1. 1 Modeling of the Counterion, B(C 6 F 5 ) 3 CH 3 -, with the QM/MM Method and its Application to Olefin Polymerization Kumar Vanka and Tom Ziegler University of Calgary

2. 2 Introduction Inclusion of solvent and counterion effects are important in theoretical studies of single site olefin polymerisation catalyst systems. The large size of the activators and counterions [B(C 6 F 5 ) 3 CH 3 -, B(C 6 F 5 ) 4 - etc.] used, makes full quantum chemical studies of these systems time consuming and expensive. The present study attempts to solve the problem by modeling the counterion B(C 6 F 5 ) 3 CH 3 - using the QM/MM (Quantum mechanics - Molecular Mechanics) method. The model used is tested by comparison of full QM to QM/MM calculations for ion-pair systems of the type [L 1 L 2 MMe + ] [B(C 6 F 5 ) 3 CH 3 - ] {L 1, L 2 = NPH 3, NCMe 2 etc.; M = Zr, Ti; Me = CH 3 }. The developed QM/MM model is then employed in studies of olefin uptake and insertion processes for the different ion-pair systems.

3. 3 Computational Details The density functional theory calculations were carried out using the Amsterdam Density Functional (ADF) program version 2000.01. 1 Geometry optimizations were carried out using the local exchange- correlation potential of Vosko et al. 2 A triple-zeta basis set was used to describe the outermost valence orbitals for the titanium and zirconium atoms, whereas a double-zeta basis set was used for the non-metals. The frozen core approximation was used to treat the core orbitals of all atoms. The gas phase energy differences between stationary points were calculated by augmenting the LDA energy with Perdew and Wang’s non- local correlations and exchange corrections. 3 The energy differences in solution was corrected from the gas phase energies by accounting for the solvation calculated by the Conductor-like Screening Model (COSMO). 4 The solvation energy calculations were carried out with a dielectric constant of 2.023 to represent cyclohexane as the solvent. The code for QM/MM has been incorporated into ADF by Woo et al. 5 1. (a) Baerends, E. J.; Ellis,D.E.; Ros, P. Chem. Phys. 1973, 2, 41. (b) Baerends, E. J.; Ros, P. Chem. Phys. 1973, 2,52. 2. Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980,58, 1200. 3. Perdew, J. P. Phys. Rev. B 1992, 46, 6671. 4. Pye, C. C.; Ziegler, T. Theor. Chem. Acc. 1999 V 101, 396. 5. Woo. T. K.; Cavallo, L.; Ziegler, T. Theor. Chim. Acta 1998, 100,307.

4. 4 Model Investigated B(C 6 F 5 ) 3 CH 3 - was substituted with BCl 3 CH 3 - in the QM portion and the phenyl groups modeled with MM atoms.

5. 5 Testing Model on Different Titanium Based Catalyst Systems Catalyst  H ipfQM  H ipfQMMM  H ipsQM  H ipsQMMM kcal/mol kcal/mol kcal/mol kcal/mol (NPH 3 ) 2 TiMe + -22.3 -21.0 81.8 93.6 (Cp)OSiH 3 TiMe + -10.4 -10.2 93.6 105.3 (Cp)SiMe 2 NMeTiMe + -13.3 -15.1 90.4 102.6 (Cp)NCMe 2 TiMe + -24.1 -21.9 87.4 97.6 (Cp)TiMe 2 + -12.9 -11.0 95.3 107.8 (Cp)SiH 2 (NH)TiMe + -13.9 -11.2 94.4 105.0 (Cp) 2 TiMe + -15.5 -15.4 79.5 94.1 The model was tested by comparing the gas phase  H ipf (enthalpy of ion-pair formation) and  H ips (enthalpy of ion-pair separation) for full QM calculations on ion-pairs of the type [L 1 L 2 TiMe + ] [B(C 6 F 5 ) 3 CH 3 - ] and calculations done using the QM/MM model for the counterion. While the  H ipf values were quite similar, the corresponding  H ips were higher in the QM/MM case by 15-20 kcal/mol

6. 6 Testing Model on Different Zirconium Based Catalyst Systems Catalyst  H ipfQM  H ipfQMMM  H ipsQM  H ipsQMMM kcal/mol kcal/mol kcal/mol kcal/mol (1,2Me 2 Cp) 2 ZrMe + -22.8 -24.8 80.5 95.6 (Cp) 2 ZrMe + -19.1 -18.7 88.5 99.5 (Cp)ZrMe 2 + -15.7 -13.3 93.3 103.3 (Cp)SiH 2 (NH)ZiMe + -16.6 -13.1 92.4 106.2 The corresponding calculations for  H ipf and  H ips were done with zirconium based catalyst systems. Results, similar to the titanium based systems were obtained.

7. 7 Inclusion of Solvent Effects Catalyst  H ipsQM  H ipsQMMM kcal/mol (NPH 3 ) 2 TiMe + 45.8 48.9 (Cp)OSiH 3 TiMe + 56.3 61.9 (Cp)SiMe 2 NMeTiMe + 55.4 61.7 (Cp)NCMe 2 TiMe + 52.4 55.6 (Cp)TiMe 2 + 58.2 62.8 (Cp)SiH 2 (NH)TiMe + 54.6 61.0 (Cp) 2 TiMe + 47.1 52.3 The difference in the gas phase values for  H ips between the full QM and the QM/MM calculations was reduced when solvent effects were considered. On doing single point calculations with cyclohexane as the solvent, the differences in  H ips between the QM and QM/MM systems was reduced to about 5 kcal/mol.

8. 8 Inclusion of Solvent Effects Catalyst  H ipsQM  H ipsQMMM kcal/mol (1,2Me 2 Cp) 2 ZrMe + 49.6 54.1 (Cp) 2 ZrMe + 50.2 56.8 (Cp)SiH 2 NHZrMe + 51.8 58.4 (Cp) ZrMe 2 + 51.6 59.7 The corresponding calculations with the zirconium based catalyst systems gave analogous results. The inclusion of solvent effects reduced the difference between full QM and QM/MM calculations to about 5-7 kcal/mol.

9. 9 Comparison in the Insertion region ACH 3 - = B(C 6 F 5 ) 3 CH 3 - Ethylene  complex Insertion Transition State For the modeling to be considered successful, the QM/MM model has to perform satisfactorily in the “insertion region”, i.e., it has to compare favourably with full QM calculations for the momomer (ethylene) complexation and insertion into the metal alkyl bond. The enthalpies of ethylene complexation and for the insertion transition state were termed  H c and  H its respectively. HcHc  H its

10. 10 Comparison in the Insertion region ACH 3 - = B(C 6 F 5 ) 3 CH 3 - Full QM Calculation : +1.51 kcal/mol QMMM Calculation : -0.73 kcal/mol Full QM Calculation : +5.90 kcal/mol QMMM Calculation : +4.00 kcal/mol Comparative calculations in the insertion region were done for the [(NPH 3 ) 2 TiMe + ] [B(C 6 F 5 ) 3 CH 3 - ] system. The QM/MM calculations compared favourably with the corresponding calculations for the full QM system. HcHc  H its HcHc

11. 11 Catalyst Systems Studied with QMMM Model [(NPR 3 ) 2 TiMe + ] [B(C 6 F 5 ) 3 CH 3 - ] R= Hydrogens, tert-butyl groups [CpNCR 2 TiMe + ][[B(C 6 F 5 ) 3 CH 3 - ] R= hydrogens, tert-butyl groups The validated QM/MM model was then employed to study ethylene complexation and insertion processes in different catalyst systems, shown above. The tertiary butyl groups on the cation were modeled with MM atoms. Results are discussed in the next few slides.

12. 12 Cis Attack of Ethylene for the [(NPR 3 ) 2 TiMe + ] System [(NPR 3 ) 2 TiMe + ] [B(C 6 F 5 ) 3 CH 3 - ] R= tert-butyl groups [(NPR 3 ) 2 TiMe + ] [B(C 6 F 5 ) 3 CH 3 - ] R= Hydrogens The approach of the ethylene cis to the methide bridge of the titanium to the counterion, was considered for complexation and insertion studies on the [(NPR 3 ) 2 TiMe + ] [B(C 6 F 5 ) 3 CH 3 - ] system, with different R groups. Results indicated that increasing steric bulk on the cation increased the total barrier to the ethylene insertion into the Ti-alkyl bond.  H c = + 1.79 kcal/mol  H its = + 3.24 kcal/mol  H c = + 8.41kcal/mol  H its = + 1.93 kcal/mol

13. 13 Trans Attack of Ethylene for the [(NPR 3 ) 2 TiMe + ] System [(NPR 3 ) 2 TiMe + ] [B(C 6 F 5 ) 3 CH 3 - ] R= Hydrogens [(NPR 3 ) 2 TiMe + ] [B(C 6 F 5 ) 3 CH 3 - ] R= tert-butyl groups  H c = -0.73 kcal/mol  H its = + 3.99 kcal/mol  H c = + 11.26 kcal/mol  H its = + 3.43 kcal/mol The approach of the ethylene trans to the methide bridge of the titanium to the counterion, was considered next, for complexation and insertion studies on the [(NPR 3 ) 2 TiMe + ] [B(C 6 F 5 ) 3 CH 3 - ] system, with different R groups. Results analogus to the cis case were obtained. For the case of the cation with bulky groups, the ethylene preferred the cis pathway over the trans, the net barrier to insertion being 4.35 kcal/mol less.

14. 14 Cis Attack of Ethylene for the [CpNCR 2 TiMe + ] System [CpNCR 2 TiMe + ][[B(C 6 F 5 ) 3 CH 3 - ] R= hydrogens [CpNCR 2 TiMe + ][[B(C 6 F 5 ) 3 CH 3 - ] R= tert-butyl groups  H c = + 5.25 kcal/mol  H its = + 7.04 kcal/mol  H c = + 10.18 kcal/mol  H its = + 3.16 kcal/mol Calculations for the cis approach of the ethylene was considered next for the [CpNCR 2 TiMe + ][[B(C 6 F 5 ) 3 CH 3 - ] system. Analogous to the previous case, increasing steric bulk on the cation increased the barrier to insertion.

15. 15 Trans Attack of Ethylene for the [CpNCR 2 TiMe + ] System [CpNCR 2 TiMe + ][[B(C 6 F 5 ) 3 CH 3 - ] R= hydrogens [CpNCR 2 TiMe + ][[B(C 6 F 5 ) 3 CH 3 - ] R= tert-butyl groups  H c = + 9.38 kcal/mol  H its = + 3.45 kcal/mol  H c = + 11.36 kcal/mol  H its = + 4.99 kcal/mol The corresponding trans attack of the ethylene monomer was also considered for the [CpNCR 2 TiMe + ][[B(C 6 F 5 ) 3 CH 3 - ] system. As before, increasing the steric bulk increased the barrier to insertion. For the case of the cation with bulky groups, the ethylene preferred the cis pathway over the trans, the net barrier to insertion being 3.01 kcal/mol less.

16. 16 Conclusions The counterion, B(C 6 F 5 ) 3 CH 3 -,was modeled with the QM/MM method The model was successfully validated with calculations comparing full QM and QM/MM calculations The validated model was then used in ethylene complexation and insertion studies of different catalyst systems Acknowledgements This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and Novacor Research and Technology Corporation.