Making CâC Bonds with Gold Catalysts: A Theoretical Study of the

Article pubs.acs.org/JPCC

Making C−C Bonds with Gold Catalysts: A Theoretical Study of the Influence of Gold Particle Size on the Dissociation of the C−X Bond in Aryl Halides Mercedes Boronat,* Tirso López-Ausens, and Avelino Corma Instituto de Tecnología Química, Universidad Politécnica de Valencia − Consejo Superior de Investigaciones Científicas, Av.de los Naranjos, s/n, 46022 Valencia, Spain ABSTRACT: The adsorption and activation of iodo-, bromo-, and chlorobenzene over gold catalysts of different size, including an extended Au(111) surface; three-dimensional Au38 and Au13 nanoparticles; and planar Au7, Au6, and Au3 clusters has been systematically investigated by means of periodic density functional theory calculations. Several adsorption modes have been explored for each molecule, and the relative stability of such modes and the degree of C−X or C−C bond activation has been rationalized in terms of their molecular orbital distribution. Analysis of the electronic properties of the gold catalyst models allows the explanation of the influence of particle size on adsorption and activation energies in the subnanometer regime, while inclusion of dispersion interaction corrections becomes crucial for describing the reactivity of larger nanoparticles.

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INTRODUCTION The formation of new C−C bonds is a key process in organic synthesis, with wide applications in fine chemistry and pharmaceutical industries.1−5 Cross-coupling reactions between aryl halides and either alkenes, alkynes, or arylboronic acids are typically catalyzed by Pd salts or complexes in homogeneous phase.6,7 Recent work has shown that gold nanoparticles supported on metal oxides,8−10 as well as small gold clusters in solution11 or in the gas phase,12 are able to dissociate the C−I bond in iodobenzene, one of the elementary steps common to all cross-coupling reactions. Density functional theory (DFT) calculations have established that iodobenzene activation over heterogeneous gold catalysts is energetically possible because, in contrast to homogeneous complexes, the charge transfer necessary to cleave the C−I bond is supplied by all gold atoms in the nanoparticle, making unnecessary a formal change in the oxidation state of gold.10,13,14 It would be of interest to study if gold is able to activate less reactive aryl bromides and chlorides. In general, higher temperatures and longer reaction times are usually needed to activate C−Br bonds, while few examples of cross-coupling reactions involving aryl chlorides can be found in the literature.15−19 In this contribution we have systematically investigated by means of DFT calculations the adsorption and activation of iodo-, bromo-, and chlorobenzene over gold nanoparticles and clusters of different size. The reactivity of these three aryl halides has been rationalized in terms of their molecular orbital distribution and of the electronic properties of the gold catalyst models. For each molecule, several modes of adsorption have been explored and a key role of dispersion interactions on the relative stability of such modes and on activation barriers for C−X bond dissociation is reported for the first time. © 2014 American Chemical Society

THEORETICAL METHODS The mechanism of C−X dissociation in aryl halides with X = I, Br, Cl was investigated by means of periodic density functional theory calculations, using the Perdew−Wang (PW91) exchange−correlation functional within the generalized gradient approach (GGA)20,21 as implemented in the VASP code.22,23 The valence density was expanded in a plane wave basis set with a kinetic energy cutoff of 500 eV, and the effect of the core electrons in the valence density was taken into account by means of the projected augmented wave (PAW) formalism.24 Integration in the reciprocal space was carried out at the Γ k-point of the Brillouin zone. Transition states were located using either the nudged-elastic-band (NEB)25 or the DIMER algorithm,26,27 and stationary points were characterized by pertinent frequency analysis calculations. van der Waals interactions were taken into consideration by adding a pairwise interatomic term Edisp to the Kohn−Shan DFT energies, which was evaluated using the revised DFT-D3 method by Grimme et al.28,29 For periodic systems, the dispersion energy is calculated according to Edisp = −

1 2

atom pairs

∑ ∑′ ∑ A≠B

T

n = 6,8

sn

CnAB |rAB + T |n ′

where T is a translation vector multiple of the unit cell. Only interactions with |rAB + T| < rmax are considered, with a cutoff value of rmax = 0.94 au. A second cutoff value of 40 au is set for the calculation of the coordination number. Received: January 23, 2014 Revised: April 2, 2014 Published: April 7, 2014 9018

dx.doi.org/10.1021/jp500806w | J. Phys. Chem. C 2014, 118, 9018−9029

The Journal of Physical Chemistry C

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Figure 1. Optimized structures of reactant (R), transition state (TS), and product (P) of iodobenzene dissociation over extended Au(111) surfaces. Golden, red, orange, and white balls correspond to Au, I, C, and H atoms, respectively.

gold-catalyzed Sonogashira cross-coupling reaction between iodobenzene and phenylacetylene,13 and this study has now been extended to bromo- and chlorobenzene. The optimized structures of reactant (R), transition state (TS), and product (P) are depicted in Figure 1. The most relevant distances are given in Table 1, and the calculated adsorption, activation, and reaction energies at DFT and DFTD3 levels are summarized in Table 2.

The metallic Au(111) extended surface was modeled by means of a (5 × 5) supercell slab containing 100 atoms in 4 layers, and during the geometry optimizations, the positions of the adsorbates and of the gold atoms of the two uppermost layers were allowed to fully relax. Two cuboctahedral gold nanoparticles of different size were considered: a Au 38 nanoparticle of ∼1 nm that contains corner atoms with coordination number 6 and a Au13 nanoparticle of ∼0.6 nm diameter containing corner atoms with coordination number 5. When decreasing particle size, a planar geometry is preferred for isolated gold clusters, and we have considered in this work three of these planar systems: Au7, Au6, and Au3. All discrete nanoparticles and clusters were placed in a 20 × 20 × 20 Å3 cubic box, large enough to avoid interactions between periodically repeated nanoparticles or adsorbates. In the case of 3D nanoparticles, only the positions of the adsorbates were allowed to fully relax during geometry optimizations, to avoid undesired deformation of the particle shape. In the case of planar clusters, all atoms in the systems were always fully relaxed. Adsorption energies Eads were calculated as the difference between the total energy of the gold−aryl halide complex and the total energies of the gold model and the aryl halide molecule separately:

Table 1. Optimized Values (Angstroms) of the C−X (X = I, Br, Cl) and C−Au Distances in the Reactant (R), Transition State (TS), and Product (P) of C−X Bond Dissociation over Extended Au(111) Surfaces rC−I rC−Au (I−Ph) rI−Au rC−Br rC−Au (Br−Ph) rBr−Au rC−Cl rC−Au (Cl−Ph) rCl−Au

Eads = E(Au−aryl halide) − E(Au) − E(aryl halide)

gas

R

TS

P

2.110 − − 1.911 − − 1.743 − −

2.126 3.407 3.230 1.916 3.519 3.561 1.742 3.625 3.838

2.531 2.408 2.856 2.355 2.320 2.849 2.251 2.277 2.786

3.899 2.092 2.800 3.883 2.091 2.721 3.873 2.090 2.626

As previously described for iodobenzene, the three aryl halides adsorb parallel to the gold surface, with the halide atom interacting weakly with two Au atoms. The optimized X−Au distances systematically increase from 3.230 Å in iodobenzene to 3.838 Å in chlorobenzene (Table 1), in line with the corresponding decrease in the calculated adsorption energies. The DFT values are between −6.8 kcal/mol for iodobenzene and −2.8 kcal/mol for chlorobenzene, and inclusion of dispersion interactions considerably increases adsorption energy values (DFTD3 in Table 2), which range from −47.3 to −30.8 kcal/mol. It has been reported that DFT-D schemes tend to overestimate dispersion interactions of organic molecules adsorbed on metal surfaces;28,36 therefore, these DFTD3-calculated adsorption energies might be larger than experimental values. The reaction proceeds in all cases via a transition state in which the C−X bond is broken and simultaneously the C atom binds to a surface Au atom, while the halide atom forms a bridge between two Au atoms (see Figure 1). After dissociation, the phenyl group is perpendicular to the surface directly attached to a Au atom, while the halide occupies a 3-fold hollow position on the catalyst surface. The calculated activation

Activation Eact and reaction ΔE energies were calculated as the difference between the total energy of the transition state (TS) or the product (P) and the total energy of the corresponding reactant complex (R):

Eact = E(TS) − E(R) ΔE = E(P) − E(R)

Molecular orbital distributions of the aryl halides and the gold nanoparticles and clusters were obtained with the Gaussian03 computer program30 using the hybrid B3LYP31,32 functional and the standard 6-31G(d,p) basis set for C and H atoms33 and the effective core potential LANL2DZ basis set for halogen and Au atoms.34,35

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RESULTS AND DISCUSSION 1. Adsorption and Dissociation of Aryl Halides over Extended Gold Surfaces. The dissociation of the C−I bond in iodobenzene over perfect Au(111) surfaces was theoretically investigated as an elementary step in the mechanism of the 9019



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Table 2. Calculated Adsorption (Eads), Activation (Eact), and Reaction (ΔE) Energies for Dissociation of the C−X Bond (X = I, Br, Cl) over Different Gold Catalyst Models Eads (kcal/mol)

ΔE (kcal/mol)

Eact (kcal/mol)

X

model

DFT

DFTD3

DFT

DFTD3

DFT

DFTD3

I I I I I

Au(111) Au38 Au13 Au7 Au3

−6.8 −12.2 −13.0 −22.8 −30.5

−47.3 −31.8 −26.0 −35.0 −36.0

15.7 11.3 8.8 10.5 15.8

7.8 9.8 3.5 11.3 11.3

−19.4 −23.1 −30.0 −16.2 −24.0

−25.9 −22.9 −29.0 −10.7 −19.0

Br Br Br Br Br


−3.7 −7.7 −7.4 −17.1 −23.7

−38.0 −25.7 −20.3 −28.5 −33.3

22.0 13.9 10.8 11.8 16.6

13.2 13.1 7.0 12.4 16.7

−12.1 −19.4 −25.0 −17.1 −21.0

−18.6 −18.5 −24.5 −11.9 −15.5

Cl Cl Cl Cl Cl


−2.8 −6.5 −5.9 −15.4 −19.6

−30.8 −22.8 −25.1 −25.3 −32.8

30.2 20.7 17.8 17.2 19.2

20.5 20.7 22.3 17.6 24.2

−3.1 −12.3 −16.8 −9.4 −18.3

−10.7 −11.1 −8.6 −5.2 −8.7

Figure 2. Optimized structures of reactant (R), transition state (TS), and product (P) of iodobenzene dissociation over a Au38 nanoparticle and of three other adsorption complexes. The optimized values of the most relevant distances for all aryl halides are summarized in Table 3. Golden, red, orange, and white balls correspond to Au, I, C, and H atoms, respectively.

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Table 3. Calculated Adsorption Energies (Kilocalories per Mole) for the Different Types of Complexes Formed by Interaction of Aryl Halides with Gold Nanoparticles and Clustersa A

a

B

C

R

model

X

DFT

DFTD3

DFT

DFTD3

DFT

DFTD3

DFT

DFTD3

Au38

I Br Cl

−6.4 −6.4 −6.5

−21.1 −20.9 −21.2

−10.4 −7.4 −6.3

−31.8 −25.7 −22.8

−12.2 −7.7 −5.0

−23.7 −17.1 −12.8

−8.9 −5.2 −3.2

−23.2 −17.8 −13.9

Au13

I Br Cl

− −6.6 −5.9

− −20.3 −25.1

−7.8 −3.2 −

−26.0 −19.6 −

−13.0 −7.4 −4.4

−24.2 −16.8 −13.0

Au7

I Br Cl

−15.1 −15.4 −15.3

−23.8 −24.0 −23.8

−22.8 −17.1 −15.4

−35.0 −28.5 −25.3

−21.2 −15.2 −11.4

−28.9 −22.1 −17.7

Au6

I Br Cl

−11.0 −11.3 −10.6

−17.2 −17.5 −16.6

−14.6 −10.4 −6.9

−19.3 −15.0 −11.2

Au3

I Br Cl

−26.4 −26.7 −26.6

−33.5 −33.3 −32.8

−30.5 −23.7 −19.6

−36.0 −29.0 −24.3

Structures are depicted in Figures 2, 3, and 5.

Table 4. Optimized Values (Angstroms) of Selected Distances in the Different Types of Complexes Formed by Interaction of Aryl Halides with Au38 and Au13 Nanoparticlesa Au38 rC−I rC−Au (I−Ph) rI−Au rC−Br rC−Au (Br-Ph) rBr−Au rC−Cl rC−Au (Cl-Ph) rCl−Au

Au13

A

B

C

R

A

B

C

2.101 2.501 5.771 1.901 2.501 5.661 1.733 2.485 5.386

2.111 2.506 2.945 1.908 2.512 3.113 1.732 2.485 3.692

2.124 3.882 2.772 1.930 3.803 2.730 1.760 3.760 2.715

2.119 3.961 2.854 1.921 3.920 2.837 1.752 3.908 2.851

− − − 1.900 2.381/2.566 (1.423)b 1.724 2.443/2.476 (1.414)b

2.142 2.744 2.766 1.936 2.818 2.832 − − −

2.131 3.837 2.692 1.931 3.713 2.676 1.760 3.620 2.670

a

Structures are depicted in Figures 2 and 3. bThe values in parentheses correspond to rCC in adsorption complexes of type A. The optimized value of the CC distance in iodo-, bromo-, and chlorobenzene in the gas phase is 1.396 Å.

energies listed in Table 2 reflect the order of reactivity of the studied halides. Dissociation of the C−Cl bond requires 30.2 kcal/mol at the DFT level and 20.5 kcal/mol at the DFTD3 level, while only 15.7 and 7.8 kcal/mol at the DFT and DFTD3 levels, respectively, are necessary to break the C−I bond. 2. Adsorption of Aryl Halides over 3D Gold Nanoparticles. A similar mechanism for iodobenzene dissociation was previously reported over a Au38 nanoparticle10,13 and is depicted in Figure 2. According to this mechanism, the halide atom of the aryl halide interacts with a corner atom of the Au38 nanoparticle with coordination number six (structure R in Figure 2), forming a strong Au−X bond that leaves the aromatic ring far from the gold atoms of the nanoparticle. In the transition state, the rupture of the C−X bond and the formation of a new Au−C bond occur simultaneously, and after dissociation, the phenyl group is directly attached to a lowcoordinated Au atom while the halide atom occupies a bridge position between two Au atoms. Besides the reactant structure R, in which the halide atom binds to gold and the aromatic ring remains far from the nanoparticle, in this work we have

explored other possible ways of aryl halide interaction with the Au38 nanoparticle (see Figure 2 for optimized structures and Table 3 for adsorption energies). On one hand, low-coordinated gold atoms can interact with the aromatic ring of the aryl halide molecules instead of with the X atoms, forming complexes of type A. In this mode of adsorption, the C−X bond is not activated but the CC bond length increases from 1.396 Å in the isolated molecules to no less than 1.413 Å (see optimized distances in Table 4). On the other hand, it is also possible for iodobenzene and bromobenzene to interact with the Au38 nanoparticle both through the aromatic ring and the halide atom, forming the adsorption complex of type B. Finally, a structure labeled C with the halide atom directly attached to a corner Au site and the aromatic ring rotated with respect to its position in structure R was also obtained for the three molecules investigated. In structure C, the three optimized C−X bond lengths are systematically larger than those on structure R, indicating a larger degree of bond activation (see Table 4). 9021



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Figure 3. Optimized structures of different adsorption complexes formed by interaction of aryl halides with a Au13 nanoparticle and of transition state (TS) and product (P) of bromobenzene dissociation over a Au13 nanoparticle. The optimized values of the most relevant distances for all aryl halides are summarized in Table 3. Golden, blue, green, orange, and white balls correspond to Au, Br, Cl, C, and H atoms, respectively.

Figure 4. Molecular orbital distribution of iodo-, bromo-, and chlorobenzene.

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Figure 5. Optimized structures of adsorption complexes of type A (top), B (center), and C (bottom) formed by interaction of aryl halides with Au7, Au6, and Au3 clusters. Selected distances in structures of type B are given in angstroms. Golden, red, blue, green, orange, and white balls correspond to Au, I, Br, Cl, C, and H atoms, respectively.

tially through the aromatic ring at both theoretical levels. In fact, the optimized Au−Cl distance in structure B is 3.692 Å, too large to indicate formation of a new bond, and the optimized values of the C−Cl and C−Au bond lengths are similar to those obtained for complex A, suggesting that only the aromatic ring interacts with gold in this system. To further explore the role of gold particle size, aryl halide adsorption over a smaller Au13 cuboctahedral nanoparticle containing gold atoms with coordination number five was also investigated. Again, different adsorption complexes formed by preferential interaction of gold with either the halide atom or the aromatic ring were obtained for each molecule (see Figure 3). For iodobenzene, it was not even possible to optimize an adsorption complex of type A with the gold atoms interacting with the aromatic ring, but only structures B and C involving formation of a strong Au−I bond. Three adsorption modes were obtained for bromobenzene on Au13 nanoparticles; all of them are of similar stability (see Table 3). At the pure DFT level, bonding via the Br atom is energetically preferred, but

The relative stability of the different adsorption complexes obtained in this study directly depends on the nature of the aryl halide and is slightly modified in some cases when dispersion interactions are included in the calculations (see Table 3). At the DFT level, the three iodobenzene adsorption complexes with the I atom directly attached to gold are more stable than complex A with only aromatic ring interaction. Inclusion of dispersion interactions not only increases adsorption energy values by 10−20 kcal/mol as expected but also preferentially stabilizes complex B with two metal−molecule bonds and with all carbon and hydrogen atoms of the aromatic ring quite close to the gold nanoparticle. In the case of bromobenzene, the Au− Br and Au−C interactions are similar in strength, and consequently, the calculated adsorption energies at the DFT level are within 2 kcal/mol. Dispersion corrections to the electronic energy preferentially stabilize the systems with the organic molecule closer to the gold nanoparticle; therefore, structure B is, like that for iodobenzene, clearly the most stable at the DFTD3 level. Finally, chlorobenzene adsorbs preferen9023



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inclusion of dispersion interactions preferentially stabilizes aromatic ring interaction, with structure A being only 0.7 kcal/ mol more stable than complex B. Finally, the most stable conformation for chlorobenzene adsorption on Au13 nanoparticle corresponds to structure A in Figure 3 (bottom panel) and involves formation of two new Au−C bonds and no direct Au−Cl bonding. To rationalize the different modes of adsorption of aryl halides on gold nanoparticles, the energy distribution and composition of the highest occupied and lowest unoccupied molecular orbitals of iodo-, bromo-, and chlorobenzene are depicted in Figure 4. Aryl halides bind to gold by electron density transfer from their highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) of the gold nanoparticle and by back-donation from the HOMO of the metal to the LUMO of the aryl halide molecule. The HOMO of iodo-, bromo-, and chlorobenzene is equivalent and consists of a combination of the pz atomic orbital on the halide atom with some π contributions from the aromatic ring. Therefore, the three molecules can interact with gold either through the aromatic ring or through the halide atom, as previously described. With respect to back-donation from the metal HOMO to the aryl halide LUMO, it is shown in Figure 4 that the LUMO of iodobenzene is an antibonding σ*(C−I) orbital, while the LUMO and LUMO+1 orbitals of bromo- and chlorobenzene are localized on the aromatic ring. Moreover, in the case of chlorobenzene, the antibonding σ*(C−Cl) orbital is clearly destabilized with respect to the two most stable empty orbitals. This means that back-donation from gold to iodobenzene will preferentially stabilize the R and C structures and will lead to activation and weakening of the C−I bond. For chlorobenzene, on the contrary, back-donation from the metal will put electron density into the aromatic π* orbitals, leading to preferential interaction through the benzene ring. Finally, the energy of the three lowest unoccupied orbitals of bromobenzene is quite similar, suggesting that all of them should be energetically accessible and therefore that no preferential stabilization of one mode of adsorption should exist, in agreement with the adsorption energy values listed in Table 3 and previously discussed. 3. Adsorption of Aryl Halides over Planar Gold Clusters. Isolated gold clusters composed by seven or less atoms are planar, and molecules interact only with the lowcoordinated atoms placed at corner of edge positions.37 Adsorption of aryl halides on Au7 clusters containing gold atoms with coordination number 3, and on Au6 and Au3 clusters containing gold atoms with coordination number 2, was investigated in this work. The optimized structures of the different types of adsorption complexes obtained are depicted in Figure 5, and calculated interaction energies and optimized distances are summarized in Tables 3 and 5, respectively. In a way similar to that described for Au38 and Au13 nanoparticles, iodobenzene and bromobenzene can form three types of adsorption complexes with Au7 cluster, while only two of such complexes are obtained for chlorobenzene. In structure A, a low-coordinated gold atom interacts with a CC bond of the aromatic ring forming two new Au−C bonds. The optimized Au−C bond lengths are around 2.35 Å in all systems (see Table 5), and the CC bond length increases from 1.386 Å in the gas phase to 1.425 Å, while the C−X bond remains unaltered. Interaction through the halide atom forming structure C causes an important activation of the C−X bond, reflected in an elongation of the C−X distance larger than 0.03

Table 5. Optimized Values (Angstroms) of Selected Distances in the Adsorption Complexes A and C Formed by Interaction of Aryl Halides with Au7, Au6, and Au3 Clustersa Au7 rC−I rC−Aub (I−Ph) rI−Au rC−Br rC−Aub (Br− Ph) rBr−Au rC−Cl rC−Aub (Cl− Ph) rCl−Au

Au6

Au3

A

C

A

C

A

C

2.103 2.346

2.145 3.859

2.102 2.427

2.129 3.828

2.103 2.259

2.150 3.723

(1.425)c 1.902 2.348

2.642 1.946 3.727

(1.419)c 1.901 2.430

2.720 1.933 3.702

(1.435)c 1.902 2.260

2.584 1.955 3.575

(1.425)c 1.734 2.350

2.567 1.774 3.611

(1.419)c 1.733 2.431

2.665 1.764 2.431

(1.435)c 1.734 2.261

2.492 1.781 3.467

(1.426)c

2.498

(1.419)c

2.609

(1.435)c

2.402

a

Structures and optimized geometries of complexes of type B are depicted in Figure 5. bFor structure A the value given is an average of two Au−C distances. cThe values in parentheses correspond to rCC in adsorption complexes of type A. The optimized value of the CC distance in iodo-, bromo-, and chlorobenzene in the gas phase is 1.396 Å.

Å in all cases. Finally, a type B complex involving both gold− halide and gold−aromatic ring interactions was obtained for iodo- and bromobenzene but not for chlorobenzene. Indeed, the optimized geometries of structures of type B depicted in Figure 5 clearly show that, while I and Br atoms are bonded to a corner Au atom, the Au−Cl distance is larger than 4 Å, indicating that there is no interaction between these two atoms. Au6 and Au3 clusters contain gold atoms with coordination number 2, and in principle, a similar interaction with aryl halides should be expected for both systems on the basis of this parameter. On the other hand, the two clusters differ in their electronic configuration: Au3 contains an odd number of electrons and is a doublet, while Au6 contains an even number of electrons and is a singlet, which could result in a different reactivity. As shown in Figure 5 and Table 5, only A and C complexes are formed on Au6 and Au3 clusters, and for all aryl halides, the adsorption energies and the degree of C−X or C C bond activation is larger on Au3 than on Au6. In regard to the relative stability of the different adsorption complexes obtained on planar clusters, the trend is analogous to that previously observed on three-dimensional nanoparticles. The halidebonded system C is the most stable for iodobenzene; aromatic ring interaction with gold is energetically preferred for chlorobenzene, and similar stability of A and C complexes is found for bromobenzene. Moreover, when formation of a structure of type B involving halide and aromatic ring bonding with gold is possible, as found on Au38 and Au13 nanoparticles, this is the most stable adsorption complex. As expected, dispersion corrections become less important as the size of the gold catalyst model decreases and do not modify the relative stabilities and trends obtained at the DFT level. The molecular orbital distribution of aryl halides shown in Figure 4 allowed the explanation of the order of stability of A, B, and C complexes for each molecule. To better understand the role of gold particle size, the HOMO and LUMO orbitals of the different gold nanoparticles and clusters considered in this work are depicted in Figure 6. 9024



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Figure 6. Molecular orbital distribution of gold clusters and nanoparticles.

As previously discussed, molecules bind to gold by two different electron density transfer processes, and the degree of charge transfer and therefore the strength of the interaction depends on two factors: the difference in energy and the spatial overlap between the orbitals involved. The frontier orbitals of planar clusters like Au3, Au6 and Au7 consist of several lobes mainly localized on the edge and corner atoms and fully accessible to interaction with reactants. This efficient overlap between molecular orbitals would explain the higher adsorption energy values obtained at the DFT level for planar clusters of decreasing size as compared to those of three-dimensional nanoparticles14,37 and extended surfaces, plotted in Figure 7 (top panel) for structures of type C. The behavior of Au6, whose interaction with aryl halides is weaker than expected according to the trend found for all other systems, is explained by the large HOMO−LUMO gap of this cluster.38 The LUMO of Au6 is the least stable among all orbitals depicted in Figure 6, making electron density transfer from the aryl halide HOMO less probable; the HOMO of Au6 lies more than 1 eV below any other HOMO, making difficult back-donation to the adsorbed molecules. Figure 7 (bottom panel) shows that inclusion of dispersion interactions does not modify this trend in the subnanometer regime and has a clear stabilizing effect only on larger nanoparticles, simulated in this study by perfect Au(111) surfaces. When aryl halides adsorb on gold through the halide atomforming structures of type C, the back-donation process from gold to the antibonding σ*(C−X) orbital produces a weakening of this bond and an elongation of the C−X optimized distance. The direct relationship between calculated adsorption energies at the DFT level and increase in the C−X bond length upon adsorption observed in Figure 8 (top panel) confirms this binding model and suggests that if a stronger interaction involves a higher degree of molecular activation, it might also involve lower activation barriers for dissociation. This hypothesis is studied in the next subsection. 4. Dissociation of Aryl Halides over Gold Nanoparticles and Clusters. The dissociation of the C−X bond in aryl halides was calculated over Au38, Au13, Au7, and Au3 catalyst models. The optimized geometries of transition states and

Figure 7. Adsorption energy at the DFT (top) and DFTD3 (bottom) levels of halide-bonded adsorption complex C as a function of coordination number of gold. Values for iodobenzene (blue circles), bromobenzene (pink squares), and chlorobenzene (empty triangles) are plotted separately. The values obtained over Au6 cluster are framed.

reaction products are depicted in Figures 2, 3, and 9, and the most relevant bond length values summarized in Table 6. The reaction mechanism is similar to that previously described for extended Au(111) surfaces. The driving force of the reaction is the formation of a new and stable Au−C bond that facilitates the dissociation of the C−X bond, producing a phenyl fragment and an adsorbed halide atom. Taking into consideration that on gold nanoparticles and clusters several 9025



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of gold particle size on the activation and dissociation of aryl halides. Cross-coupling reactions involve at least three main elementary steps: dissociation of the C−X bond, activation of the second reactant molecule, and C−C bond forming or coupling step; therefore, any trend found with gold particle size for the global process does not necessarily imply a direct influence on C−X bond dissociation. For instance, Lambert et al. studied the Sonogashira coupling between iodobenzene and phenylacetylene over an extended gold surface in vacuo39 and over gold nanoparticles of different sizes between 2.8 and 23 nm, supported on SiO2 and TiO2. They observed that the selectivity to the cross-coupling product decreased with decreasing gold particle size; however, iodobenzene conversion was complete in all cases, and the homocoupling product biphenyl was always formed in large amounts. The Ullman type homocoupling of aryl halides is a more convenient reaction to analyze this effect because it involves only two elementary steps: dissociation of the C−X bond and C−C bond forming or coupling of two aryl fragments forming a biaryl molecule. The coupling between two phenyl fragments has been now investigated over Au(111), Au38, and Au3 catalyst models. The calculated activation barriers increase from 31.8 kcal/mol over Au(111) to 38.7 kcal/mol over Au3 cluster at the DFT level, while they are similar and around 30 kcal/mol for the three systems at the DFTD3 level (see Figure 11). In all cases, formation of the C−C bond is the rate-determining step of the global process, and its activation energy does not depend on particle size. There are very few examples of gold-catalyzed homocoupling of aryl halides in the literature,40−42 and only in one case has the effect on gold particle size been explored.42 Thus, Monopoli et al. reported that gold nanoparticles of ∼1 nm diameter synthesized in aqueous medium were in general more active than larger nanoparticles of ∼20 nm diameter synthesized in tetrabutylammonium acetate. But the difference in activity was explained by the larger surface area of the former and not by a larger intrinsic reactivity of small clusters or nanoparticles, which is in agreement with the theoretical results presented here. The energy profiles for the homocoupling iodo-, bromo-, and chlorobenzene over Au(111) and Au38 systems at DFTD3 level are depicted in Figure 12, and it is clearly seen that in all cases the rate-determining step is formation of the C−C bond. But, as previously discussed, dissociation of C−Br and C−Cl bonds is more difficult than dissociation of the C−I bond, and therefore the surface concentration of intermediate phenyl species will be lower in the reactions involving bromo- and chlorobenzene. This allows the explanation of the low yields reported for the homocoupling of aryl bromides under reaction conditions that are the same as those used for aryl iodides.40,42

Figure 8. Relationship between adsorption energy of halide-bonded adsorption complex C at the DFT (top) and DFTD3 (bottom) levels and increase in the optimized C−X bond length. Values for iodobenzene (blue circles), bromobenzene (pink squares), and chlorobenzene (empty triangles) are plotted separately.

adsorption complexes of different stability can be formed in the initial step, the adsorption, activation, and reaction energies involved in the dissociation of the C−X bond in aryl halides listed in Table 2 were calculated taking in each case as reactant structure the most stable adsorption complex obtained at the corresponding theoretical level. This way, the energy necessary to convert the most stable complex for each system into the reactant structure directly involved in the dissociation process is, to some extent, included in the calculation. When comparing the results for the three aryl halides studied, the values listed in Table 2 follow the same trend previously reported over extended Au(111) surfaces: adsorption is weaker, activation energy for dissociation increases, and exothermicity decreases from iodo- to bromo- to chlorobenzene. However, the trends with gold particle size are not so clear, and the larger adsorption energies obtained on the smallest Au7 and Au3 clusters are not accompanied by a decrease in activation energy barriers. To better analyze the influence of particle size, activation energies at the DFT and DFTD3 levels are plotted in Figure 10 as a function of coordination number of gold. At the DFT level, activation barriers decrease with decreasing particle size over three-dimensional nanoparticles and then increase again over planar clusters. These results suggest that, for iodo- and bromobenzene, there might exist an optimum particle size of ∼0.5 nm. However, stabilization due to dispersion interactions is more important over larger nanoparticles, and as a consequence the dissociation process becomes favored over Au(111) facet at the DFTD3 level (see Figure 10, bottom). The trend found at the DFT level is lost, and large gold nanoparticles become as reactive as small ones. 5. C−C Coupling Step and Comparison with Experiment. It is difficult to find experimental evidence of a key role

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CONCLUSIONS The adsorption and activation of iodo-, bromo-, and chlorobenzene over gold catalyst models of different size, including an extended Au(111) surface; three-dimensional Au38 and Au13 nanoparticles; and planar Au7, Au6, and Au3 clusters has been systematically investigated by means of periodic DFT calculations. Several modes of interaction of aryl halides with gold nanoparticles and clusters have been obtained: via the halide atom, through the aromatic ring, and in some cases by double interaction both through the aromatic ring and the halide atom. The relative stability of such modes is not equivalent for the three aryl halides studied and has been explained by analysis of 9026



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Figure 9. Optimized structures of reactant (R), transition state (TS), and product (P) of aryl halide dissociation over Au7 and Au3 clusters. The optimized values of the most relevant distances for all aryl halides are summarized in Tables 5 and 6. Golden, red, blue, green, orange, and white balls correspond to Au, I, Br, Cl, C, and H atoms, respectively.

Table 6. Optimized Values (Angstroms) of Selected Distances in Transition State (TS) and Product (P) Structures Involved in Iodo- Bromo- and Chlorobenzene Dissociation over Gold Nanoparticles and Clustersa Au38 rC−I rC−Au (I−Ph) rI−Au rC−Br rC−Au (Br−Ph) rBr−Au rC−Cl rC−Au (Cl−Ph) rCl−Au a

Au13

Au7

Au3

TS

P

TS

P

TS

P

TS

P

2.475 2.208 2.781 2.319 2.188 2.664 2.223 2.172 2.547

5.566 2.073 2.783 5.532 2.072 2.655 5.463 2.072 2.542

2.429 2.183 2.679 2.301 2.156 2.593 2.226 2.128 2.506

6.616 2.047 2.217 5.867 2.042 2.598 5.740 2.042 2.490

2.162 2.440 2.682 1.991 2.365 2.613 2.131 2.093 2.493

7.067 2.033 2.690 6.146 2.035 2.571 6.094 2.034 2.460

2.210 2.436 2.641 2.034 2.343 2.577 1.936 2.234 2.480

6.225 2.018 2.543 6.170 2.017 2.390 6.113 2.017 2.263

Structures are depicted in Figures 2, 3, and 9.

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the most stable complex for iodo- and bromobenzene involves both halide and aromatic ring bonding with gold. It has been found that the electronic properties of the gold catalyst models in the subnanometer regime control the adsorption and activation of the C−X bond of aryl halides. However, when gold nanoparticles become larger, the stabilization due to dispersion interactions becomes more important and its inclusion in the calculations favors the dissociation process, making large gold nanoparticles as reactive as small ones. The complete mechanism of aryl halide homocoupling has been calculated, and the activation energies of the rate-determining step, that is, the formation of the new C−C bond, show no dependence with gold particle size. In conclusion, the trends in reactivity experimentally reported for aryl halides have been rationalized in terms of their molecular orbital distribution, and the present study allows the conclusion that decreasing gold particle size below 1 nm is not an efficient way to enhance the dissociation of aryl halides.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 34 96 387 9445. Fax: 34 96 3879444. Notes

The authors declare no competing financial interest.

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Figure 10. Activation energy barriers at the DFT (top) and DFTD3 (bottom) levels as a function of coordination number of gold. Values for iodobenzene (blue circles), bromobenzene (pink squares), and chlorobenzene (empty triangles) are plotted separately.

ACKNOWLEDGMENTS Financial support from the Spanish Science and Innovation Ministry (Consolider Ingenio 2010-MULTICAT CSD200900050, Subprograma de apoyo a Centros y Universidades de Excelencia Severo Ochoa SEV 2012 0267, MAT2011-28009 projects) is acknowledged. Red Española de Supercomputación (RES) and Centre de Càlcul de la Universitat de València are gratefully acknowledged for computational facilities and technical assistance. T.L.-A. thanks ITQ for a contract.

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REFERENCES

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Figure 11. Calculated energy profile for iodobenzene homocoupling over Au(111) surface (blue), Au38 nanoparticle (red), and Au3 cluster (green) at the DFT (solid lines) and DFTD3 (dashed lines) levels.

Figure 12. Calculated energy profile for iodobenzene (red), bromobenzene (blue), and chlorobenzene (green) homocoupling over Au(111) surface (dashed lines) and Au38 nanoparticle (solid lines) at the DFTD3 level.

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