2658
J. Phys. Chem. 1987, 91, 2658-2664
induced reactions can simply and. effectively separate the experimental variables which include translational and vibrational energies in reactant molecules as well as surface temperature. Moreover, the recycling feature of this novel reactor makes possible such separated-variable studies for reactions with much smaller cross sections than those which can be effectively studied in single pass experiments. Even so, though our investigation has revealed many new features of this much-studies isomerization of cyclopropane it is clear that much more remains to be learned before we fully understand its mechanism.
Acknowledgment. Most of this work was made possible by a grant from the donors of the Petroleum Research Fund, administered by the American Chemical Society. Partial support also
came from the National Science Foundation under Grant No. 3704 and ENG-79 10843 as well as from the Air Force Office of Scientific Research under Grant No. F49620-80-C-0026. Finally, we acknowledge the less tangible but more precious support and interest of the kind that Gil Stein provided in such generous abundance. Seduced as we have been by the properties of free jets in vacuo Gil became one of their most ardent advocates and able practitioners. Although he was more interested in gluing molecules together than in tearing them apart he understood and appreciated this application of gas dynamics to chemistry. For G.L.H. and J.B.F. Gil was a long-time friend and comrade of rare vintage. We sorely miss him and salute his memory. Registry No. Cyclopropane, 75-19-4.
Theoretical Study of the Interaction of CO with Pd Clusters: Relations between Surface and Organometallic Chemistryt Gianfranco Pacchioni* and Jaroslav Kouteckf 1 Dipartimento di Chimica Inorganica e Metallorganica. Centro C.N.R., Universitri di Milano, I-201 33 Milano, Italy, and Institut fur Physikalische Chemie, Freie Universitat Berlin, 1000 Berlin 33, West Germany (Received: July 17, 1986)
The results of a pseudopotentialconfiguration interaction investigation of the electronic structure of small Pd clusters interacting with CO are reported. The Pd clusters chosen can be considered as models of on top, bridge, and three-hollow sites on the (1 1 1) Pd surface. The results provide some insight into the nature of the Pd-CO bonding, confirming the repulsive nature of the u interaction and the essential role of the r-back-donation mechanism for the formation of the Pd-CO bond. Some interesting similarities between Pd,,-CO clusters and CO chemisorbed on a Pd (1 11) surface have been found. In particular, the three-hollow position is found to be the preferred interaction site and the MO spectra qualitativelyreproduce the photoelectron spectra of CO on Pd. However, the adopted theoretical method predicts the existence of weak bonds among the Pd atoms which retain much of their di0character. For this reason, small bare Pd clusters are probably not “optimal” models of Pd surfaces. On the other hand, the Pd,CO clusters considered provide interesting information about the nature of the bonding in organometallic Pd clusters. The analysis of the bond in these systems indicates that Pd-carbonyl clusters, where the Pd atoms formally are in the zero-oxidation state, are held together mainly through interaction with the bridging CO ligands, since the metal-metal bonds are rather weak.
Introduction Metal clusters have been proposed as possible models for the study of chemisorption phenomena because of the analogies found between reactions on catalytically active metal surfaces and on inorganic clusters’ and because of the similarity in the ligand stereochemistry on clusters and surfaces.2 The belief that the cluster-surface analogy is correct, at least to a first approximation, has stimulated the theoretical modeling of chemisorption processes with small metal clusters. The results obtained up to now are considered encouraging and seem to confirm the basic assumption that chemisorption processes can be described as local phenomena involving only few nearest neighbors to the adsorbate on the metal ~ u r f a c e . ~ The use of metal clusters in studying chemisorption still represents a challenge for the theoreticians. Catalysis occurs mainly on transition-metal surfaces, and most of the experimental studies of chemisorption deal with these systems. Unfortunately, at the present, the theoretical treatment of transition elements at the same level of accuracy as the light atoms is computationally very hard. In particular, large computational problems are connected with the study of Pd clusters due to the dimensions of the systems and ‘Presented at the NATO Advanced Research Workshop “Quantum Chemistry: the Challenge of Transition Metals and Coordination Chemistry”, Strasbourg, France, Sept, 1985. * Universitl di Milano and Freie Universitat Berlin. Freie Universitat Berlin.
*
0022-3654/87/2091-2658$01.50/0
to the presence of the heavy Pd atoms. Few theoretical studies of CO chemisorption on Pd clusters have been reported, and the methods adopted range from extended Huckel? to Xq5local spin density,6 and Hartree-Fock’ approximations. In this paper we present the results of pseudopotential configuration interaction (CI) calculations on small Pd, clusters ( n = 2, 3,4) interacting with the CO molecule. Preliminary results of this study have been reported.* Here we emphasize the methodological aspects which, although tedious, are extremely important to assess the quality of the calculations and the reliability of the results obtained. The discussion of the results has been divided into three parts. First, we analyze the nature of the metal-metal bond in small bare Pd clusters and we discuss their similarity with the corresponding bulk metal. Then the mechanism of Pd-CO bonding is described (1) Ugo, R. Catal. Rev-Sci. Eng. 1975, 11, 225. Muetterties, E. L.; Krause, M. J. Angew. Chem., Int. Ed. Engl. 1983, 22, 135. (2) Muetterties, E. L.; Rhodin, T. N.; Band, E.; Brucher, C. F.; Pretzer, W. R. Chem. Rev. 1979, 79, 91. Basset, J. M.; Ugo,R. In Aspects of Homogeneous Catalysis, Ugo,R., Ed.; Reidel: Dordrecht, 1977. (3) Baetzold, R. C.; Hamilton, J. F. Prog. Solid State Chem. 1983, 15, 1. Messmer, R. P. In The Nature of the Surface Chemical Bond, Rhodin, T. N., Ertl, G., Eds.; North-Holland: Amsterdam, 1979. (4) Kobayashi, M. Bull. Chem. SOC.Jpn. 1983, 56, 831. (5) Katsuki, S.; Taketa, H. Solid State Commun. 1981, 39, 711. (6) Andzelm, J.; Salahub, D. R. Int. J . Quantum Chem. 1986, 29, 1091. (7) Gavezzotti, A.; Tantardini, G.F.; Simonetta, M. Chem. Phys. 1986, 105, 333. (8) Pacchioni, G.; Kouteckg, J. In Quanfum Chemistry: ?he Challenge of Transition Metals and Coordination Chemistry, Veillard, A,, Ed.; NATO AS1 Series C, Vol. 176; Reidel: Dordrecht, 1986; p 465.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 10, 1987 2659
Interaction of C O with Pd Clusters
TABLE I: Computational Details and Electronic Properties for Pd,-CO Systems Pd-CO
c-u
basis set nMfxic:D T , phartree selected config De full CI, kcal/mol R,(Pd-C), au RJC-0), au
DZP 6Mf0.91 5 2378 7.8 3.979 2.190
Pd-CO
e-"
DZ 6Mf0.92 5 1927 6.0 3.983 2.1 90C
PdZ-CO
c,
DZP 7Mf0.91 30 2641 15.9 4.086 2.196
'Pd2-CO
c,
DZ 6Mf0.91 15 3410 13.2 4.093 2.196F
Pd&O
Pdd-CO
Pd,-CO
C3"
c2u
c,
expt
DZ 7Mf0.92 20 3568 17.1 4.195 2.188
DZ 6M/0.92 15 3507 8.3 4.090 2.196'
DZ 6Mf0.92 20 3214 8.2 4.312 2.196'
346 3.65,' 3.9-4.2d 2.17'
nM indicates the number of reference configurations from which all single and double excitations are generated. All configurations which contribute more than 0.5% to the C1 expansihon are chosen as leading configurations. Ejf?gives the total weight of the main configurations in the final C I wave function. bFrom ref 2. CFromref 36. "From ref 30-35. CDistancenot optimized. The C I equilibrium bond distance of the free C O molecule is 2.159 au.
with particular attention to the energetic and geometrical aspects. Finally, we try to answer the question whether small Pd,-CO clusters are better models of surfaces or of inorganic molecular clusters and we discuss the relevant aspect of this study in organometallic chemistry.
Computational Aspects Model Potential and Basis Set. The theoretical treatment of molecular systems containing heavy atoms is greatly simplified by pseudopotential techniques. Of course these procedures imply some approximations and can, in principle, produce serious errors. However, model potential calculations in theoretical chemistry are broadly used and there is now general agreement about the validity of this approach provided that some conditions are fulfilled.9 An important requirement on the atomic potential is that it should be flexible enough to correctly reproduce the low-lying atomic states. In fact, the analytic form of the potential is generally determined on the atomic ground state while, especially for transition-metal atoms, hybridization phenomena can change the configuration of the atom in the molecule. Connected with the definition of the potential is the choice of the atomic basis set which must be large enough to avoid the Occurrence of basis set superposition errors (BSSE).Furthermore, well-calibrated polarization functions are often essential for the proper description of the atomic rehybridization occurring with bond formation. In the present study the one-electron operator is constructed according to the effective core potential method of Durand and Barthelat.lo The parameters entering the definition of the operators for the He core of carbon and oxygen atoms and the Kr core of palladium atom were taken from ref 10 and 11. For Pd, which has a IS (dIo) ground state, the atomic basis set optimized on this closed-shell configuration is not appropriate for the description of complexes where the Pd atoms assume a d9s'-like configuration. Therefore, the Pd basis set was optimized on the d9si excited state.'* The addition of 5p orbitals can also contribute to a better description of the Pd-Pd and Pd-CO bonds. However, atomic configurations where the 5p orbitals are occupied are energetically very high with respect to the ground state, and their participation to the bond formation is expected to be negligible. In the present study the 5p orbitals have been optimized on the d9p1excited state of the atom. The whole basis set (basisset C of ref 12) consists of [4s,2p,5d] Gaussian functions contracted to [2s,lp,2d]. This basis set is therefore of double-!: plus polarization quality (DZP). A measure of the flexibility of the potential and the basis set employed is given by the 3D-iS atomic transition energy (T,) of Pd computed in SCF (1 1.9 kcal/mol) and CI (18.0 kcal/mol). The S C F excitation energy is smaller by -4 kcal/mol than the (9) Krauss, M.; Stevens, W. J. Annu. Rev. Phys. Chem. 1984, 35, 357. Bagus, P. S., Bauschlicher, Jr., C. W.; Nelin, C. J.; Laskowski, B. C.; Seel, M . J . Chem. Phys. 1984, 81, 3594. (10) Durand, Ph.; Barthelat, J. C. Theor. Chim. Acta 1975, 38, 283. Barthelat, J. C.; Durand, Ph.; Serafini, A. Mol. Phys. 1977, 33, 159. (11) Garcia-Prieto, J.; Novaro, 0. Mol. Phys. 1980, 41, 205. (12) Pacchioni, G.; Koutecky, J.; Fantucci, P. Chem. Phys. Lett. 1982, 92, 486.
near-Hartree-Fock limit value, 16.3 kcal/mol,13 while the CI T, is rather close to the experimental data (18.7 kcal/mol).I4 The stabilization of the dio with respect to the d9s' configuration in CI is due to the greater importance of the intrashell 4d correlation with respect to the 4d-5s intershell correlation. However, there is not doubt that this agreement is due to a fortuitus cancellation of errors. The basis set adopted, in fact, is biased toward the 3D excited state which is therefore better described than the IS ground state. Moreover, we use a nonrelativistic potential. The C I excitation energy for the 3D-1S transition should be compared with the "nonrelativistic" experimental value (36.9 kcal/mol) which is much larger than the relativistic value (18.7 kcal/mol). This shows that the relativistic corrections are larger and of opposite sign than the correlation contributions since the former act to stabilize "s-electron"-rich configurations.I5 The electronic properties of Pd-CO and Pd2-CO have been computed with both [2s,lp,2d] (DZP) and [2s,2d] (DZ) basis sets in order to determine the importance of 5p orbitals. The dissociation energies (D,) for Pd-CO and Pd2-CO are 1.8 and 2.7 kcal/mol larger in the calculation with 5p orbitals, respectively, while the equilibrium bond lengths are similar in the two approaches (Table I). The small involvement of 5p orbitals in the bonding is shown also by the data from a Mulliken population analysis (Table 11). For this reason Pd3-C0 and Pd,-CO clusters were computed without p-polarization functions in order to reduce the computational effort. Correlation Effects. The description of the chemical bond in weakly interacting systems like Pd-CO is very sensitive to the inclusion of correlation effects.16 In this paper correlation corrections have been introduced by the multireference doubly excited configuration interaction (MRD CI) procedure." The theoretical treatment of correlation effects in Pd,-CO clusters represents a serious computational problem. For technical reasons we cannot correlate more than 30 electrons. Therefore, for systems containing a larger number of valence electrons (e.g., Pd,-CO, Pd4-CO) some MOs have been frozen in the C I procedure. The choice of these MOs is rather arbitrary without the use of localization procedures.I8 In our case the cluster MOs which, for symmetry reasons, cannot interact with the C O MOs have been frozen. In this way we correlate the electrons which are essential for the formation of the Pd-CO bonding, in particular (13) Clementi, E.; Roetti, C. At. Data Nucl. Data Tables 1974, 14, 232. (14) Moore, C. E. Atomic Energy Levels, Vol. 3; US Government Printing Office: Washington, 1952; NBS Circular No. 467. (15) Martin, R. L.; Hay, P. J. J. Chem. Phys. 1981, 75,4539. McMichael Rohlfing, C.; Hay, P. J.; Martin, R. L. J . Chem. Phys. 1986, 85, 1447. (16) Kouteckf, J.; Pacchioni, G.; Fantucci, P. Chem. Phys. 1985, 99, 87. (17) Buenker, R. J.; Peyerimhoff, S. D., Theor. Chim. Acta 1974, 35, 33. Ibid. 1975, 39, 217. Buenker, R. J.; Peyerimhoff, S . D.; Butscher, W. Mol. Phys. 1978, 35, 771. In the MRD CI approach the generated singly and doubly excited configurations with respect to one or more main configurations (M) are either included directly in the secular equation or are taken into account indirectly in the extrapolation step. The selection of configurations is made by energy selection threshold T. Configurations with energy lowering below a given cutoff value (the threshold T ) are not included in the secular equation. The extrapolated energies for T - 0 (all singly and doubly excited configurations with respect to the reference) are obtained by extrapolation techniques. (18) Whitten, J. L.; Pakkanen, T.A. Phys. Reu. B 1980, 21, 4357. Fantucci, P.; Bonacic-Koutecky, V.; Kouteckg, J. Phys. Reo. B 1986, 34, 2777.
2660 The Journal of Physical Chemistry, Vol. 91, No. 10, 1987
Pacchioni and Kouteckjl
TABLE 11: Mulliken PoDulation Analysis for Pd.-CO Clusters Pd-CO C-,
Pdz-CO
basis set
DZP
DZP
DZ
DZ
DZ
Pd 5s Pd 5p Pd 4d
0.173 0.084 9.768
0.149 0.064 9.781
0.153
0.139
0.093
9.799
9.780
9.837
net charge
-0.024
0.006
0.048
0.081
0.068
c 2s c 2P, c 2P,
1.670 0.979 1.067
1.615 0.974 1.148
1.675 0.969 1.228
1.731 0.953 1.179
1.742 0.997 1.111
1.811 1.001 0.938
net charge
0.284
0.263
0.128
0.137
0.149
0.250
0 2s 0 2P, 0 2P,
1.782 1.403 3.075
1.780 1.399 3.096
1.763 1.396 3.113
1.767 1.392 3.101
1.779 1.402 3.105
1.775 1.413 3.062
net charge
-0.260
-0.275
-0.272
-0.261
-0.286
-0.250
coo
5.833 4.142
5.768 4.244
5.803 4.342
5.844 4.281
5.920 4.217
6.000 4.000
cor
Pd3-kO C3"
c 2 L '
Pd,-CO" C2"
PdS-CO" C2"
free CO DZ
"The population of the two Pd atoms directly interacting with the CO molecule has been reported (see Figure I ) .
TABLE 111: Computed CI Energies for Pd-CO (DZP Basis Set) at Different Values of the Selection Threshold P
T,
TABLE IV: Size-Consistency Effects in MRD CI Calculations of Pd,-CO Clustersa
whartree
selected config
E,,,, au
E.,,, au
En,llC l , b au
cz
A-B
0.5 2.0 5.0 15.0 30.0 60.0 100.0
3517 2665 2210 1551 1186 869 649
-51.1417 -51.1409 -51.1397 -51.1353 -51.1303 -51.1213 -51.1110
-51.1419 -51.1419 -51.1416 -51.1407 -51.1415 -51.1400 -51.1416
-51.1674 -51.1672 -51.1668 -51.1655 -51.1659 -51.1636 -51.1646
0.91 0.91 0.91 0.91 0.91 0.91 091
( R = Re)
total energies. au
"The calculations were performed for Re = 3.98 au with the I M configuration; the generated configurations are 6014. E,,, = variational energy; E,,, = extrapolated energy ( T = 0); El,,, cI = full CI energy (see text). bDavidson's c o r r e ~ t i o n . ' ~
EscF E,,, Efullc1
-50.8573' -5 1. I499 -51.1706
Esc~ E,,,
-50.8615' -51 . I 509 -51.1743
Pd-CO (DZP) -50.8592 -50.8592 -51.1420 -51 . I 505 -51.1618 -51.1591
0 5.3 1.7
-80.4291' -80.7551 -80.7830
Pd,-CO (DZ) -80.4273 -80.4273 -80.7388 -80.7491 -80.7619 -80.7595
0 6.5 1.5
-80.4352' -80.7644 -80.7925
Pdz-CO (DZP) -80.4308 -80.4308 -80.7427 -80.7544 -80.7634 -80.7672
0 7.3 2.4
El,,, c1
EsCF
the 40, 5 g , and la electrons of C O and all the cluster electrons which can interact with these C O orbitals. Nevertheless, the correlation of 30 valence electrons would be a formidable task without the extrapolation procedure of the MRD CI method. The reliability of this procedure and the error introduced in the final CI energy have been tested for the Pd-CO system (Table 111). The results show that the total energies do not depend on the selection threshold T used. By increasing T the variational energy obviously increases, while the extrapolated and full C I (Davidson correction19) energies are practically constant. Similar encouraging results have been obtained on P$-H systems.*O Size-Consistency Errors. A relevant problem in determining the DC)s is represented by size-consistency errors. Multireference single-double (SD) C I calculations are unable to remove completely this error. In principle, the size-consistency effects disappear in a full CI treatment. In our calculations the importance of this effect (quantitatively small but qualitatively relevant) is illustrated by the difference between the CI energies of a Pd,-CO supermolecule A - B computed at very high distance (100 au) and the sum of the CI energies of two separated Pd, and C O systems (A B) (Table IV). The differencies between extrapolated energies in the supermolecule and separated fragments are not negligible, considering the weak nature of the Pd-CO interaction.I6 However, the energy differencies of A - B and A + B decrease on going from extrapolated to estimated full CI energies (Table IV). The calculations of the Pd,-CO systems have been performed with six or seven main configurations chosen on the basis of their
+
(19) Langhoff, S. R.; Davidson, E. R. In?. J . Quantum Chem. 1974. 8, 61. (20) Pacchioni, G.; Kouteckg, J. Surf. Sci. 1985, 154, 126.
A-B size consistency (R = 100 au) A +B error,b kcal/mol Pd-CO (DZ) -50.8592 -50.8592 0 -5 1.1498 5.2 -51 .I415 -51.1585 -51.1611 1.6
E,,, Efull CI EscF
E,,, E,,,, c j
E ~ C F -109.9955' E,,, -1 10.2869 Ef,II c1 -1 10.3076 EscF
E,,, Eful1CI EsCF
E,,,
Pd,-CO, C3, -109.9889 -1 10.2598 -1 10.2752
(DZ) -109.9889 -1 10.2704 -1 10.2804
-139.5576' -139.8102 -139.8276
Pdd-CO (DZ) -139.5502 -139.5502 -139.7972 -139.8060 -139.8103 -139.8143
-109.9984' -1 10.2838
PdS-CO, C, (DZ) -109.9966 -109.9966 -1 10.2691 -1 10.2806
ci - 1 10.3038
-1 10.2848
-1 10.2907
0 6.6 3.3 0 5.5 2.5
0 7.2 3.1
"The details of the CI calculations are given in Table I. bComputed as E(A-B, R = 100 au) - E(A+B); A = Pd,, B = CO. 'Computed at the CI equilibrium bond length.
weight in the final CI wave function. All configurations with c2 > 0.005 have been taken as leading configurations. With respect to the ground state these configurations represent P a* excitations internal to the CO fragment. The De of Pd,-CO systems have been determined as the difference between the full CI energies of the system in its equilibrium geometry and the sum of the full CI energies of the separated fragments (Table IV). In this way the possible overestimation of De due to size-consistency errors is avoided.
-
The Journal of Physical Chemistry, Vol. 91, No. 10, 1987 2661
Interaction of C O with Pd Clusters Metal-Metal Bonds in Pd Clusters
The weak nature of the Pd-Pd bonding in small Pd clusters represents a critical point in the use of Pd clusters to study chemisorption phenomena. Miyoshi et al.,l have found, by model potential Hartree-Fock calculations, that the ground state of a tetrahedral Pd4 cluster correctly dissociating in four Pd(dlo) atoms is purely repulsive. The first bound state is a 3B2state dissociating in one Pd(d9s1)and three Pd(dIo) atoms. This state, however, lies about 1.5 eV above the ground state.21 Using a counterpoise correction analysis, Shim and Gingerich,, found that the S C F potential energy curve for the interaction between two Pd atoms in the IS (dl0) ground state is repulsive. The correct description of the Pd-Pd bond is beyond the scope of this paper. We have determined the Pd2 potential energy curve by full single-double CI calculations ( T = 0, DZP basis set). The active space consists of 10 occupied and 20 virtural orbitals and the generated configurations are 2667. Whereas the S C F curve is repulsive, the CI curve presents a minimum 3.2 kcal/mol below the dissociation limit at Re = 6.0 au. The Pd, bond length is not known, but this distance is much longer than the nearest-neighbor separation in Pd crystal, 5.2 au. A triplet state dissociating into Pd 4d95s1was also examined. This state is bound with respect to the asymptotic limit and the bond is entirely due to the s-s interaction but is higher than the singlet ground state (by about 20 kcal/mol) in analogy with the findings of Shim and Gingerich.22 SD-CI calculations of isosceles and equilateral triangle Pd3 and rhombic and tetrahedral Pd4 clusters ( r = 5.2 au) indicate a small stability (3-6 kcal/mol) for these systems, but a more accurate evaluation of the De would require a careful analysis of sizeconsistency effects. Here we can only conclude that small, ligand-free Pd clusters are very weakly bonded molecules. This result can either originate from methodological difficulties or can reflect a real physical situation. There is no doubt that the theoretical method employed entails many approximations. The most important one is probably the absence of relativistic effects which should produce a stabilization and a contraction of the 5s and 5p orbitals and, indirectly, an expansion of the d Furthermore, the correlation effects are certainly underestimated even in Pd,, and the basis set should include polarization functions of higher angular quantum number (f and g functions). Nevertheless, according to the classical M O picture, the interaction of two closed-shell Pd atoms yields an equal number of doubly occupied bonding and antibonding orbitals so that no bonding should occur. Whether the bonding does or does not occur depends on the possibility for the interacting atoms to hybridize. A similar case is represented by Be,, Zn,, and related dimers.24 Experimentally it is known that Pd, is much less strongly bound than the isovalent Ni, molecule, the corresponding De)s being 16 f 5 and 63 f 1 kcal/mol, r e ~ p e c t i v e l y . ~A~ more recent measurement on Pd, yields a binding energy of -20 kcal/mo1.22 This seems to indicate that the discrepancy between theory and experiment is most probably due to the limitations of the theoretical method. In order to get bonding in small Pd clusters the Pd atoms are expected to assume an open-shell configuration. Similarily, in alkaline-earth metal clusters and, in particular, in Be clusters, the Be atoms assume a s’pl-like electronic configuration. This atomic configuration explains the considerable stability of Be4 but is not observed in Be2or Be3 molecules where the number of Be-Be bonds is not large enough to compensate for the s2 SIP’ promotion energy.26 Moreover, while the hybridization in Be clusters is properly described already in SCF,26 Mg and Ca clusters are
-
________
~~
~~~
(21) Miyoshi, E.; Sakai, Y.; Mori, S. Chem. Phys. Lett. 1985, 113, 457. (22) Shim, I.; Gingerich, K. A. J. Chem. Phys. 1984, 80, 5107. (23) Schwarz, W. H. E.; Chu, S. Y.; Mark, F. Mol. Phys. 1983,50,603. (24) Winn, J. S. Acc. Chem. Res. 1981, 14, 341. (25) Weast, R. C.; Astle, M. J., Eds. CRC Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, 1983. (26) Bauschlicher, Jr., C. W.; Liskow, D. H.; Bender, C. F.; Schaefer 111, H. F. J . Chem. Phys. 1975, 62,4815. Whiteside, R. A.; Krishnan, R.; Pople, J. A.; Krogh-Jespersen, M. B.; von Rague-Schleyer, P.; Wenke, G. J. Comput. Chem. 1980, I , 307. Pacchioni, G. Y; Koutecky, J. Chem. Phys. 1982, 71, 181.
Pd2-C0 Pd3-CO (C,,,)
Pd3-CO (Cjv)
Pd4-C0 (C,,,)
h
Figure 1. Geometries of the Pd,-CO clusters studied. The two Pd3 clusters considered are sections of the (1 00) and ( 1 1 1) Pd surfaces, respectively, as shown on the bottom of the figure.
described as weakly stable clusters only when p and d polarization functions and correlation effects are simultaneously included in the cal~ulation.~’ The Mulliken population analysis of the calculated Pd clusters shows that the atomic configuration of Pd centers is very close to dlO. This means that the energy required to promote one electron from the 4d to the 5s orbital (about 19 kcal/mol) is not compensated for by the formation of a sufficiently strong bond. Since Pd metal exists and possesses a cohesive energy of 90 k ~ a l / m o l the , ~ ~hybridization energy is probably compensated for through the formation of many metal-metal bonds. In conclusion, the weakness of the Pd-Pd interaction may be due to the inadequacy of the computational approaches (in particular the neglect of relativistic effects). However, on the basis of the few available theoretical calculations21.22.28 we cannot rule out the possibility that very small Pd clusters are intrinsically weakly bonded species and that only Pd crystallites of intermediate size possess an appreciable stability. Chemisorption of CO on Pd Clusters
Energetic and Geometrical Aspects. The clusters investigated are, beside the linear Pd-CO molecule, Pd2-CO (C2u),Pd3(equilateral triangle)-CO (C,,), and Pd,(rhombus)-CO (C2& clusters which are sections of the (1 11) Pd surface and the Pd3(isoscelestriangle)-CO (C2J cluster section of the (100) Pd surface. These clusters can be considered as models of “on top”, bridge, and hollow adsorption sites on Pd surfaces. The Pd-Pd bond length was fixed at the nearest-neighbor distance of Pd (27) Bauschlicher, Jr., C. W.; Bagus, P. S.; Cox, B. N. J . Chem. Phys. 1982, 77,4032. Pacchioni, G.; Koutecky, J. J . Chem. Phys. 1982, 77, 5850. (28) Garcia-Prieto, J.; Novaro, 0.Int. J . Quantum Chem. 1980,18, 595.
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crystal (5.2 au). In Pd3-CO (C,"), therefore, the two Pd atoms directly interacting with CO are separated by 7.3 au (Figure 1). The Pd-C and C-O distances have been independently optimized by parabolic fitting of few calculated points of the potential curve around the minimum. The determination of the vibrational frequencies, which is of interest for comparison with experimental data, was not attempted. In fact, this requires an accurate analysis of the potential including also the anharmonic region of the curve which is beyond the scope of this work. The Deof the Pd-CO molecule computed with the DZ basis set, 6.0 kcal/mol (Table I), is reasonably close to the value obtained on the basis of more accurate calculations.I6 The interaction energy in Pd2-CO, 13.2 kcal/mol, is about twice that of Pd-CO. In Pd3-CO (C3u),where the C O molecule is coordinated in a three-hollow position, the D,= 17.1 kcal/mol is almost three times larger than in Pd-CO. Therefore, the interaction energy grows in a regular way with the number of Pd atoms directly bonded to CO. In Pd3-CO (C2u)the C O molecule interacts with only two Pd atoms and the resulting bond is weaker than in the hollow site. The "second layer" atom of Pd,-CO (C2') (Figure 1) is practically "inert" and does not significantly contributes to the bonding with CO. In Pd4-CO the two atoms on the longer diagonal of the rhombus do not appreciably interact with the C O molecule, as shown by the small weight of their atomic orbitals in the cluster-CO bonding orbitals. Therefore, the bonding in this bridge site is not affected by the presence of neighboring Pd atoms and closely resembles that of Pd2-CO. The sequence of the computed dissociation energies, hollow site > bridge site > top site, agrees with the experimental finding that at low degree of coverage C O prefers to occupy the three-hollow position on the (1 1 1) Pd surface. On increasing the coverage, intermolecular interactions cause the movement of the admolecules into bridge and on top sites as shown by the dramatic shift in C O stretching frequenciesz9 The optimization of the distance of CO from the cluster surface was carried out at the C I level. The shortest Pd-C distance is found for Pd-CO (3.98 au). In both bridge sites considered, Pd,-CO and Pd4-C0, the optimized metal-carbon distance is 4.09 au. In Pd3-C0 (C,") the Pd-C bond length is 0.1 longer than in the bridge position, and Reis even longer for the Pd, cluster section of the (100) surface (Table I). All these distances are close to those found in Pd-carbonyl clusters (3.8-4.2 au) where the Pd-Pd bond distances are very close to the bulk separation , ~ ~much ~ ~ longer than the Pd-C assumed in our c a l c ~ l a t i o n sbut bond distance 3.65 au observed for CO chemisorbed on Pd( The optimization of the C O bond lengths in Pd-CO, Pd2-CO, and Pd3-CO (C3J systems correctly shows the occurrence of a small lengthening of the C - O bond in coordinated C O (Table I). Nature of ChemisorptiveBonding. Since in clusterX0 systems the C O derived orbitals retain much of their original character, we denote them hereafter by their C O notation: 4u, 1a, 5u. In Pd,-CO systems we can distinguish three main kinds of interactions: Pd(d,)-CO(2a*), Pd(d,)-CO(Su), and Pd-Pd interactions. Actually, Andzelm and Salahub6 have recently found that also the 40 level of C O is intimately involved in the bonding with Pd clusters, but the most significant changes occur on the 5u and 2 r * levels of CO. The population analysis of the Pd,-CO complexes shows that the population of 5s and, where present, 5p orbitals increases with respect to the free cluster, but the Pd atoms still retain much of their original d'O configuration (Table 11). (29) Bradshow, A. M.; Hoffmann, F. M. Surf. Sci. 1978, 72, 513. (30) Dubrawski, J.; Kriege-Simondsen,J. C.; Feltham, R. D. J . Am. Chem. Soc. 1980, 102, 2089. (31) Mednikov, E. G.; Eremenko, N. K.; Mikhailov, V. A.; Gubin, S . P.; Slovokhotov, Y . L.; Struchov, Y . T. J . Chem. Soc., Chem. Commun. 1981, 989. (32) Goddard, R.; Jolly, P. W.; Kriiger, C.; Schick, K. P.; Wilke, G. Organometallics 1982, 1, 1709. (33) Mednikov, E. G.; Eremenko, N. K.; Gubin, S . P.; Slovokhotov, Y . L.; Struchov, V . T. J . Orgunometal. Chem. 1982, 239, 401. (34) Manojlovic-Muir, L.; Muir, K. W.; Lloyd, B. R.; Puddephatt, R. J. J . Chem. Soc., Chem. Commun. 1983, 1336.
Pacchioni and Kouteckq
Figure 2. Electron density difference contour map of Pd2-C0. Solid and dot-dashed lines indicate accumulation and depletion of electron density, respectively. The lines are drawn in intervals of 0.01 electrons/au3.
The nature of the u and a interactions is very similar in Pd,-CO systems and in the Pd-CO molecule.I6 The Pd atoms are neutral or slightly positive because of the compensation of donation and back-donation effects. However, the changes in the overall u and a populations of the C O ligand indicate that, while the u population does not appreciably change with the number of coordinated Pd atoms (Pd-CO = 5.83, Pd2-CO = 5.77, Pd3-CO (C30)= 5.80 electrons, respectively), the K population of C O ( l a + 2a*) increases with the number of Pd atoms directly interacting with CO (4.14,4.24, and 4.34 electrons, respectively) (Table 11). Therefore, there is a direct correlation between the population of the T orbitals of CO, and in particular of the 2a* orbital and the interaction energy. The decrease of the u population of CO from 6 to -5.8 valence electrons formally corresponds to a u donation from the C O molecule to the cluster, but these data should be interpreted with caution because of the limitations of the population analysis. Some authors have recently concluded that there is no u donation in metal-CO c ~ m p l e x e s . ' ~ . ~More ' reliable than the population analysis are the electron density difference contour maps. One of these maps, determined for Pd,-CO as the difference between the electron density of the complex in its equilibrium geometry and that of the separated Pd, and C O molecules, is reported in Figure 2. Two regions can be distinguished. In full analogy with Pd-C0,16 in the region corresponding to u bonding there is a decrease of the electron density, while an accumulation of electronic charge is observed in the corresponding T region. Another important effect is that the metal orbitals polarize away from the u region in order to minimize the Pauli repulsion with the CO 5u electron cloud (Figure 2). On the basis of these results it is possible to conclude that the bonding originates primarily from the a-back-donation mechanism. This mechanism is reinforced when C O is coordinated to many metal centers, as shown by the present results as well as by the experimentally observed red shift in the vibrational frequencies of p 2 - and p3-C0 bridging ligands with respect to terminal CO in transition-metal carbonyl (35) Feltham, R. D.; Elbaze, G.; Ortega, R.; Eck, C.; Dubrawski, J. Inorg. Chem. 1985, 24, 1503. (36) Behm, R. J.; Christmann, K.; Ertl, G. Surf. Sci. 1974, 4 1 , 435. (37) Bagus, P. S.; Nelin, C. J.; Bauschlicher, Jr., C. W. Phys. Reu. B 1983, 28, 5423. J. Vac. Sci. Technol. A 1984, 2, 905. (38) Cotton, F. A.; Wilkinson, G. Aduunced Inorganic Chemistry; Wiley: New York, 1980.
The Journal of Physical Chemistry, Vol. 91, No. 10, 1987
Interaction of C O with Pd Clusters
TABLE V: Ionization Potentials (eV) for PI.-CO Clusters (Koopman’s Theorem) free CO Pd-CO Pd2-CO expt calcd C,” c2v IP(5a) IP( 17r) IP(4u) IP(1a) - IP(5u) IP(4u) - IP( 1T )
14.0 16.9 19.7 2.9 2.8
15.1 17.4 21.7 2.3 4.3
16.6 17.1 21.5 0.5 4.4
Pd,-CO C3”
16.8 16.8 21.2
Pd&O
16.9 16.6 21.0 -0.3 4.4
0.0 4.4
czu
Pd,-CO C2”
expt‘
16.8 16.7 21.1 0.1 4.4
15.9 16.7 21.1 0.8 4.4
14.2 14.2 17.2 0.0 3.0
2663
From ref 36. The values are computed with respect to the vacuum by using a work function for Pd of 6.0 eV.
Ionization Potentials. One of the typical features of C O chemisorption on metal surfaces is represented by the increase of the ionization potential (IP) of the 5u M O of CO. This effect has been observed also on Pd s u r f a c e ~ ~and ~ .has ~ ~generally ,~ been attributed to the electron donation from the 5 u lone pair to the metal.4’ The stabilization of the 5u orbital is quite relevant considering that in coordinated C O this orbital is practically degenerate with the l a MO, while in free C O they are separated by 2.9 eV (Table V). On the other hand, the I P of the 4u M O is not significantly influented by the chemisorption process. The MO diagrams of Pd,-CO clusters qualitatively reproduce this feature. As an example, we report in Figure 3 the M O scheme for CO, Pd2, and Pd2-CO systems. The stabilization of the 5 u level, which in Pd2-C0 is degenerate with the l a MOs, is evident. The quantities I P ( l a ) - IP(5u) and IP(4u) - IP(1a) represent therefore useful parameters for the qualitative comparison of the M O spectra of Pd,-CO clusters with the photoemission spectra of C O on Pd. In Table V are given the IPS of 5u, l a , and 4u MOs of free and coordinated CO. On going from the gas phase to the Pd3-C0 (C3”)cluster the IP(5u) increases from 15.1 to 16.9 eV. On the other hand, the l a level is shifted to higher energies upon coordination. Consequently, the IP( l a ) - IP(5u) theoretical value, which is 2.3 eV in free CO, vanishes in Pd,-CO systems (Table V). Despite the limitations of this analysis based on IPS obtained without allowing electron relaxation (Koopman’s theorem), the trend in computed IPSis in full agreement with the photoemission spectra of CO on Pd(100).36339140 A possible interpretation of the stabilization of the 5u MO in chemisorbed C O is the following. The interaction between the very diffuse 5u lone pair and the Pd u orbitals causes a polarization of the cluster orbitals away from C O (Figure 2). The C O lone pair can partially expand over the metal centers reducing in this way the Coulomb repulsion internal to this orbital. Moreover, because of the antibonding character of the 5u MO, the elongation of the C - O distance due to the a-back-bonding mechanism also contributes to the stabilization of this MO. The diffusion of the 5u electron cloud toward the metal center explains the data of population analysis which, because of the arbitrary partition of the electrons, indicate the presence of a charge transfer from C O to Pd. However, the stabilization of the 5u MO cannot be interpreted as a sign of the formation of a dative u bonding since the u interaction has essentially repulsive ~ h a r a c t e r . ’ ~ , ~ ’ . Cluster-Surface Analogy
The present theoretical study of the interaction of CO with small Pd clusters has pointed out the existence of some items where clusters and surfaces qualitatively show similar features. The most relevant of these analogies are as follows: (a) Experimentally, it is known that CO prefers the three-hollow positions when chemisorbed on the Pd( 111) surface. Only when the coverage is increased the CO molecule is forced to occupy the bridge and then the “on top” positions because of the- mutual repulsion among chemisorbed molecules.29 The computed interaction energies for Pd clusters modeling these three chemisorption sites indicate the right sequence of stabilities. (39) Lloyd, D.R.; Quinn, C. M.; Richardson, N. V. Solid State Commun. 1976,20, 409. (40) Miranda, R.; Wandelt, K.; Rieger, D.; Schnell, R. D. Surf. Sci. 1984, 139, 430.
/
/
05
/ I
/ /
/ I
I
\
I I I I
/
2K*-
0
I
\
I
-0.5
. =!
0
W
-1.0
-1.5
co Pdz-CO Pd2 Figure 3. Schematic MO diagram for the ‘A, ground state of Pd,-CO. The notation of the MOs in Pd2-CO concerns the valence MOs only. (b) There is no direct measurement of the Pd-CO bond distance for the CO/Pd( 111) system. In CO/Pd( 100) this value is 3.65 au,36much shorter than in our Pd,-CO clusters. However, the error in the theoretical value is partially due to the absence of relativistic effects which are known to produce shorter distances. Furthermore, our optimized Pd-CO bond lengths are reasonably close to the values observed in Pd-carbonyl clusters by X-ray cry~tallography.~~~~ (c) The MO spectra of Pd,-CO clusters closely resemble the photoemission spectra of C O on Pd. The characteristic shift of the 5u level to higher ionization energies is perfectly reproduced by cluster calculations. However, the analysis of the electronic structure of the cluster allows one to conclude that this MO stabilization cannot be taken as a sign of the formation of a real dative u bonding, since the u interaction is repulsive in character. Most of the theoretical studies of chemisorption on small clusters agree with the conclusion that small clusters representing a tiny piece of a metal surface can model chemisorption processes. This idea is supported by the close analogy existing between bond distances, stereochemistry, vibrational frequencies, and bond energies of molecular clusters and surfaces.2 The possibility of describing chemisorption phenomena as local processes determined by the interaction with few nearest neighbors only is very stimulating. On the other hand, Shustorovich recently noted4*that, “these nearest neighbors, being the tip of the metal (41) Blyholder, G. J . Phys. Chem. 1964,68, 2772. Hermann, K.;Bagus,
P.S. Phys. Rev. B. 1977,16,4195.
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The Journal of Physical Chemistry, Vol. 91, No. 10, 1987
iceberg, may have not much in common with their free-cluster prototypes”. This is probably the case for palladium. Despite the fact that the Fermi level of the Pd surface (-6.0 eV43) is practically at the same energy as the cluster HOMOS (e.g., Pd, = 6.6 eV, Pd, = 6.0 eV), the electronic configuration of the Pd atoms in the clusters, very close to dI0, is deeply different from the average configuration expected for a bulk atom. There is no precise information about this point, but band structure calculations indicate a configuration intermediate between dIo and d9s’ (the atomic populations are s = 0.26, p = 0.03, d = 9.714). This means that small Pd clusters do not represent particularly good models of the corresponding metal surface. The seeming agreement found between clusters and surfaces must be interpreted cautiously. On the other hand, for the same reasons, the Pd,-CO clusters considered are probably good models of organometallic Pdcarbonyl clusters. Pd,-CO clusters are stable toward dissociation into Pd atoms and CO but this stability is largely due to the C O ligand which bonds the whole system while the metal core is only weakly bonded. This contradicts the original definition of metal clusters as “those compounds containing a finite group of metal atoms which are held together entirely, mainly or at least to a significant extent by bonds directly between metal atoms”.45 Nevertheless, the problematic nature of metal-metal bonding in molecular metal clusters has been the subject of wide discussions in past years.46 In the specific case of Pd we believe that organometallic Pd clusters are not stabilized through the formation of chemically important metal-metal bonds. This conclusion is supported directly by the theoretical results21,28 and indirectly by the observation that the isolated and characterized by X-ray crystallography Pd carbonyl clusters, where the Pd atoms are formally in zerooxidation state, always contain bridging C O ligands. In the recently isolated Pd4-(p2-CO)5(PPh3)4,where the metal atoms are in a distorted tetrahedral arrangement, the length of the five bridged Pd-Pd bonds is 5.2 au, while the unbridged Pd-Pd edge has a distance of 6.05 au.35 A possible explanation is just that the stabilization of Pd carbonyl clusters is due to the formation of three-center bonds (42)Shustorovich, E.In Quantum Chemistry: the Challenge of Transition Metals and Coordination Chemistry, Veillard, A,, Ed., NATO AS1 Series C, Vol. 176; Reidel: Dordrecht, 1986; p 445. Surf. Sci. Rep. 1986, 6, 1. (43)Bader, S.D.; Blakely, J. M.; Brodsky, M. B.; Friddle, R. J.; Panosh, R. L. Surf. Sci. 1978, 74,405. (44)Anderson, 0.K. Phys. Reo. E 1970, 2, 883. (45)Cotton, F. A. Q. Reu. Chem. SOC.1966, 416. (46)Manning, M.C.; Trogler, W. C. Coord. Chem. Reo. 1981, 38, 89. Heijser, W.; Baerends, E. J.; Ros, P. Faraday Symp. Chem. SOC.1980, 14, 21 1. Benard, M. Inorg. Chem. 1979,18, 2782. May, J. J.; Rae, A. D.; Dahl, L. F. J . Am. Chem. Soc. 1982,104,3054.Adams, R. D.; Yang, C. W. J . Am. Chem. SOC.1982,104, 41 15. Fantucci, P.; Pacchioni, G.; Valenti, V. Inorg. Chem. 1984, 23. 247.
Pacchioni and Kouteckjr involving two adjacent Pd atoms and a C O molecule (or fourcenter bonds when k,-bridging ligands are present). Of course, metal-metal bonds are certainly formed to a given extent, as shown by the existence of the Pd dimer. Generally, the characterized Pd inorganic clusters have phosphine ligands in terminal positions. Blomberg et al.47found that the addition of a water molecule to a Pd atom interacting with H2 lowers the d population and increases the d9s1character. The presence of a ligand like H,O slightly changes the ground state configuration of Pctatom and makes it more similar to Ni and therefore more reactive.47 The role of the phosphine ligands in organometallic Pd clusters may be to perturb the electronic configuration of the metal atoms and to make them more suitable for the formation of metal-metal bonds.
Conclusions The results of the pseudopotential CI calculations provide some insight into the nature of the Pd-CO bonding, confirming the repulsive character of the u interaction, recently emphasized by other s t ~ d i e s , ’and ~ , ~the ~ important role of the r-back-donation in the formation of the bond. Some interesting similarities between Pd,-CO clusters and corresponding chemisorption sites on surfaces have been observed. They concern geometrical and energetical aspects. In particular, the typical degeneracy of 1r and 5u levels in chemisorbed C O is a feature common to cluster ~ t u d i e s . ~However, -~ the nature of the bonding in small Pd clusters looks quite different from that of the bulk.21.22,28 At this level of theoretical treatment it is not clear whether the weak bonds found in small Pd clusters are due to methodological deficiencies or indicate a real physical situation, but in general small Pd clusters cannot be considered as ideal models of the metal surface and their use in the interpretation or prediction of the reaction mechanisms in surface chemistry requires some care. On the other hand, the Pd,-CO clusters considered are reasonably good models for studies of bonds in organometallic clusters. The analysis of the bond in these systems suggests that polynuclear Pd(0) complexes are stabilized mainly by the bridging CO ligands, the corresponding metal-metal interactions being rather weak. Acknowledgment. This work was supported in part by the Deutsche Forschungsgemeinschaft, SFB 6 “Structure and Dynamics of Interfaces” and in part by the Italian CNR. The authors thank Profs. E. Shustorovich and P. Siegbahn for the interesting and stimulating discussions and Profs. P. Fantucci and A. Gavezzotti for a critical reading of the manuscript. Registry No. Pd, 7440-05-3; CO, 630-08-0. (47)Blomberg, M.; Brandemark, U.; Petterson, L.; Siegbahn, P. Inr. J . Quanlum Chem. 1983, 23, 855.
