A Density Functional Study of Ethylene Insertion into the M-CH3 Bond

Mary S. W. Chan, Kumar Vanka, Cory C. Pye, and Tom Ziegler ... P. K. Das , D. W. Dockter , D. R. Fahey , D. E. Lauffer , G. D. Hawkins , J. Li , T. Zh...
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Organometallics 1995,14, 2018-2026

2018

A Density Functional Study of Ethylene Insertion into the M-CH3 Bond of the Constrained Geometry Catalysts [(SiH2-Cs&-NH)MCH3]+ (M = Ti, Zr, Hf) and (S~H~-C~H~-NH)T~CHQ Liangyou Fan,*>?Daryll Harrison,? Tom K. Woo,$ and Tom Ziegler*p$ Novacor Research & Technology Corporation, 2928-16 Street N.E., Calgary, Alberta, Canada T2E 7K7,and Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N 1N4 Received August 24, 1994@ The chain propagation mechanism of the constrained geometry catalysts (CGC) (SiH2CsHd-NH)MCHS+ (M = Ti, 1,Zr, 3,Hf, 4) and (SiH2-C5H4-NH)TiCH3, 2, has been studied theoretically by density functional theory (DFT) and molecular mechanics. DFT energy profiles have been determined for the insertion of ethylene into the M-CH3 bonds of the aforementioned CGCs (LzM-CH~ CHz=CH2 LZM-CHZ-CHZ-CH~). One of the objectives of the study was to compare the insertion process involving the cationic Ti(IV) CGC, 1,and its neutral Ti(II1)counterpart, 2. The insertion process for both oxidation states was found to be quite feasible with the Ti(IV) and Ti(II1) complexes possessing modest insertion barriers of 3.8 and 3.3 kcaVmo1, respectively. The insertion process for the Ti(IV)-, Zr(IV)-, and Hf(IV)-based CGCs were compared, and it was found that the insertion barriers increased in the order Ti < Zr x Hf. The calculated insertion barriers were calculated to be 3.8, 5.1, and 5.8 kcaVmol for the Ti, Zr, and Hf complexes, respectively. A possible chain rearrangement mechanism involving the rotation of the M-C, bond was also examined by molecular mechanics. The results suggest that this process is sterically unhindered for the half-sandwich constrained geometry catalysts whereas it is significantly more hindered for the full sandwich bis-Cp metallocenes.

+

Introduction There is currently considerable interest in metallocenes as alternatives to traditional Ziegler-Natta catalysts in olefin polymerization. Kaminsky and Brintzingerl' have pioneered a new generation of bridged cationic metallocenes with group-4 metals, Ia, that can

HZSi\e + - / C H s

Qb Ia

HZSi,

f \

\

,M*-CH3 /

N H

Ib

be used to produce high-density polyethylenes and both isotactic and syndiotactic a-olefins. Uniformity of the active site in these metallocene-based systems leads to greater uniformity of the polymer microstructure, allows for incorporation of comonomers with higher regularity, and produces plastic with molecular weight distributions which are narrower than those produced by traditional heterogeneous Ziegler-Natta catalysts. Most Novacor Research & Technology Corp. of Calgary. Abstract published in Advance ACS Abstracts, February 1, 1995. (1) (a) Ewen, J. A. J.Am. Chem. Soc. 1984,106,6355. (b) Ewen, J. A.; Jones, R. L.; Razavi, A.; Ferrara, J. D. J.Am. Chem. SOC.1988, 110,6255. (c) Kaminsky, W.; Kulper, K.; Brintzinger, H. H; Wild, F. R. W. P. Angew. Chem., Int. Ed. Engl. 1985,24, 507. (d) Kaminsky, W.; Steiger, R. Polyhedron, 1988, 7, 2375. (e) Spaleck,W.; Kiiber, F.; Winter, A.; Rohrmann, J.; Bachmann, B.; Antberg, M.; Dolle, V.; Paulus, E. F. Organometallics 1994, 13, 954. (0Stehling, U.; Diebold, J.; Kirsten, R.; Roll, W.; Brintzinger, H. H Organometallics 1994, 13, 964. +

1: University

-

recently, half-sandwich metallocenes, Ib, or constrained geometry catalysts (CGC) first recognized by BercawZe et al. are reported2 to produce polymers with side branches well beyond the traditional C3 to CSa-olefins. This long chain branching, as it is termed, along with the narrow molecular weight distributions characteristic of metallocenes allows CGC plastics to break the rules of the structure-property-processibility relationships. In other words the CGC products posses very desirable performance properties while still allowing for acceptable processibility. The most widely accepted mechanism for olefin polymerization by heterogeneous Ziegler-Natta systems as well as the homogeneous metallocene catalysts is due to Cossee.3 This propagation mechanism is shown for the metallocene systems in eq 1.

7

t =

hMYH H ""'@

IIa Active Complex

,

L2M k H H a 11b

x-Complex

s2

(1) IIC Transition State

y-agostic alkyl product

The active species IIa of eq 1coordinates an olefin to form the ncomplex, IIb, followed by the formation of

@

(2) (a)Stevens, J. C.; Timmers, F. J.;Wilson,. D. R.; Schmidt, G. F.; Nickias, P. N.; Rosen, R. K.; Knight, G . W.; Lai, S. European Patent Application EP-416-81542, March 13, 1991. (b) Canich, J. A. PCT Application WO 91/04257, April 4, 1991. (c) Devore, D. D. European Pgtent Application EP-514-828-A1, November 25, 1992. (d) Lai, S. Y.; Wilson, J. R.; Collier, R.; Knight, G . W.; Stevens, J. C. PCT Application W093/08221, April 29, 1993. (e) Shapiro, P. J.; Bunel, E.; Schaefer, W. P.; Bercaw, J. E. Organometallics 1990, 9, 867.

0276-733319512314-2018$09.0OlO 0 1995 American Chemical Society

Ethylene Insertion into M-CH3 Bonds

Organometallics, Vol. 14, No. 4, 1995 2019

the transition state IIc and the product IId in which The first point of interest is concerned with the potential performance of a neutral group-4 catalyst in the chain has been increased by two carbon units. which a single electron has been added t o the cationic studies ,~ There have been a number of e ~ p e r i m e n t a l ' ~ CGC system Ib so as to produce a dl CGC catalyst. We aimed a t providing a more detailed picture of the shall specifically deal with M = Ti since titanium d1 scheme outlined in eq 1. system on occasion have been invoked as Ziegler-Natta Molecular modeling has also been used extensively catalysts. lo in studies of the steps involved in olefin polymerization. The second objective of our investigation is related Molecular mechanics simulations have so far focused to the role of the metal. We shall study how the stability on the stereoregularity of polyolefins by analyzing the and structure of the x-complex, IIb, the geometry and steric repulsion at the assumed transition state, IIc, of of the transition state IIc, and the relative the olefin insertion step in the Cossee m e c h a n i ~ m . ~ , ~ ,energy ~~ energy of the product IId varies among the group A number of ab i n i t i ~semi-emperical,s ,~ and density 4-elements titanium, zirconium, and hafnium. functional theory7gv9(DFT)methods have been employed Finally, we have briefly examined the freedom of the in studies of the electronic factors of importance in the polymer chain in the half-sandwich constrained geomCossee mechanism. The active catalytic species in the etry catalysts, Ib, and compared it to that in the full electronic studies were assumed to be unsaturated sandwich bis-Cp metallocenes, Ia. cations, L2MR+, where M is a group IV transition metal, and the growing chain R is represented by CH3 whereas LZ varies from Cl2 and bis(cyclopentadieny1) (Cp) to Computational Details bridged bis-Cp's. The possible influence of the solvent The calculations reported here were carried out by using and the counterion (cocatalyst) was ignored in those the density functional package, ADF, developed by Baerends calculations. et aZ." a,b and vectorized by Ravenek.l'" The adopted numerical We present here a DFT-based study of the CGC integration scheme was that developed by te Velde et aZ.12A system Ib and its possible role as a catalyst in olefin set of uncontracted triple-l; Slater-type orbitals (STO) was polymerization according to eq 1. In our calculations employed for the ns, np, nd, (n + Us, and ( n + l ) p valence the growing chain is presented by a methyl group, and orbitals of the transition metal atoms.13 For the 2s and 2p any influence from the solvent or the counterion has orbitals of carbon and nitrogen, use was made of a double-c basis augmented by a n extra 3d polarization function.12 The been neglected. The zirconium-based CGC has been inner core shells were treated by the frozen-core approxstudied briefly in a previous general study on metalimationga A set of auxiliary s, p, d, f, and g STO functions, locene based homogeneous Ziegler-Natta catalyst^.^^,^,^ centered on all nuclei, was introduced t o fit the molecular Here, we provide a more comprehensive study of Ti-, density and to represent Coulomb and exchange potentials Hf-, and Zr-based constrained geometry catalytic sysa~curate1y.l~ All molecular geometries were optimized accordtems. ing to the analytic energy gradient method implemented by (3) (a) Cossee, P. J. Catal. 1964,3,80. (b) Arlman, E. J.; Cossee, P. J . Catal. 1964,3, 99. (4) (a) Fink, G.; Rottler, R. Angew. Makromol. Chem. 1984,94,25. (b) Brookhart. M.: Green, M. L. H. J . Orpanomet. Chem. 1983,250, 395. (c) Soto, J.; Steigerwald, M. L.; Grubis, R. H. J. A m . Chem. SOC. 1982,104,4479. (5) (a) Corradini, P.; Guerra, G.; Vacatello, M.; Villana, V. Gazz. Chim. Ital. 1988, 118, 173. (b) Cavallo, L.; Guerra, G.; Oliva, L.; Vacatello, M.; Corradini, P. Poly. Commun. 1989,30, 16. ( c ) Cavallo, L.; Corradini, P.; Guerra, G.; Vacatello, M. Polymer 1991, 32, 1329. (d) Cavallo, L.; Guerra, G.; Vacatello, M.; Corradini, P. Chirality 1991, 3,299. (e) Cavallo, L.; Guerra, G.; Corradini, P. Macromolecules 1993, 26, 260. (6) (a) Castonguay, L. A.; Rappe, A. K. J . Am. Chem. SOC.1992,114, 5832. (b) Hart, J. R.; Rappe, A. K. J . Am. Chem. SOC.1993,115,6159. (7) (a) Novaro, 0.; Blaisten-Barojas, E.; Clementi, E.; Giunchi, G.; Ruiz-Vizcaya, M. E. J . Chem. Phys. 1978,68, 2337. (b) Fuijimoto, H.; Yamasaki, T.; Mizutani, H.; Koga, N. J . Am. Chem. SOC.1985, 107, 6157. (c) Kawamura-Kuribayashi, H.; Koga, N.; Morokuma, K. J . Am. Chem. Soc. 1992,114,2359.(d) Kawamura-Kuribayashi, H.; Koga, N.; Morokuma, K. J . A m . Chem. SOC.1992, 114, 8687. (e) Koga, N.; Yoshida, T.; Morokuma, K Organometallics 1993, 12, 2777. (0 Siegbahn, P. E. M. Chem. Phys. Lett. 1993,205, 290. (g) Weiss, H.; Ehrig, M.; Ahlrichs, R. J . Am. Chem. SOC.1994,116,4919.(h) Bierwagen, E. P.; Bercaw, J. E.; Goddard, W. A., 111. J . Am. Chem. SOC.1994,116, 1481. (i) Koga, N.; Yoshida, T.; Morokuma, K. International Symposium: 40years ofZiegler Catalysts. Freiburg, Germany, Sep 1-3,1993; Springer-Verlag: Berlin, in press. (8) (a) Amstrong, D. R.; Pekins, P. G.; Stewart, J. J. P. J . Chem. SOC., Dalton Tram. 1972,9172. (b) Cassoux, P.; Crasnifer. F.; Labawe, J.-F. J. Organomet. Chem. 1979,165,303. ( c ) McKinney, R. J. J . Chem. SOC.,Chem. Commun. 1980,490. (d) Balazs, A. C.; Johnson, K. H. J . Chem. Phys. 1982, 77, 3148. (e) Shiga, A.; Kawamura, H.; Ebara, T.; Sasaki, T. J . Organomet. Chem. 1989, 266, 95. (0 Prosenc, M.-H.; Janiak, C.; Brintzinger, H.-H. Organometallics 1992, 11, 4036. (9) (a) Woo, T. K.; Fan, L.; Ziegler, T. Organometallics 1994, 13, 432. (b)Woo, T. K.; Fan, L.; Ziegler, T. Organometallics 1994,13,2252. (c) Meier, R. J.; van Doremaele, G. H. J.; Iarlori, S.; Buda, F. J . Am. Chem. Soc., submitted for publication. (d) Woo, T. K.; Fan, L.; Ziegler, T. International Symposium: 40 years of Ziegler Catalysts. Freiburg, Germany, Sep 1-3, 1993; Springer-Verlag: Berlin, in press.

Verslius and Ziegler15at the local density approximation (LDA) level.16 Nonlocal corrections based on Beckes's functional17 a for exchange and Perdew's functional15bfor correlation were added as a perturbation (LDALNL-P). The transition states were located by the algorithm due to Baker.'* For the molecular mechanics calculations the POLYGRAF24 package by Molecular Simulations Inc. was utilized. The catalyst backbone was fured in this model, since no force field parameters were available at the time. The L2M-C, fragment of the catalysts was held rigid with the structure of the backbones taken from the DFT-optimized y-agostic propyl structures. The POLYGRAF implementation of Allinger's (10)Rosen, R. K.; Nickias, P. N.; Devore, D. D.; Stevens, J. C.; Timmers, F. J. International Patent Application W093/19104, Sep 30, 1993. Luinstra, G. A.; ten Cate, L. C.; Heeres, H. J.;Pattiasina, J. W.; Meetsma, A.; Teuben, J. H. Organometallics 1991, 10, 3227. Eish, J. J.; Boleslawski, M. P. J . Organomet. Chem. 1987, 334, C1. (11) (a) Baerends, E. J.; Ellis, D. E.; Ros, P. Chem. Phys. 1973, 2, 41. (b) Baerends, E. J. Ph.D. Thesis, Vrije Universiteit, Amsterdam, 1975. (c) Ravenek, W. In Algorithms and Applications on Vector and Parallel Computers; te Riele, H. J. J., Dekker, Th. J.,van de Vorst, H. A., Eds.; Elsevier: Amsterdam, 1987. (12) (a)Boerrigter, P. M.; te Velde, G.; Baerends, E. J. Int. J . Quant. Chem. 1988,33,87.(b) te Velde, G . ;Baerends, E. J. J . Comput. Phys. 1992, 99, 84. (13) (a) Snijders, J. G.; Baerends, E. J.;Vernooijs, P. At. Nucl. Data Tables 1982, 26 , 483. (b) Vernooijs, P.; Snijders, J. G.; Baerends, E. J. Slater type basis functions for the whole periodic system; Internal report; Free University of Amsterdam, The Netherlands, 1981. (14) Krijn, J.; Baerends, E. J. Fit functions in the HFS-method; Internal report (in Dutch); Free University of Amsterdam, The Netherlands, 1984. (15)Versluis, L; Ziegler, T. J . Chem. Phys. 1988, 88, 322. (16)Vosko, S. H.; Wilk, L.; Nusair, M. Can. J . Phys. 1980,58, 1200. (17) (a) Becke. A. D. Phvs. Rev. 1988, A38, 3098. (b) Perdew, J. P. Phys. Rev. 1986, B33, 8822. (18)Baker, J. J . Comput. Chem. 1986, 7, 385.

2020

Organometallics, Vol. 14, No. 4, 1995

MM2I9 force field was used as a starting point with all unknown parameters approximated as follows. All torsions involving the metal center were assumed to have no barrier. The force constant for the M-C(sp3)-C(sp3) bend was approximated to be the same as the MM2 C(sp3)-C(sp3)-C(sp3) force constant of k b = 64.75 kcal/mol. The average M-Ca-Cfi bond angle from a number of DFT-optimized y-agostic propyl zirconocenes and titanocenes of 84" was used as the equilibrium angle for this bend. The C(sp3)-C(sp3)-H MM2 parameters were used for the M-C(sp3)-H bending parameters (kb=51.8 kcal/mol and 8, =109.4"). To allow for the short M-C and M-H nonbonded distances that are observed, the metal van der Waals interactions were turned off. Including the metal van der Waals interactions caused the growing chain to be unnaturally far away from the metal center. Removal of the metal van der Waals interactions resulted in geometries which were more indicative of those observed in Id, 3d, and 4d. Other interactions prevented the growing chain from collapsing onto the metal center such as the M-C(sp3)-C(sp3) bend and the steric interactions between the growing chain and the catalyst backbone. It should be noted that that the exclusion of the metal van der Waals interactions did not actually effect the rotation profiles shown in Figure 6 significantly compared to the profiles with the van der Waals interactions included. In this model elecrostatic interactions were also neglected. In these calculations the o dihedral was fixed by increasing the cen-Zr-Ca-Cp dihedral barrier to 1000 kcal/mol (This is the standard method in POLYGRAF for constraining particular internal coordinates). With o constrained and the L2MCa backbone fixed, the growing chain was fully optimized for each 10" interval from o = -180" to +180". For each o,the global minimum was searched for, which involved minimizing several different chain conformations. The lowest energy conformations are represented in Figure 6.

Results and Discussion We shall here present the results from our DFT calculations on the constrained geometry catalysts [SiH2-C5H4-NHMCH3P, where M = Ti, Zr, and Hf for x = +1 and M = Ti for x = 0. The positively charged species correspond to a formal oxidation state of IV for the metal center. It will be referred to as M(IV) for the sake of simplicity. Similarly, the neutral species will be referred to as Ti(II1)in the following discussion. We shall start with a comparison of the Ti(VI)- and Ti(II1)based systems. Comparison of Ti(VI) and Ti(II1). The optimized structure of the Ti(IV)catalyst [SiH2-C&-NHTiCH31+ is shown in l a whereas the corresponding neutral Ti(111)species is given in 2a. In both, the Si atom is nearly coplanar (within 1")with the plane defined by the centroid of the Cp ring, Ti, and the N atom, while the Ti-methyl bond is bent out of this plane as defined by the angle 8. The charged species l a displays a large bending angle of 8 = 61" whereas the bending angle for 2a is much smaller at 25". A similar difference in the degree of bending between neutral and cationic species has also been calculated by B i e r ~ a g e net~ al. ~ The bending mode is soft, and less than 3 kcaYmol is required to move the methyl group from the in-plane to the out-of-plane position. The metal-ligand bond distances are generally reduced in going from Ti(II1) to Ti(IV). The reduction (19)(a) Allinger, N.L.; Yuh, Y. H.; Lii, J. H. J . Amer. Chem. SOC. 1989,111,8551. (b) Spargue, J. T.; Tai, J. C.; Yuh, Y.; Allinger, N. L. J. Comput. Chem. 1987,8,581.

Fan et al.

W

amounts to 0.05 A for the Ti-N and Ti-CH3 bonds and 0.02 A for the Ti-Cp distance. The shortening of the metal-ligand bond distances is in keeping with the smaller radius of Ti(1V) as well as its stronger ability to accept electron density. Structure l a is stabilized by an agostic interaction between the methyl hydrogen and the Ti center. An angle of 96" between the C-H and Ti-C bonds as well as a slightly elongated C-H bond of 1.12 A are both indicative of such an interaction. The agostic interaction in the neutral species 2a is less pronounced with a H-C-Ti angle of 103", a C-H bond length of 1.12 A, and a Ti-H distance of 2.56 A. The coordination by ethylene to the vacant site of the titanium center in l a leads to a n-complex lb. The

bending angle 6 in l b has slighly increased by 3" compared to la. Also, the ethylene coordination to l a

Ethylene Insertion into M-CH3 Bonds catalyst + ethylene

Organometallics, Vol. 14, No. 4, 1995 2021

a transition state

x- complex

product

Ti(lV)-system

1

catalyst + ethylene

b

th

1 1

26.6

I

4

9

1

transition state

1 X-

complex

product

Ti(lI1)-system

Figure 1. Reaction profile for the insertion of ethylene into the M-CHs bond: (a) M = Ti(IV),(b) M = Ti(II1). results in an elon ation of the Ti-Cp and Ti-N bonds by 0.03 and 0.02 ,respectively. The Ti-CH3 bond is, on the other hand, contracted by 0.03 A. The coordination of ethylene to la is exothermic by 20.8 kcaVmol, as indicated by the reaction profile shown in Figure la. The n-complex with the neutral Ti(II1)species 2a was optimized as 2b. The methyl group of 2a has undergone a considerable movement out of the Ti-N-Si plane in order for the metal center to accommodate the incomming ethylene. The bending angles of the methyl group are quite similar in lb and 2b. The coordination of ethylene to 2a is exothermic by 22.7 kcaVmo1, Figure lb. There is a considerable difference between the charged Ti(IV) species lb and the neutral Ti(II1) complex 2b with regard to the structure of the coordinated ethylene and the way in which it is bound to the metal center. The bonding between ethylene and the do metal center in the Ti(IV) species lb is basically established by an electrostatic stabilization of the ethylene n-electrons due t o the positively charged metal center. The ethylene double bond distance in lb remains essentially the same as in the free molecule (1.34 A),and the Ti-C distances of 2.39 and 2.44 A,respectively, are rather long. The ethylene double bond in the neutral Ti(II1) species 2b is on the other hand elongated to 1.38 A. This elongation stems from a delocalitiqn of the single d-electron on titanium into the n* orbital of ethylene. The Ti(II1)-C distances to the two carbon atoms of the ethylene at 2.29 and 2.27 A,respectively, are in addition noticeably shorter than those in lb. Thus, 2b can be characterized as a real n-complex in which both donation and back-donation are important. We have carried out a full transition state optimization for the insertion processes involving the Ti(II1)and Ti(IV) species. The optimized transition state for the Ti(1V) system is given in IC whereas 2c represents the transition state for the neutral Ti(II1) system. The two transition states IC and 2c were confirmed to have a single imaginary frequency.

R

The Ti(IV) transition state IC is seen to be much closer in geometry to the n-complex lb than the propyl product Id. Thus, IC must be characterized as an early

P

transition state. The distance between the methyl and ethylene carbon atoms is shortened from 3.35 A in lb t o 3.00 A in IC,but it is still not close enough for the two atoms to be bonded at this stage of reaction. The double bond of ethylene remains unchanged at 1.34 8, in IC. The Ti-methyl distance is 0.01 A longer in IC than in the n-complex lb, while the Ti-C(ethy1ene) distance is shortened by 0.06 A. The metal to ethylene interaction in the transition state IC is thus similar to that found in the n-complex lb. It should also be noted that the local CS-axis of the methyl group is pointed toward the metal center rather than the approaching ethylene carbon. The calculated barrier for the insertion step lb IC Id is modest and amounts to 3.8 kcaVmo1. We have p r e v i o ~ s l y ~calculated ~ , ~ * ~ an even smaller barrier of less than 1kcaVmol for the insertion process involving bis-Cp systems such as Ia suggesting

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2022 Organometallics, Vol. 14, No. 4,1995

that some bis-Cp systems may undergo insertion without a barrier.7e The Ti(II1)transition state 2c is also quite similar to the corresponding n-complex 2b. The only significant difference between 2c and 2b is that the methylethylene distance is 0.27 8, closer in 2c; all other changes are minor. The calculated barrier for the insertion, 2b 2c 2d, is only 3.3 kcaVmol, Figure lb. Thus it would seem that the neutral Ti catalyst should be as active as the positively charged Ti(IV) species. The kinetic product from the insertion process, eq 1, is a y-agostic propyl complex. The optimized structure of the propyl complex is shown as Id for the Ti(IV) system and as 2d for the neutral Ti(II1) system. Structure Id displays a clear agostic interaction between Ti and the y-hydrogens. The P-carbon in Id is twisted out of the Ca-Ti-C, plane so that the hydrogens are in a staggered positions. The kinetic product Id was found to be a very stable conformation with an energy that is 12.8 kcaVmol lower than the n-complex lb. The y-agostic structure Id is not likely to be the most stable conformation for the propyl chain. Previous c a l c ~ l a t i o n son ~ ~bis-Cp ~~ systems gave a P-agostic structure as the most stable, and we expect the same t o be the case for the present system. Compared to Id, the neutral species 2d displays a weaker agostic interaction as the Ti(II1) metal center is less electron deficient. The closest y-hydrogen contact t o the titanium center is 2.20 A. The Ti-C, bond is 0.06 8, longer in 2d than in Id, which is comparable to the difference in the Ti-C,(methyl) distance for the two corresponding methyl compounds l a and 2a. The variation can be explained by the difference between the radius of Ti(II1)and Ti(IV). Further, the Ti-alkyl bond in the neutral systems is weakened by the three-electron two-orbital interaction between the odd electron on the metal center and the electron pair in the Ti-alkyl bonding orbital. The Ti(II1) propyl product 2d is only 4.2 kcaVmol more stable than the corresponding Ti(II1) n-complex 2b. Thus, the neutrg system might exhibit an equilibrium between 2d and 2b. The greater stability of the Ti(IV)-basedsystem results in a larger overall insertion enthalphy of -33.6 kcaVmol compared to the insertion enthalpy of -26.6 kcal/mol for the Ti(I1I) system. These values are in good agreement with the intrinsic enthalpy of inserting an olefin into the M-C bond (the energy gain from breaking one C-C double bond and forming a C-C single bond during the insertion). An indication of the intrinsic insertion enthalpy is given by the exothermicities of the general reaction 'CH3 + C,H, -*Cn+1Hm+3,AH"'2o (this is assuming that the M-Me and M-R bond dissociation enthalpies are roughly equivalent). For ethylene AF" is determined experimentallyz0to be 23.5 kcdmol. The difference between the the instrinsic enthalpy and the calculated enthalpy of insertion can be used to estimate the energy gained due to the additional agostic interactions in the y-agostic propyl complex, IId, as compared to the methyl complex IIa. The experimental value of AH" suggests that, for the Ti(II1) system, the agostic

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(20) (a) Christ, C. S.; Eyler, J. R.; Richardson, D. E. J. Am. Chem. SOC.1988,110, 4038. Christ, C. S.;Eyler, J. R.; Richardson, D. E. J . Am. Chem. SOC.1990,112, 596.

Fan et al.

interactions amount to about 3 kcal/molZ1whereas for the cationic Ti(IV) system the additional interactions amount to about 10 kcaVmo1. The calculated energetics for the two insertion processes involving either Ti(IV) or Ti(II1) is summarized in Figure 1. The formation of the n-complex, SI of eq 1, is exothermic for both systems. However, the ethylene complexation energy of the neutral n-complex 2b is larger by 2 kcdmol due to the more effective titanium to olefin back-donation. The two calculated activation energies of 3.8 kcaVmol, Ti(IV),and 3.3 kcal/mol, Ti(III), are modest and quite similar. Thus, by consideration of electronic effects, the insertion process involving either Ti(II1) or Ti(IV) should be kinetically quite feasible in the gas-phase. We would also expect the insertion process involving the neutral Ti(II1) system to be feasible in solution, perhaps even more so than the cationic Ti(IV) system. In solution, there should be a barrier to the formation of the n-complex, IIb, due to the displacement of weakly coordinated solvent molecules.7h For the cationic Ti(IV) system, the coordination of the solvent to the metal center is based on an electrostatic interaction equivalent to that in the olefin n-complex. Therefore, we would expect the complexation of the solvent to be of comparable strength to the complexation of the olefin. In contrast to this, the neutral Ti(II1) CGC is expected to form a much weaker complex with the solvent than with the olefin. The reason for this is that the olefin-Ti(II1) complex enjoys the stabilization due to back-donation, whereas the solvent complex would not normally possess any significant back-donation. In addition to this, the electrostatic stabilization of the neutral Ti(II1)solvent complex would not be nearly as strong as electrostatic stabilization enjoyed by the cationic Ti(Wsolvent complex. Therefore, the displacement of the solvent from the Ti(II1)complex is expected to posses a small barrier compared with the analogous displacement from its Ti(1V) counterpart. Figure 2 illustrates schematically the expected differences in the energy profile between the insertion in the gas-phase and in solution for both the neutral Ti(II1) and cationic Ti(IV) systems. We expect the effect of solvation on the energy profile of the neutral Ti(II1) system to be much less dramatic than that of its cationic Ti(IV) analogue. Furthermore, we also expect the Ti(II1)system to more readily form the olefin n-complex than the Ti(IV) complex because the neutral system will have a much smaller displacement barrier. (21) The zero-pointenergy contributions will for the most part cancel out except for those due to the agostic interactions. If one included zero-point energy corrections pe) in our estimates of the strength of the agostic interactions,the ekimate would be slightly smaller than stated since the calculated enthalpies of insertion for the Ti(II1) and Ti(IV) complexes do not included zpe corrections. However, the contribution to the zpe corection due to the agostic interactions are expected to be very small, less than 1 kcal/mol. (22) Longer chains have also been modeled (up to CS) and been shown to produce similar results. Trends and the basic behavior of the profile are expected to be the same for both long and short chain models. (23) This is somewhat of a surprise that the bis-Cp titanocene has roughly the same profile up to 180"as its larger more open zircocene counterpart. The titanocene is more sterically constrained, but when the energies are normalized with the zero energy set equal to the energy at w = On, this fact is somewhat obscured. (24) POLYGRAF version 3.0 (17/2/1992) of Molecular Simulations Inc. (MSI), 16 New England Executive Park, Burlington, MA, 1-800756-4647.POLYGRAF is a commercial molecular mechanics,molecular dynamics program system.

Ethylene Insertion into M-CHs Bonds

a. T

i

Organometallics, Vol. 14, No. 4, 1995 2023

h I

displacement barrier \

insertion

solvent complex

b. Ti(II1)

I-

y-agostic

-

\\

solvated

For the CGC type catalysts, Ib, steric crowding might not be so important, and experiments seem to indicate that the titanium homologue in this case is the most active. We report here a DFT-based study on the trend in activity of the CGC systems, Ib, along the triad Ti, Zr, and Hf. Some of the more important structural parameters from the optimized geometries of the zirconium-, 3a, and hafnium-based, 4a, CGC active complexes are compared with those of the titanium homologue in Figure 3a. Here the parameters for titanium are given in parentheses ( ), those of hafnium are given in brackets [ I, and those of zirconium are given without enclosures. The length of the metal-methyl bond increases in the order Ti Zr(IV) > Ti(II1) is somewhat surprising because one would normally expect the trend Ti(1V) > Zr(1V) x Hf(IV) > Ti(II1). As noted earlier, the insertion is only one step of the overall propagation mechanism. With the bis-Cp metallocenes our studies suggest that the insertion step is not the rate-limiting step. Instead, the rate-limiting step likely involves the rearrangement of the y-agostic kinetic product, IId (eq 1). During the insertion of the olefin molecule into the M-C bond, the coordination site of this M-C bond is vacated allowing for the complexation of the olefin and the next insertion. Initially, however, this coordination site is partially blocked by

Ethylene Insertion into M-CH3 Bonds

Organometallics, Vol. 14, No. 4, 1995 2025

-Cp,Zr+-R

-

Ti-CGC

30.0 20.0 WlOO

W=60"

0 = 120"

a = 180"

10.0

Figure 6. Rotation about the M-C, bond for w = O", 60", 120°, and 180". [ I represents a vacant coordination site.

0.0 L

the y-agostic interactions of the growing chain (eq 1and Figure 3d). To accommodate the next monomer unit, this chain must vacate the coordination site by rotating about the M-Ca bond. The rotation of the polymer chain can be characterized by the VAC-M-Ca-CP dihedral angle w shown in Figure 5 , where VAC represents the bond vector of the vacant coordination site. One can consider the VAC bond vector to be the bond vector of the M-C bond vacated during the previous insertion. For the y-agostic product w is roughly zero, where VAC, M, Ca, and Cp lie in the same plane. A rotation of w = 60", which would place one of the hydrogens (HI of Figure 5) into the coordination plane, would be enough t o vacate the site and be appropriate for the eclipsed insertion of olefin. Other conformations are also depicted in Figure 5 . In this study we have attempted to model the rotation process with a gas-phase molecular mechanics simulation where the M-C, bond vector is fixed. Although, the 8 angle bending mode is calculated to be soft (3 kcaY mol barrier to cross the cen-M-N plane), such fluctionality along with full rotation about the M-C, bond would result in inversion of the metal center between monomer insertions. If the Cossee-Arlman mechanism is assumed, rapid inversion of the metal center between insertions has consequences in syndiospecific a-olefin polymerizationz6that would ultimately lead to atactic polymerization. In solution the M-Ca rotation may be a concerted process whereby the rearrangement is assisted by complexation of solvent or monomer to the metal. In fact, such assistance may be necessary since the rotation about the M-Ca bond breaks favorable agostic interactions in both the y-agostic product and the most stable product conformer,gbthe P-agostic complex. In this simple model the polymer chain was modeled with a propyl group22 and the force field used only accounted for structural differences between catalysts and not subtle electronic differences. The molecular mechanics rotation profiles for w = -180" to +180" of TUZr bis-Cp and CGC metallocenes are shown in Figure 6 with the zero energy set equal to the molecular mechanics energy at w = 0". The energy profiles for the hafnium analogues were not shown because they were virtually identical to the profiles for the zirconocenes. The reason for this is that the hafnium complexes are almost identical in structure to their zirconium counterparts. The M-C, rotation profiles for the bis Cp titanocene and zirconocene are very similar.23 The rotation profiles of the bis Cp complexes are symmetric about w = 0" (26)Ewan, J. A.; Jones, R. L.; Razavi, A.; Ferrara, J. D. J. Am. Chem. SOC.1988, 110,6255.

-180

-120 -60 0 60 120 M-C, bond dihedral, w (deg)

180

Figure 6. Normalized molecular mechanics energy profile for the rotation of the M-C, bond for the half-sandwich constrained geometry catalysts and the full sandwich bisCp metallocenes.The energies are relative to the molecular mechanics energy at w = 0", which represents the zero energy. with a global minimum at w = 0" and another minimum at 180". The maximas for the two complexes occur at roughly w = 100". Figure 6 shows that the bis-Cp complexes possess a barrier of between 20 kcal/mol for a rotation of w = 60". These barriers are exaggerated because of the nature of the force field used (the catalyst backbone was held rigid). Although the absolute values of the energies presented may be poor, the calculations are expected to give the general behavior of the steric requirements as the M-C, bond is rotated through 360". As Figure 5 shows, a f120" rotation is severely hindered with a calculated barrier of between 30 and 40 kcal/mol. The 180" rotation of the growing chain is also unlikely because although w = 5180" is a minimum, the chain must overcome the large steric barrier at -100". This is not to say that the conformation with w = f180" is unlikely; it means that this conformation will not be achieved by the M-Ca bond rotation that was simulated. (This conformation can be attained by the bending of the angle 8 through 0" which was determined to have a barrier less than 3.5 kcaYmo1.) The energy profiles of Figure 6 suggest that the rotation of the polymer chain in the constrained geometry catalysts is much less hindered than in the bis-Cp metallocenes. The 60" rotation for the CGCs is calculated to be less than 5 kcaYmo1 compared to 20 kcaY mol for the bis Cp systems. Additionally, rotation of the M-C, bond to w = +120" (positive being toward the amido group) is also relatively unhindered with a calculated barrier of roughly 7 kcal/mol. Thus when only steric factors are considered, the growing chain of the CGCs have much more freedom than their corresponding bis-Cp analogues. The point here is that the overall chain propagation mechanism for the bis-Cp systems and the constrained geometry catalysts may be quite distinct from one another and may even have different rate determining steps. Our DFT c a l ~ u l a t i o n show s ~ ~ that ~ ~ ~the ~ bis-Cp zirconenes possess an electronic insertion barrier of less than 1kcaYmol, while the molecular mechanics rotation profile of Figure 6 suggests that they may have a large rearrangement barrier. On the other hand, its CGC counterpart, 3,has an electronic insertion barrier of over 5 kcal/mol and potentially a small rearrangement barrier.

Fan et al.

2026 Organometallics, Vol. 14,No. 4, 1995

Conclusions The reactivities of the Ti(III)-, Ti(IV)-, Zr(IV)-, and Hf(IV)-basedconstrained geometry catalysts have been studied by calculating the structures and relative stabilities of the species IIa-d in eq 1. Although the active catalysts are generally assumed t o be the positively charged methyl complexes of group N elements with a formal oxidation state of IV,the neutral spices of oxidation state I11 of titanium has been found to be as reactive as Ti(IV) in terms of reaction energies of ethylene insertion. The much stronger n-complex of Ti(II1)is the major difference between Ti(II1)and Ti(IV), which facilitate the followed insertion step. In comparison of the insertion process for the Ti(IV)-, Zr(IV)-, and Hf(IV)-based catalysts, the reaction exothermicity for the insertion process was found to be quite similar for the three species. On the other hand, the activation barrier for ethylene insertion was found t o increase in the order Ti < Zr Hf. The differences between the zirconium- and hafnium-based catalysts are minor with regard to the structure of the catalysts, the n-complexes,the transition states, the propyl products, and the relative energies. The titanium-based catalyst was found to possess the smallest insertion barrier of the three. The higher activity of the titanium-based CGC is related to a lower stability of the corresponding n-complex due to steric repulsions between ethylene and the coligands on the metal center, notably the methyl group* The insertion process is only one step in the overall chain propagation mechanism. After the insertion of

-

the olefin into the M-C bond, the growing chain must rearrange to allow for the insertion of the next monomer unit. Our molecular mechanics simulations of one possible rearrangement process, the rotation of the M-C, bond, suggest that this process is not sterically hindered for the constrained geometry catalysts. However, for their full sandwhich metallocene counterparts there is significantly more hindrance to the process. Previous calculation~~g.~~-~ suggest that there is virtually no insertion barrier for bis-Cp metallocenes while our studies show that the insertion barriers for the contrained geometry catalysts are between 3.8 and 5.8 kcall mol. Thus, we suggest that the overall chain propagation mechanisms for the half-sandwich constrained geometry catalysts and the full sandwich bis-Cp metallocenes may be distinctly different, possibly possessing different rate determining steps.

Acknowledgment. This investigation was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). We gratefully acknowledge the donors of the Petroleum Research Fund, administered by the American Chemical Society (ACS-PRF No. 27023-AC3). Dr. J. McMeeking of Novacor Research & Technology is thanked for many useful discussions. SupplementaryMaterial Available: Tables of Cartesian coordinates of DFT-optimized structures la-d, 2a-d, 3a-d, and 4a-d (11pages). Ordering information is given on any current masthead page. OM940680C