1. 1 Dishing out the dirt on ReaxFF Force field subgroup meeting 29/9/2003

2. 2 Contents - ReaxFF: general principles and potential functions -All-carbon compounds: Training set - Sample simulation: Ethylene+O 2 reactive NVE

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

4. 4 Current status of ReaxFF program and force fields Program: - 18,000 lines of fortran-77 code; currently being integrated into CMDF - MD-engine (NVT/NVE/limited NPT), MM-engine - Force field optimization methods: single parameter search, anneal - Can handle periodic and non-periodic systems - User manual (under development) available online Force fields Published: hydrocarbons, nitramines, Si/SiO/SiH, Al/AlO Advanced: proteins/CH/CN/CO/NO/NN/NH/OH/OO, MoO x, all-carbon, Mg/MgH In development: SiN/SiC, Pt/PtO/PtN/PtC/PtCo/PtCl, Ni/NiAl/NiC, Co/CoC, Cu/CuC, Zr/ZrO, Y/YO, Ba/BaO, Y-BaZrOH, BH/BB/BN/BC, Fe/FeO Method seems universally available; has been tested now for covalent, ceramic, metallic and ionic materials.

5. 5 MM or MD routine Connection table 1: 2 3 4 2: 1 5 6 3: 1 4: 1 5: 2 6: 2 Non-reactive force field Atom positions 1: x 1 y 1 z 1 2: x 2 y 2 z 2 3: x 3 y 3 z 3 4: x 4 y 4 z 4 5: x 5 y 5 z 5 6: x 6 y 6 z 6 Fixed MM or MD routine Determine connections Reactive force field Atom positions 1: x 1 y 1 z 1 2: x 2 y 2 z 2 3: x 3 y 3 z 3 4: x 4 y 4 z 4 5: x 5 y 5 z 5 6: x 6 y 6 z 6 Program structure Bond order Interatomic distance (Angstrom) 12 3 4 5 6

6. 6 ReaxFF: General rules - MD-force field; no discontinuities in energy or forces - 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 force field; force field should be able to determine equilibrium bond lengths, valence angles etc. from chemical environment

7. 7 ReaxFF CH ReaxFF SiO : System energy description 2-body multibody 3-body4-body

8. 8 Sigma bond Pi bond Double pi bond Bond energy 1. Calculation of bond orders from interatomic distances

9. 9 Bond energy 2. Bond order correction for 1-3 bond orders H H H H H H 0.95 0.97 0.10  BO C =4.16  BO H =1.17 Uncorrected bond orders Uncorrected bond order Corrected bond order - Unphysical - Puts strain on angle and overcoordination potentials  BO C =3.88  BO H =0.98 H H H H H H 0.94 0.97 0.01 Corrected bond orders - Correction removes unrealistic weak bonds but leaves strong bonds intact - Increases computational expense as bond orders become multibody interactions

10. 10 Bond energy 3. Calculate bond energy from corrected bond orders

11. 11 Nonbonded interactions - Nonbonded interactions are calculated between every atom pair, including bonded atoms; this avoids having to switch off interactions due to changes in connectivity - To avoid excessive repulsive/attractive nonbonded interactions at short distances both Coulomb and van der Waals interactions are shielded Shielded Coulomb potential +0.5 Interatomic distance (Å) Energy (kcal/mol) vdWaals: Shielded Morse potential

12. 12 Charge calculation method - ReaxFF uses the EEM-method to calculate geometry-dependent, polarizable point charges - 1 point charge for each atom, no separation between electron and nucleus - Long-range Coulomb interactions are handled using a 7th-order polynomal (Taper function), fitted to reproduce continuous energy derivatives. Taper function converges to Ewald sum much faster than simple spline cutoff.

13. 13 Interatomic distance (Å) Energy (kcal/mol) - Summation of the nonbonded and the bonded interactions gives the two-body interactions - Bond energies overcome van der Waals-repulsions to form stable bonds Total two-body interaction

14. 14 Valence angle energy 1. General shape i j k b a General shape: Ensures valence angle energy contribution disappears when bond a or bond b dissociates Modifies equilibrium angle  o according to  -bond order in bond a and bond b

15. 15 Valence angle energy 2. Bond order/valence angle energy i j k b a Bond order bond a E val,max E val 0

16. 16 Valence angle energy 3.  -Bond order/equilibrium angle i j k b a Equilibrium angle (degrees)

17. 17 Torsion angle energy 1. General shape General shape: Ensures torsion angle energy contribution disappears when bond a, b or c dissociates (similar to valence angle) i j k b a c l Controls V 2 -contribution as a function of the  -bond order in bond b

18. 18 Torsion angle energy 2.  -bond order influence on V 2 -term i j k b a c l eff V 2 V 2,max 0

19. 19 Avoid unrealistically high amounts of bond orders on atoms Atom energy BO ij i nbonds,   1 BO (C)=4 ij i nbonds,   1 BO (C)=3 ij i nbonds,   1 BO (C)=5 ij i nbonds,   1 Overcoordination energy

20. 20 0.01 0.1 1 10 100 1000 10000 100000 1000000 0100200300400 ReaxFF QM (DFT) Nr. of atoms Time/iteration (seconds) Computational expense x 1000,000

21. 21 All-carbon compounds: training set Strategy for parameterizing reactive force fields - Pick an appropriate QC-method - Determine a set of cluster/crystal cases; perform QC - Fit ReaxFF-parameters to QC-data Interatomic distance (Angstroms) Bonds Valence/ Torsions Nonbonded Non-reactive force field Interatomic distance (Angstroms) Bonds Valence/ Torsions Nonbonded Over coordination ReaxFF Complications

22. 22 - 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 (van Duin et al. JPC-A, 2001); ReaxFF can describe both hydro- and all-carbon compounds

23. 23 C-C distance (Å) Energy (kcal/mol) Bond formation between two C 20 -dodecahedrons - ReaxFF properly describes the coalescence reactions between C 20 -dodecahedrons

24. 24 Angle bending in C 9 - ReaxFF properly describes angle bending, all the way towards the cyclization limit

25. 25 C 6 +C 5 to C 11 reaction - ReaxFF properly predicts the dissociation energy but shows a significantly reduced reaction barrier compared to QC

26. 26 3-ring formation in tricyclic C 13 -ReaxFF describes the right overall behaviour but deviates for both the barrier height and the relative stabilities of the tetra- and tricyclic compounds

27. 27 c-axis (Å)  E (eV/atom) diamond graphite 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) -ReaxFF gives a good description of the diamond-to-graphite reaction path

28. 28 Relative stabilities of graphite, diamond, buckyball and nanotubes CompoundE Ref (kcal/atom)E ReaxFF Graphite0.00 a 0.00 Diamond0.8 a 0.52 Graphene1.3 a 1.56 10_10 nanotube2.8 b 2.83 17_0 nanotube2.84 b 2.83 12_8 nanotube2.78 b 2.81 16_2 nanotube2.82 b 2.82 C 60 -buckyball11.5 a 11.3 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

29. 29 Ongoing all-carbon projects - Nanotube failure, buckyball collision (Claudio) - Si-tip/nanotube interactions (Santiago) - Nanotube growth, buckyball polymerization (Weiqiao) - Buckyball/nanotube nucleation (Kevin) - Buckyball/nanotube oscillator (Haibin) - Diamond surface interactions (Sue Melnik)

30. 30 Sample simulation: Ethylene+O 2 reactive NVE -12 Ethylene, 36 O 2 - Pre-equilibrated at 4000K. Switched off C-O and H-O bonds during equilibration to avoid reactions - Time-step: 0.025 fs.; cannot go much higher due to high temperature + reactive potential - Should react; main expected products H 2 O, CO 2 and CO

31. 31

32. 32 MD-iteration - Fast reaction after initiation - Exothermic; temperature rises to 7000K - Energy is not perfectly conserved at elevated temperatures. - Future work: investigate potential; see if energy conservation can be improved.

33. 33 - ReaxFF gets pretty reasonable product distribution; probably slightly too much CO; may need to check CO+0.5O 2 to CO 2 reaction energy