Reactivity of Gold Clusters in the Regime of Structural Fluxionality

Article pubs.acs.org/JPCC

Reactivity of Gold Clusters in the Regime of Structural Fluxionality Min Gao,† Andrey Lyalin,*,‡,§ Makito Takagi,† Satoshi Maeda,*,†,‡ and Tetsuya Taketsugu*,†,‡ †

Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-8245, Japan

‡

ABSTRACT: This work present results of a systematic investigation of adsorption and dissociation of H2 on the neutral, positively, and negatively charged gold clusters Aunq (n = 2−11; q = 0, ±1) using the global reaction route mapping (GRRM) technique combined with the anharmonic downward distortion following (ADDF) and the artificial forceinduced reaction (AFIR) methods. An exhaustive search for H2 dissociation pathways is performed not only on the most stable cluster structures but also on the large number of low-energy isomers, allowing structural transformations between them. The present strategy can automatically identify the structure-dependent lowest transition states (TS) for H2 dissociation with a systematic procedure in the regime of the structural fluxionality of gold clusters at finite temperature. Temperature effects, cluster isomerization, and influence of the charge state of gold clusters on H2 adsorption and dissociation are studied. It is demonstrated that the most stable structures of the gold clusters are not always highly reactive, and an ensemble of isomeric structures must be taken into account for adequate description of the reaction rates at finite temperatures. The proposed approach can serve as a promising tool for a systematic analysis and prediction of reactivity of small metal clusters.

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dissociation, irrespective of the cluster size.11,44 It has also been suggested that for the rutile TiO2 support the active sites for H2 dissociation may be formed by a combination of gold atoms and surface oxygen atoms at the nanoparticle−surface interface.44,45 Investigations of H2 dissociation on the free gold clusters are of particular interest because in this case properties of clusters are not affected by the support and interface effects, allowing us to study mechanisms of the catalytic reactions purely related to gold. There are quite a number of theoretical works on H2 adsorption on isolated gold clusters, although quantitative experimental data are still lacking.26 It has been shown theoretically that adsorption and dissociation of H2 on free gold clusters strongly depend on the reaction site on the cluster surface as well as on the size, structure, morphology, and charge of the cluster.53,56−58 Recently, H2 dissociation on several planar Aunq clusters with n = 4, ..., 10 and q = 0, ±1 has been studied as a function of the cluster structure and different sites of attack.58 In this elegant investigation, it has been found that the formation of a well of a positive charge in the entrance channel is an important condition for H2 dissociation. Many theoretical investigations have been focused on determination of the binding energies and dissociation barriers on small neutral and charged gold clusters accounting for structural relaxations;51,53,56,61 however, most of these studies have

INTRODUCTION Gold is one of the most intensively studied elements in nanocatalysis due to its unique catalytic activity and selectivity emerging at nanoscale even at room temperatures.1,2 This feature makes gold a very promising catalyst for the chemical industry and environmental applications.3,4 The most explored type of catalytic reactions with gold nanoparticles are reactions of oxidation and epoxidation by molecular oxygen,1,2,5−15 with a strong focus on oxidation of carbon monoxide1,2,4,9,16−24 as a most simple model case, allowing us to test various approaches and theories. Heterogeneously catalyzed hydrogenation is another type of reaction where gold nanoparticles have shown their great potential as catalysts.11,25,26 It has been shown that gold nanoparticles supported on the surfaces of some metal oxides can effectively catalyze selective hydrogenation of several classes of organic molecules, including unsaturated aldehydes, ketones, hydrocarbons, and nitro compounds.26−36 Moreover, gold nanoparticles are very selective for the direct formation of hydrogen peroxide from H2 and O2 mixtures.8,37−40 Dissociative adsorption of molecular hydrogen on gold nanoparticles is the first and one of the most important steps in heterogeneously catalyzed hydrogenation reactions because often it determines the reaction rate. It has been demonstrated that H2 does not bind to the clean gold bulk surface41 but adsorbs and dissociates on the supported11,26,42−49 and free50−60 gold nanoparticles. Theoretical calculations performed by Corma and coworkers demonstrate that the active sites for H2 dissociation are usually located at low-coordinated corner or edge positions on a cluster surface and do not directly bond to the support.43 However, experimental results of Fujitani and co-workers show that perimeter interface sites play a crucial role for H2 © XXXX American Chemical Society

Special Issue: Current Trends in Clusters and Nanoparticles Conference Received: November 30, 2014 Revised: January 17, 2015

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DOI: 10.1021/jp511913t J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

atoms, respectively. The remaining core electrons are represented by the Troullier−Martins norm-conserving pseudopotentials81 in the Kleinman−Bylander factorized form.82 All calculations are spin polarized. Relativistic effects are taken into account for Au via scalar-relativistic pseudopotentials. In the SIESTA code, the basis functions and the electron density are projected onto a uniform real-space grid. The mesh size of the grid is controlled by an energy cutoff, which defines the wavelength of the shortest plane wave that can be represented on the grid. In the present work, the energy cutoff of 100 Ry is chosen to guarantee convergence of the total energies and forces. A common energy shift of 50 meV is applied. Such a DFT-based approach has been successfully used to describe the structure and stability of small gold clusters as well as H2 dissociation processes on free and TiO2-supported gold clusters.45,70 The calculated values of the dissociation energy, De, and the bond length in Au2 (2.28 eV, 2.57 Å), H2 (4.73 eV, 0.74 Å), and AuH (3.10 eV, 1.55 Å) are in good agreement with the experimental data83 of Au2 (2.31 eV, 2.47 Å), H2 (4.74 eV, 0.74 Å), and AuH (3.36 eV, 1.52 Å), demonstrating good accuracy of the present approach. The atoms in molecules method of Bader (AIM) has been used for charge analysis.84,85 In the present work all the possible pathways of H2 dissociation on the ensemble of isomers of neutral and charged gold clusters Aunq (n = 2−11; q = 0, ±1) lying in the energy range of 20 kJ/mol, relative to the most stable structures, are considered. This is a reasonable approach because the typical barrier heights of low-lying paths for the H−H bond dissociation are ∼20−30 kJ/mol, and hence, contributions from the energetically higher-lying isomers are negligible.70 The detailed description on application of the automated reaction path search methods to calculation of the most favorable pathways of chemical reactions catalyzed by small metal clusters can be found in our recent work.70 At the initial stage of calculations all energetically low-lying isomers of gold clusters (within the predefined energy range) are collected by the anharmonic downward distortion following (ADDF) method.71,73,74 The ADDF method is an uphill walking approach along the reaction pathways from an equilibrium structure to the transition state and dissociation channel. This method has been successfully applied to identify the various isomers, transition states, and intermediates.73 This stage can be performed also by the single-component artificial force induced reaction method (SC-AFIR).86−88 The SC-AFIR is a variant of the multiple-component artificial force induced reaction method70,73,76 (MC-AFIR) which has been developed for studies of bimolecular and multicomponent reactions, and it has been introduced for application of the MC-AFIR to intramolecular reactions. In the present study, both the SCAFIR and the ADDF were performed in the initial Au cluster isomer search step. At the next stage the systematic search for the reaction pathways of H2 dissociation on the ensemble of gold cluster isomers is performed by applying the MC-AFIR method.70,73,76 The idea of the MC-AFIR method is pushing reactants together randomly by artificial force. By optimizing the potential surface with artificial force, one can easily get the approximate product and transition state. The accurate product and transition state can be obtained by optimizing the MCAFIR path by the locally updated plane method89 without artificial force and confirmed by the intrinsic reaction coordinate calculations.90

considered only the most stable cluster structures as an effective (or representative) catalyst. On the other hand, it is known that gold clusters may possess a number of structural isomers, and also transformations between these isomers can be induced thermally or by the interaction with the adsorbates.57 Such effects are known as “dynamical fluxionality”62 and can occur at room temperature on a time scale typical for chemical reactions.57,63−67 Recently such structural fluxionality has been measured experimentally for ultrasmall Au clusters on ceria thin films.68 Therefore, it is rather questionable to consider only the most stable structures for description of the reactivity of gold clusters at finite temperatures. Some attempts to overcome this problem have recently been made for investigation of H2 reactions on palladium clusters, where a large pool of low-energy Pdn isomers was considered for a systematic search of the most stable PdnH2 (molecular) and Pdn2H (dissociative) adsorption complexes.69 However, only the most stable configurations have been considered for investigation of the reaction barriers. The importance of fluxionality and ensemble effects on dissociation of H2 on gold clusters has been reported by Barrio et al.;53 however, in spite of the intensive investigations on catalytic activity of gold clusters in the past decade, the role of the fluxionality effects on various chemical processes on the cluster surface remains unclear and has yet to be fully understood. Recently, we have proposed a novel effective strategy for a systematic search of the best pathway for single bond activation reactions catalyzed by small metal clusters.70 This approach is based on the global reaction route mapping (GRRM) technique71,72 and combines two automated reaction path search methods: the anharmonic downward distortion following71−74 (ADDF) and the artificial force-induced reaction73,75,76 (AFIR) methods. In the present work we report results of a systematic investigation of adsorption and dissociation of H2 on the neutral, Aun, positively, Aun+, and negatively, Aun−, charged gold clusters, with the number of atoms n = 2−11 using the automated reaction path search technique. An exhaustive search of H2 dissociation pathways is performed not only on the most stable cluster structures but also on the large number of lowenergy isomers, allowing structural transformations between them. The present strategy can automatically identify the lowest transition states (TS) for H2 dissociation with a systematic procedure. Temperature effects, cluster isomerization, and influence of the charge state of gold clusters on H2 adsorption and dissociation are studied. It is demonstrated that the most stable structures of the gold clusters are not always highly reactive. Therefore, the systematic search for reaction pathways accounting for contribution of all low-energy isomers is required for an adequate description of H2 dissociation on gold clusters. The proposed approach can serve as a promising tool for a systematic analysis and prediction of reactivity of small metal clusters in the regime of structural fluxionality.

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METHODS The calculations are carried out by the local developmental GRRM (Global Reaction Route Mapping) program73 using the energies and gradient vectors computed within densityfunctional theory (DFT) with the gradient-corrected exchange-correlation functional of Perdew, Burke, and Ernzerhof (PBE)77 as implemented in the SIESTA code.78−80 Double-ζ plus polarization function (DZP) basis sets are used to treat the 5d106s1 and 1s1 valence electrons of Au and H B


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RESULTS AND DISCUSSION The optimized geometries of the most stable neutral Aun clusters and AunH2 complexes with the number of gold atoms n = 2−11 are shown in Figures 1a and 1b, respectively.

stable AunH2 complexes by the MC-AFIR method. For a given cluster size, H2 is randomly placed in the vicinity of a cluster in a large number of nonequivalent positions in order to get the most favorable adsorption and dissociation pathways. It is seen from Figure 1 that adsorption of H2 on the neutral gold clusters Aun (n = 2−11) does not change cluster geometries, except of the small Au3 which has a structure change from a bended linear chain to a triangle. This result is in contrast to the case of O2 adsorption on the small gold clusters, where the strong structural transformations are induced by the charge transfer to the adsorbed oxygen molecule. Our calculations demonstrate that there is charge transfer between the adsorbed molecular hydrogen and the gold clusters, but it is not large and cannot promote the strong structural transformations in gold. Figure 1b shows that the H2 molecule adsorbs on a neutral gold cluster on top of a single Au atom forming a triangle between two H atoms and the bounded Au, either in the cluster plane, as for n = 3, 4, 5, 10, and 11, or perpendicular to it, as for n = 6, 7, 8, and 9. Kang et al.56 reported H2 adsorption and dissociation of H2 on the neutral, cationic, and anionic gold clusters with n ≤ 6 calculated at the PW91/def2-TZVPP level of theory. Our results are in good agreement with the PW91 values, except of the Au5H2 complex, where the isomer with the different adsorption site of H2 on the surface of Au5 is slightly favorable energetically. Although molecular adsorption of H2 is favorable energetically on the most stable neutral Aun structures, the most stable AunH2 complexes are not always the best starting point for H2 dissociation. It has been suggested that as a general rule the size and shape of the cluster influence the number and position of available sites for an electrophilic and/or nucleophilic attack.105 This makes the reactivity patterns of these clusters highly complex. According to the charge distribution analysis of small gold clusters Aun (6 ≤ n ≤ 13), the high-coordinated gold atoms possess slightly negative net charge, while the low-coordinated gold atoms possess small positive net charge.105 The results of our calculations demonstrate that preferable sites for H2 adsorption are the positively charged low-coordinated gold atoms in the most stable gold isomers. However, many of these sites are not the best for H2 dissociation. Thus, in the case of Au5, Au7, and Au10 the higher-coordinated Au atoms are more reactive and provide lower H 2 dissociation barrier in comparison with the H2 dissociation on the low-coordinated sites responsible for the strongest bonding of the molecular hydrogen. Figure 1c demonstrates that not only the nature of the adsorption sites on the cluster surface but also the isomer structure are important for H2 dissociation. Thus, the most stable isomers of Au6, Au8, and Au9 are not the best structures for H2 dissociation with the lowest barrier. Dissociation of H2 on Au6, Au8, and Au9 clusters is more favorable if it takes place on isomers with the excess in free energy relative to the most stable structures of 75.9, 16.3, and 10.4 kJ/mol, respectively. It is seen from Figure 1 that H2 prefers molecular adsorption on the low-coordinated gold atoms but dissociates with the lowest barrier on the high-coordinated atoms. One of the reasons for such an effect can be the presence of the better adsorption sites for H atoms after H2 dissociation, when it occurs on the highcoordinated gold center. Therefore, structural and morphology effects are very important for H2 dissociation on the small gold clusters. We have found that the first step in H2 dissociation on

Figure 1. Optimized structures of the most stable neutral Aun clusters (a) and AunH2 complexes (b) for n = 2−11. Initial configuration of the AunH2 complexes for the most favorable path of H2 dissociation (c). The differences in free energies of complexes presented in (c) and (b) are shown in units of kJ/mol at T = 0 K. The total number of the considered isomers lying in the energy range of 20 kJ/mol relative to the most stable structures is shown in parentheses.

The starting configurations of the AunH2 complexes leading the most favorable H2 dissociation paths are presented in Figure 1c. The differences in free energies of AunH2 complexes leading to the most favorable H2 dissociation paths (c) and the most bounded configurations of AunH2 (b) calculated at T = 0 K are shown in units of kJ/mol, under the corresponding structures in Figure 1c. There are many studies on geometry and electronic structures of gold clusters.13,65,91−103 Small gold clusters Aun with the number of atoms n up to ≈11 possess planar structures as a result of the relativistic effects, which cause strong sd hybridization,92,104 while larger gold clusters are three-dimensional. In the present work, an ensemble of gold cluster isomers lying in the energy range of 20 kJ/mol relative to the most stable structures is used for a systematic search of the most C


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clusters can considerably affect their structure. Thus, cationic gold clusters Aun+ become three-dimensional for n ≥ 8, as is seen from Figure 2a. Competition of two-dimensional (2D) and three-dimensional (3D) structures of gold clusters can play an important role in cluster reactivity. The most stable structures of the cationic gold clusters obtained in the present work are in a good agreement with the previous experimental107 and theoretical data.108 It should be noted that Au8+ possesses very flexible structure. Thus, the most stable structure of Au8+ shown in Figure 2a at T = 0 K becomes the second lowest isomer structure at T = 298.15 K due to the entropy effects. Figure 2b demonstrates that H2 adsorbs on the lowcoordinated gold atom in cationic gold clusters, in a configuration when the H2 molecule binds on the Au atom forming a H−H−Au triangle, similar to adsorption on the neutral gold clusters. However, H2 adsorption on the cationic gold clusters often results in a drastic alteration of the cluster structure. Thus, for Au5+, Au7+, Au8+, and Au9+ clusters adsorption of H2 on the low-lying isomer structures leads to the most stable configurations of Aun+H2 complexes. It should be noted that hydrogen adsorption on Au7+ promotes 2D → 3D structural transition, while H2 adsorption on Au8+ promotes 3D → 2D transition. Figure 2c presents starting configurations of Au n + H 2 complexes leading to the energetically lowest pathways for H2 dissociation. It is seen that structures of Aun+H2 complexes which are the most reactive for H2 dissociation are planar up to n = 6 and three-dimensional for n ≥ 7. Structures of gold clusters in the most reactive Aun+H2 complexes for n = 9 and 11 are considerably different from the most bounded configurations. The most stable optimized structures of anionic Aun− clusters, Aun−H2 complexes, and Aun−H2 complexes leading to the most favorable H2 dissociation are presented in Figures 3a, 3b, and 3c, respectively. The calculated geometry structures of the most stable anionic Aun− clusters are planar up to n = 11. The interatomic Au−Au distance in the anionic gold clusters is slightly expanded with respect to the corresponding neutral gold clusters, while the structures of the most stable Au3−, Au4−, Au7−, Au9−, and Au10− are different from the neutral clusters. The obtained structures of anionic gold clusters are consistent with the results of previous experimental observations and theoretical predictions.109,110 As is seen from Figure 3 the most stable anionic gold clusters cannot always provide the best adsorption sites for H2, and therefore several isomer configurations have to be taken into account to find the most stable Aun−H2 complexes. It is important to note that for all considered anionic gold clusters H2 adsorbs on gold atoms in the linear configuration, when only one H atom in H2 interacts with gold. Similar to the neutral and cationic clusters, the most stable anionic Aun−H2 complexes are not always responsible for the best pathways for H2 dissociation. From the chemical intuition one can suggest that the isomer with the strongest binding should coincide with the one responsible for the lowest dissociation path because the strong binding often implies the large charge transfer and weakening of the H−H bond. However, we have not found a clear relationship between the adsorption energy and dissociation barrier for the H2 molecule. The ratio for the case that the most stable adsorption state is consistent with the most favorable H2 dissociation path is 50% for the neutral Au2− Au11, 60% for the corresponding cationic clusters, and 30% for

gold clusters is the H−H bond breaking which occurs without cluster isomerization. This is the rate-determining step. After the initial H−H bond breaking the intermediate with the dissociated H atoms can reach the bottom of the local funnel as was discussed in our recent study.70 The optimized geometries of the most stable cationic Aun+ clusters and Aun+H2 complexes with the number of gold atoms n = 2−11 are shown in Figures 2a and 2b, respectively. Figure

Figure 2. Optimized structures of the most stable cationic Aun+ clusters (a) and Aun+H2 complexes (b) for n = 2−11. Initial configuration of the Aun+H2 complexes for the most favorable path of H2 dissociation (c). The differences in free energies of complexes presented in (c) and (b) are shown in units of kJ/mol at T = 0 K. The total number of the considered isomers lying in the energy range of 20 kJ/mol relative to the most stable structures are shown in parentheses.

2c presents the initial configurations of Aun+H2 complexes leading to the most favorable H2 dissociation path. The differences in free energies of Aun+H2 complexes leading to the most favorable H2 dissociation paths (c) and the most bounded configurations (b) calculated at T = 0 K are shown in units of kJ/mol, under the corresponding structures in Figure 2c. There are many works devoted to the structural properties and reactivity of the cationic gold clusters.55,56,97,103,106,107 Excess of the negative or positive charge on the small gold D


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reliable search of the lowest pathways of chemical reactions catalyzed by small neutral, cationic, and anionic gold clusters. The geometry configuration of H2 adsorbed on the neutral and charged gold clusters depends on the type of molecular orbitals involved in the interaction of hydrogen with gold. It has been found that in the case of the triangular structure of H2 on Au, which is a favorable configuration for the neutral and cationic gold clusters, there is a charge transfer from the highest occupied molecular orbital (HOMO) of H2 to the gold cluster.56 On the other hand in the case of the linear structures, typical for the anionic Aun−H2 systems, there is a charge transfer from the gold to the lowest unoccupied molecular orbital (LUMO) of H2.56 Natural bond orbital analysis demonstrates that in the general case both the donation (electron transfer from the HOMO of H2 to the gold cluster) and the back-donation (electron transfer from the gold cluster to the LUMO of H2) mechanisms coexist.56 Figures 4a and 4b demonstrate the n-dependence of Bader charges on hydrogen calculated for the molecular and dissociative configurations of the adsorbed H2, respectively. Lines with filled dots, triangles, and stars in Figures 4a and 4b represent the hydrogen charge for adsorption on the neutral, cationic, and anionic gold clusters, respectively. In the case of molecular adsorption of H2 on Aun and Aun+ clusters, the Bader charge on hydrogen varies from +0.05 e to +0.3 e, reflecting domination of the electron donation from the HOMO of H2 to the gold cluster. Figure 4a demonstrates that for H2 adsorption on gold clusters there is no odd−even oscillatory behavior as a function of cluster size n, well-known for O2 adsorption.13 However, in the case of H2 adsorption on the anionic clusters Aun− Bader charge can possess both positive (n = 5, 7, and 11) and negative (n = 2−4, 6, and 8−10) values, reflecting the strong competition between donation and back-donation processes. After dissociation, two hydrogen atoms possess total charge that can vary in the range from 0.0 e to −0.17 e for the neutral gold clusters and from −0.1 e to −0.45 e for the anionic complexes. In the case of H2 dissociation on the cationic gold clusters the total Bader charge on two hydrogen atoms remains positive, except n = 6 and 11. It is important to note that in most of the considered cases H2 dissociation is homolytic. However, there are several examples of the heterolytic dissociation which we found for Au22H, Au112H, Au5+2H, and Au6+2H complexes, where two hydrogen atoms possess charge of different signs. In the case of Au6+, 2H charges on H have equal values but different sign, canceling each other. Therefore, the total charge on both H after

Figure 3. Optimized structures of the most stable anionic Aun− clusters (a) and Aun−H2 complexes (b) for n = 2−11. Initial configuration of the Aun−H2 complexes for the most favorable path of H2 dissociation (c). The differences in free energies of complexes presented in (c) and (b) are shown in units of kJ/mol at T = 0 K. The total number of the considered isomers lying in the energy range of 20 kJ/mol relative to the most stable structures is shown in parentheses.

the anionic ones. Therefore, accounting for an ensemble of isomers at finite temperatures is a necessary condition for a

Figure 4. Bader charge on hydrogen calculated for molecular (a) and dissociative (b) adsorption of H2 on the neutral (dots), cationic (triangles), and anionic (stars) gold clusters with the number of atoms n = 2−11. E


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Figure 5. Calculated H−H bond length in the H2 molecule adsorbed on neutral (a), cationic (b), and anionic (c) gold clusters. Solid lines correspond to configurations related to the lowest pathways for H2 dissociation, while dashed lines correspond to the most bounded structures. Horizontal dashed line represents the H−H bond length in a free H2.

Figure 6. Change in free energy, ΔG, upon H2 adsorption on the neutral gold clusters calculated at T = 0 K (a) and T = 298.15 K (b) for the most stable configurations (filled squares) and configurations leading to the best dissociation path (filled dots). Free energy of the lowest transition state for H2 dissociation, ΔGTS, calculated relative to the sum of free energies of the noninteracting H2 and gold clusters for the most stable configurations (open squares) and configurations leading to the best dissociation path (open dots).

dissociation on Au6+ is close to zero, as one can see from Figure 4b. Both donation (depopulation of the bonding HOMO of H2) and back-donation (population of the antibonding LUMO of H2) processes responsible for the binding of the molecular hydrogen to the gold clusters result in a weakening of the H−H bond. Figure 5 demonstrates the calculated H−H bond length in the H2 molecule adsorbed on the neutral (a), cationic (b), and anionic (c) gold clusters as a function of cluster size. Solid lines in Figure 5 correspond to the starting configurations leading to the lowest pathways for H2 dissociation, while dashed lines correspond to the H−H bond length in the most bounded structures. It is seen from Figure 5 that H−H bond length in H2 adsorbed on the neutral and cationic gold clusters is elongated considerably compared with the free H2 (0.74 Å), while such elongation is relatively small for H2 adsorbed on the anionic gold clusters. Moreover, one can see that the H−H bond is longer in complexes leading to the lowest dissociation pathways, with an exception of Au8, Au10, Au8+, Au8−, Au9−, and Au10− clusters. Therefore, H−H bond elongation can serve as a descriptor of cluster ability to dissociate H2. Let us now consider energetics of the H2 adsorption on Aunq clusters with the number of atoms n = 2−11 and charge q = 0, ±1. Dashed lines with filled squares in Figures 6a and 6b represent the cluster size evolution of the change in free energy, ΔG = GAS − GIS, upon H2 adsorption on the neutral gold clusters in the most stable configuration at T = 0 K (a) and T = 298.15 K (b), respectively. Here, GAS and GIS denote the free energy of the adsorption state (AS) of the bounded hydrogen− gold complex and the initial state (IS) of the noninteracting

hydrogen molecule and the gold cluster, respectively. The free energy G is calculated as

G = H − TS

(1)

where H is the enthalpy of the system with thermal corrections; T is the temperature; and S is the entropy accounting for the translational, vibrational, and rotational degrees of freedom.111 Figure 6a demonstrates that molecular adsorption of H2 on the neutral gold clusters is exothermic at T = 0 K for all considered cluster sizes. H2 is found to be the most stable on the small Au2, Au3, and Au4 clusters with ΔG = −41 to −46 kJ/ mol, while it is less stable on Au5−11 with ΔG = −10 to −31 kJ/ mol. The stability of the adsorbed H2 on the gold clusters decreases with an increase in temperature, as seen from Figure 6b. This effect occurs due to the entropy contribution to the free energy (eq 1) because H2 loses its translational degrees of freedom upon adsorption. Thus, at T = 298.15 K molecular hydrogen is stable only on Au2, Au3, and Au4 with ΔG = −19 to −14 kJ/mol. Let us now consider dissociation of the hydrogen molecule adsorbed on the neutral gold clusters. First we perform calculations using a traditional stategy, i.e., considering dissociation of H2 on the most stable configurations of AunH2 complexes. Solid lines with open squares in Figures 6a and 6b represent the corresponding free energies of the transition states (TSs) for H2 dissociation, ΔGTS, calculated relative to the sum of free energies of the noninteracting H2 and gold clusters at T = 0 K and T = 298.15 K, respectively. Figures 6a and 6b demonstrate that H2 can dissociate on the neutral Au3 and Au4 clusters with a very low barrier, for both T = 0 K and T = 298.15 K. However, for n = 2 and 5−11 the energy of the TS state is considerably larger than the binding F


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Figure 7. Change in free energy, ΔG, upon H2 adsorption on the cationic gold clusters calculated at T = 0 K (a) and T = 298.15 K (b) for the most stable configurations (filled squares) and configurations leading to the best dissociation path (filled dots). Free energy of the lowest transition state for H2 dissociation, ΔGTS, calculated relative to the sum of free energies of the noninteracting H2 and gold clusters for configurations leading to the best dissociation path (open dots).

Figure 8. Change in free energy, ΔG, upon H2 adsorption on the anionic gold clusters calculated at T = 0 K (a) and T = 298.15 K (b) for the most stable configurations (filled squares) and configurations leading to the best dissociation path (filled dots). Free energy of the lowest transition state for H2 dissociation, ΔGTS, calculated relative to the sum of free energies of the noninteracting H2 and gold clusters for configurations leading to the best dissociation path (open dots).

energy of the molecular H2 to the neutral gold clusters. Therefore, it is likely that molecular H2 will desorb from Au2 and Au5−11, rather than dissociate. On the basis of PW91/def2TZVPP DFT calculations,56 Kang et al. suggested that H2 dissociation is also feasible on the Au5 cluster because the binding energy of H2 to Au5 is larger than the dissociation barrier. However, according to our calculations with the use of PBE functional with DZP basis set, the barrier is larger than the change in free energy upon H2 adsorption on Au5. This discrepancy can be explained by the difference in PW91/def2TZVPP and PBE/DZP energies as well as account for the thermal corrections to enthalpy in our calculations. As was discussed previously, different cluster structures can possess different reactivity. Therefore, let us consider adsorption and dissociation of the molecular hydrogen not only on the most stable structures but also on the ensemble of cluster isomers. In the present work we account for all possible isomers lying in the energy range of 20 kJ/mol, relative to the most stable structures, and perform an automatic identification of the structure-dependent lowest transition states for H2 dissociation with a systematic procedure based on the GRRM technique combined with ADDF and AFIR methods. Solid lines with open dots in Figures 6a and 6b represent the energies of the lowest TSs for H2 dissociation along the most favorable dissociation pathways, calculated at T = 0 K and T = 298.15 K, respectively. Corresponding changes in free energy, ΔG, upon H2 adsorption on the neutral gold clusters calculated for configurations leading to the best dissociation paths at T = 0 K and T = 298.15 K are represented by solid lines with filled dots

in Figures 6a and 6b, respectively. It is clearly seen that the presence of the isomer structures in the cluster ensemble results in a considerable decrease in TS energies for H2 dissociation. It is amazing that for Au5, Au7, and Au10 clusters the energy difference between the most bounded structures and structures leading to the best dissociation path is very small (0.3−3.7 kJ/ mol); however, in spite of this small difference, TS energy can be reduced dramatically. Namely, the relative free-energy values of ΔGTS define the importance of various reaction pathways,70 as follows from the conventional transition-state theory (TST). Excess of the positive or negative charge on gold clusters considerably affects H2 adsorption. Figure 7a demonstrates that H2 adsorption on the cationic gold clusters is exothermic at T = 0 K for all considered sizes n = 2−11. The absolute value of ΔG steadily decreases with an increase in cluster size, with some local minima at n = 5 and 7. At T = 298.15 K molecular hydrogen remains stable on the cationic gold clusters with the number of atoms n up to 7, as seen from Figure 7b. It has been demonstrated experimentally57 that H2 adsorbs on all gold cluster cations with n = 2−7 at T = 100 K, while at T = 200 K no adsorption has been found for Au2+. Further heating of clusters up to T = 300 K changes the reaction behavior dramatically when none of the considered clusters have been found active toward H2 adsorption, except Au5+, which adsorbs up to three H2 molecules.57 Our theoretical calculations in good agreement with experimental observations by Lang et al.57 at low temperatures, however, disagree with experiment at room temperature where no stable products of interaction of G


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The Journal of Physical Chemistry C Notes

H2 with gold cluster cations have been found experimentally for Au2+, Au3+, Au4+, and Au7+. Lines with open dots in Figures 7a and 7b show the size dependence of the lowest TS energies for H2 dissociation along the most favorable path on the ensemble of cationic gold clusters at T = 0 K and T = 298.15 K, respectively. In the case of cationic gold clusters, Aun+, TS energies calculated at T = 0 K are negative for n = 2 and 4−7, indicating that H2 dissociation on Au2+ and Au4−7+ favors H2 desorption. However, at T = 298.15 K desorption of H2 is a favorable process for all considered clusters, except of Au5+, where the calculated energy of TS (−1 kJ/mol) is very small. This result is consistent with the experimental work by Sugawara et al. 52 where H 2 dissociation on Aun+ has not been observed at room temperature and low pressure conditions. However, it should be noted that dissociation of the molecular hydrogen on the small gold cluster cations can become possible at high pressure conditions, as was shown by Cox et al.112 for the D2 + Aun+ reaction (n = 2−13 and 15). Figure 8a demonstrates that adsorption of H2 on the anionic gold clusters is exothermic at T = 0 K for all considered cluster sizes, although the change in free energy due to H2 adsorption is very small ΔG = −4 to −10 kJ/mol for all considered sizes. At T = 298.15 K H2 is not stable on the considered anionic gold clusters. The calculated ΔGTS energies for the most favorable H2 dissociation paths on anionic gold clusters (solid lines with open dots in Figures 8a and 8b) are relatively large for the small cluster sizes, decreasing with an increase in n. Therefore, dissociation of H2 on gold cluster anions is not favorable energetically due to the weak interaction of H2 with the clusters as well as the large values of ΔGTS.

The authors declare no competing financial interest. § On leave from: V. A. Fock Institute of Physics, St Petersburg State University, 198504 St Petersburg, Petrodvorez, Russia.

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ACKNOWLEDGMENTS This work was performed under the management of the “Elements Strategy Initiative for Catalysts and Batteries (ESICB)” supported by the MEXT program gElements Strategy Initiative to Form Core Research Center (since 2012) and was partly supported by the JSPS Grant-in-Aid for Scientific Research C, also a grant from Japan Science and Technology Agency with Advanced Catalytic Transformation Program for Carbon Utilization (ACT-C) at Hokkaido University. The computations were performed using in part the computer facilities of ESCIB, Kyoto, Japan, and the Research Center for Computational Science, Okazaki, Japan.

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CONCLUSION In this article, we have reported the results of a systematic theoretical investigation of adsorption and dissociation of H2 on the neutral, Aun, cationic, Aun+, and anionic, Aun−, gold clusters (n = 2−11) using the automated reaction path search technique. Temperature effects, cluster isomerization, and influence of the charge state of gold clusters on adsorption and dissociation of H2 are studied. An exhaustive search of H2 dissociation pathways has been performed not only on the most stable cluster structures but also on the large number of lowenergy isomers. It is demonstrated that the most stable structures of the gold clusters are not always highly reactive and that the most stable adsorption configurations of H2 on gold clusters do not necessarily lead to the low-energy dissociation pathways. Therefore, a systematic search for reaction pathways accounting for contribution of all low-energy isomers is required for an adequate description of H2 adsorption and dissociation on gold clusters. The proposed approach can serve as a promising tool for a systematic analysis and prediction of reactivity of small metal clusters in the regime of structural fluxionality, where several isomers of gold clusters can coexist at the finite temperature.

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