J. Phys. Chem. 1994,98, 8141-8151 8747

Site Segregation in Model Clusters of Small Bimetallic RuGe and RuSn Aggregates

Annick Goursot,* Luca Pedocchi,? and Bernard Coq Laboratoire de Chimie Organique Physique et Cingtique Chimique Appliqu&es, URA 418 CNRS, ENSCM, 8 rue de I’Ecole Normale, 34053 Montpellier Cgdex 1 , France

Received: February 1 , 1994; In Final Form: May 26, 1994”

The results of density functional calculations are reported for RuGe and RuSn model clusters, with Sn and Ge atoms located either at a high coordination site (central location) or a t a low coordination site (corner location). The model clusters have been first studied a t a fixed bulk geometry. Then, in order to simulate small bimetallic particles, their structures have been allowed to relax. The relative stabilities of the model clusters support the conclusions that the most stable aggregates are those where Sn and Ge are located a t low coordination sites. However, when relaxation occurs, the clusters distort in order to accommodate Sn or Ge a t the center of the first layer. This distorsion induces a reduction of the coordination of this central atom. The relaxation effects stabilize the RuGe particle, with Ge at both sites, leading to only a small preference for the corner site. At the opposite, the distorsion necessary to accommodate a central Sn atom costs too large amount of energy, which leads to a large preference for Sn to segregate a t a corner site. Quantum chemical calculations are shown to be very helpful in order to quantify the cluster distorsions and the site preference effects when R u is replaced by Sn or Ge.

Introduction

It is now well-established that the physical and chemical properties of metal catalysts are modified by admixture of a second transition metal.14 The widespread use of bimetallic catalysts in re-forming reactions has intensified both fundamental and applied studies of the catalytic behavior of alloy^.^ Two different concepts have been proposed to explain the role of these additives. The first one, or “electronic effect”, suggests that the electronic properties of the pure metal are modified upon addition of the second component.6 These electronic modifications have been demonstrated by XPS and UPS experiments, where shifts of the core and valence metal orbitals are interpreted in terms of electron donorelectron acceptor interactions between the two metal^.^-^ The second interpretation, or “geometric effect”, is based on the theory of ensembles.lS12 In this representation, a reaction requires an ensemble of neighboring active atoms. Many experiments haveshown that dilutionandsizeeffects13J40r blocking of sites15J6 indeed have to be taken into account. In fact, these two hypotheses may not be fully independent, and the catalytic properties of bimetallic systems could be explained with a combination of both, depending on the reaction and the operating conditions. Un- fortunately, in spite of the large amount of experimental work, there is very little theoretical analysis of these mechanisms which govern the catalytic properties of a l l0ys.~J~-2~

In any case, understanding of the bimetallic effect requires the knowledge of how the two elements are distributed between the bulk and the surface layer and further onto this surface layer between sites of different topologies. The Occurrence of surface segregation of one component and its influence on the catalytic properties of the alloys are now well-e~tablished.~.2lJ~ Two models propose that the component which should migrate preferentially to the surface possesses either the lowest heat of sublimation or thelargest atomicvolume.22 For thesame reasons, this component should segregate to sites of lower coordination,23 which is supported by model calculations on Pt/Cu, Ag, and Au particles, using coordination-dependent metal-metal potentials.24

In the case of small bimetallic particles (1-1.5 nm), surface atoms are in a majority and low coordination sites represent the

* Author to whom correspondence should be addressed.

a Abstract published in Aduance ACS Absrracrs, July 15, 1994.

Permanent address: Laboratorio di Chimica Fisica delle Interfasi, via Cavour 82, 50129 Firenze, Italy.

largest part of the surface. Recent studies of well-dispersed bimetallic Rh and Ru catalysts have analyzed the topological segregation of Cu, Sn, Pb, and Ge atoms, on the basis of hydrogenolysis reactions of various alkanes.17.2s27 These catalytic experiments have shown that the selectivity for alkane conversion differs from that obtained with monometallic Rh and Ru particles and that the change depends on the nature of the second element. In particular, they have concluded a preferential occupancy of low coordination sites by Sn, Cu, and Pb, whereas Ge appears to be randomly distributed at the surface. This conclusion has been confirmed by quantum chemical results on RhSn and RhGe model ~1usters . l~

In the present work, we present density functional theory (DFT) calculations on RuSn and RuGe clusters, with the purpose to investigate (i) the preference of Sn and Ge for high or low coordination sites and (ii) the relaxation effects which occur for small bimetallic particles. This study is performed by comparing the electronic properties and relative stabilities of model aggregates at a fixed bulk geometry and after geometry optimization. Although its role is certainly far from negligible for small particles, the interaction with the support has not been considered. It will be very interesting, in a further step, to model this support through the use of additional point charges or multipoles.

Methods

Computational Method. The calculations have been performed within the linear combination of Gaussian type orbitals-model core potential4ensity functional formalism (LCGTO-MCP- DF),28-*9 using the deMon program.3S32 The equilibrium geometries have been obtained by applying the analytical expression for the LCGTO-MCP-DF energy gradients.33 Ge- ometry optimizations have been performed within the local spin density (LSD) approximation, using the Vosko-Wilk-Nusair (VWN) parameterization for the correlation p0tential.3~ At these geometries, nonlocal exchange35 and correlation36 potentials and energies have been used.

For all atoms, the core electrons were replaced by model potentials: for the Ru atom, the (4p, 4d, 5s) electrons were included in the valence shell, whereas the (3d, 4s, 4p) electrons for Ge and (4d, 5s, 5p) electrons for Sn were treated as valence electrons, leading to 14 valence electrons for all atoms. In short notation, the patterns for the orbital basis sets are (61 1/51 I /

0022-3654/94/2098-8141$04.50/0 0 1994 American Chemical Society

8748 The Journal of Physical Chemistry, Vol. 98, No. 35, 1994

TABLE 1: Ground-State Properties for Ruz, RuCe, and RuSn Dimers

Goursot et al.

orbital energies. eV dimer state configuration interatomic dist, A stretching freq, cm-l Ru 4pa Ge 3d or Sn 4d' 2 d

R u ~ 'A, 1cr~17r~16~ 2.22 20: 1 st1 7r; 1 a,

RuGe 3zt l 0 ~ 2 ~ ~ 1 7 r ~ 1 6 ~ 3 0 2.18 RuSn 3z+ 1 ~ ~ 2 u ~ l r ~ 1 6 ~ 3 a 2.41

380 -47.10, -44.93

296 -45.36, -45.00 -29.89, -29.92 -1 1.77, -1 1.81 (89%) 240 -45.19, -44.69 -27.00, -27.02 -10.63, -10.68 (93%)

a The two numbers are the lowest orbital energies in the spin up and spin down manifold, respectively. Numbers in parentheses represent the 4s (Ge) and 5s (Sn) contributions to the 2a MO in percent.

TABLE 2: Mulliken Net Charges (9) and Bond Orders Obtained for R b M Model Clusters at Fixed Geometry (M = Ge, Sn, Ru)

Ru&e central -0.17 0.04 0.00 0.60 corner 0.01 -0.28' -0.01 0.63

RU& central -0.28 0.06 0.01 0.70 corner -0.01 -0.34" -0.01 0.62

0.10b

0.136

0.126 Ru9 -0.22" -0.07

' Central RuIst. Corner Rulst.

51*) for Sn and (51/41/41) for Ge, whereas the associated auxiliary basis sets were (3,5;3,5) for both elements.37 For Ru, a Ru(+14) MCP has been used, associated with (2211/3111/ 31 1) and (3,4;3,4) orbital and auxiliary basis sets, re~pec t ive ly .~~ The validity of the Ru MCP and valence basis sets has been verified, by comparing the results obtained with all-electron basis sets39 for R u ~ , RuSn, and RuGedimers. No significant differences were found for the bond lengths and binding energy values between these two series of calculations. For R u ~ (7A,), the equilibrium distance is found to be 2.215 and 2.225 A for the MCP and the all-electron basis sets, respectively, with related binding energies of 4.4 and 4.0 eV, with respect to spherical Ru atoms. For the heteronuclear dimers, the equilibrium bond distances were 2.407 8, (RuSn) and 2.180 A (RuGe) for MCP against 2.407 8, (RuSn) and 2.178 A (RuGe) for the all-electron basis sets. The comparison of the dissociation energies is also satisfactory: 4.05 eV (RuSn) and 4.73 eV (RuGe) with MCP vs 3.90 eV (RuSn) and 4.50 eV (RuGe) with the all-electron bases (with respect to spherical atoms). Let us note that the Sn(+14) MCP which is employed heregives more accurate results than a previous Sn(+4) MCP,40 which leads to a too short Ru-Sn bond length of 2.350 A.

Descriptionof theclusters. Theclusters Rusand Ru&i, chosen tostudy thesiteeffect,aremodelsofa (100) face, withrespectively five and four atoms in the first and second layers. Their symmetry has been fixed to C, with M located at a corner site (low coordination, three Ru first neighbors) and C4" when M occupies the center of the first layer, Le., a high coordination site (eight Ru first neighbors). A first series of calculations has been performed with fixed metal-metal bond distances of 2.65 A, modeling of bulk Ru system. In a second step, the atoms in the clusters have been allowed to relax, while keeping the symmetry constraints. Due to thecomplexity of the potential energy surface of these quite large metallic clusters and the presence of different electronic states of close energies, the optimization process has been stopped when the gradient norm reached 0.008 for Ru9 and RusGe (Ge at the center) and 0.002 for the other clusters. Since bulk Ru has no magnetic properties, these clusters have been calculated in singlet states.

Results and Discussion RUB RuGe, and RuSn Dimers. Dimers represent the smallest

system which allows us to investigate the metal-metal bond. Moreover, within our comparative study of Ge and Sn locations at corner and central coordination sites, they constitute the limiting model displaying metal atoms at very low coordination sites.

0.44 1.09 0.74 0.82 0.80 0.60' 0.80

1.006 0.40 1.10 0.70 0.80 0.80 0.62' 0.80

1.026 0.78 0.63' 0.72

1 .OOb

The main ground-state (GS) properties which are of interest for our study are presented in Table 1. R u ~ has a 7Au GS, corresponding to the configuration 1 ug2 1 nu4 1 6,3 2u: 1 6,2 1 ng2 luu. This dimer is multiply bonded, with a short equilibrium bond distance, which correlates to calculated bondorder of 3.1 5.41

RuGe and RuSn dimers have the same 3Z+ GS with the same valence electronic configuration. The metal-metal bond is achieved through two u-type MOs and one n-type MO, the d orbital being nonbonding and purely localized on the Ru atom. The first u MO is essentially a Ge 4s or Sn 5s MO (Table 1). The two u-type bonding MOs correspond to bonding combinations of the Ge or Sn ps orbital with Ru 4d, (2u) and Ru 5 s (30) orbitals. The 1n MO involves Ru d, and Ge or Sn pI bonding contributions. The Ru-Ge bond distance is clearly smaller than that of Ru-Sn. This order corresponds to that found for the atomic radii of Ge (1.25 A) and Sn (1.45 A). Moreover, the same order holds for the calculated bond orders (2.71 for RuGe and 2.55 for RuSn), stretching frequencies, and dissociation energies (see above).

These results allow us to conclude decreasing bond strengths from R u ~ to RuGe and RuSn. In our calculations, the external core orbitals have been treated as valence orbitals, since it is known that they play a role in metal-ligand bonding.42 We indeed see, from Table 1, that the Ru 4p orbitals are different for Ru2, RuGe, and RuSn. They are more stable for Ru2, and their destabilization for RuGe and RuSn parallels the weakening of the Ru-M bond, with M = Ru, Ge, and Sn. We will come back to this point in the next paragraph concerning RUBM models and will also discuss the Ge 3d and Sn 4d orbital energies.

Rug, RusCe, and RusSn Models at a Fixed Geometry. In the first step, it is interesting to analyze the main electronicdifferences displayed by the model clusters with all metal-metal bond lengths being fixed at the bulk value (2.65 A). This allows us to delineate the main trends produced by the replacement of a central or a corner Ru atom by Ge or Sn and, after, to analyze the effects of the relaxation which occurs for small clusters.

The main characteristics of the Ru-Ru and Ru-M bonds, according to the nature of M, are collected in Table 2. The results obtained for Rug are also reported for comparison. Highly coordinated metal atoms are expected to be more electronically populated than atoms with low coordination. This trend is indeed verified since Ru, Sn, and Ge atoms bear an excess of charge when they are located at the central site (eight first neighbors). Examination of Table 2 allows further analysis of the Ru-Ru and RUM bonds to be derived. Bond orders (BOs)41 are useful

Small Bimetallic RuGe and RuSn Aggregates

TABLE 3: Orbital Energies for the Ru&l Clusters.

The Journal of Physical Chemistry, Vol. 98, No. 35, 1994 8749

position of orbital energies, eV cluster the 2nd M central Ru 4p corner Ru 4p Ge 3d Sn 4d l o MOb RusGe central -45.30, -44.20 -29.59, -29.55 -12.99 (66%)

corner -45.79,-45.64 -45.40, -44.15 -29.83, -29.79 -12.09 (76%) Ru&n central -45.21, -44.17 -26.65, -26.52 -12.37 (52%)

corner -45.77,-45.62 -45.37, -44.15 -26.88, -26.81 -1 1.34 (80%) Ru9 -45.87, -45.85 -45.41, -44.27

a Two numbers are given, they represent the lowest and highest energy values for these orbitals. Main bonding MO based on Ge 4s and Sn 5s orbitals. _. The numbers in parentheses are the s contribution in percent.

quantities, which help us to compare not only bonding properties between atoms but also their evolution in the different models. Comparison of the last three columns of Table 2 shows that Ru- Ru bonds are unaffected by the replacement of Ru by Sn or Ge, whichever is the site. The M-Ru bonds in the first layer are slightly weakened (0.6-0.7) compared to a central Ru atom (0.78) but remain unchanged with respect to a corner Ru atom (0.60- 0.63).

Although the Ru central atom has eight equidistant first neighbors, four in the first layer (Rulst) and four in the second one (RuZnd), its bonding with the second layer atoms is not as efficient as with the first layer atoms (BOs of 0.63 and 0.78, respectively). In the same way, Ge or Sn atoms are more weakly bonded to RuZnd than to Rul" atoms. On the other hand, corner Rulst atoms make more efficient bonds with the second layer atoms than with the central Rulst, which is at the same distance. Since bond order calculations are based on Mulliken overlap populations, these results express that, due to different overlap possibilities, bonding strengths between first neighbor atoms may not be equivalent.

The relative energies of the RusM clusters with M at the two coordination sites indicate that the corner substitution is the most stable in both cases. Indeed, the clusters with a central M are less stable by 27.8 kcal mol-' for Ge and 42.4 kcal mol-' for Sn.

The data reported in Table 3 help to throw some light on this significant difference. They represent the energies of the external core orbitals Ru 4p, Ge 3d, and Sn 4d for the RusM model clusters. The Ru 4p orbitals for Rug are also indicated for comparison. In all cases, the lowest and highest energies are indicated for each orbital type. The valence 1u MOs based on the Ge 4s and Sn 5s orbitals are also reported. A comparison of the Ru 4p energy values shows that, when Ge or Sn are at a corner site, the lowest level is more stable by 0.4 eV. This level corresponds to the 4p orbital of the central Ru atom perpendicular to the first layer plane; the two other 4p orbitals are a t -45.7 and -45.6 eV. These three orbitals appear at -45.87, -45.85, and -45.85 eV for the Rug cluster. When Ge or Sn are a t a central position, these three levels are replaced by Ru corner levels in the -45.4, -44.2 eV band. Clusters with M in a central position are thus destabilized with respect to those with M at a corner position. In the same way, the 3d orbitals of a Ge atom or the 4d orbitals of a Sn atom in the central position are less stable than the same orbitals for Ge or Sn as corner atoms. This destabilization amounts to about 0.2 eV. At the opposite, the bonding u MO, with major Ge 4s or Sn 5s contributions, is strongly stabilized for central M atoms. This stabilization, due to a more efficient bonding combination with Ru 5 s orbitals, amounts to about 1 eV. The total electronic energy of a system can be expressed as the sum of the orbital energies minus the electron-electron interaction energy (including the Coulomb repulsion and theexchange-correlation term). Under the crude assumption that the central and corner M models have comparable electron-electron interactions, a rough estimate of the relative stabilities of corner and central M models may be obtained through the sum of their orbital energy differences. This sum, reduced to Ru 4p, Ge 3d (or Sn 4d), and the l u MOs amounts to about 60 kcal mol-', as destabilization for the central M models.

The energy shifts of these external core orbitals are related to intrinsic electronic rearrangements, which are also reflected by

the Mulliken charges. However, a more detailed analysis of the atomic configurations must be considered in order to understand why Ru 4p orbitals are more stable for a central site and, at the opposite, why 3d Ge or 4d Sn are less stable. It is general knowledge that, when a neutral atom becomes positive, its energy levels are stabilized (whereas a gain of electronic charge implies their upward shift) and that the amount of these shifts depends on the nature of the orbital where the population varies. This dependence on atomic configuration can be simply related, in a central field model, to the shielding (mainly outershielding) of the external coreelectrons. The screening of the Ru (4p) electrons by electrons in the 4d, 5s, 5p orbitals decreases in that order, leading to contraction and stabilization of the Ru (4p) orbitals, which are larger for a loss of charge in the 4d than in the 5s and 5p orbitals. The shielding of the 3d (4d) electrons of Ge (Sn) by the 4s (5s) and 4p (5p) electrons is very comparable. Owing to these general properties, it is then interesting to relate the orbital energy shifts and atomic configurations for Ru and M atoms at the central and corner sites.

For all models, including Rug, the configurations obtained for Ru atoms are very similar and specific to the sites, independently of M. The atomic configurations for a central and a corner Ru are well described as 5sl.O 5p0.4 4d6.8 (central) and 5 ~ 0 . ~ ~ 5~0.O~ 4d7.0s (corner).

If we refer to a corner Ru, we see that a central Ru gains roughly 0.35 (0.45 for RusSn) electron in 5p and 0.15 electron in 5s but loses 0.25 electron in 4d orbitals.

Since the shielding of 4d electrons is the most effective, its decrease should overcompensate the increase of the screening of the 5s and 5p electrons. Calculations performed for an isolated Ru atom (spherical) with these configurations lead to a stabiliza- tion of 0.20 eV for the lowest 4p orbital of the central Ru, with respect to the corner atom.

The atomic M configurations in the clusters are well described as 4s130 4~2.20 (Ge) and 5sZ,O 5pZ,O (Sn) a t a corner and 4s1.s0 4pZ.'O (Ge) and 5 ~ 1 . 5 0 5~2.80 (Sn) at the center. For both central Ge or Sn, loss in 4s or 5s population, with respect to the corner location, is overcompensated by gain in the 4p or 5p orbital, which leads to the destabilization of the 4d Ge and 5d Sn levels. Calculations for isolated (spherical) Ge and Sn atoms with these fixed configurations lead indeed to destabilizations of 0.70 and 0.35 eV for Ge 3d and Sn 4d, respectively, for a central M with respect to a corner M.

The Ru, Ge, and Sn configurations obtained for the dimers RuSn and RuGe are similar to those reported for the corner atoms in RusM, which explains the similarity of their Ru 4p, Ge 3d, and Sn 4d energies (cf. Table 1). In that sense, we can say that the dimers are good models for low coordination Ge or Sn atoms.

It is worth comparing the 4p orbital energies for Ru atoms in the Rug and RusM clusters and looking at their behavior when one Ru is replaced by Ge and Sn. The central Ru 4p orbitals a t -45 .87 eV for Rug are to be compared with -45.79 eV for RusGe (corner) and -45.77 eV for Rus Sn (corner). There is thus a small destabilization of these Ru 4p orbitals in the presence of a second element. This small destabilization of about 0.1 eV occurs also for the low coordination Ru 4p orbitals. We can thus conclude that the presence of a second element as Ge or Sn induces a destabilization of the Ru 4p orbitals, with respect to pure Ru

8750

TABLE 4 Mulliken Net Charges (q) , Interatomic Distances, and Bond Orders (BOs) Obtained for R q M Model Clusters (M = Ge, Sn, Ru) after Geometry Optimization

The Journal of Physical Chemistry, Vol. 98, No. 35, 1994 Goursot et al.

position of 4 interatomic distances (A) and BOs in parentheses cluster the 2nd M M RulBt Rulnd M-RulSt M-Ru~"~ R u ~ ~ ~ - R u ' ~ ~ RuiSt-Ru2nd(b) R u ~ ~ ~ - R u ~ ~ ~ RuaGe central -0.36 0.16 -0.07 2.38 3.00 2.36 2.57

(0.80) (0.24) (1.24)

0.08b (0.69) (0.99) (0.74) (0.90) (1.41) corner -0.15 -0.12" 0.03 2.4gb 2.42 2.56 2.5 1 2.30

Ru& central -0.04 0.02 -0.01 2.88 2.91 2.24

corner -0.01 -0.28" -0.01 2.88 2.91 2.57 2.49 2.31 (0.46) (0.44) (1.55)

0.116 (0.66) (0.72) (0.78) (0.88) (1.34)

Ru9 -0.2OU 0.005 2.52 2.65 2.32 0.10b (0.73) (0.60) (1.35)

@ Rulst at central position. Ruist at corner position. RuZnd first M neighbors. RuZnd other than first M neighbors.

(0.77) 2.53c

(0.73) 2.75d

(0.55) 3.05

(0.45) 2.46c

(0.89) 2.74d

(0.60) 2.70

(0.55)

(a

Figure 1. Relaxed structures of Rug (a), RugGe with a central Ge (b), RuBGe with a corner Ge (c), Ru&n with a central Sn (d), and Ru&n with a corner Sn (e). Bonding between first-neighbor atoms is indicated by straight lines when bond distances are less than 2.7 A.

aggregates, whichever is the site occupied by this second element. XPS results concerning shifts of metal core orbitals for bimetallic surfaces, combined with thermal desorption experiments, have suggested that such destabilizations can be related to a decrease of the metal cohesive energy.'*

Relaxed Structures for Rug, Ru&e, and RqSn Models. The bond distances, bond orders, and Mulliken net charges obtained after geometry optimization are collected in Table 4. Pictures of the relaxed structures are displayed in Figure 1. Before drawing conclusions from these results, it is noteworthy that simple arguments based on atoms size or the results from previous works allow some general trends to be anticipated:

(A) Ru-Ru bond distances are smaller in clusters than for the bulk, related to the decrease of the average atomic coordination. An average value of about 2.60 h;, associated with a coordination

between 4 and 5 , was determined from EXAFS experiments on very small alumina-supported Ru p a r t i c l e ~ . ~ 3 > ~ ~

(B) Comparison of the atomic radii (1.30 A for Ru; 1.25 A for Ge; 1.45 %I for Sn) leads us to anticipate that the cluster should distort more strongly to accommodate Sn than Ge. Moreover, the size mismatch for the (Ru,Ge) pair (3.8%) is far less than for the (Ru,Sn) pair (1 1.5%), which leads us to predict that Sn should segregate to corner sites more preferentially than does Our results are fully in line with those arguments and, moreover, allow those trends to be quantified:

(1) The five model clusters display the same kind of distortion, with the central atom coming out of the first layer plane (cf. Figure 1). Its distance from this plane increases from 0.36 h; for Ru (Rug) to 0.68 A for Ge and 0.85 8, for Sn (central M models). When Ge and Sn are at corner sites, the geometry of the first layer is more disturbed, due to the lower C, symmetry. In this case, both the central Ru and corner M atoms are shifted upward by about 0.30-0.35 A.

(2) For Rug, as well as for the bimetallic models, there is a clear shortening of the distance between the Ru atoms of the first and second layers. This is particularly obvious for the corner Ru atoms. Except for the central Sn cluster, which is very much distorted, this distance is roughly constant (2.30-2.36 A). This shrinking effect, which is characteristic for small parti~les,~3 reflects a bond strengthening between the two layers with bond order values increasing from 1 .O (frozen geometry) to 1.4 (relaxed geometry). Due to the upward shift of central Ru atoms, their distance to the second layer is not shortened as much, and there is also a clear bond strengthening (bond orders increased from 0.6 to 0.9), except for Rug.

(3) One of the most striking features displayed from Table 4 and Figure 1 is the strong distortion undergone by the cluster model with a central Sn atom. Moreover, central Ge and Sn models are very different. The eight Ru-Sn bonds are strongly weakened, lengthening to 2.9 A, as well as the Ru-Ru bonds in the second layer. The only strong bonds in this cluster correspond to the Ru-Ru interactions between layers. At the opposite, the bond distances (and bond orders) obtained for the central Ge cluster reflect a substantial bonding between all first neighbor atoms, except between Ge and the Ru atoms of the second layer. Indeed, this bond distance is increased to 3.0 A, which reveals its weakening (its bond order decreases from 0.44 at the frozen bulk geometry to 0.24 at the relaxed geometry).

(4) The main differences between the relaxed structures with Ge and Sn at the corner sites concern the Ru-M distance. When compared to the fixed geometry, the Ru-Ge distance is decreased, whereas Ru-Sn is increased, as would be expected from the respective Ge and Sn atomic radii.

From these remarks, we can infer that accommodation of Sn at a central site requires a strong distortion of the cluster, even

Small Bimetallic RuGe and RuSn Aggregates The Journal of Physical Chemistry, Vol. 98, No. 35, 1994 8751

of the Ru part. At the opposite, a Ge atom at the center or Ge and Sn at corner sites do not perturb the whole structure as much.

It is worth noting that the way the clusters with central M atoms stabilize their energy implies a large weakening of the Ru-M bonds, which could be described as a decrease of coordination. A central Sn is connected to eight Ru atoms with a bond order reduced almost by half, and a central Ge has four strong bonds with Rulst atoms and four very weak bonds with Ru*nd atoms. There is no obvious loss of coordination for Ge or Sn at the corner sites.

The calculated energy differences between central and corner sites confirm the picture given by the geometric structures: the corner site is more stable by 32 kcal mol-' for Sn, whereas it is favored by only 10 kcal mol-' for Ge. In both cases, the stabilization gained by the cluster relaxation is substantial and concerns central and corner sites. However, while the difference in stability between these two sites is decreased by 18 kcal mol-' for Ge clusters, its decrease is only 10 kcal mol-' for the Sn models, which expresses the difficulty to accommodate a Sn atom at a central site.

The calculated atomic net charges (Table 4) corresponding to the optimized clusters are very different from those obtained at the frozen bulk geometry (Table 2). In the latter case, Sn and Ge atoms in the central sites were bearing negative charges and were quasi-neutral at the corner sites. For the relaxed clusters, central and corner Sn are almost neutral, but Ge atoms have gained electronic charge.

In fact, the structural changes exhibited by the clusters involve orbital rehybridizations and different compositions of the MOs. The orbital energies for the central and corner M clusters are thus substantially modified with respect to the frozen bulk geometry. For example, the relative stabilities of Ge 3d and Sn 4d orbitals for central and corner M models are now reversed, the stabilization of l a for a central M is reduced to 0.8 eV (Ge) or 0.6 eV (Sn), and the bonding MOs based on Ru (5s + 4d) and Sn 5p or Ge 4p orbitals are substantially destabilized (0.4-0.6 eV) for all models.

These results allow us to infer that, since large and small bimetallic particles must have different kinds of relaxation, the electronic rearrangements, which are correlated with these structural changes, will be different, leading probably to different chemical reactivity.

Conclusions

On the basis of our work, we can draw some conclusions that we believe shed some light on the intricated geometric and electronic factors which govern the bonding mechanisms and thus the chemical properties of bimetallic particles.

In the case of rigid systems, fixed at the bulk geometry, Ge or Sn as the second element display a clear preference to occupy low coordination sites. However, the smaller size of Ge and its larger aptitude to make stronger bonds with Ru atoms induce a smaller destabilization for Ge at a high coordination site.

Small particles exhibit large relaxation effects with shorter bond lengths and increased bonding between layers. In order to accommodate Ge or Sn at the center of the first layer, the cluster distorts so as to reduce the coordination of this central atom. The relaxation which occurs in the presence of a Ge atom stabilizes the particle a t both central and corner sites, leading to only a small preference for the site location. On the contrary, a central Sn costs a large amount of energy to distort the cluster, weakens all bonds in each layer, and leads to a large preference for Sn to segregate at corner sites.

Moreover, since geometric relaxation must be size dependent (large particles are closer to the bulk geometry), site segregation and chemical properties of bimetallic particles, which are determined by electronic rearrangements in the molecular orbitals, not only depend on the nature of the second element but may also vary with the size of the particle.

Acknowledgment. This work has been supported by the European Economic Community in the form of a Stimulation Action Science (No. SC1 *-CT91-068 l ) , which funded study visits of L. Pedocchi to our laboratory. We are grateful to CSCS (Manno, Switzerland) for a grant of computer time.

References and Notes

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