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: 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 Polymerization System Typical Computational Model 2

3. Introduction continued 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. 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. 3

4. The Combined QM/MM Method QM region MM region 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. 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 main features of approach 4 electronic effects through bonds can be problematic

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 critical to polymerization activity of catalyst. Without them no polymerization occurs, only dimerization! 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 5

6. 16.8 kcal/mol 9.7 kcal/mol calculated propagation barrier Reaction Profile catalytic resting state 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 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 termination favoured! 6

7. Reaction Profile 16.8 9.7 propagation termination resting state 13.2 18.6 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. bulky aryl ligands doubles termination barrier QM/MM with bulk pure QM - no bulk The QM/MM model shows that the bulky aryl ligands to: bulky ligands inhibit the termination process Exp: 10-11 kcal/mol propagation barrier calc QM/MM: 13.2 propagation vs. termination QM/MM (  H ‡ ) Exp. (  G ‡ ) 5.6 5.4 bulky ligands enhance the activity provides good agreement with experimental barriers QM/MM working exceptionally well for these systems! 7

8. Modeling the Counter Ion with QM/MM 8 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 Partitioning in QM/MM model of Ti catalyst - (B(C 6 F 5 ) 4 - ) counter-ion complex We have developed a QM/MM model of (B(C 6 F 5 ) 4 - ) shown on the right QM region MM region The real counter-ion (B(C 6 F 5 ) 4 - ) is 44 atoms in size, but the QM part of the QM/MM model is only 6 atoms in size.

9. Modeling the Counter Ion with QM/MM 9 Ti F F F F F 2.19 (2.18) 2.41 (2.33) 1.68 (1.69) 73° (74°) 1.37 (1.39) 1.38 (1.42) 1.39 (fixed) To test the validity of the QM/MM model we compare it to full DFT calculations on the interaction between [TiH(NH 2 ) 2 ] + and [B(C 6 F 5 ) 4 ] - QM/MM model (pure DFT calculation) QM/MM model of [TiH(NH 2 ) 2 ] + [B(C 6 F 5 ) 4 ] - complex Preliminary results show good agreement between the QM/MM model and the full DFT calculation QM/MM: 86 kcal/mol full DFT: 88 kcal/mol Binding Energy: Hirshfeld Charges on Ti QM/MM: +0.57 e full DFT: +0.56 e free [TiH(NH 2 ) 2 ] + +0.87 e in Ti-counter-ion complex RESULTS

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

11. 11 Plane Wave Advantage in AIMD Traditional quantum chemical methods use localized basis sets (e.g. Gaussians). AIMD, uses plane wave basis functions 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 N e 3 where N e 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. plane wave basis (periodically repeating) atom centered basis (i.e. Gaussians) simulation cell

12. full system 140 atoms, 346 electrons Calculation of ‘real’ system is only 3.5 times slower with AIMD! This is compared to 40 times slower for traditional methods 12 Plane Wave Advantage in AIMD truncated model system 34 atoms, 102 electrons AIMD Simulation of Cp* 2 Ta 2 H 2 (  -ArNSiHPh) 2 22 seconds per MD step with AIMD77 seconds

13. The interconversion between a  -agostic to  -agostic metal-alkyl complexes for the Constrained Geometry Catalyst (CpSiH 2 N H Ti + -C 3 H 7 ) has been studied with AIMD 13 Studying Fluxionality and Timescales with AIMD 2.0 0.51.01.52.02.53.03.5 2.5 3.0 3.5 4.0 4.5 0.0 Time (ps) Ti - H  distance (Å)  -agostic bonding region      A 25°C simulation reveals a rapid interconversion between complexes.  The simulation also shows that some kind of agostic interaction is maintained throughout.

14. 14 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. olefin hydride (expected product) allyl dihydrogen (observed product)  may provide explanation for H 2 gas production observed many in olefin polymerization  allyl formation can be used to explain many stereo-errors in propene polymerization Evidence for a Allyl-Dihydrogen Complex from AIMD Using the AIMD method to study the  -hydrogen elimination process we discovered that the expected olefin hydride will readily form an allyl dihydrogen complex which is 7 kcal/mol more stable. Resconi, L.; Camurati, I.; Sudmeijer, O. Top. Catal. 1999, 7, 145.

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

16. Review of Our Work (contains contents of poster in more detail) 16 References 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. Car-Parrinello Ab initio Molecular Dynamics Method (Reviews) 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. AIMD Simulation of Cp* 2 Ta 2 H 2 (  -ArNSiHPh) 2 Burckhardt, U.; Casty, G. L.; Tilley, T.D.; Woo, T. K.; Rothlisberger, U. JACS., submitted. Parrinello, M. Solid State Comm. 1997, 102, 107. Car, R.; Parrinello, M. Phys. Rev. Lett. 1985, 55, 2471. 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..