Free and Zeolite-Supported Hexarhodium Clusters with Light Impurity

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J. Phys. Chem. B 2004, 108, 180-192

Free and Zeolite-Supported Hexarhodium Clusters with Light Impurity Atoms Georgi N. Vayssilov*,† and Notker Ro1 sch*,‡ Faculty of Chemistry, UniVersity of Sofia, Sofia 1126, Bulgaria, and Institut fu¨r Physikalische und Theoretische Chemie, Technische UniVersita¨t Mu¨nchen, 85747 Garching, Germany ReceiVed: July 31, 2003; In Final Form: October 25, 2003

The effect of hydrogen, carbon, and oxygen impurity atoms on the structure of gas-phase and zeolite-supported Rh6 clusters was studied computationally with a gradient-corrected density functional method. Measured metalmetal distances of Rh6 clusters on zeolite support were 10-20 pm longer than the optimized distances of a ligand-free Rh6 cluster. Variations of the cluster charge and adsorption of a ligand-free cluster on a model zeolite fragment did not substantially increase the Rh-Rh distances. Structures with impurity atoms inside the metal cluster were calculated to be less stable than structures where light atoms were adsorbed at the cluster surface. A structure with three H impurity atoms bridging Rh-Rh bonds of a zeolite-supported Rh6 cluster was found to agree best with EXAFS data on experimentally observed clusters. Model clusters with C or O impurity atoms were not considered pertinent due to the large variation of calculated Rh-Rh distances in these clusters, at variance with experimental findings. Analysis of the charge distribution in neutral and ionic clusters suggested that C and O impurity atoms affect the electron density distribution on the metal atoms of the Rh6 cluster in opposite ways and that adsorption of a Rh6 cluster on a zeolite fragment polarizes the cluster electron density resulting in two types of Rh centers of different reactivity, cationic and neutral as well as negatively charged Rh species. Impurity atoms substantially affected the electron distribution in supported Rh6 clusters, and they changed the chemical reactivity of the clusters. In the model structure that corresponded best to the experimental distances, Rh atoms in direct contact with the support were oxidized after reaction with zeolite hydroxy groups.

1. Introduction Because of peculiar, often size-dependent chemical, electronic, and optical properties, supported transition-metal clusters are of interest as specific catalysts and as components of microelectronic and optical devices.1 System properties do not only depend on the cluster size but often are crucially affected by one or more impurity atoms in the clusters; such heteroatoms can considerably change electronic and chemical properties as shown in the present work. Here, on the basis of density functional modeling and by comparison with extended X-ray absorption fine structure (EXAFS) data of the literature, we intend to clarify whether impurity atoms are present in reported experimental structures of hexarhodium clusters supported on zeolite.2 We will demonstrate that an impurity changes the electron distribution of the cluster in a substantial way, and more specifically, we will show how this effect depends on the type and location of the impurity atoms. Also, we will illustrate the synchronous effect of ligand atoms and zeolite support on the polarization of a transition-metal cluster. Transition-metal clusters in zeolite cages form an important class of supported clusters.3-6 Zeolites are very suitable supports/ hosts for small clusters because the dimensions of their cavities determine the formation of transition-metal clusters of nanometer and sub-nanometer size. Experimental investigations were aimed at establishing preparation procedures that yield small supported clusters of nearly uniform size and structures inside zeolite * Authors to whom correspondence may be addressed. E-mail: gnv@chem. uni-sofia.bg (G.N.V.); [email protected] (N.R.). † University of Sofia. ‡ Technische Universita ¨ t Mu¨nchen.

cages;4-6 spectroscopic measurements were carried out to characterize how the electronic and chemical properties of very small transition-metal clusters vary with cluster nuclearity. One of the most efficient synthesis methods relies on removing CO ligands from supported carbonyl cluster precursors in such a way that the number of metal atoms of a cluster remains unchanged.6-12 Valuable structural information on the clusters produced in this way was obtained using EXAFS spectroscopy.7 The experimental nearest-neighbor distances of many supported metal clusters were found to be close to the nearest-neighbor distances of the corresponding bulk.7,9-12 However, recent computational studies of our group13,14 revealed large deviations between calculated metal-metal (M-M) distances and the corresponding experimental values as measured by EXAFS for “bare” supported metal clusters.9,15,16 The systems under study were Ir4 clusters supported on faujasite9,13 and Osn (n ) 4, 5) clusters supported on MgO.11,14 Note that these findings were not unique; calculations on other supported metal clusters also showed significantly contracted M-M distances compared to the bulk nearest-neighbor distances.17,18 One possible explanation of these findings is that the metal clusters studied experimentally are not completely free of ligands. Indeed, attachment of a H atom to an Ir4 cluster and of a C atom to Osn clusters resulted in notably elongated nearest-neighbor M-M distances;13,14 however, these elongated distances were still smaller than the experimental values.9,11 With the present work, we aimed at a more comprehensive study of how type, position, and number of impurity atoms affect the structure of a metal cluster, using Rh6 clusters supported on Y zeolite as an example. Fully or partially decarbonylated

10.1021/jp036241l CCC: $27.50 © 2004 American Chemical Society Published on Web 12/04/2003

Hexarhodium Clusters with Light Impurity Atoms rhodium clusters in Y zeolite, consisting of about six Rh atoms, had been prepared by decarbonylation of supported [Rh6(CO)16] as precursor.2 Notwithstanding the substantial studies on such samples, several questions remain, associated with limitations of EXAFS spectroscopy as a characterization method and the lack of other incisive experimental techniques for investigating such small entities dispersed in porous solids. We focused on a comparison between calculated and measured Rh-Rh distances, and on this basis, we tried to argue whether additional ligand atoms (other than those provided by the supporting framework) are present in the metal cluster. We checked which atoms, easily available in the system (H, C, O), can lead to a value of the Rh-Rh distance close to the experimental one, and we identified likely positions of such impurity atoms in or on the cluster. C and O atoms might be produced during the decarbonylation of the precursor cluster. Hydrogen could come from OH groups of the support; in experimental samples, hydroxyl groups are always present because they are necessary for a successful synthesis of supported metal clusters by aggregation of smaller metal-containing species and for the decarbonylation of supported metal carbonyl clusters, even in Na-exchanged forms of zeolites.7,8 Because the charge of supported metal clusters is not known, we also investigated the influence of the overall cluster charge on Rh-Rh distances for both bare and ligated clusters. Furthermore, we compared computed results for structural parameters and electronic properties of free and supported clusters. This information will be helpful when interpreting experimental data for Rh clusters on other supports produced by different synthetic methods.19 In a preliminary communication,20 we reported that protons of zeolite OH groups support prefer to migrate onto supported Rh6 clusters, resulting in an oxidation of metal atoms in close contact with the support. This conclusion was supported by results of the present extensive computational modeling and by comparison with experiments.

J. Phys. Chem. B, Vol. 108, No. 1, 2004 181

Figure 1. Structures of the Rh6 cluster in various models: (a) C4h symmetry, Rh6-C4h; (b) in C3 symmetry, twisted, Rh6-C3(tw); and (c) in C3 symmetry, straight, Rh6-C3(pr), trigonal prism. Distances are in pm; values of relativistic calculations are in italics.

2. Method All calculations were carried out with the linear combination of Gaussian-type orbitals fitting-functions density functional method (LCGTO-FF-DF)21,22 as implemented in the program ParaGauss for parallel computers.23,24 We used the gradientcorrected exchange-correlation functional suggested by Becke (exchange) and Perdew (correlation) (BP).25 The Kohn-Sham orbitals were represented by Gaussian-type basis sets, contracted in generalized form: (6s1p) f [3s1p] for H; (9s5p1d) f [5s4p1d] for O and C; (12s9p1d) f [6s4p1d] for Al and Si.26 A (17s12p8d) basis set of Rh27 was extended by two s (0.01303, 0.2253), three p (0.03666, 0.09165, 0.2291), and two d (0.04588, 0.1147) exponents to yield a (19s15p10d) basis set which finally was contracted to [8s6p4d]. The auxiliary basis set used in the LCGTO-FF-DF method to determine the Hartree part of the electron-electron interaction was derived from the orbital basis set in the usual fashion and augmented for each atom by five “polarization” exponents of the p- and d-type.21 To estimate the influence of relativistic effects on the bond lengths, we modeled the ligand-free and some of the ligated clusters with the scalar-relativistic variant of the LCGTO-FF-DF method,22,28 which employs a second-order Douglas-Kroll transformation to decouple electronic and positronic degrees of freedom of the Dirac-Kohn-Sham equation.29,30 The geometry of the model clusters was optimized with the help of analytical energy gradients,31,32 honoring pertinent symmetry constraints. Gasphase Rh6 clusters with and without impurity atoms were modeled in C4h, C3, and C2V symmetries (Figure 1). These

Figure 2. Rh6 cluster supported on a zeolite fragment in C3 symmetry: (a) charged zeolite model Rh6(+3)/zeo(-3); (b) neutral zeolite model Rh6/zeo.

structures were chosen because each Rh atom has four metal atom neighbors, as observed in zeolite-supported Rh6 clusters; experimentally, the coordination number of Rh centers is 3.53.9.2 In addition, the structure of the cluster in C3 symmetry complies with the symmetry of the zeolite model (Figure 2). Binding energies (BE) of impurity atoms to the cluster Rh6 were calculated relative to a free impurity atom, and the most stable structures of the bare Rh6 cluster were an octahedron and a straight triangular prism in nonrelativistic and relativistic calculations, respectively (see below, Table 1). All reported charges were obtained by a Mulliken population analysis. To model the zeolite support, we used a six-ring model cluster of faujasite structure (Figure 2), similar to models employed in our previous studies on zeolites exchanged with rhodium and main-group metal ions.33 The model cluster contains six T-atoms: three Al and three Si atoms arranged in an alternating sequence according to the Loewenstein rule.34 Thus, we

182 J. Phys. Chem. B, Vol. 108, No. 1, 2004

Vayssilov and Ro¨sch

TABLE 1: Characteristicsa of Rh6 Clusters for Different Positionsb of the Coordinated Atoms: BE(X) Per Impurity Atom X, Relative Energies ∆E of Anionic and Cation Clusters, Average 〈R〉 and Spread ∆R of Rh-Rh Distances modelb

nc

∆E d,e

Rh6-C4h Rh6-C3(tw) Rh6-C3(pr) C(in)/Rh6-C4h C(out)/Rh6-C3 O(in)/Rh6-C4h O(out)/Rh6-C3 H(in)/Rh6-C4h H(in)/Rh6-C3 H(out)/Rh6-C3 H(out)/Rh6-C3 k H(out)/Rh6-C2V(pr) H(out)/Rh6-C2V(oct) 4H(t)/Rh6-C4h 4H(b)/Rh6-C4h 3H(b-side)/Rh6-C3h(pr) 3H(b-side)/Rh6-C3(pr) 3H(b-side)/Rh6-C3(tw) 3H(b-top)/Rh6-C3(pr) 3H(b-top)/Rh6-C3(tw)

6 6 0 2 4 0 4 1 1 1 1 1 1 6 0 3 3 5 1 3

0 /11 3 /13 4/0 111 0 396 0 89 44 35 42 24 0 278 0 127 114 0 13 17

BE(X)e,f

608/655 719/856 47/48 443/590 138/186 182/243 191/323 185 202 227 182 252 196 201 239 234 233

∆Eaniong

∆Ecationg

〈R〉h

∆R i

-133 -109 -155

589 602 564

-151

563

-173 -143 -141 -192

553 521 552 586

259 259 249 278 271 284 270 264 255 248 255 254 259 257 260 268 263 269 257 266

0 1 1 1 50 0 50 3 7 8 18 45 10 6 11 47 27 18 25 29

a Energies in kJ/mol, distances in pm. b Notation according to Figures 3-5. c Number of unpaired electrons of the neutral cluster. d Energy difference relative to the most stable structure of the same composition. e Energies of nonrelativistic calculations with respect to a bare Rh6-C4h cluster; in italics energies of relativistic calculations with respect to a bare Rh6-C3(pr) cluster. f Atomization energy of H2 calculated at 2 × 233 kJ/mol and of O2 at 2 × 321 kJ/mol; the corresponding values of relativistic calculations are 2 × 325 and 2 × 470 kJ/mol, respectively. g Energy difference of cationic and anionic cluster relative to the corresponding neutral cluster. h Average value of the Rh-Rh distances in the cluster. i Difference between smallest and largest nearest-neighbor Rh-Rh distances in the cluster. k Second local minimum, found when starting the optimization from the geometry of the cationic cluster.

employed C3 symmetry for zeolite-supported Rh6 clusters. The free valences of silicon and aluminum atoms of the zeolites model ring on the side of the supported metal cluster were saturated by OH groups, whereas on the opposite side hydrogen atoms were used for bond saturation. The structures of the supported clusters and the zeolite fragment were optimized, constraining the distances between the T-atoms to crystallographically determined values.35 Six-rings with two Al and four Si atoms are the most probable for Y zeolite,36 used in the experimental work, yet the properties of zeolite oxygen centers and OH groups in a six-ring with two or three Al atoms are very similar.33 Thus, a six-ring with three Al atoms, used as a zeolite model in the present calculations, is expected to yield essentially the same kind of interaction of a metal cluster with the support as a six-ring with two Al centers. To check whether a certain optimized model structure corresponds to the experimentally observed cluster, we used the following criteria related to the EXAFS data:2 (a) The calculated Rh-Rh distance should be close to the experimental value of 267-269 pm;2,37 the uncertainty of the EXAFS in the experiment is estimated to (1%, i.e., the RhRh distances in the experimental sample could be between 264 and 272 pm; some computational error is also expected. (b) The well-defined peak in the high-quality EXAFS spectra2 suggests that the clusters are uniform (the Debye-Waller factor is ∆σ2 ) 0.004 Å2) and differences of Rh-Rh distances in a cluster are relatively small. Following the criterion of Teo,38 uncertainties are estimated at ∼10 pm; accordingly, optimized model structures with a larger spread of Rh-Rh distances were excluded. (c) For zeolite-supported structures, Rh-Oz distances are also compared. Experimental values from EXAFS are 210-217 pm;2,37 note that, for the BP exchange-correlation functional used here, calculated distances between metal atoms and oxygen centers of the support are typically overestimated by 2-5 pm.14,33b,40

3. Results and Discussion We started with optimized structures of ligand-free Rh6 clusters in the gas phase and on zeolite support; the obtained Rh-Rh distances were 8-20 pm shorter than the EXAFS distances (Tables 1 and 2). Therefore, we proceeded with ligated Rh6 clusters in the gas phase and we considered C and O atoms as impurities; these atoms can be produced by decomposition of adsorbed CO molecules during the decarbonylation of the supported precursor [Rh6(CO)16]. However, the obtained RhRh distances of the optimized clusters containing carbon or oxygen were scattered in a rather wide interval of ∼50 pm, also not compatible with the reported EXAFS spectra.2 We continued our search for a compatible structure with various Rh6 clusters that contained one to four hydrogen impurity atoms because hydrogen is also available in the system from intrazeolite hydroxyl groups. In none of the 13 model structures studied were the Rh-Rh distances uniform or, at the same time, close to the experimental values of 267-269 pm. Next, we checked whether varying the charge of the cluster leads to the desired Rh-Rh distances, yet charge was found to have a little effect on the structure of both ligand-free and ligated clusters, like in Ir4.13 Finally, in section 3.4, we will present structural modes that are closest to the experimental situation, namely, hydrogenligated Rh6 clusters supported on a zeolite fragment. In addition to the discussion on the calculated and experimental Rh-Rh distances, we also considered the stability of different adsorption modes of the impurity atoms at the transition-metal cluster. We paid special attention to the polarization of the electron charge distribution in the transitionmetal cluster, induced by impurity atoms or the support, either as separate or simultaneous effect. The observed trends are expected to have important implications for the reactivity of such clusters. 3.1. Ligand-Free Clusters in the Gas Phase. Nonrelativistic optimizations suggested that there are three structures of a bare Rh6 cluster with very similar stability: (i) an octahedron

Hexarhodium Clusters with Light Impurity Atoms

J. Phys. Chem. B, Vol. 108, No. 1, 2004 183

TABLE 2: Pertinent Properties of Zeolite-Supported Rh6 Clusters: BE (kJ/mol) and Distances (pm) model

na

BEb X/Rh6

BEc X

g

experiment Rh6(3+)/zeo(3-) ∆(Rh6-C3(tw))h Rh6/zeo ∆(Rh6-C3(pr))h C/Rh6/zeo ∆(C(out)/Rh6-C3)h ∆(Rh6/zeo)i O/Rh6/zeo ∆(O(out)/Rh6-C3)h ∆(Rh6/zeo)i H/Rh6/zeo ∆(H(out)/Rh6-C3)h ∆(Rh6/zeo)i 3H(b-top)/ Rh6(3+)/zeo(3-) ∆(3H(b-top)/Rh6-C3)h ∆(Rh6(3+)/zeo(3-))i 3H(b-side)/ Rh6(3+)/zeo(3-) ∆(3H(b-side)/Rh6-C3)h ∆(Rh6(3+)/zeo(3-))i

3

-

-

0

73

-

2

96 23 187 114 148 75

742 23 557 114 266 75 237 4 255 16 -

2 1 0 0

Rhz-Rhz

Rht-Rht

Rhz-Rht

267-269 259 0 251 2 259 -1 8 258 0 7 255 8 4 251 -1 -8 260 0 1

252 -7 251 2 311 3 60 317 10 66 268 22 17 281 -1 28 260 -3 8

256, 259 -3, 0 250, 307 2; 59 254, 267 -4; 7 4; -40 246, 258 -11; -1 -4; -49 249, 275 -1; 25 1; -32 261, 262 -5; -4 5; 3 262, 267 -13; -11 6; 8

distancesd 〈R〉e ∆R f 257

7

265

56

273

57

270

61

262

26

264

29

262

7

Rh-X

Rh-Oz

186 -1 203 6 180 -23 165, 179 -7; 7 176 -9; 9 -

210-217 217, 220 237 223 -14 245, 236 8; -1 224 -13 220, 221 3; 1 218, 220 1, 0

Rh-Siz 284 265 267 2 235 -30 270 5 286 2 284 0

a Number of unpaired electrons. b BE of the whole cluster to the neutral zeolite fragment, zeo. c X denotes the corresponding impurity atom, H, C, or O. d Rhz and Rht denote the atoms of the “lower” layer of the Rh6 cluster, closer to the zeolite fragment, and atoms of the “top” layer of the Rh6 cluster, bound to the impurity atoms, respectively, Figures 2, 6, and 7. e Average value of the Rh-Rh distances in the cluster. f Difference between the smallest and largest neighboring Rh-Rh distance in the cluster. g Experimental value for zeolite-supported rhodium clusters, ref 2. h Difference relative to the quantity obtained for the corresponding gas-phase ligated cluster. i Difference relative to the quantity obtained for the corresponding zeolite-supported cluster.

modeled in C4h symmetry (Figure 1a), Rh6-C4h; (ii) a twisted triangular prism in C3 symmetry (Figure 1b), Rh6-C3(tw); and (iii) a straight trigonal prism in C3 symmetry (Figure 1c), Rh6C3(pr). The two former structures were most stable with six unpaired electrons, whereas the last structure is most stable as singlet; all structures were optimized at fixed numbers of unpaired electrons, ranging from zero to eight. The structures are calculated essentially degenerate, with Rh6-C4h being 3 and 4 kJ/mol more stable than Rh6-C3(tw) and Rh6-C3(pr), respectively (Table 1). The Rh-Rh distance in the clusters with six unpaired electrons is calculated at 259 pm and at 249 pm in the cluster Rh6-C3(pr); in each case, metal-metal distances that are not equivalent by symmetry differ by at most 1 pm (Figure 1). The scalar-relativistic calculations yielded the same multiplicities for the most stable electronic states of each of the three different structures (six for Rh6-C4h and Rh6-C3(tw) and zero for Rh6-C3(pr)) as the nonrelativistic calculations, but the energy differences between the structural isomers were larger. An additional difference from the nonrelativistic results is the change of the order of stability; Rh6-C3(pr) is 11 and 13 kJ/ mol more stable than Rh6-C4h and Rh6-C3(tw), respectively (Table 1). As usual,17,39 shorter metal-metal distances result (Figure 1, numbers in italics) when relativistic effects are accounted for in the calculations; the nearest-neighbor distances shrink 4 pm in Rh6-C4h and Rh6-C3(tw) and 3 pm in Rh6C3(pr). The experimental metal-metal nearest-neighbor distances of zeolite-supported “bare” Rh6 clusters2 are 267-269 pm. As the BP functional used here often slightly overestimates elongated bond lengths compared to experiment,40 the fact that Rh-Rh distances are calculated shorter than the EXAFS results should not be attributed to the exchange-correlation approximation. Interatomic Rh-Rh distances between 232 and 260 pm for stable structures of Rhn clusters (n ) 3-6) were also obtained in recent DF calculations with another gradient-corrected functional (PW91).41

3.2. Zeolite-Supported Ligand-Free Clusters. To check whether the Rh-Rh bond is elongated due to the interaction with the zeolite support, we modeled the adsorption of a Rh6 cluster at the model zeolite six-ring containing three Si and three Al atoms (see above). We used two types of models in C3 symmetry. In the first one, denoted as Rh6(+3)/zeo(-3) (Figure 2a), the zeolite cluster is without charge-compensating protons and, hence, carries a charge of -3 e. Instead of three protons from the bridging OH groups (as in the second model, Figure 2b), charge compensation of the zeolite cluster is accomplished by the supported Rh6 cluster itself with an assigned charge of 3 e. In this way, the whole system is neutral. In the optimized geometry of this complex (Figure 2a), the structure of the Rh6 cluster is very similar to the gas-phase Rh6 cluster of the same symmetry (Figure 1b). Similar to Ir4,13 the important Rh-Rh distances of the supported Rh6 cluster are 252-259 pm, just as calculated for the gas-phase cluster (Table 2). The distances between the Rh atoms of the “lower” layer of the cluster (Rhz atoms) and the closest zeolite oxygen centers are 217-220 pm (Table 1), i.e., similar to the values derived from EXAFS for the zeolitesupported cluster,2 210-217 pm. According to a Mulliken analysis, the charge separation in the complex Rh6(+3)/zeo(-3) deviates from the formal assignment; the Rh6 cluster and the zeolite fragment carry ∼1.5 e positive and negative charges, respectively (Table 3). In the second model, denoted as Rh6/zeo, the substrate cluster is neutral; the negative charge of the six-ring due to the presence of three Al atoms is compensated by three protons attached to some of the oxygen centers of the zeolite ring (Figure 2b). Accordingly, both subsystems, the rhodium cluster and the zeolite cluster model, were formally neutral. The binding energy of the neutral Rh6 cluster to the neutral zeolite fragment was calculated at 73 kJ/mol (Table 2), i.e., 24 kJ/mol per Rh-Oz bond. The overall BE is less than half of that of tetrahedral Co4 and Ni4 clusters on a regular MgO (001) surface,42 192 and 225 kJ/mol, respectively. The geometry of Rh6 supported on

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TABLE 3: Calculated Mulliken Charges (e) of Zeolite-Supported Rh6 Clusters model Xa Rh6(3+)/zeo(3-) Rh6/zeo C/Rh6/zeo ∆(C/Rh6)c ∆(Rh6/zeo)d O/Rh6/zeo ∆(O/Rh6)c ∆(Rh6/zeo)d H/Rh6/zeo ∆(H/Rh6)c ∆(Rh6/zeo)d 3H(b-top)/Rh6(3+)/zeo(3-) 3H(b-side)/Rh6(3+)/zeo(3-)

-0.44 0.01 -0.56 -0.02 -0.24 -0.07 -0.13 -0.19

Rhtb -0.11 -0.31 0.20 0.02 0.51 0.37 0.30 0.68 0.09 -0.01 0.40 0.24 -0.05

charges Rhzb 0.62 0.32 0.05 0.08 -0.27 -0.03 -0.14 -0.35 -0.01 0.03 -0.33 0.39 0.74

Zeo

Rh6

-1.53 1.53 -0.03 0.03 -0.31 0.75 0.30 -0.28 0.72 -0.46 1.02 0.48 -0.43 0.99 0.00 0.24 0.06 0.03 0.21 -1.50 1.89 -1.50 2.07

a X denotes an impurity atom, H, C, or O. b Rhz denotes atoms of the “lower” Rh triangle of the Rh6 cluster, closer to the zeolite fragment, and Rht denotes atoms of the “top” layer of the Rh6 cluster, bound to the impurity atoms; see Figures 2 and 6. c Difference relative to the charge obtained for the corresponding gas-phase ligated cluster. d Difference relative to the charge obtained for the zeolite-supported cluster Rh6/zeo.

the neutral zeolite fragment (Figure 2b) was optimized as a partially twisted triangular prism with shortest Rh-O distances of 237 pm (Table 2), i.e., ∼20 pm longer than the experimental result. As expected, Rh atoms do not interact with oxygen centers participating in bridging OH groups (Figure 2b). The Rh-Rh distances of this supported cluster were calculated at 250-251 pm, i.e., even shorter than in the gas-phase ligandfree clusters (Tables 1 and 2). There was also one longer RhRh distance of 307 pm between Rh atoms at the short diagonal of each side of the twisted prism (Figure 2b). At variance with the first model with a charged zeolite cluster, there was essentially no transfer of electron density between the zeolite (-0.03 e) and the Rh6 cluster (Table 3). The supported cluster Rh6/zeo features a closed-shell electronic structure, whereas the other model structure Rh6(+3)/ zeo(-3) has three unpaired electrons. The interaction of metal clusters with ligands17,43 (e.g., oxygen centers of the support) is well-known to quench unpaired electrons of the cluster. Thus, the observed lower multiplicity of the adsorbed Rh6 cluster compared to the gas-phase clusters Rh6-C4h and Rh6-C3(tw) is not unexpected. The mean value of the Rh-Rh distances in the model Rh6(+3)/zeo(-3) is 257 pm, whereas the corresponding value of Rh6/zeo is 265 pm. However, in the latter case, the difference between the smallest and largest Rh-Rh distances, ∆R, is too large, 56 pm, compared to experiment (Table 2). Thus, by the criteria stated above, the cluster support interaction does not render the calculated Rh-Rh distances of Rh6 compatible with experiment. 3.3. Ligated Clusters in the Gas Phase. Because adsorption on a zeolite does not induce a suitable elongation of the RhRh bonds of Rh6, we continued our investigation by modeling the influence of different impurity (ligand) atoms on the bond distances of the metal cluster. First, we focused on clusters in the gas phase with H, C, and O atoms as ligand species. We considered the location of these two impurity atoms on the transition metal cluster and their influence on the cluster structure. C Atom Impurity. Coordination of a carbon impurity atom inside the cluster, model C(in)/Rh6-C4h (C4h symmetry, Figure 3a) elongates the Rh-Rh distance to 278-279 pm. The BE of

Figure 3. Structures of Rh6 clusters with carbon and oxygen impurity atoms inside or on the surface of the metal cluster: (a) C(in)/Rh6C4h; (b) C(out)/Rh6-C3; (c) O(in)/Rh6-C4h; (d) O(out)/Rh6-C3. Distances are in pm; values of relativistic calculations are in italics.

the C atom is 608 kJ/mol (Table 1). Coordination of a C atom outside of Rh6 at a 3-fold hollow position, C(out)/Rh6-C3 (Figure 3b), was calculated 111 kJ/mol more stable than in C(in)/ Rh6-C4h (Table 1). In C(out)/Rh6-C3, the triangle of Rh atoms closer to the C atom is considerably expanded, with Rh-Rh distances of 308 pm (Figure 3b). The other base triangle and all other Rh-Rh distances remain essentially as in the ligandfree cluster of the same symmetry, at 258-260 pm (Figure 1b). The Rh-C distance is 196-197 pm in C(in)/Rh6-C4h, 10 pm longer than in C(out)/Rh6-C3 (Figure 3b). We also attempted to optimize the geometry in C3 symmetry with the C atom inside the cluster, starting from a trigonal prismatic cluster (Figure 1c) with the C atom close to the center. During optimization, the impurity atom shifted continuously to the outside of the cluster, in the direction of the structure C(out)/ Rh6-C3. That final structure was also obtained when we started the geometry optimization from a twisted triangular prism. None of the two clusters containing a C atom exhibited a singlet electronic state; the cluster C(in)/Rh6-C4h had two and the cluster C(out)/Rh6-C3 four unpaired electrons. O Atom Impurities. Inclusion of an oxygen atom inside the Rh6 cluster, O(in)/Rh6-C4h (C4h symmetry constraint), was calculated to be slightly exothermic, 47 kJ/mol, with respect to a free O atom and a bare Rh6 cluster (Figure 3c). However, such binding likely is an artifact of gradient-corrected exchangecorrelation functionals which are known to place oxygen atoms too high in energy.40 If one uses an oxygen molecule as reference44 (BE per O atom ) 321 kJ/mol, Table 1), then the cluster O(in)/Rh6-C4h is 274 kJ/mol less stable than Rh6 and 0.5 × O2. As in the corresponding carbon-containing model C(in)/Rh6-C4h, the Rh6 cluster expanded, with Rh-Rh distances of 284 pm (Figure 3c); the Rh-O distances were calculated at 199-201 pm. The structure of the metal cluster with an O atom coordinated at the 3-fold hollow position of a base triangle of the twisted prism, obtained in the optimization of the bare cluster in C3 symmetry (Figure 3d), was similar to the structure of the corresponding cluster with a C atom. This structure, O(out)/ Rh6-C3, was 396 kJ/mol more stable than O(in)/Rh6-C4h; the BE of the O atom was calculated at 443 kJ/mol (Table 1). The BE of an O atom to the cluster was substantially larger (by 122

Hexarhodium Clusters with Light Impurity Atoms kJ/mol) than the BE per atom of an O2 molecule. Thus, O2 easily dissociates on two Rh6 clusters. The BE of an O atom at the Rh6 cluster is similar to the oxygen BE on a planar Ni4 cluster and a twisted square prism Ni8 cluster, 442 and 398 kJ/mol, respectively, also calculated with the BP functional.18 The distances between Rh atoms close to the ligand atom, 307 pm, were much longer than in the ligand-free cluster whereas the other Rh-Rh distances remained unchanged, 257259 pm. The Rh-O distance was calculated at 197 pm, slightly shorter than for coordination of the O atom inside the cluster. Similar to the C atom, optimization of the O ligand inside the cluster in C3 symmetry lead to an extrusion of the impurity atom, resulting in a position outside the cluster, similar to that shown in Figure 3d. Whereas the cluster O(in)/Rh6-C4h exhibited a singlet electronic structure, the more stable structure, O(out)/Rh6-C3, had four unpaired electrons, similar to the corresponding structure with a C atom impurity. The sum of the binding energies of the two most stable structures calculated for the adsorption of individual C and O atoms at model clusters, 1162 kJ/mol, is 21 kJ/mol larger than the formation energy of a CO molecule from single atoms, 1141 kJ/mol, calculated in the same approximation. Thus, CO dissociated on two Rh6 clusters is similar in energy to the initial state of the dissociation process, but the calculated energy preference for dissociative adsorption is too small to be conclusive. Geometry optimization at the scalar relativistic level yielded similar structures of C and O ligated clusters as the corresponding nonrelativistic calculations; bonds were again calculated slightly shorter. The binding energies of each impurity atom outside the cluster, calculated at the scalar relativistic level, were 132-147 kJ/mol larger than those obtained in the corresponding nonrelativistic calculations. On the other hand, for the impurity atoms inside the Rh6 cluster, the increase of the BE was calculated to be much smaller, 43 kJ/mol for C impurity (Table 1). The BE of O atoms in the O(in)/Rh6-C4h cluster at the scalar relativistic level, 48 kJ/mol, is only 1 kJ/mol larger than the corresponding nonrelativistic result. The dissociation energies of O2 (atomization energy 940 kJ/mol) and CO (atomization energy 1415 kJ/mol) molecules at Rh6 clusters, estimated at the scalar relativistic level, 120 and 31 kJ/mol, respectively, are very similar to the corresponding nonrelativistic values, 118 and 21 kJ/mol (Table 1). These results obtained for carbon and oxygen impurity atoms suggest that coordination of an impurity atom in a 3-fold hollow position outside the cluster is notably more stable than a position inside the cluster. The reduced BE inside the cluster is likely due to Pauli repulsion between the impurity and the metal cluster atoms. For both clusters in C3 symmetry with an impurity atom, C(out)/Rh6-C3 and O(out)/Rh6-C3, we calculated two different Rh-Rh distances, 257-260 pm (9 interatomic distances) and 307-308 pm (3 interatomic distances). Although, the experimental value of the Rh-Rh distance could be obtained as an average value of these distances (271 and 270 pm for the clusters with C and O impurities, respectively), the large difference between the two groups of calculated distances, ∆R ) 50 pm in both cases, does not fit the well-resolved peak of the EXAFS spectrum.2 For this reason, we concluded that C or O atoms are not responsible for the extension of the interatomic distances in the experimentally observed Rh6 species. Because even one impurity carbon or oxygen atom causes too large an extension

J. Phys. Chem. B, Vol. 108, No. 1, 2004 185

Figure 4. Location of one H atom impurity. H atom inside a Rh6 cluster with different symmetry constraints: (a) H(in)/Rh6-C4h; and (b) H(in)/ Rh6-C3. H atom outside a Rh6 cluster (c) at a 3-fold hollow position, H(out)/Rh6-C3; (d) in bridging position of a triangular prism, H(out)/ Rh6-C2V(pr); and (e) in bridging position of an octahedron, H(out)/ Rh6-C2V(oct). Distances are in pm; values of relativistic calculations are in italics.

of the Rh-Rh distances, above 300 pm, we refrained from modeling structures with more than one C or O impurity atom per cluster. H Atom Impurities. Because of these negative conclusions on C or O impurity atoms, we focused our attention on clusters with hydrogen impurity atoms. The optimized structures of a hydrogen atom inside the Rh6 cluster in C4h and C3 symmetry are shown in parts a and b of Figure 4. In C4h symmetry, H(in)/ Rh6-C4h (Figure 4a), the H atom inside the metal cluster caused an expansion of the cluster with Rh-Rh distances increased to 263-266 pm. However, lowering the symmetry to C3 (Figure 4b) resulted in a structure with a BE value of 182 kJ/mol, i.e., 44 kJ/mol more stable than the C4h structure (Table 1). Optimization in C3 symmetry with a H atom inside the Rh6 cluster, H(in)/Rh6-C3, lead to a straight trigonal prism (eclipsed structure) instead of the initial octahedral structure (staggered structure). The impurity H atom was not located at the center of the prism, but closer to one of the base triangles. Three different Rh-Rh distances were calculated for this structure: 253 pm between Rh atoms of the triangle far from the impurity atom; 260 pm between Rh atoms of the base close to the H atom; and 251 pm between two Rh atoms of different base triangles. Thus, only one of these distances is slightly longer than the Rh-Rh distances of the ligand-free cluster and the other two are even shorter. Hence, in general, one cannot expect an elongation of Rh-Rh bonds due to an impurity H atom inside the cluster, as calculated in the case of a C4h symmetry constraint. The shortest Rh-H distances of the structures with a H atom inside the cluster were 183-188 pm. Next, we located a hydrogen atom outside the Rh6 cluster. We optimized the structure of the Rh6 cluster H(out)/Rh6-C3 (C3 symmetry, Figure 4c) with one H atomic ligand at a 3-fold hollow position at the base of the trigonal prism of metal atoms.

186 J. Phys. Chem. B, Vol. 108, No. 1, 2004 The metal cluster formed an almost perfect straight trigonal prism with Rh-Rh distances of 246 and 247 pm at the two bases; the distance between the two bases was 250 pm. Thus, all Rh-Rh distances were close to the values of the bare Rh6 cluster of the same structure, Rh6-C3(pr) (Figure 1c). The binding energy of the H atom for this structure, 191 kJ/mol, was slightly larger than the BE of a H atom inside the cluster H(in)/Rh6-C3, 182 kJ/mol, (Table 1). The Rh-H distance was 203 pm (Figure 4c). Two models with a H atom bridging an Rh-Rh bond were studied in C2V symmetry H(out)/Rh6-C2V (pr) and H(out)/Rh6C2V(oct); these structure were based on a triangular prism and an octahedron, respectively (parts d and e of Figure 4). In both cases, the BE of the impurity atom was larger than in the other structures with one H atom (prism, 202 kJ/mol; octahedron, 227 kJ/mol). In H(out)/Rh6-C2V(oct), the Rh-Rh bond to which the H atom is attached and its neighboring bonds in the “equatorial” tetragon were 265-266 pm (Figure 4e), similar to the experimental result; however, the remaining Rh-Rh bonds were 9-10 pm shorter. When the impurity atom was bridgebonded to a triangular prism (Figure 4d), the interatomic RhRh distances varied even more; the distance between two Rh atoms bridged by a H atom was considerably elongated, 293 pm, whereas the other Rh-Rh distances, 248-250 pm, were similar to the bare Rh6-C3(pr) cluster. Despite the similar type of bonding of the impurity atom, the Rh-H bond lengths differed by 12 pm in the octahedral (178 pm) and prismatic clusters (166 pm). We also studied the influence of more than one H ligand on the structure of the cluster. We started by modeling structures in C4h symmetry with four hydrogen impurity atoms. In the cluster 4H(t)/Rh6-C4h, the ligands were in terminal position to Rh atoms (Figure 5a) with BE ) 182 kJ/mol per adsorbed H atom. Compared to the bare Rh6-C4h cluster (Figure 1a), RhRh distances were not substantially affected by the adsorption of H atoms in terminal positions (Figure 5a); they change from 256 to 255 and 261 pm. In 4H(t)/Rh6-C4h, there were two types of Rh-Rh distances, 255 and 261 pm. Rh-H bonds were 166 pm, similar to the bridge-bonded H atom in the model H(out)/ Rh6-C2V (pr). The other model structure in C4h symmetry that we tested, 4H(b)/Rh6-C4h, exhibited four H atoms coordinated in bridging positions at “equatorial” Rh-Rh bonds of an octahedron. We modeled such bonding for the example of a cluster representing a tetragonal bipyramide in C4h symmetry (Figure 5b). This type of bonding yielded the largest BE value per H atom, 252 kJ/ mol. In fact, this value is 20 kJ/mol larger than the calculated BE per H atom in the hydrogen molecule, 233 kJ/mol. Thus, thermodynamics favors dissociation of a hydrogen molecule on two Rh6 clusters, similar to the case of an O2 molecule (see above). Most importantly, each Rh-Rh bond with a H atom attached in bridging fashion was elongated by 11 pm to 267 pm; this calculated value is similar to the experimentally measured EXAFS value. Rh-Rh bonds that do not interact with a H atom, however, had the same bond length, 256 pm, as in the ligand-free cluster Rh6-C4h (Figure 1a). Rh-H distances were calculated at 183 pm, between the values obtained for H coordination at a 3-fold hollow and a terminal position but larger than all other structures with bridge-bonded hydrogen. Guided by the observation that bridge-bonding of H ligands was calculated most stable (Table 1), we studied several more structures of Rh6 cluster ligated with three H ligands in bridging position. The two least stable among these five structures were 3H(b-side)/Rh6-C3V (Figure 5c) and 3H(b-side)/Rh6-C3 (Figure

Vayssilov and Ro¨sch

Figure 5. Location of several H atoms outside a Rh6 cluster. Structures in C4h symmetry: (a) H in terminal positions, 4H(t)/Rh6-C4h; and (b) H in bridging positions, 4H(b)/Rh6-C4h. Structures in C3V or C3 symmetry with H bridging Rh-Rh bonds: at the sides of a straight triangular prism, (c) 3H(b-side)/Rh6-C3V(pr), (d) 3H(b-side)/Rh6-C3(pr); at the sides of a twisted triangular prism, (e) 3H(b-side)/Rh6-C3(tw); at “top layer” Rh-Rh bonds of (f) a straight prism, 3H(b-top)/ Rh6-C3(pr), and (g) a twisted triangular prism, 3H(b-top)/Rh6-C3(tw). Distances are in pm.

5d) where the ligands were bound to each of the side Rh-Rh bonds of a straight triangular prism. In the cluster with higher symmetry, C3V, the ligand atoms were located in the vertical symmetry planes of the prism. When the symmetry constraint was reduced to C3, the ligand atoms shifted toward the sides of the prism. The BE values of one impurity atom in these structures, 196 kJ/mol for 3H(b-side)/Rh6-C3V and 201 kJ/mol for 3H(b-side)/Rh6-C3, were similar to that of H atoms in threehollow positions of clusters such as H(out)/Rh6-C3 (Table 1). H bridged Rh-Rh bonds of either model, 3H(b-side)/Rh6-C3V and 3H(b-side)/Rh6-C3, were substantially extended, to 299 and 280 pm, respectively. The other Rh-Rh distances, 252-255 pm (parts c and d of Figure 5), were elongated by only 3-6 pm compared to the initial Rh6-C3(pr) cluster. Next in the order of increasing stability were the structures where H ligands were bound to Rh-Rh bonds of the base triangles of straight or twisted triangular prisms, 3H(b-top)/Rh6C3(pr) (Figure 5f) and 3H(b-top)/Rh6-C3(tw) (Figure 5g). The BE values per H atom of these structures were calculated at 233-234 kJ/mol (Table 1), close to the atomization energy of a H2 molecule, 233 kJ/mol per atom. Similarly to other structures with bridge-bonded H atoms, Rh-Rh bonds closest to the H impurities were elongated to 274 and 281 pm in the straight and twisted prism, respectively. Rh-Rh distances of the other basic triangles of both prisms were much shorter, ∼250 pm. The main structural difference between the two clusters is the distance between Rh atoms that belong to different base triangles

Hexarhodium Clusters with Light Impurity Atoms of the prisms. That Rh-Rh distance was 248 pm in the straight prism (Figure 5f) and 266 pm in the twisted prism (Figure 5g). The Rh-H distances of all four clusters described above were very similar, 170-172 pm (parts c, d, f, and g of Figure 5). The twisted triangular prism with impurity H atoms bonded to three of the side Rh-Rh bonds, 3H(b-side)/Rh6-C3(tw) (Figure 5e), was calculated as the most stable structure with three bridge-bonded H ligands. With 239 kJ/mol, the BE per H atom of this model was the second largest, only 13 kJ/mol smaller than for 4H(b)/Rh6-C4h. In 3H(b-side)/Rh6-C3(tw), the coordination of the H atoms was between 2-fold and 3-fold; H atoms were located 167 and 185 pm from the two closest Rh atoms but interacted with a third Rh atom of the same face, 195 pm away. This structure features two groups of Rh-Rh distances, Rh-Rh bonds within the two bases (260 and 263 pm) and on the side of the prism (275 and 278 pm). The multiplicity of the Rh6 clusters containing H impurity atoms depended considerably on the number of H atoms and the geometry of the cluster (Table 1). All structures with one adsorbed H atom were doublets, i.e., the lowest possible multiplicity. Among the Rh6 clusters with three H atoms, 3H(b-top)/Rh6-C3(pr) had one, 3H(b-side)/Rh6-C3(tw) had five, and the remaining three structures had three unpaired electrons. The cluster 4H(b)/Rh6-C4h was a singlet, whereas the other cluster with four H atoms in terminal positions, 4H(t)/ Rh6-C4h, featured six unpaired electrons. Similar to the ligand-free clusters, relativistic calculations gave somewhat shorter distances. For all three structures modeled at the relativistic level, H(in)/Rh6-C4h, H(in)/Rh6C3, and H(out)/Rh6-C3 (parts a, b, and c of Figure 4), both Rh-Rh and Rh-H distances (numbers in italics in Figure 4) were 2-4 pm shorter than in the corresponding nonrelativistic structures. Although the structures of the clusters were similar, the binding energies of the impurity atom to the cluster in the scalar relativistic calculations was substantially larger, e.g., the BE in the cluster H(out)/Rh6-C3 increased by 132 kJ/mol (Table 1). However, the order of stability of different structures remained unchanged (Table 1). We saw that the Rh-H distance for adsorption outside the cluster increased with the coordination number of the H atom, 166 pm for coordination to one Rh atom, 166-185 pm for coordination to two Rh atoms (but typically around 170 pm), and 203 pm for coordination to three Rh atoms. The higher coordination of a H atom inside the Rh6 cluster (both in C4h and C3 symmetry) does not result in longer Rh-H bonds because that would entail concomitant loss Rh-Rh bonding. From these results on hydrogen ligands inside or outside a Rh6 cluster we conclude that (i) the BE of a H atom is larger outside the cluster than inside, (ii) the most stable location of a H atom is bridging a Rh-Rh bond, which in turn elongates by 10-30 pm, and (iii) adsorption of a H2 molecule on a Rh6 cluster occurs in dissociative fashion. Comparison of the optimized Rh-Rh distances of these model clusters with experiment does not reveal any stable structure that would fit the EXAFS values, 267-269 pm. With an averge Rh-Rh distance of 264 pm and a difference ∆R ) 3 pm, the cluster H(in)/Rh6-C4h fulfils this criterion, but this structure is unstable with respect to symmetry breaking. It is 44 kJ/mol higher in energy than H(in)/Rh6-C3 and 89 kJ/mol higher than the most stable model with one H atom, H(out)/Rh6-C2V(oct). Most of the other structures studied have rather short average Rh-Rh distances, 248-260 pm (Table 1). The average Rh-Rh distances of the clusters 3H(b-side)/ Rh6-C3h(pr), 3H(b-side)/Rh6-C3(pr), 3H(b-top)/Rh6-C3(tw), and 3H(b-side)/Rh6-C3(tw) are 263-269 pm, in acceptable

J. Phys. Chem. B, Vol. 108, No. 1, 2004 187 TABLE 4: Mulliken Charges q (in e) of Atomic Centers of Neutral and Charged Clusters Rh6 q(Rh) Rh6-C4h H(in)/Rh6-C4h 4H(t)/Rh6-C4h 4H(b)/Rh6-C4h C(in)/Rh6-C4h O(in)/Rh6-C4h

Qa

Rh(side)

Rh(top)

-1 0 1 -1 0 1 0 0 0 0

-0.17 0.00 0.13 -0.04 0.13 0.31 0.11 0.27 0.20 0.14

Qa -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1

q(X)

q(Rh6)

-0.15 0.00 0.23 0.01 0.17 0.31 0.06 -0.20 0.18 0.14

-0.86 -0.87 -0.87 -0.14 -0.17 -1.17 -0.87

-1.00 0.00 1.00 -0.14 0.86 1.86 0.56 0.68 1.16 0.84

Rh(close)

Rh(far)

q(X)

q(Rh6)

-0.13 0.00 0.17 -0.07 0.10 0.26 -0.05 0.10 0.28 0.01 0.18 0.12 -0.17 0.07 0.29

-0.20 0.00 0.17 -0.08 0.09 0.26 -0.22 -0.04 0.10 -0.19 -0.03 0.35 0.03 0.11 0.22

-0.57 -0.57 -0.58 -0.19 -0.17 -0.15 -0.47 -0.45 -0.44 -0.56 -0.54 -0.52

-0.45 0.57 1.56 -0.81 0.18 1.14 -0.54 0.45 1.41 -0.42 0.54 1.53

q(Rh) Rh6-C3(tw) H(in)/Rh6-C3 H(out)/Rh6-C3 C(out)/Rh6-C3 O(out)/Rh6-C3

a

Overall charge of the cluster (in e).

agreement with experiment, yet the differences ∆R are too large, 27-47 pm (Table 1). The cluster 3H(b-side)/Rh6-C3(tw) exhibits a somewhat smaller value ∆R ) 18 pm, suggesting structural similarity with the experimentally observed clusters. Indeed, for a similar cluster model adsorbed on a zeolite fragment, 3H(b-side)/Rh6(3+)/zeo(3-), we calculated Rh-Rh distances compatible with the EXAFS results (see section 3.4). Charged Clusters. Another important property of the metal clusters is their overall charge. We checked how the geometry of ligated clusters and their charge distribution changed when the charge of the cluster varied by one electron (in some cases by two electrons, Tables 4 and 5). In general, optimized structures of cationic and anionic clusters did not differ substantially from those of the corresponding formally neutral clusters; Rh-Rh distances and distances between Rh atoms and impurity atoms usually varied at most 4 pm (Table 5). An exception was the cationic cluster H(out)/Rh6-C3 with one H atom in a 3-fold hollow position; there, the Rh-H distance decreased 28 pm, and the Rh-Rh distance between the metal atoms bound to the impurity atom increased by 18 pm, whereas the other Rh-Rh distances were below 250 pm. Motivated by this observation, we performed a new geometry optimization of the neutral cluster H(out)/Rh6-C3, starting from the cationic structure. This optimization yielded a second equilibrium structure, very similar to that of the optimized cationic cluster, with a Rh-H distance of 175 pm and a Rh-Rh distance close to the H impurity of 268 pm (Table 5). This second neutral structure was 7 kJ/mol less stable than the initially found neutral structure of H(out)/Rh6-C3 (Table 1). In summary, by varying the overall cluster charge, we were not able to generate stable structures with Rh-Rh bonds (Table 5) sufficiently extended to become similar to those derived from EXAFS spectra, 267-269 pm. Moreover, with changes of the

188 J. Phys. Chem. B, Vol. 108, No. 1, 2004

Vayssilov and Ro¨sch

TABLE 5: Influence of the Overall Cluster Charge Q (in e) on Rh-Rh and Rh-X Distances of Ligand-Free and Ligated Rh6 Clusters Rh-Rh Rh6-C4h H(in)/Rh6-C4h

Q

Rh(side)

Rh(top)

-1 0 1 -1 0 1

260 259 260 267 266 265

259 259 253 265 263 265

Q

Rh(close)

-1 0 1 -1 0 1 -1 0 1 -1 0 1 0 -2 -1 0 1 2 -2 -1 0 1

254 259 259 248 249 248 258 260 251 248 246 264 268 310 302 308 312 312 315 305 307 311

Rh-X other

Rh-Rh Rh6-C3(tw) Rh6-C3(pr) H(in)/Rh6-C3 H(out)/Rh6-C3 H(out)/Rh6-C3a C(out)/Rh6-C3

O(out)/Rh6-C3

side

top

188 188 188

186 184 188

Rh-X

Rh(far)

other

side

252 253 255 248 247 249 250 260 257 258 261 261 259 259 258 259

262 259 254 251 248 247 254 251 255 252 250 248 246 259, 261 259, 262 258, 260 259, 261 258, 260 257, 259 259, 260 257, 259 256, 258

184 183 184 201 203 175 175 187 189 187 184 185 199 198 197 196

top

a

Second local minimum, found when starting the optimization with the geometry of the cationic cluster.

cluster charge, we did not observe any clear trend for expansion or contraction of the clusters (Table 5). 3.4. Ligated Clusters Supported on a Zeolite Fragment. Finally, we modeled the simultaneous influence of impurity atoms and zeolite support on the structure of a Rh6 cluster. We used two classes of models based on the two cluster models Rh6/zeo and Rh6(+3)/zeo(-3) employed previously in the study of ligand-free supported Rh6 clusters (section 3.2). The first group of models consisted of a neutral zeolite fragment Rh6/zeo in C3 symmetry with a C, O, or H atom located at the 3-fold hollow position “on top” of the Rh6 cluster. As described above for the gas-phase models, these adsorption complexes furnished some of the most stable structures of ligand atoms. The optimized structures of the supported cluster models are shown in Figure 6; the corresponding BE values and interatomic distances are given in Table 2. The structure optimization of the supported clusters was performed at the nonrelativistic level. The optimized structure of the supported cluster C/Rh6/zeo (Figure 6a) was similar to that of the gas-phase cluster C(out)/ Rh6-C3 (Figure 3b). The shorter Rh-Rh distances were 254259 pm, i.e., ∼2 pm shorter than in the gas-phase cluster but 4-8 pm longer than in the supported ligand-free cluster Rh6/ zeo (Table 2). The longer Rh-Rh distance of 308 pm in the gas-phase cluster increased to 311 pm in the supported cluster. The two Rh-Rh distances at the side of the Rh6 cluster were not equal, 254 and 267 pm; the latter distance is similar to the experimental value, 267-269 pm.2,37 The BE of a C atom is 23 kJ/mol larger than that of a carbon atom at the gas-phase cluster Rh6 (Figure 3b).

Figure 6. Structures of ligated Rh6 clusters supported on a neutral zeolite fragment: (a) C/Rh6/zeo; (b) O/Rh6/zeo; and (c) H/Rh6/zeo.

At variance with a C impurity, the BE of an oxygen atom at a supported Rh6 cluster, O/Rh6/zeo, was calculated considerably larger, by 114 kJ/mol, than the BE at the corresponding gasphase model (Table 2). Also for Ni4 and Ni8 clusters on MgO, the oxygen binding energy was calculated larger (by 72 and 27 kJ/mol, respectively) on the supported transition-metal cluster than on analogous clusters in the gas phase.18 As in the case of C/Rh6/zeo, the shorter Rh-Rh distances of O/Rh6/zeo were similar or shorter than in the corresponding gas-phase cluster O(out)/Rh6-C3. However, the longer Rh-Rh distance increased to 317 pm. This is likely an effect of a “lateral” interaction of the Rht atoms of the top layer of the cluster with oxygen centers from the saturating OH groups at the Al centers of the zeolite fragment (Figure 6b). This interaction seems to be important because the Rht-Oz distances to the oxygen centers of saturating OH groups, 236 pm, are shorter than the Rhz-Oz distance to oxygen centers of the six-ring, 245 pm (Table 2). Another peculiarity of the supported cluster O/Rh6/zeo were the short distances of the Rh atoms of the “lower” layer of the metal cluster to the Si atoms of the six-ring, 235 pm, whereas in the other zeolite-supported Rh6 clusters, Rh-Si distances were above 260 pm (Table 2). The geometry of the supported Rh6 cluster with a H impurity atom, H/Rh6/zeo (Figure 6c), differs from the structure of the corresponding gas-phase cluster H(out)/Rh6-C3. Whereas the metal centers of H(out)/Rh6-C3 form a straight trigonal prism (Figure 4c), the prism of H/Rh6/zeo is considerably twisted, similar to the ligand-free Rh6 cluster Rh6/zeo supported on a neutral zeolite fragment (Figure 2b). In addition to slight changes in the short Rh-Rh distances, by ∼4 pm relative to the gasphase cluster H(out)/Rh6-C3 with H at the 3-fold hollow position, new longer Rh-Rh distances of 268-275 pm appear due to the twisting of the Rh6 framework (Table 2). The Rh-H distance, 180 pm, is similar to that of the second structure, 175

Hexarhodium Clusters with Light Impurity Atoms

Figure 7. Structures of Rh6 clusters supported on a zeolite fragment ligated with three H atoms in Rh-Rh bridging positions (a) at “top layer” Rh-Rh bonds, 3H(b-top)/Rh6(+3)/zeo(-3) and (b) of edges at the side of the prism, 3H(b-side)/Rh6(+3)/zeo(-3).

pm, of the neutral gas-phase cluster H(out)/Rh6-C3, derived from the cationic form (Table 5). The BE of a H impurity atom at the supported metal cluster, 266 kJ/mol, is 75 kJ/mol larger than the BE to the gas-phase cluster H(out)/Rh6-C3. Similarly, the BE of the whole H/Rh6 cluster to the neutral zeolite fragment is 75 kJ/mol larger than the BE of the ligand-free Rh6 cluster to the zeolite support in the model Rh6/zeo (Table 2). The Rh-Rh distances of the ligated Rh6 clusters in the models C/Rh6/zeo and O/Rh6/zeo were calculated similar to the distances of the corresponding ligated gas-phase models C(out)/Rh6-C3 and O(out)/Rh6-C3. Average Rh-Rh distances were close to the experimental value, 270-273 pm, but the difference ∆R between the smallest and largest Rh-Rh distances was even larger than in the gas-phase clusters, 57 and 61 pm (Table 2). The structure with a H impurity in a 3-fold position at the supported Rh6 cluster H/Rh6/zeo also exhibited a rather large ∆R, 26 pm. Because bridge bonding of H atoms to gas-phase clusters was found most stable, we modeled two structures with three H atoms in bridging positions of the supported Rh6 cluster based on the model Rh6(3+)/zeo(3-). In the first structure, 3H(b-top)/Rh6(3+)/zeo(3-), the H atoms were coordinated to the Rh-Rh bonds at the top base of the twisted triangular prism (Figure 7a), similar to the gas-phase structure 3H(b-top)/Rh6C3(tw). In the second structure, 3H(b-side)/Rh6(3+)/zeo(3-) (Figure 7b), the impurity atoms were attached to Rh-Rh bonds at the “sides” of the prism, similar to the gas-phase structure 3H(b-side)/Rh6-C3(tw). Both structures, with top-bound and side-bound impurity atoms, are stable; the BE values are 237 and 255 kJ/mol per H atom, respectively. These values are calculated with respect to the cluster Rh6(3+)/zeo(3-) and three H atoms. Both clusters shown in Figure 7 have the same composition as the ligand-free Rh6 cluster of the neutral model Rh6/zeo (Figure 2b). Thus, the 3H/Rh6(3+)/zeo(3-) structures can formally be produced by migrating three protons of zeolitebridging OH groups onto the Rh6 cluster.20 Both structures with hydrogen on the transition-metal cluster, 3H(b-top)/Rh6(3+)/ zeo(3-) and 3H(b-side)/Rh6(3+)/zeo(3-), are considerably more stable than the initial supported complex Rh6/zeo, by 317 and 370 kJ/mol for H on top and in side coordination, respectively. This could be considered as an important step in

J. Phys. Chem. B, Vol. 108, No. 1, 2004 189 the oxidation of transition-metal particles by surface OH groups hypothesized in various cases;45 this aspect was discussed in more details in ref 20. The optimized Rh-Rh distances in the structure 3H(b-top)/ Rh6(3+)/zeo(3-) (Table 2) are similar to those of the corresponding gas-phase cluster 3H(b-top)/Rh6-C3(tw) (Figure 5g); the main difference is that the Rh-Rh bonds at the sides of the supported metal cluster are 5 pm shorter (Table 2). Although the average Rh-Rh distance of 264 pm in 3H(b-top)/Rh6(3+)/ zeo(3-) is close to the experimental value, large internal deviations of the Rh-Rh distances (∆R ) 29 pm) render this cluster an unlikely model of the experimental system. The other model structure, 3H(b-side)/Rh6(3+)/zeo(3-), and the corresponding gas-phase cluster 3H(b-side)/Rh6-C3(tw) differ mainly by shorter Rh-Rh bonds at the sides of the twisted triangular prism in the supported structure, despite the fact that three of these bonds are decorated by H impurities. Because of this shortening, the average Rh-Rh distance of the supported cluster 3H(b-side)/Rh6(3+)/zeo(3-) is slightly reduced, to 262 pm, accompanied with a substantial decrease of the difference between the largest and smallest Rh-Rh distances; ∆R is only 7 pm (Table 2). Because the average Rh-Rh distance of 262 pm deviates very little from the target interval 264-272 pm (see section 2) and ∆R is less than 10 pm, we consider the structural parameters of the model cluster 3H(b-side)/Rh6(3+)/ zeo(3-) (Figure 7b) to be consistent with the zeolite-supported hexarhodium cluster investigated experimentally.2 Our model structure entails a Si center at 284 pm from the Rhz centers, not taken into account in the EXAFS refinement.2 To some extent, this could have affected the accuracy of the determined structural parameters (distances or coordination number) of the backscattering centers at similar distances and, in addition to limitations of the computational model, may rationalize the difference between the calculated Rh-Rh distances of the model 3H(b-side)/Rh6(3+)/zeo(3-) and the EXAFS-derived value. An additional argument supporting the above analysis is based on the Rhz-Oz distances. The optimized distances between of the zeolite oxygen centers and adjacent “lower layer” Rh centers, 218 and 220 pm, fit well the experimental EXAFS values, 210217 pm. The experimental number of Rh-Oz contacts, 1.11.3, obtained by EXAFS2 closely corresponds to the structure of our model 3H(b-side)/Rh6(3+)/zeo(3-) where none of the “top layer” Rht atoms has any zeolite oxygen neighbor Oz whereas each Rhz center has two oxygen neighbors. Thus, on average, one Rh atom of the supported Rh6 cluster has one Oz neighbor. Calculated (218-220 pm) and experimentally derived (210217 pm) values of Rh-Oz distances for the zeolite-supported hexarhodium cluster are close to the corresponding calculated and experimental values of the cationic dicarbonyl complex RhI(CO)2 supported on zeolite Y, 219-220 pm and 216 pm, respectively.46 This observation clearly suggests that the nature of the metal center in both types of supported species is similar, namely, Rh centers bound to zeolite oxygen centers in the supported hexarhodium cluster are oxidized; in fact, these metal centers have effective charges similar to those of RhI in the supported dicarbonyl species, ∼0.53 e (Mulliken).46 This is in line with the hypothesis, described in our preliminary communication,20 that transition-metal particles due are oxidized by surface OH groups. Indeed, the calculated Mulliken charge of Rhz centers in the cluster 3H(b-side)/Rh6(3+)/zeo(3-) is 0.74 e (Table 3). Note that the Rhz-Oz bonds are significantly stronger in 3H(b-side)/Rh6(3+)/zeo(3-) than those in the neutral

190 J. Phys. Chem. B, Vol. 108, No. 1, 2004 zeolite model Rh6/zeo as indicated by a very substantial shortening, by 20 pm, of Rhz-Oz distances. 3.5. Influence of the Impurity Atoms and Support on the Charge Distribution. Charge Distribution in Ligated Clusters. In model structures of the gas-phase Rh6 clusters containing impurity atoms, the corresponding ligand atom carried a negative charge, resulting in a positive charge of the Rh6 framework (Table 4). The charge separation was stronger when the impurity atom was inside the cluster; in clusters of C4h symmetry, the ligand charge was -1.17, -0.87, and -0.87 e, for C, O, and H impurity atoms, respectively. Reduction of the symmetry of H(in)/Rh6-C4h to C3 symmetry (H(in)/Rh6-C3) also resulted in a reduction of the charge separation with a hydrogen charge of -0.57 e. The negative charges of ligands in positions outside the Rh6 cluster are much smaller in absolute value, -0.45 e for C, -0.54 e for O, and -0.14 to -0.17 e for H (Table 4). It is interesting to compare the positive charge distribution on the Rh6 framework of ligated clusters with different impurity atoms located in 3-fold hollow positions outside the clusters. In the case of C or H ligands, C(out)/Rh6-C3 and H(out)/Rh6C3, the electron density mainly decreases at the metal atoms close to the impurity atom; their positive charges are 0.18 and 0.10 e, respectively, whereas the Rh atoms farther from the ligand are essentially neutral, with charges of -0.03 e (C) and -0.04 e (H) (Table 4). On the other hand, in the cluster with a O impurity, O(out)/Rh6-C3, the positive charge (0.11 e) of the Rh atoms farther from the O atom is slightly larger than the charge of Rh atoms close to the impurity (0.07 e). Trends in Charged Clusters. Because both HOMO and LUMO orbitals of ligated clusters are essentially localized on Rh atoms, any variation of the charge of the whole cluster mainly influences the electron density on the metal atoms whereas the impurity atoms are hardly affected (Table 4). The HOMO-LUMO gap varies with the type of the impurity atoms; for example, the ligand-free gas-phase Rh6 cluster in C3 symmetry has a gap of 0.48 and 0.52 eV, as straight and twisted prisms, respectively, whereas with an impurity atom in a 3-fold hollow position, the gap is 0.57, 0.28, and 0.09 eV, for H, C, and O impurities, respectively. With an impurity H atom inside the cluster in both symmetries studied, the charges of the Rh atoms vary synchronously with the total charge of the cluster. In the two structures of H(out)/ Rh6-C3, where the H ligand is at a 3-fold hollow position, Rh atoms far from the ligand carry more electron charge (by -0.14 to -0.18 e) than metal centers bound to which H is bound. Interestingly, C and O impurity atoms affect the charge distribution of the Rh6 framework in opposite ways. An excess or lack of one electron in the cluster C(out)/Rh6-C3 mainly influences the Rh atoms far from the C atom; in the anionic cluster, each of these atoms carries a charge of -0.19 e, whereas in the cationic form, this charge is 0.35 e. On the other hand, the charge of the Rh atoms bound to the C ligand varies in narrow limits, from 0.01 to 0.18 e. When the O atom is located at the 3-fold hollow position, O(out)/Rh6-C3, both the excess charge (positive or negative) is mainly distributed on the Rh atoms close to the ligand (-0.17 and 0.29 e, respectively). This observation is important for predicting how C and O ligand atoms affect the reactivity of metal clusters; an O impurity atom should affect mainly the reactivity of Rh atoms close to it, whereas a C impurity is expected to afect the reactivity of Rh atoms far from it. Effect of the Support. In section 3.2, we considered two models of a zeolite-supported Rh6 cluster, Rh6(+3)/zeo(-3) with a cluster supported on an ionic zeolite fragment and Rh6/zeo

Vayssilov and Ro¨sch with a neutral support. The charge separation in the whole complex Rh6(+3)/zeo(-3) is much smaller than the formal assignment ((3 e) implied by our notation. The calculated Mulliken charges are about half as large, (1.53 e (Table 3). The Rhz atoms, in contact with zeolite oxygen centers, carry a positive Mulliken charge, 0.62 e per atom. Although the whole Rh6 cluster is positively charged, the Rh atoms of the top layer, Rht, exhibit a small negative charge, -0.11 e per atom. In the other model, Rh6/zeo, when a neutral Rh6 cluster is adsorbed on a formally neutral zeolite cluster, the Mulliken analysis indeed classifies both fragments as essentially neutral, with 0.03 e on Rh6 and -0.03 e on the zeolite fragment (Table 3). Yet, the neutral Rh6 framework is noticeably polarized due to the support, as indicated by differently charged Rh centers: (a) The metal atoms Rhz adjacent to the zeolite fragment are slightly positively charged, 0.32 e per atom, and are expected to react similar to cationic centers RhI. (b) The metal atoms Rht in the “top layer” of the cluster are negatively charged, -0.31 e per atom, and their reactivity resembles that of electron-rich metallic Rh species.1,47 This redistribution of electron density inside the metal framework can be very important for the catalytic activity of these supported species. The calculated (Mulliken) charges of the two types of Rh atoms correlate with the core level energies (estimated by the eigenvalue of the corresponding orbital). For example, the Rh 3s level of negatively charged Rht atoms is 0.50 eV less stable than the corresponding level of Rhz centers close to zeolite fragment. In addition, occupied molecular orbitals close to the Fermi level are mainly localized on “top layer” Rh atoms, whereas all metal atoms contribute to the HOMO group of the reference gas-phase cluster Rh6-C3(tw). Although the Fermi level is destabilized by 0.37 eV after adsorption of the cluster on the zeolite support, the HOMOLUMO energy gap, 0.53 eV, remains essentially unchanged compared to the corresponding gas-phase cluster Rh6-C3(tw), 0.52 eV. Simultaneous Effect of Impurity Atoms and Support. Calculated Mulliken charges allow us to analyze roughly the simultaneous effect of impurity atoms and zeolite support on the charge distribution in a Rh6 cluster (Table 3). Similar to the ligated gas-phase clusters, the Rh6 framework of the supported moiety of the complexes C/Rh6/zeo, O/Rh6/zeo, and H/Rh6/zeo carry positive charges; the value increases from 0.24 e for H to 0.75 e for C and 1.02 e for an O impurity atom. In the complex H/Rh6/zeo, the zeolite fragment is neutral but the presence of the support slightly changes the charge distribution in the cluster H/Rh6 compared to the gas-phase cluster; the electron density on the H atom increases by 0.07 e at the expense of Rh atoms close to the zeolite support (Table 3). Different charge rearrangements take place in the other two structures studied with C and O impurities, where part of the electron density of the Rh6 framework spills to the support. Consequently, the zeolite fragment is negatively charged, -0.31 e in C/Rh6/zeo and -0.46 e in O/Rh6/zeo. In the former case, the electron density distribution in the supported cluster is similar to the gas-phase cluster C/Rh6-C3; the charges of the C atom and the Rh atoms bound to it change by only 0.01-0.02 e. Most of the electron density transferred from the supported metal cluster to the zeolite fragment is taken from Rh atoms bound to the zeolite; their electron density decreases by 0.08 e compared to the gas phase. The charge distribution in the cluster O/Rh6/zeo differed from both the gas-phase cluster O/Rh6-C3 and the supported ligandfree cluster Rh6/zeo. At variance with the corresponding clusters

Hexarhodium Clusters with Light Impurity Atoms with H and C impurities, most of the electron density transferred to the zeolite fragment derives from the top layer of Rh atoms, 0.30 e per atom relative to the situation in the corresponding gas-phase cluster O(out)/Rh6-C3. This is likely due to the strong interaction of Rh centers with the oxygen centers of the saturating OH groups (Figure 6b). The opposite trend is found for the lower layer of Rh atoms where the electron density of each Rhz atom increases by 0.14 e compared to the gas-phase (Table 3). In general, an impurity atom in a 3-fold hollow position strongly affects the polarization of the electron density of the supported metal cluster. Whereas in the supported ligand-free cluster Rh6/zeo, the top layer of Rh atoms is negatively charged, -0.31 e per atom, these atoms carry positive charges in the supported clusters with H, C, and O impurities, 0.09, 0.20, and 0.37 e, respectively (Table 3). The Rh atoms of the lower layer (with a charge of 0.32 e in Rh6/zeo) are practically neutral in the ligated supported clusters, with charges ranging from -0.03 to 0.05 e. This change of the electron density of Rh atoms due to the presence of an impurity can be reflected in an alteration of the chemical reactivity of ligated clusters compared to ligandfree clusters. Both supported clusters in the structures 3H(b-top)/Rh6(3+)/ zeo(3-) and 3H(b-side)/Rh6(3+)/zeo(3-) carried a half of the positive charge assigned to them, 1.50 e, and, consequently, the zeolite fragments have a negative charge of -1.50 e (Table 3). Because of the overall positive charge of the 3H/Rh6 species in both structures, the core levels of all Rh centers are strongly stabilized compared to their energies of the neutral gas-phase cluster Rh6. Therefore, core-level binding-energy shifts ∆E(Rh3d) are highly positive, even for Rh atoms where small negative Mulliken charges were calculated, e.g., Rht atoms in the top layer of 3H(b-side)/Rh6(3+)/zeo(3-) with q(Rht) ) -0.05 e and ∆E(Rh3d) ) 1.7 eV. However, formally, the core levels of Rh atoms in these supported species are to be compared to a hexarhodium cluster with a formal charge of 3 e where the core levels are considerably more stabilized than in the neutral cluster. As mentioned in section 3.4, the charge distribution in the model cluster 3H(b-side)/Rh6(3+)/zeo(3-), which is most similar to the experimentally observed species, clearly showed oxidation of the “lower layer” of Rh atoms bound to zeolite fragment, likely to RhI.20 The ∆E(Rh3d) value of these Rhz centers is 2.1 eV, i.e., the levels are 0.4 eV more stable than those of Rht atoms. 4. Conclusions Similar to previous computational studies on supported transition-metal clusters,13,14 we found that the experimentally observed metal-metal distances of Rh6 clusters supported on Y zeolite,2 267-269 pm, were more than 8-20 pm longer than the optimized distances of ligand-free Rh6 clusters in the gas phase, 249-259 pm. Variations of the cluster charge did not substantially affect the metal-metal distance. Our calculations also showed that adsorption of a ligand-free Rh6 cluster on a zeolite fragment does not cause an elongation of the Rh-Rh bonds required for improved agreement with experiment. The binding energy of the Rh6 cluster on the zeolite fragment was estimated to be only 24 kJ/mol per Rh-substrate bond. This value is much smaller than the metal-substrate bonds of tetrahedral Co4 and Ni4 clusters on the regular sites of the MgO(001) surface, 64 and 75 kJ/mol for the metal-support bond.42 Modeling the interaction of “ligand” atoms H, C, or O with Rh6 revealed that structures with impurity atoms inside the metal cluster are less stable than structures with ligands adsorbed at

J. Phys. Chem. B, Vol. 108, No. 1, 2004 191 the surface of the cluster. In the former case, symmetry constraints can result in an elongation of Rh-Rh bonds. Relativistic effects reduce Rh-Rh as well as Rh-ligand bonds by 1-5 pm; also, the binding energies of impurity atoms to the metal cluster are larger in a scalar relativistic description, especially for ligands at positions outside the cluster. Rh6 clusters in C3 symmetry with C or O atoms adsorbed at 3-fold hollow positions, C(out)/Rh6-C3 and O(out)/Rh6-C3, featured two different types of Rh-Rh distances, 257-260 pm similar to ligand-free clusters with octahedral structure, and a rather large one, 307-308 pm. When these clusters were supported on a zeolite fragment, the first type of Rh-Rh bonds became shorter, whereas the second type of distances increased. Because of the rather wide interval ∆R ) 50 pm, in which the Rh-Rh distances of the optimized clusters with C or O impurities spread, such species are unlikely to correspond to the clusters described in the experiment.2 H atoms at 3-fold hollow positions outside the metal framework induce a slight shortening of the Rh-Rh bonds compared to the corresponding ligand-free clusters. An increase of the Rh-Rh distance (by 10-30 pm) was calculated for H adsorption at bridging positions; furthermore, among the structures studied, this bonding situation was identified as the most stable coordination of H ligands to the cluster Rh6. None of the studied structures of gas-phase Rh6 clusters with H ligands agreed with the structural characteristics observed experimentally, either the average Rh-Rh distance was too short or the spread ∆R between shortest and longest Rh-Rh distances was above 20 pm. The structure, whose pertinent characteristics agreed most closely with experiment, was the model 3H(b-side)/ Rh6-C3(tw) (Figure 5e) with an average Rh-Rh distance of 264 pm and ∆R ) 18 pm. The relatively large value of ∆R was substantially reduced to an acceptable value of 7 pm when the cluster was supported on zeolite, in the model 3H(b-side)/ Rh6(3+)/zeo(3-) (Figure 7b). The latter Rh6 framework approached closest the characteristics of the experimental cluster, with a calculated average Rh-Rh distance was 262 pm, only 2 pm below the target interval defined by the EXAFS analysis and the corresponding experimental error.2 In addition, the RhOz distances of this structure, 218-220 pm, agreed well with the experimental values of 210-217 pm.2 Analyzing the charge distribution of neutral and ionic clusters, we found that C and O impurity atoms affect the electron density distribution on the Rh framework in different ways. In a cluster with a C impurity, variation of the overall cluster charge influences mainly Rh atoms far from the ligand, whereas in an O-ligated cluster, Rh atoms close to the ligand are affected. More importantly, we noted a polarization of the electron density of a neutral Rh6 cluster adsorbed on a neutral zeolite fragment; in that system, two types of Rh atoms occurred carrying positive and negative charges (∼(0.3 e). The charge distribution of supported clusters can be crucial for the catalytic activity of the whole cluster because one type of Rh centers behaves as cations, whereas the reactivity of the other type of Rh atoms should be similar to that of electron-rich metallic species.1,47 Impurity atoms can cause a substantial charge redistribution in supported clusters. After adsorption of an impurity atom (H, C, or O), only neutral or positively charged Rh atoms were present, resulting in a modified reactivity of the metal clusters. All impurity atoms studied, both in the gas phase and on support, carried a negative charge and likely are also reactive. An analysis of the charge distribution and structural parameters of the model cluster corresponding to the experimental species, 3H(b-side)/

192 J. Phys. Chem. B, Vol. 108, No. 1, 2004 Rh6(3+)/zeo(3-), suggested oxidation of the “lower layer” of the Rh atoms, likely to RhI, by the hydroxy groups of the zeolite. Acknowledgment. We thank M. A. Denecke, B. C. Gates, S. Kru¨ger, K. M. Neyman, and J. Rothe for helpful discussions. This work was supported by the Alexander von Humboldt Foundation under an institute partnership project, Deutsche Forschungsgemeinschaft, Fonds der Chemischen Industrie (Germany), and the National Science Fund (Bulgaria). References and Notes (1) Metal Clusters in Catalysis; Gates, B. C., Guczi, L., Kno¨zinger H., Eds.; Elsevier: Amsterdam, 1986. (2) Weber, W. A.; Gates, B. C. J. Phys. Chem. B 1997, 101, 10423. (3) Barthomeuf, D. Catal. ReV. 1996, 38, 521. (4) (a) Sachtler, W. M. H. Acc. Chem. Res. 1993, 26, 383. (b) Sachtler, W. M. H.; Zhang, Z. AdV. Catal. 1993, 39, 129. (5) Shen, G. C.; Liu, A. M.; Shido, T.; Ichikawa, M. Top. Catal. 1995, 2, 141. (6) Gates, B. C. Chem. ReV. 1995, 95, 511. (7) Alexeev, O.; Gates, B. C. Top. Catal. 2000, 10, 273. (8) Kubelkova, L.; Vylita, J.; Brabec, L.; Drozdova, L.; Bolom, T.; Novakova, J.; Schulz-Ekloff, G.; Jaeger, N. I. J. Chem. Soc., Faraday Trans. 1996, 92, 2035. (9) Kawi, S.; Gates, B. C. J. Phys. Chem. 1995, 99, 8824. (10) Kawi, S.; Chang, J.-R.; Gates, B. C. J. Phys. Chem. 1993, 97, 10599. (11) Alexeev, O.; Panjabi, G.; Gates, B. C. J. Catal. 1998, 173, 196. (12) Deutsch, S. E.; Mestl, G.; Kno¨zinger, H.; Gates, B. C. J. Phys. Chem. B 1997, 101, 1374. (13) Ferrari, A. M.; Neyman, K. M.; Mayer, M.; Staufer, M.; Gates, B. C.; Ro¨sch, N. J. Phys. Chem. B 1999, 103, 5311. (14) Goellner, J. F.; Neyman, K. M.; Mayer, M.; No¨rtemann, F.; Gates, B. C.; Ro¨sch, N. Langmuir 2000, 16, 2736. (15) Beutel, T.; Kawi, S.; Purnell, S. K.; Kno¨zinger, H.; Gates, B. C. J. Phys. Chem. 1993, 97, 7284. (16) Gates, B. C. In Catalysis by Di- and Polynuclear Metal Cluster Complexes; Adams, R. D., Cotton, F. A., Eds.; VCH: Weinheim, 1998; p 509. (17) Pacchioni, G.; Kru¨ger, S.; Ro¨sch, N. In Metal Clusters in Chemistry; Braunstein, P., Oro, L. A., Raithby, P. R., Eds.; Wiley-VCH: Weinteim, 1999; p 1392. (18) Giordano, L.; Pacchioni, G.; Illas, F.; Ro¨sch, N. Surf. Sci. 2002, 499, 73. (19) (a) Frank, M.; Ku¨hnemuth, R.; Ba¨umer, M.; Freund, H.-J. Surf. Sci. 2000, 454-456, 968. (b) Frank, M.; Ba¨umer, M. Phys. Chem. Chem. Phys. 2000, 2, 3723. (c) Frank, M.; Ba¨umer, M.; Ku¨hnemuth, R.; Freund, H.-J. J. Phys. Chem. B 2001, 105, 8569. (20) Vayssilov, G. N.; Gates, B. C.; Ro¨sch, N. Angew. Chem., Int. Ed. Eng. 2003, 42, 1391. (21) Dunlap, B. I.; Ro¨sch, N. AdV. Quantum Chem. 1990, 21, 317. (22) Ro¨sch, N.; Kru¨ger, S.; Mayer, M.; Nasluzov, V. A. In Recent DeVelopment and Applications of Modern Density Functional Theory. Theoretical and Computational Chemistry; Seminario, J. M., Ed.; Elsevier: Amsterdam, 1996; Vol. 4, p 497. (23) Belling, T.; Grauschopf, T.; Kru¨ger, S.; Mayer, M.; No¨rtemann, F.; Staufer, M.; Zenger, C.; Ro¨sch, N. In High Performance Scientific and Engineering Computing, Lecture Notes in Computational Science and

Vayssilov and Ro¨sch Engineering; Bungartz, H.-J., Durst, F., Zenger, C., Eds.; Springer: Heidelberg, 1999; Vol. 8, p 439. (24) Belling, T.; Grauschopf, T.; Kru¨ger, S.; No¨rtemann, F.; Staufer, M.; Mayer, M.; Nasluzov, V. P.; Birkenheuer, U.; Hu, A.; Matveev, A. V.; Ro¨sch, N. ParaGauss; Technische Universita¨t Mu¨nchen, 1999; version 2.1. (25) (a) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (b) Perdew, J. P. Phys. ReV. B 1986, 33, 8822; 1986, 34, 7406. (26) (a) Van Duijneveldt, F. B. IBM Res. Report RJ 1971, 945. (b) Gaussian Basis Sets for Molecular Calculations; Huzinaga, S., Ed.; Elsevier: Amsterdam, 1984. (c) Veillard, A. Theor. Chim. Acta 1968, 12, 405. (d) Strodel, P.; Neyman, K. M.; Kno¨zinger, H.; Ro¨sch, N. Chem. Phys. Lett. 1995, 240, 542. (e) Ferrari, A. M.; Neyman, K. M.; Ro¨sch, N. J. Phys. Chem. B 1997, 101, 9292. (27) Gropen, O. J. Comput. Chem. 1987, 8, 982. (28) Ha¨berlen, O. D.; Ro¨sch, N. Chem. Phys. Lett. 1992, 199, 491. (29) Douglas, M.; Kroll, N. M. Ann. Phys. 1994, 82, 89. (30) Hess, B. A. Phys. ReV. A 1986, 33, 3742. (31) Nasluzov, V. A.; Ro¨sch, N. Chem. Phys. 1996, 210, 413. (32) No¨rtemann, F. Dissertation, Technische Universita¨t Mu¨nchen, 1998. (33) (a) Vayssilov, G. N.; Lercher, J. A.; Ro¨sch, N. J. Phys. Chem. B 2000, 104, 8614. (b) Goellner, J. F.; Gates, B. C.; Vayssilov, G. N.; Ro¨sch, N. J. Am. Chem. Soc. 2000, 122, 8056. (c) Vayssilov, G. N.; Ro¨sch, N. J. Phys. Chem. B 2001, 105, 4277. (d) Vayssilov, G. N.; Ro¨sch, N. J. Catal. 1999, 186, 423. (e) Vayssilov, G. N.; Ro¨sch, N. Phys. Chem. Chem. Phys. 2002, 4, 146. (34) Loewenstein, W. Am. Mineral. 1954, 39, 92. (35) Olson, D. H. Zeolites 1995, 15, 439. (36) Klinowski, J.; Ramdas, S.; Thomas, J. M. J. Chem. Soc., Faraday Trans. 2 1982, 78, 1025. (37) These values were chosen as experimental reference values as reported in Table 5 of ref 2 because for these samples no additional C or O atoms (except those of the zeolite) were observed and the Rh coordination number, 3.5-3.9, corresponded to isolated Rh6 clusters. Samples with higher coordination numbers contained larger Rh particles that are not relevant to the present study. (38) Teo, B. K. Acc. Chem. Res. 1980, 13, 412. (b) Teo, B. K.; Lee, P. A.; Simons, A. L.; Eisenberger, P.; Kincaid, B. M. J. Am. Chem. Soc. 1977, 99, 3854. (39) Xiao, C.; Kru¨ger, S.; Ro¨sch, N. Int. J. Quantum Chem. 1999, 74, 405. (40) Go¨rling, A.; Trickey, S. B.; Gisdakis, P.; Ro¨sch, N. In Topics in Organometallic Chemistry; Brown, J., Hofmann, P., Eds.; Springer: Heidelberg, 1999; Vol. 4, p 109. (41) (a) Lacaze-Dufour, C.; Mineva, T.; Russo, N. Int. J. Quantum Chem. 2001, 85, 162. (b) Mineva, T.; Russo, N.; Freund, H.-J. J. Phys. Chem. A 2001, 105, 10723. (c) Chien, C.-H.; Blaisten-Barojas, E.; Pederson, M. R. Phys. ReV. A 1998, 58, 2196. (42) Giordano, L.; Pacchioni, G.; Ferrari, A. M.; Illas, F.; Ro¨sch, N. Surf. Sci. 2001, 473, 213. (43) Pacchioni, G.; Ro¨sch, N. Acc. Chem. Res. 1995, 28, 390. (44) Gisdakis, P.; Antonczak, S.; Ro¨sch, N. Organometallics 1999, 18, 5044. (45) (a) Hadjiivanov, K. I.; Vayssilov, G. N. AdV. Catal. 2002, 47, 307. (b) Zaki, M.; Kunzmann, G.; Gates, B. C.; Kno¨zinger, H. J. Phys. Chem. 1987, 9, 1, 1486. (c) Basu, P.; Panayotov, D.; Yates, J. T., Jr. J. Am. Chem. Soc. 1988, 110, 2074. (d) Miessner, H.; Burkhardt, I.; Gutschick, D.; Zecchina, A.; Morterra, C.; Spoto, G. J. Chem. Soc., Faraday Trans. 1 1989, 85, 2113. (46) Vayssilov, G. N.; Ro¨sch, N. J. Am. Chem. Soc. 2002, 124, 3783. (47) Gates, B. C. Catalytic Chemistry; Wiley: New York, 1992.