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Dishing out the dirt on ReaxFF

Dishing out the dirt on ReaxFF. Force field subgroup meeting 29/9/2003. Contents. - ReaxFF: general principles and potential functions All-carbon compounds: Training set Sample simulation: Ethylene+O 2 reactive NVE . ReaxFF. Simulate bond formation in larger molecular systems.

Jims
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Dishing out the dirt on ReaxFF

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

  2. Contents • - ReaxFF: general principles and potential functions • All-carbon compounds: Training set • Sample simulation: Ethylene+O2 reactive NVE

  3. ReaxFF Simulate bond formation in larger molecular systems ReaxFF: general principles and potential functions 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. 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, MoOx, 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. Non-reactive force field Reactive force field 3 5 1: x1 y1 z1 2: x2 y2 z2 3: x3 y3 z3 4: x4 y4 z4 5: x5 y5 z5 6: x6 y6 z6 1: 2 3 4 2: 1 5 6 3: 1 4: 1 5: 2 6: 2 1: x1 y1 z1 2: x2 y2 z2 3: x3 y3 z3 4: x4 y4 z4 5: x5 y5 z5 6: x6 y6 z6 1 2 4 6 Atom positions Connection table Atom positions Fixed Bond order Determine connections MM or MD routine MM or MD routine Interatomic distance (Angstrom) Program structure

  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. ReaxFFCH ReaxFFSiO: System energy description 2-body 3-body 4-body multibody

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

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

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

  11. +0.5 +0.5 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 Energy (kcal/mol) vdWaals: Shielded Morse potential Interatomic distance (Å)

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

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

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

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

  17. b a l j c i k 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) Controls V2-contribution as a function of the -bond order in bond b

  18. b a l j c i k eff V 2 Torsion angle energy 2. -bond order influence on V2-term V2,max 0

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

  20. Computational expense 1000000 100000 10000 x 1000,000 1000 Time/iteration (seconds) QM (DFT) 100 ReaxFF 10 1 0.1 0.01 0 100 200 300 400 Nr. of atoms

  21. ReaxFF Non-reactive force field Over coordination Nonbonded Nonbonded Valence/ Torsions Valence/ Torsions Bonds Bonds Interatomic distance (Angstroms) Interatomic distance (Angstroms) 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 Complications

  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. Bond formation between two C20-dodecahedrons Energy (kcal/mol) Energy (kcal/mol) C-C distance (Å) - ReaxFF properly describes the coalescence reactions between C20-dodecahedrons

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

  25. C6+C5 to C11 reaction - ReaxFF properly predicts the dissociation energy but shows a significantly reduced reaction barrier compared to QC

  26. 3-ring formation in tricyclic C13 • ReaxFF describes the right overall behaviour but deviates for both the barrier height and the relative stabilities of the tetra- and tricyclic compounds

  27. 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

  28. Relative stabilities of graphite, diamond, buckyball and nanotubes 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. 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. Sample simulation: Ethylene+O2 reactive NVE • 12 Ethylene, 36 O2 • 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 H2O, CO2 and CO

  31. 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. MD-iteration

  32. - ReaxFF gets pretty reasonable product distribution; probably slightly too much CO; may need to check CO+0.5O2 to CO2 reaction energy

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