First-principle MD studies on the reaction pathways at T=0K and at finite temperatures

1. First-principle MD studies on the reaction pathways at T=0K and at finite temperatures Artur Michalaka,b and Tom Zieglera aDepartment of Chemistry, University of Calgary, Calgary, Alberta, Canada bDepartment of Theoretical Chemistry Jagiellonian University Cracow, Poland September 5, 2014

2. MD simulations along the IRP  A. Michalak, T. Ziegler „First-principle Molecular Dynamics along Intrinsic Reaction Paths”, J. Phys Chem. A 105, 2001, 4333-4343.

3. Reaction free energies • assumed reaction coordinate • dynamics with constraint for points on assumed RP • free energy change obtained by integration of the force on constraint (thermodynamic integration) TS min.

4. Slow-growth simulations TS • the reaction coordinate l is changed in a continuous manner min.

5. Slow-growth simulations D A backward sampling forward sampling RC Typical problem – hysteresis in free energy profiles

6. Choice of reaction coordinate Rapid changes of the PES shape in the direction perpendicular to RP TS min. Direction perpendicular to RP

7. Choice of reaction coordinate Smooth changes of the PES shape in the direction perpendicular to RP TS min. Direction perpendicular to RP

8. Reaction free energies Standard approach: MD sampling along assumed reaction paths Alternative approach: MD sampling along pre-determined reaction paths IRP: Fukui, K. Acc. Chem. Res.1981, 14, 363.

9. MD along IRP 2) finite temperature sampling with linear constraint: • in slow-growth simulations the vector f and constraint value are changed in every timestep; • for every step the force on constraint, F j, is calculated; • free-energy change is obtained by integrating F:

10. Computational details DFT calculations with Becke-Perdew XC Becke A.D. Phys. Rev. A1988, 38, 3098. Perdew, J.P. Phys. Rev. B1986, 33, 8822. Projector augmented wave (PAW) method Blochl, P. Phys. Rev. B1994, 50, 17953. IRC predetermined by the steepest descent in mass-weighted coordinates from TS structures Slow-growth MD simulations along IRP at 300K

11. HCN  CNH isomerization CNH HCN TS IRP:

12. HCN  CNH IRP (T=0K) MD along IRP (300K) MD with constraint RNH -RCH = const.

13. HCN  CNH Hydrogen path MD along IRP MD with constraint RNH -RCH = const.

14. HCN  CNH Hydrogen path MD along IRP MD with constraint RNH -RCH = const.

15. HCN  CNH Hydrogen path MD along IRP MD with constraint RNH -RCH = const.

16. Conrotatory ring opening of cyclobutene gauche-butadiene cyclobutene TS

17. Conrotatory ring opening of cyclobutene gauche-butadiene cyclobutene TS IRP:

19. Prototype SN2 reaction : Cl- + CH3Cl  CH3Cl + Cl- Cl- + CH3Cl TS Cl-CH3 + Cl-

20. Prototype SN2 reaction : Cl- + CH3Cl  CH3Cl + Cl- Cl- + CH3Cl TS Cl-CH3 + Cl- IRP (T = 0 K ):

21. E [kcal/mol] s [amu-1 bohr] 0 TS D -1 E IRC D G 3 -2 -3 2 -4 vdW complex s[amu-1 bohr] -5 1 IRC s[amu-1 bohr] C-Cl2 0 1 2 3 Cl1 - Cl2 Cl1-C 3 0 5 4 3 2 R [A] 2 1 IRC Cl1-C-Cl2 Cl1-C-H 0 0 90 60 30 180 120 150 Angle Prototype SN2 reaction : Cl- + CH3Cl  CH3Cl + Cl-

22. CH2=CH-CH2Cl isomerization Cl -CH2-CH=CH2 TS CH2=CH-CH2-Cl IRP (TS  R):

23. Cl-CH2-CH=CH2

24. Cl-CH2-CH=CH2 TS conf. 2 (gauche) conf. 1 (cis)

25. Cl-CH2-CH=CH2 TS IRP (T = 0 K) conf. 2 (gauche) conf. 1 (cis)

26. Cl-CH2-CH=CH2 TS IRP (T = 0 K ) T = 300 K conf. 2 (gauche) conf. 1 (cis)

27. R [A] E [kcal/mol] IRC Cl-C3 0 4 Cl-C1 D E C1-C2 IRC C2-C3 D G -10 s [amu-1 bohr] 3 -20 -30 8 2 -40 6 1 s [amu-1 bohr] 0 2 4 6 8 s [amu-1 bohr] 0 2 4 6 8 4 2 0 0 90 60 30 120 Angle IRC Cl-C1-C2-C3 Cl-C1-C2 C1-C2-C3 CH2=CH-CH2Cl isomerization TS cis-

28. Ethylene + butadiene cycloaddition TS finite separation separated reactants Finalproduct Csproduct

29. torsion

30. Ethylene/methyl acrylate copolymerization

31. Ethylene/methyl acrylate copolymerization Pd- and Ni-diimine catalysts active inactive

32. b-agostic +ethylene p-complex insertion g-agostic b-agostic Ethylene polymerization mechanism

33. Methyl acrylate/ethylene copolymerization Two possible acrylate binding modes: O-complex p-complex

34. p- / O- complexes Ni- (inactive): O-complex preferred Pd- (active) p-complex preferred

35. 35 R [A] R [A] Pd: p Pd: O RPd-C (300K) RPd-C (700K) RPd-O (300K) RPd-O (700K) RPd-C (300K) RPd-O (300K) timestep timestep R [A] R [A] Ni: p Ni: O RNi-C (300K) RNi-C (700K) RNi-O (300K) RNi-O (700K) RNi-C (300K) RNi-O (300K) timestep timestep Fig 5. The two M-C(p) and the M-O distances from the unconstrained MD simulations for the MA O- and p- complexes with the Ni- and Pd-diimine catalysts.

36. Pd-O Ni-p Pd-p Ni-O p-complex / O-complex isomerization reactions

37. O-complex  p-complex isomerization – Pd-catalyst MD simulation with constraint R(Pd-C)-R(Pd-O)=const.

38. O-complex  p-complex isomerization – Ni-catalyst MD simulation with constraint R(Pd-C)-R(Pd-O)=const.

39. O-complex  p-complex isomerization – Ni-catalyst Reaction product: O,C-bound complex MINIMUM on PES MD simulation with constraint R(Pd-C)-R(Pd-O)=const.

40. Chelate formation after acrylate insertion

41. Chelate opening: ethylene insertion E [kcal/mol] MD simulations with constraint R(Colefin-Calkyl) =const.

43. Two-step chelate opening very high insertion barriers lower for Ni-catalyst Ni – high barrier (higher than insertion) Pd – low barrier (lower than insertion) low insertion barriers, comparable to insertion barriers in ethylene homocopolymerization

44. Conclusions This in not a MD movie (yet...) Acknowledgements. This work was supported by the National Sciences and Engineering Research Council of Canada (NSERC), Nova Chemical Research and Technology Corporation as well as donors of the Petroleum Research Fund, administered by the American Chemical Society (ACS-PRF No. 36543-AC3). A.M. acknowledges NATO Fellowship. Important parts of the calculations was performed using the UofC MACI cluster.