J. Phys. Chem. 1991, 95, 112-1 18
112
All-Electron and Relativistic Effective Core Potential Study of Rhodium Compounds Gilbert J. Mains* Department of Chemistry, Oklahoma State university, Stillwater, Oklahoma 74078
and John M. White Department of Chemistry, University of Texas, Austin, Texas 7871 2 (Received: March 27, 1990; In Final Form: July 2, 1990) Ab Initio molecular orbital calculations have been made for Rh, (x = l-4), Rh(C0)2, RhCO, Rh,CO, RhH, RhH3, RhC, HRhC, RhCH, Rho, Rho2, Rh-02, H,RhOH, and Rh,03. All-electron calculations used the best basis set of Huzinaga, the Shim extension, and a further extension. Effective core potential calculations were performed by using the Los Alamos single- and double-{ basis sets. In addition relativistic effective core potential calculations were employed. The Rh, calculations find a node in the HOMO that may offer an explanation for variation in catalytic efficiency with cluster size. Rhodium carbonyls were found to be weakly bound at the SCF level and will require correlation for meaningful investigation. RhH, was confirmed to have C,, symmetry. The energy and structures shown by the RhCH calculations suggest a mechanism for methanation. Unoptimized structures for RhzO3 suggest that the oxygen triple-bridged structure is more stable than the bent O=RhORh=O structure.
Introduction The chemistry of transition metals is very rich and, despite extensive exploration, remains one of the most important challenges to theoretical and experimental chemistry. Indeed, few books undertake comprehensive discussion of all transition compounds’ and even review articles2-6 are very limited in scope. The source of the richness stems primarily from the near degeneracy of the 3d and 4s (or 4d and 5s) electrons that permit the promotion of d electrons into the next higher quantum shell and the near degeneracy of the d orbitals themselves, both of which lead to a large variety of electronic states. These partially filled d orbitals give rise to the extraordinary catalytic properties of the transition-metal surfaces. Further complexity is introduced by relativistic effects including significant spin-orbit coupling. Rhodium, one of the most intriguing transition metals, lies within the 4d block elements and finds extensive use in catalysis.’.* While a number of rhodium-containing molecules, Le., RhH,9 RhH2,10RhC,” RhCH3,I2 RhHC0,I3 Rh(CO),,I3 and R h P l 4 have been examined theoretically, there has been no broad study like that reported here. Computational Methods All molecular orbital calculations were performed with the GAUSSIAN86 and GAUSSIAN88 program, developed by Pople and his colleague^,'^ on Vax 1 1 /780, Cray XMP/48, and CRAY-2 ( I ) Cotton, F. A.; Wilkinson, G. Advanced Inorganic Chemistry; John Wiley & Sons. Inc.: New York, 1988. (2) Bauschlicher, C. A,; Langhoff, S. R. Annu. Rev. Phys. Chem. 1988, 39, 181.
( 3 ) Rao, C. N. R. Annu. Rev. Phys. Chem. 1989, 40, 291. (4) Merer, A. J. Annu. Rev. Phys. Chem. 1989, 40, 407. (5) Morse, M. D. Chem. Rev. 1986, 86, 1049. (6) Shim, 1. Mat.-Fsy. Medd-K. Dan. Vidensk. Selsk. 1985, 41, 147. (7) Dickson, R. S. Homogeneous Catalysis with Compounds of Rhodium and Iridium; D. Reidel Pub. Co.: Dordrecht, Holland, 1985. (8) See: Cannon, K. C.; Jo, S. K.; White, J. M. J . A m . Chem. Soc. 1989, 111, 5064 and citations therein. (9) Balasubramanian, K.; Liao, D. J . Chem. Phys. 1988, 88, 317. (IO) Balasubramanian, K.; Liao, D. J . Phys. Chem. 1988, 92, 6259. ( I I ) Shim, 1.; Gingerich, K. J . Chem. Phys. 1984, 81, 5937. (12) Bauschlicher, C. W.; Langhoff, S. R.; Partridge, H.; Barnes, L. A. J . Chem. Phys. 1989, 91, 2399. (13) (a) McKee, M. L.; Worley, S . D. J . Phys. Chem. 1988,92,3699. (b) McKee, M. L.; Dai, C. H.; Worley, S. D. J . Phys. Chem. 1988, 92, 1056. (14) Balasubramanian, K.; Liao, D. J . Phys. Chem. 1989, 93, 3989. (15) (a) GAUSSIANB~: Frisch, M. J.; Binkley, J. S.; Schlegel, H. B.; Raghavachari, K.: Melius. R.; Martin, R. L.: Stewart, J. J. p.; Rohlfing, C. M.; Kahn, L. R.; Defrees, D. J.; Seeger, R.; Whiteside, R. A,; Fox, D. J.; Fluder, E. M.; Pople, J . A. Carnegie-Mellon Quantum Chemistry Publishing Unit, : M. J.; Head-Gordon, Pittsburgh, PA 15213; 1984. (b) G A u S S I A N ~ ~Frisch, M.; Schlegel, H . B.; Raghavachari, K.; Binkley, J. S.;Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whitesides, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Fluder, E. M.; Topiol, S.; Pople, J. A . Gaussian, Inc., Pittsburgh, PA.
0022-3654191/2095-0112$02.50/0
computers. For the all-electron calculations, the energy surfaces were explored by using the Huzinaga basis set,I6 with and without extra p and d functions as described later. Electron correlation was included, using Merller-Plesset perturbation theory.” These facilities are part of the aforementioned programs. Vibrational frequencies for optimized molecules were calculated from analytical second derivatives18 and were used to ensure that the computed structures were stable states. Restricted H F calculations were used for closed-shell molecules and analogous U H F procedures were used for the higher multiplicity calculations. Although the spin contamination was usually small, (S2)values before and after spin annihilation are reported. Where optimizations were incomplete, only the final total spin, S, is reported. The figures were prepared on a Macintosh microcomputer by copying the optimized G A U S S I A N ~ output ~ / ~ ~ into Molecular Editor19 and then cutting and pasting the resultant structure into MacDrawm so that the atoms could be identified and electron spins labeled.
Results and Discussion Rh. The energy levels of atomic Rh are well known spectroscopically21and are depicted graphically in Figure 1, where the different electron configurations giving rise to the various states are shown on the arrows. The spin-orbit effects are of the order of 10 kcal/mol and are clearly not negligible. The calculated energies for these states using various basis sets are given in Table 1, where the following basis set notation has been employed: HB is Huzinaga’s best basis set16 and is described as 4333/433/43, where the numbers denote the number of Gaussians used in the SHIM following orbital sequence, 1s,2~,3~,4~,5~/2p,3p,4p/3d,4d; is Huzinaga’s best basis set augmented with two 5p functions,6 exponents = 0.2 and 0.09, respectively, and SHIM-SU adds a single 5d function, exponent = 0.100 to the S H I M basis set; LANLlMB and LANLlDZ, are the Los Alamos effective core basis sets resident in GAUSSIANBBby Hay and Wadt;22RECP is the relativistic core basis set of LaJohn et aI.*, Both pseudopotential basis sets employ 3/3/4 Gaussians to describe the 5s/5p/4d orbitals. All calculations were restricted to five d orbitals (16) Huzinaga, S.; Andzelm, J.; Klobukowski, M.; Radzio-Andzelm, E.; Sakai, Y.; Tatewaki, H . Gaussian Basis Sets f o r Molecular Calculations; Elsevier: Amsterdam, 1984. (17) Maller, C.; Plesset, M. S. Phys. Reu. 1934, 46, 678. (18) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. f n t . J . Quantum Chem., Quantum Chem. Symp. 1979, 13, 225. (19) Wargo, R.; McFerren, D.; Smith, A. Drexel University, Philadelphia, PA, 1986. (20) Cutter, M. Apple Computer, Inc., Cupertino, CA, 1985. (21) Moore, C. E. Atomic Energy Levels, Natl. Bur. Stand. ( U S . ) Circ. 467: US.GPO: Washington, DC, 1949. (22) Hay, P. J.; Wadt, W. R. J . Chem. Phys. 1985, 82, 270. (23) LaJohn, L. A.; Christiansen, P. A.; Ross, R. B.; Atashroo, T.; Ermler, W . C. J . Chem. Phys. 1987, 97, 2812.
0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. I, 1991 113
All-Electron and RECP Study of Rh Compounds TABLE I: Summary of Rh Atom and Ion Calculations: Energies (au) basis seta UHF/ Huzinaga MP2/Huzinaga M P3/ Huzinaga M P4/ Huzinaga PUH F/SH IM PM P2/S H I M PMP3/SHI M PMP4/SHIM PUHF/SHIM-SU PMP2/SH IM-SU PMP3/SH I M-SU PMP4/SHIM_SU PUHF/LANLIMB PMP2/LANLl MB PMP3/LANLI MB PMP4/LANLI MB PUH F/LANLI DZ PMP2/LANLI DZ PMP3/LANDLIDZ PMP4/LANLI DZ PU H F/RECP PMP2/RECP PMP2/RECP PMP4/RECP experimentd
Rh (2D) -468 1.6876 -468 1.6894 -468 1.6900 -468 I .69 10 -4681.6141 -468 1.7060 -468 1.7095 -4681.71 16 -468 1.6948 -468 1.751 1 -468 1.7469 -468 1.7647 -22.01 25 -22.01 75 -22.0192 -22.0208 -22.0738 -22.1493 -22.1466 -22.1604 -22.3987 -22.4062 -22.4086 -22.41 02
Rh (4F) -468 1.6600 -468 1.6640 -468 1.6652 -468 1.6658 -468 1.7 132 -468 1.7227 -468 1.7253 -468 1.7264 -468 1.7226 -468 1.7520 -468 1.7542 -468 1.7593 -22.0894 -22.0927 -22.0939 -22.0947 -22.09 17 -22.1369 -22.1403 -22.1478 -22.3 963 -22.4040 -22.4067 -22.4082
‘All calculations used 5 d orbitals. bRh(4F)
-
-
Rh(2D). ERh(4F)
Rh’ (3F) -468 1.49 1 1 -468 1.4915 -468 1.49 I6 -468 1.49 17 -468 1.4977 -468 1SO30 -468 1SO39 -468 1.5042 -468 1 SO43 -468 1 S246 -468 1.5255 -468 1.5279 -21.8567 -2 1.8595 -21.8609 -21.8621 -21.8633 -21.899 1 -21.901 1 -2 1.9067 -22.1 562 -22.1 61 3 -22.1629 -22.1641
Rh+(3F)
+ e-.
*
AEcxcitb -0.0276 -0.0254 -0.0248 -0.0252 +0.099 1 +0.0167 +0.0158 +0.0148 +0.0278 +0.0009 +0.0073 -0.0054 +0.0769 +0.0752 +0.0747 +0.0739 +O.O 179 -0.01 24 -0.0063 -0.01 26 -0.0024 -0.0022 -0.00 19 -0.0020 +0.34‘
AEionil 0.1 689 0.1 725 0.1736 0.1741 0.21 55 0.2 197 0.22 14 0.2222 0.2183 0.2274 0.2287 0.23 14 0.2327 0.2332 0.2330 0.2326 0.2284 0.2371 0.2392 0.241 1 0.2401 0.2427 0.2438 0.2441 0.2742
dReference 21. EAverage over j.
40 n 7
0
E
I K!
30
V Y 20
v
x t n L
a,
c
10
W n
““.5
a4Fj.5
“3.5
“‘F1.5
a24.5
a%5
a%
“’F2.5
“”p.5
‘“9,s
“’p0.5
State Figure 1. Spectroscopic energy levels and electronic configurations for Rh. The ordinate is in kcal/mol and the abscissa designates the spectroscopic state using the notation of ref 21. The exact (spectroscopic) energy (kcal/mol) is shown on the top of each bar and the assigned electron configuration is shown at the end of the vertical arrow.
instead of the computationally convenient six. The effects of correlation using second, third, and fourth-order Merller-Plesset perturbation theory, MP2, MP3, MP4(SDTQ), are shown. As can be seen, the SHIM modification improves the energy at the U H F level. We have carried this one step further and added a diffuse d function, exponent = 0.1, in the basis set SHIM-SU, which further improves the total energy and ionization energy. Observe that none of the basis sets provide an adequate description of the 4F-2D energy difference. In fact, the better basis sets inverted the order of these two states upon addition of correlation. The lowest 2D state is only 0.0128 au above the ground state. The proximity of these states is one of the many reasons that calculations are difficult for transition metals. The ionization potential, 0.2742 au (7.36 eV), is better reproduced at all levels of calculation and is only 10.9% too low when the relativistic effective core basis set was used. Excitation is poorly described at all levels and one should consider transition states, etc., calculated for transition metals with considerable caution. Morokuma et al.24*25 performed calculations with two PH3 molecules 2.60 A on either side of Rh to simulate the Wilkinson catalyst, but for the SHIM basis set the systems with added phosphine became (24) Daniel, C.; Koga, N.; Han, J.; Fu, X. Y.; Morokuma, K. J. Am. Chem. SOC.1988, 1 IO, 3773. (25) Koga, N.; Morokuma, K. J. Phys. Chem. 1990, 94, 5454.
Figure 2. Structures for Rh, isomers. Electron-pair bonds are shown as heavy black lines. Approximate atomic locales of other electrons are shown by vertical heavy arrows. Arrow pointing up is a spin; arrow pointing down is p spin. (a) Rh2 ground state, 5Z. UHF/RECP bond length: 2.21 1 A, (s2) before annihilation = 6.0738, after = 6.0012. (b) Rh3, *A1, lowest energy, not o timized. UHF/RECP bond lengths: Rhl-Rh2 = Rhl-Rh3 = 2.94 Rh2-Rh3 = 3.745 A, s = 3.535. (c) Rhombic Rh4, 9A”, lowest energy, not optimized. UHF/RECP bond lengths: Rhl-Rh2 = Rhl-Rh4 = 3.265 A, Rhl-Rh3 = 3.115 A, Rh2-Rh4 = 5.591 A. Bond angles: Rh3-Rh2-Rhl = 62’. s = 4.0319. (d) Tetrahedral Rh4, ’A”, lowest energy, not optimized. UHF/RECP bond lengths: Rhl-Rh2 = Rhl-Rh2 = Rhl-Rh4 = 3.062 Bond angles: Rh-origin-Rh = 109.5’. s = 3.2758.
1,
highly polar. The dominant Mulliken population corresponded to do2d I 2d-ll d22d-21 SI, as expected for the 4F state, although there was some mixing among the d orbitals in these calculations due to symmetry breaking of the Fock matrix. The HOMO is in the a system and is an “s” orbital for the 4F state and a “des" hybrid orbital for the 2D state.
114
The Journal of Physical Chemistry, Vol. 95, No. 1, 1991
TABLE 11: Summary of Rhz Calculations: Energies (au) and Interatomic Distance (A) basis set Rh#Z) re Rh2(lX) re -9363.3167 2.283 -9363.3107 2.623 UHF/SHIM-SU 2.945 UHF/LANLIMB -44.07918 2.147 -44.08496 UHF/LANLIDZ -44.14423 2.181 n.c.' 3.266 -44.67376 2.21 1 -44.6931 U H F/ R ECP "n.c. = no calculation.
Rhz. Since there have been extensive studies of diatomic rhodium using both relativistic effective core potential^'^ and all-electron calculations,6,26we shall report only on the differences between our calculations and those reported previously. These results are presented in Table I1 and Figure 2a. Balasubramanian,I4 who found a ground state, noted the possibility of 11 2 diatomic states in the absence of spin-orbit coupling so it is not surprising that different authors find different ground states. In our work, the 5Z was the lowest U H F energy state found at the all-electron level, in agreement with S h i m 6 It is interesting to note that both Los Alamos pseudopotential calculations give internuclear distances significantly shorter than the all-electron or the RECP calculation. The Mulliken population analysis of this state found only one bonding electron in the u orbital, regardless of which basis set was used. For the all-electron calculation, the 5 Z population is du,2d~,4ds~d*g2du,1db,4sugi and only the sugl (the HOMO) has significant overlap and contributes to the bonding, in agreement with the early work of Norman and Kolari.26 For the core potential case, the 52 populations is du,Zd*,4ds,4d?rBZd8,4du~1su~1, with only the sugl contributing to the bonding. However the order of the d6, and d* were inverted in the Los Alamos core calculations. The 5Zcould %e formed from the combination of two atoms accompanied by a redistribution of one s electron into the 6 orbitals. It could also be formed by the combination of a 4F and a 2D atom. Nothing can be learned from examination of the dissociation energies since the Rh2 diatomics are all unstable relative to the atoms at these levels of calculation, as found by Shim6 Thermochemical measurements of Cocke and Gingerich2' find a dissociation energy of 66.9 f 5.0 kca I / mol. T h e all-electron ' Z population obtained was dr,4dr2d62db;dsu;, where the bonding was accomplished by do s hybridization. The single-{ Los Alamos basis set (LANLI MB) and the RECP basis set were also able to hybridize and optimize, as shown in Table 11. However, hybridization did not occur in the Los Alamos double-{calculation that dissociated. Note that both the Los Alamos single-{ (LANLIDZ) and the RECP calculations found the ' Z state to be the ground state. The all-electron population was found to be d ~ , ~ d a , ~ d 6 ~ d 6 , 4 d ~ , Since ~ d u , the ~ . outer eletrons were all antibonding. it is not surprising that the state was dissociative. Rhj. The lowest energy obtained for all-electron calculation was -1 4045.1 392 au using the SHIM basis set. The unoptimized geometry of this state corresponds to an apex angle of 87' and bond lengths of 2.28 A. The Mulliken population analysis indicated bonding between the apex atom and each of Rh atoms on the legs of the isosceles triangle and no bonding interactions between the terminal atoms. A number of runs using the SHIM-SU basis sets resulted in energies that were higher (-14045.0738 au) but which indicated that the apex Rh atom, 1.85 A distant, was donating some of its outer s electron to a diffuse orbital similar to the sug bond of the diatomic molecule, constrained to the bulk rhodium distance, 2.69 A. This diffuse orbital result is similar to that observed by Sellers28for Nb3 and is entirely reasonable. The only prudent conclusion, based on these limited all-electron calculations, is that energies and bonding analysis are very sensitive to the basis set used. Triatomic rhodium was also extensively explored by using the RECP basis sets. A similar result was obtained, Le., the apex Rh atom donated
+
(26) Norman, J. G . , Jr.: Kolari, H. J. J . Am. Chem. SOC.1978, 100, 791. (27) Cocke, D. L.: Gingerich, K. A . J . Chem. Phys. 1974, 60, 1958. (28) Sellers, H. J. Phys. Chem. 1990. 94, 1338.
Mains and White electrons into the one-electron bond between the Rh atoms, spilling a small amount into the p orbitals. However on further optimization of structure, the three atoms formed an isosceles triangle, bond angle 80" with bond lengths 2.94 A, giving the lowest energy, -67.2498 au. The HOMO has a node between Rh, and Rh2-Rh3, see Figure 2b. Dropping the multiplicity from eight to six raised the RECP energy to -67.2069 au. Our current model for Rh3 is that of an atom weakly bound to Rh2 by a scarcely occupied, diffuse orbit. Rh4. Attempts at all-electron calculations failed because of disk limitations of the various computers used. However, we were successful in performing RECP calculations on tetraatomic Rh, but not full optimizations. Two starting configurations of Rh, were explored, a planar rhomobohedral configuration and a tetrahedral arrangement, as shown in Figure 2. The tetrahedral conformer (Figure 2d) had a total electronic energy of -89.6 160 au, corresponding to a UHF atomization energy of 15.6 kcal/mol. The state appears to be 'A,, but the assignment is uncertain. The HOMO orbital is diffuse, does not involve the d orbitals of the p system, and is antibonding, Le., has a node between the on-top atom and the base. The on-top atom has three unpaired electrons like a atom; the lower three atoms share the remaining three electrons and are more like 2D atoms. The planar structure (Figure 2c) is much more tightly bound. The 9A" energy was -89.67140 au, corresponding to an U H F atomization energy of 54.1 kcal/mol, the lowest Rh4 energy found. Examination of the highest orbitals revealed that significant a-system spd hybridization was involved in the bonding. Although there are eight unpaired spins to be distributed, three are located on each of the Rh atoms that are farthest apart and only one each on the Rh atoms that are closest together. Thus the Rh atoms that are further apart are not very different from atoms, whereas those closest together are more like 2D atoms. These clusters are formed by converting 2.2 s orbitals from three 4F atoms to d electrons and placing the remaining 1.8 electrons in the top two molecular orbitals, which are very different for these conformers. The Mulliken population analysis of the rhombus shows that all the Rh atoms are bonded together, the largest off-diagonal terms are between the Rh atoms that are closest together, and the HOMO is nodeless. There is no dp orbital involvement in the a-system molecular orbital of the on-top atom in the tetrahedral conformer, accounting in part for the much weaker atomization energy. Interestingly, the only stable structure of Rh4(CO)12is tetrahedral.29 Experimentally, Kaldor et aL30 found that Rh, clusters are more reactive toward D, when x > 2. Rh, had about 20% of the reactivity of bulk Rh. Rh4 clusters are almost half as reactive as larger clusters. If the interaction between hydrogen and Rh, is dissociatve, one would expect electron donation into the u* state of H2, which would be best accomplished by cluster orbitals with an node. As we have noted, in the case of Rh,, the HOMO does exhibit a node at the apex Rh atom. In the case of the Rh4 rhombus structure, the HOMO was symmetric and nodeless. On the other hand, the HOMO for tetrahedral Rh4 does have a node between the on-top atom and the three-atom base. It is tempting to visualize a H, (D2) molecules interacting with the HOMO of Rh, or Rh4, which could donate into the empty u* state and cause dissociation. Using this application of Woodward-Hoffman rules,31one could then understand why a Rh atom and Rh2 are not reactive whereas Rh, and higher clusters show catalytic behavior. Indeed, the variation in reactivity for cluster sizes of 5 to 17 found by Kaldor may be due to the number of nodes found in the HOMO'S of these clusters. Figure 2 illustrates this nodal behavior, which certainly requires further study. This idea suggests that on-top Rh atoms could be more labile than atoms in a plane, i.e., reconstruct more easily, and show higher catalytic activity. There is experimental evidence that flat Rh particles are less reactive than multifaceted particles.32 Tetrahedral Rh4 should (29) Heilweil, E. J.; Casassa, M . P.; Cavanagh, R. R.; Stephenson, J. C. Annu. Reo. f h y s . Chem. 1988, 40, 143. (30) Zakin. M. R.; Cox, D. M.; Kaldor, A. J . Chem. f h y s . 1988,89, 1201. ( 3 1 ) Woodward, R. B.; Hoffmann, R. The Conseruation ofOrbital Symmetry; Academic Press: New York. 1969
The Journal of Physical Chemistry, Vol. 95, No. I , 1991 115
All-Electron and RECP Study of Rh Compounds
TABLE 111: Summary of RhJCO), Calculations: Energies (au), Bond Lengths (A), and Bond Angles (dez) basis set Rh(C0)2 rRhC rco LC-Rh-C LRh-C-0 Rh(CO)(*Z) rRhC rco UHF/SHIM-SU UHF/LANLl MB U H F/LAN L 1 DZ U H F/RECP
n.c." n.c. -247.52 1Ob -247.9 157'
2.09' 2.1 Ob
1.17' I . 12'
103' 103'
1 78' 1 78'
-4794.4540 -134.7014' -1 34.7205' -135.1535'
2.074 2.156' 2.156' 2.1'
1.1 18 1.18' 1.18' 1.13'
Rh(C0)(4X) -4794.4255' -134.7449' -1 34.7667 -135.1749'
rRhC
rco
2.2' 2.077' 2.077' 2.90'
1.1 1 1.17' 1.171' 1.10'
'
On.c. = no calculation. 'Not optimized. 'See refs 13 and 34.
be more readily ionized than planar Rh4. Finally, we should note that reducing the multiplicity (coupling the electron spins) raised the energy for both the rhombic and the tetrahedral conformers, Le., for the planar rhombic the 7A'' state was -89.6477 au, only 14.8 kcal/mol higher, and for the tetrahedral structure, the 9A1energy was raised to -89.601 1 au, some 9.3 kcal/mol. It is interesting that the 7A' rhombus does show a node in the HOMO. In view of the proximity of these states at the UHF level, one must expect that these states will be even closer together when correlation is added. Thus, planar Rh4 can generate a node in its HOMO without the expenditure of much energy. The energy required to promote a planar atom to the on-top position in Rh4 is -35 kcal/mol at the U H F level and probably would be reduced considerably when correlation is added. Thus, if the existence of a node is the prerequisite for catalytic behavior, Rh4 can achieve it easily. Rh,-CO. The adsorption of C O on Rh surfaces is a much studied phenomena of considerable practical importance, especially in automotive three-way catalysts. It is this fact that motivates e ~ p e r i m e n t a land ~ * ~theoretical ~ of these systems. It is well established that the mechanism by which CO interacts with transition-metal surfaces is via a CJ lone-pair electron donation from the carbon atom into the vacant metal orbital combined with a d r metal back-donation into the ?r* orbitals of CO. The sum of forward and back donation results in almost no net electron transfer. A number of adsorption sites on rhodium have been identified,32consistent with the weak Lewis acid/base adduct nature of the interaction. The results of our studies are summarized in Table I11 and Figure 3. The first ECP studies were reported by McKee, Dai, and W ~ r l e y , who ' ~ found Rh-CO in the ,A state was bound at the U H F level by only 4.4 kcal/mol using LANLIDZ, and this binding energy improved to 41.5 kcal/mol at MP3. On the basis of LANLlMB, Rh-CO was unbound at the U H F level but was bound by 20.1 kcal/mol at MP3. The UHF dissociation energy (into CO and ,D atom) was 1.7 kcal/mol in agreement with McKee. Experimentally the desorption energy of C O from an on-top site is about 30 kcal/ mol.35 Note that the CO distance is increased slightly by electron donation from the Rh into the ?r* orbitals of the CO. The normal mode analysis provided a CO stretch frequency of 21 16 cm-', when the usual 0.89 correction is applied, in good agreement with e~periment.,~ The similarly corrected (0.89) Rh-C stretch frequency is calculated to be 347 cm-', compared to the experimental values36between 420 and 470 cm-*. The addition of a second CO, perpendicular to the first, could not be optimized in a reasonable period of time by use of either the LANLl DZ basis or the RECP basis. In both cases, the C-Rh-C bond angles increased from 90' to 103' and the Rh-C-0 bond angles decreased from 180' to 178'; however, the U H F energy surfaces are very flat. The final result is given in Figure 3a. McKee was able to optimize this structure using the LAND1 Z basis set, suggesting that our final structure is close to the optimum. It is interesting that the bonding energy for the dissociation of Rh(CO), was 48.3 kcal/mol for the LANLDl Z case and 25.8 kcal/mol for the latter. On the basis of the McKee, Dai, and Worley results,13one could expect these numbers to increase significantly upon including correlation. In fact, these studies suggest that progress in these calculations (32) Dictor, R.; Roberts, S. J . Phys. Chem. 1989, 93, 5846. (33) Barnes, L. A.; Bauschlicher, C. W. J. Chem. Phys. 1989, 91, 314. (34) McKee, M. L. (private communication). (35) Paebles, H. C.; White, J. M.; Campbell, C. T. S u r - Sci. 1985, 150, 120. (36) Dubois, L. H.; Somorjai, G. A. Surf. Sci. 1980, 91, 514.
W
t
(4 Figure 3. Structures for rhodium carbonyl isomers. Electron-pair bonds are shown as heavy black lines. Approximate atomic locales of other electrons are shown by vertical heavy arrows. Arrow pointing up is a spin; arrow pointing down is p spin. (a) Rhodium dicarbonyl, 2B2,lowest energy, not optimized. UHF/RECP bond lengths: Rh-C = 2.100 A, C-0 = 1.1 17 A. Bond angles: C-Rh-C = 103O, Rh-C-0 = 178'. s = 0.5 192. (b) Rhodium carbonyl, 2Z optimized. UHF/SHIM-SU bond lengths: Rh-C = 2.074 A, C-0 = 1 . I 18 A. s = 0.5017. (c) Rhodium carbonyl, 4X,optimized. UHF/LANLIDZ bond lengths: Rh-C = 2.077 A, C-0 = 1.171 A. Bond angles: 180'. s = 1.5002. (d) Dirhodium carbonyl, not optimized, 3B2. UHF/RECP bond lengths: RhRh = 2.69 A, Rh-C = 1.902 A, C-0 = 1.099 A. s = 1.0270.
will require optimization that includes correlation. We report now exploratory calculations in which CO was brought up to 5Z, 3Z, and 'Z states of Rh,. Two all-electron calculations using the SHIM-SU basis sets in which the C O molecule was located 1.9 A from the 32state of Rh,, first directly above a Rh atom and then centrally above the Rh-Rh bond in a bridge position. The difference in U H F energy was 21.3 kcal/mol, favoring the bridge configuration. Exploration of these systems using the RECP basis set had limited success. The lowest energy obtained was for a 3B2state, CO in the bridged position, 1.9 A from two Rh atoms at the bulk distance (2.69 A), Le., -157.7417 au, corresponding to a UHF dissociation energy of 13.2 kcal/mol into 31:Rh, and CO. RhH. Since the electronic states and potential energy surfaces using core potentials for RhH have been reported in some detai19*37 and incorporating relativistic effects and spin-orbit coupling, we shall again give our results as they differ from the previous authors (Table IV and Figure 3). The 3-21G basis set was used for hydrogen. The 3A state is the ground state, in agreement with previous studies. The bond length is somewhat longer than in the RECP results, as expected. The bonding orbital is an dsp hybrid, but the d orbital contribution is negligible, and the bond disso(37) Langhoff, S. R.; Pettersson, L. G. M.; Bauschlicher,C. W.; Partridge, H. J. Chem. Phys. 1987,86, 268. (38) Huber, K. P.; Herzberg, G. Constants of Diatomic Molecules; Van Nostrand Reinhold: New York, 1979.
116 The Journal of Physical Chemistry, Vol. 95, No. 1, 1991
Mains and White
TABLE IV: Summary of RhH Calculations basis set UHF/HB UH FISH I M-SU UHF/LANLIDZa UH F/LANLI DZ" U H FIRECP'
Reference 13.
R h H (3A) n.cC -4682.2674 -22.6618 -22.6833 (see ref)
rC
1.690 1.708? 1.708 1.55 (javg)
RhH('II) -4682.6349 n.c. n.c. n.c. (see ref)
TC
1.687
1.62 (javg)
RhH('Z) -4682.5755 -4682.2242 -22.5950 -22.6278 (see ref)
re
1.636 1.591 I .673? 1.673 1.56 G avg)
Reference 28. cn.c. = no calculation.
TABLE V Summary of RhH3 Calculations: Energies (au), Bond Lengths (A), and Bond Angles (deg) basis set UHF/ H B//U H F/ H B UH F/LANL I MBD UHF/LANLI DZ//LANLI MB" U H F/RECP
R h H 3( 'A') -4683.6998 -23.6992 -23.9331 -24.0737
LH-R-H 97.18 86.3 86.3 80.6
re 1.515 1.518 1.518 1.476
RhH3(TS) -4683.5908 -23.6206 -23.8293 -2 3.9 374
re
1.552 1.537 1.536 1.489
LH-R-H 120.0 120.0 120.0 120.0
Reference 34.
TABLE VI: Summary of RhC Calculations: Energies (au) and Distances basis set RhC(ZZ) re UHF/HB -4719.4535' 2.12 UHF/SHIMr -4723.22 1.55 UH F/LAN L I DZ n.c. U H F/ REC P -60.1388 1.812 exptd 1.613
(A) RhC(211)
re
RhC(411)
1.65 2.044
-4719.5752 -4723.1 7 -59.8066 -60.0956
n.ca -4723.20 -59.8614 n.c.
2.123 1.94 1.984 1.933
1.655
"n.c. = no calculation. bNot optimized.
