time that a dodecahedral structure has been predicted as the global minimum by a systematic PES exploration rather than enforced by a biased model, thus making a first step in rationalizing the common occurrence of this and other type of structures in experiments, such as the complete 45-atom anti-Mackay icosahedron,51 which results from capping each of the pentagonal faces of the 33-atom dodecahedral structure. DFT calculations confirm the energetic preference for dodecahedral structures in bimetallic Pt13Ag20 and Pt13Pd20 clusters, and their character of low-energy isomers for Pt13Cu20, thus providing a possible rationalization of the experimental observation of nanoparticles with dodecahedral symmetry.15 No electronic closure was found for any of the Pt-based clusters studied here.

Acknowledgments 13 ACS Paragon Plus Environment


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APA acknowledges CONACYT-México for financial support through project 180424. AF acknowledges financial support by the ERC-AG SEPON project.

Supporting Information. We provide coordinates of the relaxed structures of the ground state configurations and higher energy isomers for the Pt-based clusters analyzed in this article. This information is available free of charge via the Internet at http://pubs.acs.org.

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TABLES

Table 1. Gupta parameters used in the present work. Parameter

Pt-Pt

Ag-Ag

Ag-Pt

Au-Au

Au-Pt

Cu-Cu

Cu-Pt

Pd-Pd

Pd-Pt

A(eV)

0.2975

0.1031

0.175

0.2061

0.25

0.0855

0.16

0.1746

0.23

ξ(eV)

2.695

1.1895

1.79

1.790

2.20

1.224

1.82

1.718

2.2

p

10.612

10.85

10.73

10.229

10.42

10.960

10.786

10.867

10.74

q

4.004

3.18

3.59

4.036

4.02

2.278

3.141

3.742

3.87

r0(Å)

2.7747

2.8921

2.833

2.884

2.83

2.556

2.666

2.7485

2.76



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Table 2. Selected nearest-neighbor distances (D) for the global minima dodecahedral structures of Pt13M20 (M=Cu, Ag, Au, Pd=) clusters considered in this work. r0 is the radial distance of the 12 Ih Pt atoms, M-Pt and M-M are the closest M-Pt and M-M distances, respectively. Multiplicity (m) indicates the distance's frequency of occurrence. All distances are in Å.48

D

Pt13

Pt-Ag

Pt-Cu

Pt-Pd

Pt-Au

m

r0

2.566

2.626

2.627

2.668

2.670

12

M-Pt

-

2.711

2.588

2.599

2.669

60

M-M

-

3.054

2.944

2.964

3.028

30


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Figure captions

Figure 1. Gupta potential global minima structures and low-lying isomers of Pt13M20 (M=Cu, Ag, Au, Pd) clusters. The binding energy difference (in eV) with respect to the most stable structure is given below each structural motif. Dark (blue) spheres represent Pt atoms, while gray (orange, light blue, yellow and cherry) spheres represent Cu, Ag, Au and Pd atoms.

Figure 2. DFT relaxed structures and low-lying isomers of Pt13M20 (M=Cu, Ag, Au, Pd) clusters. The binding energy difference (in eV) with respect to the most stable structure is given below each structural motif. Color coding is similar to Figure 1.



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Borbón-González et al. Figure 1.


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Borbón-González et al. Figure 2.



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Table of Contents Image


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Global Minimum Pt13M20 (M = Ag, Au, Cu, Pd) Dodecahedral Core

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