Application of the ReaxFF reactive force fields to nanotechnology

1. Application of the ReaxFF reactive force fields to nanotechnology Adri van Duin, Weiqiao Deng, Hyon-Jee Lee, Kevin Nielson, Jonas Oxgaard and William Goddard III Materials and Process Simulation Center, California Institute of Technology

2. Contents • ReaxFF: background, rules and current development status • - Ni-catalyzed nanotube growth • - Validation of the all-carbon ReaxFF potential • - Building the Ni/NiC potential • - Testing the Ni-cluster description: magic number clusters • - Study of the initial stages of nanotube formation

3. ReaxFF Simulate bond formation in larger molecular systems ReaxFF: background and rules Hierarchy of computational chemical methods Empirical methods: - Allow large systems - Rigid connectivity QC methods: - Allow reactions - Expensive, only small systems Atoms Molecular conformations Design years Electrons Bond formation FEA Time MESO Grids MD Grains QC Empirical force fields 10-15 ab initio, DFT, HF Ångstrom Kilometres Distance

4. System energy description 2-body 3-body 4-body multibody

5. Key features • To get a smooth transition from nonbonded to single, double and triple bonded systems ReaxFF employs a bond length/bond order relationship. Bond orders are updated every iteration. • Nonbonded interactions (van der Waals, Coulomb) are calculated between every atom pair, irrespective of connectivity. Excessive close-range nonbonded interactions are avoided by shielding. • All connectivity-dependent interactions (i.e. valence and torsion angles) are made bond-order dependent, ensuring that their energy contributions disappear upon bond dissociation. • ReaxFF uses a geometry-dependent charge calculation scheme that accounts for polarization effects.

6. General rules - MD-force field; no discontinuities in energy or forces even during reactions. - User should not have to pre-define reactive sites or reaction pathways; potential functions should be able to automatically handle coordination changes associated with reactions. - Each element is represented by only 1 atom type in the force field; force field should be able to determine equilibrium bond lengths, valence angles etc. from chemical environment.

7. Current status • ‘Finished’ ReaxFF force fields for: • Hydrocarbons (van Duin, Dasgupta, Lorant and Goddard, JPC-A 2001, 105, 9396) • (van Duin and Sinninghe Damste, Org. Geochem.2003, 34, 515 • - Si/SiO2(van Duin, Strachan, Stewman, Zhang, Xu and Goddard, JPC-A 2003, 107, 3803) • Nitramines/RDX (Strachan, van Duin, Chakraborty, Dasupta and Goddard, PRL 2003,91,09301 • Al/Al2O3(Zhang, Cagin, van Duin, Goddard, Qi and Hector, PRB in press) • Force fields in development for: • All-carbon materials • Transition metals, metal alloys and metals interacting with • first row elements • Proteins • Magnesium hydrides

8. Ni-catalyzed nanotube growth Concept: grow nanotubes from buckyball building blocks Longer nanotube - Exothermic reaction - Huge activation barrier - Probably needs catalyst

9. Validation of the ReaxFF all-carbon potential • QC-data taken from hydrocarbon training set: • Single, double and triple bond dissociation • C-C-C, C-C-H and H-C-H angle bending • Rotational barriers around single, double and aromatic C-C bonds • Conformation energy differences • Methyl shift and H-shift barriers • Heats of formation for a large set of strained and unstrained non-conjugated, conjugated and radical hydrocarbons • Density and cohesive energies for diamond, graphite, cyclohexane and buckyball crystals • - All-carbon ReaxFF should also work for hydrocarbons

10. All-carbon data added to the hydrocarbon training set Relative energies for all-carbon phases a: Experimental data; b: data generated using graphite force field (Guo et al. Nature 1991) • ReaxFF gives a good description of the relative stabilities of these structures

11. Even-carbon acyclic compounds are more stable in the triplet state; odd-carbon, mono and polycyclic compounds are singlet states • Small acyclic rings have low symmetry ground states (both QC and ReaxFF) • ReaxFF reproduces the relative energies well for the larger (>C6) compounds; bigger deviations (but right trends) for smaller compounds • Also tested for the entire hydrocarbon training set; ReaxFF can describe both hydro- and all-carbon compounds

12. Energy (kcal/mol) Energy (kcal/mol) C-C distance (Å) • ReaxFF gives good energies for key structures in buckyball growth • Training set includes all hydrocarbon cases used for ReaxFFCH

13. Angle bending in C9 - ReaxFF properly describes angle bending, all the way towards the cyclization limit

14. Diamond to graphite conversion Calculated by expanding a 144 diamond supercell in the c-direction and relaxing the a- and c axes QC-data: barrier 0.165 eV/atom (LDA-DFT, Fahy et al., PRB 1986, Vol. 34, 1191) graphite DE (eV/atom) diamond c-axis (Å) • ReaxFF gives a good description of the diamond-to-graphite reaction path

15. Applications of all-carbon ReaxFF: buckyball+nanotube collisions Impact velocity: 6 km/sec (1500K) Impact velocity: 9 km/sec (2500K)

16. Side impact • Materials are too stable, extremely high impact velocities are required to start reaction • Catalyst required to lower reaction barriers

17. Transition metal catalysis: Ni 1: ReaxFF and QC EOS for Ni bulk phases • ReaxFF gives a good fit to the EOS of the stable phases (FCC, BCC, A15) • ReaxFF properly predicts the instability of the low-coordination phases (SC, Diamond)

18. Testing the force fields for Ni magic number clusters Liquid Energy/atom (kcal) Icosahedron Amorphous solid FCC MD-iterations

19. MD-heatup/cooldown simulations Liquid Energy/atom (kcal) cooldown heatup • ReaxFF gets the right trend for fcc/icosahedron transition • ReaxFF heat of melting converges on Ni bulk melting temperature (1720K) Amorphous solid Temperature (K) Icosahedron FCC

20. 2. Results for Ni-C interactions Ni-C bond breaking in H3C-Ni-CH3 Energy (kcal/mol) Ni-C bond breaking in Ni=CH2 Energy (kcal/mol) Bond length (Å)

21. Ni-C bond breaking in Ni(CH3)4 Energy (kcal/mol) Ni dissociation from 5-ring compound Energy (kcal/mol) Bond length (Å)

22. Ni dissociation from 6-ring compound Energy (kcal/mol) Ni dissociation from benzene Energy (kcal/mol) Bond length (Å)

23. Ni dissociation from benzyne Energy (kcal/mol) Bond length (Å) C-Ni-C angle bending in benzyne/Ni complex Energy (kcal/mol) Angle (degrees)

24. C-Ni-C angle bending in H3C-Ni-CH3 Energy (kcal/mol) Angle (degrees)

25. Ni-assisted C2-incorporation reactions • ReaxFFNi can describe the binding between Ni and C • A similar strategy has been used to make ReaxFF descriptions for Co/C and Cu/C, allowing us to compare their catalytic properties

26. Influence adsorbed Ni on buckyball reactions ReaxFF-minimized buckyball ReaxFF-minimized buckyball+2 Ni 2 2 1 1 R12= 1.45 Å R12= 1.49 Å • ReaxFF predicts that buckyball C-C bonds get substantially weakened by adsorbed Ni-atoms • Might lower buckyball coalescence reaction activation barrier

27. Energy (kcal/mol) Reaction coordinate Influence adsorbed Ni on reaction barrier Low-T ReaxFF restraint MD-simulation • Ni-atoms lower reaction barrier • Overall reaction becomes exothermic due to formation of Ni-Ni bonds • May explain Ni catalytic activity

28. Influence Ni on initial stages of buckyball growth MD NVT-simulation (1500K); 5 C20-rings, 10 C4-chains (blank experiment) t=125 ps. t=0 ps. • C4 reacts with rings to form long acyclic chains • No branching

29. MD NVT-simulation (1500K); 5 C20-rings, 10 C4-chains and 15 Ni-atoms t=125 to t=750 ps. t=0 to t=125 ps.

30. A closer look at the 750 ps. product • Ni-atoms help create cage-structures • 750 ps. product has no internal C-C bonds • Ni-atoms leave ‘finished’ material alone and move away to defect and edge sites • Total simulation time: 4 days on 1 processor • Future work: Co, Fe

31. Metal-catalyzed nanotube growth Inital configuration • Start configuration: 20 C6-rings, 5 metal atoms on edge • NVT simulation at 1500K • Add C2-molecule every 100,000 iterations

32. Ni-atoms can grab C2-monomers and fuse them as new 6-membered rings

33. Metal-catalyzed nanotube growth Results after 2,000,000 iterations Metal=Ni Metal=Co No metal Metal=Cu -Ni and Co lead to greatly enhanced ring formation. Cu is far less active.

34. Conclusions • ReaxFF has proven to be transferable to transition metals and can handle both complex chemistry and chemical diversity • The low computational cost of ReaxFF (compared to QC) makes the method highly suitable for screening heterogeneous and homogeneous transition metal catalysts