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

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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

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Tim

e

DistanceÅngstrom Kilometres

10-15

years

QC

ab initio,DFT,HF

ElectronsBond formation

MD

Empiricalforce fields

AtomsMolecular

conformations

MESO

FEA

Design

Grains

Grids

Hierarchy of computational chemical methods

ReaxFF Simulate bond formationin larger molecular systems

Empirical methods:- Allow large systems- Rigid connectivity

QC methods:- Allow reactions- Expensive, only small systems

ReaxFF: background and rules

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underover

torsvalCoulombvdWaalsbondsystem

EE

EEEEEE

++

++++=

System energy description

2-body

multibody

3-body 4-body

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-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.

Key features

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General rules

- MD-force field; no discontinuities in energy or forces even during reactions.

- User should not have to pre-define reactive sites or reactionpathways; potential functions should be able to automatically handlecoordination 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.

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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

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Ni-catalyzed nanotube growth

Longer nanotube

Concept: grow nanotubes from buckyball building blocks

- Exothermic reaction- Huge activation barrier- Probably needs catalyst

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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

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Compound ERef (kcal/atom) EReaxFF

Graphite 0.00a 0.00

Diamond 0.8a 0.52

Graphene 1.3a 1.56

10_10 nanotube 2.8b 2.83

17_0 nanotube 2.84b 2.83

12_8 nanotube 2.78b 2.81

16_2 nanotube 2.82b 2.82

C60-buckyball 11.5a 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

Relative energies for all-carbon phases

All-carbon data added to the hydrocarbon training set

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Binding energies in all-carbon compounds relative to Graphite

0

20

40

60

80

100

120

Acyclic C2Acyclic C3Cyclic C3Acyclic C4Cyclic C4C4 pyramidAcyclic C5Cyclic C5Acyclic C62_C3Cyclic C6Acyclic C7Cyclic C7Acyclic C8C8 3ringC8 3ringIIC8 cubeCyclic C8Acyclic C9Cyclic C9Acyclic C10Cyclic C10Tricyclic C10Acyclic C12Acyclic C13Cyclic C13Tricyclic C13Acyclic C14Cyclic C15Cyclic C17Bicyclic C17Acyclic C20Hexacyclic C20C20-dodecaC60-buckyballDiamond

Relative binding energy (kcal/atom)

Reax

QC

- 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

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0

50

100

1.5 2 2.5

DFTReaxFF

0

50

100

1.5 2 2.5

DFTReaxFF

C-C distance (Å)

Ene

rgy

(kca

l/m

ol)

Ene

rgy

(kca

l/m

ol)

- ReaxFF gives good energies for key structures in buckyball growth-Training set includes all hydrocarbon cases used for ReaxFFCH

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Angle bending in C9

- ReaxFF properly describes angle bending, all the way towards the cyclization limit

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0

0.05

0.1

0.15

0.2

10 15 20

c-axis (Å)

E (

eV/a

tom

)

diamond

graphite

Diamond to graphite conversionCalculated 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

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Applications of all-carbon ReaxFF: buckyball+nanotube collisions

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Impact velocity:6 km/sec(1500K)

Impact velocity:9 km/sec(2500K)

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Impact velocity: 6 km/sec

Impact velocity: 8 km/sec Impact velocity: 10 km/sec

Side impact

-Materials are too stable, extremely high impact velocities are required to start reaction

- Catalyst required to lower reaction barriers

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Transition metal catalysis: Ni

1: ReaxFF and QC EOS for Ni bulk phasesQC

0

25

50

75

100

0 5 10 15 20 25

Energy (kcal/mol)

ReaxFF

0

25

50

75

100

0 5 10 15 20 25

FCC

BCC

A15

SC

Diamond

0

5

10

15

20

25

0 5 10 15 20 25

Volume/Atom (A 3)

0

5

10

15

20

25

0 5 10 15 20 25

Volume/Atom (A3)

FCC

BCC

A15

SC

Diamond

-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)

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-85

-80

-75

0 400000 800000

Icosahedron

FCC

Liquid

Amorphoussolid

MD-iterations

Ene

rgy/

atom

(kc

al)

Testing the force fields for Ni magic number clusters

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-85

-80

-75

-70

0 400 800 1200 1600

55 atoms

147 atoms

309 atoms

561 atoms

Temperature (K)

Ene

rgy/

atom

(kc

al)

IcosahedronFCC

Liquid

Amorphoussolid

MD-heatup/cooldown simulations

heatup

cooldown

- ReaxFF gets the right trend for fcc/icosahedron transition

- ReaxFF heat of melting converges on Ni bulk melting temperature (1720K)

200

50

100

150

1 2 3 4

DFT singletDFT tripletReaxFF

0

50

100

150

1 2 3 4

DFT singletDFT tripletReaxFF

NiCH3CH3

NiCH3CH3

Ni-C bond breaking in H3C-Ni-CH3

Bond length (Å)

Ene

rgy

(kca

l/mol

)E

nerg

y (k

cal/m

ol)

Ni-C bond breaking in Ni=CH2

Ni CH2

Ni CH2

2. Results for Ni-C interactions

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0

50

100

150

1 2 3 4

DFT singletDFT tripletReaxFF

Ni-C bond breaking in Ni(CH3)4

Bond length (Å)

Ene

rgy

(kca

l/mol

)

NiCH3

CH3

CH3

CH3

NiCH3

CH3

CH3CH3

Ni dissociation from 5-ring compound

Ene

rgy

(kca

l/mol

)

Ni

HH

HH

Ni

HH

HH

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0

25

50

2 3 4

DFT singletDFT tripletReaxFF

0

50

100

150

1 2 3 4

DFT singletDFT tripletReaxFF

Bond length (Å)

Ni dissociation from 6-ring compound

Ene

rgy

(kca

l/mol

)

Ni

HH

H

H H

Ni

HH

H

H H

Ni dissociation from benzene

Ni

Ni

Ene

rgy

(kca

l/mol

)

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0

50

100

1 2 3 4

DFT singletDFT tripletReaxFF

Ni dissociation from benzyne

Ene

rgy

(kca

l/mol

)

Bond length (Å)

Ni

Ni

C-Ni-C angle bending in benzyne/Ni complex

Angle (degrees)

Ene

rgy

(kca

l/mol

)

Ni

Ni

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0

10

20

60 90 120 150

DFT singletReaxFF

Angle (degrees)

Ene

rgy

(kca

l/mol

)Ni

CH3CH3

Ni

CH3

CH3Ni CH3

CH3

C-Ni-C angle bending in H3C-Ni-CH3

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Ni-assisted C2-incorporation in C 20-ring

-250

-200

-150

-100

-50

0

Incorporation pathway

Relative energy (kcal/mol)

QC

ReaxFF

Ni-assisted C2-incorporation on nanotube edge

-400

-350

-300

-250

-200

-150

-100

-50

0

50

100

Growth pathway

Relative energy (kcal/mol)

QM/MM

ReaxFF

(A)

(B)

(C)

(D)

(E)

(F)

(G)

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

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R12= 1.45 Å

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21

R12= 1.49 Å

Influence adsorbed Ni on buckyball reactions

- ReaxFF predicts that buckyball C-C bonds get substantially weakened by adsorbed Ni-atoms- Might lower buckyball coalescence reaction activation barrier

ReaxFF-minimized buckyball

ReaxFF-minimized buckyball+2 Ni

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-100

-50

0

50

100

150

1.522.533.544.555.5

No Ni

Ni

En

erg

y (k

cal/m

ol)

Reaction coordinate

Low-T ReaxFF restraint MD-simulation

Influence adsorbed Ni on reaction barrier

- Ni-atoms lower reaction barrier- Overall reaction becomes exothermic due to formation of Ni-Ni bonds- May explain Ni catalytic activity

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Influence Ni on initial stages of buckyball growth

MD NVT-simulation (1500K); 5 C20-rings, 10 C4-chains (blank experiment)

t=0 ps. t=125 ps.

- C4 reacts with rings to form long acyclic chains- No branching

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MD NVT-simulation (1500K); 5 C20-rings, 10 C4-chains and 15 Ni-atoms

t=0 to t=125 ps. t=125 to t=750 ps.

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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

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Metal-catalyzed nanotube growth

- Start configuration: 20 C6-rings, 5 metal atoms on edge

- NVT simulation at 1500K

- Add C2-molecule every 100,000 iterations

Inital configuration

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QuickTime™ and aGIF decompressorare needed to see this picture.- Ni-atoms can grab C2-monomers and fuse them as new 6-membered rings

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Metal-catalyzed nanotube growth

Results after 2,000,000 iterations

Metal=Ni

Metal=Co

Metal=CuNo metal

-Ni and Co lead to greatly enhanced ring formation. Cu is far less active.

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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