Carbonyl insertion into metal-hydrogen and metal ... - ACS Publications

Mar 23, 1993 - sequence of second-row transition metal atoms. ... of the row, due to a repulsive interaction between the oxygen lone pair and occupied...
0 downloads 0 Views 2MB Size
Download PDF
J. Phys. Chem. 1993,97, 9341-9350

9341

Carbonyl Insertion into Metal-Hydrogen and Metal-Methyl Bonds for Second-Row Transition Metal Atoms Margareta R. A. Blomberg,' Christina A. M. Karlsson, and Per E. M. Siegbahn Department of Physics, University of Stockholm, Box 6730, S - 11 3 85 Stockholm, Sweden Received: March 23, 1993; I n Final Form: June 24, 1993"

The carbonyl insertion reaction into metal-hydrogen and metal-methyl bonds has been studied for the entire sequence of second-row transition metal atoms. The energetics of this reaction have been calculated including correlation effects of all valence electrons. The carbonyl addition complexes, the transition states for the insertion reaction, and the product formyl and acetyl complexes have been characterized. From gas-phase values the exothermicity of carbonyl insertion into the metal-methyl bond can be estimated to be about 10 kcal/mol. The actually computed exothermicity is 5-7 kcal/mol larger than this value for the atoms to the left, due to $-bond formation, and 7-8 kcal/mol smaller than the gas-phase value for the atoms in the middle of the row, due to a repulsive interaction between the oxygen lone pair and occupied 4d-orbitals. Since the metal-hydrogen bond is normally stronger than the metal-methyl bond, the exothermicity is smaller for insertion into a metal-hydrogen bond. On the other hand, the directionality of the methyl group makes the insertion barrier height smaller for insertion into metal-hydrogen bonds. The addition of chloride ligands will significantly enhance the insertion process for complexes of metals to the right. Ligands are also needed to block formation of stable carbonyl complexes.

I. Introduction The carbonyl ligand is one of the most common ligands in transition metal complexes. It is also directly involved in several important catalytic reactions.lS2 Several of these catalytic processes involve carbonyl insertion into metal-carbon bonds as one of the steps. Carbonyl insertion into a metal-alkyl bond occurs, for example,in alkene carbonylationand in the Monsanto process for production of acetic acid.

+

-

-

MR CO MR(C0) MCRO In these processes cobalt and rhodium complexes are the most importantcatalysts, but iron, ruthenium,and palladium complexes can also be used.2 Although examples of such alkyl to acyl insertions are known for all of the transition elements' the corresponding carbonyl insertion into a metal-hydrogen bond is much less common. It has been suggested that the latter reaction should be highly endothermic for most transition metals.2 Observation of carbonyl insertion into metal-hydrogen bonds has been made only for a few very special systems including a thorium complex3and possibly also a zirconium complex.4 Formyl formation has also been observed for rhodium complexes, but the mechanism is believed to be a radical chain mechanism.5 Reaction 1 with R = methyl or hydrogen has been the subject of a large number of theoretical studies, both of semiempiricaltype and of ab initio type. The current understanding of this reaction has recently been reviewed by Koga and M ~ r o k u m a . ~One . ~ of the problems studied in detail theoretically for some specific systems is the question of why carbonyl insertion into metal-carbon bonds seems to be preferred compared to insertion into metal-hydrogen bonds.6-8 The conclusion on this point from the studies by Koga and Morokuma6v7and by Nakamura and Dedieu8is that insertion into metal-carbon bonds is thermodynamically more favorable than the corresponding hydrogen reaction, which is in line with the previous suggestions based on experimental estimates of metalmethylandmetal-hydrogenbondstrengths. Even if thedifference in the thermodynamicsof reaction 1 for methyl and hydrogen is mostly due to the metal-carbon bonds being weaker than the metal-hydrogen bonds, there are other, less well understood, factors which also influence the energetics of this process. A *Abstract published in Aduance ACS Abstracts, August 15, 1993.

compensating factor favoring insertion into metal-hydrogen bonds is that there is a larger gain in energy from the carbon-hydrogen bond formed in the insertion reaction into the metal-hydrogen bond than from the carbon-carbon bond formed in the insertion reaction into the metal-carbon bond. The overall favoring of carbonyl insertion into metal-carbon bonds is unlike the rather similar olefin insertion reaction, where olefin normally prefers to insert into metal-hydrogen rather than into metal-carbon bonds. A structural problem believed to be of significant importance for the carbonyl insertion reaction has been addressed in several studies. This is concerned with the tendency for the metal to have an attractive interaction with the oxygen lone pair in the product acyl or formyl complexes. This question has been studied theoretically, in particular for the RMn(C0)s complex, by Berke and Hoffmanng and by Ziegler, Versluis, and Tschinke.10 Different conclusions were reached in these studies. In the local density study an $-complex with a short metal-oxygen distance was found,'Owhereas in the extended Hiickel study the +complex where the metal-oxygen distance is long was found to be most table.^ In another study, at the Hartree-Fock level, Axe and Marynickl found the q*-complexto be more stable in agreement with the conclusion drawn by Ziegler et al. Carbonyl insertion into a metal-hydrogen bond has also been studied for an early transition metal complex, that of ScC12HC0, by Rapp6.'2 In this case only the +form of the formyl complex was found to be stable. Experimentally, $-acyl structures have been established for early transition metal and actinide complexes, e.g., by Floriani and co-workers for zirconium and titanium complexes.l3 Electron correlationeffects are generally found to be important for transition metal complexes. For carbonyl insertion this has been the subject of several investigations. Dedieu et al.14 found that correlation effects are of large importance for the relative energeticsof carbonyl insertion into a manganese complex. This was shown to be due to an unbalanced treatment, without correlation effects included,of the ?r backdonation Mn-CO bond in the reactant compared to the treatment of the covalent MnCHO bond in the product. For carbonyl insertion intoa palladium complex, electron correlation effects were found to be less important and actually go in the opposite direction compared to the case for the manganese complex. This is in agreement with the results of an earlier study by Koga and Morokuma for another

0022-3654/93/2097-9341$04.00/00 1993 American Chemical Society

9342 The Journal of Physical Chemistry, Vol. 97, No. 37, I F ’93

palladium c0mplex.1~ In general, electron correlation effects to describe ‘R backdonation are much more important for first-row transition metals than for those of the second row. The discrepancy between the results of a study by Antolovic and Davidson16 and of a local density study by Versluis et al.” for a cobalt complex can probably also be explained by the lack of a description of correlation effects in the study by Antolovic and Davidson. Another problem studied for the carbonyl insertion reaction has been whether this reaction should be regarded as a hydride migration rather than a carbonyl insertion. The conclusion reached by Nakamura and Dedieu8is that it is the hydride that migrates. This result is in line with experimental results for carbonyl insertion into a metal-methyl bond on a manganese model complex, showing that it is the alkyl group that migrates.8 For this question to be meaningful, systems with a sufficient number of ligands have to be studied. In the present study, which mostly concerns transition metal complexes without additional ligands, there is no difference between the two ways to view the reaction and in the following the reaction will be called carbonyl insertion in analogy with the previously studied olefin insertion. The carbonyl insertion reaction is of fundamental significance since it is one of the simplest examples of transition metal reactions involving a three-centered transition state. The rather similar olefin insertion reaction is in this respect different since it involves a four-centered transition state. The main orbital interactions involved in the carbonyl insertion reaction have been the focus of numerous previous investigations and are by now well characterized. The key orbital is the HOMO, which is a bonding combination of the hydrogen 1s-orbital and the carbonyl T * orbital, somewhat destabilized by the 5aCOorbita1, and an empty spd-hybrid orbital on the metal. This orbital description was used by Nakamura and Dedieu8to rationalize their finding that it is the hydride that migrates. Berke and Hoffmanng have also used orbital interaction diagrams of this type to explain the fact that the carbonyl insertion into a metal-hydrogen bond is easier than that into a metal-alkyl bond. The present study is part of a more general systematicapproach toward the understanding of the electronic structure aspects of the reactivity of second-row transition metal complexes. Until now, about 500 systems have been studied at the same level of accuracy. Thegeneralideasin this project arethat thedominating electronic structure effects occur at the transition metal atom and that these effects are therefore present already for the naked systems without ligands. Strong indications that this is actually so can, for example, be seen in the large similarity in geometries and key orbital interactions for ligated and nonligated systems. It should be added that ligand effects will not be neglected in the present approach but will be discussed in terms of their modifications of the electronic structure on the metal atom. Typically, the addition of ligands will modify the electronic spectrum of the metal and therefore change the reactivity of the metal. Other effects such as direct electron transfer between the metal and the ligands obviously also occur in some cases. The direct steric effect ligands have on the reactivitiesof the complexes will only be addressed at a qualitative level in terms of, for example, blocking bonding sites. This aspect will be discussed also in the present paper. The details of the steric effects can, of course, be important but are normally not connected with the electronic structure aspects, and the present electronic structure methods are therefore not very useful for studying such effects. The main emphasis in the work presented here is on the new data produced by the correlated calculations. This data should be more accurate than what has been obtained in previous studies and should be of enough accuracy to be regarded on the same footing as if it had been generated by a moderately accurate experimental technique. Since wave functions are also generated in the calculations, these can be used to interpret the results, but this

Blomberg et al.

TABLE I: Geometries, Occupations, and Energies for the Naked MeW-Carbonyl, MCO, Systems. The Energies Are Calculated Relative to Ground-State Metal Atoms and CO. The Bmding Energies of the Corresponding Metal-Ethylene Systems Calculated at the Same Level of Accuracym Are Also Given for Comparison atomic ground OCCUMhE(C0) hE(C2H4) metal state state pationo CO [AI [kcal/moll [kcal/moll -1 1.2 -18.3 Y 2D(5s24d1) Zr F( 5s24d2) -14.6 -19.0 Nb 6D(5s14d4) -25.7 -19.6 -1.9 -2.5 Mo 7S(Ss14dS) Tc 6S(5s24dS) -11.5 +3.6 -32.0 -22.8 Ru sF(5s14d7) -31.5 -30.9 Rh ‘F(5s14d8) -26.1 Pd lS(5s04d10) -33.1 Theorbital notations u,, ud, and uzzareonly approximatelydescribing the actual character of the orbital. aspect of the present study should not be overemphasized. In general, it has been found that the present results are best analyzed in terms of general chemical concepts. For representative cases of previously published studies in the present project, see refs 19-22. Even if there has been a large number of previous theoretical studies on the carbonyl insertion process, only two of the systems studied in the present paper have actually been studied before. One of these studies is on carbonyl insertion in the Rh(C0)H system by McKee et al.23 For this system, carbonyl insertion was found to be strongly endothermic and without any barrier for the reverse process of C-H dissociation of the formyl group. The other study was made by Pacchioni et on the same rhodium complex and the corresponding palladium complex. The results are quite different from those obtained by McKee et al., which is probably due to the use of an inadequate ECP in the study by Pacchioni et al. 11. Results and Discussion

The discussion of the results is divided into five subsections. In the first subsection the naked transition metal carbonyl systems will be discussed. In the second subsection the effects on the metal carbonyl systems from adding either a hydride or a methyl ligand will be analyzed. The third and fourth subsections constitute the main part of the present work and concern the carbonyl insertion reaction into the metal-hydrogen or the metalcarbon bonds. In the third subsection the inserted products are discussed, and in the fourth subsection the transition states and the barrier heights are compared. Finally, in the fifth subsection ligand effects are discussed including some preliminary results for the effects on the reaction of additional chloride ligands. a. The Naked Metal-Carbonyl Complexes. The main topic of this paper is carbonyl insertion into metal-hydrogen and metalcarbon bonds. However, before this reaction is discussed the results for the naked metal-carbonyl systems deserve some attention, since this is the first time results for an entire transition metal row are available at this level of accuracy, although the corresponding cationic systems have been studied previously.25 The results for the metal-carbonyls are given in Table I. It is of particular interest to compare these results to previously published results for the second-row transition metal-ethylene systems30 which also bind with a donation-backdonation mechanism. The ethylene results are therefore also given in the table. The carbonyl binding energies are furthermore plotted in Figure 1. The binding energies of carbonyl and ethylene to naked transition metal atoms show a similar behavior across the row. The largest binding energies are found to the right and these are in both cases around 30 kcal/mol. The binding energies are

The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 9343

The Carbonyl Insertion Reaction M -H,

+

CO +AE-H,

MCO

TABLE Ik Summary of Calculated Energies (kcal/mol) for the CO Insertion Reaction into a Metal-Hydrogen B o d MH + CO + AE MCHO. The Energies Are Calculated Relative to Ground-State Metal Hydride and CO

-

M Y Zr Nb Mo Tc Ru

MH+CO

M(CO)H -3.4 -21.3 -25.0 -16.3

-24.0 -34.5 -34.9 -17.9

Rh Pd

t

I I

Y

I

Zr

I

I

Nb

Mo

Tc

Ru

I

Rh

w

Figure 1. Metal-carbonyl binding energies for naked metal atoms and for metal hydrides, calculated relative to free carbonyl and metal atoms or metal hydrides, respectively, using the ground state of each system. 10-15 kcal/mol smaller for the atoms to the left than for those to the right and the binding energies for the atoms in the middle of the row are quite small. However, a closer inspection of the electronic structure of the carbonyl and ethylene systems shows that there are also some marked differences between the systems. One such difference is that the ground-state spin is higher for the carbonyls of zirconium, niobium, and molybdenum. The gradual occupation of the d-orbitals going from left to right in the periodic table is also different. This is partly due to the obvious difference in symmetry of the two systems. For the linear carbonyl systems the interaction between the ligand and the metal in the s-system is attractive for both the x- and the y-component, whereas only one of these interactions is attractive for the ethylene systems. For the carbonyls both these ?r-components are singly occupied for the atoms to the left, from zirconium to molybdenum, and doubly occupied from technetium to palladium. The interaction in the a-system is somewhat more complicated. This interaction is best described as an attraction between the carbon lone pair and an unshielded metal nucleus. The interaction between the metal s-electrons and the carbon lone pair is repulsive, which means that atomic states with low 4s occupation are preferred. This is best seen on the ground-state occupation for the zirconium system. For ZrCO the metal atom is thus in the excited d3s1 state rather than in its ground dZs2 state. The trend of the carbonyl binding energies can be understood from two factors. One factor is the occupation of the metal d-shell, described above, and the other is the 4s occupation in the lowlying atomic states. One reason the binding energies are larger for the atoms to the right is thus that the ground-state 4s occupation is normally lower to the right than to the left, which leads to a lower repulsion toward the CO lone pair for the atoms to the right. Another reason is that for the atoms to the right both the 4d, components are doubly occupied, which leads to a better backdonation than for the atoms to the left where these orbitals are singly occupied. To achieve the occupation with two doubly occupied 4 4 orbitals, the technetium atom has to be promoted to an excited state, which leads to some loss of binding energy for TcCO. For technetium an excitation is also required from the ground state s*-occupation to an sl-occupation with lower a-repulsion. A similar excitation is needed for most atoms to the left. Of the complexes for the atoms to the left, NbCO has the largest binding energy since the niobium atomic ground state has a singly occupied 5s-orbital. For zirconium a promotion to an excited state is needed, and for yttrium there is only one occupied 4d,-component, leading to a less efficient backdonation than for both zirconium and niobium. For the molybdenum complex finally, the binding energy is smallest since this is the only complex where both the repulsive 5s- and 4d,-orbitals are required to be occupied. For the complexes of the atoms to the left of molybdenum the 4d,-orbital is unoccupied, and for the

MCOH' -1.8 -13.6

-19.1 13.9

7.8 -3.0 -19.7 7.7

MHCO -16.4 ~~~

-21.3 -14.6 -0.2 -2.4 0.6 -5.3 -4.9

TABLE III: Summary of Calculated Energies (kcal/mol) for the CO Insertion Reaction into a Metal-Methyl Bond: MCH3 + CO + AE MCCH3O. The Energies Are Calculated Relative to Ground-State Metal-Methyl Systems and CO

-

M Y

Zr Nb Mo

Tc Ru

Rh Pd

MCHi+CO 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

M(COKH3

MCOCH3'

~~

-1.5 -20.2 -25.5 -16.8 -21.3 -3 1.9 -34.9 -19.7

14.9 11.2 2.7

21.9 16.7 3.2 -12.0 13.5

MCCHiO -15.4 -14.8 -16.8 -3.0 -2.5 -5.6 -10.8 -10.9

atoms to the right the 5s0-statecan be mixed in to hybridize away the repulsive electrons. This state cannot be mixed into the wave function for the atoms to the left since it has the wrong spin. b. Ligand Effectson the Metal-CarbonylSystems. The metalcarbonyl systems with one additional hydride or methyl group represent important stationary points for the presently studied carbonyl insertion reactions. The carbonyl binding energies are rather strongly modified by the presence of a hydride ligand as seen from the second column in Table I1 and from Figure 1. The results of adding a methyl ligand are, as expected, extremely similar to those of adding a hydride ligand, see the second column of Table 111, and in the rest of this subsection only the hydride ligand will therefore be discussed. The electronic structure of the MH and MCH3 systems has been described in refs 26 and 27. The main ligand effects on the carbonyl binding energy can be relatively easily rationalized by considering differences in promotion energies between the metal hyrides and the naked metal atoms. Starting from the left with Y(CO)H, the carbonyl binding energy decreases substantially when the ligand is added. The reason for this is that a promotion to an excited state is needed for YH, which is a closed-shell singlet, in order to form the a-backdonation bond to CO. In contrast, for zirconium a larger promotion energy is paid for the zirconium atom than for ZrH in order to bind the carbonyl. As already mentioned above in subsection a, the doubly occupied 5s-orbital in the ground state of the zirconium atom is strongly repulsive toward thecarbon lone pair and the atom is therefore promoted to a 5s' state. To the right in the periodic table, there is a large decrease in the binding for palladium when a ligand is added. The reason for this is again 5s repulsion. The ground state of the palladium atom is a 5sostate with low repulsion toward the carbonyl, whereas in order to form the bond to the hydrogen there has to be a promotion to the 5s' state with a larger repulsion to the carbonyl. In contrast, for both ruthenium and rhodium the same atomic so state can be used to bind the carbonyl for both the naked atoms and the hydrides and the ligand effects on the binding energies are therefore rather small for these systems. In the middle of the row for molybdenum and technetium the addition of a hydride ligand leads to substantial increases of the carbonyl binding energies. In both these systems the added ligand has to a large extent removed an electron from the repulsive sd, region. This leads directly to a larger binding for the molybdenum system. For technetium, this leads to a possibility to use a higher spin

9344

Blomberg et al.

The Journal of Physical Chemistry, Vol. 97, No. 37, 1993

?

TABLE I V Geometries and Metal Populations for the

Product Metal-Formyl Systems, MCHO, of the CO Insertion Reaction into a Metal-Hvdroeen Bond

Y Zr Nb Mo Tc Ru Rh Pd

‘A’ =A1’ 6A1 5A1’ ‘A’’ ‘A’ 2A‘

2.28 2.19 2.25 2.97 2.94 2.99 2.80 2.93

2.40 2.24 2.23 2.20 2.12 2.15 1.97 2.09

+O. 17 +o. 12 +0.19 +O. 17 +O. 17 +0.14 +0.08 +0.34

0.78 2.04 3.86 4.88 5.89 7.03 8.70 9.27

1.52 1.38 0.70 0.82 0.79 0.69 0.09 0.30

0.46 0.40 0.21 0.10 0.09 0.08 0.06 0.08

state for binding the carbonyl than was the case for the naked atoms, which in turn leads to a smaller loss of both promotion energy and exchange energy and thus to a larger carbonyl binding energy. Also for the ligated carbonyl systems, interesting comparisons can be made to the previously studied corresponding olefin systems.28 The first point to note here is that for theolefin systems the hydride ligand effect has the same sign as for the carbonyl systems in most cases, but the effect is generally much larger for the olefin systems. This is particularly true for the systems to the left in the periodic table, where the bonding in the olefin systems is much more covalent than for the carbonyl systems. In fact, these olefins are best described as metallacycles. As already mentioned above, the naked metal-olefin systems to the left therefore have a lower spin than the corresponding carbonyls. For the naked atoms this leads to substantial losses of exchange energy when the covalent bonds are formed in the metallacycle. This exchange energy loss will be smaller when hydride ligands have already been added to the metal since these ligands are also covalently bound which reduces the spin prior to the bonding of the olefin. For the zirconium olefin system, the addition of a hydride ligand therefore increases the olefin binding energy by as much as +24.3 kcal/mol and for the niobium system the increase is + 1 1.3 kcal/mol. The corresponding energies for the hydride ligand effect in the less covalently bound carbonyl systems are +6.4 kcal/mol for zirconium and -1.4 kcal/mol for the niobium system. c. The Insertion Products. The energies of the insertion products for carbonyl insertion into metal-hydrogen bonds, the formyl complexes, are given in the final column in Table 11. The corresponding energies for the acetyl complexes, which result from carbonyl insertion into metal-carbon bonds, are given in Table 111. Details of the geometries and population analysis for the formyl complexes are given in Table IV. The corresponding results for the acetyl complexes are very similar and are therefore not given here. The energies of the insertion products of both hydrogen and methyl insertion are plotted in Figure 2. It should be noted that these energies are reaction energies starting from the metal-hydride or metal-methyl systems. This means, for example, that the energies for the acetyl complexes given in the table and in the figure display differences in binding energy trends for the acetyl systems and the corresponding methyl systems. The structure of the acetyl complex is shown in Figure 3 for one metal to the left in the periodic table (yttrium) and for one metal to the right (palladium). Before the discussion of the carbonyl insertion reaction starts it is worthwhile to consider some of the simplest thermodynamic consequencesof the insertion process. These concern the strengths of the carbon-hydrogen bond formed in the metal-hydrogen insertion reaction and the carbon-carbon bond formed in the metal-methyl insertion reaction. Reasonable estimates of these bond strengths can be obtained by consideringthe corresponding gas-phase reactions without the metal present. The calculated reaction energy between a hydrogen atom and carbon monoxide is thus 16.0 kcal/mol, while the corresponding reaction energy for the methyl radical is 9.5 kcal/mol. The simplest estimate for the exothermicity of the carbonyl insertion into the metal-methyl

M -R

+co

+

AE--M%

lot 0. -10. -20

-30

t I

1

I

I

1

I

1

I

I

Y

Zr

Nb

Mo

Tc

Ru

Rh

Pd

Figure 2. Reaction energies for the insertion of carbonyl into a metalhydrogen bond or a metal-methyl bond, calculatedrelative to freecarbonyl and metal hydrides or metal methyls, respectively,using the ground state of each system. Negativevalues for Ucorrespond toexothermic insertion reactions.

Figure 3. Structure of the insertion products, exemplified by the acetyl complexes of yttrium and palladium.

bond, where one metal-carbon bond is formed and one is broken, is thus about 10 kcal/mol. This is in very good agreement with the values actually computed for the atoms to the right but somewhat lower than those for the atoms to the left and higher than those for the metals in the middle of the row. A similar estimate for the reaction energy of the carbonyl insertion into the metal-hydrogen bond is more complicated since a metal-hydrogen bond is broken and a metal-carbon bond is formed. A simple estimate of these reaction energies can therefore not be given at this point. The first point to note for the reaction energies of the product insertion complexes concerns the overall energetics of the insertion process. As mentioned in the Introduction, the general experimental evidence is that carbonyl insertion should be easier into a metal-carbon than into a metal-hydrogen bond. From the results in the tables and in the figures it can be seen that it is only for the metals to the far right, ruthenium-palladium, that the stabilitiesare considerably larger for the acetyl than for the formyl complexes. For most of the other metals the stabilities of the two types of complexes are about the same, and for zirconium the

The Carbonyl Insertion Reaction formyl complex is actually the more stable one. It is expected that these trends will not be strongly modified by the presence of ligands. It is interesting to note that the only observations of carbonyl insertion into metal-hydrogen bonds actually concern metals to the left in the periodic table in line with the present results that theseshould have the most favorablereaction energies. Another result worth noting in the tables and in the figures is that the product formyl and acetyl complexes represent the lowest point on the potential surface only for the yttrium systems. For the zirconium-formyl system the energy is the same as for the Zr(C0)H system, but for all the other systems studied here the addition complex M(C0)H is the most stable structure. If the carbonyl insertion reaction should proceed from the addition complex, ligands are therefore needed, see further discussion in subsection e. Without additional ligands the insertion rearrangement reaction is particularly endothermic for the atoms to the right arid it is difficult to see that electronic structure effects of ligands could change the results for, for example, rhodium where the endothermicity in the formyl case is 29.6 kcal/mol. Instead, ligands are needed to stericallyblock the carbonyl addition site. It can therefore be predicted that carbonyl insertion will not occur, except for yttrium and possibly zirconium complexes, unless the complexes are covalently saturated with ligands, in which case the carbonyl addition complex will be a weakly bound, much less interesting, intermediate. The main trends of the formyl and acetyl reaction energies as seen in Figure 2 can be described in the following way. The largest reaction energies are found for the atoms to the left. For the acetyl complexesthe reaction energiesgo through a minimum in the middle of the row and then start to increase again toward the right. For the formyl complexes the reaction energies from molybdenum to palladium are almost constant, but with slightly smaller reaction energy for ruthenium and technetium. For both the formyl and acetyl complexes there is a marked decrease in the reaction energies between niobium and molybdenum of about 14 kcal/mol. Also worth noting, as mentioned above, is that to the left the formyl and acetyl reaction energies are about the same whereas to the right the ones of acetyl are larger. Three main effects can explain the above trends. First, there is a clear attractive interaction between the oxygen lone pair and empty 4d-orbitals for the atoms to the left. Only yttrium, zirconium, and niobium have empty 4d-orbitals, and this explains the marked decrease in the reaction energies going from niobium to molybdenum for both the formyl and the acetyl complexes. The strength of the present systematic approach is that the differential size of the lone-pair attraction can be estimated. This is best done by a comparison to the metal-methyl binding energies,Z9where the lone-pair effect is absent. In Figure 4 the metal-methyl binding energies are for this purpose plotted together with the metal-formyl binding energies. (The metalacetyl binding energies are almost identical to the metal-formyl binding energies.) It is clearly seen in this figure that the metalmethyl binding energies are about 5 kcal/mol weaker than the other two binding energies for yttrium, zirconium, and niobium where the attractive lone-pair effect is present. Once all 4dorbitals become occupied, for molybdenum, the interaction with the oxygen lone pair turns to be repulsive by 6-7 kcal/mol Going further to the right, the second important effect responsible for the reaction energy trends for the carbonyl insertion can be noted. The difference between the metal-methyl and the other two binding energies becomes much smaller than in the middle of the row. The origin of this effect is that the atoms to the right can mix with the low-lying 5s0-state to form sd-hybrids, which effectively avoids the repulsion with the oxygen lone pair. This type of hybridization is less efficient for the atoms in the middle of the row since the 5s0-state for these atoms is much higher in energy. A simple comparison of trends has thus given quantitative information about specific bonding effects. It would be difficult

The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 9345

AE [kcallmoil

I

-10

-201

-701

/ ,

,

,

,

l

l

Y

Zr

Nb

Mo

Tc

Ru

/

Rh

l

W

Figure 4. Binding energies of the metal-methyl and metal-formyl complexes, calculated relative to metal atoms and free methyl or formyl radicals, respectively, using the ground state of each system.

to reach similar conclusions using any energy decomposition method where this type of lone-pair effect would be hard to strictly define. It should finally also be noted that the attraction between the oxygen lone pair and the empty 4d-orbitals can be clearly seen in the geometries of the complexes to the left, see Figure 3. This effect was mentioned in the Introduction and has been noted previously in several other both experimental3,4J3 and theoretical studies.I”l2 The third major factor responsible for the trends in the reaction energies is that metal-hydrogen bonds are stronger than metalcarbon bonds. This effect does not enter the trend of the acetyl binding energies since a metal-carbon bond is broken and a metalcarbon bond is formed in the insertion process. However, for the formyl complexes, a metal-carbon bond is formed and a metalhydrogen bond is broken leading to a total loss of energy in this process. This energy loss is particularly large for the atoms to the right. The binding energies of the naked M-H and M-CHJ systems have been published previously for the transition metals M of the entire second r0w.2~ The energy difference between these bonds is an almost steadily increasing function going from left to right in the periodic table, with a difference for yttrium of 4.2 kcal/mol and for palladium of 12.8 kcal/mol. This effect explains the result that the reaction energy difference between the formyl complexes of yttrium and palladium is larger (by 7 kcal/mol) than the corresponding difference for the acetyl complexes. d. The Carbonyl Insertion Reaction. One of the main results of the present study is that the barrier heights for carbonyl insertion into metal-carbon bonds are always much higher than those for insertion into metal-hydrogen bonds. The barrier heights are given in Tables I1 and I11 and are also shown in Figure 5 . Details of the geometries and population analysis for the transition states of the hydride insertion reaction are given in Table V. The corresponding results for the alkyl insertion reaction are very similar and are therefore not given here. The structure of the transition state for the alkyl insertion reaction is shown in Figure 6 for one metal to the left in the periodic table (yttrium) and for one metal to the right (palladium). The difference in barrier height between the alkyl and the hydride insertion processes is largest for the atoms to the left with values of about 20 kcal/mol. The differencesfor the complexesfrom molybdenum to palladium are in the range 6-9 kcal/mol. Based on previous s t ~ d i e s , l ~ . 2 ~ . ~ ~ the fact that the insertion barrier is higher for metal-methyl bonds than for metal-hydrogen bonds is not surprising. This is analogous to the same finding for olefin insertion and also in line with the fact that the oxidative addition of C-H bonds has higher

9346

The Journal of Physical Chemistry, Vol. 97, No. 37, 1993

Blomberg et al.

? M - R + CO + AE +*::-':R]"

C

AE [kcallmoll

I

(

Y

,

Zr

I

Nb

I

Mo

I

TC

I

Ru

I

Rh

'

Pd

Figure 5. Transition-state energies for carbonyl insertion into metalhydrogen and metal-alkyl bonds, calculated relative to free carbonyl and metal hydrides or metal methyls, respectively, using the ground state of each system. Negative values for AE correspond to barrierless insertion reactions.

TABLE V Geometries and Metal Populations for the Transition State of the CO Insertion Reaction into a Metal-Hydrogen Bond M state M-H M-C C-H d M ) 4d 5s 'A' 2.14 Y 2.34 1.45 +0.08 0.89 1.55 Zr Nb Mo Tc Ru Rh Pd

2A'' 5A' 6A' 5A" 2A' 'A' 2A'

1.89 1.90 2.02 2.00 2.08 1.90 1.90

2.34 2.37 2.13 2.03 1.91 1.84 2.02

2.44 2.77 1.64 1.57 1.23 1.30 1.46

+0.04 +0.08 +0.12 +o. 17 +0.11 +o.o 1

+0.07

2.39 4.02 4.72 5.90 7.50 8.56 9.40

1.14 0.62 0.69 0.50 0.22 0.25 0.26

5~ 0.41 0.39 0.23 0.42 0.37 0.11 0.12 0.21

barriers than the addition of the H-H bond. The origin of these trends is always the same, namely, that the metal-alkyl bond is much more directional than the metal-hydrogen bond. The spherical hydrogen atom can bind in several directions simultaneously, and the bonding can therefore gradually turn from the one in the reactants to the one in the products. In contrast, the directional metal-alkyl bond first has to be more or less broken in the reactant before the alkyl can start to bind in the product. It is furthermore interesting to note that the barrier height difference between the hydride and the corresponding alkyl reactions are for all these different types of reactions of rather similar magnitude. For example, for the olefin insertion reaction the insertion into metal hydrogen bonds is typically 10-20 kcal/ mol easier than for insertion into the alkyl bonds. This similarity between different systems is one reason a picture is suggested where this effect is connected with direct differences between the hydride and the alkyl bonds themselves. It was mentioned in the Introduction that the experimental experience is that carbonyl prefers to insert into metal-alkyl bonds rather than into metal-hydrogen bonds. From the present results for the barrier heights of the reaction, it is clear that this cannot be explained as a kinetic effect. Instead, in agreement with previous studies- it must be concluded that it is a thermodynamic property. However, of the presently studied systems, the yttrium complexes are the only ones for which the carbonyl insertion product is more stable than the carbonyl adduct systems, and in this case the insertion is actually more exothermic for the formyl system than for the acetyl system. The systems for which the carbonyl insertion into metal-methyl bonds is thermodynamically favored compared to the insertion into metal-hydrogen bonds are found to the far right. Of the ligand-free systems studied here, the rhodium complexes are particularly interesting. As seen in Tables I1 and 111, and in

/ \ Figure6. Transition-state structuresfor the carbonyl insertion exemplified by the yttrium and palladium methyl complexes.

Figure 5, these complexeshave very low barriers for the insertion. The barriers for the nearby atoms, ruthenium and palladium, are much higher. This is in agreement with what has been found previously for the olefin insertion process in ligand-free complexes** and the explanation is the same. Two factors are responsible for the low barrier for the rhodium complexes. First, the critical bonding orbital at the transition state has a 4d-bond at the metal, binding simultaneously to the methyl carbon (or hydrogen) and to the carbonylcarbon. Secondly, the 5s-electrons of the metal act very repulsively in the insertion process. Therefore, at the transition state the metal atoms to the right prefer to be in a 5s0-statewhich is the least repulsive state toward the ligands. For this purpose, the rhodium atom is particularly suited,sincethe 5s0-stateis both low-lying and capableof forming a d-bond at the transition state. For ruthenium, the 5so-state is much higher and there will also be a loss of exchange energy when the d-bond is formed since there is a second open d-orbital for ruthenium. For palladium the 5s0-state is the ground state but this state has a closed 4d-shell and can therefore not form any d-bond. The result for palladium is a compromise between the nonrepulsive, but nonbonding, 5s0-stateand the bonding, but high-lying and repulsive, %*-state. For the rhodium complex it can finally be added that the present results are in perfect agreement with the results by McKee et al.,23but there is a large disagreement with the results of Pacchioni et al.24 In agreement with the conclusion drawn in the review by Koga and Morokuma? it is concluded here that the ECP used in ref 24 is probably inadequate. e. Ligand Effects. The main effect of ligands on the carbonyl insertion process is to blockbondingsites for the carbonyladdition reaction. This aspect of ligands was already discussed in subsection c. Without blocking ligands, the carbonyl insertion will not occur for any other than yttrium and possibly zirconium

The Carbonyl Insertion Reaction complexes for thermodynamicreasons. Concerningthe electronic structure effects of adding ligands, the most important effects will occur when covalent ligands are added. By covalent ligands are here meant ligands that change the oxidation state of the metal. In this subsection some brief comments will be made concerning the addition of the simplest form of covalent ligands, namely, hydrogen atoms. Some preliminary results concerning the electronic structure effects of adding chlorine ligands will also be mentioned. The effects of adding covalently bound hydrogen ligands on the strength of metal-carbon and metal-hydrogen bonds have been discussed in detail in a previous study.29 In general, the metal-hydrogen bonds are stronger than metal-alkyl bonds. The main origin of this difference is a larger repulsion between the metal 4d-electrons and the ligand electrons for the alkyl bond since the number of repulsive electrons is larger on carbon than on hydrogen. The difference in bond strength between the metalhydrogen and the metal-alkyl bonds therefore increases with the number of 4d-electrons for the metals to the right. As already mentioned in subsection c, this is the main origin for the preference for carbonyl insertion into metal-alkyl bonds for these metals. An interesting finding in the previous study of covalent ligand effects is that the difference in alkyl and hydride bond strengths decreases the higher theoxidation state is. For very highoxidation states of V and VI, the alkyl bonds actually become marginally stronger than the hydride bonds. The explanation for this trend is again that direct repulsion between the ligand electrons and the metal 4d-electrons dominate the differencein bond strengths. As more covalent ligands are added, increasing the oxidation state, the metal 4d-electrons are either removed from the metal or effectively hybridized away from the repulsive region. The consequence of this effect for carbonyl insertion is that addition of large numbers of covalent ligands, thus increasingthe oxidation state, will favor insertion into hydride bonds compared to insertion into alkyl bonds. In the present project on the reactivity of second-row transition metal complexes, a large number of comparisons have by now been made on the effect of changing hydride ligands to chloride ligands. In general, this turns out to have a surprisingly small effect for themetals to theleft, but therecan bemajor destabilizing effects on the covalent bonds to other ligands in some cases for the metals to the right. Examples of this effect can be found already for some simple triatomic molecules.30 For MH2 the two hydride bond strengths are in general rather similar. However, replacing one of the hydrides with a chloridereduces the remaining hydride bond strength in, for example, RhHCl by 26 kcal/mol. In contrast, for the atoms to the left there is hardly any effect of a similar exchange. The origin of the destabilizing effect for the atoms to the right is most easily understood by comparing the spectral properties of the neutral metal atoms and the corresponding cations. To covalently bind hydrogen the optimal binding state of the atom is the sl-state. This state is also the ground state for neutral metal atoms to the right like rhodium and ruthenium. The ground state of the cations of these atoms is, on the other hand, the so state which thus needs to be promoted to efficiently be able to form covalent bonds. The bonds to the cations of the atoms to the right are therefore in general weaker than the bonds to the neutral atoms. When chlorine is bound to a metal atom, the metal atom is effectively transformed into a cation, which thus explains the destabilizing effect for the atoms to the right from chloride ligands. For the atoms to the left, the cations form equally strong bonds as the neutral atoms and no destabilizing effect of adding chloride ligands is therefore found for these atoms. Another important effect for the metals to the right is that, as the destabilizingchloride ligands have been added, the systems will be strongly stabilized again by the addition of lone-pair ligands. Preliminary results of adding chloride ligands on the carbonyl addition complexes illustrate these effects. The

The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 9341 main result is that the carbonyl binding energies are strongly increased by the presence of chloride ligands for rhodium and palladium, but for the metals to the left there is no such effect. The net effect for these unsaturated systems is that the addition of chloride ligands will not thermodynamically favor the carbonyl insertion product in comparison to the addition complex. However, for covalently saturatedsystems where thecarbonyl addition complex is just weakly bound or not bound at all, chloride ligands are predicted to kinetically favor the carbonyl insertion for the atoms to the right. The reason for this is again that the addition of chloride ligands will turn the metal atoms into cations with so-groundstates. From the results in Table I for rhodium, which has a low-lying so-state already as a neutral atom, it can be seen that this state is very favorable for the carbonyl insertion, due to its low repulsion toward ligands. In line with this prediction, results for the transition state of olefin insertion indicate that the presence of chloride ligands markedly lowers the barrier for the insertion process.31 It is interesting to note in this context that the commercially used Wilkinson catalyst is a rhodium-chloride complex and also that the catalyst used in the Monsanto carbonylation process is a rhodium-iodide complex, which is expected to have similar properties as the corresponding chloride complex.

111. Conclusions Based on the present halculations, the main trends of the energetics of the carbonyl insertion process for second-row transition metals can be easily rationalized. The simplest case is the insertion into the metal-carbon bond, since one metalcarbon bond is broken and one is formed in this process. The exothermicityof this reaction comes from the new carbon-carbon bond formed. Based on gas-phase values this bond strength can be estimated to be about 10 kcal/mol, which is in reasonable agreement with the exothermicities actually calculated. A detailed inspection of the individual reaction energies for the different metals reveals that the exothermicitiesare about 5 kcal/ mol larger for the atoms to the left and 7-8 kcal/mol smaller for the atoms in the middle of the row. For the atoms to the right the values are close to 10 kcal/mol. The origin of these minor differences between the metals can be found in the interaction between the metals and theoxygen lone pair in the acetyl products. To the left there is thus a 5 kcal/mol attraction between the lone pair and empty 4d-orbitals. This attraction can also be seen in the product complexes which form +structures for yttrium, zirconium, and niobium, which all have empty 4d-orbitals. For the atoms to the right of niobium, which all lack empty 4dorbitals, the interaction between the metal and the oxygen lone pair is basically repulsive. This explains the somewhat smaller exothermicities toward the middle of the row. For the atoms to the far right there is an additional effect that essentially removes the repulsive interaction with the lone pair. This effect is a mixing between the bonding %'-state and the low-lying 5s0-state,which leads to an efficient hybridization away from the oxygen lone pair. For rhodium and palladium the exothermicities of the carbonyl insertion are therefore quite close to the value of 10 kcal/mol predicted from the gas-phase value. Since the exothermicity of the carbonyl insertion has such a simple origin, it is expected that ligands should have only minor effects on the exothermicity. Electronic structure effects due to ligands are thus not expected to affect the bond strengths of the metal-methyl and the metal-acetyl bond very differently. It is also difficult to imagine steric ligand effects which will have a strong differential effect on these bonds at least in favor of the metal-acetyl bond. This means that for the carbonyl rearrangement, from the carbonyl adduct to the inserted product, to be exothermic it is required that the metal-carbonyl bond should not be stronger than 10 kcal/mol. Since normal metal-carbonyl bond strengths are in the range 25-35 kcal/mol, the carbonyl insertion cannot be regarded as a migratory insertion process

9348 The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 from a normal, stable, carbonyl complex. The prediction from the present results is that the carbonyl involved in the insertion should come from outside to a complexwhich is already covalently saturated. This should lead to a carbonyl adduct which is at most very weakly bound, or it should lead to a direct insertion reaction. It is interesting to note here that it has been suggested, on the basis of experimental results on the common cobalt catalyst for the hydroformylationprocess, that theinserting carbonyl might not be precoordinated to the metal but the process would rather occur via a transition state where cobalt-carbonyl bond making occurs concurrently with cobalt-alkyl bond breaking and alkylcarbonyl bond making.2 However,in contrast to such a hypothesis, IR spectroscopy on a model manganese system has shown that the carbonyl insertion into the methyl bond actually occurs intramolecularly.'8 Ligands are thus predicted to have only a minor influence on the exothermicity of the carbonyl insertion reaction into a metalcarbon bond, but the influence on the kinetics of the reaction can still be substantial. Previous calculations in the present project have shown that chloride ligands sometimes can have a dramatic influence on barrier heights. For the olefin insertion reaction into a metal-hydrogen bond the barrier height was lowered by about 40 kcal/mol by exchanging a hydride ligand with a chloride ligand for complexes of rhodium and palladium. The origin of this effect is that when chloride ligpnds are added, the metal atoms are effectively transformed into cations. The ground state of the metal cations to the right is the so-state which has a minimal repulsion toward ligands, and this will therefore lead to lower barriers for the carbonyl insertion when chloride ligands have been added. The effectiveness of the so-state in the transitionstate region of the insertion reaction can also be seen on the results of the naked rhodium atom, which has a low-lying so-state and a very low barrier for the insertion. For the atoms to the left no similar effect from adding chloride ligands is expected. An interesting aspect of the present study is the difference between thecarbonyl insertion into a metal-hydrogen and a metalmethyl bond. Experimentally, insertion into the metal-methyl bond appears to be preferred. This fact is not explained by a kinetic effect since the barrier heights are always higher for the insertion into the metal-methyl bond. The origin of the difference in barrier heights is the more directional character of the methyl bond than of the hydride bond. Instead, the favoring of insertion intoa metal-carbon bond has a thermodynamicorigin. The reason this reaction is favored is that metal-hydrogen bonds are normally stronger than metal-methyl bonds. This is particularly true for the atoms to the right. For the atoms to the left, the present results show that insertion into metal-hydrogen bonds can actually be favored. One way to favor insertion into hydride bonds is to increase the oxidation state of the metal. Previous systematic studies have shown that this makes the metal-methyl and metalhydrogen bond strengths more similar, thus removing the thermodynamicpreference for insertion into metal-methyl bonds.

Appendix A. Computational Details In the calculationsreported in the present paper for the carbonyl insertion into the second-row transition metal hydrogen bonds, reasonably large basis sets were used in a generalized contraction scheme32 and all valence electrons were correlated. Relativistic effects were accounted for using first-order perturbation theory including the mass-velocity and Darwin termsSJ3 For the metal atoms the Huzinaga primitive b a ~ i s 3was ~ extended by adding one diffuse d-function, two p-functions in the 5p region, and three f-functions, 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-(contraction, and the 4d orbital was described by a triple-(contraction. The

Blomberg et al.

f functions were contracted to one function giving a [7s,6p, 4d, 1fJ contracted basis. For carbon and oxygen the primitive (9s, 5p) basis of H u ~ i n a g a 3was ~ used, contracted according to the generalized contraction scheme to [3s, 2pJ, and one d function, with exponent 0.63 for carbon and 1.33 for oxygen, was added. For hydrogen the primitive (5s) basis from ref 35 was used, augmented with one p function with exponent 0.8 and contracted to [3s, lp]. Most of the geometry optimizations were performed at the SCF level using the GAMESS set of program^,,^ and in these cases somewhat smaller basis sets were used. First, for the metal atoms a relativistic ECP according to Hay and WadtJ7was used. The frozen 4s and 4p orbitals are described by a single-f contraction, the valence 5s and 5p orbitals are described by a double-( basis, and the 4d orbital is described by triple-{ basis, including one diffusefunction. The rest of the atoms are described by standard double-{ basis sets. It should further be noted that for most of the optimizations, a C, symmetry constraint was used, in the first place to reduce computational time in the following correlated calculation and also to improve convergence of the geometry. This symmetry constraint is expected to have noeffect or only a very small effect (less than 1 kcal/mol) on the energy. For the optimized transition-state geometries the Hessian was calculated for a few cases, for both M-H and M-CHJ insertion, and was found to have only one imaginary frequency. For example, for CO insertion into M-H the imaginary frequency is 642 cm-1 for the yttrium case and 1044 cm-l for the palladium case. Since the transition-state geometries are very similar for all metals it is assumed that all of them are true transition states having only one imaginary frequency. The ligand-free metalcarbonyl systems are exceptions to the general optimization scheme. For these systems, the metal-carbon bond distance was optimized at the correlated level using the same methods and basis sets as in the rest of the correlated calculations. The C-O bond distance was determined in the same way but only for the palladium system. This C-O bond distance was then used for all the other ligand-free carbonyls. The correlated calculations were performed using the modified coupled pair functional (MCPF) method,3s which is a sizeconsistent, single reference state method. The metal 4d and 5s electrons and all electrons on the ligands except the C 1s and 0 1s electrons were correlated. A few words should be said about the level of calculation chosen in the present study. As described above the geometries are optimized at the SCF level and the relative energiesare calculated at the MCPF level, Le., electron correlation effects are included. First, it should be emphasized that the correlation effects on both the reaction energies and the barrier heights are large. The size of the correlation effects also varies strongly across the periodic table so that the diagrams shown in the figures would have appeared very differently if SCF results had been used instead of correlated results.20328 The conclusion is that correlation effects have to be included in the calculations to give reliable trends for activation energiesand binding energies. In this context it should be noted that the correlation effects for this type of systems are well described by the single reference MCPF method.19J9*40 Furthermore, the use of SCF optimized geometriesgiving reliable results, can be questionedin particular since the correlation effects are so large. There are several results on systems similar to those studied in the present paper showing that SCF-optimized and MCPF-optimized geometries give very similar relative energies.19~~1 The origin of this surprising behavior is that in the most interesting region of the potential energy surfaces (including both the transition state and the insertion products) the SCF and the MCPF surfaces are quite paralle1.42 Another reason SCF geometries can be used is that the potential energy surfaces are often rather flat in both the transition-stateregion and the insertion product region, so that discrepancies in SCF- and MCPF-

The Carbonyl Insertion Reaction optimized structures have very small effects on the relative energies. A more systematic investigation of the accuracy of the geometry optimizationschemeis in progress.43 For seven different metal hydride methyls, containing different second-row metals and a varying number of ligands, equilibrium geometries were determined both at the SCF level and at the QCISD (quadratic configuration interaction singles and doubles) level. The energy of each structure was obtained at the MCPF level. For each system the total energies calculated in the SCF and in the QCISD geometries are very similar, within 1.5 kcal/mol, with the energies at the SCF geometries actually lowest in all cases. Also, a preliminary test of the barrier height for the oxidative addition of water to the palladium atoms, comparing the MCPF energies for the SCF and the QCISD optimized geometries, gives agreement within 1 kcal/mol. The conclusion is that the use of SCF-optimized structures gives reliable results for the trends in activation energiesand binding energies for second-rowtransition metal complexes if correlation effects are included in the energy calculations. For the first-row transition metals, on the other hand, there are indications that geometries optimized at the SCF level may often have too large errors, at least for some type of systems, see, for example, refs 44 and 45. This is one of the reasons second-row metals were chosen for this study. The present level of calculation, where all valence electrons are correlated using basis sets including f-functions on the metal, is a major improvement compared to calculations done at the HartreeFock level. However, even in the present treatment the errors compared toexact resultscannot be neglected. Exact errors are difficult to give but reasonable estimates can be given. The present treatment has an error of 3 kcal/mol for the H-H bond and about 5 kcal/mol for the C-H bond. It is reasonable to expect that the error should be 7-8 kcal/mol for a bond involving a second-row transition metal. These error estimates are essentially confirmed in recent comparisons with measured bond strengths in cationic system^.^^^^' Three points are important to note in this context. First, the errors in the bond strengths are not random but highly systematic. The bond strengths are thus always underestimated. This means that corrections for these errors are expected to leave the trends shown in the figures and the tables essentially unchanged. Second, even though an error in a bond strength of 7 kcal/mol is not negligible it should be remembered that the errors at the Hartree-Fock level are almost 1 order of magnitude larger, and that useful results still have been generated at this level. The same argument can of course be applied to an even greater extent to results obtained at the extended HUckel level. Third, to increase the accuracy notably from the present level is extremely costly. For example, a large correlated calculation of the C-H bond strength in methane including d-functions on hydrogen and f-functions on carbon still gives an error of 2 kcal/mol,48to be compared to the present error of 5 kcal/mol. Finally, all the results reported are for the ground state of each system. In most cases the ground state of the reactants has a different total spin than the ground state of the products. Two comments can be made in this context. First, the question of whether the binding energies should be given relative to reactants with the same spin as the products or relative to the spin of the ground-state reactants is mainly a pedagogical problem. One set of energies can be easily transferred to the other set usingavailable excitation energies. The common praxis has been to relate to the energies for the ground spin states of the reactants, and this praxis will be followed here. The main advantage with this praxis is that the procedure is well defined. A more serious question concerning the spin states is what actually happens dynamically during the reaction. If the reaction starts with ground-state reactants and ends up with ground-state products with a different spin, the spin has to change through spin-orbit effects. These effects are known to be strong for transition metals so this surface

The Journal of Physical Chemistry, Vol. 97, NO.37, 1993 9349

hopping is intuitively expected to occur with a high probability. This problem has been studied in detail by who showed that in the case of the association reaction between the nickel atom and carbon monoxide, the crossingprobability is near unity. Also, in order to rationalize the experimental results for the oxidative addition reaction between the nickel atom and water, a highcrossingprobabilityhas to beassumed.9 Since the potential surface for the high-spin reactants is normally strongly repulsive, the crossing between the two spin surfaces will in most cases occur far out in the reactant channel, long before the saddle point of the reaction is reached. This is at least true in the most interesting cases where the low-spin surface of the reactants is not too highly excited. This means that the probability for surface hopping through spin-orbit coupling will affect the preexponential factor of the rate constant but not the size of the barrier. The computed barrier heights discussed here should therefore in most cases be directly comparable to experimental measurements of activation energies. All the present calculations have been performed on a FX-80 ALLIANT computer, and the final energy evaluations were performed using the STOCKHOLM set of programs.51

References and Notes (1) Collman, J. P.; Hegedus, L. S.;Norton, J. R.; Finke, R. G . Principles and Applications of Organotransition Metal Chemistry; University Science Books: Mill Valley, 1987. (2) Masters, C. HomogeneousTransition-metal Catalysis; Chapman and Hall: London, 1981. (3) Moloy, K. G.; Marks, T. J. J . Am. Chem. Soc. 1984, 106, 7051. (4) Manriquez, J. M.; McAlister, D. R.; Sanner, R. D.; Bercaw, J. E. J. Am. Chem. SOC.1978,100, 2716. (5) Paonessa, R. S.;Thomas, N. C.; Halpern, J. J . Am. Chem. Soc. 1985, 107,4333. (6) Koga, N.; Morokuma, K.In Transition Metal Hydrides; Dedieu, A., Ed.; VCH Publishers: New York, 1992; Chapter 6. (7) Koga, N.; Morokuma, K. Chem. Rev. 1991, 91, 823. (8) Nakamura,S.;Dedieu,A. Chem.Phys.Lett. 1984,111,243. Dedieu,

A.; Nakamura, S. In The Challenge of Transition Metals and Coordination Chemistry; Veillard, A., NATO Advanced Study Institute Series; Reidcl: Dordrecht, 1986; Vol. 176, p 277. (9) Berke, H.; Hoffmann, R. J . Am. Chem. SOC.1978, 100, 7224. (10) Ziegler, T.; Versluis, L.; Tschinke, V. J . Am. Chem. Soc. 1986,108, 612. (11) Axe, F. U.; Marynick, D. S.J. Am. Chem. SOC.1988, 110, 3728. (12) Rap*, A. K. J. Am. Chem. Soc. 1987,109, 5605. (13) (a) Fachinetti, G.; Floriani, C.; Marchetti, F.; Merlino, S.J. Chem. SOC.,Chem. Commun. 1976,522. (b) Calderazzo, F. Angew. Chem., Int. Ed. E n d . 1977. 16. 299. 714) Dedieu, A.; Sakaki, S.; Strich, A.; Siegbahn, P. E. M. Chem. Phys. Lett. 1987, 133, 317. (15) Koga, N.; Morokuma, K. J . Am. Chem. SOC.1986, 108, 6136. (16) Antolovic, D.; Davidson, E. R. J . Am. Chem. SOC.1987,109,5828. (17) Versluis, L.; Ziegler, T.; Baerends, E. J.; Ravenek, W. J. Am. Chem. SOC.1989, 111, 2018. (18) See, for example: Elschenbroich, Ch.; Salzer, A. Organometallics; VCH Publishers: Weinheim, 1989. (19) Blomberg, M. R.A.;Siegbahn,P. E. M.;Svensson, M.J. Am. Chem. SOC.1992, 114, 6095. (20) Blomberg, M. R. A.; Siegbahn, P. E. M.;Svensson, M. J . Phys. Chem. 1992, 96, 9794. (21) Siegbahn, P. E. M.; Blomberg, M. R. A. J. Am. Chem. Soc. 1992, 114, 10548. (22) Siegbahn, P. E. M. Chem. Phys. Lett. 1993, 201, 15. (23) McKee, M. L.; Dai, C. H.; Worley, S.D. J . Phys. Chem. 1988,92, 1056. (24) Pacchioni, G.; Fantucci, P.; Kouteckg, J.; Ponec, V. J . Coral. 1988, 112, 34. (25) Barnes, L. A.; Rosi, M.; Bauschlicher, C. W., Jr. J . Chem. Phys. 1990. 93,609. (26) Langhoff, S. R.; Pettersson, L. G. M.; Bauschlicher, C. W., Jr.; Partridge, H. J. Chem. Phys. 1987, 86, 268. (27) Bauschlicher, C. W., Jr.; Langhoff, S.R.; Partridge, H.; Barnes, L. A. J. Chem. Phys. 1989, 91, 2399. (28) Siegbahn, P. E. M. Chem. Phys. Lett. 1993,205,290. Siegbahn, P. E. M. J. Am. Chem. Soc. 1993, 115, 5803. (29) Siegbahn, P. E. M.; Blomberg, M. R. A,; Svensson, M. J . Am. Chem. Soc. 1993, 115, 4191. (30) Siegbahn, P. E. M. Theor. Chim. Acta, in press. (31) Siegbahn. P. E. M. To be Dublished. (32) (a)-Almlbf, J.; Taylor, P. R. J. Chem. Phys. 1987, 86, 4070. (b) Raffenetti, R. C. J. Chem. Phys. 1973, 58, 4452.

9350 The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 (33) Martin, R. L. J. Phys. Chem. 1983.87.750. Sec also: Cowan, R. D.; Griffin, D. C. J . Opr. Soc. Am. 1976,66, 1010. (34) Huzinaga, S. J. Chem. Phys. 1977,66,4245. (35) Huzinaga, S. Approximate Atomic Functions, 11. Department of Chemistry Report; University of Alberta: Edmonton, Alberta, Canada, 1971. (36) 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.; Npyen, K. A.; Windus, T. L.; Elbcrt, S. T. QCPE Bull. 1990,10,52. (37) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985,82, 299. (38) Chong, D. P.; Langhoff, S. R. J. Chem. Phys. 1986,84, 5606. (39) Blomberg,M.R.A.;Siegbahn,P. E. M.;Nagashima,U.; Wennerbcrg, J. J. Am. Chem. Soc. 1991,113,476. (40) Bauschlicher, C. W., Jr.; Partridge, H.; Sheehy, J. A,; Langhoff, S. R.; Rosi, M. J. Phys. Chem. 1992, 96,6969. (41) Sodupe, M.; Bauschlicher, C.W., Jr.; Langhoff, S. R.; Partridge, H. J. Phys. Chem. 1992, 96, 2118. Rosi, M.; Bauschlicher, C. W., Jr. Chem. Phys. Lerr. 1990,166,189. Bauschlicher, C. W., Jr.; Langhoff, S. R. J. Phys. Chem. 1991,95, 2278.

Blomberg et al. (42) Siegbahn, P. E. M.; Blomberg, M. R. A,; Svensson, M. J. Am. Chem. Soc. 1993,115, 1952. (43) Siegbahn, P. E. M.; Svenason, M. To be published. (44) Antolovic, D.; Davidson, E.R. J. Chem. Phys. 1988,88,4967. (45) Veillard, A,; Daniel, C.; Rohmer, M.-M. J. Phys. Chem. 1990, 91, 5556. (46) Sunderlin, L. S.; Armentrout, P. B. J. Am. Chem. Soc. 1989, 111, 3845. (47) Blombcrg, M. R. A,; Siegbahn, P. E. M.; Svensson, M. To be

published. (48) Bauschlicher, C. W., Jr.; Langhoff, S . R. Chem. Phys. Lerr. 1992, 177, 133. (49) Mitchell, S. A. In Gas-Phase Metal Reactions; Fontijn, A., Ed.; Elsevier: Amsterdam, 1992; Chapter 12. (50) Mitchell, S. A,; Blitz, M. A.; Siegbahn, P. E. M.; Svensson, M.

Submitted for publication. (51) 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. Alml6f.