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Tom Woo § , Tom Ziegler Department of Chemistry, University of Calgary, Calgary, Alberta.

More Realistic Molecular Modelling of Catalytic Processes with the Combined QM/MM and ab initio Molecular Dynamics Method. Tom Woo § , Tom Ziegler Department of Chemistry, University of Calgary, Calgary, Alberta. email: tkwoo@cobalt24.chem.ucalgary.ca

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Tom Woo § , Tom Ziegler Department of Chemistry, University of Calgary, Calgary, Alberta.

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  1. More Realistic Molecular Modelling of Catalytic Processes with the Combined QM/MM and ab initio Molecular Dynamics Method Tom Woo§, Tom Ziegler Department of Chemistry, University of Calgary, Calgary, Alberta. email: tkwoo@cobalt24.chem.ucalgary.ca §new address: Department of Chemistry, University of Western Ontario, London, Ontario. ABSTRACT: The combined Quantum Mechanics and Molecular Mechanics (QM/MM) and the ab initio molecular dynamics methods (AIMD) are fast emerging as powerful computational tools. Both methods allow for the incorporation of effects that are often neglected in traditional high level calculations, which may be critical to the real chemistry of the simulated system. In this presentation, these methods will be introduced with ‘real-life’ examples that showcase their unique capabilities. 1

  2. Introduction At the atomic level, a typical ‘single-site’ olefin polymerization catalyst system consists of: Typical Polymerization System • cationic transition metal catalyst • typically with a large ligand frame work • counter-ion • solvent and free monomer This often contrasts a typical computational model of a ‘single-site olefin polymerization catalyst system. Typical Computational Model 2

  3. Introduction continued Finite Temperature Effects: Another element often neglected in standard quantum chemical simulations are finite temperature and entropic effects. Traditional methods typically map out the potential energy surface at the zero-Kelvin limit. Using two novel computational methods: a) Combined Quantum Mechanics and Molecular Mechanics (QM/MM) method b) Car-Parrinello ab initio Molecular Dynamics method we are incorporating these often neglected effects into our quantum mechanical (DFT) potential energy surface. 3

  4. MM region QM region The Combined QM/MM Method In this method part of the system is treated by an electronic structure calculation(DFT) with the remainder of the system being treated by a molecular mechanics approach. The method allows for catalytic processes involving extended ligand frameworks to be simulated in computationally tractable times. main features of approach • molecular system divided into QM and MM regions • QM and MM regions interact via Coulomb and van der Waals forces • molecule treated as a whole • QM calculation performed on ‘capped’ system with fictitious dummy atoms • electronic effects through bonds can be problematic 4

  5. Simulating the Ligand Framework with QM/MM Application of the combined QM/MM method to study Brookhart’s Ni(II) diimine olefin polymerization catalyst. bulky aryl ligands In 1996 Brookhart’s lab developed an innovative ‘single-site’ olefin polymerization catalyst. Brookhart et al. J. Am. Chem. Soc. 1995, 117, 2343. Bulky aryl ligands critical to polymerization activity of catalyst. Without them no polymerization occurs, only dimerization! 5

  6. DFT Calculations on Truncated Model System At the time, simulating the catalyst with the bulky aryl ligands at the DFT level was too time consuming, and thus a truncated model system was used whereby the aryl ligands were neglected. truncated QM model system Reaction Profile calculated propagation barrier 16.8 kcal/mol The calculated barriers for chain growth and chain termination revealed that for the model system the termination was much favoured over the chain propagation process. This suggested that without the bulky ligands the catalyst was, at best, a dimerization catalyst, in agreement with experimental findings. calculated termination barrier 9.7 kcal/mol catalytic resting state termination favoured! 6

  7. QM/MM Calculations of Brookhart's Catalyst Combined QM/MM calculations in which the bulky aryl ligands were treated by the AMBER95 force field and the nickel-diimine fragment was treated at the non-local density functional theory level have been performed. The QM/MM model shows that the bulky aryl ligands to: Reaction Profile QM/MM with bulk pure QM - no bulk • bulky ligands inhibit the termination process 18.6 16.8 • bulky ligands enhance the activity bulky aryl ligands doubles termination barrier 13.2 • provides good agreement with experimental barriers 9.7 propagation barrier Exp: 10-11 kcal/mol calc QM/MM: 13.2 propagation vs. termination resting state Exp. (G‡) 5.6 propagation termination QM/MM (H‡) 5.4 QM/MM working exceptionally well for these systems! 7

  8. Modeling the Counter Ion with QM/MM Since most ‘single-site’ olefin polymerization catalysts are cationic, they are accompanied by an anionic counter-ion. The nature of these counter-ions can have a drastic effect on the polymerization capabilities of the catalyst. Unfortunately, the counter-ions often dwarf the catalyst itself in size. The QM/MM method offers access to investigating the effect of the counter-ions in a computational tractable manner MM region QM region • We have developed a QM/MM model of (B(C6F5)4-) shown on the right • The real counter-ion (B(C6F5)4-) is 44 atoms in size, but the QM part of the QM/MM model is only 6 atoms in size. Partitioning in QM/MM model of Ti catalyst - (B(C6F5)4-) counter-ion complex 8

  9. 2.19 (2.18) F Ti 1.38 (1.42) 1.68 (1.69) F 2.41 (2.33) 1.39 (fixed) 73° (74°) F 1.37 (1.39) F F Modeling the Counter Ion with QM/MM To test the validity of the QM/MM model we compare it to full DFT calculations on the interaction between [TiH(NH2)2]+ and [B(C6F5)4] - Preliminary results show good agreement between the QM/MM model and the full DFT calculation RESULTS Binding Energy: QM/MM: 86 kcal/mol full DFT: 88 kcal/mol Hirshfeld Charges on Ti QM/MM model free [TiH(NH2)2]+ +0.87 e (pure DFT calculation) in Ti-counter-ion complex QM/MM: +0.57 e full DFT: +0.56 e QM/MM model of [TiH(NH2)2]+ [B(C6F5)4]-complex 9

  10. Ab Initio Molecular Dynamics (AIMD) sometimes called Car-Parrinello molecular dynamics What is it? • ab initio molecular dynamics is the simulation of molecular motion at a specified temperature where the potential is determined at the DFT level. Fi = mi ai • nuclei move according to Newton’s equations of motion, e.g. • each frame of the simulation encompasses a whole electronic structure calculation. 10 ps simulation requires 10 000 time steps AIMD is expensive but gives access to: • finite temperature effects • insight into dynamic processes • determine time scales of processes • determine ensemble averages finite temperature free energy barriers, DG‡ • uses PLANE WAVE basis functions scale differently than traditional Gaussian basis sets 10

  11. Plane Wave Advantage in AIMD • Traditional quantum chemical methods use localized basis sets (e.g. Gaussians). AIMD, uses plane wave basis functions atom centered basis (i.e. Gaussians) plane wave basis (periodically repeating) simulation cell • Plane wave functions are periodically repeating, such that the simulation actually corresponds to a infinitely repeating periodic crystal. • Traditional quantum chemical methods scale at least with Ne3 where Ne is the number of electrons in the system. • AIMD scales with the physical volume of the simulation cell. The computational effort scales almost linearly with the volume of the cell. • This has its advantages and disadvantages. For systems where atoms ‘fill’ most of the space, such as a solid or liquid, it is advantageous. 11

  12. Plane Wave Advantage in AIMD AIMD Simulation of Cp*2Ta2H2(m-ArNSiHPh)2 truncated model system full system 34 atoms, 102 electrons 140 atoms, 346 electrons 22 seconds per MD step with AIMD 77 seconds Calculation of ‘real’ system is only 3.5 times slower with AIMD! This is compared to 40 times slower for traditional methods 12

  13. g g b b 4.5 4.0 3.5 Ti - Hg distance (Å) 3.0 2.5 g-agostic bonding region 2.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Time (ps) Studying Fluxionality and Timescales with AIMD The interconversion between a g-agostic to b-agostic metal-alkyl complexes for the Constrained Geometry Catalyst (CpSiH2NHTi+-C3H7) has been studied with AIMD • A 25°C simulation reveals a rapid interconversion between complexes. • The simulation also shows that some kind of agostic interaction is maintained throughout. 13

  14. olefin hydride allyl dihydrogen (observed product) (expected product) Exploring the Potential Energy Surface with AIMD Since AIMD simulates the thermal motion of a molecule it can explore the potential energy surface of a system more globally than traditional methods. This is especially useful for transition metal complexes which typically have flat and complex potential energy surfaces. Evidence for a Allyl-Dihydrogen Complex from AIMD Using the AIMD method to study the b-hydrogen elimination process we discovered that the expected olefin hydride will readily form an allyl dihydrogen complex which is 7 kcal/mol more stable. • may provide explanation for H2 gas production observed many in olefin polymerization • allyl formation can be used to explain many stereo-errors in propene polymerization Resconi, L.; Camurati, I.; Sudmeijer, O. Top. Catal.1999, 7, 145. 14

  15. Conclusions • combined QM/MM and Car-Parrinello ab initio molecular dynamics methods are unique and powerful quantum chemical tools for studying catalysis • wide scope of applicability • The computational methods are practical and effective tools for studying catalysis • we are moving toward more realistic quantum chemical models of catalytic systems Acknowledgements Collaborators Professor Ursula Rothlisberger, ETH Zurich Professor Don Tilley, Berkely Dr. Liqun Deng, AT&T Dr. Peter Margl, DOW Dr. Peter Bloechl, IBM Funding NSERC Killam Memorial Foundation Alberta Heritage Scholarship Fund Nova Chemicals of Calgary 15

  16. References Review of Our Work (contains contents of poster in more detail) • Woo, T. K.; Margl, P. M.; Deng, L.; Cavallo, L.;Ziegler, T. Catalysis Today 1999, 50, 479-500. Combined QM/MM Method (general articles) • Singh, U. C.; Kollman, P. A. J. Comp. Chem.1986, 7, 718. • Gao, J.; Thompson, M. ACS Symposium Series 712: Methods and Applications of Combined Quantum Mechanical and Molecular Mechanical Methods; American Chemical Society: Washington, DC, 1998. Combined QM/MM Study of Brookhart’s Catalyst • Deng, L.; Woo, T. K.; Cavallo, L.; Margl, P. M.; Ziegler, T. J. Am. Chem. Soc., 1997, 119, 6177. Car-Parrinello Ab initio Molecular Dynamics Method (Reviews) • Parrinello, M. Solid State Comm.1997, 102, 107. • Car, R.; Parrinello, M. Phys. Rev. Lett.1985, 55, 2471. AIMD Simulation of Cp*2Ta2H2(m-ArNSiHPh)2 • Burckhardt, U.; Casty, G. L.; Tilley, T.D.; Woo, T. K.; Rothlisberger, U. JACS., submitted. AIMD Simulations of the Constrained Geometry Catalyst • Woo, T. K.; Margl, P. M.; Lohrenz, J. C. W.; Blöchl, P. E.; Ziegler, T. J. Am. Chem. Soc., 1996, 118, 13021-13036. • Margl, P. M.; Woo, T. K.; Blöchl, P. E.; Ziegler, T. J. Am. Chem. Soc., 1998, 120, 2174.. 16

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