Reaction of Second-Row Transition-Metal Cations with Methane - The

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J. Phys. Chem. 1994,98, 2062-2071

Reaction of Second-Row Transition-Metal Cations with Methane Margareta R. A. Blomberg,' Per E. M. Siegbahn, and Mats Svensson Department of Physics, University of Stockholm, Box 6730, S-113 85 Stockholm, Sweden Received: September 15, 1993; In Final Form: December 3, 1993@

A b initio quantum chemical calculations, including the effects of electron correlation, are performed on the methane C-H insertion reaction for the second-row transition-metal singly charged cations. Comparisons are made to experimental studies of alkane activation by naked transition-metal cations. The accuracy of the calculations is estimated through a comparison to a few highly accurate calculations, yielding typical bond energy errors of 3-8 kcal/mol in the present calculations. Applying these estimated errors to the calculated relative energies leads to good agreement with the experimental results for alkane activation, in most cases. An exception is ethane activation by the molybdenum cation, which is experimentally observed to be exothermic. In contradiction to this observation, a C-H insertion barrier of about 15 kcal/mol is predicted on the basis of the present calculations. Comparison between the naked cations and the naked neutral metal atoms for the methane activation reaction shows that although the cations have a lower C-H insertion barrier for the metals to the left and in the middle of the periodic table, for the metals to the right the insertion threshold is higher for the cations than for the neutrals. Also, for almost all second-row metals, the insertion product is less stable for the cations than for the neutrals. These differences between the neutrals and the cations can be understood in terms of differences in atomic spectra.

I. Introduction During the past decade a large amount of accurate experimental information on gas-phase reactions between transition-metal cations and simple molecules has become available.14 Besides the natural interest in these reactions by themselves, this information is also of large importance from a theoretical point of view to evaluate the accuracy of quantum chemical results. Even though ab initio quantum chemical calculations on transition-metal complexes are much more accurate than they used to be, the errors are still far from negligible. A fact of major importance in this context is that the errors in this type of calculation are always systematic. For example, the binding energies are always underestimated. On the basis of experience from more accurate calculations, crude estimates of these systematic errors for particular types of bonds can be obtained. By comparison to experimental results for cations, these estimates can be tested and refined and they can then be used to correct the theoretical values and make these results much more useful for quantitative purposes. Due to the technical difficulty to experimentally determine the energetics of neutral species, the information on reactions for neutral transition-metal systems is much more scarce than it is for the cations. It is only during the last few years that reliable data from neutral reactions have started to becomes a ~ a i 1 a b l e . s ~One indication from this type of experiment is that naked transition-metal atoms appear to be less reactive toward alkanes than cations are.& These reactions, for both the neutrals and the cations, normally proceed in several steps, andonly the final productsareobserved. Typically,neutral fragmentsof thealkanes, e.g. Hzareeliminated. The experimental results furthermore indicate that the first step in many of these reactions is the oxidative addition of the cation into a C-H bond, and the barrier for this step is thus an important part of the observed reactions. In the current paper we present the results from calculations on the reaction between the second-row transition-metal singly charged cations and methane. The main part of this investigation is concerned with the insertion of the metal into the C-H bond, forming a metal methyl hydride: *Abstract published in Advance ACS Abstracts, January 15, 1994.

By comparison of the methane activation by naked transitionmetal cationswith the same process for the naked neutrals, studied at the same level of previous accuracy,8.9 further understanding of the oxidative addition reaction mechanisms can be obtained. For many chemical reactions in solution,charged complexesplay an important rule. It is therefore of general chemical interest to investigatethe effect of a positive charge on the metal on a simple reaction like C-H activation in methane. Furthermore, the C-H activation in alkanes is experimentally observed for Rh(1) and Ir(1) complexes, and the simplest possible model of this oxidation state of the metal is a singly charged metal cation. Calculations have also been performed on the methane activation reaction where covalent ligands like hydride'O and chloridell were added to the metal, and comparisonscan therefore be made between the cationic results and the MX (X= H, C1) results, thus evaluating the cationic modeling of metals in oxidation state I. To extend the possibilities for comparisons to gas-phase experiments, a few calculations have also been performed on other parts of the potential surface for the M+ + CH4 interaction, and also on the reaction with a larger alkane, ethane. This study is part of a larger project concerned with reaction mechanismsfor chemical reactions involving second-row transition metals and different classes of small molecules. One such class of molecules is alkanes, for which C-HE and C-Cz activation have been studied. Another class is alkenes, for which *-mordination,I3C-H activation? and insertion into M-H14 and M-CIS bonds have been investigated. Reactions between second-row transition metals and HzO,l6 NH3,17 and CO1*have also been studied, and investigations of several other reactions are in progress. The reactions studied are chosen because they are elementary steps in important catalytic reactions like methane activation, alkane and alkene functionalization, Ziegler-Natta polymerization, water-gas shift reaction, etc. In contrast to the traditional approach for theoretical studies of organometallic reaction mechanisms, where calculations on a few realistic systems have been p e r f 0 r m e d , 1 ~the ~ ~present ~ approach uses simple model systems and focuses on trends. For this purpose the reactions of

0022-36S4/94/2098-2062%04.50/0 0 1994 American Chemical Society

The Journal ojPhysical Chemistry, Vol. 98, No. 8, 1994 2063

Reaction of Second-Row Transition-Metal Cations TABLE 1: Calculated Energies for the $ Complexes of the Mf-CHI Systems, Relative to the Ground-State Mt + CHI Asymptote, Optimized M-C Bond Distances, and the Charges and 4d-Populations on the Metal M+ ground +complex state State AE [kcal/mal] R(M-C) [A] q M 4d +0.8 1.2 4.4 3.02 Y+ 3A~ 'S(s'p 2.70 +0.7 2.6 Zr+ "(d5') 'BI -10.4 Nb+

'D(d')

I&

-11.8

Mot

Tc+

6S(dS) 'S(d5s1)

6A~ 'AI

Ru+ Rh+

'F(d7) 'F(d*)

'BBI

-8.8 4.5 -13.3

Pd+

'D(d9)

0

3A2

2.65 2.80 3.12 2.59 2.65 2.54

-13.0 -17.0

+0.7 +n.8

+0.9 +0.9 +0.8 +0.8

3.9 5.0 5.0 6.9 7.9 9.0

The ID(d's1) state is 3.4 kcal/mol above the ground state. M**CH, + A E - [ M - C H ' ] '

Ai [krollmol]

t

I

Y

,

21

I

I

I

Nb

MO

Tc

,

Ru

, Rh

I

Pd

I

Figure 1. Energies for the MCH.+ molecular complexes, calculated relative to M+ and free CHI using the ground state of each system. For AEm see section 11.

naked transition-metal atoms with different small molecules have been performed as a starting point. As a second step, auxiliary ligands are introduced to investigate the ligand effects on the reaction mechanisms.l0."J4 For most reactions the entire second row of the transition metals is studied. 11. Results

The results from the present calculations will be presented in three subsections below. In the first subsection the molecular complexes formed between the cation and the nearly undistorted methane molecule will be described. In the second subsection the barrier heights and reaction energies for the C-H insertion process will be presented. In the third subsection the accuracy of the results will be discussed and the size of the errors in the calculated relative energies will be estimated. It should be noted that these errors are not random hut are expected to be highly systematic. This means that corrections for these errors leave the trends shown in the figures and the tables essentially unchanged. In the presentation of the results and in most of the discussion the directly calculated relative energies will be used, to conform to the previously published papers within this project. The corrected energies will only be used in the comparison to the gas-phase experimental results. Molecular Complexes. The interaction between the metal ion and the polarizable methane molecule via the long-range chargeinduced dipole force causes a precoordination of methane to the cation as the first step in thereaction. Thecalculatedcoordination energiesaregiveninTahle 1 andin Figure 1. With theexception of yttrium and technetium, the variations of the binding energies ofthemolecularcomplexesarerathersmall withenergiesmainly in the range 10-15 kcal/mol. However, there is a tendency for increased interactionenergiesgoingtoward the right in the periodic table, which is mainly due to the decrease of the atomic radii going from left to right. Furthermore, the least repulsive atomic stateis thesostate, since thes-electronsare themost diffuseones.

m

Figure 2. StNctureofthemethanemolecularcomplexes,MCH,+,shown by the example of rhodium.

This state is the ground state for the cations to the right of the periodic table, and this is thus another factor contributing to the larger binding energies to the right. Thevery low binding energy of the yttrium complex, 0.4 kcal/mol, is explained by the fact that yttrium, as theonly second-row metalcation, has ans2ground state, which is very repulsive. The lowest state of the molecular complex therefore correlates with an excited state of the cation. The lowest excited state of the yttrium cation is an SIstate (3D), and to decrease the repulsion further, also the highly excited so state has to be mixed in. All together this leads to a very low binding energy for the yttrium methane complex. In the case of technetium, the low binding energy is explained by the fact that the ground state of the technetium cation is an SIstate and that the so state has the wrong spin to mix in. Also the zirconium cation has an SI ground state, but in this case the so state has the correct spin and only a small excitation energy, yielding a fairly strongly bound complex. For molybdenum there is a slight deviation in the trend of increasing binding energies toward the right. The somewhat smaller binding energy for molybdenum as compared to niobium is caused by a longer bond distance in the molybdenum case, which in turn is caused by the fact that for the molybdenumcationall d-orbitalsareoccupied. Thismeans that the repulsion for molybdenum cannot be reduced by mixing empty and occupied d-orbitals. For niobium and toward the left there is one or more unoccupied d-orbital which decreases the repulsion toward the methane molecule. The mixing in of the so state, where this is possible, can be clearly seen on the 4dpopulations, which are given in Table 1. The structure of the molecular complexes is shown in Figure 2 by theexampleofrhodium. Theq'coordinationisa constraint in the present calculations. In a previous study.8 also 7' and 7 ) coordinations were tried for a similar neutral complex, and the energies were found to be rather similar to each other, with the 1 2 structure slightly lower than the other two. Musaev, Koga, and Morokuma'' also found the 1 2 structure to be the lowest one for the RhCHl+ complex. They obtained a binding energy of 6.9 kcal/mol using their main basis set, increasing to 16.8 kcal/mol when an f-function for rhodium was added. It is difficult to compare these results to our value of 13.0 kcal/mol obtained with our standard basis, which includes f-functions on the metals, since we obtain a binding energy decrease of only 1.5 kcal/mol from deleting the rhodium f-functions in our calculation, as compared to about 10 kcal/mol in ref 21. Inwrtion Products and TransitionStates. The reaction energies for the insertion reaction are given in Table 2, and they are also shown in Figure 3. The corresponding barrier heights are shown in Table 3 and in Figure 4. The structure of the transition state is shown in Figure 5 by the example of yttrium. In the insertion product the dominating bonding state is the SI state, which forms two covalent bonds to hydrogen and methyl involving the metal s-electron and one of the unpaired d-electrons. As can be seen from the population analysis in Table 2, there is also a mixing in of the so state. For the insertion reaction, the spin in the product is two steps lower than in the reactant due to the formation of two covalent bonds, and this lowering of the spin state occurs already before the transition-state region. The transition state

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TABLE 2 Calculated Energies for the MHCH3+ Insertion Products, Relative to the Ground-State M+ + CHI Asymptote, Optimized Geometries, and the Charges and 4d-Populations ou the Metal' AE [kcal/ M-H M-C H-M-C tilt(CH3) [degl 4" 4d state moll [A] [A] [degl

Y+

-11.9 -12.2 Nb+ 3A" 2.6 Mot 'A' 33.7 Tc+ 15.1 Rh+ 'A' 28.0

Zr+

1.94 1.84 1.75 1.68 1.65 1.55

!A' IA'

2.27 2.18 2.12 2.08 2.09 2.07

107.1 108.7 107.5 112.2 82.3 90.2

+1.03 1.09 +0.982.15 +0.92 3.43 + O M 4.64 +0.785.43 +0.607.68

2.5 3.1 3.7 0.1 4.4 2.3

For Ru+ and Pd+ no minima were found for this structure.

, Y

, 21

,

,

,

Nb

Mo

Tr

, Ru

,

,

Rh

Pd

Figure 4. Barrier heights for the M+ insertion into the C-H bond in methane, calculated relative to M+ and free CHI using the ground state of each system. For AE,, see section 11. The corresponding results for the neutral naked atoms are taken from ref 9 and far MCI from ref I I .

I , Y

,

,

,

,

21

Nb

No

lc

I

Ru

, Rh

# I

W

Figurrl Energies for the MHCH,+ insertion prcducts,calculatedrelative to M+ and free CHI using the ground state of each system. Negative values for AE correspond to exothermic insertion reactions. For AEseesection It. Thecorrespondingresults for theneutral nakedatomsare taken from ref 9 and for MCI from ref 11.

TABLE 3 Calculated Energies for the Transition States of the M+ CHI Insertion Reaction, Relative to the Ground-State M+ + CHI Asymptote, Optimized Geometries, and the Charges and 4d-Populations on the Metal' AE(add) [kcal/ M-H M-C H-M-C tilt(CH3) [A] [A] [deal [degl qu 4d state moll

+

Y+

'A'

Zr+ 'A'

Nb+ )A' Mo* 'A' Tc+ 'A' Rh+ ]A'

25.9 16.2 21.5 43.8 23.0 23.9

1.98 1.87 1.78 1.69 1.66 1.59

2.25 2.21 2.18 2.16 2.20 2.14

43.3 42.1 44.3 49.6 53.0 73.0

33.0 30.4 27.0 21.2 14.3 6.8

+0.79 1.38 +0.80 2.49 +0.81 3.51 +0.774.79 +0.785.59 +0.58 7.75

For Rut and Pd+ no transition states were found.

is a result of a crossing between two surfaces, and the height of the barrier is determined by two factors? One factor is the exothermicityofthereaction;i.e.strongbondsin the final product lower the barrier. The other factor is the position and character of the low-spin atomic asymptote; i.e. a low-lying atomic state with the same spin as the product and with a low s-population lowersthe barrier. Thelow s-population isimportant todecrease the repulsion toward the methane closed-shell electrons. In particular, a low-lying low-spin coupled so state seems to be important for a low barrier. For yttrium to molybdenum this corresponds to an excited so state, since the lowest so state is

Figure 5. Structure of the transition states for the M+ insertion into the C-H bond in methane, shown by the example of yttrium. high-spin coupled. The importance of the sQstate in the transitionstate region can be seen by the increased d-population at the transition state (Table 3) as compared to the insertion product (Table 2). The yttrium and zirconium cations have low-lying SI states, and the insertion products are bound by as much as 12 kcal/mol relative to the atomic ground states. The transition state for yttriumisconsiderably higher thanforzirconium.26ascompared to 16 kcal/mol. This difference is caused by the fact that the low-spin coupled so state is about 0.8 eV higher for yttrium than for zirconium. The niobium and technetium cations both have low-lying SI states, and the unstable insertion products, unbound by 3-15 kcal/mol, are due to the loss of exchange energy upon bond formation. Both these cations have low-lying low-spin coupled so states, and the fairly high barriers, 21-23 kcal/mol, are, as for the insertion products, caused by loss of exchange energy. For the molybdenum cation the SI state is very high in energy, 37 kcal/mol above the ground state, and the loss of exchange energy upon bond formation is high for both the SIand sostates. For this reason theenergies for both theinsertion product and the transition-state structure are significantly higher for molybdenum than for niobium and technetium. The ruthenium, rhodium, and palladium cations all have sQ ground states, and the SI states are high in energy. This type of spectrum leads to potential surfaces which are different from the rest of the systems studied here. As discussed above, the low repulsion of the so state leads to rather strongly bound (13-17

The Journal of Physical Chemistry, Vol. 98, No. 8,1994 2065

Reaction of Second-Row Transition-Metal Cations kcal/mol) 02 complexes, and this structure is actually the only minimum for these metals. For rhodium the geometry optimization is actually the only minimum for these metals. For rhodium the geometry optimization a t the HartreeFock level yields a minimum for the insertion product and a late transition state. At the correlated level, however, the transition-state energy is lower than the insertion product energy (Tables 2 and 3). For ruthenium and palladium, no insertion minima are obtained in the geometry optimization procedure, and therefore no results are given for these metals in Tables 2 and 3. For rhodium the ground state in the insertion product region is a triplet state, corresponding to a covalently bound d7 s1 configuration and originating from the 5F excited atomic state. (The quintet state of the rhodium atom forms two covalent bonds to the doublet hydrogen and the doublet methyl group, yielding a triplet state of the final product.) As mentioned above, the d population is much higher than seven, indicating that an electrostatically bound d8 so configuration is mixed in, originating from the 3Fatomic ground state. The high energy of the s1 states of these metals causes high energies for insertion product structures, as can be seen for rhodium, where the insertion product is 28 kcal/mol above the reactants. The low energy of the so states leads to comparatively low energies in the transition-state region, and therefore there are no elimination barriers for these metals. The potential surface for the interaction between Rh+ and methane has been calculated by Musaev, Koga, and Morokuma.21 They determined the stationary points at the CASSCF level and calculated the energetics using the multireference configuration interaction technique (MR-SDCI). The calculations were performed using a relativistic effective core potential for the rhodium atom and basis sets of similar quality to ours but without f-functions on rhodium. They obtained a very flat surface in the region of the insertion product with a rather similar structure for the transition state and the product. Similar to the results of our calculations, at the correlated level the minimum disappears and the transition-state energy becomes slightly lower than the insertion product, 32.9 and 33.6 kcal/mol above the Rh+ CH4 dissociation limit, respectively. The corresponding values obtained in the present study are 23.9 and 28.0 kcal/mol, respectively. Qualitatively, the results of the two theoretical studies are thus rather similar, showing that the energy in the insertion region is high above the isolated systems, with no elimination barrier. The lower endothermicity of the insertion reaction obtained in our calculations shows that a better basis set is more important than a multiconfiguration description. Accuracy of the Results. In the present study one of the goals is to make direct comparisons to gas-phase experimental results. For this purpose it is important to estimate the absolute errors in the calculated energetics, which will be done in this subsection. Comparison to experimental results also gives the possibility to evaluate these error estimates. Also, for comparison to experimental results, zero-point vibrational energies have to be included in thecalculated energies. Thecorrections on the relative energies due to differences in zero-point vibrational energy are estimated by calculating these energies for a few typical systems. The most severe error in the calculated relative energies comes from limitations in the one-particle basis sets and in the correlation treatment. These errors will be estimated on the basis of comparisons either to very accurate calculations on a few systems or to experimental results. It is important to note that one of the most important properties of ab initio methods is that the errors are always systematic. For example, bond strengths are always underestimated. Therefore, much more useful information is obtained if trends of results are studied. The trends will not be changed from the corrections for the error estimates done here. The zero-point vibrational energies were calculated at the Hartree-Focklevel. Thevalueobtained for methaneis 30.1 kcal/ mol, and the values obtained for the methane insertion product

+

and the transition state for the yttrium cation are 25.2 and 25.0 kcal/mol, respectively. Thus, the correction for zero-point energies lowers the insertion barrier and increases the binding energy of the insertion product with about 5 kcal/mol. A correction of 5 kcal/mol is therefore introduced for ail metals for these two points on the potential surface. Calculations on the C-H insertion reaction for ethane show that the same correction applies also for larger alkanes. To obtain the zero-point vibrational energy correction for the experimentally observed elimination reaction M+ + CH4 MCH2+ H2, zero-point vibrational energies were calculated also for YCH2+ and for H2. The values obtained for these systems are 13.9 and 6.4 kcal/mol, respectively. A zero-point energy correction of 10 kcal/mol, lowering the elimination product energies, is therefore applied for this reaction. A zero-point energy correction of 10 kcal/mol is calculated also for the ethane elimination reaction M+ + C2Hs MC2H4+ + H2. To estimate the error in the calculated energies due to limitations in basis sets and correlation treatment, the following procedure is adopted. First, it can be noted that with the type of computational methods used here binding energies are always underestimated. Second, it can be assumed that the error in the binding energy for a certain type of bond is approximately constant, independent of the number of bonds or the particular molecule. By assignment of an estimated error for each type of bond involved in the reacting molecules and comparison of the number of bonds of each type for reactants and products, the error in the calculated reaction energy can be estimated. There are two types of bonds involved in the C-H insertion reaction, C-H bonds and M-R bonds (R = H or C). In the elimination process observed in the gas-phase experiments, also the H-H bond is involved in the reaction. The error in the C-H bonds is estimated on the basis of comparison to very accurate calculations on CH4, CH3, and CH2 by Bauschlicher and Langhoff.22 For both C-H bond energies obtained from the energies of these three molecules, our calculations give a value very close to 5 kcal/mol smaller than the best estimate in ref 22. We therefore assign a value of 5 kcal/mol for the error in the C-H bond energies in our calculations. For the H-H bond we compare our calculated De with the corresponding experimental value23and find an error of 3 kcal/ mol. To estimate the error in M-R bonds, comparison is made to the highly accurate calculations on the MCH2+ systems by Bauschlicher et al.*4 Our calculated binding energy for YCH2+ is 17 kcal/mol lower than the best estimate obtained in ref 24. Since there are two Y-C bonds in the carbene, we assign an error of 8 kcal/mol for each M-C bond. The same error estimate of 8 kcal/mol is used for M-H bonds, even though preliminary calculations on MH+ indicate that the error in M-H bonds might be somewhat smaller than the error in M-C bonds. Calculations of the binding energy of several second-row MCH2+ systems, using the present level of calculation and the geometries from ref 24, show that the size of the error in M-R bonds is about the same for metals to the right in the periodic table. It should be noted that since the error at the present level of accuracy for C-H bonds is 5 kcal/mol, an error of 8 kcal/mol for M-R bonds appears quite reasonable. Using the above assigned errors for different bond types, the errors in the reaction energies can be estimated. First, for the C-H insertion reaction there is one C-H bond broken and two M-R bonds formed, yielding a net error in the reaction energy of 16 - 5 = 11 kcal/mol. Together with the zero-point energy correction of 5 kcal/mol this gives a total correction of 16 kcal/ mol in the reaction energies for the insertion reaction. Since the elimination barrier is rather insensitive to the level of calculation: it is assumed that the error estimate for the insertion product is valid also for the transition-state energy. Thus, for all metals both the transition-state energy and the insertion product energy

-

+

-

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The Journal of Physical Chemistry, Vol. 98, No. 8,1994

are stabilized by 16 kcal/mol when the corrections are applied. The resulting corrected relative energies EWrare shown in Figures 3 and 4. For the molecular complexes the correction has to be calculated in a differenty way since it does not involve normal M-R bonds. The correction is obtained from a comparison between the calculated and the experimental binding energies for Fe(CH4)+ and Co(CH4)+. The experimental Do value for Fe(CH4)+ is 13.7 kcal/mol,2s and the calculated binding energy is 7.6 kcal/mol. The corresponding values for the cobalt system are 22.926and 17.0kcal/mol, respectively. Thus a total correction of 6 kcal/mol is obtained, which is applied to all the molecular complexes (see E,, in Figure 1). For comparison to gas-phase experiments, an error estimate is needed also for the complete elimination reaction M+ + CH4 ---c MCH2+ H2. In this reaction two C-H bonds are broken, and two M-R bonds and one H-H bond are formed, yielding a correction of 9 kcal/mol, lowering the product side. The same correction can be used for the ethane elimination reaction M+ + C2Hs MC2H4+ H2 for the metals to the left in the periodic table, where the MC2H4+ can be considered as a metallacycle and the bond counting gives the same result as for the methane reaction. Together with the zero-point energy correction of 10 kcal/mol mentioned above, this gives a total correction of 19 kcal/mol for the elimination reactions. The above estimated errors in the calculated relative energies might seem very large, and it should be noted that in previous calculations on potential energy surfaces for chemical reactions involving transition metals the errors have normally been much larger. For example, for the elimination of H2 from Rh+ + CH4, Musaev et al.21 have made a correction 38.5 kcal/mol, to be compared to our correction of 19 kcal/mol. For intermediate points on the potential surface, Musaev et al.21have smoothly adjusted the relative energies, leading to a corrected value for the RhHCH3+ insertion product of about 0 kcal/mol (read from Figure 10 in ref 21) relative to the Rh+ CH4 dissociation limit, implying a correction of about 33 kcal/mol for this point. The present error estimate (together with zero-point energy) of 16 kcal/mol for the insertion product leads to a corrected value of +12 kcal/mol for RhHCH3+.

+

-

+

+

111. Discussion In this section the results for methane C-H activation by second row transition-metal cations will be discussed. The section is divided into three subsections. In the first subsection comparisons will be made to gas-phase experiments on alkane activation by transition-metal cations. In the second subsection comparisons will be made to the neutral metal atoms for the same reaction to investigate the charge effect on the reaction mechanism. In the third subsection comparisons will be made to simple ligated complexes for the same reaction to discuss influence of the oxidation state on the reaction mechanism. Comparison to Gas-Phase Experiment. For the reactions of cations of the transition metals with alkanes, the experimental information is abundant. Most of the metal cations investigated are very reactive toward larger alkanes, while almost only thirdrow metal cations seem to react with methane at low collision energies.27 The products observed in these reactions are ionic fragments with formulas indicating that neutral molecules like H2 and CHI have been eliminated after an initial addition of the alkane to the metal. Thus, what is classified as reaction in these studies goes several steps further than the oxidative addition reaction studied in the present paper. However, the metal insertion in the alkane C-H bond is normally believed to be the first step in many of these reactions. There are at least two possible explanations for why certain cations are not observed to react with certain alkanes, the first one being that the barrier height is too high for the first C-H insertion step (or some later step) and the second one being that the final products (ionic metal

fragment plus neutral molecule) are too high in energy; Le. the overall reaction is endothermic. In the present study only the energetics of the first C-H insertion step is investigated for most metals. The second-row metal cations yttrium,xD molybdenum,30 ruthenium, rhodium, and palladium31z2were experimentally found to be unreactive with methane at low energies, while all these metals did react with larger alkanes. Zirconium is stated to react with methane at thermal energies.33 The most favorable pathway for the reaction of metal cations with methane is M+

+ CH,

-

MCH;

+ H2

(2) For this reaction to be exothermic a binding energy of more than 110 kcal/mol is required for M+-CHz2 and none of the experimentally known M+-CH2 binding energies are that large.34 Therefore this reaction is expected to be endothermic for most metals, which is supposed to be the main reason methane activation by metal cations has not been observed.2 The M+-CH2 binding energies have also been calculated by Bauschlicher and coworkers24for all first- and second-row transition metals, and none was found to exceed 110 kcal/mol; the strongest bound metal was found to be zirconium with an estimated binding energy of 101 f 3 kcal/mol. Those theoretical results thus support the conclusion that the reactions with methane are endothermic, at least for first- and second-row metal cations. From the experimental study of endothermic reactions a threshold energy is obtained, lower than which no reaction is observed. This threshold energy gives the endothermicity of the reaction, and from the endothermicity, in turn, binding energies of the reaction products can be determined. For example, from the endothermicityof reaction 2, the M+-CH2 binding energy can be obtained. The binding energy of Y+-CH2 is determined in this way.29 As assumption underlying such a determination of binding energies from reaction endothermicities is that there is no barrier higher than the final endothermicity involved in the reaction. The results from the present study can be used to investigate whether this assumption is valid for the first C-H activation step. To place the comparison between the present and the experimental results on a somewhat firmer ground, calculations were performed also on later parts of the methane interaction surface for the case of the yttrium cation, and also on some steps of the reaction between the yttrium cation and ethane. For the case of yttrium, the endothermicity of reaction 2 is calculated to be 37.8 kcal/mol. Using the correction due to zeropoint energy and the limited correlation treatment estimated in section I1 above, an estimate of the true endothermicity of 19 kcal/mol is obtained. Furthermore, the insertion barrier is calculated to be 26 kcal/mol for the yttrium cation, which is decreased to 10 kcal/mol when the correction is applied. The insertion barrier of 10 kcal/mol is thus lower than the endothermicity of 19 kcal/mol for the elimination reaction, in agreement with the experimental assumption for the determination of the Y+-CH2 binding energy. Finally, a four-center transition state between the YHCH3+ insertion product and the final elimination products YCH2+ and H2 was calculated to be 10 kcal/mol below the final products. The experimentally determined endothermicity of reaction 2 for the case of yttrium is 15 f 3 kcal/m01.~~The excited 'D state is stated to be the reactive state, at least for the ethane reaction. The experimental excitation energy for this state is 3.4 kcal/mol. For the reaction of the excited triplet state of the yttrium cation with methane, there is one spin transition involved and the reaction can occur in the following way. The 3D state forms a molecular adduct with methane, bound by about 6 kcal/mol relative to the ground-state asymptote, if the correction to the binding energy for the molecular complexes is added. As discussed in section 11, the triplet state was found to form the lowest molecular complex for the yttrium cation. Between the

The Journal of Physical Chemistry, Vol. 98, No. 8, 1994 2067

Reaction of Second-Row Transition-Metal Cations molecular complex and the transition state for the insertion reaction there is a spin transition, since the transition-state structure is a singlet state, the triplet state being about 20 kcal/ mol higher in energy in this region of the potential surface. Relative to the 1s ground state of the yttrium cation, the barrier height is estimated to be about 10 kcal/mol and the insertion product is bound by as much as 28 kcal/mol. The final elimination products, YCH2+ H2,which are also in a singlet state, are 19 kcal/mol higher in energy than the lS ground state of the yttrium cation and methane. The four-center transition state and the HZ molecular complex preceding the elimination products are both about 10 kcal/mol below the energy of the elimination products. The calculated potential surface for the reaction between the yttrium cation and methane is thus in good agreement with the experimental information on this reaction, where an endothermicity of 15 f 3 kcal/mol is obtained.29 As mentioned above, Musaev, Koga, and Morokuma have studied the Rh+ CHI interaction surface.2' They obtained a barrier between the RhHCH3+ insertion product and the RhCH2+ H2 elimination products, which is 11.3 kcal/mol above the elimination products and which is not altered by the corrections they introduce for the limitationsof their calculations. It therefore seems to be a difference between the yttrium and the rhodium cations in this respect, and a corresponding determination of the Rh+-CH2 binding energy from the endothermicity of the Rh+ + CHI RhCH2+ H2 reaction would not be valid. It should be noted that relative to the insertion product the calculated barrier to the four-center transition state is 35.2 kcal/mol for rhodium21 and 38.9 kcal/mol for yttrium. Thus, it is the more strongly bound insertion product that makes this transition state fall below the elimination product in the yttrium case. The reaction between the yttrium cation in the 3D state and ethane, yielding H2 elimination products, is furthermore found to be exothermic in the ion beam experiment^.^^ To extend the comparison between experiment and theory, some points on the potential surface for the reaction between the yttrium cation and ethane were calculated. First, the reaction M+ + C2Hb MC2H4+ Hz was calculated to be endothermic by 15.9 kcal/ mol relative to the ground state of the yttrium cation. Applying the correction of 19 kcal/mol for zero-point energy and higher correlation effects leads to an estimated exothermicity of 3 kcal/ mol relative to the ground state of the yttrium cation and 6 kcal/ mol relative to the excited 3D state. Furthermore, the height of the insertion barrier is calculated to be 18.2 kcal/mol, which is lowered to 2.2 kcal/mol relative to the ground-state yttrium cation when the correction is applied. Relative to the excited 3D limit of the yttrium cation, the corrected insertion barrier is below zero by about 1 kcal/mol. Thus, for the 3D state of the yttrium cation, the reaction with ethane occurs without an insertion barrier and the final product is exothermic; also for this reaction, agreement with the experimental observations is obtained. In this context it is interesting to try to extrapolate the present results for the methane activation to the ethane activation reaction also for the other second-row cations. For the case of yttrium, the C-H insertion barrier was lowered by 8 kcal/mol on going from methane to ethane. If it is assumed that the change in the barrier is the same for all second-row cations, Le. all methane insertion barriers are lowered by 8 kcal/mol, and if the correction for zero-point energy and higher correlation effects is added, the barriers for zirconium, niobium, technetium, and rhodium fall very close to or below the ground-state dissociation limit, in agreement with experiments. For ruthenium and palladium no activation barrier could be determined for the methane reaction, and therefore no extrapolation can be done for these atoms. However, for molybdenum the barrier to C-H insertion in ethane is in this way estimated to be 20 kcal/mol, which is in contradiction to the experimental observation that the molybdenum cation should react exothermally with ethane to eliminate one or two

+

+

+

-

+

+

-

hydrogen molecules.30 Since this is the only case where a clear contradiction between experiment and theory occurs, it was decided to explicitly calculate the transition state for C-H activation of ethane by the molybdenum cation. It was found that the difference between methane and ethane was somewhat larger for molybdenum than for yttrium, but still there is a remaining estimated barrier for 15 kcal/mol for C-H insertion in ethane by molybdenum when all corrections are applied. For this case there is thus a disagreement between theory and experiment. One possible explanation for the observation of exothermic reactions between ethane and the molybdenum cation could be that excited states are involved in the experiment, which might be consistent with the fact that a low cross section is obtained.30 It should further be noted that the same experimental observations lead to the conclusions that acetylene is bound to the molybdenum cation by at least 74.6 kcal/mol,30 which is in strong contradiction to results of Bauschlicher et al.,35who obtain a value of 19.6 kcal/mol for the acetylene binding energy to Mo+. This result is thus a further indication that therearesome problems in the experiments on the molybdenum cations. Charge Effect. The methane activation by neutral naked transition-metal atoms has been studied previou~ly,~.~ and to simplify the comparison between the neutral and cationic reaction mechanisms, the results from that study9 are reproduced in Figure 3 for the insertion products and in Figure 4 for the transition states. The most notable difference between the neutral and the cationic metal atoms in their interaction with methane is that for the cations molecularly bound complexes are formed for all secondrow metals with binding energies up to 17 kcal/mol relative to theground-state atomicdissociation limit. For the neutral secondrow metals, such a complex is formed only for the palladium atom, with a binding energy of 4 kcal/mol.8 One assumption often madeis that theattraction energy found between thecation and the alkane can be considered to be constant for the entire entrance channel of the reaction, lowering reaction barriers compared to the corresponding neutral system by the binding energy of the molecular complex of thecation. The present results do not support such a simple assumption. A comparison of the barrier height for the C-H insertion reaction between the cations and the neutrals (Figure 4) reveals that, although the barrier is lower for the cations for most of the metals, the energy difference does not correspond to the binding energy of the molecular complex. For example, for technetium the barrier is lowered by about 18 kcal/mol on going to the cation, while the molecular complex is bound by only 4.5 kcal/mol. The assumption works better for the niobium and molybdenum cations where the barrier is lowered by 5-7 kcal/mol and the molecular complex is bound by 9-1 2 kcal/mol. An even stronger argument against a constant charge effect is that for the metals to the right in the periodic system the insertion barriers for the cations are higher than for the neutrals. Furthermore, the fact that for all second-row metals the insertion product is less bound for the cations than for the neutrals (see Figure 3) shows that the difference between the cations and the neutrals in their reaction mechanism for C-H insertion is not a simple charge effect. Rather, as will be shown below, it is more useful to describe these differences as being caused by differences in atomic spectra, even if the attractive force for the cations also plays a role. As discussed above, there are two factors determining the barrier heights for the neutral atoms in their reactions with methane. First, there is the repulsion between the metal electrons and the closed-shell electrons of methane, which is minimized for the metal so states. For the cations the energy in the entrance channel is also lowered by the attractive force due to the chargeinduced dipole interaction. Second, the covalent binding in the final insertion product has to build up in the transition-state region, and this is optimal for the s1 state of the metal atoms. The

2068

The Journal of Physical Chemistry, Vol. 98, No. 8,1994

[kcal /mol]

O t Zn, ,

I

,

,

,

I

W Figure 6. Elimination barriers for the metal methyl hydridesof the naked neutral atoms and cations. The results for the neutral atoms are taken from ref 9. Y

Nb

Mo

Tc

fd~

Rh

decreased bonding in the insertion product for most second-row cations compared to the neutrals can be explained by the lower s-populations in the cationic ground states. The so state binds less efficiently than the s1 state. This can be seen in niobium, molybdenum, and rhodium, which have so ground states for the cations. For these metals the insertion product is destabilized by 15-30 kcal/mol for the cations. Furthermore, for ruthenium and palladium, which also have so ground states, there are no minima in the region of the insertion product structure. The decreased repulsion in the transition-state region for the cations is to a large extent caused by the lower s-population in theatomicground stateof thecations. For example, for zirconium and technetium, the neutrals have s2 ground states, while the corresponding cations have s1 ground states and the lower repulsion in this type of state leads to decreased barrier heights by 13-18 kcal/mol for the cations. However, for cations like niobium and molybdenum, the decrease in repulsion on going from an s1ground state for the neutral atom to an so ground state for the cation is to a large extent counterbalanced by a decrease in builtup covalent bonding, due to the lower bonding capacity of the so state. The balance between the bonding capacity and the amount of repulsion for different atomic states has a general effect on the shape of the potential surfaces which can most easily be seen by considering the reverse reaction, the reductive elimination of methane from metal methyl hydride. For this reaction there is a very clear trend toward lower elimination barriers going from the neutral metal atom to the cation (see Figure 6). Since there is also a trend of lowering the elimination barrier going from left to right in the periodic table, from 46 kcal/mol for the yttrium atom to 6 kcal/mol for the palladium atom, the elimination barrier for the atoms to the right is actually removed for the cations. Thus the low bonding capacity of the so state together with high excitation energies of the SI state leads to a different shape of the potential curves for the metals to the right. As mentioned above, for the ruthenium, rhodium, and palladium cations there is no elimination barrier and consequently no stable insertion product. For rhodium, a minimum for the insertion product was found at the SCF level, but the elimination barrier disappeared at the correlated level. Oxidation State. The chemical properties of an element are considered to be closely connected to its oxidation state, and for example, text books in inorganic chemistry are often organized after the oxidation states of the elements. A question of general

Blomberg et al. interest for theoretical studies of reaction mechanisms is whether simple models of metal complexes have to leave the metal in the same oxidation state as in the real complex. It is therefore of interest to make comparisons between naked neutral metal atoms and naked metal cations in terms of their modeling of ligated metal(1) complexes. From the results of the present and previous studies, it is found that the energy curve for the reaction between methane and an actually observed ligated Rh(1) complex like RhCl(PH&, for example, is more similar to that of the naked neutral atom than that of the naked cation. From many similar results obtained, it can be concluded that the oxidation state of the metal is not a dominating property of the metal complex, at least for the present rather simple models. The actual metal in the metal complex is much more important than the oxidation state of this metal. Another question of interest for model studies is how good a model a metal cation is of a strongly ionic complex like MCl, and also how the difference from less ionic complexes like M H can be understood from the results for the naked neutral and cationic metals. In previous studies,lOJ1on ligand effects on methane activation, the reactivities of MCl and M H have been investigated. In the comparison between MC1 and M H it was found that the chloride ligand has a tendency to destabilize the methane insertion complexes as compared to the hydride ligand for the metals to the right in the periodic table. This effect can indeed be understood by the comparison between the naked metal atoms and the cations in their reactivity with methane. Since MC1 is quite ionic, it should resemble M+ while M H should resemble the neutral M atom. In previous sections it was noted that the product of the methane reaction for the metals to the right is less stable for M+ than it is for M. This is exactly the same effect as noted in the previous study yielding less stable methane insertion products for MCl than for M H to the right. However, it is important to note in this context that neither of these simple model systems by themselves give quantitative agreement with the ligated M(1) complexes for the energetics of the methane activation reaction. This can be seen from Figures 3 and 4, where the results for the monochlorides11 are shown together with the results for the naked cations and the naked neutrals. The following main conclusions can be drawn from inspection of the results in Figures 3 and 4. Considering the atoms to the left and in the middle of the periodic table, from yttrium to technetium, it can first be noted that for the insertion product both the neutral and the cationic naked complexes are less bound than thechloridecomplex. For niobium to technetium the neutral complex is closer to the ligated complex than the cationic complex is. Also, in the transition-state region (see Figure 4) the ligated complex has a lower energy (except for yttrium) than both the neutral and the cationic naked complexes. In this case, however, thecationic resultsarecloser to theresultsof theligated complexes. For the metals zirconium to technetium, in fact, the cations seem to be rather good models for the MCl complexes in describing the trend in the barrier heights. As discussed above, one reason for the lower barrier of the cations compared to the neutrals is the decrease in the amount of repulsive s-electrons in the lowlying atomic states for cations. A covalent ligand added to the metal will have a similar effect; the s-electrons will be involved in the bonding between the metal and the chloride ligand and will therefore be removed from the partof thespacewhere themethane molecule is approaching. This will lead to a decrease of the repulsion in a manner similar to that for the cations. For the reaction energies, Le. the binding energies of the insertion products, the cations have lower binding energies than the neutrals. This was explained above by thedecreased bonding ability of the cations due to a decreased s-population in the low-lying atomic states compared to the neutrals. As can be seen in Figure 3, the addition of a chloride ligand to the metal has an opposite effect for the metals to the left; Le., the insertion product is somewhat stabilized.

Reaction of Second-Row Transition-Metal Cations In a previous paper on the effects of covalent ligands on the methane activation reaction, it was shown that several effects, e.g. promotion energies and loss of exchange energy upon bond formation, had to be involved to fully explain these results.1° A comparison between the cations and the ligated M(1) complexes in terms of specific effects is therefore rather complicated. If the rightmost end of the periodic table, from ruthenium to palladium, is considered, the following observations can be made from the results in Figures 3 and 4. It can first be noted that the cations give potential surfaces which are qualitatively different from those of the naked neutrals. As was mentioned above, this difference could be used to understand the difference between different ligated complexes in their reactivity with methane. On theother hand, theligated metal complexes and thenaked neutrals give qualitatively similar results. These results can be taken to indicate that the neutral metal atoms give the best agreement with the ligated complexes for the energetics. For example, the theoretical results for methane activation by naked metal atoms show that among the second-row metals rhodium has the lowest barrier for methane activation, in good agreement with the fact that rhodium complexes are the only second-row complexes that have been experimentally observed to activate alkanes.36 This conclusion could be drawn although rhodium in the complexes that have been experimentally observed to activate alkanes is in the oxidation state I and the calculations were performed for zero-valent metals. An important limitation of the cationic modeling of ligated metal(1) complexes is the lack of counterions. In this context it is interesting to note that the reaction energetics of the cations comes much closer to the MC1 results if a negative charge is placed at the same position as the chloride ligand.

IV. Conclusions The present investigation of the reaction between methane and second-row transition-metal cations has given further insight into the mechanisms for oxidative addition reactions. Comparisons to the corresponding neutral reactions, which have been studied previously, show that there are many similarities. For example, the dominating bonding state in the insertion product is the atomic s1 state, and the height of the insertion barrier is dependent on not only the binding energy of the insertion product but also the position of atomic low-spin states with low repulsion. Furthermore, the curve for the binding energies of the insertion products has a minimum for the atoms in the middle of the periodic table, and the curve for the barrier heights has a maximum for these metals, which in both cases is due to the large loss of exchange energy upon bond formation for systems with many open-shell electrons. There are, however, also marked differences between the results for the cations and the neutrals. First, the chargeinduced dipole interaction causes the formation of rather strongly bound molecular complexes for the cations. Also, in the transitionstate region the cations have lower energies than the neutrals for most metals (yttrium to technetium), which is due to the lower s-population in the cations, leading to a lower repulsion. On the contrary, in the insertionproduct region, the cations are less bound than the neutrals, which is again due to the lower s-population, leading to less efficient covalent bonding. The comparisons between the cations and the neutrals show that the differences between the potential surfaces cannot be described by a simple charge effect but are also to a large extent determined by differences in the atomic spectra between the cations and the neutrals. The experimental observations mentioned in the introduction that transition-metal cations are more reactive toward alkanes than neutral atoms are not well illustrated by the present investigation. Although the barrier heights for yttrium to technetium are lower for the cations, there are still barriers left for most of the metals. Furthermore, for ruthenium to palladium, the insertion thresholds are larger for the cations than for the

The Journal of Physical Chemistry, Vol. 98, No. 8, 1994 2069 neutrals. On the other hand, the fact that barriers are obtained for methane activation by the cations is not in contradiction to the experimental observations, since none of these metals are observed to react exothermally with methane. For larger alkanes the insertion barriers are lowered, as demonstrated for the case of ethane and some of the cations in the present study. From the present study, together with the results from several previous studies?-" it can be concluded that the oxidation state of the metal is not a determining factor for the reactivity of a metal complex toward methane. Comparing the results for the simple ligated MCl complexes with the M(1) model in the form of the naked metal cations and with the M(0) model in the form of the naked neutral metal atoms shows that, for certain parts of the reaction potential surfaces, the results for the neutrals are closer to the MCl results and, for other parts, the cations are closer. For the alkane activation by the RhCl(PH3)2 complex, which has been observed to occur experimentally, the neutral naked atom actually is a better model than the cation. Even if the naked rhodium atom has too high a barrier for the reaction, it still has the lowest one of all second-row metals. It is only for the initial molecular complex that the cation gives results closer to the ligated complex than the neutral atom does. One of the most important results of the present study is that the accuracy of the calculations can be evaluated. It should first be pointed out that the present level of calculation gives more accurate results than what has previously been typical for studies of chemical reactions involving transition metals. Still there are rather large errors in the resulting relative energies. First, these errors are not random; bond energies are always underestimated. Thus, trends are much more accurate than singleresults. Second, even if higher levels of accuracy can be obtained in calculations on a few rather small systems, the present level of calculation represents a reasonable limit for what today is practical, if results leading to a more general chemical understanding are to be obtained. However, by comparison to the most accurate calculations for a limited number of systems, the systematic errors in the results can be estimated. Thus, the calculated bond energies are estimated to be between 3 and 8 kcal/mol too low, depending on the type of bond. Applying these corrections to the present results for methane activation by the second-row transition-metal cations generally leads to a good agreement with gas-phase experiments.

Appendix: Computational Details In the calculationsreported in the present paper on the oxidative addition reaction of methane to the cations of second-row transition-metal atoms, reasonably large basis sets were used in a generalized contraction scheme. All valence electrons were correlated using size-consistent methods. For the metals, the Huzinaga primitive basis37 was extended by adding one diffuse d-function, two p-functions in the Sp region, and three f-functions, yielding a (17s, 13p, 9d, 3 0 primitive basis. The core orbitals were totally contracted3*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 by a triple-{contraction. The f-functions were contracted to one function giving a [7s, 6p, 4d, lfl contracted basis. For carbon the primitive (9s, 5p) basis of Huzinaga39 was used, contracted according to the generalized contraction scheme to [3s, 2p] and one d-function with exponent 0.63 added. For hydrogen the primitive (5s) basis from ref 40 was used, augmented with one p-function with exponent 0.8 and contracted to [3s, lp]. These basis sets are used in the energy calculations for all systems. In the geometry optimizations for the insertion products and the transition states, performed at the SCF level using the GAMESS41or GRADSCF4*set of programs, somewhat smaller basis sets were used. For themetals, a relativistic ECP according

2070 The Journal of Physical Chemistry, Vol. 98, No. 8, 1994

to Hay and Wadt43 was used. The frozen 4s and 4p orbitals are described by a single-fcontraction, thevalence 5s and 5p orbitals are described by a double-( basis, and the 4d orbital by a triple-f basis, including one diffuse function. The rest of the atoms are described by standard double-cbasis sets. The geometries of the molecular complexes were determined at the correlated level using the same basis set as in the energy calculations. Only the M-C distances were optimized, and the CH4 unit was kept undisturbed in an 92 coordination. The correlated calculations were in all cases performed using the modified coupled pair functional (MCPF) method," which is a size-consistent, single reference state method. The zeroorder wave function is determined at the SCF level. The metal valence electrons (4d and 5s) and all methane valence electrons were correlated. Because of rotation between valence and core orbitals, a localization of the core orbitals has to be performed, and this was done using a localization procedure developed by Petterss0n,4~in which (S)of the core orbitals is minimized. Relativistic effects were accounted for using first-order perturbation theory including the mass-velocity and Darwin terms.46 Most of the present calculations were performed on an FX-80 ALLIANT and on an IBM Risc6000 computer. The GRADSCF calculations were performed on the CRAY-XMP at the Swedish National Supercomputer Center. The final energy evaluations were performed using the STOCKHOLM set of programs.4' A few words should be said about the level of calculationchosen in the present study. As described above, most geometries are optimized at the SCF level and the relative energies are calculated at the MCPF level; i.e., 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 ofcorrelated results.*3J5 The conclusion is that correlationeffects have to be included in the calculations to give reliable trends for activation energies and binding energies. In this context it should be noted that the trends in correlation effects for this type of system are well described by the single-reference MCPF meth0d,8,24348 Second, it can be questioned if the use of SCF-optimized geometries give reliable results, in 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 e n e r g i e ~ . ~ 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 parallel.9 Another reason SCF geometries can be used is that the potential energy surfaces are often rather flat in both the transition-state region and the insertion product region, so that discrepancies in SCF- and MCPFoptimized structures have very small effects on the relative energies. The conclusion is that the use of SCF-optimized structures gives reliable results for the trends in activation energies and binding energies if correlation effects are included in the energy calculations. For the absolute accuracy in the calculated relative energies see section I1 above. 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 using available excitation energies. The common practice has been to relate to the energies for the ground spin states of the reactants, and this procedure will be followed here. The main advantage with this

Blomberg et al. procedure is that it 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 bestrong for transition metals, so this surface hopping is intuitively expected to occur with a high probability. This problem has been studied in detail by Mitche1l:o who showed that in the case of the association reaction between the nickel atom and carbon monoxide, the crossing probability is near unity. Also, in order to rationalize the experimental results for the oxidative addition reaction between the nickel atom and water, a high crossing probability has to be assumed:' 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 a t 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 surfacehopping 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.

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