Density functional study of ethylene adsorption on palladium clusters Fahmi, A.; van Santen, R.A.

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1 Density functionl study of ethylene dsorption on plldium clusters Fhmi, A.; vn Snten, R.A. Published in: Journl of Physicl Chemistry DOI: /jp953002s Published: 01/01/1996 Document Version Publisher s PDF, lso known s Version of Record (includes finl pge, issue nd volume numbers) Plese check the document version of this publiction: A submitted mnuscript is the uthor's version of the rticle upon submission nd before peer-review. There cn be importnt differences between the submitted version nd the officil published version of record. People interested in the reserch re dvised to contct the uthor for the finl version of the publiction, or visit the DOI to the publisher's website. The finl uthor version nd the glley proof re versions of the publiction fter peer review. The finl published version fetures the finl lyout of the pper including the volume, issue nd pge numbers. Link to publiction Cittion for published version (APA): Fhmi, A., & Snten, vn, R. A. (1996). Density functionl study of ethylene dsorption on plldium clusters. Journl of Physicl Chemistry, 100(14), DOI: /jp953002s Generl rights Copyright nd morl rights for the publictions mde ccessible in the public portl re retined by the uthors nd/or other copyright owners nd it is condition of ccessing publictions tht users recognise nd bide by the legl requirements ssocited with these rights. Users my downlod nd print one copy of ny publiction from the public portl for the purpose of privte study or reserch. You my not further distribute the mteril or use it for ny profit-mking ctivity or commercil gin You my freely distribute the URL identifying the publiction in the public portl? Tke down policy If you believe tht this document breches copyright plese contct us providing detils, nd we will remove ccess to the work immeditely nd investigte your clim. Downlod dte: 03. Nov. 2018

2 5676 J. Phys. Chem. 1996, 100, Density Functionl Study of Ethylene Adsorption on Plldium Clusters A. Fhmi* nd R. A. vn Snten Schuit Institute of Ctlysis, Lbortory of Inorgnic Chemistry nd Ctlysis, EindhoVen UniVersity of Technology, P.O. Box 513, 5600 MB EindhoVen, The Netherlnds ReceiVed: October 11, 1995; In Finl Form: Jnury 17, 1996 X Fully optimized geometries nd dsorption energies obtined from nonlocl density functionl clcultions re presented for Pd n (C 2 H 4 ) (n ) 1-6) clusters. The dsorption mode cn be π or di-σ ccording to the cluster size. The di-σ dsorption mode is chrcterized by strong distortion for both the ethylene nd the metl cluster. The potentil energy surfces for the C-H ctivtion show tht the d 10 configurtion of plldium is suitble for the formtion of the π moleculr complexes, wheres the d 9 s 1 configurtion is suitble for the formtion of the σ bonds of the vinyl-hydride products. 1. Introduction In recent yers, numerous experimentl nd theoreticl investigtions of chemisorption of ethylene on vriety of trnsition metl surfces hve been crried out utilizing wide rnge of techniques. Upon dsorption on metl surfce, ethylene undergoes dehydrogention-hydrogention processes tht led to severl C x H y species on the surfce. Despite vrious experimentl studies, rection mechnisms leding to these species nd their locliztion on the surfce re not well determined. At low temperture (100 K), ethylene is moleculrly dsorbed on the metl surfce. Two dsorption modes re often discussed: the di-σ dsorption mode where ethylene intercts with two metl toms nd the π dsorption mode where ethylene intercts with single metl tom. High-resolution electron energy loss spectroscopy (HREELS) experiments provide vibrtionl spectr for dsorbed intermedites on the metl surfce. The comprison with the spectr of C 2 H 4 Br 2 ( model for di-σ bonded C 2 H 4 ), Zeise s slt ( model for π-bonded C 2 H 4 ), nd gseous C 2 H 4 llow Stuve nd Mdix 1 to introduce πσ prmeter to chrcterize the dsorption of C 2 H 4. The πσ prmeter is zero for gseous C 2 H 4 nd unity for C 2 H 4 Br 2. For dsorbed ethylene, the πσ prmeters for Pd(100), 1 Pd(111), 2 nd Pd(110) 3 surfces re 0.78, 0.43, nd 0.39, respectively. These vlues re ttributed to the formtion of di-σ complex on Pd(100) nd π complex on Pd(111) nd Pd(110) surfces. Extended Huckel clcultions 4,5 hve shown tht the dsorption mode of ethylene is controlled by subtle blnce between ttrctive two-electron interctions nd repulsive four-electron ones (the Puli repulsion). Ethylene behves differently in the two dsorption modes. At 80 K, the two modes coexist on the Pd(100) surfce. 1 While the π-bonded ethylene desorbs upon heting from 100 to 300 K, the di-σ-bonded ethylene dehydrogentes into codsorbed tomic hydrogen nd vinyl species. The difference in rectivity should be relted to the difference in geometry nd electronic structure of ethylene in the two dsorption modes. In this work, we present density functionl study of the interction of ethylene with plldium. Clusters of 1-6 metl toms re used. The two dsorbed ethylene species π nd di-σ re described. The ctivtion of the C-H bond of ethylene is nlyzed for the single tom nd the dimer. One of the min spects of our clcultions is full geometry optimiztion of the whole system C 2 H 4 /Pd n. This pproch is different from X Abstrct published in AdVnce ACS Abstrcts, Mrch 1, the common pproch tht consists in freezing the cluster, which is supposed to simulte metl surfce, nd optimizing the dsorbte. On one hnd our pproch will give informtion bout the mgnitude of the locl relxtion induced by the dsorption of ethylene on the plldium surfce. On the other hnd, our clcultions should describe the interction of ethylene with plldium clusters in the gs phse. The clcultion method is described in section 2. The moleculr properties of the bre Pd n clusters re presented in section 3. Adsorption nd ctivtion of the C-H bond by the plldium single tom nd dimer re discussed in sections 4 nd 5, respectively. Section 6 is devoted to the evolution of the ethylene dsorption with the cluster size. 2. Method of Clcultion A density functionl method is used to determine geometries, dsorption energies, nd trnsition sttes for the C 2 H 4 /Pd n (n ) 1-6) systems. We hve performed qusi-reltivistic spinunrestricted, frozen-core clcultions using the Amsterdm Density Functionl (ADF) progrm. 6 The progrm represents the moleculr orbitls s liner combintions of tomic Sltertype orbitls nd solves the Khon-Shm one-electron equtions using the Vosko-Wilk-Nusir 7 locl spin density pproximtion (LDA). To correct the overbinding inherent to LDA, nonlocl grdient corrections for the exchnge (Becke functionl 8 ) nd correltion (Perdew functionl 9 ) terms were computed self-consistently. Reltivistic effects were tken into ccount by first-order perturbtion theory. 10 For the crbon tom, frozen core potentil is used for the 1s electrons; for the plldium tom, electrons up to the 4p shell re frozen. The bsis sets re of double-ζ qulity except the plldium d orbitls which re triple-ζ. Adsorption energies hve been clculted ccording to the expression: E ds ) E (C2 H 4 /Pd n ) - (E Pd n + E C2 H 4 ) where E Pdn nd E C2H 4 re totl energies of the bre cluster nd ethylene, respectively, nd E (C2H 4/Pd n) is the totl energy of the dsorbte/substrte system. A negtive E ds vlue corresponds to stble dsorbte/substrte system. 3. Bre Pd n (n ) 1-6) Clusters 3.1. The Plldium Single Atom. As reference point, we hve clculted the splitting between the two lowest sttes /96/ $12.00/ Americn Chemicl Society

3 Ethylene Adsorption on Plldium Clusters J. Phys. Chem., Vol. 100, No. 14, TABLE 1: Moleculr Properties for the Triplet nd Singlet Sttes of the Plldium Dimer Pd 2 stte binding energy (kcl/mol) Pd-Pd (Å) of the plldium single tom. The clculted energy difference between the 1 S(d 10 ) ground stte nd the 3 D(d 9 s 1 ) excited stte is 26 kcl/mol; the experimentl vlue is 22 kcl/mol The Plldium Dimer. In greement with previous theoreticl clcultions (Hrtree-Fock 12 nd DFT 13 ), we found the ground stte of the plldium dimer to be triplet. The clculted moleculr properties re summrized in Tble 1 for the triplet nd the singlet sttes. Bonding energies re reltive to two Pd(d 10 ) toms. The triplet stte is more stble by 4 kcl/ mol. The estimted experimentl bonding energy for the dimer is between 16 nd 26 kcl/mol 14 ccording to the technique of evlution. The Mulliken popultion nlysis shows tht the singlet stte is composed of two intercting d 10 toms. The Pd-Pd bond length is shorter nd the vibrtionl frequency is higher for the triplet stte The Pd n (n ) 3-6) Bre Clusters. For the Pd n (n ) 3-6) bre clusters, only compct structures were investigted. A density functionl nlysis of the structure of smll plldium clusters show tht compct structures re more stble thn open structures, nd sttes of triplet spin re more stble thn sttes of singlet spin. 15 Our clcultions show tht for Pd 3, the tringulr geometry (D 3h ) is more stble by 29 kcl/mol reltive to the liner geometry (D h ). For smll clusters, the tomic rrngements re controlled by locl bonding nd orbitl overlpping rther thn long-rnge interction s it is in the bulk structure. Cluster geometries re cluster size dependent nd experimentl structure determintions often proceed vi indirect methods (for instnce N 2 dsorption for the determintion of the structures of Ni n clusters 16 ). The other investigted geometries re Pd 4 (T d ), Pd 5 (D 3h ), nd Pd 6 (O h ). The clculted properties re shown in Tble 2. All these clusters present ground sttes of spin triplet, previous DFT, or Hrtree-Fock studies of Pd 17 3 nd Pd 18 4 clusters hve shown tht these clusters re indeed triplet. The optimized Pd-Pd bond remins close to the bulk vlue, 2.75 Å. 19 The Pd-Pd bond strength decreses with the cluster size but is still fr from the experimentl vlue, 15 kcl/mol. 19 The Mulliken popultions (for n ) 3, 4, 6) show decrese of the s electrons nd increse of the d electrons with the cluster size. The energy bnd clcultion for the plldium bulk structure 20 gives 0.37 nd 9.63 electrons for the vlence s nd d orbitls, respectively. 4. The Pd(C 2 H 4 ) Complex frequency (cm -1 ) Mulliken popultions: s/p/d triplet /0.02/9.43 singlet /0.02/9.80 TABLE 2: Pd n Moleculr Properties of the Pd n Bre Clusters tomic coordintion Mulliken popultions: s/p/d Pd-Pd (Å) Pd-Pd bond strength (kcl/mol) 1 0/0/ /0.02/ D 3h /0.03/ T d /0.04/ D 3h 3 (top) 0.42/0.04/ (bse) 0.52/0.04/ O h /0.04/ The Pd(C 2 H 4 ) complex ws first synthesized by Ozin nd Power 21 using C 2 H 4 /Xe mtrices. This complex hs lso been subject of theoreticl investigtions. Blomberg et l., using n b initio Hrtree-Fock method, clculted the bonding energy TABLE 3: Adsorption Energies (kcl/mol) Reltive to Free Species nd Geometries (Å nd deg) for the Moleculr Complex, the Trnsition Stte, nd the Vinyl-Hydride Product of the Pd(C 2 H 4 ) Complex Pd(C 2H 4) trnsition stte H-Pd-C 2H 3 E ds C-C Pd-C Pd-H H-Pd-C For the trnsition stte, the brrier height reltive to the π complex is 36 kcl/mol. Figure 1. Potentil energy surfces for the ctivtion of the C-H bond of ethylene by the plldium single tom () nd dimer (b); the reference for dsorption energies (in kcl/mol) corresponds to free molecules (Pd + C 2H 4 or Pd 2 + C 2H 4) in their equilibrium geometries. For the trnsition sttes the brrier heights (reltive to π nd di-σ dsorption for Pd nd Pd 2, respectively) re indicted. TS1, TS2, nd TS3 for Pd 2C 2H 4, correspond to the side-on prllel, side-on perpendiculr, nd end-on pproches (see Figure 3). of the complex 22 nd the ctivtion of the C-H bond of ethylene by the plldium single tom. 23 During the interction of ethylene with trnsition metl dontion nd bck-dontion processes tke plce. The dontion involves trnsfer of electrons from the ethylene π orbitl to the metl unoccupied orbitls, wheres the bck-dontion popultes the ethylene π* orbitl with electrons from the occupied metl orbitls. This is the well-known Dewr-Chtt- Duncnson mechnism. 24 Both dontion nd bck-dontion re ttrctive interctions. The repulsion (Puli repulsion) is due to the interction between the occupied orbitls of ethylene nd the trnsition metl. The first consequence of the dontion nd bck-dontion processes is the wekening of the C-C bond strength, the bond length increses from 1.34 Å in the gs phse to 1.40 Å in the complex. The formtion of the Pd-C bonds induces smll rehybridiztion of the crbon tom from sp 2 towrd sp 3 (see Tble 3). The dihedrl ngle between the HCC plne nd the CCPd plne increses from 90 to 98 ; for complete sp 3 hybridiztion, this ngle should be 120. The ground stte of the complex is singlet with bonding energy of -39 kcl/mol. This vlue is close to tht clculted by Blomberg et l., kcl/mol. The overll chrge trnsfer is bck-dontion of 0.07 electrons to ethylene. The dontion to the metl is smll, 0.01 electrons. The potentil energy surfce for the ctivtion of the C-H bond is shown in Figure 1. The most interesting spect of this potentil is perhps tht the trnsition stte is below the Pd + C 2 H 4 symptote; the energy difference to the symptote is 3 kcl/mol. The brrier height is 36 kcl/mol nd the energy

4 5678 J. Phys. Chem., Vol. 100, No. 14, 1996 Fhmi nd vn Snten Figure 2. Adsorption modes of ethylene on Pd 2, () π nd (b) di-σ, nd vrious geometries for the vinyl-hydride product, (c) pseudo-squre plnr, (d) trns, nd (e) cis. difference between the trnsition stte nd the vinyl-hydride product is smll, 6 kcl/mol. Our results re in good greement with Siegbhn et l. 23 clcultions, which found brrier height of 31 kcl/mol nd n energy difference of 3 kcl/mol between the trnsition stte nd the vinyl hydride product. 5. Interction of Ethylene with the Plldium Dimer Two kind of complexes cn be formed (Figure 2, prts nd b): π nd di-σ complexes. The moleculr properties of the two complexes re presented in Tble 4. The di-σ complex is more stble nd is chrcterized by lrge chrge trnsfer from the dimer to ethylene (bck-dontion). The di-σ dsorption mode gives strong interction nd strong distortion of ethylene towrd the sp 3 hybridiztion, wheres the π dsorption mode gives smll interction nd smll distortion. The sme trend ws found by Extended Huckel clcultions for the dsorption of C 2 H 4 on Pd(111) nd Pt(111) surfces. 4 Tble 4 lso shows the decomposition of the interction energy of ethylene with the dimer. The interction energy is decomposed in three contributions: 25 the Puli repulsion E p, the electrosttic interction E elec, nd the orbitl interction E orb. The Puli repulsion rises from the interction between occupied orbitls of C 2 H 4 nd Pd 2 ; the electrosttic interction corresponds to the interpenetrting chrge distributions; nd the orbitl interction represents the energy chnge upon the formtion of the moleculr orbitls of the C 2 H 4 /Pd 2 system. This energy clculted with the Ziegler trnsition-stte method 25d for the optimized dsorbte/substrte system corresponds to the interction between two distorted frgments nd is not the dsorption energy tht refers to free molecules in their equilibrium geometries (the sum E p + E elec + E orb is not equl to E ds ). The Puli repulsion is stronger for the di-σ dsorption. However, the compenstion by the other contributions is lrge enough to fvor the di-σ dsorption mode. We hve lso nlyzed the ctivtion of the C-H bond of ethylene by the plldium dimer. Three structures for the vinyl-hydride product (H-Pd 2 -C 2 H 3 ) were investigted: the pseudo-squre plnr structure (Figure 2c, the vinyl plne is perpendiculr to the plne contining the two Pd toms nd the hydrogen tom), the trns (Figure 2d) nd the cis (Figure 2e) structures. The optimized prmeters re given in Tble 5. The squre structure is the most stble structure, therefore the vinylhydride H-Pd 2 -C 2 H 3 presents squre geometry equivlent to tht of H-Pd 2 -CH 3 resulting from CH 4 ctivtion. 17 On the other hnd, becuse of the steric repulsion, the cis structure is less stble thn the trns structure by 4 kcl/mol. The potentil energy surfce for the ctivtion of the C-H bond by the plldium dimer is presented in Figure 1 together with tht of the single tom. The comprison of the stbility of the π complexes nd vinyl-hydride products of PdC 2 H 4 nd Pd 2 C 2 H 4 (see Figure 1) shows tht the d 10 configurtion (the plldium single tom) is optiml for the formtion of the π complex, wheres the d 9 s 1 configurtion (tht of Pd 2 is d 9.43 s 0.55 ) should be optiml for the formtion of the σ-bonds of the vinylhydride product. Indeed, the PdC 2 H 4 π-complex is stble by 39 kcl/mol reltive to free molecules in their ground sttes, wheres the Pd 2 C 2 H 4 π-complex is stble only by 23 kcl/mol. On the other hnd, the vinyl-hydride H-Pd-C 2 H 3 is stble only by 6 kcl/mol, wheres H-Pd 2 -C 2 H 4 is stble by 38 kcl/ mol. Three trnsition sttes were investigted (Figure 3). In the end-on pproch (TS3), the Pd-Pd xis is perpendiculr to the C-H bond nd only one Pd tom is involved in the interction. The other Pd tom is kept fr from ethylene. In the side-on perpendiculr pproch (TS2), the two molecules re prllel nd the Pd-Pd xis is kept perpendiculr to the C-H bond. For the side-on prllel pproch (TS1), the Pd-Pd xis is kept prllel to the C-H bond. When only one Pd tom of the dimer ctivtes the C-H bond (TS3), the clculted brrier reltive to π dsorption is very close to tht of the single tom (37 vs 36 kcl/mol). The brrier reltive to di-σ dsorption is lrger, 60 kcl/mol, nd is consequence of the energy difference between π nd di-σ dsorption modes. The side-on perpendiculr pproch ws found for the ctivtion of N 26 2 nd CH 17 4 by Pd 2. The trnsition stte (TS2) is chrcterized by long Pd-Pd distnce (2.92 Å). While the vinyl group is ttched to the two Pd toms, the hydrogen tom is ttched to the vinyl nd to one Pd tom. The brrier is 48 kcl/mol. The side-on prllel pproch ws suggested by Nktsuji et l. 27 for the ctivtion of H 2 by Pd 2. Then the finl product H-Pd-Pd-H presents cis configurtion. Blomberg et l. 17 hve found tht the squre configurtion, where ech hydrogen is ttched to the two Pd toms, is more stble by 26 kcl/mol. Therefore the side-on prllel pproch is not necessrily the optiml pthwy for H-H ctivtion on Pd 2. The trnsition stte (TS1) for C 2 H 4 /Pd 2 side-on prllel pproch gives the lowest brrier reltive to di-σ dsorption, 36 kcl/mol. The min reson seems to be the prticiption of the second crbon tom in the interction with the dimer, which is missing in the other trnsition sttes. The topology of the trnsition stte is close to the di-σ dsorption. The inctive CH 2 group remins ttched to one Pd tom, while the ctivtion tkes plce on the other Pd tom. Here gin the ctivtion is ensured by only one Pd tom; therefore, the brrier is equl to tht of the single tom. Our clcultions show clerly tht the plldium single tom nd dimer ctivte the ethylene C-H bond. This result supports moleculr bem experiments from Fyet et l. 28 where plldium clusters with up to 25 toms were found to ctivte ethylene. However, while in these experiments the dimer is more rective thn the single tom, in our clcultions Pd 2 nd Pd present the sme brrier height.

5 Ethylene Adsorption on Plldium Clusters J. Phys. Chem., Vol. 100, No. 14, TABLE 4: Adsorption Energies (in kcl/mol) Reltive to Free C 2 H 4 nd Pd 2 Species, the Decomposition of the Interction Energy between C 2 H 4 nd Pd 2 for the Optimized C 2 H 4 /Pd 2 Geometry, Overll Chrge Trnsfer ( Bck-Dontion to Ethylene), nd Geometries (Å nd deg) for π nd di-σ Complexes of Pd 2 (C 2 H 4 ) b dsorption mode E ds E D E elec E orb chrge trnsfer Pd-Pd Pd-C C-C hydrogen dihedrl ngle π e di-σ e E p, Puli repulsion; E elec, electrosttic interction; E orb; orbitl interction. b The hydrogen dihedrl ngle is the ngle between the HCC nd the CCPd plnes. TABLE 5: Ethylene Dissocition on Pd 2 structure E ds or brrier height Pd 1-Pd 2 Pd 1-C/Pd 2-C Pd 1-H/Pd 2-H C-H C-C HPd 2C 2H 3 squre trns cis trnsition stte end-on side-on perpendiculr / / side-on prllel / / The dsorption energies (in kcl/mol) for the vinyl-hydride product re reltive to free C 2H 4 nd Pd 2 species; the brrier heights (in kcl/mol) for the trnsition sttes re reltive to the di-σ moleculr complex; nd the distnces re in Å. Figure 4. Cluster distortion under the di-σ dsorption mode (distnces in Å). Figure 3. Vrious trnsition sttes for the C-H ctivtion by Pd 2: TS1, side-on prllel pproch; TS2, side-on perpendiculr pproch; nd TS3, end-on pproch. 6. Adsorption of Ethylene on Pd n (n ) 3-6) Clusters In this section, we present the results for the dsorption of ethylene on Pd n (n ) 3-6) clusters. The two dsorption modes π nd di-σ re studied. The most surprising result is the chnge in the cluster structure ssocited with the di-σ dsorption mode. For Pd n (n ) 3-5) clusters, the bond between the two Pd toms involved in the dsorption is broken (see Figure 4). Ethylene induces reconstruction of the clusters: from the tringle towrd the liner structure for Pd 3 nd from the tetrhedron towrd the plnr structure for Pd 4. Such effects were lredy suggested by Prks et l. 16 for N 2 dsorption on Ni n clusters. In their investigtion of the structure of nickel clusters, they hve found tht in some cses nitrogen cuses chnge in the cluster structure. In Figure 4 we notice tht the Pd-Pd distnce nd therefore the distortion decreses with the cluster size. Therefore this effect will be wek on the plldium surfce nd will correspond to locl relxtion of the surfce. The structurl effect ssocited with the π dsorption mode is smller, nd there is n increse of the bond length between the tom involved in the dsorption nd its first neighbors. This is generl trend for the dsorption on trnsition metl surfce, TABLE 6: Structures of π nd Di-σ C 2 H 4 Pd n Complexes spin Pd-Pd C-C hydrogen dihedrl ngle Pd n π di-σ π di-σ π di-σ π di-σ 1 S S T S T S T S T S T T Spin (S for singlet nd T for triplet), Pd-Pd distnce (Å) of toms involved in the dsorption nd the geometry of dsorbed ethylene (Å nd deg). nd metl toms involved in the dsorption re often pulled out from the surfce. For the distortion of dsorbed ethylene (Tble 6), we found the sme trend s for the dimer, higher distortion (rehybridiztion) for the di-σ dsorption mode. The C-C bond length is longer when C 2 H 4 is di-σ. A comprison cn be mde with the benzene dsorption on Rh(111), LEED nlysis 29 hs shown tht the benzene is dsorbed on 3-fold position, nd then, hlf of the C-C bonds re on top positions nd the other hlf re on bridge positions. In correltion with our results, the C-C bond on top (equivlent to π dsorption) is shorter thn the C-C bond on bridge (equivlent to di-σ dsorption). The experimentl vlue of the C-C bond for dsorbed ethylene on

6 5680 J. Phys. Chem., Vol. 100, No. 14, 1996 Fhmi nd vn Snten is pproprite for the π interction, wheres the d 9 s 1 configurtion is pproprite for the di-σ interction (the dimer is d 9.43 s 0.55 ). Acknowledgment. We thnk Dr. Mtthew Neurock for fruitful discussions. We thnk the theoreticl group of the Free University of Amsterdm for the use of the ADF progrm. This work ws supported by the Eindhoven University of Technology. We kindly cknowledge the computtionl resources llocted from the Ntionl Computing Fcilities (NCF) Foundtion under project SC-183. References nd Notes Figure 5. Evolution of the ethylene dsorption with the cluster size Pd n (n ) 1-6). Pd(111), Å, is close to the clculted vlues for the di-σ dsorption mode, Å. However, HREELS experiments support π dsorption on Pd(111) 2 nd Pd(110), 3 wheres for Pd(100) 1 both π nd di-σ modes were observed. Tble 6 lso shows the spin stte of the C 2 H 4 Pd n complexes. In the di-σ dsorption, the rection between ethylene nd the cluster cn be described s n oxidtive ddition rection in which the π bond of ethylene is broken nd two metl-crbon σ bonds re formed. Therefore ll the di-σ complexes re singlet except the C 2 H 4 Pd 6 complex where the distortion of ethylene is the smllest. The distortion of ethylene is smller in the π dsorption nd the spin of the cluster is not perturbed. Therefore ll the π complexes except the C 2 H 4 Pd complex re triplet. The ltter is singlet becuse the single tom Pd(d 10 ) is singlet. The evolution of the dsorption energy with the cluster size is sketched in Figure 5. The dsorption energy oscilltes nd decreses with the cluster size towrd the experimentl vlue, 13 kcl/mol. 31 Chemicl physics of gs-phse clusters 28,32 show tht rective properties of smll metl clusters re different from those of the bulk. In some cses the chnge in the cluster size by one metl tom cn be ccompnied by lrge chnge in the rectivity, nd curves like Figure 5 were often found in experiments. We notice tht for Pd 3-5 clusters, which collpse under the di-σ dsorption, the best dsorption mode is π, wheres the Pd 2 nd Pd 6, which give π nd di-σ distortions of the sme mgnitude, the di-σ dsorption is more fvorble. 7. Conclusion In this work we hve presented density functionl clcultions on the dsorption of ethylene on smll plldium clusters, Pd n (n ) 1-6). The dsorption mode cn be π or di-σ ccording to the cluster size. The dsorption energy oscilltes nd decreses with the cluster size towrd the experimentl vlue. The π dsorption is mximum for the single tom, wheres the di-σ dsorption is mximum for the dimer. Pd n (n ) 3-5) clusters re not stble ginst dsorption, they undergo structurl chnges to ccommodte ethylene. The Pd-Pd bond for toms involved in the di-σ dsorption is broken. Ethylene shows stronger rehybridiztion with the di-σ dsorption, the C-C bond length nd the hydrogen dihedrl ngle re lrge compred with the vlues obtined with the π dsorption. Both the single tom nd the dimer ctivte the C-H bond of ethylene in greement with the moleculr bem experiments in the gs phse. The potentil energy surfces re chrcterized by very stble moleculr complexes compred with vinyl-hydride products. These potentils show tht the d 10 configurtion (the single tom) (1) Stuve, E. M.; Mdix, R. J. J. Phys. Chem. 1985, 89, 105. (2) Gtes, J. A.; Kesmodel, L. L. Surf. Sci. 1982, 120, L461. (3) Nishijim, M.; Yoshinobu, J.; Sekitni, T.; Onichi, M. J. Chem. Phys. 1989, 90, (4) Sutet, P.; Pul, J. F. Ctl. Lett. 1991, 9, 245. (5) Sutet, P.; Pul, J. F. J. Phys. Chem. 1994, 98, (6) () Berends, E. J.; Elis, D. E.; Ros, P. Chem. Phys. 1973, 2, 41. (b) Boerrigter, P. M.; te Velde, G.; Berends, E. J. Int. J. Quntum Chem. 1988, 33, 87. (c) Berends, E. J.; Ros, P. Int. J. 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