Understanding Structure, Size, and Charge Effects for the H 2 Dissociation Mechanism on Planar Gold Clusters

Understanding Structure, Size, and Charge Effects for the H2 Dissociation Mechanism onPlanar Gold Clusters

Alexandre Zanchet,† Anaıs Dorta-Urra,†,‡ Alfredo Aguado,‡ and Octavio Roncero*,†

Unidad Asociada UAM-CSIC, Instituto de Fisica Fundamental, C.S.I.C. Serrano 123, 28006 Madrid, Spain,and Unidad Asociada UAM-CSIC, Departamento de Quimica Fisica, Facultad de Ciencias C-XIV, UniVersidadAutonoma de Madrid, 28049 Madrid, Spain

ReceiVed: July 20, 2010; ReVised Manuscript ReceiVed: NoVember 19, 2010

The H2 dissociation on several planar Aunq gold clusters, with n ) 4, ..., 10 and charges q ) 0, (1, has been

studied in detail as a function of the nuclear configuration of the cluster and at different sites of attack. It isfound that the formation of a well in the entrance channel is a necessary condition for the dissociation tooccur. This well always appears in sites of Aun

q where there is a defect in the electronic density with respectto that of the n neutral and isolated gold atoms or, in other words, where there is a positive charge due to thepolarization of the electronic density associated to the electronic correlation. When H2 attacks on linear sidesof three atoms, on the middle gold atom, the reactivity is fully determined by this entrance well. On thecontrary, when attacking corners there is a second step, in which a b2 antibonding orbital crosses the a1

HOMO orbital. The b2 orbital is strongly stabilized by an important bonding overlap between the H2 and thetwo neighboring gold atoms orbitals. For obtuse corners, with atoms of coordination 3, the stabilization dueto this H-Au bonding overlap occurs at shorter distances than for acute angles, of coordination 2, simplybecause the neighboring gold atoms are structurally closer. Thus, the crossing occurs at shorter H-H distancesfor the obtuse angle, yielding lower dissociation barriers, while for the acute case the barrier is always high.The height of the barrier as a function of the charge is explained by the occupation of the frontier orbitals.For those cases in which the Aun

- anion presents the entrance well, the stabilizing b2 orbital has typically themaximum occupation yielding the lower reaction barriers. The relaxation of the gold cluster in the reactionis analyzed by optimizing the total system at the stationary points. For the relaxed case, the MEP’s obtainedare nearly parallel to those obtained for the frozen gold cluster, which validates the main conclusions of thiswork.

1. Introduction

The study of the reactivity of gold nanoparticles1 is receivingincreasing interest since the discovery of their catalyticproperties.2,3 These properties of gold nanoparticles dependstrongly on their structure and is typically attributed to lowcoordinated atoms appearing at the edges of clusters4-6 andcorrugated metal surfaces.7 Gold nanoparticles present verydifferent structures8 such as nanowires,9-11 planar (2D)clusters,12-18 and cages,19-21 analogous to fullerenes.22 Theoccurrence of such a rich variety of structures is attributed toimportant relativistic effects, which cause the 6s and 5d orbitalsto become closer in energy than in other coinage atoms, allowingan sd hybridization,13 which produces a stabilization and makespossible planar23,24 and spherical aromatic structures.19

From a fundamental point of view, gold clusters present veryinteresting properties. Noble metal surfaces are chemically inertbecause their d-shells are full.25 Among them, gold is the noblestmetal.26 On the other side, a single gold atom in its groundelectronic state is not reactive with H2, presenting a reactionbarrier higher than 1.5 eV.27 In between these two limits, goldnanoclusters of a few nanometers present important catalyticproperties, which depend on the size, charge, and structure ofthe cluster. Thus, it is important to understand the collectivephenomena which cause these medium size systems to be so

reactive and attempt to systematize the mechanisms and mainfactors determining their catalytic properties. Finding physicaltrends of the reaction mechanisms of small nanostructures orclusters may help in designing new nanocatalytic materials.

One of the most studied reactions on gold particles is theoxidation of CO. Many theoretical studies have been devotedto study the potential well of O2 and CO complexes withAun.28-34 Neither O2 nor CO dissociates on gold clusters,28-34

but these diatomic molecules attach to the gold particles andtheir bonds become weakened, facilitating the reaction betweenthem in a second step. Another important kind of reaction ingold chemistry is the partial hydrogenation of unsaturatedhydrocarbons, which takes place very selectively.35 The dis-sociative adsorption of hydrogen molecules on gold particlesis an important step in this kind of reaction and is relativelysimple, which may help to understand the reaction mechanismsystematically.

There are many studies about the reactivity of H2 moleculeson isolated5,6,36-41 as well as on supported42-44 gold particles.The reactivity shows strong variations depending on the numberof gold atoms40 and charge. Theoretical studies have beenfocused on the determination of the dissociation barriers5,6

considering the relaxation of the gold cluster. These studiesprovide clear and important information on the highly complexcatalytic properties of gold particles, which change rathererratically as a function of size and charge of the system. It isthen important to establish the parameters governing the

* To whom correspondence should be addressed.† Instituto de Fisica Fundamental.‡ Universidad Autonoma de Madrid.

J. Phys. Chem. C 2011, 115, 47–57 47

10.1021/jp106733s 2011 American Chemical SocietyPublished on Web 12/13/2010

reactivity of such gold clusters. The smaller Aun clusters (up to≈n ) 10) are known to be planar.12-18,45,46 The adsorption ofatomic38 and molecular36,39 hydrogen on planar Aun occurspreferentially in the plane of the clusters. On the contrary, sitesabove the cluster plane are rather inert. In addition, the higherreactivity of the dangling orbitals along the perimeter of theplanar clusters is highly directional, showing clear sites ofpreference. This is interpreted by the d-character of thehybridized frontier orbitals of gold clusters.38 The sd hybridiza-tion, attributed to relativistic effects,13 favors planar Au clusterswith a sort of aromatic binding structure in which all the orbitalsin the clusters are saturated, leaving only free orbitals at theedges. Folding the planar structure of the clusters disturbs theplanar hybridization, and the atoms in the edge line becomeagain very reactive as recently shown for Au10 clusters.47 Thus,the reactivity of small gold clusters is attributed not only to thelower coordinated atoms but also to the availability of orbitalsto form new bonds.

The aim of this work is to analyze systematically the role ofthe size, charge, and structure of planar gold clusters on thereactivity of H2 on Aun

q clusters (neutrals q ) 0, cations q )+1, and anions q ) -1), with n ) 4 to 10 atoms. For thispurpose, density functional theory (DFT) calculations areperformed for selected nuclear configurations of Aun

q, chosento be either the ground or nearly the most stable conformer ofthe neutral species, according to the data found in the literature.A schematic representation of the geometries of the clustersstudied are depicted in Figure 1. As no wells were found forH2 outside the plane of the cluster, all the directions of attack

explored in this work lie in the plane, as shown in Figure 1,and the gold clusters retained in a frozen geometry. The role ofthe relaxation of the gold cluster is further analyzed byoptimizing the geometries of the stationary points found for thefrozen gold cluster. The results obtained for all these clustersare interpreted in terms of a simple two-step reaction model:first, the formation of a H2-Aun

q complex and, second, the H2

dissociation. The main factors determining these two steps areanalyzed in detail to provide a systematic understanding of thereactivity.

This paper is organized as follows. The theoretical methodis described in section 2. The main results are shown in section3, with the description of the two steps of the reactionmechanism proposed. Finally, in section 4 some conclusionsare offered.

2. Theoretical Treatment

Reactivity on metallic clusters is very sensitive to the detailsof the potential energy surfaces, which must be obtained withhigh accuracy. However, high level ab initio calculations arerestricted to small Aun+H2 systems, as for example, the casesfor n ) 2, 3, and 437,47 calculated using a coupled cluster methodincluding single and double excitations and triples perturbatively(CCSD(T)). In this work, most of the calculations are performedusing a DFT method with the Generalized Gradient Approxima-tion (GGA) with the PW91 functional.48 The results obtainedwith this method were compared to CCSD(T) calculations in aprevious study,47 obtaining very good agreement for Aun+H2

(n ) 3 and 4), with differences ∼0.1-0.2 eV, which can beconsidered to be satisfactory.

All the calculations are performed with the MOLPRO suiteof programs,49 using the correlation-consistent polarized VTZbasis of Dunning50 for hydrogen (including 23 spd functions).Gold atoms are described by the ECP60MWB effective corepseudopotential with a basis set composed of 36 uncontractedspd orbitals.51 In this potential, 19 valence electrons areconsidered; a lower number of valence electrons is not ap-propriate, because a considerable and artificial increase in thereaction barrier is then obtained.37,47

A restricted open shell Kohn-Sham49 method was used todeal with open shell systems. To check the convergence, specialattention was paid to the ordering of the molecular orbitals (MO)along the minimum energy path (MEP). In many cases, acrossing between HOMO and LUMO takes place along theMEP, and single reference methods such as DFT are known topresent convergence problems (typically convergence to a higherexcited state), in particular near the crossing. To avoid thisproblem, a higher multiplicity (triplet or quadruplet) calculationis first performed to optimize as many frontier orbitals aspossible, followed by the calculation of the desired lowermultiplicity of the cluster (singlet or doublet depending on itssize and charge). This allows a reordering of the HOMO,SOMO, and LUMO orbitals to better converge the ground state.

In general, all the calculations are performed within the Cs

symmetry group, considering the plane containing the Aun

cluster. When H2 approaches the cluster in the plane of Aun, itinteracts with a′ orbitals of the Cs symmetry group, withoutaffecting the a′′ orbitals (out of plane).

This symmetry group will thus be the one taken as referencefor our calculation. In addition, calculations at different sym-metries (C2V wherever possible and with no symmetry whennecessary) were also performed for analysis purposes. Finally,CCSD(T) calculations were also performed for some selectedcases to analyze the curve crossings and compare differentmethods.

Figure 1. Schematic representation of nuclear geometries and initialattack sites of the Aun (n ) 4-10) planar clusters. For simplicity, theAu-Au distances are kept constant and equal to 2.75 Å (the equilibriumdistance of Au7). S, A, and O denote linear sides and acute and obtusecorners, respectively. Also, two different structures of Au10

q have beenconsidered: one triangular and the other hexagonal.

48 J. Phys. Chem. C, Vol. 115, No. 1, 2011 Zanchet et al.

http://pubs.acs.org/action/showImage?doi=10.1021/jp106733s&iName=master.img-000.jpg&w=238&h=318

As discussed above, H2 dissociation is only possible when itapproaches the perimeter of the gold clusters in the plane. Thegold clusters are kept frozen at their equilibrium geometry. Thus,the search for the MEP is restricted to four dimensions, two foreach hydrogen atom in the plane of the gold cluster. The initialconfiguration corresponds to H2 in its equilibrium distance, andat 10 Å from the closest gold atom, considered to be theasymptotic energy (taken as the energy origin). The search isstarted by determining the final chemisorption well. This is doneby looking first for the minimum energy configuration of a singlehydrogen atom chemisorbed to the cluster. Keeping the firsthydrogen in this position, the second hydrogen is moved aroundthe AunH complex until the global chemisorption well is found.

To find the MEP, we decided to not follow the general wayof an automatic algorithm. Instead, we decided to use anapproach generally used to study the reactivity of small systemssuch as atom+diatom, which is the exploration of the potentialenergy surface (PES). Due to the multidimensionality of theproblem, only the relevant parts of the PES (allowing us to gofrom entrance channel to the final minimum) were sampled,and the MEP was estimated from there. This method does notgive the barrier heights with the same precision, but it allows abetter overview of the global mechanism and eventualy can beused for a complementary dynamic study.

The first step is to find the minimum energy path for theapproach of H2 to the cluster. To do so, we explore the entrancechannel of the PES by sampling the H2 center-of-mass in theplane around the cluster, building a two-dimensional grid. Thisis done for several orientations of the H2 molecule and a fewH2 internuclear distances between the two classical turningpoints of bare H2, thus sampling the four degrees of freedom.The sampling is reduced for the symmetric clusters. From allthis mapping, it is found that the most characteristic directionsof attack follow a top mechanism except for triangular Au10

which presents a bridged one as will be discussed later. Thedifferent characteristic directions of attack are shown in Figure1. Furthermore, it is found that the preferred orientation of H2

axis is perpendicular to the vector indicated in Figure 1.The next step of the reaction is the dissociation of H2, taking

place once the distance between H2 and Aunq is sufficiently short.

To find that part of the MEP, the same procedure is followed.For several H2 orientations, bidimensional cuts of the PES arecalculated as a function of R, the distance between H2 center-of-mass and Aun

q (sampled between the distance of the morestable configuration found in the entrance channel and the valueof R corresponding to the chemisorption well), and r, theinternuclear distance (sampled between the equilibrium distanceof H2 and the distance between the hydrogens at the chemi-sorption well), as explained in ref 47.

Au7-+H2 and Au6

++H2 (s) can be considered as prototypicalcases, because the symmetry of the system allows the charac-terization of the MEP from a single bidimensional cut of thePES, as shown in Figure 2, as a function of r (the H-H distance)and R (the distance from the closest gold atom and the H2 centerof mass). This situation of maximum symmetry for the MEP isalso found for many of the cases studied. Three stationary pointsare characterized in Figure 2: (A) the well in the entrancechannel, in which H2 internuclear distance is very similar tothe bare equilibrium distance, (B) the transition state at the topof the low barrier, with the two hydrogen atoms alreadyseparated, and (C) the chemisorption well, corresponding to aAu-H-Au-H-Au double-bridge well which is very analogousfor all the cases studied. The dissociation of H2 along the MEPconstrains the orientation of the two hydrogen atoms as shown

in Figure 2. This occurs to maximize the overlap between theH2 antibonding orbital with the orbitals of the closest gold atoms,as will be discussed below.

3. H2 Reactivity on Planar Gold Clusters

The MEPs for the H2 dissociation on Aunq, n ) 4-10 and q

) 0, (1, and different geometries of approach are shown inFigure 3. After careful examination, these results can besummarized as follows:

1. Low dissociation barriers are only obtained for those casesin which there is a deep adsorption well of ≈0.4-0.6 eV in theentrance channel: if there is no absorption well, the reactionbarrier is higher than 0.5 eV. Hereafter, this well in the entrancechannel will be referred to as “entrance” well.

2. The entrance well appears preferentially for cations, butits existence does not always involve low barriers to dissociateH2.

3. For acute angle sites, the H2 dissociation barrier is alwaysvery high (except for Au9

-). For sites corresponding to broaderangles (either in the obtuse angles or sides of clusters), theneighboring gold atoms can participate in such a process, thuslowering the reaction barriers.

4. Sides with only two gold atoms are not reactive, and thepreferential site becomes the closest neighbor in a corner. Insides with three gold atoms, H2 attacks the central gold atom.For four-atom sides (triangular Au10 clusters), the H2 moleculeforms another type of bond in the entrance channel, attached totwo gold atoms as in Au-H-H-Au, leading to a differentreaction mechanism. This was previously studied for linear goldchains.47

5. In those cases where Aun- anions show entrance wells, their

reaction barrier is lower than those of the corresponding neutralor cation systems.

6. There is not a clear trend for the reaction depending onthe number of electrons or gold atoms.

Figure 2. Potential energy surface (eV) for the H2+Au7- reaction

(bottom panel) and for the H2+Au6+ (side) (top panel), as a function of

the H-H distance, r, and the distance from the closest gold atom andthe H2 center of mass, R. The geometry of the stationary pointsalong the MEP are showed as insets. Distances are in angstroms.

H2 Dissociation Mechanism on Planar Au Clusters J. Phys. Chem. C, Vol. 115, No. 1, 2011 49


According to the above-mentioned results, we can concludethat the existence of the entrance well is a necessary conditionfor the reaction to occur, but not sufficient. Thus, the H2

dissociation mechanism can be divided in two steps: theformation of the Aun

q-H2 entrance well and the dissociation ofH2 to form the Au-H-Au-H-Au double-bridge chemisorptionwell. The understanding of the reactivity is typically interpretedin terms of the f+ and f- Fukui functions,52 as recently appliedfor Aun clusters.53 These functions approximately correspondto the HOMO/LUMO orbitals of the systems. Because theHOMO/LUMO orbitals obtained for Aun

+, Aun0, and Aun

- arevery similar, such arguments are not valid to explain the differentreactivity obtained for different cluster charges q. Therefore,other arguments have to be considered to understand the reactionmechanism, especially in the entrance step.

A. Formation of the “Entrance Well”. The entrance wellhas a typical binding energy of 0.4-0.6 eV, while the double-bridge chemisorption well is of 0.8-1.5 eV. The entrance wellis rather strong, and it could be considered as a weakchemisorption well, but at the same time it corresponds to acomplex in which H2 keeps most of its fundamental features,with a slight elongation of the H-H distance, and appearspreferentially for the Aun

+ cations. This leads us to think thatthe origin of this well is the electrostatic interactions due to theanisotropy of the charge distribution of Aun

q.To analyze the charge distribution of Aun

q with a proper spatialdistribution, we shall assume that isolated gold atoms have aspherical electronic distribution which corresponds to a neutralsituation. Thus, we calculate the electronic distribution of Aun

q,

dAunq, and subtract the n densities of isolated and neutral gold

atoms, dAui, placed at the same positions they are in the clusters,

i.e.,

This electronic difference, shown in Figure 4 for the systemsunder study, provides information about the charge distributionof the system and how each gold atom is polarized within theclusters. Density defect regions (in red) could be associated toregions positively charged, while regions with electronic excess(in blue) are negative. This is valid not only for neutral clustersbut also for cations and anions.

In general, the electronic density accumulates above andbelow the cluster plane, forming a rather delocalized anduniform electronic distribution which could be considered as aresult of the metallic character of the clusters. The uniformelectronic distributions at both sides of the clusters can explainwhy they do not present reactivity when attacked perpendicularlyto the plane.

The entrance wells appear precisely when the H2 attacks thesites of Aun

q with electronic density defects, as shown in theMEPs of Figure 3. It can be considered that these sites presenta net positive charge which induces larger polarization on H2

and generates deeper wells. This fact is true not only for cationsbut also for neutral clusters, and more surprisingly for anions.

Figure 3. Minimum energy path (eV) for H2 dissociation on Aunq (n ) 4 -10, q ) 0, (1) for the initial attack sites shown in Figure 1.

Q ) dAunq - ∑

i

n

dAui(1)



In this last case, the normal tendency is to present an excess ofelectron density. In the few cases in which an anion presents asite with an electronic density defect, the corresponding MEPpresents a well, and usually there is no barrier for the H2

dissociation. This clear connection between electronic densitydefects and the formation of the entrance well indicates that itplays an important role in the reactivity of these systems.

When the same calculations are repeated at Hartree-Focklevel (HF), the corresponding MEPs do not show the entrancewell, while the electronic density difference is qualitativelyanalogous to that obtained at the DFT-PW91 level of theory.Thus, the formation of this well may be attributed to theelectronic correlation, which depends on the whole density ofthe system and not on a precise orbital. The stabilization isdisplayed by the total energy along the MEP, with contributionsfrom all occupied molecular orbitals, while the individualenergies of frontier orbitals do not show any well in the entrancechannel, as seen in Figure 5.

B. H2 Dissociation. Once the entrance well is formed, H2

dissociation requires the breaking and formation of new bonds,

which is governed by the evolution of the frontier orbitals. Insome cases, there is a crossing between the HOMO/LUMOorbitals along the MEP before the formation of the chemisorp-tion double-bridge Au-H-Au-H-Au bond. Typically, suchcrossing arises from the decrease in energy of an orbital with dcharacter, through bonding with the antibonding orbital ofhydrogen.

For acute corners, this crossing always takes place. However,the neighboring gold atoms form an angle of about 60°, alongwhich the orbitals are preferentially aligned. Thus, H2 dissocia-tion would imply a distortion of the gold molecular orbitals fromthe Au-Au-Au backbone structure, requiring much energy,as will be further analyzed below. This explains why the reactionbarriers associated to these sites are quite high, typically on theorder of 0.5-1 eV. Also, the relative barrier height for cation,neutral, and anion structures closely follows the filling of thefrontier orbitals. Note that these are the barrier heights whenconsidering a fixed geometry of the gold clusters. If we let thestructure of the gold cluster relax, these barriers will be lowered,as discussed below.

The orbital crossing for obtuse corners is not always as clearas in the previous case: the Au-Au-Au backbone structurepresents a favorable orientation, generally leading to a very lowbarrier. When cation, neutral, and anion systems have a well inthe entrance channel (n ) 7, 8, and 9), the relative energylandscape of the MEP closely follows the filling of frontierorbitals. In these cases (n ) 7, 8, and 9), the frontier orbitalspresent a crossing and the LUMO (or SOMO) orbital presentsa considerable stabilization along the MEP. Anions are furtherstabilized because one more electron populates this orbital. Forn ) 5 and 10, the entrance well is deeper for the cation,disappearing progressively with the increase in the number ofelectrons. Thus, even when the frontier orbitals for these cases(n ) 5 and 10) present a similar behavior, with a decrease ofenergy along the MEP of the last filled orbital of the anion,this stabilization cannot compensate for the different depth ofthe entrance well. Thus, for n ) 5 and 10, the cation is themost reactive. The particular case of n ) 4 presents somedifferences because the kind of bonds are completely differentfrom the rest of the cases.

When H2 approaches the central atom of the side of the Aun

cluster (for n < 10), the frontier orbital energies do not cross,except for n ) 8. The filling of the frontier orbitals explainsthe relative reactivity of cation, neutral, and anion species, andwhen the anion presents the entrance well (n ) 9), it is also theone with the lower barrier for the H2 dissociation. In the rest ofthe cases (n ) 4, ..., 8), the anions do not present a well in theentrance channel. Note that the sides of the polygons consideredare, in general, much less reactive than the corners because theypresent lower electronic density defects, making the formationof the entrance well less favorable.

When there are four atoms in a side, as in the triangular Au10

case, the reaction mechanism becomes different. The H2 formsa Au-H-H-Au bond in between the two central atoms in theentrance channel. Such a mechanism was previously reportedfor linear Aun chains with four or more atoms.47 Similarly towhat happens in linear chains as a consequence of the Peierlsdistortion, the atoms tend to form pairs.54-56 Thus, the H2 formsbonds preferentially in sites in which there are an even numberof gold atoms at each side (for n even) or the maximum oddnumber of atoms (for odd values of n).47 In this situation, eachhydrogen atom bonds with a different gold atom, leading to awell in the entrance channel, weakening the H2 in such a waythat it can dissociate more easily. In addition, a similar

Figure 4. Density difference for each Aunq cluster (n ) 4-10, and q

) 0, (1) calculated according to eq 1. Blue/red for positive/negativedensity difference, associated to regions with net negative/positivecharge.



mechanism was reported for linear edges of monatomic rowson a defective Au(111) surface.6 This reaction mechanism isconsidered to be rather general when four or more gold atomsare in an edge of a gold cluster, either linear, planar, or three-dimensional.

From all this analysis, it is quite clear that in the second partof the H2 dissociation, a crossing between orbitals plays anessential role. Recently, such crossing was analyzed in detailfor the Au-H2 case using multireference configuration interac-tion methods with and without spin-orbit couplings.27 Here wewill perform a similar analysis below.

C. Curve Crossings, Symmetry and Comparison withCCSD(T) Calculations. In many cases, the MEP appears inthe most symmetric configuration, which can be treated in theC2V point group, including the plane of the system and a C2

axis passing through the H2 center of mass and the gold atombeing attacked. In addition to this, gold orbitals out of the planedo not participate in the H2 binding. Thus, the frontier orbitalscan be easily classified as a1 (totally symmetric) and b2

(antisymmetric with respect the C2 axis). Typically, the frontierorbitals of Figure 5 are one a1 (or two for n even) and one b2.This last orbital corresponds to an antibonding H2 orbital. Theseorbitals can cross within the C2V point group, but the crossingis avoided in the Cs point group used to determine the MEPsand for the calculation of the molecular energies along the MEP(Figure 5).

Within the C2V symmetry, different A1 and B2 states can bedefined depending on the filling of the frontier orbitals. Thesestates can cross because they are of different symmetry, but as

soon as the symmetry breaks, they become coupled and thecrossing is avoided, thus giving rise to conical intersections.Such effects can be analyzed here because highly symmetricgold clusters are considered. Thus, the crossings are illustratednot only by the crossings between the a1 and b2 orbital energiesin Figure 5 but also by the crossing between the A1 and B2

electronic states, as shown below.As an example of attack on an angle, the electronic

configurations for Au7+ in the ground 1A1, excited 1B1, and 2A1

states are a12, a1

1b21, and a1

1b20a1

1, respectively. The crossing takesplace near the reaction barrier, allowing the transfer of oneelectron to the antibonding b2 orbital, which facilitates the H2

dissociation. In the Au70, the B2(a1

2b11) ground state crosses with

the excited A1(a11b1

2) also at the end of the MEP, populating theb2 antibonding orbital with two electrons, enhancing the H2

dissociation even more than in the cation case. On the contrary,Au7

- does not show any crossing among different electronicstates, because its A1(a1

2b22) ground state already has two electrons

in the antibonding b2 orbital and the reaction takes place withoutany barrier. In Figure 6, CCSD(T) and DFT results are comparedfor the three states reported, showing a rather good overallagreement, which demonstrates the accuracy of the DFTtreatment.

In the Au6q (side) there are no orbital crossings, and hence

the states do not cross either. A comparison with CCSD(T)calculations is presented in Figure 7 for the ground electronicstate, which again shows a good agreement. In this case, theantibonding b2 orbital is not one of the frontier orbitals, andthe reaction is determined by the entrance well. Thus, the cation,

Figure 5. Molecular orbital energies (eV) along the MEP for the different cases considered in Figure 1. The energies for cations, neutrals, andanions are very similar, nearly quantitatively, but shifted. Thus, we only show the energies of the neutral Aun cluster, for simplicity.



which shows a rather deep well, is reactive, showing a barrierbelow the asymptotic energy, while the neutral and anion presentrelatively high barriers. This is the general scenario for thereactions starting by the attack on the central atom of linearsides with three atoms.

The general situation for the H2 attack on angular edges isthat an antibonding b2 orbital, with a large contribution onhydrogen, gets stabilized, crossing with the HOMO a1 orbital.Both HOMO and LUMO orbitals are, in general, antibondingwith respect to gold-H2 interaction, and the b2 is, in addition,antibonding with respect to the H2 bond. In the b2 orbital, thehydrogen atoms are facing a lobe of the d gold orbital with theopposite sign. However, at a given H-H separation, eachhydrogen atom somehow bypasses the closest d-lobe allowingthe formation of a bonding interaction with the remote lobes ofthe same d orbital, and with the neighboring gold atoms as well(see Figure 8). Such a strange bonding interaction produces animportant stabilization of the b2 orbital, which crosses with the

lower a1 orbital. For obtuse angles, such bonding overlap isproduced closer to the entrance well (and shorter H-Hdistances) than for acute angles, simply because the neighboringatoms are structurally closer. Thus, the crossings for obtuseangles are produced closer to the entrance well, yielding to lowerreaction barriers.

Another difference between obtuse and acute corners lies inthe entrance well: while anions never present a negative densitydifference (positive charge in red in Figure 4) for acute angles,and hence no well in the entrance channel, cations generallydo. However, in order to produce a sufficient stabilization toreduce the reaction barrier height, the maximum number ofelectrons in the b2 antibonding orbital is also needed. This ismore probable for anions than for cations as the orbitals getprogressively populated. Therefore, we arrive at the conclusionthat the reactivity in corners requires a well in the entrancechannel, an obtuse angle, and the maximum population in theb2 antibonding frontier orbital to lower the reaction barrier.

When the H2 attacks the central gold atom of a linear side ofthree gold atoms, the b2 antibonding orbital does not participatein the reaction. The a1 HOMO orbital is bonding with respectto H2 bond and antibonding with respect to the H2-Aun bond,and the frontier orbitals do not cross in general. However, inthis case H2 only has to separate sufficiently to form thechemisorption well, up to a distance which is much shorter thanin the angular sites. Thus, the only condition required to getlow reaction barriers is the presence of the entrance well, whichis in general more easily achieved in the case of cations.

Figure 6. Energy of the lower A1 and B2 electronic states along theMEP for Au7

q (q ) 0, (1). DFT results are shown as solid lines, andCCSD(T) as points.

Figure 7. Energy of the lower A1 electronic state along the MEP forthe Au6

q side (q ) 0, (1). Solid lines correspond to DFT results, andpoints to CCSD(T) results.

Figure 8. Frontier molecular orbitals for some selected configurationsalong the MEP for the Au6 (acute), Au6 (side), and Au7 (obtuse). Thepoints chosen correspond to the stationary points along the MEPs shownin Figure 3 and are very similar for all the Aun

q clusters attacked onequivalent sites. Thus, the geometries of the stationary points shownin this figure can be taken as general for the rest of the cases.





D. The Role of the Relaxation of the Gold Cluster andStationary Points. In order to investigate the role of freezingthe gold cluster, geometry optimizations were performed tosearch the different stationary points (gradient equal zero) alongthe MEP for Au6

+ cation and Au7- anion, as typical examples of

attack in sides and acute and oblate corners.The starting point for the geometry optimization are the

stationary points obtained along the MEP of the frozen cluster.At the stationary points, the frequencies were calculated to verifytheir nature. Typically, six of the frequencies are considerablylarger and correspond to motions of the two H atoms (groupedin four motions in the plane and two out of the plane). For thesaddle points, one of the frequencies is imaginary and corre-sponds to the motion of the two hydrogen atoms. The geometriesand energy obtained are shown in Figure 9.

For the isolated clusters, the frozen and optimized geometriesare very similar. As stressed above, to compare the reactivityof the different clusters, ionized or not, the frozen geometrywas built for the higher symmetry isomer and with the Au-Auequal to 2.75 Å (the equilibrium distance for Au7). By changingthe charge of the cluster, after the optimization, equilibriumdistances and angles slightly change, but the overall shaperemains the same, reducing the higher symmetry of the frozenstructures. These small structure modifications explain theenergy difference observed between the isolated structures.

It is interesting to note that energy difference between frozenand optimized structures remain approximately constant alongall MEPs. The light H atoms do not seem to interact stronglyenough with the gold clusters to modify their structures. Onlywhen the reaction barrier is high, as in the case of Au6+H2 forthe acute corner attack, does the gold cluster structure changein an attempt to find a lower energy path toward dissociation.These structural changes essentially consist of an opening ofthe angle of the corner to favor the interaction with H2, thusconfirming our conclusion that the acute corners are notfavorable to dissociate H2. In this case the structural changesof the gold cluster are important, and the energy change is larger,but the reaction barrier remains rather high without changingthe overall conclusions extracted above. For all the rest of thecases, either if there is no barrier or it is low, the gold clusterstructure does not change appreciably along the MEP, and theenergy for the frozen and relaxed cases are nearly parallel.

Another interesting example is the Au9q+H2 case, in Figure

10, because it presents all the attack sites considered. At thesame time, the anion presents no barrier on the corners and avery low one on the side while the cation always presentsbarriers. The relaxed MEPs are again nearly parallel to the frozenones. In addition, the optimized geometries of the stationarypoints are very similar to the corresponding frozen geometries,in most of the cases. It should be noted that in this larger case,the gold clusters change slightly more than in the smaller casesdiscussed above. This is specially evident for the chemisorptionwell obtained for the side attack of Au9

-+H2. This situation isgeneral when applied to the rest of the clusters studied here.When the reaction barrier is small the gold cluster does notappreciably change its structure. Any change would lower theenergy, thus facilitating the reaction. For high barriers, however,the gold cluster geometry changes considerably but the energybarrier remains high for all the cases studied.

For some larger three-dimensional gold clusters, however, itwas found that fluxionality played an important role in thereaction with H2.5 The Au29 cluster, for example, with atruncated pyramid shape, changed significantly in the chemi-sorption well and presented no barrier for the H2 dissociation.

This result is completely different to what is found here. Thereason for this disagreement is attributed to the structure. Smallgold clusters are planar because spin-orbit couplings promotean sd hybridization, which creates quite rigid cluster structuresespecially because nonplanar geometries are energeticallyforbidden. In larger three-dimensional clusters this restrictiondoes not exist anymore, which provides the system with someextra degrees of freedom to relax.

Figure 9. Geometry of the stationary points obtained with the frozenand relaxed gold cluster for the cases of (a) triangular Au6

++H2 (sideattack), (b) triangular Au6

++H2 (acute corner attack), and (c) Au7-+H2

(oblate corner attack).



4. Conclusions

The reactivity of H2 on different planar Aunq clusters, with n

) 4, ..., 10 and charges q ) 0, (1, has been studied for somestable cluster geometries, with the H2 attacking different sites.The MEPs for the different cases were found, within the planeof Aun, using a DFT-GGA method. Further CCSD(T) calcula-tions performed along the MEPs show a rather good agreementwith the DFT results, with an average error of ≈0.2-0.3 eV,which does not change the conclusions derived from the DFTresults.

It is found that all the Aun present an active site for at leastone charge q, and that the necessary condition for the reaction

to occur is the formation of a well in the entrance channel. Sucha well is associated to sites with a deficit in electronic densityor, in other words, to sites with a positive charge, and it is dueto the electronic correlation, depending on the whole densityand not on individual orbitals. Thus, calculating the densitydifference allows the determination of the active sites of positive,neutral, or negative charged clusters.

For linear sides of three atoms, the H2 attacks the centralgold atom directly, and no change of orbitals is produced. Theonly required condition for the reaction to occur is the formationof the entrance well. Because linear sides have less propensityto accumulate positive charge, the most reactive cases appear

Figure 10. Geometry of the stationary points obtained with the frozen and relaxed gold cluster for the cases of Au9-+H2 and Au9

++H2 for alldifferent attack sites considered.



for cationic clusters. Linear sides of four atoms present adifferent mechanism in which a Au-H-H-Au complex isformed in the entrance channel, as analyzed in detail for linearAun chains.47

For corners, the reaction proceeds in two steps: the formationof the entrance well and a curve crossing between a b2

antibonding and an a1 bonding orbital. The b2 antibonding orbitalis highly stabilized at a long H-H distance by the formation ofa bonding overlap of some of the lobes of the d orbitals of thecloser gold atoms. This stabilization is more effective for obtuseangles, corresponding to Au atoms of coordination 3, than foracute angles, corresponding to Au atoms of coordination 2,because the so-called bonding overlap is produced at shorterH-H distances, producing lower barriers. Also, this process isfavored for those cases in which the b2 antibonding orbital hasa larger occupation, which is usually the case for anions withodd values for n.

To analyze the effect of the relaxation of the clusters, thegeometries obtained for the stationary points were optimized,starting from those geometries found for the frozen gold clusters,and the corresponding energies are shifted down in energy. Theagreement between the frozen and relaxed MEPs is very good,and the geometries are very similar. The largest changes appearfor the cases with a high barrier, typically when the site of attackis an acute corner. In such cases the gold cluster geometrychanges considerably and the reaction barrier gets lower, butnot enough to allow dissociation. This behavior is attributed tothe rigidity introduced by the sd hybridization in planar goldclusters.

The analysis presented here shows a clear scenario of thefactors affecting the reactivity of planar gold clusters and ions.We arrive at the conclusion that the necessary condition for asite in the cluster to be active is that it presents a deficit in theelectronic density (or partial positive charge). This finding isvery interesting because it helps to understand the reactivity,and, in addition, it may simplify the search for reaction paths.These concepts should be extended to larger three-dimensionalclusters, isolated or supported in an oxide surface, to check theirgenerality. In this last case, it is known that the gold particlesare reactive on the perimeter interface with the oxide surface.43,44

Recently a theoretical simulation of Au13 on a TiO2 surfaceindicated that the active sites for H2 dissociation are corner oredge atoms not directly bonded to the oxygen atoms of thesurface.43 Gold atoms attached to oxygen atoms present apositive charge, but the bond with oxygen should significantlychange their reactivity, explaining why it does not fit withinthe reaction mechanism discussed in this work. Thus, furtherwork on supported gold clusters is needed to extend theconclusions of this work to such species.

Acknowledgment. We acknowledge Profs. R. Hernandez-Lamoneda, F. Flores, J. Ortega, and Drs. J. I. Martınez and L.Molina for very interesting discussions. This work has beensupported by Comunidad Autonoma de Madrid (CAM) underGrant No. S-0505/MAT/0303 and by Ministerio de Ciencia eInnovacion under Project Nos. CTQ2007-62898 and CTQ2007-63332. The calculations have been performed at CESGA andIFF computing centers.

References and Notes

(1) Coquet, R.; Howard, K. L.; Willock, D. J. Chem. Soc. ReV. 2008,37, 2046.

(2) Hutchings, G. J. J. Catal. 1985, 96, 292.(3) Haruta, M.; Yamada, N.; Kobayashi, T.; Iijima, S. J. Catal. 1989,

115, 301.

(4) Lemire, C.; Meyer, R.; Shaikhutdinov, S.; Freund, H.-J. Angew.Chem., Int. Ed. 2004, 43, 118.

(5) Barrio, L.; Liu, P.; Rodriguez, J.; Campos-Martin, J. M.; Fierro, J.J. Chem. Phys. 2006, 125, 164715.

(6) Corma, A.; Boronat, M.; Gonzalez, S.; Illas, F. Chem. Commun.2007, 3372.

(7) Falicov, L. M.; Somorjai, G. A. Proc. Natl. Acad. Sci. U.S.A. 1985,82, 2207.

(8) Hakkinen, H. Chem. Soc. ReV. 2008, 37, 1847.(9) Yanson, A. I.; Bollinger, G. R.; van den Brom, H. E.; Agrait, N.;

van Ruitenbeek, J. M. Nature 1998, 395, 783.(10) Ohnishi, H.; Kondo, Y.; Takayanagi, K. Nature 1998, 395, 780.(11) Hakkinen, H.; Barnett, R. N.; Landman, U. J. Phys. Chem. B 1999,

103, 8814.(12) Hakkinen, H.; Landman, U. Phys. ReV. B 2000, 62, R2287.(13) Hakkinen, H.; Moseler, M.; Landman, U. Phys. ReV. Lett. 2002,

89, 033401.(14) Gilb, S.; Weis, P.; Furche, F.; Ahlrichs, R.; Kappes, M. M. J. Chem.

Phys. 2002, 116, 4094.(15) Furche, F.; Ahlrichs, R.; Weis, P.; Jacob, C.; Gilb, S.; Bierweiler,

T.; Kappes, M. M. J. Chem. Phys. 2002, 117, 6982.(16) Fernandez, E. M.; Soler, J. M.; Garzon, I. L.; Balbas, L. C. Phys.

ReV. B 2004, 70, 165403.(17) Gruene, P.; Rayner, D. M.; Redlich, B.; van der Meer, A. F. G.;

Lyon, J. T.; Maijer, G.; Fielicke, A. Science 2008, 321, 674.(18) Lechtken, A.; Neiss, C.; Kappes, M. M.; Schooss, D. Phys. Chem.

Chem. Phys. 2009, 11, 4344.(19) King, R. B.; Chen, Z.; v. R. Schleyer, P. Inorg. Chem. 2004, 43,

4564.(20) Wang, J.; Jellinek, J.; Zhao, J.; Chen, Z.; King, R. B.; v. R. Schleyer,

P. J. Phys. Chem. A. 2005, 109, 9265.(21) Bulusu, S.; Zeng, X. C. J. Chem. Phys. 2006, 125, 154303.(22) Johansson, M. P.; Sundholm, D.; Vaara, J. Angew. Chem., Int. Ed.

2004, 43, 2678.(23) Tanaka, H.; Neukermans, S.; Janssens, E.; Silverans, R. E.; Lievens,

P. J. Am. Chem. Soc. 2003, 125, 2862.(24) Wannere, C. S.; Corminboeuf, C.; Wang, Z.-X.; Wodrich, M. D.;

King, R. B.; v. R. Schleyer, P. J. Am. Chem. Soc. 2005, 127, 5701.(25) Feibelman, P. J.; Harris, J. Nature 1994, 372, 135.(26) Hammer, B.; Norskov, J. K. Nature 1995, 376, 238.(27) Zanchet, A.; Roncero, O.; Omar, S.; Paniagua, M.; Aguado, A.

J. Chem. Phys. 2010, 132, 034301.(28) Sanchez, A.; Abbet, S.; Heiz, U.; W.-D. Schneider, H. H.; Barnett,

N. R.; Landman, U. J. Phys. Chem. A 1999, 103, 9573.(29) Wallace, W. T.; Whetten, R. L. J. Phys. Chem. B 2000, 104, 10964.(30) Wu, X.; Senapati, L.; Nayak, S.; Selloni, A.; Hajaligol, M. J. Chem.

Phys. 2002, 117, 4010.(31) Yoon, B.; Hakkinen, H.; Landman, U. J. Phys. Chem. A 2003, 107,

4066.(32) Okumura, M.; Kitagawa, Y.; Haruta, M.; Yamaguchi, K. Appl.

Catal. A 2005, 291, 37.(33) Yoon, B.; Koskinen, P.; Huber, B.; Kostko, O.; von Issendorf, B.;

Hakkinen, H.; Moseler, M.; Landman, U. Chem. Phys. Chem. 2007, 8, 157.(34) Molina, L. M.; Lesarri, A.; Alonso, J. Chem. Phys. Lett. 2009, 468,

201.(35) Haruta, M. CATTECH 2002, 102.(36) Kang, G.-J.; Chen, Z.-X.; Li, Z.; He, X. J. Chem. Phys. 2009, 130,

034701.(37) Varganov, S. A.; Olson, R. M.; Gordon, M.; Mills, G.; Metiu, H.

J. Chem. Phys. 2004, 120, 5169.(38) Molina, L. M.; Alonso, J. A. J. Phys. Chem. C 2007, 111, 6668.(39) Ghebriel, H. W.; Kshirsagar, A. J. Chem. Phys. 2007, 126, 244705.(40) Cox, D. M.; Brickman, R.; Creegan, K.; Kaldor, A. Z. Phys. D

1991, 19, 353.(41) Sugawara, K.; Sobott, F.; Vakhtin, A. B. J. Chem. Phys. 2003, 118,

7808.(42) Rodriguez, J. A.; Liu, P.; Vines, F.; Illas, F.; Takahashi, Y.;

Nakamura, K. Angew. Chem., Int. Ed. 2008, 47, 6685.(43) Boronat, M.; Illas, F.; Corma, A. J. Phys. Chem. A 2009, 113, 3750.(44) Fujitani, T.; Nakamura, I.; Akita, T.; Okumura, M.; Haruta, M.

Angew. Chem., Int. Ed. 2009, 48, 9515.(45) Olson, R. M.; Varganov, S.; Gordon, M. S.; Metiu, H.; S. Cretien,

P. P.; Kowalski, K.; Kucharski, S. A.; Musial, M. J. Am. Chem. Soc. 2005,127, 1049.

(46) Choi, Y. C.; Kim, W. Y.; Lee, H. M.; Kim, K. S. J. Chem. TheoryComput. 2009, 5, 1216.

(47) Zanchet, A.; Dorta-Urra, A.; Roncero, O.; Flores, F.; Tablero, C.;Panigua, M.; Aguado, A. Phys. Chem. Chem. Phys. 2009, 11, 10122.

(48) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.;Pederson, M. R.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671.

(49) Werner, H.-J. MOLPRO, version 2006.1, a package of ab initioprograms, 2006. See http://www.molpro.net.

(50) Dunning, T. H. J. Chem. Phys. 1988, 90, 1007.


(51) Andrae, D.; Hay�ermann, U.; Dolg, M.; Stoll, H.; Preu�, H. Theor.Chim. Acta 1990, 77, 123.

(52) Parr, R. G.; Yang, W. Density-Functional theory of atoms andmolecules; Oxford Univesrity Press: New York, 1989.

(53) De, H. S.; Krishnamurty, S.; Pal, S. J. Phys. Chem. C 2010, 114,6690.

(54) Hoffmann, R. ReV. Mod. Phys. 1988, 60, 601.(55) Peierls, R. F. Quantum theory of solids; Clarendon: Oxford,

1955.(56) Snijders, P. C.; Weitering, H. H. ReV. Mod. Phys. 2010, 82, 307.

JP106733S


Documents

Understanding Structure, Size, and Charge Effects for the H 2 Dissociation Mechanism on Planar Gold Clusters