Theoretlcal Studies of the First- and Second-Row Transition-Metal

NASA Ames Research Center, Moffett Field, California 94035 (Received: March 2, 1990; ... The study of gas-phase bimolecular reactions of transition-me...
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8656

J . Phys. Chem. 1990, 94, 8656-8663

Theoretlcal Studies of the First- and Second-Row Transition-Metal Dimethyls and Their Positive Ions Marzio Rosi,? Charles W. Bauschlicher, Jr.,* Stephen R. Langhoff, and Harry Partridge N A S A Ames Research Center, Moffett Field, California 94035 (Received: March 2, 1990; In Final Form: June 8, 1990)

Using the modified coupled-pair functional (MCPF) method and Gaussian basis sets of better than double-{ plus polarization quality, we have determined equilibrium structures for the ground and selected low-lying excited states of the first- and second-row transition-metal dimethyls and their positive ions. For all these metals, the dimethyl insertion products are studied to elucidate trends in the bonding. We also study the electrostatically bound M+-C2H6complexes for selected metals where this structure is more stable than the insertion product. In most of the dimethyls there is significant sd hybridization leading to a C-M-C bond angle of less than 134'. For Mn, Fe, Co, Ni, and Cu, the greater stability of the 3d"4s2as compared with the 3d"+I4s1 atomic occupation leads to 4s4p hybridization, resulting in linear equilibrium structures. The metal-methyl binding energies are compared with the experimental data when available and with analogous calculations on the monomethyl transition-metal systems. Comparison of the first and second methyl binding energy reveals large variations, which can be explained in terms of the energy separations between the atomic states and the loss of atomic d-d exchange.

I. Introduction The study of gas-phase bimolecular reactions of transition-metal systems with organic molecules is an active area of research. This is particularly true of reactions involving transition-metal ions, since the bond energies can be determined by such techniques as guided ion beam mass spectrometry, collision-induced dissociation using ion cyclotron resonance, and Fourier transform and photoionization mass spectrometries.IP2 In particular, guided ion beam mass spectrometry has yielded accurate bond strengths for many of the transition-metal hydride and methyl positive i0ns.l However, only very recently has there been any experimental data for two-ligand transition-metal ions such as M(CH3),+. An understanding of the thermochemistry of such species is important to bridge the gap between gas-phase metal-ligand chemistry and condensed-phase systems. These two-ligand bond energies are related directly to the energetics of reactions involving insertion of the metal into hydrocarbon bonds (oxidative addition). Experimental data for the second ligand binding energy are presently available for the S C ( C H ~ ) ~Ti(CH3I2+,4 +? V(CHJ2+? Fe(CHJ2+,6 C O ( C D ~ ) * +and , ~ Ni(CH3)2+8ions. To our knowledge, no experimental data exist for any of the neutral transition-metal dimethyls. Theoretical calculations offer an attractive alternative to experiment for determining the spectroscopic constants and bond energies of transition-metal systems. Accurate calculations are now available for both the neutrals and ions of the first- and second-row transition-metal m o n o h y d r i d e ~ ~and - ~ ~ monomethyls.'6-21 These studies show that the bonding is similar for the transition-metal monohydrides and monomethyls. Fewer investigations have been performed for twdigand systems, though some data exist, particularly for the dihydride species. For example, Balasubramanian and co-workers have studied the lowlying electronic states of S C H , , ~YH2,23 ~ NbH2?4 AgH2,25PdH,,26 T c H , , ~ RuH,,,' ~ RhH2,28 YH,+,29 ZrH,+,2g NbH,+,30 and MoH,+.~O Schilling, Goddard, and Beauchamp3' have carried out generalized-valence-bond and configuration-interaction (CI) calculations to compare the bonding in the O H 2 +and MoH,' systems. Alvarado-Swaisgood and HarrisonI5 have studied the ScH2+ion. Rappe and Uptonj2 have considered the reaction of Sc+ with H2 to form ScH,+. Siegbahn, Blomberg, and Bauschl i ~ h e r have ) ~ studied the lowest low-spin and high-spin potential surfaces of FeH,, CoH,, and CuH,. Blomberg et al.,' have performed complete-active-space self-consistent-field/externally contracted C1 calculations for NiH2, PdH, and Ni(CH3)2. They find that the bonding in NiH, and Ni(CH,), is very different, 'Current address: Department of Chemistry, University of Perugia, I06100, Perugia, Italy.

0022-3654/90/2094-8656$02.50/0

and attribute this to the greater directionality of the M-C bond than the M-H bonds. These observations have also been noted

(1) Armentrout, P. B.; Georgiadis, R.; Polyhedron 1988, 7, 1573 and references therein. (2) Buckner, S. W.; Freiser, B. S. Polyhedron 1988. 7, 1583. (3) Sunderlin, L.; Aristov, N.; Armentrout, P. B. J. Am. Chem. Soc. 1987, 109, 78. (4) Sunderlin, L.; Armentrout, P. B. In?. J. Muss Spectrom. Ion Processes. In press. (5) Aristov, N.; Armentrout, P. B. Private communication. (6) Burnier, R. C.; Byrd, G. D.; Frieser, B. S. J . Am. Chem. SOC.1981, 103, 4360. (7) Hanratty, M. A.; Beauchamp, J . L.; Illies, A. J.; van Koppen, P.; Bowers, M. T. J . Am. Chem. SOC.1988, 110, I . (8) Halle, L. F.; Crowe. W. E.; Armentrout, P. B.; Beauchamp, J. L. Organometallics 1984, 3, 1694. (9) Chong, D. P.; Langhoff, S. R.; Bauschlicher, C. W.; Partridge, H. J . Chem. Phys. 1986,85, 2850. (10) Langhoff, S. R.; Pettersson, L. G. M.; Bauschlicher, C. W.; Partridge, H. J. Chem. Phys. 1987, 86, 268. ( 1 1) Pettersson, L. G. M.; Bauschlicher, C. W.; Langhoff, S. R.; Partridge, H. J. Chem. Phys. 1987, 87,481. (12) Schilling, J. B.; Goddard, W. A,, 111.; Beauchamp, J. L. J . Am. Chem. SOC.1986, 108, 582. (13) Schilling, J. B.; Goddard, W . A,, 111.; Beauchamp, J. L. J . Phys. Chem. 1987, 91, 5616. (14) Schilling, J. B.; Goddard, W. A,, 111.; Beauchamp, J. L. J . Am. Chem. SOC.1987, 109, 5565. (I 5 ) Alvarado-Swaisgood, A. E.; Harrison, J. F. J . Phys. Chem. 1985,89, 5198. (16) Alvarado-Swaisgood, A. E.; Harrison, J. F. J . Phys. Chem. 1988,92, 2757. (17) Alvarado-Swaisgood,A. E.; Allison, J.; Harrison, J. F. J . Phys. Chem. 1985, 89, 2517. (18) Ziegler, T.; Tschinke, V.; Becke, A. J . Am. Chem. SOC.1987, 109, 1351.

(19) Bauschlicher, C . W.; Langhoff, S. R.; Partridge, H.; Barnes, L. A. J. Chem. Phys. 1989, 91, 2399. (20) Schilling, J. B.; Goddard, W. A,, 111; Beauchamp, J. L. J . Am. Chem. Soc. 1987, 109, 5573. (21) Blomberg, M. R. A.; Schule, J.; Siegbahn, P. E. M . J . Am. Chem. SOC.1989, I 1 I, 6 156 and references therein. (22) Balasubramanian, K. Chem. Phys. Lett. 1987, 135, 288. (23) Balasubramanian, K.; Ravimohan, Ch. Chem. Phys. Lett. 1988,145, 39. (24) Balasubramanian, K.; Ravimohan, Ch. J . Phys. Chem. 1989, 93, 4490. (25) Balasubramanian, K.; Liao, M. Z. J . Phys. Chem. 1989, 93, 89. (26) Balasubramanian, K.; Feng, P. Y . ;Liao, M. 2.J . Chem. Phys. 1988, 88, 6955. (27) Balasubramanian, K.; Liao, D. J . Phys. Chem. 1988, 92, 6259. (28) Balasubramanian, K.; Wang, J. Z. J . Chem. Phys. 1989, 91, 7761.

0 1990 American Chemical Society

Transition-Metal Dimethyls and Their Positive Ions

The Journal of Physical Chemistry, Vol. 94, No. 24, 1990 8657

n

Figure 1. Dimethyl structure.

by Low and G ~ d d a r din ~their ~ study of the oxidative addition and reductive elimination reactions involving Pd and Pt. Finally, Quelch and Hillier35 have optimized the geometry and computed the harmonic frequencies of CH3CuH at the Hartree-Fock level. Considering that the C-C bond strength in C2H6 is significantly larger than the M-C bond strength in MCH3 or MCH3+,insertion of the metal into the C-C bond is not always thermodynamically favorable. Thus for some metal ions the most stable structure is one where the metal ion is bound electrostatically to C2H6. However, even in cases where the ethane complex is more stable, a barrier to interconversion might result in a metastable insertion product once it is formed. Thus to compare with guided ion beam experiments, both species and their interconversion would have to be studied. Also, most reactions involve metal atoms complexed with ligands, and many ligands preferentially stabilize the insertion product^.^',^^ Thus in this work we focus on a comparison of the bonding in the dimethyl systems and investigate the M+-C2H6 complexes only for those systems where this structure is thermodynamically much more favorable than the insertion product. The methods employed in this study are briefly described in the next section. The results section is subdivided into a discussion of the M(CH3)2+and M(CH3)*systems and a comparison with other work. Our conclusions are given in section IV. 11. Methods

We use the same basis sets and correlation approach that was used in our earlier study of the transition-metal m0nomethy1s.l~ For the C and H basis sets we use the (13s 8p 6d)/[4s 3p Id] and (8s 6p)/[3s lp] atomic natural orbital (ANO)36basis sets. The first-row transition-metal basis sets are of the form (14s 1 l p 6d 3f)/[8s 6p 4d I f l . Note that the sets o f f functions designed for 3d correlation from ref 19 are used, Le., those based on a three-term fit” to a Slater-type orbital; the exponent varies in steps of 0.4, from 1.6 for Sc to 4.8 for Cu. For the second-row transition-metal atoms we use the relativistic effective core potentials (RECPs) developed by Hay and These RECPs include the outermost core orbitals, the 4s and 4p, in the valence shell and can therefore be used in a correlated treatment. The supplemented valence basis sets and (3f)/[ 1 fl polarization sets described in ref 19 are employed. The final second-row transition-metal basis sets are of the form (6s 5p 5d 3f)/[5s 4p 4d If]. As discussed in ref 19, further supplementation of the basis sets with diffuse or polarization functions has only a small effect on the results. In all calculations only the pure spherical harmonic components of the basis functions are used. In all of the dimethyl S C F calculations, the orbitals are constrained to transform according to C, symmetry, even though at (29) Das, K. K.;Balasubramanian, K. J. Chem. Phys. 1989, 92, 2433. (30) Das, K. K.; Balasubramanian, K. J. Chem. Phys. 1989, 91, 6254. (31) Schilling, J. B.; Goddard, W. A., 111.; Beauchamp, J. L. J. Phys. Chem. 1987, 91. 4470. (32) RappC, A. K.; Upton, T. H.J . Chem. Phys. 1986, 85, 4400. (33) Siegbahn, P. E. M.; Blomberg, M. R. A.; Bauschlicher, C. W. J . Chem. Phys. 1984, 81, 1373. (34) Low, J. J.; Goddard, W. A. Organomerollics 1986, 5, 609. I.ow. J. J.; Goddard, W. A. J. Am. Chem. Soc. 1986, 108, 6115. (35) Quelch, G. E.; Hillier, 1. H. Chem. Phys. 1988, 121, 183. (36) Almlijf, J.; Taylor, P. R. J. Chem. Phys. 1987, 86, 4070. (37) Stewart, R. F.J. Chem. Phys. 1970, 52,431. (38) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 299.

Figure 2. Ethane complex with C, symmetry.

Figure 3. Ethane complex with C,symmetry.

linear C-M-C geometries the systems have D3hsymmetry. Studies show that the D3d structure is only 1 kcal/mole more stable. Two structures are considered for the ethane complexes, both with a staggered configuration for ethane. The dimethyl structure, together with the two ethane structures, are pictured in Figures 1-3. Extensive electron correlation must be included in order to compute accurate De values. Previous studies of the transitionmetal hydrides”’ and mono methyl^'^ suggest that the modified coupled-pair functional (MCPF) approach39is an appropriate level of treatment for these systems. For the ground states of the dimethyls the percentage of the MCPF wave function contained in the reference configuration drops from about 85% for the transition-metal atoms on the left side of the row to about 75% for Fe(Ru) to Ni(Pd). Previous experience has shown that for single bonds the MCPF method yields reliable results even when the reference percentage is as low as 60%. Thus we expect that the MCPF results for the dimethyls should be as reliable as for the monomethyls and hydrides. For the M(CH3)2systems, we have correlated the metal nd and (n + 1)s electrons and the seven valence electrons on each CH3. While correlation of the 3s and 3p electrons on the left side of the first transition row affects the atomic separations,4 the hydride calculationsg suggest that metal inner-shell correlation has only a small effect on D,. Likewise correlation of the 4s and 4p electrons for the second transition row is expected to shorten the M-C bond length by up to 0.1 a. and to affect the atomic separations on the left-hand side of the row but is not expected to have a large effect on DClo Therefore, we do not consider correlation of these “semicore” electrons in this work. For the open-shell systems we impose the first-order interacting space restriction41 to reduce the CI expansion length. (39) Chong, D. P.; Langhoff, S. R.J. Chem. Phys. 1986,84,5606. See also; Ahlrichs, R.; Scharf, P.;Ehrhardt, C. J . Chem. Phys. 1985, 82, 890. (40) Moore, C. E. Atomic Energy Levels, U S . Natl. Bur. Stand. (US.) Circulation No. 467, 1949.

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The Journal of Physical Chemistry, Vol. 94, No. 24, 1990

TABLE I: Experimental Atom and Ion Excitation Energies (in eV) for the First- and Second-Row Transition-Metal Atoms' atom

ion

lower state

upper lower upper state expt state state expt First-Row Transition-Metal Atoms s c 3d'4s2 (2D) 3d24s' (4F) 1.43 3d14s1('D) 3d2 (3F) 0.60 Ti 3d24s2(3F) 3d34s' (5F) 0.81 3d24s1(4F) 3d3 (4F) 0.10 V 3d34s2(4F) 3d44s1 (6D)0.25 3d4 (5D) 3d34s1(SF) 0.33 3d44s1(6D) 1.52 C r 3dS4s1(7S) 3d44s2(5D)1.00 3dS (%) Mn 3d54s2 (%) 3d64s' (6D) 2.14 3dS4s' (7S) 3d6 ('D) 1.81 0.25 Fe 3d64s2('D) 3d74s' (SF) 0.87 3d64s' (6D) 3d7 (4F) 3d74s1('F) 0.43 co 3d74s2(4F) 3d84s' (4F) 0.42 3ds OF) Ni 3d94s1OD) 3d84s2 ('F) 0.03 3d9 (2D) 3d84s' (4F) 1.08 cu 3dI04s1 ('S) 3d94s2 (2D) 1.49 3dI0 (IS) 3d94s1 (3D)2.8 I

Y Zr Nb Mo Tc Ru Rh Pd Ag

Second-Row Transition-Metal Atoms 4d15s' (3D)0.15 4d15s2(2D)4d25s1 (4F) 1.36 5s2 (IS) 4d25s2 ('F) 4d35s1 ('F) 0.59 4d25s1(4F) 4d3 (4F) 0.32 4d'Ss' (SF) 0.33 4d45s1 (6D) 4d35s2 (4F) 0.18 4d4 ('D) 4d45s' (6D) 1.59 4dS5s1(7S) 4d45s2 (5D) 1.47 4dS (%) 4d55s2 (%) 4d65s1 (6D)0.41 4d'Ss' (7S) 4d6 (5D) 0.52 4d65s' (6D)1.09 4d75s' (5F) 4d65s2 (5D)0.87 4d7 (4F) 4d75s1('F) 2.13 4d85s' (4F) 4d9 (2D) 0.34 4d8 ('F) 4dI0 (IS) 4d95s1 ('D) 0.95 4d9 (2D) 4d85s1(4F) 3.19 4d95s1(3D) 5.04 4dI05s' ( 2 S ) 4d95s2 (2D)3.97 4d1" (IS)

OThe results are the j-averaged values are reported in ref 40.

This is not expected to affect the accuracy of the computed De values. The bonding in the dimethyls commonly involves a contribution from several atomic asymptotes. The promotion energy required to reach the excited states is an important factor in determining the contribution from these atomic states. Since we commonly refer to these quantities, we have summarized the experimental separations between the most relevant states of the metal atom and ion in Table I . As shown in previous work,19 the level of theory used here reproduces the experimental separations reasonably well. In the previous study of the hydrides and monomethyls, we included relativistic effects42for the first-row transition-metal atoms using first-order perturbation theory.43 In general, this increases the error in the atomic separations and would, therefore, be expected to degrade the description of the molecular systems. However, this was avoided by dissociating to the asymptote that most resembled the molecule and adding empirical corrections for correlation and the computed error in the atomic separations. This approach worked well because the bond was mostly s-like and the error was primarily in the treatment of the largely spectator d electrons. In the dimethyls the strong d involvement in the bonding makes such a correction scheme less appropriate. Thus we ignore relativistic effects for the first transition row, as they increase the error in the atomic separations. We discuss the errors associated with this approach below. The M(CH3)2De value is determined with respect to M in its computed ground state (the calculated ground states agree with experiment for all ions and for all neutral atoms except Ni) and two planar CH3 molecules. Since this was not the same procedure used for the monomethyls, we have recomputed the monomethyl binding energies using this new procedure. The dissociation energy of the ethane complex is computed with respect to M+ and free ethane. To facilitate a discussion of the bonding, we report Mulliken d populations and total charges on the metal based on the MCPF natural orbitals. In discussing the thermochemistry of the ethane structures, we use the MCPF value of 90.3 kcal/mol for the C-C bond energy of C2H6. The calculations were performed on the NASA Ames CRAY Y-MPl832 and CRAY X-MP114se comDuters using the MOLECULE-SWEDEN44 and GRADSCfl'' program'systems.

-

(41) Bunge, A. J . Chem. Phys. 1970, 53,20. McLean, A. D.; Liu, B. Ibid. 1973, 58, 1066. Bender, C. F.; Schaefer, H. F. Ibid. 1971, 55, 7498. (42) Cowan, R. D.; Griffin, D. C. J . Opt. SOC.Am. 1976, 66, 1010. (43) Martin, R. L. J . Phys. Chem. 1983, 87, 750.

Rosi et al. 111. Results and Discussion A . Metal Ion-Ethane Complex. We consider the ethane

complexes for the Cr+, Mo+, Cu+, and Ag+ ions, since these are the systems where this structure is definitely preferred over the insertion product. For Ag+ and Cu', the geometry is optimized at the S C F level by using analytic first and second derivative methods using the same RECP treatment for Ag and basis sets of better than double-{ quality (the basis sets are smaller than the ones employed in the MCPF calculation). The binding energy is then computed by using the MCPF method (at the S C F geometry) in the larger basis described in the Methods section. For Ag+-C2H6 we find two stationary points, with similar binding energies of 11.1 (C, structure) and 9.7 kcal/mol (C2 structure)s e e Figures 2 and 3. For Cu+-C2H6only a C2structure is found with a binding energy of 16.2 kcal/mol. At the S C F level, the dimethyl structures for both Cu+ and Ag' convert to the ethane complexes without a barrier. The ethane in the complex is only slightly distorted from the free ligand geometry. For example, the Ag+-C$& C, binding energy is only 0.8 kcal/mol smaller if the free C2H6geometry is used. Therefore, the Cr+-C2H6 and Mo+-C2H6 structures were optimized at the MCPF level, using the free C2H6 geometry. For the C2 and C, structures there are only one and two degrees of freedom, respectively. We find the C, structure to be the most stable for both Cr+ and Mo', with binding energies of 10.7 and 9.0 kcal/mol, respectively. The C2 structures are about 1.5 kcal/mol less stable. Since the bonding is electrostatic in origin, it varies with the size of the metal ion, and so the maximum binding energy of about 16 kcal/mol occurs for the Cu+ complex, as Cu+ has the smallest ionic radius. The binding energy decreases to about 10 kcal/mol for Cr+ and Mo', and it is likely that metal ions to the left of Cr+ and Mo' will have even smaller binding energies. B. Dimethyl Compounds. We optimize the dimethyl geometry at the MCPF level using a numerical grid approach. To reduce the number of degrees of freedom, we fix the C-H bond length at 2.07 a,, since studies of representative dimethyls as well as previous studies of the monomethyl systems indicated that this bond distance is nearly optimal in all of the systems. For Mn(CH3)2 and Fe(CH3)2in linear C-M-C geometries, we find the staggered and eclipsed structures to be virtually identical in energy. Thus for all other metals we consider only the eclipsed form. With this restriction the linear geometries have D3,, symmetry. When we bend the C-M-C bond, the symmetry on each MCH3 subunit is fixed as C3vto maintain the overall symmetry to be C2". The molecules can be bent such that the two hydrogens in the C-M-C plane approach each other, or such that the four hydrogens out of the plane approach. This latter geometry is pictured in Figure 1. We optimized SC(CH,)~+ at the SCF level and found that this structure is only 0.04 kcal/mol above the optimal one where the two methyls both rotate in the same direction by about 10'. Thus we ignore the methyl rotation to retain higher symmetry. With these restrictions there are three geometrical parameters to optimize: the C-M distance and the C-M-C and M-C-H bond angles. For some systems all three parameters were fully optimized. However, since the M-C-H angle is weakly coupled to the other two degrees of freedom, for most systems we optimized r(M-C) and L(C-M-C) for an initial choice of L(MCH) and then optimized L(MCH) separately. The other two parameters were reoptimized only when L(MCH) changed by more than a few degrees. We previously used this procedure for the monomethyls,19 as did Schilling et aL20 We orient the molecule such that the metal and carbons lie in the xy plane, with they axis containing the C, element of the C, group. Therefore the a l irreducible representation contains the metal s, dk2-X2-y2,and d,2+ orbitals and the positive combination of the open-shell orbitals on the methyls. The b2 irreducible (44) MOLECULE-SWEDEN is an electronic structure program system written by J . Almlof, C. W. Bausch!icher, M. R. A. Blomberg, D. P. Chong, A. Heiberg, S. R. Langhoff, P.-A. Malmqvist, A. P. Rendell, B. 0. Roos, P. E. M. Siegbahn, and P. R. Taylor. (45) GRADSCF is a vectorized SCF first- and second-derivativecode written by A. Komornicki and H. King.

The Journal of Physical Chemistry, Vol. 94, No. 24, 1990 8659

Transition-Metal Dimethyls and Their Positive Ions TABLE 11: MCPF Spectroscopic Constants and Populations for the First-Row Transition-Metal Dimethyl Positive Ions

re( M-C) bo) L(C-M-C) L( M-C-H) 3d population net metal charge T. (cm-')

SC(CH3)2+ 'A,

2A,

4.027 106.5 110.8 1.05 1.33

3.898 105.8 108.9 2.15 1.18

3A7

rc(M-C)(ao) L(C-M-C) L( M-C-H) 3d population net metal charge T. (cm-I)

re( M - W a o ) L(C-M-C) L( M-C-H) 3d population net metal charge T, (cm-')

3.767 110.6 107.3 4.42

3.914 111.1 109.3 2.21 1.24 709

1.10

3.931 95.6 108.7 2.23 1.19 2165

'A,

3.873 97.7 107.8 3.19 1.09 1342

3.815 100.2 113.1 3.17 1.09 2912

3.827 96.3 106. I 5.24

3.732 97.0 105.4 6.28 0.94

1.01

3.746 96.4 105.9 6.33 0.95 470

'B, 3.753 101.2 105.2 7.38 0.86 Ni( C H ,)

L(C-M-C j L( M-C-H) 3d population net metal charge T, (cm-I)

Ti(CH3)2+ 2Bl 2A2

V(CH3)2t 'BI

3.808 105.9 108.6 3.30 1.14

re( M-C)(ao) f(C-M-C) L( M-C-H) 3d population net metal charge T. (cm-I)

91.2 106.4 8.48 0.80

Co(CH3)2+ 'A2 3.800 94.7 105.2 7.32 0.90 1322

,+

TABLE III: MCPF Spectroscopic Constants and Populations for the Second-Row Transition-Metal Dimethvl Positive Ions

3A1 3.785 97.5 105.0 7.37 0.90 1451

Cu(CH3)2+

90.9 103.1 9.48 0.70

180.0 99.4 9.64 0.6 1 5442

representation contains the metal d, orbital and the negative combination of the open-shell methyl orbitals. The bl and a2 irreducible representations contain the dyz and d,, orbitals, respectively. For the dimethyls, both the la, and 1b2 bonding orbitals are doubly occupied and the remaining d orbitals are not involved in the bonding. I . Transition-Metal Dimethyl Positive Ions. The optimized structures and selected Mulliken populations for the ground state and selected low-lying states for the first- and second-row transition-metal dimethyl positive ions are summarized in Tables I1 and 111, respectively. The bonding in all molecules arises from a mixture of the metal d"s' and d"+l atomic states, as is evident in the d populations, although obscured to some extent by the large metal to methyl charge donation by Sc+, Y+, and Zr+. Since all of the ground states involve two sd hybrids on the metal, the bonding is similar in both rows, resulting in the same ground state for the corresponding first- and second-row transition-metal dimethyl positive ions. All of the states involve two metal-carbon u bonds, one in a , and one in b2 symmetry. The l a , bonding orbital (in valence notation) involves a variable degree of metal s and d character. This leaves four nonbonding metal valence orbitals, 2al, 3a,, I b,, and la2. The ratio of s and d character in the two nonbonding a , orbitals depends to a large extent on the separation of the metal dnsl and del asymptotes. When the d"sl atomic state is more stable, there is greater s character in the bonding orbital, conversely more of the s character is in the 3al orbital when the del state is low-lying. Thus for the dimethyl ions sd hybridization occurs for all systems resulting in strongly

3B1 r,(M-C)(ao) L( C-M-C) L( M-C-H) 4d population net metal charge T, (cm-I)

r,(M-C)(ao) L(C-M-C) L( M-C-H) 4d population net metal charge

r.(M-C) (an) L(C-MiC j' L( M-C-H) 4d population net metal charge T, (cm-I)

4.120 101.8 110.0 2.00 1.22

4.343 105.7 111.7 1.01 1.37

Mo(CH3)2+ 4B2 3.952 115.2 108.3 4.50 1.15 3BI

)Al

3.875 105.4 105.2 7.54 0.87

3.716 114.6 107.3 7.96 0.83 566

Tc(CH3)2+ 5B* 3.928 96.8 107.4 5.25 1.08

3.835 93.5 108.3 8.73 0.77

4.035 97.0 109.3 3.22 1.13

4.030 109.1 109.4 3.13 1.15 55

Ru(CH~)~+ 'B2 3.861 106.8 106.4 6.43 0.95 'A,

)B2

4.056 80.6 103.0 9.60 0.80

4.472 180.0 97.8 9.78 0.76 3412

bent ground states, regardless of the order of the dnsl and dn+l atomic states. The bond angle depends on the amount of d character in the bond, since sd hybrid orbitals prefer angles of 90°, whereas pure d orbitals bonding to C prefer angles of 60°. In contrast, when only one metal carbon bond is formed, such as for the monomethyls, the atomic separations dramatically affect the bonding, often resulting in different ground states for the first and second transition rows. A comparison of the ground states of the dimethyl positive ions gives insight into the relative stability of the nonbonding metal valence orbitals. Since Sc+ and Y+ have only two valence electrons, both S C ( C H ~ )and ~ + Y(CH3)2+have singlet ground states with both metal electrons in the bonding orbitals. As more electrons are added, they fill the nonbonding valence orbitals in the order 2al, la2, lb,, and 3al. For Ti+(Zr+) to Mn+(Tc+) the open-shell electrons are high-spin coupled. From Fe+(Ru+) to Cu+(Ag+) the electrons begin to pair in the same order as the first electron was added. From the small separations between some of the excited states, it is clear that the nonbonding orbitals are relatively close in energy. For the Cu+ and Ag+ ions, it is interesting to compare the bonding in the mono- and dimethyls. The bonding in CuCH3+ and AgCH3+ is very different from the other monomethyls, as it involves one-electron bonds where the methyl supplies the electron. This bonding mechanism occurs in the case of one ligand, because it is not energetically favorable to pay the large promotion energy to reach the d9s' state of the ion, which is required to form a two-electron bond. Thus for Cu(CH&+ and Ag(CH3)2+,we considered the 3B2state, which is the comparable state involving the d10 metal ion occupation where two one-electron bonds are formed by using the methyl electrons. For C U ( C H ~ )the ~ + 3B2 state lies considerably higher in energy than the 'A, state, which is derived from the 3d94s1state and forms two-electron bonds. Although for Ag(CH3)2+the 'Al state lies lower, the promotion energy is sufficiently large that the bonding in the ground state involves a contribution from both two-electron and one-electron bonding mechanisms. Thus one-electron bonding becomes less favorable in the dimethyl, since it is preferable to promote to the d9 s1 occupation so that two two-electron bonds can be formed. This illustrates the case where the bonding mechanism changes between the mono- and dimethyl systems, because the promotion energy is amortized over two bonds. Since the bonding in all of the transition-metal dimethyl positive ions involves a considerable degree of sd hybridization, all of the ions are bent. The C-M-C bond angle only varies from 115.5 to 90.9', except for Ag+ where the bond angle is 8 0 . 6 O . The Ag(CH3)2+system is somewhat

8660

The Journal of Physical Chemistry, Vol. 94, No. 24, 1990

Rosi et al. 120

TABLE IV: Summary of the De Values (kcal/mol) for the M(CH&+ Molecules sc Ti V Cr Mn

Fe

co Ni cu Y Zr Nb Mo Tc Ru Rh Pd Ag

DefM(CHd,I 108.0 95.8 86.9 46.6 67.3 83.9 87.7 85.0 65.9 116.8 122.1 101.1 67.5 90.1 85.8 80.6 82.9 46.8

OComputed as D,[M(CH,),+]

D.[MCH,l 51.5 50.8 43.3 22.4 40.9 50.9 48.6 39.2 25.4 59.6 57.9 47.6 30.1 45.7 40. I 36.7 46.8 18.7

A0

5.0 -5.8 0.3 1.8 -14.5 -17.9 -9.5 6.6 15.1 -2.4 6.3 5.9 7.3 -1.3 5.6 7.2 -10.7 9.4

100

w M

8

b

8

80

1c

W

QQ

60 Cr 0

- 2D,[MCH3+].

anomalous, as the bonding involves more than one bonding mechanism. This introduces considerable multireference character into the wave function, making the MCPF treatment less reliable. The M-C-H angle also shows a small variation, ranging from 1 1 1.7 to 1 03.0°. As was discussed in our earlier workI9 on the monomethyls, this variation in bond angle is highly correlated with the direction of charge donation. Comparing the energies of the planar CH3+,CH3, and CH3- structures with those in which the hydrogens have been bent 2 2 O out of the plane (corresponding to M-C-H angles of 90° and 1 1 2 O ) , CH3+ is destabilized by 40 kcal/mol, CH3 is destabilized by 8 kcal/mol, and CH, is stabilized by 8 kcal/mol. Thus the M-C-H angle decreases from left to right in each transition row, since there is donation of charge from the metal to the methyl for the early elements, but methyl to metal donation for the late elements, as a consequence of the larger metal ionization potentials. The binding energies for the dimethyl positive ions are compared with the corresponding monomethyl ions in Table IV. With a C-C bond energy of 90.3 kcal/mol and an M+-ethane interaction energy of 10 f 5 kcal/mol, some of the dimethyls are not stable. However, as noted in the Introduction, it is still interesting to study how the first and second ligand binding energies vary with the metal, especially as the addition of many ligands can stabilize the insertion products. Since the bonding in the ground states of all of the dimethyl positive ions, except possibly Ag(CH3)2+,arises from the dnsl atomic state, the magnitude of the binding energies is determined by two considerations. First, the binding energies are generally less for those metals for which promotion is required to reach the d"s' atomic state. Second, as the number of open-shell d electrons increases, the loss of d-d exchange becomes an important factor in determining the binding energy. Thus the smallest binding energies are found for Cr(CH3)2+,which has a large number of open shells and a sizeable Cr+ promotion energy, and Ag(CH3)2+,which has a very large Ag+ promotion energy. The binding energies are larger for the second-row dimethyls in the case of Y+ through Ru+, but Rh(CH3)2+through Ag(CH3)2+ have smaller binding energies than the corresponding first-row systems, because of the large promotion energy required to reach the d"s' occupation for the Rh, Pd, and Ag ions. The effect of promotion energy and loss of exchange energy on the binding energies of single ligand systems has been considered previously.' For MH+, MCH+, MCH2+, and MCH3+, a plot of the dissociation energy versus promotion energy (corrected for loss of exchange energy) is nearly linear, with only the right side of the second row showing any significant deviation. Using the "double bond correction" for the dnsl metal ion occupation from Carter and Goddard,* we have made a similar plot for the (46) Carter, E. A.; Goddard, W. A. J . Phys. Chem. 1988, 92, 5679

40 0

10 20 30 40 50 60 70 80 90 100

Promotion Energy(kcal/mole) Figure 4. Plot of our metal ion-dimethyl dissociation energies versus promotion energy corrected for loss of exchange (taken from ref 46).

dimethyls-see Figure 4. The same linear relationship is found for the dimethyls, especially for those ions with small promotion energies. As the promotion energy becomes larger, the bonding contains more d*' or metal neutral character, and it is less valid to assume the metal is promoted to the d"s' state before bonding occurs. This is well illustrated by Pd atom where the d population of 8.77 electrons clearly indicates that the metal is not promoted to 4d85sl. However, Figure 4 demonstrates that the bonding is much more consistent than is implied by the dissociation energies. Whereas the trends in the dimethyl positive ion binding energies can be simply explained in terms of promotion energies and loss of d-d exchange energy, the bonding in the monomethyls is much more diverse, as it is determined by several competing mechanisms-see the discussion in ref 19. Therefore, there is a significant variation in the first vs the second methyl binding energy. For example, the second methyl binding energy of Pd+ is smaller than the first, while the reverse is true for Ni+. The difference arises because Ni+ binds from a mixture of the 3d84s' and 3d9 atomic states to both one and two methyls, while Pd+ binds to one methyl from the 4d9ground atomic state without promotion and to two methyls from the 4d85s' excited-state occupation. Thus for Ni+, the first methyl pays the small promotion energy and the second is more strongly bound, while for Pd+ the second methyl binding energy is less, since the second bond pays the promotion energy. Cu+ also has a larger second ligand binding energy, because of the change from one-electron to two-electron bonding. The large decrease in binding energy for the second methyl in Mn+, Fe+, and Co+ is probably related to the loss of exchange energy, as the bonding for both the mono- and dimethyls involves a comparable contribution from the atomic states with little change in the d population when the second methyl bonds. 2. Neutral Dimethyl Compounds. The MCPF optimized structures and selected Mulliken populations for the ground-state and selected low-lying states for the first- and second-row transition-metal dimethyl neutrals are summarized in Tables V and VI, respectively. It is interesting to compare the bonding in these neutral systems with the corresponding isoelectronic positive ions. Although there is considerable similarity, there are several notable differences. First, the filling order for the open-shell d orbitals in Sc(Y) to Cr(Mo) changes to 2a,, lb,, 3a,, and la2; this filling order is also consistent with the ground states that have been reported for the dihydrides.22-28 While the filling order for Ru to Pd is consistent with the isoelectronic positive ions, the dimethyls

The Journal of Physical Chemistry, Vol. 94, No. 24, 1990 8661

Transition-Metal Dimethyls and Their Positive Ions TABLE V: MCPF Spectroscopic Constants and Populations for the First-Row Transition-Metal Dimethyl Molecules WCHdi2A, ,B, r,(M-C)(ao) L(C-M-C) L( M-C-H) 3d population net metal charge T, (cm-I)

r,(M-C)(ao) L(C-M-C) L( M-C-H) 3d population net metal charge T. (cm-ll

re( M-C) (ad L( C- M-C) L( M-C-H)

3d population net metal charge T. (cm-I)

4.179 121.4 112.0 0.97 0.79

Ti(CHd2

4.435 160.8 113.3 1.28 1.05 3388

V(CH3)2 4B, 4A2 4.031 3.991 134.0 122.8 111.7 111.4 3.26 3.30 0.86 0.81 1256

3.913 180.0 1 11.5 6.14 0.78

'B,

'A2

'A,

4.109 132.8 111.5 2.16 0.84

4.237 131.0 112.3 2.35 0.97 2930

4.212 142.0 112.0 2.33 0.96 9741

Cr(CH3), 5B2 3.909 117.4 110.5 4.42 0.78

3.922 180.0 111.7 6.08 0.74 3442

CO(CH~)~ re( M-CNao) L( C- M-C)

L(M-C-H) 3d population net metal charge T. (cm-I)

4B2 3.837 180.0 112.1 7.67 0.24

Mn(CH,), 6AI 4.010 180.0 111.6 5.08 0.8 1

3.671 11 1.2 109.4 6.51 0.58 14907

3.690 104.8 109.2 6.70 0.57 17467

Y(CH')2. Zr(CH3)2 'B, 'A, 'A, 2A, re(M-C) (ao) 4.488 4.293 4.210 4.252 L( C-M-C) 114.3 120.7 114.4 93.2 L( M-C-H) 111.8 111.0 110.2 110.2 4d population 0.95 2.17 1.87 2.28 net metal charge 0.71 0.69 0.53 0.59 T. (cm-') 162 4267

re(M-C)(ao) L(C-M-C) L( M-C-H) 4d population net metal charge T, (cm-')

re(M-C)(ao) L( C-M-C) L( M-C-H) 4d population net metal charge T. (cm-I)

Ni(CHd2

'BI 3.822 180.0 111.8 8.16 0.71

'B2 3.781 147.1 111.1 8.19 0.65 47

IA, 3.512 97.0 108.9 8.76 0.35 666

'A, 3.163 139.3 110.6 8.12 0.66 2612

c~(CH3)irc(M-C)(ao) L(C-M-C) L( M-C-H) 3d population net metal charge T, (cm-I)

TABLE V I MCPF Spectroscopic Constants and Populations for the Second-Row Transition-Metal Dimethyl Molecules

2AI 3.707 180.0 111.4 9.27 0.49

,B2 3.644 126.2 109.5 9.31 0.48 960

of Mn to Ni are unique in that they are linear. This is a consequence of the dns2atomic states being very low lying, so that sp hybridization is more favorable than sd hybridization. The lowest energy structure of C U ( C H ~is) ~also linear for similar reasons, as are C U H and ~ ~C U ~ H C H ~ . 'One ~ exception to this trend is that the 6A, ground state of T c ( C H ~ has ) ~ an open-shell b2 orbital but still has a bent equilibrium structure. Previous theoretical studies of the transition-metal hydrides have shown that the ground states of these species can be predicted from simple empirical rules involving the mixings of the low-lying atomic states!' Since the open-shell d electrons have pseudolinear symmetry due to the small metal-hydrogen interaction, these rules are applicable to the linear transition-metal dimethyls. For example, these rules correctly predict the ground states to be analogues of 6Z+, 4@, 3A, and ?2+ symmetry for Mn(CH3)2 through C U ( C H ~ )respectively. ~, For the Fe through Cu metals, these ground states are analogous to those found for the dihydrides. However, there are several low-lying bent states for Ni(CH3)2, as a consequence of the near degeneracy of the 3F(3d84s2)and 'D(3d94sl) atomic states of Ni atom. In fact, our prediction of a 03Anground state for Ni(CH3)2 may be incorrect, since the low-lying (1.9 kcal/mol) IAl state has a much larger 3d population. Considering the calculations are biased in favor of the 3d84s2atomic state, a higher level of correlation treatment may bring the 'A, state below both the 3Bl("3A") and 3Bz states of Ni(CH3)2. Note that the H-Ni-H bond angle for the 'A, state

re(M-C)(ao) L(C-M-C) L( M-C-H) 4d population net metal charge T, (cm-I)

4.065 111.9 109.9 4.60 0.57

3.872 97.5 109.0 6.71 0.42

4.065 147.4 110.6 6.35 0.71 1796

4.207 159.5 111.3 5.14 0.81

3.830 108.2 110.2 7.16 0.45 6917

Pd(CHd2 IA, 'B2 3.786 3.889 90.2 138.6 108.3 107.7 8.96 8.86 0.37 0.42 11163

Nb(CH3)z 4B, 4B2 4.154 4.150 126.1 101.2 110.9 110.3 3.37 3.44 0.68 0.61 1120

3.944 112.2 109.7 5.61 0.50 5286

3.796 95.0 109.6 8.00 0.38

4.170 163.0 111.0 5.62 0.81 16043

3.871 89.2 108.7 7.89 0.33 3814

Ag(CH3)Z 2B2 2Al 4.115 4.179 125.7 180.0 105.4 107.8 9.68 9.57 0.31 0.55 7240

of NiH28 is significantly smaller than the C-Ni-C angle in Ni(CH3)2. Thus while there is considerable similarity between the dihydrides and dimethyls, some notable exceptions occur that are related to the greater directionality of the bonding to the methyls. The C U ( C H ~molecule )~ is unique in that it has a low-lying 2B2 bent state that involves a combination of sd and sp hybridization. For the linear ground state, the open-shell orbital is 94% on Cu, while for the excited state the open-shell orbital involves 32% CH3 character. Thus, the 2B2excited state involves some contribution from the 3d1°4sl atomic state, resulting in a two-electron bond in al symmetry between the Cu and CH3, but a one-electron bond in bz symmetry where the CH3 groups donate an electron to Cu. This one-electron bonding is similar to that observed in CuCH3+. For Ag(CH3)2,the much larger promotion energy to 4d95s2is not compensated by the formation of the second two-electron bond, which results in a 2B2ground state involving a one-electron bond in b2 symmetry. The stability of the dns2occupation is also responsible for the different filling order of the orbitals for the neutrals and positive ions of the metals on the left side of both transition rows. For the neutrals the 3al orbital gains more s character and becomes considerably more stable than the a2 orbital that contains only d character. The enhanced s character increases the C-M-C angle relative to the ions but does not lead to linear structures. Since the more comparable radial extents of the s and d orbitals on the left-hand side of the row favors sd hybridization, the lowest energy structures all have bent geometries. The late elements of the second transition row, Ru-Pd, fill in the same order as the ions, since the 4dn5s2occupation is very high in energy. Thus, in analogy with the isoelectronic ions, the bonding is dictated by the mixing of the 4dn+'5s1and 4dn+2metal atomic states. This leads to C-M-C angles similar to those found for (48) Blomberg, M. R. A,; Siegbahn, P. E. M. J . Chem. Phys. 1983, 78,

(47) Walch, S. P.; Bauschlicher, C. W. J . Chem. Phys. 1983, 78, 4597.

5682.

8662

The Journal of Physical Chemistry, Vol. 94, No. 24, 1990

TABLE VII: Summary of the De Values (kcal/mol) for the M(CH& Molecules

sc Ti V Cr Mn Fe co Ki

cu

Y Zr Nb Mo Tc Ru

Rh Pd Ag

4[M(CH,),I

DJMCH31

A0

98.6 95.6 99.3 77.2 84.7 93.4 87.1 90.3 69.4 110.3 113.6 108.2 82.6 86.0 86.3 98.8 82.9 44.2

47.4 39.8 43.9 36.2 28.0 31.7 36.3 48.5 48.4 62.4 53.9 50.4 39.2 26.9 40.1 48.8 36.1 36.2

3.8 16.0 11.5 -0.2 28.7 30.0 14.5 -6.7 -27.4 -14.5 5.8 7.4 4.2 32.2 6.1 1.2 10.7 -28.2

"Computed as D,[M(CH,),] - 2D,[MCH3].

the ions, which are significantly smaller than for the neutrals of the early elements. The bonding in Tc(CH,)~ is similar to that in Mn(CH3)2 through CU(CH,)~, since the ground state is derived from the d"s2 occupation. Although there is considerable sp hybridization, the 6A, ground state still has a bent (1 59.5') structure (the optimal structure is about 1 kcal/mol below the linear structure). The fact that the 6A, state of T c ( C H ~ is) ~bent is probably a consequence of the comparable radial extents of the 4d and 5s orbitals, which facilitates sd hybridization. The a , bonding orbital contains 15 and 24% contribution from the Tc 5s and 4d orbitals and 62% from the CH, orbitals. The b2 bonding orbital contains 12% Tc 5p character, but is strongly polarized toward CH,, as 79% of the orbital is on the CH, groups. Since the 6A, state retains the favorable d-d exchange energy, it is over 14.3 kcal/mol more stable than the 4Bzstate. The bonding in the 4Bz state involves sd hybridization, as this state is derived from the excited 6D(4d65s1) atomic state, which lies 9.5 kcal/mol above the %(4d55s2)state. The fact that the 4B2state is not the ground state, in spite of the small promotion energy, shows that loss of d-d exchange energy is an important factor in determining the relative stability of the states. There is metal to CH, charge donation for all of the neutral systems, with the early transition elements donating more charge than the late elements. This trend follows the first ionization potential of the metals. The M-C-H angle shows the same general decrease with increasing metal IP as observed for the ions. The binding energies for the mono- and dimethyl neutral systems are compared in Table VII. Since the C-C bond strength in C2H6 is 90.3 kcal/mol, the dimethyls of Cr, Cu, and Ag are not thermodynamically stable. However, considering that the metal-C bond strength is probably underestimated by more than the C-C bond strength in CZH6, the neutral dimethyls may be stable for most of the remaining metals, except possibly Mn, Mo, and Pd. Nevertheless, the trends in the first vs second binding energy are of interest, especially considering that the addition of other ligands can preferentially stabilize the dimethyl structures. There is a larger variation in the first vs second binding energy for the neutral systems than for the ions. The large increase in the second binding energy relative to the first for the Ti, V, Mn, Fe, Co, and Tc metals is due to the fact that these metals have dns2ground states, so that the first methyl must pay the cost of sp hybridization. A similar effect is found for Pd atom, where the first bond pays the cost of promoting the metal from the 4d" to the 4d95s' occupation. The CU(CH,)~and Ag(CH3)2molecules have a substantially smaller second binding energy, since Cu and Ag atoms can bond to the first methyl directly from their d"s' ground states, but for the second methyl to bond, these atoms must first promote to the d9s2state and sp hybridize to form two-electron bonds. The bonding in the YCH, and ScCH, molecules is dif-

Rosi et al. ferent from the other monomethyls in that the bonding arises from the d's2 state by sd hybridization; one hybrid bonds with the methyl while the second is a doubly occupied lone pair. When the second methyl bonds, the hybridization on the metal must again change, so that both the first and second methyls must pay a promotion energy to bond. The analogous first and second ligand binding energies for Sc(CH,), suggests that both hybridizations cost about the same. However, the binding energies for YCH, and Y(CH3)2 indicate that the second hybridization costs more, because the comparable size of the Y 5s and 4d orbitals facilitates the formation of sd hybrid orbitals. C. Comparison with Other Work. In the earlier subsections we have focused on how the nature of the bonding differs between the mono- and dimethyls. However, in order to compare with experiments for the bare metal ions, we must also consider the relative stability of the ethane complex. For example, by measuring the energy of the process MC2H6+

+

MCH3' -I-CH3

and comparing that to the M-C binding energy in MCH3+, the difference between the first and second methyl binding energy can be determined, unless MC2H6+is actually the ethane complex. Using a C-C binding energy of 90.3 kcal/mol and an electrostatic stabilization of 10 f 5 kcal/mol, it is clear that Cr+, Cu+, Mo', and Ag+ will form the ethane complex and that Sc+, Ti+, Y + ,Zr', and Nb+ will form the dimethyls. Limitations in the calculations make it difficult to unambiguously decide on the optimal structure for the other metal ions, because the computed errors are significantly larger for M(CH3)2+than for M+-C2H6. This is based on the fact that our calculated C-C bond energy is in excellent agreement with experiment49 for C2H6 and the electrostatic interaction is well described by the SCF/MCPF approach. Previous studies on the monomethyls show that limitations of the oneparticle basis set and errors in the computed atomic separations result in an underestimation of the bond energy by about 4-6 kcal/mol per CH,. Thus if the dimethyl binding energy is increased by 12 kcal/mol, while the ethane-complex binding is not changed, the two structures will have nearly equal energies for the remaining metals. However, the relative mono- and dimethyl binding energies should be more accurate, since there is some cancellation of errors, so the computed differences in the first and second methyl binding energies are probably accurate to better than 3 kcal/mol. To account for differences in the treatment of the dimethyls and the ethane complex, we add 6 kcal/mol per M-C bond to the methyl and dimethyl and use an estimate of 100 f 5 kcal/mol for the ethane complex when comparing with experiment. It should also be noted that most of the experiments have been carried out at 298 K. Assuming that the system is an ideal gas with only translational and rotational degrees of freedom, the experimental D,298 values should be reduced by 2.4, 1.5, and 3.8 kcal/mol for the products CH, MCH3+,M+ C2H6, and M+ + 2CH3, respectively. Given the qualitative nature of our corrections to the computed dissociation energies, we have not corrected the experimental values to 0 K, but instead have noted that even our corrected Dovalues are expected to be a few kcal/mol smaller than experiment. There have been only a few experimental determinations of the binding energies of the dimethyl positive ions. Armentrout and c o - ~ o r k e r s ~have - ~ measured the second methyl binding energy for Sc(CH,),+, Ti(CH3)2+,and V(CH3)2+. We find the second methyl binding energy to be 5 kcal/mol smaller than the first for Ti(CH3)2+,whereas Sunderlin and Armentrout4 find the second binding energy to be 10.8 f 8 kcal/mol larger. Including a 6 kcal/mol correction per M-CH3 bond leads to an estimated binding energy of 108 kcal/mol for the dimethyl as compared with our estimate of 100 f 5 kcal/mol for the ethane complex. This leads us to conclude that the dimethyl is formed. Thus, the correct binding energy for Ti(CH3)2+probably lies near the lower bound

+

~~

(49) Kerr, J. A. Chem. Rev. 1966,66,465.

+

Transition-Metal Dimethyls and Their Positive Ions of the experimental estimate. For V+ the dimethyl structure is probably more stable, but this fact is not unambiguously resolved by our calculations. From our calculations it is clear that Sc(CH3)2+ forms the dimethyl structure. Armentrout and cow o r k e r ~find ~ ~the ~ second methyl binding energy to be 1 kcal/mol larger than the first for Sc+ and 2 kcal/mol smaller for V+. Given that the uncertainty in the experimental values is 5 kcal/mol, both theory and experiment support similar values for the first and second methyl binding energies in SC(CH3)2+ and V(CH3)2+. Note that similar binding energies have been found both theoreticallyIs and experimentally' for the first and second hydrogen binding energies of the ScH2+ion. This is expected considering the similar bonding mechanisms in the dihydrides and dimethyls. Schilling et aL3' have calculated the binding energies for the monohydrides and dihydrides of Cr+ and Mo+. They find a large decrease in the binding energy of the second hydrogen for Cr+ but a small increase for Mo+. In contrast, we find an increase of 1.8 and 7.3 kcal/mol in the second binding energy of Cr(CHJ2+ and M O ( C H ~ ) ~respectively. +, This difference is unexpected considering the similarity in the bonding for the dihydrides and dimethyls. The calculations show the second methyl in Fe(CH,),* to be 18 kcal/mol less strongly bound than the first. The ethane complex would yield a "second methyl" binding energy of about 43 f 5 kcal/mol, or 14 f 5 less than the first. Both structures are consistent with the experimental work of Burnier et a1.,6 since their estimated lower bound of >38 f 2 kcal/mol for the second ligand binding energy is significantly less than the recommended value' of 58 f 2 kcal/mol for the first ligand binding energy. Thus much more accurate experimental values for the second ligand binding energies will be required to determine whether the preferred structure is Fe+-C2H6 or Fe(CH3)2+. Beauchamp and co-workers' report a binding energy of 110 f 3 kcal/mol for C O ( C D ~ ) ~ +Both . our estimate of 100 f 5 kcal/mol for the ethane complex and 99.7 kcal/mol for the dimethyl are about 10 kcal/mol less. Using these experimental values' for both the mono- and dimethyl binding energies leads to a second ligand binding energy that is 12 f 7 kcal/mol less than the first, whereas our theoretical calculations predict that it is 9.5 kcal/mol less. On the other hand, using the values from ref 7 for the dimethyl binding and the best value' for the monomethyl binding leads to a second ligand binding energy that is 12 kcal/mol larger than the first. Thus there remains uncertainty regarding the optimal structure and further experimental investigations appear warranted. Finally, combining the second methyl binding energy (749 f 5 kcal/mol) measured* for Ni(CH3)2+with the recommended value' of 47 f 5 kcal/mol for the monomethyl leads to the prediction of a small increase for second binding energy for Ni+. The computed increase of 6.6 kcal/mol is consistent with the experimental value within its error bars. Using the ethane complex

The Journal of Physical Chemistry, Vol. 94, No. 24, 1990 8663 would yield a second binding energy that is 10 f 5 kcal/mol larger than the first. As with Fe and Co, experiment gives little insight into the preferred structure. IV. Conclusions The bonding in the dimethyl transition-metal positive ions is shown to arise from sd hybridization, leading to bent equilibrium ground-state structures for all systems. The ground states can be explained based on the relative stability of the nonbonding d orbitals. For the neutral metal dimethyl compounds, both sd and sp hybridization are more important than for the ions due to the stability of the d"s2 occupation. The increase in s character in the bond leads to larger C-M-C angles. For Mn(CH3)2through CU(CH,)~,sp hybridization leads to linear structures. The significant variation in the binding energies of the first and second methyls can be understood in terms of the promotion energies and loss of d-d exchange energy. The computed differences between the first and second methyl binding energies are in reasonable agreement with the limited experimental data. Since this work provides a consistent set of binding energies for the first- and second-row transition-metal dimethyl neutrals and positive ions, considerable insight is gained into the bonding. In future work, we will consider how these binding energies change as other ligands are added. Since insertion of M+ into the C-C bond is not thermodynamically favorable for some metals, the lowest energy structure becomes an electrostatically bonded metal-ethane complex. The calculations show that Cr+, Mo', Cu+, and Ag' will probably exist as the ethane complex, while Sc+, Ti+, Y+, Zr+, and Nb+ form the dimethyl systems. For the remaining metals, the two structures are close in energy, and the greater difficulty in describing metal< bonds as compared with C-C bonds precludes a definitive determination of the lowest energy structure. Acknowledgment. This work was done while one of the authors (M.R.) held a CNR fellowship. We would like to thank Knut Faegri, Tim Lee, Alistair Rendell, and Peter Taylor for helpful discussions. Registry No. Sc(CH,),', 93383-04-1; Ti(CH3)2t, 127713-49-9; V(CH3)2', 129965-24-8; Cr(CH3)2t, 129965-25-9;M~I(CH,)~',12996526-0; Fe(CH3),', 129965-27-1; CO(CH3)2t, 129965-28-2; Ni(CHp),', 129965-29-3; Cu(CH,)Z', 129965-30-6; Y(CH3)2', 129965-31-7; Zr(CHJ,', 129965-32-8; Nb(CH3)2', 129965-33-9; Mo(CH~)~',12996534-0; Tc(CH,)z', 129965-35-1; Ru(CH3)2', 129965-36-2; Rh(CHp)2', 129965-37-3; Pd(CH3)2', 129965-38-4; Ag(CH3)2', 129965-39-5; SC(CH,),, 129944-30-5; Ti(CH3)*, 129944-31-6; V(CH3)2, 129944-32-7; C T ( C H ~ 91846-24-1; )~, Mn(CH3),, 33212-68-9; Fe(CH3)2, 108890-32-0; C O ( C H ~ 108890-3 )~, 1-9; Ni(CH3)2,54836-89-4; C U ( C H ~ )86568-38-9; ~, Y(CH3),, 129944-33-8; Zr(CH3),, 129944-34-9; Nb(CH3)2, 12994435-0; Mo(CH3)2, 129944-36-1; Tc(CH,),, 129944-37-2; R u ( C H ~ ) ~ , 129944-38-3; Rh(CH,),, 129944-39-4; Pd(CH3)2, 93895-88-6; Ag(CH,)2, 129944-40-7.