Trends of Metal-Carbon Bond Strengths in Transition Metal

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J. Phys. Chem. 1995, 99, 12723-12729

12723

Trends of Metal-Carbon Bond Strengths in Transition Metal Complexes Per E. M. Siegbahn Department of Physics, University of Stockholm, Box 6730, S-113 85 Stockholm, Sweden Received: January 23, 1995; In Final Form: h a y 31, 1995@

Two different types of trends of metal-carbon (M-C) bond strengths have been investigated for the sequence of second row transition metal atoms. In the first trend the bond strength dependence on the hybridization on carbon has been studied. It is found that sp hybridized carbon atoms form much stronger M-C bonds than sp2 hybridized carbon atoms. The bonds formed by sp3 hybridized carbon atoms are still weaker. The M-C bond strengths decrease markedly to the right in the periodic table. The second trend studied is the M-C bond strength dependence for different alkyl groups. It is found that metal-methyl bonds are stronger than metal-ethyl bonds which in turn are slightly weaker than metal-propyl(n) bonds. The weakest metalalkyl bonds studied here were found for bonds to isopropyl groups. The difference between the metal-alkyl bond strengths are largest to the left in the periodic table, and the difference essentially disappears to the right. All these trends of M-C bond strengths can best be explained by invoking ionic contributions in the M-C bonding and repulsive effects, depending on the number and type of ligands on the bonding carbon atom. The geometric structures show almost no signs of n-bonding between the metal and carbon in the present systems, not even for the M-ClH systems where this might have been expected.

I. Introduction The activation of C-H bonds of hydrocarbons by transition metal complexes continues to be an important area of organometallic chemistry and homogeneous catalysis.' In particular, the activation of unstrained alkanes is still a challenging problem. In the activation of different types of C-H bonds several trends have been noted. For example, C-H bonds of longer alkane chains are easier to activate than those of smaller alkanes.* Also, the ease of activation of C-H bonds depends on the hybridization of carbon as sp3 sp2 sp, and it increases depending on the substitution on carbon as tertiary (3") secondary (2") primary (1"). These findings can be summarized by the surprising trend that stronger C-H bonds are in general easier to activate than weaker C-H bonds. To rationalize these trends, Jones and Feher3 concluded that it is the product M-C bond strengths that dominate in the determination of the position of the hydrocarbon activation equilibria, not the reactant C-H bond strengths. On the basis of the wellknown order of C-H bond strengths, -+

+

-

-+

H-Ph

> H-vinyl

> H-CH,

H-CHR,

> H-CH,R > H-CR,

> > H-CH,Ph

(1)

the following order of M-C bond strengths was suggested, M-Ph >> M-vinyl>> M-CH, >> M-CH,R >> M-CHR, >> M-CR, >> M-CH,Ph

(2)

The >>-sign for the M-C bond strengths as compared to the >-sign for the C-H bond strengths would thus explain the observed trends of activation. Even though the general features of metal-carbon bond strengths in transition metal complexes are roughly known from experiments, very little is known in quantitative detail. Such information is valuable, for example, in order to predict exactly how much the exothermicity will change in the C-H oxidative addition reaction going from one hydrocarbon to another one. 'Abstract published in Advance ACS Ahstracrs, July 15, 1995.

0022-3654f9.512099-12723$09.00/0

In this context accurate quantum chemical calculations can give valuable information. The main advantage of using a theoretical method to study trends of bond strengths is that a systematically selected set of molecules can be studied without additional problems such as the appearance of instabilities. Also, the trends can be made free from additional unwanted effects as much as possible. For example, it is clear that to some extent metalcarbon bond strengths will depend on the number and specific type of the additional ligands present in a saturated complex. In a calculation these ligands can at a first stage be removed without problems. An argument against this procedure might be that these strongly unsaturated complexes are not representative of the complexes actually observed. As will be demonstrated in this study by systematic comparisons to available experimental information, this argument does not hold if the trends are chosen in a reasonable way. Another argument against a theoretical study aimed at giving quantitative information might be that the accuracy of quantum chemical methods for transition metals is not high enough. Although perhaps true a year ago, this argument does not hold any longer either. The increased experience obtained from treating transition metal complexes by quantum chemical methods has led to a much better understanding of the errors obtained in typical correlated calculations. In fact, recent work has shown that the errors obtained are highly systematic, and this fact can be used to vastly improve the accuracy of the information from quantum chemical calculations. In a recently suggested scheme where the correlation energy is it has been demonstrated that the accuracy obtained for transition metal containing systems is about the same as that obtained using the most advanced experimental techniques. The present study will focus on two trends. First, metalcarbon bond strengths will be studied for different hybridization on carbon. The set of molecules M-CH3, M-C2H3, and M-C2H was selected without additional ligands, where M is the entire sequence of second row transition metals. The second trend studied is for metal-alkyl bonds for alkyl chains of different lengths and for different numbers of substitutions on the bonding carbon. The M-CHs, M-ClH5, M--C3H,(n), and

0 1995 American Chemical Society

12724 J. Phys. Chem., Vol. 99, No. 34, 1995 M-C3H,(iso) systems were chosen for this study, again for the entire sequence of second row transition metals.

Siegbahn TABLE 1: Metal-Carbon Bond Strengths (kcdmol) with Diflerent Hybridizations on Carbon for Second Row Transition Metal Atom@

11. Computational Details

The underlying calculations of the present paper are the same as those that have been described in detail in several previous papers6 The basis set are of double f plus polarization type and can be described in the following way. For the metals the Huzinaga primitive basis7 was extended by adding one diffuse d-function, two p-functions in the 5p region, and three ffunctions, yielding a (17s, 13p, 9d, 3f) primitive basis. The core orbitals were totally contracted except for the 4s and 4p orbitals which have to be described by at least two functions each to properly reproduce the relativistic effects. The 5s and 5p orbitals were described by a double f contraction and the 4d by a triple 5 contraction. The f-functions were contracted to one function giving a [7s, 6p, 4d, lfl contracted basis. For first row atoms the primitive (9s, 5p) basis of Huzinaga8 was used, contracted according to the generalized contraction scheme to [3s, 2p], and one d-function was added. For hydrogen the primitive (5s) basis from ref 8 was used, augmented with one p-function and contracted to [3s, lp]. The geometries of the present systems have been fully optimized at the SCF level using valence double f basis sets and the GAMESS set of programs9 It may appear that this type of low level geometry optimization is not in balance with the accurate method used for the energy evaluation at the optimized geometries, described below. However, it has been shown both that the geometries obtained at this level are surprisingly accurate and also that the energy is rather insensitive to small deviations from exact geometries for second row transition metal complexes. Io These conclusions concem both equilibrium geometries and transition states. In order to be directly comparable to experiments, the calculated energies have to be corrected for zero-point vibrational effects. These effects were calculated using the GRADSCF program' I for the yttrium systems only, and these effects were then used for all metals. The correlation method chosen was the modified coupled pair functional (MCPF) method,I2 which is a size-consistent, single reference state method. The zeroth order wave functions were determined at the SCF level. All valence electrons were correlated including the 4d and 5s electrons on the metal atoms. Even though the absolute accuracy of the MCPF calculations is not very high, the fact that the errors are highly systematic can be used to significantly reduce the errors. The accuracy is mainly limited by the basis set size in the final MCPF calculations. The lack of triple excitations is another rather important factor. In comparison to these other errors, the error in the geometry optimization step can normally be neglected. On the basis of comparisons to calculations of high accuracy and comparisons to experiments, it has recently been demonstrated that the present type of treatment gives a remarkably stable fraction of the Correlation effects. Using the present basis sets and methods, it has been shown that this fraction is close to 80%. A simple estimate of the remaining correlation effects is then obtained by simply adding 20% correlation energy to each system. This is the general idea behind the PCI-80 scheme which has recently been p r ~ p o s e d . ~It. ~was shown in refs 4 and 5 that this parametrization gives a major improvement of the results compared to an unparametrized treatment. For a benchmark test consisting of the atomization energies of 32 neutral first row systems the PCI-80 scheme gives an average absolute deviation compared to experiments of only 2.4 kcaV mol. Pople et al.I3 have shown that for the same systems the MP2 method using polarized basis sets gives an average absolute

Y Zr Nb Mo

Tc Ru Rh

Pd H

66.9 58.6 56.6 45.3 47.7 48.5 52.0 41.6 102.7

76.8 67.1 67.3 55.3 54.9 58.9 62.4 50.3 108.3

116.5 102.9 102.6 89.4 81.8 89.1 92.3 76.1 127.3

For comparison the corresponding C-H bond strengths are also given. deviation of 22 kcaYmol and for the QCISD method the deviation is actually larger with 29 kcaymol. For transition metal systems the improvement at the PCI-80 level compared to an unparametrized treatment is sometimes quite dramatic. Tests against a large number of experimentally studied small second row transition metal complexes show that the accuracy of the PCI-80 scheme for bond strengths is probably at least as high as that available from experiments for these system^.^ Before the correlation treatment the core orbitals were localized using an 6 minimization procedure. Relativistic effects were accounted for using first order perturbation theory, including the mass-velocity and Darwin terms.14 It can be added that this treatment of relativistic effects has been shown from numerous applications during the past decade to give both accurate energies and geometries. The calculations were performed using the STOCKHOLM set of program^.'^

111. Results and Discussion Two trends of metal-carbon bond strengths will be discussed here. The first trend is the variation of the M - C bond strengths with the hybridization on carbon. The PCI-80 results for M-CH3, M-C2H3, and M-CzH are given in Table 1 and shown in Figure 1 for all second row transition metals. For comparison the corresponding C-H bond strengths are also given. In Table 2 and Figure 2 the differential bond strengths are given compared to the M-CH3 bond strengths. In Table 3 the metal-carbon bond distances are compared to the typical single bond distances in M-CH3 and the typical double bond distances in M=CH2, Where n-bonding is present. The second trend of M-C bond strengths studied is the one for different alkyl groups. The results for M-CH3, M-CZH~, M-C3H7(n),and M-C3H7(iso) are given in Table 4, and displayed in Figure 3. For comparison the bond strengths of the diatomic M-H systems are also given. In Table 5 and Figure 4 the corresponding differential bond strengths are given compared to the M-CH3 bond strengths. It can be added that great care was exercised in finding the ground states of the present systems (see further below). In the following only these ground state results are discussed. A few comments can first be given on the computed C-H bond strengths in the hydrocarbons given in Tables 1 and 4. For most of these PCI-80 bond strengths there is good agreement with experiment or best previous theoretical values. For methane the calculated value is 102.7 kcaYmo1 (exp 103.2 kcaY moll6), for ethylene 108.3 kcaYmol(lO9.7 kcaYmo1 17), and for ethane 99.8 kcaYmol (100.8 kcaYmol I*). Also the calculated values for the two C-H bonds in propane, 100.6 kcaYmol (terminal carbon) and 98.2 kcaYmol (central carbon), are expected to be quite accurate. For acetylene the computed value is not as good with 127.3 kcdmol compared to the experimental

J. Phys. Chem., Vol. 99, No. 34, 1995 12725

Metal-Carbon Bond Strengths in Transition Metal Complexes

AE

AE

(kcal/mol)

(kcal/mol) 50

120 0 \

40 100

30 80

\

+\

b

C2H3

'\

20

C2H3

60

10

40

.

Y

Zr

Nb

Mo

Tc

Ru

Rh

Pd

0

.

.

Y

Zr

Nb

Mo

Ru

Tc

Rh

Pd

.

Figure 1. Metal-carbon bond strengths with different hybridizations

Figure 2. Difference between the metal-R and metal-methyl bond

on carbon for second row transition metal atoms.

strengths with different hybridizations on carbon for second row transition metal atoms.

TABLE 2: Difference between the Metal-R and Metal-Methyl Bond Strengths (kcdmol) with Different Hybridizations on Carbon for Second Row Transition Metal Atom@

TABLE 3: Variations of the Metal-Carbon Bond Distance (A) with Different Hybridizations on Carbon for Second Row Transition Metal Atoms ~~~~

Y Zr Nb Mo Tc Ru Rh Pd H

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

9.9 8.5 10.7

10.0 7.2 10.4 10.4 8.7 5.6

~

49.6 44.3 46.0 44.1 34.1 40.6 40.3 34.5 24.6

For comparison the corresponding relative C-H bond strengths are also given.

value of 131.3 kcal/mol.I7 About 1.0 kcal/mol of this discrepancy of 4.0 kcaymol comes from the computed zero-point vibrational effect. Normally, a zero-point vibrational effect calculated at the SCF level should be scaled by about 0.9, but this has not been done in the present case since a similar scaling does not work for transition metal complexes. The remaining absolute error of 3.0 kcal/mol for acetylene, which is a quite acceptable deviation for the present purpose of studying trends, is due to a well-known slight problem of the PCI-80 scheme to treat multiple b ~ n d i n g . ~ The first conclusion that can be drawn from the results in Table 1 is that the trend of the bond strengths follows the one given in (2) based on experiments. The acetylenic M-C2H bond is stronger than the metal-vinyl bond which in tum is stronger than the metal-methyl bond. Since the same relation holds also for the corresponding C-H bonds, one part of the explanation for the trend must be the same for these systems. There are several ways to rationalize this trend for the C-H bond strengths. The first way is to argue that the strength of the R-H bond depends inversely on the stability of the isolated R radical fragment by it~e1f.I~ The large C-H bond strength of acetylene, for example, is due to an instability of C2H. The

M

M-CH,

Y Zr

2.32 2.25 2.23 2.20 2.15 2.17 2.15 2.11

Nb Mo Tc Ru Rh Pd

M-C2H3

M-CzH

2.32 2.22 2.21 2.17 2.13 2.13 2.11 2.08

2.29 2.20 2.19 2.15 2.11 2.08 2.08 2.07

M=CH2 2.08 1.96 1.94 1.90 1.87 1.87 1.89 1.86

TABLE 4: Metal-Hydrogen and Metal-Alkyl Bond Strengths (kcaymol) for Second Row Transition Metal Atom# M

M-H

Y

70.0 58.8 63.0 54.0 52.1 62.4 68.2 53.4 104.8

Zr Nb Mo Tc Ru Rh Pd

H

M-CH, 66.9 58.6 56.6 45.3 47.1 48.5 52.0 41.6 102.7

M-CZH~

M-C3H,(n)

61.6 54.7 53.3 42.2 44.9 46.5 50.3 40.9 99.8

" For comparison the corresponding C-H given.

62.9 55.9 54.6 43.6 46.1 47.7 51.8 42.0 100.6

M-C,H7(iso) 58.3 51.7 51.0 40.6 43.2 45.1 50.3 41.1 98.2

bond strengths are also

instability can be explained by the fact that the carbon hybridization energy is shared by the C-C and C-H bonds in acetylene, whereas the hybridization for one of the carbon atoms is paid completely for by the C-C bond in CzH, leading to a weaker C-C bond in C2H than in a~ety1ene.I~A similar argument can be made for ethylene in comparison to methane. The second rationalization for the trend of C-H bond strengths relates the bond strength to the amount of s-character in the hybrid. The strongest C-H bond should be the one with most s-character in the bond since the 2s-orbital has a lower energy than the 2p-orbital for the carbon atom. It is of some historical

Siegbahn

12726 J. Phys. Chem., Vol. 99, No. 34, 1995

AE

AE

(kcal/mol)

(kcallmol) 0

70

60

-5

50 I

/

C 3 H7(i)

i

d' -10

40

Y Zr Nb Mo Tc Ru Rh Pd Figure 3. Metal-hydrogen and metal-alkyl bond strengths for second row transition metal atoms. TABLE 5: Difference between the Metal-Alkyl and the Metal-Methyl Bond Strengths (kcdmol) for Second Row Transition Metal Atom@ M M-CH, M-C2H5 M-C3H7(n) M-C3H7(iso) -8.6 -4.0 -5.3 Y 0.0 -6.9 -2.7 -3.9 Zr 0.0 Nb

Mo Tc Ru Rh

Pd H

0.0 0.0 0.0 0.0 0.0 0.0 0.0

-3.3 -3.1

-2.0

-5.6

-1.7

-4.7

-2.8 -2.0

-1.6 -0.8 -0.2

-4.5

-1.7 -0.7 -2.9

+0.4 -2.1

-2.8 -1.7 -0.5

-4.5

For comparison the corresponding relative C-H bond strengths are also given. interest in this context to note that the Pauling bond strength concept*O does not work well in this case. The bond strength power should then be related to the concentration of charge in the bonding hybrid, and sp3 hybridized bonds with a maximum amplitude of 2.00 should thus form stronger bonds than sp hybridized bonds with amplitude 1.93. In the present case this trend is contrary to what is observed. This deficiency of Pauling's bond strength concept has been pointed out previously on several occations, most notably by Coulson2' and prior to that by Forstes,22for example. The final two explanations for the trends of the C-H bond strengths are the ones we find most useful here since they work well also for the additional trends discussed below. In the third explanation the C-H bond strength will depend on repulsion to the additional number of ligands on carbon. In acetylene carbon has only one additional ligand, in ethylene carbon has two, and in methane carbon has three additional ligands. The repulsion between hydrogen and these ligands is thus largest for methane and smallest for acetylene. A better description of this repulsion is probably to relate it to a local repulsion with bonding hybrid orbitals proportional to the number of ligands, rather than to a repulsion to the ligands itself. The final, fourth explanation for the trends of the C-H bond strengths relates the strength to the amount

.

Y Zr Nb Mo Tc Ru Rh Pd . Figure 4. Difference between the metal-alkyl and the metal-methyl bond strengths for second row transition metal atoms. of ionic character of the bond. Since acetylene is most acidic, it has the largest bond strength followed by ethylene and methane. A second important conclusion which can be drawn from the results in Table 2 and Figure 2 is that the difference due to hybridization on carbon between the M-C bond strengths is significantly larger than for the corresponding C-H bond strengths. The difference between the C-H bond in ethylene and the one in methane is 5.6 kcdmol, while the corresponding difference for the M-C bonds is 8-10 kcallmol. The corresponding differences for acetylene is 24.6 kcdmol for the C-H bond and 35-50 kcallmol for the M-C bonds. There are two quite different possibilities to rationalize this effect. Either the effect has the same origin for both M-C and C-H bonds but is larger for M-C bonds or there is an additional effect appearing for the M-C bonds. If the first possibility is true, an explanation is needed for why the effect is larger for M-C than for C-H bonds. It is first clear that the explanation given above for the C-H bonds based on the instability of the free R radicals should be exactly the same for M-R and R-H bonds and thus cannot explain the difference of the effects. It also appears that the explanation based on the s-character of the carbon hybrid suffers from the same problem. The stabilization due to increased s-character should be a local carbon effect and thus be the same for M-C and C-H bonds. However, the third and fourth explanations given above are well in line with a larger effect for M-C than for C-H bonds. If repulsion toward the electrons on carbon is a major factor, it is clear that this will give a larger effect for a metal than for hydrogen since the metal is larger and has more electrons. Also, if the ionic contribution to the bond is important, the effect will be larger for M-C bonds since the ionization potential is smaller for the metal than for hydrogen. In support for these explanations it can be noted that the bond strengths in Table 1 increase markedly to the left in the periodic table where the repulsion between the metal and carbon is smaller due to the lower number of d-electrons on the metal and where the ionization potential is smaller.

Metal-Carbon Bond Strengths in Transition Metal Complexes The second possible explanation for the larger difference for M-C than C-H bonds due to hybridization is that a new effect, which is not present for hydrogen, appears for the metal. One such possible effect is the attractive interaction between the metal d-orbitals and the n-and n*-orbitals on C2H3 and C2H. The empty d-orbitals to the left could accept electrons from the n-orbitals, and the occupied d-orbitals, mainly to the right, could donate electrons to the n*orbitals. In order to give more information about possible n-bonding between the metal and carbon in these systems, the M-C bond distances are given in Table 3 and are compared to the typical single M-C bond distances in M-CH3, where no n-bonding is present, and also to the typical double M-C bond distances in M=CH2,23 where n-bonding is present. As seen in this table, the M-C bond distances in both M-C2H3 and M-C2H are in most cases quite close to the single M-C bonds in M-CH3 and in all cases very far away from the double bond distances in M-CH2. It can be added that small deviations from single M-C bond distances should be expected due to carbon hybridization even without M-C n-bonding. The small deviations seen in Table 3 are also energetically unimportant. The C-C bond distances in M-C2H3 (all of them 1.35 A) are also very close to the one in ethylene (1.33 A), and the C-C bond distances in M-CzH (all of them 1.22 A) are also very close to the one in acetylene (1.20 A). The effects of n-bonding can therefore safely be excluded as responsible for any of the trends seen in Tables 1 and 2. An argument for some importance of n-bonding might otherwise have been found for the acetylenic systems where an increased difference in bond strengths to the left can be noticed; see Table 2. A simple explanation for this increase could have been an attraction between the empty d-orbitals and the n-orbitals. However, this explanation is thus not correct, and the trend is instead explained by the increasing contribution of ionic bonding to the left due to the lower ionization potentials for these metals. It can be noted that there is no similar effect for the vinylic systems, in line with the much smaller ionic contribution in this case. In summary, an explanation based on the varying degree of ionic bonding and on the larger repulsion from the metal atom than from the hydrogen atom appears to be the simplest way to understand most of the observed trends. The geometric structures of M-ClH3 are surprisingly similar to ethylene and the ones for M-C2H equally similar to acetylene, which means that a direct comparison of M-C and C-H bond strengths is highly relevant for these systems. The second major trend investigated in the present study is the trend of the M-C bond strengths going from smaller to larger alkyl groups. A few main observations can be drawn from the results shown in Tables 4 and 5 and in Figures 3 and 4. First, the bond strengths decrease from methyl to ethyl but actually increase somewhat going from ethyl to n-propyl. Second, the weakest bonds are formed with the isopropyl radical. Third, the difference between the M-CH3 and the other M-C bond strengths also decreases going to the right. Finally, just as for the M-C bonds discussed above, the bond strengths decrease going from left to right in the periodic table. Most of these trends can be well explained by similar explanations as the ones given above for the trends of the M-C bond strengths with different hybridizations on carbon. The simplest trend to explain is the one for the M-C bond strengths for methyl, ethyl, and isopropyl. This trend follows, for example, from the simple fact that a methyl group is more repulsive toward the metal d-electrons than a hydrogen atom. The methyl group has no methyl substituent, ethyl has one, and isopropyl two methyl substituents. The fact that n-propyl forms

J. Phys. Chem., Vol. 99, No. 34, 1995 12727 slightly stronger M-C bonds than ethyl, even though both groups have one methyl substituent, must with this explanation be due to a larger electron delocalization for the larger n-propyl group which reduces the repulsion toward the metal somewhat. Another simple explanation relates the trends to ionic contributions. The negative carbon charge is largest for methyl and smallest for isopropyl due to the larger delocalization of electrons when methyl groups are present. The decreased carbon charge for the more substituted alkyls therefore leads to a smaller contribution of ionic bonding and thus also leads to smaller bond energies for these metal-alkyls. An important trend, seen best in Table 5 and Figure 4, is that the differences of the M-C bond strengths decrease markedly to the right in the periodic table. To the right the four different M-C bond strengths are thus almost perfectly the same, while, in contrast, to the left for yttrium the M-C bond strength difference between methyl and isopropyl is as large as 8.6 kcaymol. The simplest way to explain this trend is based on the ionic picture given above. In this picture this decrease is simply due to the smaller contribution of ionic bonding to the right due to the higher ionization potentials. If the picture based on repulsion is kept, on the other hand, it is still possible to explain this trend. Since the difference between the M-C bond strengths in this case should be due to a varying degree of repulsion toward the metal d-electrons, the metal atoms to the right must have a property that reduces this repulsion. This property should be sd hybridization. To efficiently form sd hybrids to avoid the repulsion toward carbon, the metal atom must have low lying so and s i states. This only occurs to the right. To the left, the so state is high, but instead the s2 state is low lying. The metal atoms to the left therefore often prefer to form sp hybrids rather than sd hybrids, but this hybridization is more costly and less efficient for avoiding repulsion. The fact that the difference in M-C bond strengths changes from left to right in the periodic table obscures the simple reasoning behind the relations given in (1) and (2). To the left the M-C bond strength differences are indeed larger than for the corresponding C-H bonds, but this is no longer true to the right. In fact, for the metal atoms to the far right the M-C bond strength difference is actually smaller than the C-H bond strength difference. It should be noted that differences in intrinsic M-C bond strengths are not the only possible explanation for a difference in reactivity for transition metal complexes with different alkanes. One important additional effect, not discussed in the present paper since it is not present for the systems discussed here, is a possible formation of agostic bonds. The strengths of agostic bonds will critically depend on the additional ligands present and is therefore not as easy to systematize as the M-C bonds of the present study. A systematic study, of a slightly different kind, of agostic bonds will nevertheless be attempted in the near future. Another important related aspect in alkane activation, not discussed here either, is the ability of the metal complex to form molecular precursor complexes. The goal of the present study has instead been to isolate and generalize some of the aspects of importance when discussing alkane activation. The trends of the bond distances and bond angles of the metal-alkyl systems follow the ones expected on the basis of the above analysis of the energetics. The metal-methyl systems have basically C3vsymmetry with M-C-H bond angles varying from palladium with 109.9' to yttrium with 111.5". The bond distances vary from 2.11 8, for palladium to 2.32 8, for yttrium in line with the large radii of the atoms to the left. These M-C bond distances stay almost exactly the same for the larger

12728 J. Phys. Chem., Vol. 99, No. 34, 1995

metal-alkyl systems. For the metal-ethyl systems the increased repulsion toward the methyl substituent leads to a distortion of the M-C-C angles compared to the corresponding M-C-H angles for the metal-methyl systems. The M-C-C bond angle of the ethyl systems increases from 113.7' for palladium to 117.8' for yttrium. The larger distortion of the yttrium system occurs because it is easier to distort this system since the repulsion toward the d-electrons is smaller than for palladium. The bond angles are almost the same for the metalpropyl(n) systems in line with the similar bond energy for the metal-ethyl and metal-propyl(n) systems. However, a slight additional increase of the M-C-C bond angle for the metals to the left of about 1' can be noticed for the n-propyl systems. Since the repulsion as measured by the M-C bond energy is larger for the isopropyl than for the n-propyl systems still larger M-C-C bond angles might be expected for the isopropyl systems. However, this is not the case with M-C-C angles of 111.4' for palladium increasing to 113.3' for yttrium. The reason for these smaller angles is trivial and has to do with the fact that there are two methyl substituents for isopropyl and only one for n-propyl. An increase of the M-C-C angle for the isopropyl systems therefore leads to a closer critical M-H distance than the same increase does for the n-propyl systems. The charges given by the Mulliken populations support the above explanation for the trends of the M-C bond strengths based on the ionicity of the bonds. The first trend of these charges show that the positive charge on the metal decreases going to the right in the periodic table. The decreasing contribution of ionic bonding to the right should therefore be a contributing factor for the smaller bond energies to the right. The second trend of the charges shows that although the metal charge stays approximately the same between the different alkyl systems, the carbon charge changes. The negative carbon charge is largest for methyl and smallest for isopropyl in line with the expected larger delocalization of electrons on the methyl groups. The decreased carbon charge for the more substituted alkyls should therefore lead to a smaller contribution of ionic bonding and thus also to smaller bond energies for these metalalkyls. Again, how much of the trends that originate from direct repulsion and how much from variations of the ionic bonding is difficult to determine and is also a somewhat academic question. Both effects can safely be concluded to contribute, and any attempt to obtain an exact division of these effects will certainly at the end anyway depend strongly on rather arbitrary definitions and is therefore likely to be counterproductive. Instead, the goal of the present study is first to produce accurate bond energies, not available for these systems previously, and secondly to provide simple rationalizations for the trends found. It should finally be noted that if a theoretical study of the present type should be meaningful, utmost care has to be exercised in finding proper ground states of the selected systems. In fact, only when the final results were assembled could several cases of wrong ground state assignments be detected. A severe complication in this context is the almost linear symmetry around the M-C bond present for most systems. For example, a single occupation of one of the components of a pseudo xor &orbital rather than the other near degenerate component will give final bond strengths that are quite similar but not the same. For example, for Ru-C3H7(n) three different 4A" states were found with different occupations of these nearly degenerate orbitals. The second lowest solution has a bond strength 1.5 kcaymol smaller than the one given in Table 4,and the third solution is another 2.5 kcdmol higher in energy. In this context these minor differences can turn around the final chemical conclusions completely.

Siegbahn

IV. Conclusions This study has been one of a series of studies of trends of second row transition metal bond strengths. Previous studies have focused on large general effects and mostly how these effects vary from left to right in the periodic table. For example, the comparative studies of metal-hydrogen and metal-halogen bonds24.25showed that the trend of the latter bonds are dominated by a large increase going to the left due to increased attraction to empty d-orbitals, whereas the variation of the former bonds is more sensitive to promotion and exchange effects. Differences between metal-hydrogen and metal-halogen bonds to the left were shown to be as large as 90 kcal/mol while the difference decreased to 10-20 kcal/mol to the right. Similarly, a comparative study of the metal-oxygen and metal-methylene bond strengths also showed quantitatively large effects on the trends.23 In another detailed study of the effects of the oxygen lone pairs in formyl and acetyl ligands, energetic trends of the order of 5-10 kcdmol were demonstrated.26 Very recently, lone-pair ligand effects for other ligands were studied, and effects ranging from small up to 25 kcaymol were found.27In contrast, the present study focuses on trends where the variation sometimes is in the range 0-5 kcal/mol, and this is much more demanding on the accuracy and systematic character of the investigation. Another difference is that the main emphasis here is put on the variation of the differences of bond strengths; see Figures 2 and 4, rather than on the variation of the absolute bond strengths. This type of trend of bond strength differences is probably of a higher general chemical interest since it should be generalizable to a larger extent to more realistic transition metal complexes. For example, this type of trend is independent of promotion and exchange effects. The main conclusions of the present study can be summarized as follows. Differences between the strengths of M-C bonds for different hybridizations on carbon follow the same order and have the same origin as the differences between the corresponding C-H bond strengths. A similar conclusion can be drawn for metal-alkyl bonds for different alkyl groups. This means that the strongest M - C bonds are found for the acetylenic M-C2H systems, and the weakest ones studied here are the ones for the M-C3H7(iso) systems. The strengths of all M-C bonds decrease rapidly to the right in the periodic table. Also the differences between different M-C bond strengths decrease to the right. These trends can best be explained by ionic contributions to the bonds and repulsive effects between the metal and the electrons on carbon and its ligands. For example, acetylene is the most acidic of the hydrocarbons studied here and M-C2H is therefore the strongest bond found. For the alkyl groups electron delocalization leads to less negative carbon atoms for the more substituted alkyls and therefore to weaker ionicity in the bonding. Also, substituting hydrogen atoms with alkyl groups on the bonding carbon atom leads to more repulsion toward the metal and weaker M-C bonds. References and Notes (1) Schultz, R. H.; Bengali, A. A,; Tauber, M. J.; Weiller, B. H.; Wasseman. E. P.; Kyle, K. R.; Moore, C. B.; Bergman, R. G. J. Am. Chem. SOC. 1994, 116, 7369. Bengali, A. A,; Schultz, R. H.; Moore, C. B.; Bergman. R. G . J . Am. Chem. SOC. 1994, 116, 9585. Bengali, A. A,; Bergman, R. G.; Moore, C. B. J . Am. Chem. SOC. 1995, 117, 3879. (2) Wasserman, E. P.; Morse, C. B.; Bergman, R. G. Science 1992, 255, 315. (3) Jones. W. D.: Feher. F. J. Acc. Chem. Res. 1989. 22. 91 (4)Siegbahn, P. E. M.; Blomberg, M. R. A,; Svensson, M. Chem. Phys. Lett. 1994, 223, 35. ( 5 ) Siegbahn. P. E. M.; Svensson, M.; Boussard, P. J. E. J . Chem. Phys. 1995, 102, 5377. (6) Blomberg. M. R. A,; Siegbahn, P. E. M.; Svensson, M. J . Am. Chem. SOC. 1992, 114, 6095. Siegbahn, P. E. M.; Blomberg, M. R. A,;

Metal-Carbon Bond Strengths in Transition Metal Complexes Svensson, M. J . Am. Chem. Soc. 1993, 115, 4191. Siegbahn, P. E. M.; Blomberg, M. R. A. Organomefallics 1994, 13, 354. (7) Huzinaga, S. J . Chem. Phys. 1977, 66, 4245. (8) Huzinaga, S. J. Chem. Phys. 1965, 42, 1293. (9) GAMESS (General Atomic and Molecular Electronic Structure System): Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A,; Jensen, J. H.; Koseki, S.; Gordon, M. S.; Nguyen, K. A.; Windus, T. L.; Elben, S. T. OCPE Bull. 1990, 10, 52. (IO) Siegbahn, P. E. M.; Svensson, M. Chem. Phys. Lett. 1993, 216, 147. (11) GRADSCF is a vectorized SCF first- and second-derivative code written by A. Komornicki and H. King. (12) Chong, D. P.; Langhoff, S. R. J. Chem. Phys. 1986, 84, 5606. (13) Johnson, B. G.; Gill, P. M. W.; Pople, J. A. J. Chem. Phys. 1992, 97, 7846. (14) Martin, R. L. J. P h y . Chem. 1983, 87, 750. See also: Cowan, R. D.; Griffin, D. C. J. Opt. Soc. Am. 1976, 66, 1010. (15) STOCKHOLM is a general purpose quantum chemical set of programs written by P. E. M. Siegbahn, M. R. A. Blomberg, L. G. M. Pettersson, B. 0. Roos, and J. Almlof. (16) Leopold, D. G.;Murray, K. K.; Miller, A. E. S.; Lineberger, W. C. J. Chem. Phys. 1985, 83, 4861, and references cited therein.

J. Phys. Chem., Vol. 99, No. 34, 1995 12729 (17) Ervin, K. M.; Gronert, S.;Barlow, S. E.; Gilles, M. K.; Harrison, A. G.; Bierbaum, V. M.; DePuy, C. H.; Lineberger, W. C.; Ellison, G. B. J . Am. Chem. Soc., in press. (18) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J . Chem. Phys. 1991, 94, 7221. (19) Bauschlicher, C. W., Jr.; Langhoff, S. R. Chem. Phys. Lett. 1991, 177, 133. (20) Pauling, L. The Nature ofthe Chemical Bond, 3rd ed.; Come11 University Press: Ithaca, NY, 1960. (21) Coulson, C. A. Valence, 2nd ed.; Oxford University Press: Oxford, UK, 1961. (22) Forstes, Z. Phys. Chem. 1939, B43, 58. (23) Siegbahn, P. E. M. Chem. Phys. Lett. 1993, 201, 15. (24) Siegbahn, P. E. M. Theor. Chim. Acta 1993, 86, 219. (25) Siegbahn, P. E. M. Theor. Chim. Acfa 1994, 87, 441. (26) Blomberg, M. R. A.; Karlsson, C. A. M.; Siegbahn, P. E. M. J . Phys. Chem. 1993, 97, 9341. (27) Siegbahn, P. E. M. J . Am. Chem. Soc. 1994, 116, 7722.

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