Ab Initio Studies on the Ziegler-Natta Polymerization Reaction

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J. Phys. Chem. 1994, 98, 12053-12058

Ab Initio Studies on the Ziegler-Natta Polymerization Reaction Mechanisms. The Role of Cocatalysis Shogo Sakai Department of Information Systems Engineering, Faculty of Engineering, Osaka Sangyo University, Daito 574, Japan Received: June 4, 1994; In Final Form: September 2, 1994@

As a model of olefin polymerization by a Ziegler-Natta catalyst, the mechanism of the insertion reaction of ethylene into CH3TiCWlH2 has been studied by ab initio SCF methods, a many-body perturbation theory, and a localized molecular orbital (LMO) charge centroid analysis. The structures of the reactant, the intermediate, the transition state, and the product have been optimized with the RHF/3-21G method. The reaction is two-step process: the first forms ethylene-Ti n complex with about 4 kcaYmol bamer, and the second step is the carbon-carbon bond formation (the insertion of ethylene into the Ti-C bond) through a pull-push mechanism. For the cocatalysis, the A1-C1 bonds alternation occurs at the second step. It is clarified that the cocatalysis play a role in facilitating the pull-push mechanism through the A1-C1 bonds alternation. The activation energy banier in the ethylene insertion process for the model without the cocatalysis (AlH2Cl) is 20.5 kcaVmol higher than that for the model including the cocatalysis at the present calculation level.

1. Introduction It is well-known that Ziegler-Natta catalysis polymerization is one of the most important industrial polymerization reactions, and many experimental studies have been reported.l-l0 However, the fundamental carbon-carbon bond formation in this process is not fully understood. For the generic mechanism of olefin insertion Cossee mechanismlo has been accepted widely as the most plausible. The first step is olefin coordination to a vacant site of Tixtom. In the second step olefin is inserted into the Ti-C bond through a four-membered cyclic transition state.

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ab initio MO methods. Castonguay and Rappel7 studied the stereotacticity of ansa-zirconium metallocene Ziegler-Natta propylene polymerization catalysts using a combination of ab initio MO methods and empirical force field molecular mechanics techniques. Morokuma and co-workers18 investigated ethylene insertion of CH3TiC12+ as a model of homogeneous olefin polymerization. Morokuma and co-workerslg also studied homogeneous olefin polymerization with silylene-bridged zirconocene catalyst and its regio- and stereoselectivity by ab initio and molecular mechanics methods. In previous papers,20J I proposed a pull-push mechanism for olefin insertion on the basis of a simple Cossee model (CH3AlH2 ethylene) by a LMO charge centroid analysis in 1991. It is considered that a cocatalyst such as aluminum is very important for the ZieglerNatta polymerization. However, no theoretical studies have been reported for the mechanism of cocatalysis of ZieglerNatta type polymerization. In the present paper, I studied the Ziegler-Natta type reaction on the basis of the following model: For this olefin polymeri-

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Several theoretical studies of Ziegler-Natta catalysis polymerization have been reported. Most of these papers discuss the reaction mechanism in Ziegler-Natta polymerization based on Cossee’s model. Cossee’s model was treated with semiempirical SCF MO methods by Armstrong and co-workers” and by Novaro and co-workers.12 Their results suggested that the Ziegler-Natta mechanism might be explained by a concerted motion of the olefin and alkyl group that would bring about a transition from octahedral coordination to a trigonal-bipyramidal coordination for the Ti atom. This view was also confirmed with the ab initio SCF MO method by Clementi and coworkers.13J4 Balazs and Johnson15demonstrated the reaction CH3TiC14 C2& by using a SCF-X,-SW MO method. Fujimoto and co-workers16 examined the interaction between C2& and CH3TiC12+ and between C 2 b and HTiC1Zf by using

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Abstract published in Advance ACS Abstracts, October 15, 1994.

0022-365419412098-12053$04.50/0

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zation, a heterogeneous as well as homogeneous catalyst has been adopted. Heterogeneous catalysts are usually transition metal halides with cocatalysts such as aluminum alkyl compounds. A typical Ziegler-Natta catalyst can be made by mixing Tic14 (or TiC13) and A12Ek in heptane. I chose this model of the propagation step in heterogeneous polymerizations, in which TiC13CH3-AlClH2 has been considered to be a reactive intermediate for group 4 transition metal catalysts. The Cossee model can be extended to a description of the “soluble catalysts”22systems such as the couple CpzTiClz and &A1 (Cp

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12054 J. Phys. Chem., Vol. 98, No. 46, 1994

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Transition state for Ethylene Addition

H ' CI (31

Complex 2.298

Transition state Insertion

CI (3)

Product ( Cs Symmetry )

' b

Dihrdrol=l21.8

CI (31

Figure 1. RHF optimized geometries (in A and deg) of the reactant, the transition state of ethylene addition, the ethylene-Ti JC complex, the transition state of insertion, and the product for ethylene insertion into the Ti-CH3 bond of CH3TiCLAlHz. = cyclopentadienyl) which also show catalytic properties and,

in this case, the intermediates are suggested to occur as in our

model. In spectroscopic study of the formation of ion pairs in CpzTiCl2 and Me-AlC12 system, both groups of Long23 and Eisch9 did not observed the ions (Cp2Ti+CH3 and AlCL-). The possibility that Cp2TiClz:C12AlCH3 might be the active catalyst is ruled out by the UV studies of Long23and the kinetic studies of Fink.24 EischZ5 and co-workers, by H, C, and A1 NMR spectroscopy, also concluded that the ion pairs ((Cp2TiCH2SiMe#-AlCL-: included Ti-Cl-A1 bridged bond) in Cp2Ti(Cl)CHzSiMe3 and AlC13 system are effective catalysts for the polymerization of ethylene. Therefore, I conclude that above model included Ti-Cl-A1 bridged bond is a good simple model for the propagation step in the heterogeneous Ziegler-Natta polymerization. The model of this type was used for the first ab initio molecular orbital calculation of the Ziegler-Natta catalytic reaction by Clementi and co-workers13 in 1977. Recently Nova1-0~~ also calculated the model with better basis set than that by Clementi et al.13 Both groups calculated the potential energy at the fixed geometry (not full geometry optimization). In this study, three subjects are reported. The first is the electronic reaction mechanism for a titanium catalytic model by the LMO centroid analysis. The second is the energy profile along the reaction pathway. For this purpose, the stationary points geometries included transition state are optimized by ab initio MO method. The third purpose is the most important in the present study: the role of cocatalysis for olefin insertion mechanism.

2. Calculation Methods All equilibrium and transition-state geometries were determined by the analytically calculated energy gradients with the restricted Hartree-Fock (RHF) wave functions. The stationary points were identified as the equilibrium or the saddle point by examining the calculated normal vibrational frequencies. The force constant matrix and thereby the vibrational frequencies were calculated by analytical second derivative procedure^,^^^** and zero-point vibrational energy corrections (ZPE) were obtained at this level. The basis functions used for Ti atom throughout the paper were 3-21G of Dobbs and Hehre.29 For C, H, C1, and A1 atoms the standard 3-21G basis function^^^^^^ were used. This set is denoted at the following sections as BSI. For better energies, the 6-31G(d) basis f ~ n c t i o n s for ~~,~~ carbon atom and the (8s/4p/3d) contracted functions34 for Ti atom were used, denoted as BS-11. Additional calculations were performed, at the HF-optimized structures, with electron correlation (excluding inner shells) incorporated through the second- and third-order M~ller-Plesset perturbation theory (MP2 and MP3)35-39to obtain improved energy comparisons. In order to study the electronic reaction mechanism along the reaction pathway, a localized molecular orbital (LMO) centroid analysis of the reactions was carried out by following a method described e l s e ~ h e r e . ~ ~The ~ * calculation ~ * ~ ~ - ~of~ the localized orbitals was based on the Foster-Boys method,44 in which the sum over all the orbitals of the average interelectronic separation between the two electrons in a given orbital, Ci(#?@)lrpVl#?(v)),is minimized. This requirement maximizes the separation between the centroids Ri, Rj of two different orbitals, where W = (#i@)lrl#i@)) defines the position of the 4; orbital centroid. The location of the centroid, Ri, is used to represent the position of the electrons in the following discussion. Ab initio calculations were carried out by GAUSSIAN9245 and programs. 3. Results and Discussion (A) Complex Formation and Insertion for Ziegler-Natta Catalysis. The calculated stationary point geometries for the

. I Phys. . Chem., Vol. 98, No. 46, 1994

Ziegler-Natta Polymerization Reaction Mechanisms

TABLE 1: Total and Relative Energies of Stationary Points Geometry for Ziegler-Natta Reaction Model total energy" "3-1 MP3/BS-I1 ZPEb -3032.523 57 -3037.980 35 72.1 reactant 72.9 -3032.524 70 -3037.975 04 addition TS -3032.532 38 -3037.981 89 73.6 complex -3037.971 71 75.1 -3032.508 68 insert TS 76.0 -3032.562 92 -3038.019 10 product without AlH2Cl system -2333.402 88 -2338.763 51 61.2 reactant -2338.721 47 63.7 -2333.358 76 TS -2333.442 97 -2338.802 96 65.2 product Units of the total energy is hartrees. Units of the zero point energy is kcdmol. Units of the relative energy is kcaumol.

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AEc 0.0 4.1

0.5 8.4 -20.4 0.0

28.9 -20.8

CI'

CI CI

Complex Transition State Figure 2. Mechanism of ethylene insertion into Ti-CH3 bond of CHsTiCLAlHz. for C3H7 part (not shown here). However, the force constant reaction of CH3TiC4AlH2 with ethylene are illustrated in Figure matrix of the cis-type product has two negative eigenvalues (138 1. In the reactant geometry, the Ti-Cl(1) bond is about 0.3 8, and 288 cm-' for a" symmetry). Hence, the cis-type product longer than the Ti-Cl(2) bond, and the A1-Cl(2) bond length is not really a stable product. This cis-type product is about is longer by 0.2 8, than the AI-Cl(1) bond length. From the 11 kcal/mol above in energy than the trans-type in Figure 1 at facts, it is considered that the reactant molecule (Ziegler-Natta the HF/BS-I calculation level. In the insertion transition state, catalysis model) is the complex between CH3TiCl3 and AlH2the agostic interaction is found; one C-H bond in the methyl C1 species. The complexation energy between these species is group is longer than that in a isolated methyl group, while the about 18 kcal/mol at the MP3/BS-I1 calculation level. In the agostic interaction is not found at the complex, the reactant, reactant, we distinguish two groups for Ti-C1 and AI-C1 and the product geometries. The agostic interaction at the bonds: bonding (Ti-Cl(2) and A1-Cl( 1)) and interaction (Tiinsertion transition state is also found'* in CH3TiC12+ ethylene Cl(1) and A1-Cl(2)). The Ti-Cl(2) bonding region is the reaction. The agostic interaction reduces the energy barrier by reverse side of a vacant coordination (ethylene coordination a few kcal/m01.~~The geometries in the active site at the position of ethylene-Ti n complex on C,symmetry plane) for insertion transition state are similar to those in the previous Ti atom center, while the Ti-Cl(1) interaction region is the calculation1*for the reaction of CH3TiC12+ ethylene: Tireverse side of Ti-CH3 bond for Ti atom center. That is, it is C(methy1) = 2.09 A, C(methy1)-C(one side of ethylene) = 2.17 considered that the vacant coordination and the interaction sides A, C-C(ethy1ene) = 1.41 A, and Ti-C(other side of ethylene) are the spreading directions of the Ti-Cl(2) and Ti-CH3 = 2.12 8,. This is not surprising; these geometry parameters antibonding orbitals, respectively. are also similar to those for the reaction of the simple model The C1(3)-Ti-C1(4) angle (out of C, symmetry plane) H2AlCH3 ethylene in our previous paper.20 Accordingly, the changes from 115" to 168" during the ethylene-Ti n complex insertion reaction into metal-carbon bond might be essentially formation. At the transition state (addition TS) of ethylenethe same as the pull-push mechanism in our previous paper. Ti n complex formation, the C1(3)-Ti-C1(4) angle is about The electronic reaction mechanisms for this Ziegler-Natta 137", and the distance between Ti atom and the C-C center of model are discussed at the next section. ethylene is about 1 8, longer than that of ethylene-Ti n (B) LMO Centroid Analysis. The LMO charge centroids complex. Accordingly, the energy barrier comes from the for all stationary point geometries are displayed in Figure 3. rearrangement of the electronic configuration of Ti atom. The The centroid is interpreted as the electron location, and a black Ti-Cl( l), Ti-C1(2), AI-Cl( l), and A1-Cl(2) bond lengths at circle in the figure denotes the centroid of a and p spin electrons the ethylene-Ti n complex are almost similar to those in the pair. Only centroids of some interesting bonds are exhibited reactant, respectively. in the figure. In the first step (ethylene-Ti n complex At the insertion transition state, the Ti-Cl(2) bond increases formation), the drastic movements of the centroids are not found by 0.17 8, in length from that of the complex, and the Ti-CIthrough the transition state of ethylene addition. In the complex, (1) bond length decreases by 0.22 b; from that of the complex. two centroids in the ethylene part denote originally o and n The AI-Cl(1) bond length increases by 0.07 A from that of electrons in the C=C double bond. In the second step (ethylene the complex, and the A1-Cl(2) bond decreases by 0.11 8, in insertion into the Ti-C bond), the n electrons in ethylene part length from that of the complex. At the product, the Ti-Cl(2) move to the Ti-C(ethy1ene) region at the transition state and and the AI-Cl(1) bonds become the interaction sides, while forms the new Ti-C bond. The electrons, belonged to the Tithe Ti-Cl( 1) and the Al-Cl(2) bonds become the bonding sides. C(methy1) bond, move to the c-C (methyl-ethylene) region at Consequently, the AI-Cl (and Ti-C1) bonds alternation occurs the transition state of insertion and lead to new C-C bond through ethylene insertion into the Ti-C bond. This mechanism formation. This is completely the same mechanism as the is shown in Figure 2. previous proposed one on the simple A1 model;20 that is, this The insertion reaction proceeds from the transition state with insertion step is the pull-push mechanism. the conservation of C, symmetry and leads to cis-type product

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Transition State for Insertion

t

d Reactant

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-20.8

Transition State for Addition

Product

Figure 4. Potential energy profiles for ethylene insertion into the TiCHJ bond of CH3TiCMlH2 and CH3TiC13.

Transition state for Ethylene Addition

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Transition state Insertion

bond region (reverse direction of the Ti-Cl(2) bond for Ti atom center) easily. We can say that this process is a back-donation mechanism as the S N reaction. ~ At the same viewpoints, the Ti-Cl( 1) bond, reverse side of methyl group for Ti atom center, decreases in length, and the electrons in the C1( 1) region move to Ti side to form the Ti-Cl( 1) bond. Hence, the electrons in the Ti-C(methy1) bond are pushed to methyl side (or new C-C bond region); the Ti-C(methy1) bonding interaction decreases. Consequently, the AI-Cl (or Ti-C1) bonds switching mechanism facilitates the pull-push mechanism of the insertion reaction. (C) Potential Energy Profile. The potential energy profile along the reaction pathway of CH3TiCldlH2 ethylene is illustrated in Figure 4. From the figure, the reaction is two step; the first is the formation of AlH2(Ch)TiCH3-C2& complex through the transition state of ethylene addition, and the second step is the ethylene insertion into the Ti-C bond. Both groups of Clementi12-14 and N ~ v a r did o ~ not ~ report about the transition state of ethylene addition in the first step for their reaction profiles by using the similar reaction system, because both groups assumed the angle C1(3)-Ti-C1(4) = 180" for their reaction models. Thus the transition state of addition causes from the rearrangement of electronic state of Ti atom. The energy barrier height of the transition state of addition is about half of that of the transition state of insertion at the MP3BS-I1 ZPE level. As a result, the second step (insertion reaction) is the rate-determining process. This predicted activation energy is 8.4 kcaVmol, which is comparable to the experimental estimated value 10.6 kcal/mol!* @) Cl3TiCH3 Ethylene Reaction. To study the effect on the cocatalysis for the potential energy profile of the ZieglerNatta model reaction discussed in previous section, the potential energies of CH3TiC13 ethylene reaction (eliminated cocatalysis part: AlH2Cl) are also calculated at the same level. The stationary point geometries of the reaction are shown in Figure 5. In this reaction system, the complex between CH3TiC13 and ethylene is not found. The potential energy profile is drawn in Figure 4. The activation energy barrier height of ethylene insertion is 28.9 kcaVmol above the reactant (the isolated CH3Tic13 and ethylene) at the MP3BS-I1 calculation ZPE level and is about 20 kcaVmol higher than that of CH3TiCl.&lH2 ethylene system discussed before. From the transition-state geometry, the agostic interaction is not found. The TiC(ethy1ene) and Ti-C(methy1) bond lengths at the transition state in Figure 5 are longer than those in Figure 1, respectively. Three Ti-Cl bonds increase in length at the transition state From the reactant. Consequently, C1 atoms in CH3TiCl3 model do not play a role in decreasing the activation energy. On the other hand, the heat of reaction for CH3TiC13 ethylene is 20.8 kcaY mol at the MP3BS-I1 ZPE level and is almost the same to that of CH3TiCldlH2 ethylene system discussed before.

H"s. \.

.e-n

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Product

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Figure 3. Location of charge centroids of localized orbitals for the reactant, the transition state of ethylene addition, the ethylene-Ti n complex, the transition state of insertion, and the product for ethylene insertion into the Ti-CH3 bond of CH3TiCMlH2.

At the insertion transition state, the Ti-Cl(2) bond, reverse direction of ethylene coordination side for Ti atom center, increases in length. This means the electrons in the Ti-Cl(2) bond localize to the Cl(2) atom direction along the reaction pathway. Then the originally n electrons move to new Ti-C

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Ziegler-Natta Polymerization Reaction Mechanisms

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of new cocatalysis. The reaction pathway of CH3TiCl3 ethylene (not including the cocatalyst, AlHZCl) was also calculated at the same theoretical level. In this reaction pathway, ethylene-Ti n complex is not found. The energy barrier height at the insertion transition state is 28.9 kcdmol above the reactant and is 20.5 kcdmol higher than that of CH3TiCWlH2 ethylene system. In comparison with the CH3TiCWlH2 ethylene system, this high barrier for CH3TiCl3 ethylene system arises from two points. (1) CH3TiCl3 ethylene system does not form a complex. Accordingly it needs the rearrangement energy of the electronic configuration of Ti at the transition state; the C1-Ti-C(methy1) angle changes about 70" from the reactant to the transition state. (2) At the transition state, the agostic interaction does not occur, because of the narrow C1Ti-C1 angle (out of plane), while the heat of reaction is -20.8 kcdmol, and comparable to that (-20.4 kcal/mol) for CH3TiCkAlH2 ethylene system. Accordingly, the cocatalysis works effectively only for the transition state of insertion. In our model, CH3TiCl&lH* ethylene, active center has not been experimentally identified as real Ziegler-Natta catalysis. However, calculated potential energy surfaces seem quite probable. The predicted activation energy (8.4 kcdmol) is comparable to the experimentally determined barrier of 10.6 kcdmol. Though total charge of our model, CH3TiC14AlH2 ethylene, is neutral, the natural net charge of Ti atom in active center is 2.202e for the reactant, 2.223e for the addition TS, 2.241e for the complex, 2.190e for the insert TS, and 2.200e for the product. This is totally supported by the experimental studies, as, for example, the demonstration that the growing polymerization activity is clearly related to the existence of active Ti3+ centers, as has been proven for soluble titanium catalysi~.~'-5~

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Transition state Insertion

2.201

I

\

2.310

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140.2

Product 1.999

Figure 5. RHF optimized geometries (in A and deg) of the reactant, the transition state of ethylene insertion, and the product for ethylene insertion into the Ti-CH3 bond of CH3TiC13.

Therefore, the cocatalysis works for only the transition state of insertion (activation energy barrier).

4. Conclusion The reaction mechanisms for the Ziegler-Natta polymerization catalysis were studied by ab initio molecular orbital methods. The reaction is a two-step process: the first is ethylene-Ti n complex formation, and the second step is ethylene insertion into the Ti-C(o1efin) bond. The first step has 4.1 kcdmol energy barrier height above the reactant. The complex is almost the same energfg to the reactant. On the other hand, the energy barrier height in the second step is 8.4 kcal/mol above the reactant, and the transition state in the insertion reaction is 4.3 kcal/mol higher in energy than that in the complex formation. From the LMO centroid analysis, the ethylene insertion into the Ti-C bond is the pull-push mechanism as shown in the previous paper20 for the simple A1 model. The Ziegler-Natta catalysis model used here is the complex between CH3TiC13 and AlHZC1 species. We can also consider that the model is a special situation of the smallest degree of separation between ion pairs CH3Ti+C12 and AlH2C12in homogeneous Ziegler-Natta catalysis as suggested by experimental s t ~ d i e s . ~A~theoretical ,~~ study of the relation between the contact ion pairs and separated ion pairs in homogeneous catalysis is in progress. The exchange of the bonding and interaction sites for the Ti-Cl(2 and 1) and the A1-Cl(1 and 2) bonds occurs through the insertion process, namely the Al-C1 (and Ti-C1) bonds altemation occurs through the ethylene insertion. Accordingly, the cocatalyst, AlHzCl, plays a role in facilitating the pull-push mechanism through the AI-C1 (and Ti-Cl) bonds altemation mechanism. The AlC1 bonds altemation during the ethylene insertion process is expected to exist in heterogeneous catalysis. In the view point of the altemation mechanism, we have a possibility of design

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Acknowledgment. The present research is supported in part by Grant-in-Aid for Scientific Research on Priority Area 'Theory of Chemical Reactions" from the Ministry of Education, Science and Culture. This work is also supported in part by the Grant-in-Aid for Special Research from the Sangyo Institute of Osaka Sangyo University, for which I express my gratitude. The computer time was made available by the Computer Center of the Institute for Molecular Science (IMS) and by the Information Systems Engineering Department of Osaka Sangyo University with its CONVEX C240 minisupercomputer,and all of them are gratefully acknowledged. References and Notes (1) Ziegler, K.; Holzkamp, E.; Breil, H.; Martin, H. Angew. Chem. 1955,67, 541. (2) Natta, T. Macromol. Chem. 1955,16, 213. (3) Ivin, K. J.; Rooney, J. J.; Stewart, C. D. J . Chem. SOC., Commun. 1978,604. (4) Katz, T. J.; Lee, S . J. J. Am. Chem. SOC. 1980,102, 422. ( 5 ) Uppal, J. S.; Johnson,D. E.; Staley, R. H. J. Am. Chem. SOC. 1981, 103, 508. (6) Soto, J.; Steigenvald, M. L.; Grubbs, R. H. J . Am. Chem. SOC.1982, 104, 4479. (7) Clarke, T.C.; Yannoni, C. S . J . Am. Chem. SOC.1983,105,7787. (8) Clawson, L.; Soto, J.; Buchwald, S . L.; Steigenvald, M. L.; Grubbs, R. H. J . Am. Chem. SOC. 1985,107, 3377. (9) Eisch, J. J.; Piotrowski, A. M.; Brownstein, S. K.; Gabe, E. J.; Lee, F. L. J . Am. Chem. SOC. 1985,107, 7219. (10) Cossee, P. J. J . Catal. 1964,80. (11) Armstrong, D. R.; Perkins, P. G.; Stewart, J. J. P. J . Chem. Soc., Dalton Trans. 1972,1972. (12) Novaro, 0.; Chow, S . ; Magnouat, P. J . Catal. 1976,41, 91. (13) Giunchi, G.; Clementi, E.; Ruiz-Vizcaya, M. E.; Novaro, 0. Chem. Phys. Lett. 1977,49, 8. (14) Novaro, 0.; Blaisten-Barojas, E.; Clementi, E.; Giunchi, G.; RuizVizcaya, M. E. J . Chem. Phys. 1978,68, 2337. (15) Balazs, A. C.; Johnson, K. H. J . Chem. Phys. 1982,77, 3148. (16) Fujimoto, H.; Yamasaki, T.; Mizutani, H.; Koga, N. J. Am. Chem. SOC. 1985,107, 6157.

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