DFT Study of the Transition States and Products of Methyl Radical

Organometallics 2009, 28, 6469–6479 DOI: 10.1021/om900656t

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DFT Study of the Transition States and Products of Methyl Radical Addition to Olefins Coordinated in an Asymmetrical Mode to [Cp2Zr(OtBu)]þ: Predictions of Reversed Regioselectivities Compared to the Noncoordinated Reactions Faraj Hasanayn* and Mohammed S. El-Makkaoui Department of Chemistry, American University of Beirut, Beirut, Lebanon Received July 24, 2009

The addition of free alkyl radicals to olefins is known to encounter a small activation energy and to be highly regioselective, typically favoring the less substituted carbon of the double bond. The ability to modify the reactivity and regioselectivity of the given reaction can be of interest from both fundamental and practical perspectives. Olefins are known to bind to the [d0-Cp2Zr(OtBu)]þ fragment (Zr) relatively weakly, affording adducts having a nonclassical asymmetrical bond between Zr and the double bond of the olefins. In the present study electronic structure methods based on density functional theory (B3LYP) have been used to investigate how the kinetics and thermodynamics of methyl radical addition to a systematically varied series of mono- and 1,1-disubstituted ethylene may change when they are coordinated to Zr. In general, methyl addition to the unsubstituted carbon of the coordinated olefins is found to encounter an increased activation energy compared to the noncoordinated reactions. In contrast, the barriers of addition to the substituted carbon of the coordinated olefins are slightly smaller than the barriers in the noncoordinated reactions. These effects lead to opposite regioselectivities in the free and the coordinated reactions of several olefins. However, even when the kinetic regioselectivity reverses upon coordination, the thermodynamic preference for addition to the terminal carbon in the noncoordinated reactions remains unchanged. These results are discussed qualitatively on the basis of unconventional geometries calculated in the coordinated reactants, transition states, and products.

Introduction The formation of C-C bonds by addition of free alkyl radicals to unsaturated organic substrates is a fundamental reaction in organic and polymer chemistry.1,2 The coordination of such substrates to a metal should modify the energies of their radical addition reactions in one way or another, and this can provide new means to manipulate reactivity and selectivity in free radical chemistry. Indeed, there have been several studies in which a free alkyl radical has been added to

arene,3,4 allyl,5,6 carbene,7 or other ligands8 coordinated to various transition metal complexes. In spite of a growing interest in this approach, there is still limited understanding of how coordination to a metal may influence the transition states and thermodynamics of radical addition reactions. We have been interested in making contributions in this area by using electronic structure methods. To this end, we recently completed studies on alkyl addition to carbon monoxide coordinated to different dn-metal fragments.9,10 The results provided mechanistic understanding of a work by Boese and Goldman in which d8-ML5 metal carbonyls were observed to

*Corresponding author. E-mail: [email protected]. (1) (a) Giese, B. Radicals in Organic Syntheses: Formation of CarbonCarbon Bonds; Pergamon: Oxford, 1986. (b) Curran, D. P. In Comprehensive Organic Synthesis; Trost, B. M., Flemming, I. M., Semmelhack, M. F., Eds.; Pergamon: Oxford, 1991; Vol. 4. (c) Fossey, J.; Lefort, D.; Sorba, J. Free Radicals in Organic Chemistry; Wiley: New York, 1995. (d) McCarroll, A. J.; Walton, J. C. Angew. Chem., Int. Ed. 2001, 40, 2225. (2) (a) Kamigaito, M.; Ando, T.; Sawamoto, M. Chem. Rev. 2001, 101, 3689. (b) Matyjaszewski, K.; Xia, J. Chem. Rev. 2001, 101, 2921. (c) Hawker, C. J.; Bosman, A. W.; Harth, E. Chem. Rev. 2001, 101, 3661. (3) (a) Schmalz, H.-G.; Siegel, S.; Bats, J. W. Angew. Chem., Int. Ed. 1995, 34, 2383. (b) Merlic, C. A.; Walsh, J. C. J. Org. Chem. 2001, 66, 2276. (c) Merlic, C. A.; Miller, M. M.; Hietbrink, B. N.; Houk, K. N. J. Am. Chem. Soc. 2001, 21, 4904. (4) (a) Lin, H.; Zhang, H.; Yang, L.; Li, C. Org. Lett. 2002, 4, 823. (b) Lin, H.; Yang, L.; Li, C. Organometallics 2002, 21, 3848. (c) Cao, L.; Shen, M.; Li, C. Organometallics 2005, 24, 5983. (d) Byers, J. H.; Jason, N. J. Org. Lett. 2006, 8, 3453. (e) Byers, J. H.; Neale, N. R.; Alexander, J. B.; Gangemi, S. P. Tetrahedron Lett. 2007, 48, 7903.

(5) (a) Casty, G. L.; Stryker, J. M. J. Am. Chem. Soc. 1995, 117, 7814. (b) Ogoshi, S.; Stryker, J. M. J. Am. Chem. Soc. 1998, 120, 3514. (c) Carter, C. A. G.; McDonald, R.; Stryker, J. M. Organometallics 1999, 18, 820. (d) Carter, C. A. G.; Greidanus, G.; Chen, J.-X.; Stryker, J. M. J. Am. Chem. Soc. 2001, 123, 8872. (6) (a) Reid, S. J.; Freeman, N. T.; Baird, M. C. Chem. Commun. 2000, 18, 1777. (b) Reid, S. J.; Baird, M. C. J. Chem. Soc., Dalton Trans. 2003, 20, 3975. (c) Reid, S. J.; Baird, M. C. J. Organomet. Chem. 2004, 689 (7), 1257. (7) (a) Merlic, C. A.; Xu, D. J. Am. Chem. Soc. 1991, 113, 9855. (b) Merlic, C. A.; Xu, D.; Nguyen, M. C.; Truong, V. Tetrahedron Lett. 1993, 34, 227. (8) Merlic, C. A.; Walsh, J. C. Tetrahedron Lett. 1998, 39, 2083. (9) Hasanayn, F.; Nsouli, N. H.; Al-Ayoubi, A.; Goldman, A. S. J. Am. Chem. Soc. 2008, 130, 511. (10) Nsouli, N. H.; Mouawad, I.; Hasanayn, F. Organometallics 2008, 27, 2004.

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mediate effective photocatalytic carbonylation of alkanes by a free radical mechanism.11 More recently we initiated calculations to investigate how the kinetics, regioselectivity, and thermodynamics of alkyl addition to olefins may change when the olefin is coordinated to chemically relevant transition metal fragments. Our preliminary results on methyl addition to propylene coordinated to [d8-Rh(PCP)] (Rh) and [d0-Cp2Zr(OtBu)]þ (Zr) showed distinct and opposite effects in the two metal systems.12 Coordination to Rh slightly disfavored the kinetics, yet it strongly favored the thermodynamics. As in the free reaction, attack on the terminal carbon of the Rh-coordinated propylene was kinetically more favored, but addition to the substituted carbon gave the thermodynamic product. In contrast, the barriers in the reaction of the Zr-coordinated propylene were smaller than in the free reaction and actually favored attack onto the substituted site of the double bond. Nonetheless, addition to the terminal carbon remained thermodynamically favored in the Zr system. Such effects are important to the theory and practice of free radical chemistry. In particular, the effects predicted for the Zr system can be of potential practical value in expanding the scope of C-C bond making by the alkyl radical addition method. In the present work we provide a more detailed account of olefin coordination to Zr and subsequent reaction with the methyl radical. To better understand the factors that control the transition states and products in this system, we consider the coordination and reaction of a set of systematically substituted mono- and 1,1-disubstituted ethylene. Consistent with experimental observations, the olefins are calculated to bind to Zr in varying degrees of asymmetry. The activation energies and trends of methyl addition to the two sites of the double bond are found to be largely different in the free and the coordinated reactions, leading to reversed regioselectivities for many of the olefins. On the other hand, the thermodynamics are found to be quite comparable in the two systems. These findings are discussed qualitatively on the basis of unconventional geometries calculated in the coordinated reactants, transition states, and products.

Computational Details The calculations were performed at the B3LYP density functional level13 using Gaussian 03.14 The Hay-Wadt (11) (a) Boese, W. T.; Goldman, A. S. J. Am. Chem. Soc. 1992, 114, 340. (b) Boese, W. T.; Goldman, A. S. Tetrahedron Lett. 1992, 33, 2119. (12) Hasanayn, F.; Gozem, S. Organometallics 2008, 27, 5426. (13) (a) Becke, A. D. Phys. Rev. B 1988, 37, 785. (b) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (c) Johnson, B. G.; Gill, P. M. W.; Pople, J. A. J. Chem. Phys. 1993, 98, 5612. (d) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. (14) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; G. Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision B.05; Gaussian, Inc.: Pittsburgh, PA, 2003.

Hasanayn and El-Makkaoui relativistic ECP replaced the 28 core electrons of Zr.15 The molecules were calculated in three stages. First, full geometry optimization to a minimum or a transition state and normal mode vibrational analysis were conducted in the gas phase using the 6-31G(d,p) basis set on the main group elements16 and the double-ζ basis set supplied with the ECP on Zr along with a set of 10f polarization functions with exponent = 0.875 generated by the Frenking group.17 The Harmonic vibrational frequencies calculated at this stage were used without scaling to obtain the enthalpy and entropy terms at 1 atm and 298 K.18 In the second stage, the force constant matrix generated from the frequency calculation in the first stage was utilized to fully optimize the geometries again in the gas phase using this time two polarization functions on each element, namely, the standard 6-31(2d,2p) on the main group elements and a second f function with exponent = 0.292 on Zr estimated as a third of the first exponent of Frenking. The larger basis set does not have any major effects on the geometries or the energies. Finally, the larger basis set was used to calculate the energy of the gas phase geometries in a polarizable CH2Cl2 solvent continuum.19 In all of these calculations the doublet states were of the unrestricted type (UB3LYP) and afforded spin expectation values close to 0.75 even before spin annihilation. However, the spin densities computed using the unrestricted wave functions allocate small negative spin densities to some atoms, reaching up to -0.08 in some cases. To avoid complications in the analysis of the results due to such artifacts, we report Mulliken charges and spin densities obtained using ROB3LYP wave functions in the gas phase. For most of the coordinated molecules we considered possible alternative conformations defined within the olefin moiety or the Zr-olefin bond, but we report results only for the lowest energy conformer, which is in general uniformly the one that keeps the substituent away from the bulky OtBu ligand. The above computational model is popular in studies of chemically relevant transition metal complexes, and it is about the highest theoretical level we could apply in an efficient manner to deal with the large size and large number of the reactions we have to calculate in the present study. For the coordination of the olefins to [Cp2Zr(OtBu)]þ there are experimental data that we use to evaluate the calculated coordination energies. However, there have been several studies that noted limitations of the DFT methods in providing accurate energies of certain free radical reactions.20,21 Because there were no experimental data available to validate the B3LYP level in methyl radical addition to metal-coordinated olefins, when we initiated the study we calculated isobutene coordination to the model [Rh(PH3)2(CH3)] and [ZrCl3]þ fragments and subsequent reaction with the methyl radical at both the B3LYP and the CCSD-T levels.12 The activation and reaction energies showed good agreement at these two levels. Furthermore, the Radom group had found the B3LYP level to be “respectable” for the purpose of reproducing trends in the activation energies and reaction energies of radical addition reactions of the free olefins,22 which is one of the major objectives we are after in this (15) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 279. (16) (a) Rassolov, V. A.; Ratner, M. A.; Pople, J. A.; Redfern, P. C.; Curtiss, L. A. J. Comput. Chem. 2001, 22, 976. (b) Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80, 3265. (17) Ehlers, A. W.; B€ ohme, M.; Dapprich, S.; Gobbi, A.; H€ ollwarth, A.; Jonas, V.; K€ ohler, K. F.; Stegmann, R.; Veldkamp, A.; Frenking, G. Chem. Phys. Lett. 1993, 208, 111. (18) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (19) Miertus, S.; Scrocco, E.; Tomasi, J. Chem. Phys. 1981, 55, 117. (20) (a) Izgorodina, E. I.; Coote, M. L.; Radom, L. J. Phys. Chem. A 2005, 109, 7558. (b) Izgorodina, E. I.; Brittain, D. R. B.; Hodgson, J. L.; Krenske, E. H.; Lin, C. Y.; Namazian, M.; Coote, M. L. J. Phys. Chem. A 2007, 111, 10754. (21) Zhao, Y.; Truhlar, D. G. J. Phys. Chem. A 2008, 112, 1095. (22) Fischer, H.; Radom, L. Angew. Chem., Int. Ed. 2001, 40, 1340.

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work. Indeed, in our study of methyl addition to free CO and to [Mo(CO)6], [Ru(CO)5], and [Pd(CO)4], the B3LYP barriers were systematically smaller (by 3-4 kcal/mol) than the CCSD-T ones, but the conclusions about the effects of coordination to the different metal centers were nearly quantitatively similar at the two levels.9

Results and Discussion Olefin Coordination to [Cp2Zr(OtBu)]þ (Zr). Olefins of the [d -Cp2Zr(X)]þ fragment (X = alkyl) have been long implicated in olefin polymerization by zirconocene-type catalysts,23 but their detection has been complicated because of rapid alkene insertion into the Zr-X bond. Stoebenau and Jordan solved this problem by using the ancillary ligands X = OtBu24 and X = C6F525 and discovered that the asymmetrical olefins coordinate in this system in an asymmetrical mode. Very recently, Baird and Ziegler successfully detected an olefin of [Cp2Zr(Me)]þ and also gave experimental and theoretical evidence for asymmetric coordination.26 Table 1 lists the set of olefins we consider in the present study. The table gives the calculated coordination energy between the olefins and [Cp2Zr(OtBu)]þ (Zr) and the bond distance between Zr and the two carbons of the double bond, Zr-CH2 and Zr-Csub, as defined in eq 11. Also included in the table are experimental equilibrium constants (Kexp) measured by Stoebenau and Jordan for eq 2 at -89 °C in CD2Cl2.24b 0

Ethylene is calculated to bind to Zr nearly symmetrically, with relatively long Zr-carbon distances of 2.87 and 2.91 A˚. Comparable parameters were calculated by Lin for the ethylene adduct of [Cp2Zr(Me)]þ.27 At these distances, the valence ethylene-based MOs (Figure 1; isosurface = 0.04) suggest the Zr-ethylene bond has a small σ-type bonding component (ligand to metal σ-electron donation). Any π-type bonding interactions between the filled MOs involving the metal and the ancillary ligands and the π*-MO of ethylene appear to be at best minimal. Such π-interactions (23) (a) Coates, G. W. Chem. Rev. 2000, 100, 1223. (b) Resconi, L.; Cavallo, L.; Fait, A.; Piemontesi, F. Chem. Rev. 2000, 100, 1253. (c) Chen, E. Y.-X.; Marks, T. J. Chem. Rev. 2000, 100, 1391. (24) (a) Stoebenau, E. J.; Jordan, R. F. J. Am. Chem. Soc. 2003, 125, 3222. (b) Stoebenau, E. J.; Jordan, R. F. J. Am. Chem. Soc. 2006, 128, 8162. (25) (a) Stoebenau, E. J.; Jordan, R. F. J. Am. Chem. Soc. 2004, 126, 1117. (b) Stoebenau, E. J.; Jordan, R. F. J. Am. Chem. Soc. 2006, 128, 8638. (26) Sauriol, F.; Wong, E.; Leung, A. M. H.; Donaghue, I. E.; Baird, M. C.; Wondimagegn, T.; Ziegler, T. Angew. Chem., Int. Ed. 2009, 48, 3342. (27) Zhao, H.; Ariafard, A.; Lin, Z. Inorg. Chim. Acta 2006, 359, 3527.

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had been proposed to be important in some d0-zirconocene carbonyl complexes.28,29 Consistent with the long Zr-C bond distances, the calculated coordination energy of ethylene to Zr is relatively small: ΔΕcoord = -15.1 or -12.9 kcal/mol in the gas and solution phase, respectively. Adding the thermal and entropy terms affords ΔG°coord =-3.9 kcal/mol (gas phase, at 298 K and 1 atm). In comparison, ΔΕcoord and ΔΕcoord(sol) for the bonding of a molecule of dichloromethane to Zr are -11.8 and -7.4 kcal/mol, respectively. The difference in the coordination energies between the given two substrates, ΔΔΕcoord = -3.3 or ΔΔΕcoord(sol) = -5.6 kcal/mol, is close to the experimental enthalpy of -3.6 kcal/mol determined for the same substitution reaction in eq 2.24b Unlike ethylene, all of the other olefins in Table 1 are calculated to bond to Zr in a mode that exhibits significant degree of asymmetry, with Zr-CH2 being pronouncedly shorter than Zr-Csub. The data show that greater degrees of asymmetry are generally associated with shorter Zr-CH2 bonds and more negative coordination energies. To start with, the Zr-CH2 and Zr-Csub distances in the Zr-propylene complex are 2.73 and 3.19 A˚, respectively. The gaseous ΔEcoord of propylene is slightly more exothermic than ethylene (-16.0 vs -15.1 kcal/mol). However, when the solvent effects are included in the calculations, the binding of ethylene becomes slightly more favored (ΔΕcoord(sol) = -12.9 vs -12.4 kcal/mol). Experimentally, Kexp for ethylene and propylene, 7.0 and 5.4, respectively, as well as the associated enthalpies (-3.6 and -3.8 kcal/mol; also from ref 24b) are comparable. Although the calculations are not expected to reproduce such small differences, the gas phase results suggest that the properties of the methyl substituent (possibly its stronger electron-donating ability compared to H) increase the driving force of coordination. The increase is however very small, and it is not unlikely to get reversed by differences in the solvation energies of the two complexes. Consistently, coordination of the more electron rich n-butene is slightly more exothermic than coordination of propylene in the gas phase (-16.0 vs -16.6 kcal/mol), but the two binding energies become the same when the solvent effects are added (ΔΕcoord(sol) = -12.9 kcal/mol). Experimentally, the Kexp values of n-hexene and propylene are similar: 5.4 vs 4.8. The studies by Jordan included olefins having heteroatom substituents. Among these, vinyl-OMe and vinyl-SMe coordinated to Zr via the heteroatom rather than the double bond. The calculations reproduce these observations, giving binding energies that are 1.8 or 3.2 kcal/mol more negative when these two substrates are coordinated by O or S, respectively. The more bulky vinyl-OtBu on the other hand coordinates via the double bond. For the sake of obtaining systematic data on the factors that dictate asymmetric coordination we include the results for binding of vinyl-OMe and vinyl-SMe via the double bond in Table 1, and we later also consider their reaction with the methyl radical. For the olefins having heteroatoms, the gas phase trends in ΔΕcoord do not change when solvent effects are included, so (28) (a) Manriquez, J. M.; McAlister, D. R.; Bercaw, J. E. J. Am. Chem. Soc. 1978, 100, 2716. (b) Manriquez, J. M.; McAlister, D. R.; Sanner, R. D.; Bercaw, J. E. J. Am. Chem. Soc. 1976, 98, 6733. (29) (a) Antonelli, D. M.; Tjaden, E. B.; Stryker, J. M. Organometallics 1994, 13, 763. (b) Guo, Z.; Swenson, D. C.; Guram, A. S.; Jordan, R. F. Organometallics 1994, 13, 766.

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Table 1. Calculated Energy of Olefin Coordination to Zr (in kcal/mol) and Equilibrium Geometric Parameters of the Resulting Zr-Olefin Complex (in A˚)a

1 2 3 4 5 6 7 8 9 10 11 12 13 14

olefin

ΔEcoord

ΔEcoord(sol)

ΔG°coord

CH2dCH2 CH2dCHMe CH2dCHEt CH2dCHF CH2dCH(OMe) CH2dCH(NMe2) CH2dCH(OtBu) CH2dCHCl CH2dCH(SMe) CH2dCH(SiMe3) CH2dCH(CH2SiMe3) CH2dCMe2 CH2dC(OMe)2 CH2dCCl2 CH2Cl2

-15.1 -16.0 -16.6 -14.5 -23.9 -32.2 -27.5 -10.4 -19.6 -14.4 -21.5 -15.8 -31.8 -7.8 -11.8

-12.9 -12.4 -12.4 -12.0 -18.6 -26.5 -19.5 -6.9 -13.3 -7.6 -14.8 -10.8 -23.8 -3.0 -7.4

-3.9 -4.5 -5.3 -3.7 -13.9 -21.3 -16.3 0.1 -8.8 -2.9 -10.2 -4.3 -20.2 2.5 -2.8

Kexp 7.0 5.4 4.8 Zr-Ob large 2.59 > 2.50 A˚, whereas Zr-Csub increases: 3.12 < 3.27 < 3.36 A˚. At the same time, ΔΕcoord(sol) becomes significantly more exothermic: -12.0 (F), -18.6 (OMe), and -26.5 kcal/mol (NMe2). For vinyl-OtBu, Zr-CH2 (2.56 A˚) is slightly shorter than in vinyl-OMe (2.59 A˚), and ΔΕcoord is slightly more exothermic (-19.5 vs -18.6 kcal/mol). In line with the general discussions used by Lin,27 as well as the arguments used by Caulton30 and Matchett31 to account for asymmetrical coordination in the [CpFe(CO)2(olefin)]þ system, the calculated structural and ΔΕcoord trends among the latter three olefins can be qualitatively rationalized on the basis of the relative ability of the substituents to stabilize the resonance structure that places a negative charge on the terminal carbon of the double bond (eq 3). Promotion of negative charge on CH2 should be more feasible when Csub has a strong σ or π electron donor. Both of these properties increase in the order F < OMe < NMe2, and this coincides with the trend (30) Watson, L. A.; Franzman, B.; Bollinger, J. C.; Caulton, K. G. New J. Chem. 2003, 27, 1769. (31) (a) Matchett, S. A.; Schmiege-Boyle, B. R.; Cooper, J.; Fratterelli, D.; Olson, K.; Roberts, J.; Thommen, J.; Tigelaar, D.; Winkler, F. Organometallics 2003, 22, 5047. (b) Matchett, S. A.; Zhang, G.; Fratterelli, D. Organometallics 2004, 23, 5440. (c) Matchett, S. A.; Frattarelli, D.; Hoekstra, R. J. Organomet. Chem. 2007, 692, 4978.

of increased asymmetry and increased binding energy of the corresponding olefins to Zr.

Substituting vinyl-F by vinyl-Cl is calculated to significantly reduce ΔΕcoord: -12.0 (F) vs -6.9 kcal/mol (Cl). According to this result, vinyl-Cl should bind to Zr less strongly even than ethylene (-12.9 kcal/mol), which is in agreement with the observed small Kexp of vinyl-Cl in Table 1 (