More Realistic Molecular Modelling of Catalytic Processes with the Combined QM/MM and ab

initio Molecular Dynamics Method

Tom Woo§, Tom ZieglerDepartment 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

IntroductionAt 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.

N

Ni

N

i-P r

i-P ri-P r

i-P r R

RR

Cl

Cl

Cl Cl

ClCl Cl

Cl

Cl ClCl

Cl

ClCl

Cl

Cl

Cl

Cl

Cl

Cl

B

F5

F5

F5

F5

Cl

Cl

Cl

Cl ClCl

Cl

Cl

Cl

Cl

Cl

Cl

+

Typical Polymerization System

N

Ni

N

R

HH

+HH

Typical Computational Model

2

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

The Combined QM/MM Method

N

Ni

N

i-Pr

i-Pri-Pr

i-Pr R

RR

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

N

Ni

N

R

H H

HH

main features of approach

4

• electronic effects through bonds can be problematic

Simulating the Ligand Framework with QM/MM

Application of the combined QM/MM method to study Brookhart’s Ni(II) diimine olefin polymerization catalyst.

N

Ni

N

i-Pr

i-Pri-Pr

i-Pr R

RR

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

16.8 kcal/mol

9.7 kcal/mol

calculatedpropagation barrier

Reaction Profile

catalyticresting state

N

Ni+N

HH

HH

R

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.

calculatedtermination barrier

termination favoured!

6

Reaction Profile

16.8

9.7

propagationtermination

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 bulkpure 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

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(C6F5)4

-) counter-ion complex

• We have developed a QM/MM model of (B(C6F5)4

-) shown on the right

B-F

F

F

FF

F

FF

F F

F5

F5

Ti +

NH 2H2N

H

QM regionMM region

• 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.

FF

HH

Modeling the Counter Ion with QM/MM

9

Ti

F

F

F

F

F

2.19

(2.18)2.41

(2.33)

1.68

(1.6

9)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(NH2)2]+ and [B(C6F5)4] -

QM/MM model(pure DFT calculation)

QM/MM model of [TiH(NH2)2]+ [B(C6F5)4]-complex

Preliminary results show good agreement between the QM/MM model and the full DFT calculation

QM/MM: 86 kcal/molfull DFT: 88 kcal/mol

Binding Energy:

Hirshfeld Charges on Ti

QM/MM: +0.57 e full DFT: +0.56 e

free [TiH(NH2)2]+ +0.87 e

in Ti-counter-ion complex

RESULTS

Fi = mi 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 functionsscale differently than traditional Gaussian basis sets

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 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.

plane wave basis(periodically repeating)

atom centered basis(i.e. Gaussians)

simulation cell

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

Si

N

TaTa

N Si

truncated model system

34 atoms, 102 electrons

TaTa

SiSi

NN

AIMD Simulation of Cp*2Ta2H2(-ArNSiHPh)2

22 seconds per MD step with AIMD 77 seconds

The interconversion between a -agostic to -agostic metal-alkyl complexes for the Constrained Geometry Catalyst (CpSiH2NHTi+-C3H7) has been studied with AIMD

13

Studying Fluxionality and Timescales with AIMD

Ti

Ti

2.0

0.5 1.0 1.5 2.0 2.5 3.0 3.5

2.5

3.0

3.5

4.0

4.5

0.0Time (ps)

Ti -

H

dis

tan

ce (

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

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.

Ti +R2Si

N

R

H PTi +

R2Si

N

R

H

PH

olefin hydride(expected product)

allyl dihydrogen(observed product)

Ti +R2Si

N

R

H

PH

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

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.

•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 ZurichCollaborators

Dr. Liqun Deng, AT&T Dr. Peter Margl, DOW Dr. Peter Bloechl, IBM

Professor Don Tilley, Berkely

FundingAlberta Heritage Scholarship FundKillam Memorial Foundation

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*2Ta2H2(-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..