116
Langmuir 1991, 7, 116-125
Theoretical Studies of Chemisorption and Dimer Model Systems: Mfiller-Plesset and Configuration Interaction Calculations on PdH, PdC, PdO, PdF, Pd2, and PdCO Peter Schwerdtfeger,'f+John S. McFeaters, John J. Moore,$ and Don M. McPherson School of Engineering and the Center of Information Science, University of Auckland, Private Bag, Auckland, New Zealand
Ralph P. Cooney' and Graham A. Bowmaker Department of Chemistry, University of Auckland, Private Bag, Auckland, New Zealand
Michael Dolg and Dirk Andrae Institut fur Theoretische Chemie, Universitat Stuttgart, Pfaffenwaldring 55, 07000 Stuttgart-80, West Germany Received December 19, 1989. I n Final Form: May 16, 1990 Ab initio SCF studies have been performed to study the molecular properties of several single-bonded palladium compounds, PdH, PdC, PdO, PdF, Pdz, and PdCO, which are important in surface and materials science. Electron correlation effects were evaluated by a second- and third-order Mdler-Plesset (MP) perturbation theory and a size-consistency-corrected configuration interaction with single and double substitutions (CISC). Relativistic effects were investigated for PdH and PdF. The ground state of PdC has been calculated at the CISC level to be a 311state which is only 0.26 eV below the 32-state (previously assigned ground state) and 0.51 eV below the 1Z+state. PdC is predicted to be stable in the gas phase, and the possibility of preparing this compound is investigated. The bonding in CO chemisorbed on palladium is studied by using the model Pd-CO system. The effect of d,-a* back-bonding, discussed at the Hartree-Fock and CI level, is compared with results from multiple-scattering X a calculations. The C-0 stretching frequency shift for CO on palladium was analyzed at various levels of theory, and the results indicated that the decrease in the CO force constant associated with chemisorption is not solely the result of d,-a* back-bonding. At the CISC level, the calculated chemisorption shift of Au = -72 cm-l in the C-0 stretching frequency compared well with the infrared experimental value (-95 cm-l) for PdCO monomer in a Kr matrix and with terminal CO on the surface of palladium hydrosols (-78 cm-l), while the calculated MP2 value of Aw = -122 cm-' overestimated the experimental result. The calculations indicated that the CO bond distance decreases only slightly (-0.007 A) as a result of chemisorption on single palladium atoms.
Introduction Investigations of the electronic structures of chemisorbed species on transition-metal surfaces and of related organometallic compounds of transition metals have been the topic of increasing interest in the last decade.'I2 Hence, theoretical studies on numerous transition-metal compounds have been performed, mostly involving all-electron Hartree-Fock (HF) and configuration interaction (CI) methods for the first transition series or by using approximations like the pseudopotential method (PP),3t4the t Current address: Research School of Chemistry, The Australian National University, G.P.O. Box 4, Canberra, A.C.T. 2601, Australia. t Permanent address: Department of Metallurgical and Materials Engineering, Colorado School of Mines, Goldon, CO 80401. (1) Hartley, F. R. The ChemistryofPlatinumand Palladium;Applied Science Publishers: London, 1973. (2) (a) Schaefer, H. F., 111 Surf. Chem. Cat. 1977,10,287. (b) Cohen, M. L. Annu. Rev. Phys. Chem. 1984,34,537. (c) Kang, D. B.; Andersen, A. B. Surf. Sci. 1985, 155, 639. (d) Gavezotti, A.; Simonetta, M. Adu. Quantum Chem. 1985,12,103. (e) Shusterovich, E. Surf. Sci. Rep. 1986, 6 , 1. (0 Koutecky, J.; Fantucci, P. Chem. Reu. 1986,86, 539. (g) Abel, E. W.; Stone, F. G. A. Organometallic Chemistry; Vol. I-XV; The Royal Society of London: London, 1971-1987; Vols. I-XV. (h) Shusterovich, E. Acc. Chem. Res. 1988, 21, 183. (i) March, N. H. Chemical Bonds Outside Metal Surfaces;Plenum: New York, 1986. (3) (a) Bardsley, J. N. Case Stud. At. Phys. 1974,4, 299. (b) Dixon, R. N.; Robertson, I. L. Theor. Chem. (London) 1978,3, 100. (4) Gavezotti, A.; Tantardini, G. F.; Miessner, H. J.Phys. Chem. 1988,
92, 872.
0743-7463/91/2407-Ol16$02.50/0
multiple-scattering X a appr~ximation,~ or the extended Huckel tight-binding method for the solid stateas As a result of recent improvements in computer technology and in molecular ab initio programs, all-electron SCF calculations including correlation by perturbation methods or CI are now feasible for compounds of the second transition series. Relativistic contributions to ground-state properties like the metal-ligand bond distance or the dissociation energy of compounds in the second-row transition series are expected to be minor and can be treated perturbati~ely.~,8 Hence, calculations on small molecules incorporating metals such as palladium, silver, or zinc need not be limited to semiempirical approximations. On the other hand, molecular SCF calculations should alsobe performed to test the reliability of the applied approximations, e.g., to test the quality of adjusted pseudopotentials at the HF level. (5) (a) Johnson, K. H. Annu. Reu. Phys. Chem. 1975,26,39. (b) Messmer, R. P. Surf. Sci. 1981, 106, 225. (c) Case, D. A. Annu. Reu. Phys. Chem. 1982, 33, 151. (d) Yang, C. Y. In Relativistic Effects in A t o m , Molecules and Solids; Plenum Press: New York, 1981; p 335. (6) Silvestre, J.; Hoffmann, R. Langmuir 1985, I, 621. (7) (a) Pyykko, P. Chem. Rev. 1988, 88, 563. (b) Pyykkb, P. Adu. Quantum Chem. 1978, 11, 353. (8) Relativistic effects can be very large for properties dependent upon the electron density near the nucleus (e.g., the electric field gradient), even for the first transition element series (ref 9). (9) Schwerdtfeger, P.; Aldridge, L. P.; Boyd, P. D. W.; Bowmaker, G. A. Struct. Chem. In press.
0 1991 American Chemical Society
Langmuir, Vol. 7,No. 1, 1991 117
Molecular Properties of Single-Bonded Pd Compounds Compounds of nickel and platinum have been studied more extensively than those of p a l 1 a d i ~ m . lThis ~ ~ ~is surprising since accurate ab initio calculations on molecules containing nickel or platinum are more difficult to perform than palladium, because Pd has a closed shell dl0 ground state in contrast to nickel (dW) or platinum (d9~'),~5 and spin-orbit coupling for ground-state properties in palladium is considered to be small in contrast to platinum compound~.~5 Therefore, we would expect that an SCF procedure should be able to describe the correct groundstate symmetry and that the single group formalism (A-S coupling for linear molecules) still holds. Moreover, electron correlation in nickel compounds is very important, but difficult to compute, and perturbation series like the Moller-Plesset procedure do not convergesatisfactorily.z6 However, it has been demonstrated recentlyz0that the ground state of Pdz may be a 3Xu+ state, only 0.16 eV below the IZg+state at the CI level. It is therefore of interest to study correlation and relativistic effects on palladium compounds by using different methods and to compare the results of these calculations with those performed on nickel or platinum species. During the last decade, modeling of surface phenomena using ab initio methods has been of increasing interest, mainly due to important developments in the experimental study of such systems. Thus, experimental studies of the adsorption of carbon monoxide on palladium metal from (10) (a) Malmberg, C.; Scull", R.; Nylin, P. Ark. Fys. 1969,39,495. (b) Osman, R.; Ewig, C. S.; vanWazer, J. R. Chem. Phys. Lett. 1976,39, 27; 1978,54, 392. (c) Demuynck, J. Chem. Phys. Lett. 1977,45,74. (d) Chen, B. H.; Foyt, D. C.; White, J. M. Surf. Sci. 1977, 67, 218. (e) Serafiii, A.; Barthelat, J. C.; Durand, Ph. Mol. Phys. 1978,36,1341. (f) Garcia-Prieto, J.; Novaro, 0.Mol. Phys. 1980,41, 205. (g) Garcia-Prieto, J.; Novaro, 0. Int. J. Quantum Chem. 1980, 18, 595. (h) Basch, H.; Cohen, D.; Topiol, S. Isr. J. Chem. 1980,19,233. (i) Basch, H. Faraday Soc. Symp. 1980, 14, 149. (j) Anikin, N. A.; Bagaturyants, A. A.; Zhidomirov, G. M.; Kazanskii, V. B. Russ. J. Phys. Chem. 1981,55, 1154. (k) Bagus, P.; Bjorkman, C.; Phys. Reu. A 1981,23, 461. (1) Sakai, Y.; Huzinaga, S. J. Chem. Phys. 1982, 76, 2552. (m) Pettersson, L. G. M.; Wahlgren, U.; Gropen, 0. Chem. Phys. 1983,80,7. (n) Rogosik, J.; Kuppers, J.; Dose, V. Surf. Sci. 1984, 148, L653. (0)Koutecky, J.; Pacchioni, G.; Fantucci, P. Chem. Phys. 1984,84,453. (p) Baykara, N. A.; Andzelm, J.; Salahub, D. R.; Baykara, S. Z. Int. J.Quantum Chem. 1986, 29,1025. (4)Nakatsuji, H.; Hada, M. In Applied Quantum Chemistry; Smith, V. H., Schaefer, H. F., Morokuma, K., Eds.; D. Reidel: Dordrecht, 1986; p 93. (r) Low, J. J.; Goddard, W. A. J.Am. Chem. SOC.1986,108, 6115. (s) Low, J. J.; Goddard, W. A. Organometallics 1986,5, 609. (t) Schilling, J. B.; Goddard, W. A,; Beauchamp, J. L. J. Am. Chem. SOC. 1987,109,5573. (u) Balasubramanian, K. J.Chem. Phys. 1987,87,6573. (v) Yang, C. Y.; Yu, H. L.; Case, D. A. Chem. Phys. Lett. 1981,81, 170. (11) Osman, R.; Ewig, C. S.; VanWazer, J. R. Chem. Phys. Lett. 1976, 39, 27. (12) (a) Pacchioni, G.; Koutecky, J.; Fantucci, P. Chem. Phys. Lett. 1982, 92, 486. (b) Pacchioni, G.; Koutecky, J. In The Challenge of Transition Metals and CoordinationChemistry;Veillard, A., Ed.; D. Reidel: Dordrecht, 1986; p 465. (13) Shim, I. Gingerich, K. J. Chem. Phys. 1982, 76, 3833. (14) Shim,.I.; Gingerich, K. J. Chem. Phys. 1984,80, 5107. (15) Rohlfing, C. M.; Hay, P. J. J. Chem. Phys. 1985, 83, 4641. (16) (a) Salahub, D. R. In Applied Quantum Chemistry;Smith, V. H., Schaefer, H. F., Morokuma, K., Ed.; D. Reidel: Dordrecht, 1986; p 185. (b) Andzelm, J.; Salahub, D. R. Int. J. Quantum. Chem. 1986,29,1091. (17) Rohlfing, C. M.; Hay, P. J.; Martin, R. L. J. Chem. Phys. 1986, 85. 1447. (18) Langhoff, S. R.; Pettersson, L. G. M.; Bauschlicher, C. W.; Partridge, H. J. Chem. Phys. 1987,86, 268. (19) (a) Balasubramanian, K.; Feng, P. Y.; Liao, M. Z. J. Chem. Phys. 1987,87,3981. (b) Balasubramanian, K.; Feng, P. Y.; Liao, M. Z. J. Chem. Phys. 1988,88, 6955. (20) Balasubramanian, K. J. Chem. Phys. 1988,89,6310. (21) Langhoff, S. R.; Bauschlicher, C. W. Annu. Reu. Phys. Chem. 1988, 39, 181. (22) Blomberg, M. R. A.; Lebrilla, C. B.; Siegbahn, P. E. M. Chem. Phys. Lett. 1988, 250, 522. (23) Blomberg, M. R. A.; Schule, J.; Siegbahn, P. E. M. J. Am. Chem. Soc. 1989, 111, 6156. (24) Lee, S.; Bylander, D. M.; Kleinman, L. Phys. Reu. B 1989,39,4916. (25) Moore, C. E. Atomic Energy Levels; Natl. Bur. Stand. (US.) Circ. No. 467, US.GPO Washington, D.C., 1958. (26) Raghavachari, K.; Trucks, G. W. J. Chem. Phys. 1989,91,1062.
the gas phase, as well as from solution in electrochemical and colloidal systems, have become a subject of fundamental importance in surface chemi~try.~~-~O Extensive infrared spectroscopic data are now available for matrixisolated PdC0,31CO on finely divided supported metal catalyst~,~g single-crystal m e t a l ~ , ~working 9 electrodes,30 and metal colloids.= For palladium surfaces, the dominant form of adsorbed CO is bridgedz9 with a molecular frequency in the characteristic region PdO > Pd2, ing stability in the order PdC indicating that a suitable formation regime must be carefully chosen. To prepare PdC, some energetic process is needed to get Pd and C into vaporized atomic states, e.g., cold or hot plasma processing, vacuum sputtering, or laser evaporation. In all processing routes, extreme care is needed to assure an environment free of hydrocarbons, Hz,and 02 to avoid unwanted palladium compounds. Figure 1shows the equilibrium diagrams for the stoichiometric mixtures of palladium with carbon, hydrogen, oxygen, and methane, produced over a temperature range of 1000-6000 K. The palladium compounds are not present in high proportion in any of the diagrams. Polymerization of carbon is a favored process. There are two reasons for the low mole fractions of these species. First, many transition metal oxides and most transition metal carbides dissociate to their elements upon vaporization. Examples of this would include NiO and Secondly, the CISC method used to calculate the dissociation energies underestimates the (unknown) experimental value. A factor of 2, for example, in the dissociation energy corresponds to a change in mole fraction of approximately 2 orders of magnitude for PdC. However, the mole fractions of gas-phase palladium compounds calculated by using the CISC data suggest that PdC could be observed at least by mass spectrometric methods and studied by matrix isolation. The low gas-phase mole fractions of PdC do not necessarily bar their production by plasma-processingtechniques. Many species recombine upon condensation to the desired product. An example of such a system is the production of TiN.56 Because there are no thermodynamic data available for the solid phase, calculations cannot be made for this process. However, if PdC is formed, it is expected that a one-to-one stoichiometric ratio of Pd and C may be maintained due to a phenomenon which occurs during condensation of metal carbides from the gas phase (see, for example, refs 37 and 57). The equilibrium diagrams suggest that it would be possible to produce PdH by using an RF plasma. The molecule is relatively stable at temperatures where nucleation and condensation of the gas-phase species would begin to occur. Rapid cooling may produce a stable phase with the result that decomposition to hydrogen does
-
(54) The assignment of the ground state of Pdz in Lee's paper (ref 24) to be a 32; state must be a typographical error. (55) Margave, J. L. The Churacterization of High Temperature Vapors; Wiley: New York, 1967. (56) Yoshida, T.; Kawasaki, A.; Nakagawa, K.; Akashi, K. J. Mater. Sci. 1979, 14, 1624. (57) Toth, L. E. Transition Metal Carbides and Nitrides; Academic Press: New York, 1971.
Schwerdtfeger et al.
122 Langmuir, Vol. 7,No.1, I991 Table 11. Basis Set Studies on CO. basis set H F limit best HF-LCAO best CI-LCAO HFS limit exptl A STO3G 3-21G 4-31G 6-31G 6-311G 6-311+G 6-311+G*
method ref 59 ref 60 ref 61 ref 62 ref 32
HF MP2 HF HF HF HF HF
HF HF MP2 MP3 MP4 CISD CISC
E
re
-112.790 95 -112.789 1 1.128 1.126 1.128 -112.786 742 1.105 -113.209217 1.138 -111.225 450 1.146 -112.093 299 1.129 -112.552 356 1.128 -112.667 222 1.131 -112.699 492 1.124 -112.701 582 1.123 -112.771 008 1.105 -113.115070 1.139 -113.111 145 1.122 -113.140 337 1.148 -113.097 250 1.124 -113.124 097 1.132 -112.130 037
k.
Ue
-0.104 +0.110 -0.049 -0.122 -0.110 +0.176 -0.106 -0.124 +0.397 +0.600 +0.573 +0.476 +0.506 +0.185 -0.285
19.26 19.09 19-01 22.99 18.32 24.54 17.28 17.17 21.13 20.69 20.72 23.76 18.29 21.30 16.16 17.61 -0.045 19.60
a Total energies in au, optimized bond distances re in A, force constants k, in mdyn A-1 (reduced mass for CO mrd = 6.856 209; ref 32), and dipole moments we in D. The various standard basis sets have been taken from ref 38.
not occur. This is the case at room temperature for the palladium hydride system PdH,, which is stable only with mole fractions x < 0.8.58 Pd-CO. Table I1 shows the molecular properties of CO at the different levels of approximation. The calculations denoted as “HF limit” have been carried out previouslyby Sundholm using numerical HF procedure^.^^ HF wave functions and dipole moments in CO have been studied extensively in the since it is well-known that most standard basis sets at the HF level cannot reproduce the sign of the dipole moment correctly (i.e., the negative sign in p e is defined as C-O+). In contrast, basis set effects on force constants have not been studied in detail, and often very small basis sets are used in theoretical calculations of CO adsorbed on metal surface^.^ To avoid basis set superposition errors in CO frequency calculations, we carried out HF and MP2 calculations for CO using extensive uncontracted basis sets for both the C and 0 atom (basis set A in Table II),63 i.e., a (15s/8p/ 2d) basis set for C and a (15s/9p/2d) basis set for 0 (6.35.1 and 8.43.1 in Csizmadias notation)41plus additional (2s/ lp/2d) functions for C with exponents (0.04;0.016/0.03/ 0.92;0.256) and (2s/2p/2d) functions for 0 withexponents (0.075;0.029/0.054;0.019/1.324;0.445), which should almost reproduce the HF limit given in ref 43. This is indeed the case if we compare the resulting total energy to the total energy obtained by S ~ n d h o l m .The ~ ~ CISD bond length given in Table I1 is about 0.04 8, too short. This is in agreement with the CISD studies on CO recently carried out by Ahlrichs and S ~ h a r f . ~ ~ I t is well-known that HF often overestimates experimental force constants, in our case by more than 20%. Both MP and CI force constants are closer to experiment. (58) Muetterties, E. L. In Transition Metal Hydrides; Muetterties, E. L., Marcel Dekker: New York, 1971. (59) (a) Sundholm, D. Thesis, Helsinki, 1985. (b) Baerends, E. J.; Vernooijs, P.; Rozendaal, A.; Boerrigter, P. M.; Krijn, M.; Feil, D.; Sundholm, D. THEOCHEM 1985,133,147. (60) (a) Christiansen, P. A,; McCullough, E. A. J. Chem. Phys. 1977, 67,1877. (b) Huo, W. M. J. Chem. Phys. 1965,43, 624. (61) Cooper, D. M.; Langhoff, S. J. Chem. Phys. 1981, 74,1200. (62)Laaksonen, L.; Sundholm, D.; Pyykko, P. Int. J. Quantum. Chem. 1985, 27, 601. (63) The molecular properties for CO+ in this basis set: (HF) E = -112.308 684 au, re = 1.088 A, k, = 1.501 au; (MP2) E = -112.688 702 au, re = 1.092 A, k , = 2.158 au. CO- was not stable at the HF level according to the dissociation CO- CO + e-. (64) Ahlrichs, R.; Scharf, P. In Ab-Initio Methods in Quantum Chemistry; Lawley, K. P., Ed.; Wiley: New York, 1987.
-
The basis set studies on CO in Table I1 show that the polarization functions used in the 6-311+G* basis set are necessary to obtain a value for k, comparable to that of basis set A. Similar basis set studies on ke(C0) were performed by Blomberg et al.,65and their best CASSCF value agrees quite well with our CISC value. Hence, the CISC method within the 6-311+G* basis set is sufficiently accurate to study frequencyshifts in PdCO. Gavezottiand co-workers4used small basis sets to study the chemisorption of CO on a Pt cluster. Their CO force constant of 17.01 mdyn A-1 underestimates the HF limit by more than 25%. Using very small basis sets such as the STO-3Gbasis set, which overestimates the CO stretching frequency, or the 3-21G basis set, which underestimates the CO stretching frequency, can lead to large basis set superposition errors in k,(CO) and therefore to unreliable results for the CO frequency shift due to chemisorption. The 6-311+G* basis set used produces reasonable results; with the MP2 method, the force constants with these basis sets (6-311+G* and basis set A) are in almost exact agreement (Table 11). Blomberg et al. pointed out that the agreement of the MP2 force constant with experiment may be quite f o r t u i t o ~ s .That ~ ~ this is indeed the case can be seen by comparing the results of the MP2-4 series in Table 11, which indicates that the MPn series converges quite slowly for the CO force constants. However, the CISC value is in good agreement with experiment, and we have used this 6-311+G* basis set to study the CO frequency shift in PdCO. To obtain higher accuracy, larger basis sets, higher substitutions in the CI wave function, and corrections due to anharmonicity effects are necessary, as shown recently by Cooper and LanghofPl (see the best CI-LCAO in Table 11). The experimental stretching frequency for the CO molecule has been taken from Mantz et al.,awho obtained the harmonic fundamental CO stretching frequency (we) by high-resolution FTIR spectroscopy of CO in the inner cone of a C2H2/02 flame. Their value for ueis 2170 cm-l, about 20 cm-l higher than the IR matrix isolation value obtained for CO by Leroi et al. (2149 cm-l)M and the gasThis difference phase value of Lautsch et al. (2143 ~m-l).’5~ is due to anharmonicity effects in the CO potential curve, which are neglected in our calculations. In order to relate our data for the CO frequencyshift to experimentalresults, we assume that the anharmonicity constant x, does not change for CO as a result of chemisorption. The calculations on PdCO are shown in Tables 111-V in Figures 2 and 3. Experimental data are available from IR matrix isolation studies on Pd(CO), (n = 1-4) by Darling and Ogden.31 Theoretical calculations on these compounds have been performed previously by Osman et al.,ll Pacchioni et a1.,12 Rohlfing et al.,15 Salahub and Andzelm,l6and Blomberg et al.22923In all cases, pseudopotential approximations have been used except for Salahub and Andzelm’s LCGTO-LSD and Blomberg’s relativistic all-electron calculations. Andzelm and Salahub also studied CO adsorption on a larger palladium cluster using this approach.16 As shown in Table 111, HF gives only a very weak Pd-C bond in PdCO. This can also be seen from the HF orbital energies, which show the sequence expected from the isolated fragments CO and Pd; Le., we obtain for the occupied orbital field the sequence in orbital energies Pdbd,) > Pd(d8) > Pd(d,) > CO(sp,) > CO(p,) > .... The Pd(sd,) HOMO mixes slightly antibonding (65) Blomberg, M.; Brandemark, U.;Johansson, J.; Siegbahn, P.; Wennerberg, J. J. Chem. Phys. 1988,88,4324. (66) Leroi, G.E.; Ewing, G.E.; Pimentel, G. C. J.Chem. Phys. 1964, 40. 2298. ~. , ----
(67) Lautsch, W.; Rausheet, H.; Grimm, W.; Broser, W. Z. Naturforsch. 1957,12b, 307.
Molecular Properties of Single-Bonded Pd Compounds
Langmuir, Vol. 7,No. 1, 1991 123
Table 111. Molecular Properties for Pd-CO. molecule PdCO (lZ+)
method HF
MP2
ref ref ref ref ref ref ref
MP3 CISD CISC HF CI HF MP2 NR/CPF R/CPF LSD
12 12 15 15 22 22 16
rePdC
reCO
De
kePdC
kgCO
Cl.
upc
W.CO
2.211 1.909 1.996 1.993 1.965 2.722 2.230 2.056 1.882 1.99 1.91 1.83
1.107 1.153 1.132 1.127 1.139 1.128 1.155 1.130 1.185
0.130 1.126 0.589 0.601 0.801 0.065 0.455 0.57 1.62 0.95 1.43 2.9
0.376 2.261 1.375 1.480 1.763
23.472 16.327 21.021 20.699 18.713
1.434
169 407 321 333 362
2417 2057 2306 2291 2186
317
2045
1.86
exptl molecule PdOC (IC+)
1.34 method HF MP2
repdo
reCO
4.152 3.398
1.106 1.140
1.796
16.44
De 0.004 0.018
kePdO
keCO
Cle
0.003 0.006
23.964 18.412
0.075
a Optimized bond distances re in A, dissociation energies De in eV, force constants ke in mdyn A-1, and dipole moments p e in D. Experimental value from Darling and Ogden (ref 31). The optimized HF total energy of PdCO is E = -5050.187 949 57 au and for PdOC is E = -5050.183 312 19 au. Positive sign in the PdCO dipole moment corresponds to Pd+CO-.
Table IV. Molecular Properties. for P d C O for Various 'c P d C Bond Distances #d method rco
AE
kco
Aw
rPdC inf 2.3 2.2 2.1 2.0 1.9 1.8 inf 2.3 2.2 2.1 2.0 1.9 1.8 inf 2.3 2.2 2.1 2.0 1.9 1.8 inf 2.3 2.2 2.1 2.0 1.9 1.8
HF 1.1053 1.1058 1.1067 1.1079 1.1097 1.1120 1.1151 0 -0.123 -0.130 -0.107 -0.037 +0.137 +0.483 23.550 23.504 23.469 23.241 22.932 22.540 22.054 0 -5.7 -7.4 -19.2 -35.2 -55.6 -81.2
MP2 1.1397 1.1422 1.1440 1.1464 1.1494 1.1530 1.1573 0 -0.661 -0,807 -0,954 -1.076 -1.125 -1.027 18.368 17.810 17.527 17.172 16.755 16.281 15.758 0 -32.6 -49.4 -70.6 -95.8 -124.8 -157.3
MP3 1.1229 1.1235 1.1244 1.1257 1.1275 1.2299 1.1330 0 -0.422 -0.497 -0.561 -0.590 -0.541 -0.347 21.937 21.704 21.540 21.319 21.033 20.669 20.219 0 -12.4 -21.2 -33.1 -48.6 -68.4 -93.2
CISD 1.1213 1.1221 1.1231 1.1246 1.1266 1.1292 1.1324 0
-0.418 -0,499 -0.568 -0.600 -0.551 -0.350 21.740 21.456 21.273 21.028 20.722 20.346 19.895 0 -15.2 -25.1 -38.3 -55.0 -75.6 -100.7
CISC 1.1317 1.1330 1.1343 1.1359 1.1382 1.1410 1.1443 0 -0.533 -0.637 -0.733 -0.794 -0.775 -0.603 19.988 19.624 19.409 19.116 18.838 18.461 18.028
Table V. Mulliken Population Analysis for PdCO. atom Pd
orbital 5s 5Pa 5Px
4d, 4 4 4da q 2s 2PS 2Px q 2s 2Pa 2PW q
C
0
HF -0.009 -0.065 -0.005 1.817 1.898 2.000 +0.471 1.886 0.999 0.578 -0.187 1.967 1.356 1.469 -0.281
NR-MSXa 0.670 0.250 0.005 1.780 1.887 2.000 -0.484 1.161 1.163 0.558 +0.560 1.358 1.616 1.549 -0.072
R-MSXa 0.745 0.229 0.006 1.752 1.879 2.000 -0.496 1.149 1.153 0.570 +0.558 1.358 1.613 1.545 -0.061
a H F (ref 38), nonrelativistic (NR) and quasirelativistic (R) multiple scattering Xa (MSXa) methods (ref 69) a t r(Pd-CO) = 1.9 A. q is the total atomic charge.
-0.2
0
-20.4 -31.7 -49.1 -65.1 -86.7 -111.9
-0.4
-0.6
ODistances r in A, total energy difference AE in eV, C-0 stretching force constants k in mdyn A-l, C-0 frequency shift Au in cm-'. inf: rPdC= 50 A.
-0.8
carbon s- and p,-orbitals, whilst the CO(sp,) mixes slightly bonding Pd(sd,) orbitals. The experimental frequency for monomeric PdC160 has been measured to be 2044.7 cm-l in a Kr matrix.% This results in a frequency shift of about -95 cm-l with respect to matrix-isolated CO (2140 cm-1).mt3'J Our calculated frequency shifts on the different levels of the theory a t the optimized geometries are as follows: AW(HF) = -12.6, Aw(MP2) = -122.0, Aw(MP3) = -49.3, AW(CI) = -56.2, and Ao(C1SC) = -72.2 cm-'. The CISC value is in reasonable agreement with e ~ p e r i m e n t .The ~ ~ chemisorption-induced frequency shift (-78 f 2 cm-l) for terminal CO on palladium colloids by Mucalo and Gooney% is almost coincident with the (CISC) value (-72 cm-l). This suggests that relativistic effects may not be very important for the frequency shift in CO. It was pointed out recently that relativistic effects tend to be smaller in ligand-
-1.o
-1.2
r(Pd-CO)
A
Schwerdtfeger et al.
124 Langmuir, Vol. 7, NO.1, 1991
simply due to the fact that HF cannot describe the d,. (Pd)-a*(CO) back-bonding correctly. Large differences in populations are obtained for the a Pd-CO bond, so that the 2s(CO) 5s5pg(Pd) charge transfer is not correctly described within the HF approximation. This results in a reversed charge distribution in PdCO, i.e., Pdo.6+CO0.& at the HF level compared to PdoWOo.5+obtained from MSXa calculations. However, this does not change the sign of the dipole moment in PdCO, Table 111. CI accounts for this charge transfer in the a-bond by including excitations into the Pd(5s) orbital. Hence, correlation is necessary for the proper description of the Pd-CO bonding, and we assume that this will also be the case for studying CO adsorption of Pd-cluster or Pd-surfaces. As also shown in Table V, relativistic effects do not change the charge distributions significantly and therefore may not be very important for the PdCO molecule. However, Blomberg et al. showed recently that relativistic effects shorten the Pd-CO bond length by 0.08 A and increase the Pd-CO dissociation energy by about 0.48 eV.22 Blomberg et a1.,& B a u ~ c h l i c h e rand , ~ ~ Kao and M e s ~ m e analyzed r~~ the frequency shift in the CO stretching frequency of NiCO in detail. Blomberg et al.65obtained similar results on NiCO compared to our results on PdCO; the CO frequency shift at the SCF level in NiCO has been calculated to be -125 cm-', 88% of the experimental value (-142 cm-1).'3 However, the frequency shift has been found to be very sensitive to the orbital range chosen in the CISD procedure.65 Also, Bauschlicher found little CO Ni u-donation but large Ni(n) CO(A*)back-donation. This is in contrast to our findings on PdCO (Table V) and may explain why the experimental CO frequency shift in PdCO is smaller than that of NiCO. Mavridiset al. recently found little metal to ligand A-donation for CO binding to monocations of the early transition metals.74 To study the PdCO interaction in more detail, we restricted the active orbital range in the CI procedure in different ways. We firstly allowed only for CO Pd a-donation. Secondly, we added two more virtual orbitals to the active orbital range, allowing also for P d ( r ) CO(A*)back-donation (excitations only into the first three LUMOs). Thirdly, we restricted the occupied space to the first HOMO of a-symmetry, which describes the Pd-CO a-bond (mainly the Pd(4d,)-CO(a) bond), and to the first five orbitals, describing mainly the 4d core of palladium. The CISC results are shown in Table VI. We first notice that the low-lying occupied CO orbitals are important for obtaining C-0 force constants comparable to experiment. However, this seems not to be the case for the CO frequency shift. HF results in about 50% of the total frequency shift if compared to the CISC value (66.3 cm-'). Allowing only for excitations into the first a-orbital has little effect on Au; an increase of only 3.4 cm-' has been calculated compared to the HF value. Pd(?r) CO(A*) backdonations are important, as can be seen from a further increase Aw of 20.0 cm-'. Obviously, the correlation of the palladium 4d orbitals is important for obtaining most of the frequencyshift in PdCO, even if the CO force constants are overestimated and similar to the HF value. Similar effects have been obtained a t the MP2 and MP3 levels. Another result of the bond weakening in CO due to chemisorption on Pd is a slight increase in the CO bond length as shown in Figure 2, which has been calculated to be about 0.007 A at the CI level. Similar results were
-
-160
I
.. ..
8 -
9
1
,
I
.
- ,
.
r(Pd-CO) r
.
r
,
.
r .
9
A
. I . .
Figure 3. HF, MP2, MP3, and CI frequency shifts for the C-0 stretching mode of Pd-CO. For the experimental frequency shift (refs 28 and 311,r,(Pd-CO) = 1.965 8, from the CISC calculations is assumed.
Note that the data listed in Table V have been obtained by a numerical four-point fit procedure, while the force constants in Table I1 are obtained where possible by using analytical gradients.% The grid for the polynomial fit has been kept constant to avoid numerical errors within one series of PdCO calculations, i.e., rco = 1.06,1.10,1.14, and 1.18A. The HF method underestimates the experimental frequency shift -Au by more than 70 cm-'. This is partly due to the long Pd-CO distance at the HF level (2.2 A). Figure 3 shows that most of the frequency shift is gained at smaller Pd-C bond distances. However, when we compare the HF with the calculated CI value at 1.9 A (cf. Table IV), HF still underestimates the experimental value of -95 cm-'. Note that Pacchioni and Koutecky calculated an increase in the CO force constant due to chemisorption on palladium.12 They argued that a full vibrational analysis is necessary in order to obtain a reasonable result for the CO stretching frequency. This certainly contradicts our results on PdCO. As mentioned above, the basis set for the CO molecule must be carefully chosen to obtain a sensible description of the CO stretching in Pd,CO systems. Recently, Barnes and Bauschlicher carried out ab initio calculations on several early transition metal carbonyls.'j8 These authors also report values for the frequency shift of single-bonded ScCO (330 cm-l), TiCO (280 cm-I), and VCO (240 cm-l). These frequency shifts correlate with the A* back-donation, which decreases from Sc to V.G8 The relatively low frequency shift in PdCO suggests that A* back-donation is much weaker in this compound (but is larger, for example, in PdzC0).22 To analyze this in more detail, we performed a Mulliken population analysis for PdCO at rPdC = 1.9 A as well as nonrelativistic and quasirelativistic MSXa calculations,69 which include correlation in an empirical way. The MSXa calculations are particularly useful to compare with HF results, since this method is used by many workers.70 The palladium 4d, populations are very similar in all three approximations, as are the carbon and the oxygen 2p, populations (Table V). Hence, it seems that the underestimation of the CO stretching force constant is not (68) Barnes, L. A.; Bauschlicher, C. W. J . Chem. Phys. 1989,91,314. (69) Cook,M.;Case, D. A. Program XASW, VAX-IBM version 2; personal communication. (70) Salahub, D. R.; Zerner, M.C. The Challenge of d and f Electrons: Theory and Computation;American Chemical Society: Washington, DC, 1989.
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-
-
-
-
(71)Bauschlicher, C. W.Chem. Phys. Lett. 1985, 115, 387. (72) Kao, C. M.;Messmer, K. P. Phys. Reu. B 1985, 31,4835. (73) DeKock, R. L. Inorg. Chem. 1971,10,1205. (74) Mavridis, A.; Harrison, J. F.; Allison, J. J . Am. Chem. SOC.1989, 111,2482.
Molecular Properties of Single- Bonded Pd Compounds Table VI. CI Frequency Shifts for Difference Active Orbital Ranges. method active OS active VS k(PdC-0) k(C-0) Aw CISCa CISC b CISC c CISC d CISCe CISC f
0 full full full 1 5
0 full 1 3 full fill
22.907 18.815 23.246 22.973 23.139 22.271
24.550 19.988 23.961 24.077 24.077 24.077
-33.2 -66.3 -36.6 -56.6 -48.0 -69.8
a At a fixed Pd-CO distance of 1.993 A (CISD value in Table 111) and 50 A (free C-0). Force constants k(PdC-0) and k(C-0) in mdyn A-l, C-0 frequency shift Au in cm-1. Restrictions to the full active orbital range are indicated in the columns active OS (occupied space) and VS (virtual space), which gives the number of the active occupied and virtual orbitals, respectively. In detail: (a) HF; (b) full active orbital range; (c) excitations restricted to the a-LUMO; (d) excitations restricted to the first three orbitals of u- and n-symmetry; (e) excitations restricted to the u-HOMO; (0 excitations restricted to the palladium 4d core.
obtained by Pacchioni and Koutecky.12 This effect is very small but may become large for CO bonding at +positions on palladium surfaces, which show a larger frequency shift (-193 cm-li than that measured for the +position.28 Recently, McKee and Worley studied Rh/CO species.75 These authors calculated an increase in the CO bond distance of 0.012 8, when bound on single Rh (the frequency shift in RhCO is about the same compared to PdC0).76 Our calculated MP2 Pd-CO bond distance com ares quite well with Rohlfing and Hay's result15of 1.882 obtained by using relativistic pseudopotentials. This indicates that relativistic effects in Pd-CO are quite small; e.g., the relativistic change in the bond distance is probably smaller than 0.03 8, and therefore within the accuracy of the approximations used. The Pd-CO bond distance of SalahublGof 1.83 8, is probably too short, due to the local spin density approximation (LSD) used (compare to Blomberg's relativistic CPF bond distance of 1.91 A).zz Experimental data for the Pd-CO distance are available only for $-bridged CO on Pd(100) surface from LEED The calculated Pd-CO (r(Pd-CO) = 1.93 f 0.07 stretching frequency of 333 cm-l at the CISD level is in reasonable agreement with the experimental value of Darling and Ogden.31
x
Conclusions The equilibrium diagrams for the plasma processing of PdC (Figure 1)show that this compound may be prepared (75) McKee, M. L.; Worley, S. D. J. Phys. Chem. 1988,92, 3699. (76) (a) Yates, J. T.; Duncan, T. M.; Worley, S. D.; Vaughan, R. W. J. Chem.Phys. 1979, 70,1219. (b) Rice, C. A.; Worley, S. D.; Curtis, C. W.; Guin, J. A.; Tarrer, A. R. J. Chem. Phys. 1981, 74, 6487. (77) Behm, R. J.; Christmann, K.; Ertl, G.; VanHove, M. A,; Thiel, P. A.; Weinberg, W. H. Surf. Sci. 1979,88, L59.
Langmuir, Vol. 7, No. 1, 1991 125
in small mole fractions via plasma synthesis. However, thermodynamic data for the solid-state PdC are necessary to determine whether synthesis in larger amounts is possible. However, plasma processing could be used as a source of species such as PdC which could be studied by spectroscopic methods. Of particular interest are the ground states of PdC and PdO. CISC calculations suggest that for both molecules the 311state may be the ground state. However, the limitations of the CISD method have been discussed, and MCSCF studies would be necessary to obtain more accurate results for the molecularproperties of the diatomic palladium compounds presented in this paper. It may be interesting to note that in all cases the MP3 results compare well with CISD, but this is not the case for the MP2 method. This suggests that MP3 is appropriate to study ground states of larger palladium compounds. In this connection, it can be noted that the MP3 dissociation energy for RhCO calculated by McKee and Worley is in very good agreement with the experimental result.75 The CO frequency shift in PdCO has been analyzed by HF, MP, and CI methods. The bond weakening in CO, which is due mainly to d,(Pd)-?r*(CO) back-bonding,leads to a frequency shift of -95 cm-' 31 (calculated CI value -72 cm-l) and to an increase in the CO bond length of about 0.007 8,. However, the T* back-bonding is smaller than found in other transition metal c a r b o n y l ~ , 6which ~~~~ explains the relatively small frequency shift in CO chemisorbed on palladium surfaces. The agreement with the measured frequency shift on palladium colloids and gasphase PdCO indicates that PdCO is a good model for chemisorption of CO on $-positions on palladium surfaces. Also, Andzelm and Salahub pointed out that the PdC distance and binding energy are rather insensitive to the cluster size.16 A detailed theoretical analysis of CO adsorption on surfaces compared to adsorption on small metal clusters using ab initio methods would be very useful. Acknowledgment. We are very grateful to the IBM New Zealand Ltd., the CIS Computer Centre at the University of Auckland, the Rechenzentrum der Universitat Stuttgart, and the ANU Supercomputer Facility in Canberra for providing large amounts of computer time. P.S. is very indebted to the Alexander von HumboldtStiftung and the University Grants Committee (New Zealand) for financial support. We thank Peter D. W. Boyd and Laurie P. Aldridge for critically reading this paper, Murray K. Wu for preparing the equilibrium diagrams of PdC, and the referee of this paper, whose critical comments resulted in some significant improvements. Registry No. Pd, 7440-05-3; P d H , 13940-18-6; PdC, 1231334-7; PdO, 1314-08-5; PdF, 85302-83-6; Pdl, 12596-93-9; Pd(CO), 41772-86-5.
