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Calculated model for metal cluster catalysis: H2 dissociation
Surface Science 51 (1975) 1-13 0 North-Holland PubIishing Company
CALCULATED MODEL FOR METAL CLUSTER CATALYSIS: H, DISSOCIATION
R.C. BAETZOLD Research Laboratories, Eastman Kodak Company, Rochester, New York 14650, U.S.A. Received 25 February 197.5: revised manuscript received 7 May 1975
Extended Hiickel theory is applied to a pathway for Hz dissociation that is catalyzed by metal clusters such as Agz, Pdg, and Cue. At constant metal-H bond length, a potential barrier for elongation of H-H is observed. This barrier and the initial adsorption energy lead to a lower-energy path for Hz dissociation on group VIII than on group I!3 metal clusters, in general accord with experiment. Interactions of molecular orbitals banse this effect, which is based upon the number of valence d and s electrons. The CFSO-BEBO model, when applied to the reaction coordinate studied here, would be appropriate since the sum of bond orders is constant within 20 percent variation.
1. Introduction can act as catalysts in a variety of reactions. Hamilton in electroless-deposition [2] studies that a critical size cluster is required for active catalysis. As few as six Pd atoms were shown to be catalytic. The reducing agents employed by them have included the amine-boranes, which were studied recently by Lelental (31. Other reactions catalyzed by transitionmatal clusters have been studied extensively by Sinfelt [4]. These include hydrogenation and dehydrogenation reactions of hydrocarbons catalyzed by pure metal clusters of Cu or Ni of mixed metal clusters such as Ru/Cu. The manner in which a metal particle can influence an adsorbed reducing agent is a key question in catalysis. Presumably, this interaction determines whether the metal particle can catalyze dissociation or even electron transfer from a reducing agent. Two reducing agents have been investigated primarily in this report, H2 and NH3BH3. Experimental data are available for the abilities of various metals to dissociate H2 [5,6], and NH3BH3 dissociation is thought to be the critical step in some metal electroless-deposition [3] reactions. The molecular orbital method has been used recently to treat the bonding of H with a variety of metal atoms. Fassaert et al. [7] have determined the interaction of H with various arrangements of Ni atom clusters. They showed that this adsorption primarily involves the 4s orbitals of Ni rather than the 3d orbitals, and that the d Transition-metal
clusters
and Loge1 [ 1] have shown
2
R.C. Baetzold/Modei for metal cluster catalysis
orbitals of eg symmetry do not play an important role in H adsorption as some models have predicted. Calculations by Deuss and Van der Avoird [8] for 11, on Ni and Cu surfaces have shown that the unoccupied d orbitals can cause unactivated H, dissociation on Ni, but not Cu in accord with experimental work 1451. The interaction of H atoms with Ni has also been calculated by the CNDO method [9], and this work generally supports the above conclusions. Calculations for HI on boron surface [lo] using the extended Htickel method have examined dissociative adsorption. There is a calculated barrier of 1S eV for adsorption of the H2 molecule on the B surface. An additions study has recently appeared treating H adsorption on W surfaces by extended Huckel theory [ 111. This work has shown H to be more favorably adsorbed in single coordination with a W atom, a fact that has been used to interpret LEED data. The above studies have modeled the bulk metal surface by a few metal atoms. Previous calculations [ 121 have led us to believe that the electronic properties of small metal clusters are unlike those derived from bulk measurements. It seems, therefore, that the present calculations are based on models that are more adequate for supported metal crystallites than for bulk single crystal surfaces.
2. CalcuIation method The familiar noniterative extended Hiickel method [ 131 was employed in this work. Exponents of the Slater orbitals were taken from the tables of Cusachs and Corrington [ 141 for single-zeta type or the work of Basch and Gray [ 151 for doublezeta type. Ionization potentials were taken from the data of Moore [ 161 and shown in table 1. The reaction coordinate considered in H, dissociation involves placing the Hz molecule near a metal cluster at a metal-H distance near that determined from atomic radii. The metal-H distance is kept constant and the H--H bond is stretched from its equilibrium length. The calculations show that in the region of the bond length of Hz in the equilibrium gas phase little charge is exchanged with the metal cluster (
R. C. Baetzoldfbfodel for metal cluster catalysis
3
Table 1 Atomic input data
Atom
Orbital
&
4d 5s
Pd
5P 4d 5s 5P
cu
3d 4s
Ni
4P 3d 4s
CO
4P ed 4s
P
4P 3s
S
3P 3s
0
3P 2s 2P
Matrix element -Iiii (eV) 11.58 7.56 3.83 8.33 7.32 2.00 10.62 7.66 3.96 10.00 7.63 3.84 9.39 7.28 3.83 18.65 10.11 20.60 11.60 32.20 15.80
Coefficients (c) and exponents (6) in orbitals cr
11
c2
g2
0.589 1.0 1.0
6.070 2.244 2.244
0.637 -
2.663 _ -
0.526 l\O 1 .o
5.983 2.152 2.152
0.637 -
2.613 -
0.593 1.0
5.950 1.550
0.574 -
2.300 -
1.0 0.568 1.0 1.0
1.550 5.750 1.500 1.500
0.629
0.555 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
5.550 1.450 1.450 1.881 1.629 2.122 1.827 2.246 2.227
0.646 -
-
-
2.000 _ 1.900 -
3. Results
A first criterion in determining H2 adsorption on metal clusters is to find equilibrium positions. Calculations were performed keeping the H-H bond length constant while varying the metal-H bond length as the HZ molecule approached a cluster directly over a bond. Fig. 1 shows these data for planar 3X3 Pdg and fig. 2 shows them for planar 3 X3 Agg . Potential minima are observed in some cases, but they correspond to metal-H bond lengths much less than expected on the basis of the sum of the atomic radii. Since this may be a deficiency of the calculations, data will be reported at metal-H distances determined by the atomic radii, as is frequently done [ 131, and not by the potential minima. Data are reported assuming adso~tion of the Hz molecule and then allo~ng the H-H bond to elongate giving binding energies relative to H2 and the cluster model.
R.C. BaetzoldlModel for metal cluster catalysis
4
-4-
1.0 0.82 io.74 1.4 l
o-
4-
L
2.88
6I
1.0
I.5
,
H-W
dis+on&$)
I
2.5
Fig. 1. Binding energy of Hz to planar 3 X 3 Pdg versus H-Pd bond length for various values of H-H bond length (A).
+/
6 t I
1.0
I
1.5
I
2.0
H-Ag distance (A)
I
2.5
Fig. 2. Binding energy of Hz to planar 3 X 3 Ag9 versus H-Ag bond length for various values of H-H bond length (A).
R. C. Baetzold/ModeI for metal cluster catalysis
1.0
1.5
2.0
2.5
H-H distance (%) Fig. 3. Binding energy of Hz to various clusters versus H-H bond length for constant metal-H bond length equal to 1.68 A.
3.2. Potential energy curves A potential energy curve for HZ on planar Pdg , Agg , and Pd, A& determined by the above procedure is shown in fig. 3. The HZ molecule has a positive binding energy in the Pd, cluster case only, although when the H-H distance is sufficiently large, it could be adsorbed to all of the cluster models. As the H-H bond is lengthened, electrons are transferred to H from the clusters so that hydride ions are predicted at large separation. An activation barrier denoted by a decrease in binding energy upon H-H elongation is observed for each cluster in fig. 3. This is caused by destabilization of the 1s symmetric molecular orbital (M.O.) of HZ. Net destabilization continues with H-H elongation until the antisymmetric M.O. of H, drops below the HOMO of the metal cluster, at which point electrons are transferred to form hydride ions. The activation barrier is small for many metal clusters and has been determined to be 0.10 eV for Pd, . This is similar in size to the low activation barriers to HZ dissociation observed experimentally on bulk Pd metal In order for dissociation to occur on Agg , there is the activation barrier of 0.08 eV, plus the initially large negative binding energy to be overcome. These effects correlate with experimental activation energies for para-hydrogen conversion over bulk Pd-Ag alloys [ 17 1. Activation energy increases from 2 kcal/mol on Pd to 11 kcal/mol on Ag in general agreement with the barriers to HE dissoaiation in fig. 3.
R.C. BaetzoldjModel for metal cluster catalysis
6
Table 2 Hz adsorption on Pd models (Pd-H = 1.68 A) __..-._ Model
Hz adsorption energy (eV)
Activation barrier (eV)
2H adsorption energy (eV)
Pdz Pdg linear over center bond Pdg linear over end bond
1.03
0.12
4.34
0.93
0.11
4.21
0.99
0.12
4.27
0.28 1.08 0.69 0.63 ____l_---
0.64 0.10 0.15 0.20
3.36 4.28 4.49 4.00
Pdg linear along molecular axis Pdg - planar 3 X 3 Pdg - planar fee Pd13 - 3d fee
-
3.3. Effect of cluster size and shape Palladium clusters of various size and geometry have been treated using the model described above. An H2 molecule is placed directly over a bond in each cluster with the Pd-H length of 1.68 A. Table 2 shows data for several cases. The adsorption energy for H2 adsorbed to Pd clusters is not strongly dependent on size, but does depend upon cluster shape and how the H2 interacts. The fee shapes have nine atoms in the top plane with or without four in a second plane. The fee structures have a significantly lower adsorption energy than the linear or planar 3X3 clusters. Adsorption of H2 collinear with the linear Pd9 axis is not energetically favorable. The activation barriers for dissociation and H-adsorption energy are significantly different only for the collinear case. The site of ‘I2 adsorption on the planar 3X3 Pd9 model has been examined. Fig. 4 shows binding-energy curves for adsorption over a Pd-Pd bond, between rows and symmetrically above a Pd atom. The Pd-H distance is 1.74A in these calculations and here the single Slater orbitals were employed. Greatest binding of H2 takes place when it is betweenrows of Pd atoms, and this position has a somewhat smaller activation energy for dissociation than the other sites. Site position does not exert a big effect here. It is instructive to compare these results with fig. 3 for H2 adsorption over a bond when double-zeta d orbitals are employed. The binding energies are greater and the activation barriers much smaller when the more diffuse double-zeta d orbitals are employed. This effect clearly shows the importance of d orbitals in dissociation and, therefore, the importance in calculations of using the best orbital representation for them. 3.4. r~teruction of ~a~e~nctio~s
The reason for the differences in H2 binding energy to Pd and Ag clusters can
R. C. Baetzold/Model for metal cluster catalysis
-2
,
r
T
. over atom A over bond 0 between rows
-I
7 u
0
%
2
I
I
I
I
1.0 H-k’dlstonce
(A)
2.5
2.0
Fig. 4. Binding energy of Hz to positions on the Pdg planar 3 x 3 model. Single Slater orbitals were employed.
Pd2-H2
‘d2
H2
H&i2
42
.* ” --.
-
-4
-L.’
/’
z
-
-.*x
-,
zz
\
a”*
/‘\
AU9
I States
z
zz
d States
Q9 _e---_ ---
---
Fig. 5. Energy levels of isolated and interacting Pd2 -Hz and Ag2 -Hz (H-H = 0.74 A).
8
R.C. BaetzoldfModel for metal cluster catalysis
best be seen by considering adsorption to the homonuclear metal diatomics. Fig. 5 shows the energy levels of interacting and noninteracting H, and Pd2 or Agz. The ua level of H, is stabilized by adsorption to both species. The d levels of Ag2 and Pd, are not shifted much by interaction with H,, although a few tenths of an eV stabilization is achieved in both cases. The ug 5s levels of the metals are destabilized and the CJ~5s levels are stabilized as shown. This effect is a direct result of perturbation theory, as discussed before [ 181. Since the ug 5s levels are unoccupied in Pd, but occupied in Ag and other IB metals, the destabilization is effective only in Ag and not Pd. The net result is to make adsorption energetically unfavorable on Ag2. A similar effect would be expected for the other IB metals. In the case of larger aggregates of metal atoms, similar effects are observed. It is clear that electron occupation of molecular orbitals having energy levels just above filled closed d shells causes negative adsorption energies. 3.5. Various metal clusters Various metal substrate models have been examined for H, dissociation. Table 3 lists several of these. The best catalysts are expected to have small barrier heights for dissociation and positive HZ adsorption energies, as is found for Pd, . Addition of electronegative elements like P or 0 to Cu has an effect on these parameters. The electronegative element takes electrons from the ua-s molecular orbitals of the metal atoms, making adsorption energies more positive. However, because these electronegative atoms have low-energy orbitals they also destabilize the Hz uR orbital if they interact directly. When the electronegative element does not interact directly with the H, it promotes catalysis as indicated by the HZ adsorption energy data in table 2 for CugPq. Oxides inhibit catalysis in the same way P does if the H interacts directly. Planar Pd, 0, and Cu, 0, models for H, dissociation are treated in fig. 6. Clearly these clusters would be poor Hz dissociation catalysts because of the negative adsorption energy. This effect results from the destabilization of the H ug molecular orbital by interaction with 0 2p orbitals. The effect of metal cluster size on H, adsorption is shown by comparing data in table 2 for diatomic and larger clusters of Pd, Ag, and Cu. There is little difference between Pd, and Pdg , but larger differences are seen for the comparable-size Ag and Cu clusters. This effect is similar to the dependence of the highest occupied molecular orbitals (HOMO) on size for the different clusters. It decreases with increasing size for Ag and Cu, but remains roughly constant on Pd clusters [ 121. The HOMO is primarily composed of d orbitals in the case of Pd, and s orbitals in the case of Ag and Cu, and this factor is important in determining catalysis. Data are presented for Hz adsorption to mixed metal, planar 3 X 3 models in table 2. Copper added to nickel results in a more negative Hz adsorption energy in the order Nig > Ni,Cu, > Cu, > Ni2Cu7. The HZ is added over a Ni-Cu bond in the case of the mixed metals. There is not a continuous trend with composition across this series, although the total energy required for dissociation determined by barrier
R.C. BaetzoldJModel for metal cluster catalysis
9
Table 3 Ha dissociation Model
Description
Double- or single-zeta orbitals
AE barrier height (eV)
BE Hz ads. energy (eV)
BE H- ads. energy (eV)
cu9p4
Ha Hz Ha Ha
Single Single Single Single Single Double Double Double Double Double Double Double Double Double Double Double Double Double
0
-3.0 7.0 -3.84 -1.85 0.15 1.08 -0.61 -0.78 -0.01 0.13 -0.11 -0.65 -1.10 1.03 -1.41 -2.50 0.14 0.15
-2.0 5.5 -0.8 -2.45 4.41 2.14 1.36 1.61 0.72 1.36 2.23 0.40 0.58 2.17 1.67 1.37 1.24 1.38
_
CbPA Pds
04
&SO4 AgloSs Pd9 Ag9 cu9
Ni9 co9 Pds A&
Ni4Cus NiaCu7 Pdz Agz Cu2 cuqco5 CU2CO7
near near near near
P Cu Pd-0 Cu-0
1.0
1.10 0.43 1.20 1.13 0.10 0.08 0.31 0.44 0.15 0.17 0.71 0.52 0.12 0 0.72 0.46 0.23
1.5
H-H
2.0
2.5
distance (%)
Fig. 6. Binding energy of Hs to planar CusO4 and planar Pds04 versus H-H bond length.
R. C. Baetzold/Model for metal cluster catalysis
1.5
2.0
2.5
H-H distance (8) Fig. 7. Bond order for Hz dissociation on planar 3x 3 Pd9: (0) H-H bond order; bond order, positive; (o) H-Pd bond order, negative; (0) total bond order.
(A)
H-pd
height minus binding energy increases continuously with copper added. In the case of Co/Cu mixtures, dissociation is promoted by adding Co to Cu and would appear to go easily on pure Co. Since oxide formation could interfere with this picture, these results must be applied cautiously to experimental situations. Strongly adsorbed H, observed experimentally on Cu/Ni alloys [6] can be correlated with the ability of the mixed clusters to dissociate HZ. Experimentally, the amount of strongly adsorbed H, increases from zero on Cu with addition of Ni. The overall barrier to dissociation decreases on adding Ni to Cu in accord with this effect. 3.4. Bond-energy
bond-order
model
The crystal field surface orbital-bond energy bond order (CFSO-BEBO) model [ 191 has recently been applied successfully to a variety of processes such as Hz interaction with Pt. One of the interesting assumptions made in this model is that bond order is conserved during the reaction coordinate describing the interaction process. It is of interest to determine whether bond order is conserved during the particular reaction coordinate examined in this paper for Hz dissociation. Bond orders determined from the dissociation of HZ on the planar 3X3 Pd, model are shown in fig. 7. The bond order plotted is a reduced bond order determined by summing the Mulliken orbital overlap population Ppv,
R.C. Baetzold/Model for metal cluster catalysis
11
Fig. 8. Bond order for Hz dissociation on Agz. (0) H-H bond order; (A) H-Ag bond order, negative; (m) H-Ag bond order, positive; (o) Ag-Ag bond order, negative; (0) total bond order.
Pwy = 2
C CGCivy 0cc:pied
over all orbitals cc, v on the two atoms A, B involved; on A on B
(1) (Sp, is the overlap integral.) The H-H overlap population decreases rapidly with bond elongation from the equilibrium length while the H-Pd contribution is increasing. The bond order between H and the nearest Pd is positive, but it is negative between this H and the Pd atom closest to the other H atom. The Pd-Pd bond order becomes very small and is negative for some cases upon Hz adsorption. The total bond order is found by summing these terms, allowing for the appropriate number of interactions. It is nearly constant during most of the reaction with about 20 percent as the maximum change during the reaction. The bond orders for Hz adsorbed to Agz are shown in fig. 8. The behavior is very similar to the Pd, case, except that the Ag-Ag bond order is negative. Summation of the total bond order, as described before, gives a function reasonably constant throughout the reaction path. It is concluded from these examples that conservation
12
R.C. Baetzold/Model for metal cluster catalysis -6-
1
1
1
-4-
6I
1.5
2.0
Fig. 9. Binding energy of NHJ-BHs
I
2.5 B-N distance (%I
I
3.0
to Agz and Pd2 versus B-N bond length.
of bond order for the model treated here is a good approximation. 3.7. BHj -NH3 dissociation A comparison of the catalytic ability of metal clusters to dissociate H2 and BHsNH3 is interesting. We observe a strong calculated similarity between the two reactions, indicating that good hydrogenation catalysts are the ones to try with this type of reducing agent. Fig. 9 shows potential energy curves for adsorption of BH3-NH3 to diatomic metals as the B-N bond is stretched. At the equilibrium BN band length, the ability to adsorb this molecule is similar to what we observed for Pd2 and Ag2 adsorbing H2. The reasons for the differing abilities of Pd, and Ag2 to adsorb NHsBH3 are the same here as discussed in the case of H2. The p orbitals of B and N destabilize ag levels of Ag2 just as the 1s orbitals of H did in the earlier case. The results of fig. 9 show that the B-N bond can be elongated easily and that Pd2 greatly aids the process. Catalysis by Ag2 would occur if the B-N bond length is greater than 2.5 A. Both Ag2 and Pd2 would adsorb the dissociation fragments.
4. Conclusions (1) The model for H2 and BH3--NH3 treated here for catalytic dissociation exhibits many features consistent with experiment. Small activation barriers are observed
R. C. BaetzoldfModel for metal cluster catalysis
13
on Pd clusters, and strong adsorption energies, in opposition to negative adsorption energy found on Ag and other group IB clusters. (2) Possible differences in group VIII, IB metal cluster catalytic behavior for Hz dissociation are explained in terms of the degree of occupancy of diffuse s-type molecular orbitals. Destabilization of this M.O. upon interaction with Hz is responsible for negative adsorption energies on group IB metal clusters. (3) The shape of small Pd clusters or site of H, adsorption does not have a strong effect on Hz dissociation parameters. The use of double-zeta d orbitals, which are rather diffuse, leads to calculated results more favorable for dissociation on Pd. (4) The CFSO-BEBO model is obeyed for the reaction coordinate examined here. Bond order is conserved to within 20 percent during the reaction.
References [l] [2] [3] [4] [S] [6] [7] [S] [9]
J.F. Hamilton and P.C. Logel, J. Catalysis 29 (1973) 253. E.B. Saubestre, Metal Finishing 60 (1962) No. 6,67; No. 7,49; No. 8,45; No. 9,59. M. LelentaI, J. Catalysis 32 (1974) 429. J.H. Sinfelt, J. Catalysis 29 (1973) 308. D.A. Cadenhead and N.J. Wagner, J. Catalysis 21 (1971) 312. J.H. Sinfett, J.L. Carter and D.J.C. Yates, J. Catalysis 24 (1972) 283. D.J.M. Fassaert, H. Verbeek and A. van der Avoird, Surface Sci. 29 (1972) 501. H. Deuss and A. van der Avoird, Phys. Rev. B8 (1973) 2441. G. Blyholder, J.C.S. Chem. Commun. (1973) 625; Surface Sci. 42 (1974) 249. [lo] J.B. Moffat, J. CoIloid Interface Sci. 44 (1973) 415. [ 111 L.W. Anders, R.S. Hansen and L.S. BarteII, J. Chem. Phys. 59 (1973) 5277. [12] R.C. Baetzold, J. Chem. Phys. 55 (1971) 4363. [13] R. Hoffmann, J. Chem. Phys. 39 (1963) 1397. [14] L.C. Cusachs and J.H. Corrington, in: Sigma M.O. Theory, Eds. 0. Sinanoglu and K. Widberg (Yale University Press, New Haven, 1970). [ 151 H. Basch and H.B. Gray, Theoret. Chim. Acta 4 (1966) 367. [ 161 C.E. Moore, Nat. Bur. Stand. Circ. l-3 (1949) 467. [17] E.G. Allison and G.C. Bond, Catalysis Revs. 7 (1972) 233. [18] R.C. Baetzold, J.Catalysis 29 (1973) 129. R.C. Baetzold, Surface Sci. 36 (1972) 123. [19] W.H. Weinberg and R.P. Merrili, Surface Sci. 39 (1973) 206; 33 (1972) 493; W.H. Weinberg, J. Catalysis 28 (1973) 459.
CALCULATED MODEL FOR METAL CLUSTER CATALYSIS: H, DISSOCIATION
R.C. BAETZOLD Research Laboratories, Eastman Kodak Company, Rochester, New York 14650, U.S.A. Received 25 February 197.5: revised manuscript received 7 May 1975
Extended Hiickel theory is applied to a pathway for Hz dissociation that is catalyzed by metal clusters such as Agz, Pdg, and Cue. At constant metal-H bond length, a potential barrier for elongation of H-H is observed. This barrier and the initial adsorption energy lead to a lower-energy path for Hz dissociation on group VIII than on group I!3 metal clusters, in general accord with experiment. Interactions of molecular orbitals banse this effect, which is based upon the number of valence d and s electrons. The CFSO-BEBO model, when applied to the reaction coordinate studied here, would be appropriate since the sum of bond orders is constant within 20 percent variation.
1. Introduction can act as catalysts in a variety of reactions. Hamilton in electroless-deposition [2] studies that a critical size cluster is required for active catalysis. As few as six Pd atoms were shown to be catalytic. The reducing agents employed by them have included the amine-boranes, which were studied recently by Lelental (31. Other reactions catalyzed by transitionmatal clusters have been studied extensively by Sinfelt [4]. These include hydrogenation and dehydrogenation reactions of hydrocarbons catalyzed by pure metal clusters of Cu or Ni of mixed metal clusters such as Ru/Cu. The manner in which a metal particle can influence an adsorbed reducing agent is a key question in catalysis. Presumably, this interaction determines whether the metal particle can catalyze dissociation or even electron transfer from a reducing agent. Two reducing agents have been investigated primarily in this report, H2 and NH3BH3. Experimental data are available for the abilities of various metals to dissociate H2 [5,6], and NH3BH3 dissociation is thought to be the critical step in some metal electroless-deposition [3] reactions. The molecular orbital method has been used recently to treat the bonding of H with a variety of metal atoms. Fassaert et al. [7] have determined the interaction of H with various arrangements of Ni atom clusters. They showed that this adsorption primarily involves the 4s orbitals of Ni rather than the 3d orbitals, and that the d Transition-metal
clusters
and Loge1 [ 1] have shown
2
R.C. Baetzold/Modei for metal cluster catalysis
orbitals of eg symmetry do not play an important role in H adsorption as some models have predicted. Calculations by Deuss and Van der Avoird [8] for 11, on Ni and Cu surfaces have shown that the unoccupied d orbitals can cause unactivated H, dissociation on Ni, but not Cu in accord with experimental work 1451. The interaction of H atoms with Ni has also been calculated by the CNDO method [9], and this work generally supports the above conclusions. Calculations for HI on boron surface [lo] using the extended Htickel method have examined dissociative adsorption. There is a calculated barrier of 1S eV for adsorption of the H2 molecule on the B surface. An additions study has recently appeared treating H adsorption on W surfaces by extended Huckel theory [ 111. This work has shown H to be more favorably adsorbed in single coordination with a W atom, a fact that has been used to interpret LEED data. The above studies have modeled the bulk metal surface by a few metal atoms. Previous calculations [ 121 have led us to believe that the electronic properties of small metal clusters are unlike those derived from bulk measurements. It seems, therefore, that the present calculations are based on models that are more adequate for supported metal crystallites than for bulk single crystal surfaces.
2. CalcuIation method The familiar noniterative extended Hiickel method [ 131 was employed in this work. Exponents of the Slater orbitals were taken from the tables of Cusachs and Corrington [ 141 for single-zeta type or the work of Basch and Gray [ 151 for doublezeta type. Ionization potentials were taken from the data of Moore [ 161 and shown in table 1. The reaction coordinate considered in H, dissociation involves placing the Hz molecule near a metal cluster at a metal-H distance near that determined from atomic radii. The metal-H distance is kept constant and the H--H bond is stretched from its equilibrium length. The calculations show that in the region of the bond length of Hz in the equilibrium gas phase little charge is exchanged with the metal cluster (
R. C. Baetzoldfbfodel for metal cluster catalysis
3
Table 1 Atomic input data
Atom
Orbital
&
4d 5s
Pd
5P 4d 5s 5P
cu
3d 4s
Ni
4P 3d 4s
CO
4P ed 4s
P
4P 3s
S
3P 3s
0
3P 2s 2P
Matrix element -Iiii (eV) 11.58 7.56 3.83 8.33 7.32 2.00 10.62 7.66 3.96 10.00 7.63 3.84 9.39 7.28 3.83 18.65 10.11 20.60 11.60 32.20 15.80
Coefficients (c) and exponents (6) in orbitals cr
11
c2
g2
0.589 1.0 1.0
6.070 2.244 2.244
0.637 -
2.663 _ -
0.526 l\O 1 .o
5.983 2.152 2.152
0.637 -
2.613 -
0.593 1.0
5.950 1.550
0.574 -
2.300 -
1.0 0.568 1.0 1.0
1.550 5.750 1.500 1.500
0.629
0.555 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
5.550 1.450 1.450 1.881 1.629 2.122 1.827 2.246 2.227
0.646 -
-
-
2.000 _ 1.900 -
3. Results
A first criterion in determining H2 adsorption on metal clusters is to find equilibrium positions. Calculations were performed keeping the H-H bond length constant while varying the metal-H bond length as the HZ molecule approached a cluster directly over a bond. Fig. 1 shows these data for planar 3X3 Pdg and fig. 2 shows them for planar 3 X3 Agg . Potential minima are observed in some cases, but they correspond to metal-H bond lengths much less than expected on the basis of the sum of the atomic radii. Since this may be a deficiency of the calculations, data will be reported at metal-H distances determined by the atomic radii, as is frequently done [ 131, and not by the potential minima. Data are reported assuming adso~tion of the Hz molecule and then allo~ng the H-H bond to elongate giving binding energies relative to H2 and the cluster model.
R.C. BaetzoldlModel for metal cluster catalysis
4
-4-
1.0 0.82 io.74 1.4 l
o-
4-
L
2.88
6I
1.0
I.5
,
H-W
dis+on&$)
I
2.5
Fig. 1. Binding energy of Hz to planar 3 X 3 Pdg versus H-Pd bond length for various values of H-H bond length (A).
+/
6 t I
1.0
I
1.5
I
2.0
H-Ag distance (A)
I
2.5
Fig. 2. Binding energy of Hz to planar 3 X 3 Ag9 versus H-Ag bond length for various values of H-H bond length (A).
R. C. Baetzold/ModeI for metal cluster catalysis
1.0
1.5
2.0
2.5
H-H distance (%) Fig. 3. Binding energy of Hz to various clusters versus H-H bond length for constant metal-H bond length equal to 1.68 A.
3.2. Potential energy curves A potential energy curve for HZ on planar Pdg , Agg , and Pd, A& determined by the above procedure is shown in fig. 3. The HZ molecule has a positive binding energy in the Pd, cluster case only, although when the H-H distance is sufficiently large, it could be adsorbed to all of the cluster models. As the H-H bond is lengthened, electrons are transferred to H from the clusters so that hydride ions are predicted at large separation. An activation barrier denoted by a decrease in binding energy upon H-H elongation is observed for each cluster in fig. 3. This is caused by destabilization of the 1s symmetric molecular orbital (M.O.) of HZ. Net destabilization continues with H-H elongation until the antisymmetric M.O. of H, drops below the HOMO of the metal cluster, at which point electrons are transferred to form hydride ions. The activation barrier is small for many metal clusters and has been determined to be 0.10 eV for Pd, . This is similar in size to the low activation barriers to HZ dissociation observed experimentally on bulk Pd metal In order for dissociation to occur on Agg , there is the activation barrier of 0.08 eV, plus the initially large negative binding energy to be overcome. These effects correlate with experimental activation energies for para-hydrogen conversion over bulk Pd-Ag alloys [ 17 1. Activation energy increases from 2 kcal/mol on Pd to 11 kcal/mol on Ag in general agreement with the barriers to HE dissoaiation in fig. 3.
R.C. BaetzoldjModel for metal cluster catalysis
6
Table 2 Hz adsorption on Pd models (Pd-H = 1.68 A) __..-._ Model
Hz adsorption energy (eV)
Activation barrier (eV)
2H adsorption energy (eV)
Pdz Pdg linear over center bond Pdg linear over end bond
1.03
0.12
4.34
0.93
0.11
4.21
0.99
0.12
4.27
0.28 1.08 0.69 0.63 ____l_---
0.64 0.10 0.15 0.20
3.36 4.28 4.49 4.00
Pdg linear along molecular axis Pdg - planar 3 X 3 Pdg - planar fee Pd13 - 3d fee
-
3.3. Effect of cluster size and shape Palladium clusters of various size and geometry have been treated using the model described above. An H2 molecule is placed directly over a bond in each cluster with the Pd-H length of 1.68 A. Table 2 shows data for several cases. The adsorption energy for H2 adsorbed to Pd clusters is not strongly dependent on size, but does depend upon cluster shape and how the H2 interacts. The fee shapes have nine atoms in the top plane with or without four in a second plane. The fee structures have a significantly lower adsorption energy than the linear or planar 3X3 clusters. Adsorption of H2 collinear with the linear Pd9 axis is not energetically favorable. The activation barriers for dissociation and H-adsorption energy are significantly different only for the collinear case. The site of ‘I2 adsorption on the planar 3X3 Pd9 model has been examined. Fig. 4 shows binding-energy curves for adsorption over a Pd-Pd bond, between rows and symmetrically above a Pd atom. The Pd-H distance is 1.74A in these calculations and here the single Slater orbitals were employed. Greatest binding of H2 takes place when it is betweenrows of Pd atoms, and this position has a somewhat smaller activation energy for dissociation than the other sites. Site position does not exert a big effect here. It is instructive to compare these results with fig. 3 for H2 adsorption over a bond when double-zeta d orbitals are employed. The binding energies are greater and the activation barriers much smaller when the more diffuse double-zeta d orbitals are employed. This effect clearly shows the importance of d orbitals in dissociation and, therefore, the importance in calculations of using the best orbital representation for them. 3.4. r~teruction of ~a~e~nctio~s
The reason for the differences in H2 binding energy to Pd and Ag clusters can
R. C. Baetzold/Model for metal cluster catalysis
-2
,
r
T
. over atom A over bond 0 between rows
-I
7 u
0
%
2
I
I
I
I
1.0 H-k’dlstonce
(A)
2.5
2.0
Fig. 4. Binding energy of Hz to positions on the Pdg planar 3 x 3 model. Single Slater orbitals were employed.
Pd2-H2
‘d2
H2
H&i2
42
.* ” --.
-
-4
-L.’
/’
z
-
-.*x
-,
zz
\
a”*
/‘\
AU9
I States
z
zz
d States
Q9 _e---_ ---
---
Fig. 5. Energy levels of isolated and interacting Pd2 -Hz and Ag2 -Hz (H-H = 0.74 A).
8
R.C. BaetzoldfModel for metal cluster catalysis
best be seen by considering adsorption to the homonuclear metal diatomics. Fig. 5 shows the energy levels of interacting and noninteracting H, and Pd2 or Agz. The ua level of H, is stabilized by adsorption to both species. The d levels of Ag2 and Pd, are not shifted much by interaction with H,, although a few tenths of an eV stabilization is achieved in both cases. The ug 5s levels of the metals are destabilized and the CJ~5s levels are stabilized as shown. This effect is a direct result of perturbation theory, as discussed before [ 181. Since the ug 5s levels are unoccupied in Pd, but occupied in Ag and other IB metals, the destabilization is effective only in Ag and not Pd. The net result is to make adsorption energetically unfavorable on Ag2. A similar effect would be expected for the other IB metals. In the case of larger aggregates of metal atoms, similar effects are observed. It is clear that electron occupation of molecular orbitals having energy levels just above filled closed d shells causes negative adsorption energies. 3.5. Various metal clusters Various metal substrate models have been examined for H, dissociation. Table 3 lists several of these. The best catalysts are expected to have small barrier heights for dissociation and positive HZ adsorption energies, as is found for Pd, . Addition of electronegative elements like P or 0 to Cu has an effect on these parameters. The electronegative element takes electrons from the ua-s molecular orbitals of the metal atoms, making adsorption energies more positive. However, because these electronegative atoms have low-energy orbitals they also destabilize the Hz uR orbital if they interact directly. When the electronegative element does not interact directly with the H, it promotes catalysis as indicated by the HZ adsorption energy data in table 2 for CugPq. Oxides inhibit catalysis in the same way P does if the H interacts directly. Planar Pd, 0, and Cu, 0, models for H, dissociation are treated in fig. 6. Clearly these clusters would be poor Hz dissociation catalysts because of the negative adsorption energy. This effect results from the destabilization of the H ug molecular orbital by interaction with 0 2p orbitals. The effect of metal cluster size on H, adsorption is shown by comparing data in table 2 for diatomic and larger clusters of Pd, Ag, and Cu. There is little difference between Pd, and Pdg , but larger differences are seen for the comparable-size Ag and Cu clusters. This effect is similar to the dependence of the highest occupied molecular orbitals (HOMO) on size for the different clusters. It decreases with increasing size for Ag and Cu, but remains roughly constant on Pd clusters [ 121. The HOMO is primarily composed of d orbitals in the case of Pd, and s orbitals in the case of Ag and Cu, and this factor is important in determining catalysis. Data are presented for Hz adsorption to mixed metal, planar 3 X 3 models in table 2. Copper added to nickel results in a more negative Hz adsorption energy in the order Nig > Ni,Cu, > Cu, > Ni2Cu7. The HZ is added over a Ni-Cu bond in the case of the mixed metals. There is not a continuous trend with composition across this series, although the total energy required for dissociation determined by barrier
R.C. BaetzoldJModel for metal cluster catalysis
9
Table 3 Ha dissociation Model
Description
Double- or single-zeta orbitals
AE barrier height (eV)
BE Hz ads. energy (eV)
BE H- ads. energy (eV)
cu9p4
Ha Hz Ha Ha
Single Single Single Single Single Double Double Double Double Double Double Double Double Double Double Double Double Double
0
-3.0 7.0 -3.84 -1.85 0.15 1.08 -0.61 -0.78 -0.01 0.13 -0.11 -0.65 -1.10 1.03 -1.41 -2.50 0.14 0.15
-2.0 5.5 -0.8 -2.45 4.41 2.14 1.36 1.61 0.72 1.36 2.23 0.40 0.58 2.17 1.67 1.37 1.24 1.38
_
CbPA Pds
04
&SO4 AgloSs Pd9 Ag9 cu9
Ni9 co9 Pds A&
Ni4Cus NiaCu7 Pdz Agz Cu2 cuqco5 CU2CO7
near near near near
P Cu Pd-0 Cu-0
1.0
1.10 0.43 1.20 1.13 0.10 0.08 0.31 0.44 0.15 0.17 0.71 0.52 0.12 0 0.72 0.46 0.23
1.5
H-H
2.0
2.5
distance (%)
Fig. 6. Binding energy of Hs to planar CusO4 and planar Pds04 versus H-H bond length.
R. C. Baetzold/Model for metal cluster catalysis
1.5
2.0
2.5
H-H distance (8) Fig. 7. Bond order for Hz dissociation on planar 3x 3 Pd9: (0) H-H bond order; bond order, positive; (o) H-Pd bond order, negative; (0) total bond order.
(A)
H-pd
height minus binding energy increases continuously with copper added. In the case of Co/Cu mixtures, dissociation is promoted by adding Co to Cu and would appear to go easily on pure Co. Since oxide formation could interfere with this picture, these results must be applied cautiously to experimental situations. Strongly adsorbed H, observed experimentally on Cu/Ni alloys [6] can be correlated with the ability of the mixed clusters to dissociate HZ. Experimentally, the amount of strongly adsorbed H, increases from zero on Cu with addition of Ni. The overall barrier to dissociation decreases on adding Ni to Cu in accord with this effect. 3.4. Bond-energy
bond-order
model
The crystal field surface orbital-bond energy bond order (CFSO-BEBO) model [ 191 has recently been applied successfully to a variety of processes such as Hz interaction with Pt. One of the interesting assumptions made in this model is that bond order is conserved during the reaction coordinate describing the interaction process. It is of interest to determine whether bond order is conserved during the particular reaction coordinate examined in this paper for Hz dissociation. Bond orders determined from the dissociation of HZ on the planar 3X3 Pd, model are shown in fig. 7. The bond order plotted is a reduced bond order determined by summing the Mulliken orbital overlap population Ppv,
R.C. Baetzold/Model for metal cluster catalysis
11
Fig. 8. Bond order for Hz dissociation on Agz. (0) H-H bond order; (A) H-Ag bond order, negative; (m) H-Ag bond order, positive; (o) Ag-Ag bond order, negative; (0) total bond order.
Pwy = 2
C CGCivy 0cc:pied
over all orbitals cc, v on the two atoms A, B involved; on A on B
(1) (Sp, is the overlap integral.) The H-H overlap population decreases rapidly with bond elongation from the equilibrium length while the H-Pd contribution is increasing. The bond order between H and the nearest Pd is positive, but it is negative between this H and the Pd atom closest to the other H atom. The Pd-Pd bond order becomes very small and is negative for some cases upon Hz adsorption. The total bond order is found by summing these terms, allowing for the appropriate number of interactions. It is nearly constant during most of the reaction with about 20 percent as the maximum change during the reaction. The bond orders for Hz adsorbed to Agz are shown in fig. 8. The behavior is very similar to the Pd, case, except that the Ag-Ag bond order is negative. Summation of the total bond order, as described before, gives a function reasonably constant throughout the reaction path. It is concluded from these examples that conservation
12
R.C. Baetzold/Model for metal cluster catalysis -6-
1
1
1
-4-
6I
1.5
2.0
Fig. 9. Binding energy of NHJ-BHs
I
2.5 B-N distance (%I
I
3.0
to Agz and Pd2 versus B-N bond length.
of bond order for the model treated here is a good approximation. 3.7. BHj -NH3 dissociation A comparison of the catalytic ability of metal clusters to dissociate H2 and BHsNH3 is interesting. We observe a strong calculated similarity between the two reactions, indicating that good hydrogenation catalysts are the ones to try with this type of reducing agent. Fig. 9 shows potential energy curves for adsorption of BH3-NH3 to diatomic metals as the B-N bond is stretched. At the equilibrium BN band length, the ability to adsorb this molecule is similar to what we observed for Pd2 and Ag2 adsorbing H2. The reasons for the differing abilities of Pd, and Ag2 to adsorb NHsBH3 are the same here as discussed in the case of H2. The p orbitals of B and N destabilize ag levels of Ag2 just as the 1s orbitals of H did in the earlier case. The results of fig. 9 show that the B-N bond can be elongated easily and that Pd2 greatly aids the process. Catalysis by Ag2 would occur if the B-N bond length is greater than 2.5 A. Both Ag2 and Pd2 would adsorb the dissociation fragments.
4. Conclusions (1) The model for H2 and BH3--NH3 treated here for catalytic dissociation exhibits many features consistent with experiment. Small activation barriers are observed
R. C. BaetzoldfModel for metal cluster catalysis
13
on Pd clusters, and strong adsorption energies, in opposition to negative adsorption energy found on Ag and other group IB clusters. (2) Possible differences in group VIII, IB metal cluster catalytic behavior for Hz dissociation are explained in terms of the degree of occupancy of diffuse s-type molecular orbitals. Destabilization of this M.O. upon interaction with Hz is responsible for negative adsorption energies on group IB metal clusters. (3) The shape of small Pd clusters or site of H, adsorption does not have a strong effect on Hz dissociation parameters. The use of double-zeta d orbitals, which are rather diffuse, leads to calculated results more favorable for dissociation on Pd. (4) The CFSO-BEBO model is obeyed for the reaction coordinate examined here. Bond order is conserved to within 20 percent during the reaction.
References [l] [2] [3] [4] [S] [6] [7] [S] [9]
J.F. Hamilton and P.C. Logel, J. Catalysis 29 (1973) 253. E.B. Saubestre, Metal Finishing 60 (1962) No. 6,67; No. 7,49; No. 8,45; No. 9,59. M. LelentaI, J. Catalysis 32 (1974) 429. J.H. Sinfelt, J. Catalysis 29 (1973) 308. D.A. Cadenhead and N.J. Wagner, J. Catalysis 21 (1971) 312. J.H. Sinfett, J.L. Carter and D.J.C. Yates, J. Catalysis 24 (1972) 283. D.J.M. Fassaert, H. Verbeek and A. van der Avoird, Surface Sci. 29 (1972) 501. H. Deuss and A. van der Avoird, Phys. Rev. B8 (1973) 2441. G. Blyholder, J.C.S. Chem. Commun. (1973) 625; Surface Sci. 42 (1974) 249. [lo] J.B. Moffat, J. CoIloid Interface Sci. 44 (1973) 415. [ 111 L.W. Anders, R.S. Hansen and L.S. BarteII, J. Chem. Phys. 59 (1973) 5277. [12] R.C. Baetzold, J. Chem. Phys. 55 (1971) 4363. [13] R. Hoffmann, J. Chem. Phys. 39 (1963) 1397. [14] L.C. Cusachs and J.H. Corrington, in: Sigma M.O. Theory, Eds. 0. Sinanoglu and K. Widberg (Yale University Press, New Haven, 1970). [ 151 H. Basch and H.B. Gray, Theoret. Chim. Acta 4 (1966) 367. [ 161 C.E. Moore, Nat. Bur. Stand. Circ. l-3 (1949) 467. [17] E.G. Allison and G.C. Bond, Catalysis Revs. 7 (1972) 233. [18] R.C. Baetzold, J.Catalysis 29 (1973) 129. R.C. Baetzold, Surface Sci. 36 (1972) 123. [19] W.H. Weinberg and R.P. Merrili, Surface Sci. 39 (1973) 206; 33 (1972) 493; W.H. Weinberg, J. Catalysis 28 (1973) 459.