Dishing out the dirt on ReaxFF
Force field subgroup meeting 29/9/2003
1
Contents
- ReaxFF: general principles and potential functions
-All-carbon compounds: Training set
- Sample simulation: Ethylene+O2 reactive NVE
2
ReaxFF: general principles and potential functions
Hierarchy of computational chemical methods
MESO
MD
ReaxFF
QC
10-15
Design
FEA
Time
years
Atoms
Molecular
conformations
Electrons
Bond formation
Grids
Grains
Empirical
force fields
Empirical methods:
- Allow large systems
- Rigid connectivity
QC methods:
- Allow reactions
- Expensive, only
small systems
Simulate bond formation
in larger molecular systems
ab initio,
DFT,
HF
Ångstrom
Kilometres
Distance
3
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.
4
Program structure
Non-reactive force field
Reactive force field
3
1: x1 y1 z1
2: x2 y2 z2
3: x3 y3 z3
4: x4 y4 z4
5: x5 y5 z5
6: x6 y6 z6
4
Atom positions
1: 2 3 4
2: 1 5 6
3: 1
4: 1
5: 2
6: 2
1
2
4
6
Connection table
1: x1 y1 z1
2: x2 y2 z2
3: x3 y3 z3
4: x4 y4 z4
5: x5 y5 z5
6: x6 y6 z6
Atom positions
Fixed
3
Bond order
5
BOij  f (rij )
2
1
Determine
connections
0 MM or MD routine
1
1.5
2
2.5
Interatomic distance (Angstrom)
3
MM or MD
routine
5
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
6
ReaxFFSiO: System energy description
Esystem  Ebond  EvdW aals  ECoulomb  Eval  Etors
2-body
3-body
4-body
 Eover  Eunder
multibody
 E pen  Econj
ReaxFFCH
7
Bond energy
1. Calculation of bond orders from interatomic distances
3
Bond order (uncorrected)
Sigma bond
Pi bond
2
Double pi bond
Bond order
pb o , 2


r


ij
'
BOij  exp  pbo,1      Sigma bond

 ro  
pb o , 4

 rij  
 exp  pbo,3      Pi bond

 ro  
pb o , 6

 rij  
 exp  pbo,5     

 ro  
1
Double pi bond
0
1
1.5
2
2.5
3
Interatomic distance (Å)
8
Bond energy
2. Bond order correction for 1-3 bond orders
Corrected bond orders
Uncorrected bond orders
H
0.95
H
1
H
H
H
SBOC=4.16
SBOH=1.17
- Unphysical
- Puts strain on angle and
overcoordination potentials
H
H
H
0.9
Corrected bond order
H
S BO
0.8
0.94
0.7
0.6
0.5
H
0.4
H
SBOC=3.88
SBOH=0.98
0.3
0.2
0.1
0
0
H
- Correction removes unrealistic
weak bonds but leaves strong bonds
intact
- Increases
0.2
0.4computational
0.6
0.8expense
1 as
bond
orders become
Uncorrected
bond multibody
order
interactions
9
3.5
3.7
4.1
4.5
5
6
Bond energy
3. Calculate bond energy from corrected bond orders
 
E bond  De  BOij  exp pbe,1 1 BOij 



p be,2

 De  BOij  De  BOij
3
Bond order (uncorrected)
100
Sigma bond
0

Bond order
2
Bond energy (kcal/mol)
Pi bond
Double pi bond
1
1
2
2.5
3
-100
-200
Sigma energy
Pi energy
-300
-400
0
1.5
Double pi energy
Total bond energy
-500
1
1.5
2
2.5
Interatomic distance (Å)
3
Interatomic distance (Å)
10
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
Energy (kcal/mol)
1000
+0.5
+0.5
ECoulomb  C 
750
qi  q j
r  1/   
3
ij
3 1/ 3
ij
Unshielded Coulomb
Shielded Coulomb potential
Shielded Coulomb
500
Unshielded vdWaals
Shielded vdWaals
250
vdWaals: Shielded Morse potential
0
0
0.5
1
1.5
2
2.5
3
Interatomic distance (Å)
11
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.
NaCl-crystal (33.84x33.84x33.84
Ѓ)
Coulomb energy
-160000
-170000
Taper 7
Ewald (12.5 Ѓ inner
space cutoff)
Spline 3
-180000
-190000
-200000
0
5
10
15
20
Outer cutoff
25
30
35
12
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)
750
Bond energy
Shielded vdWaals energy
500
Total pair energy
250
0
0
1
2
3
-250
-500
Interatomic distance (Å)
13
Valence angle energy
1. General shape
a
i
General shape:
j
b
Modifies equilibrium
angle o according
to -bond order in bond a and
bond b
k


Eval  f ( BOa )  f ( BOb )  f ijk  o BOa , BOb

Ensures valence
angle energy contribution
disappears when bond a
or bond b dissociates
14
Valence angle energy
2. Bond order/valence angle energy


Eval  f ( BOa )  f ( BOb )  f ijk  o BOa , BOb

f ( BOa )  1  exp  1  BO
2
a

a

j
i
b
k
Eval
Eval,max
0
0
0.5
1
1.5
2
Bond order bond a
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Valence angle energy
3. -Bond order/equilibrium angle


Eval  f ( BOa )  f ( BOb )  f ijk  o BOa , BOb

f ( BOa )  1  exp  1  BOa2


a
j
b
i
k
neighbours( j )




  

o ( BOa , BOb )  180  o,o  1  exp  3   2   BO jn 


n

1








Equilibrium angle
(degrees)
180
160
140
120
100
0
0.5
1
1.5
2
neighbours( j )

BO
 jn
n 1
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Torsion angle energy
1. General shape
a
i
General shape:
j
b
c
l
k


1
1

Etors  f ( BOa )  f ( BOb )  f ( BOc )   V2  1  cos 2 ijkl  f BOb  V3  1  cos 3 ijkl 
2
2

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
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Torsion angle energy
2. -bond order influence on V2-term
a
i
j


b
c
k
l
1
1






Etors  f ( BOa )  f ( BOb )  f ( BOc )   V2  1  cos 2 ijkl  f BOb  V3  1  cos 3 ijkl 
2
2

2


f BOb  exp  4 1  BOb




V2,max
V2eff

0
0
0.25
0.5
BOb
0.75
1
18
Overcoordination energy
Avoid unrealistically high amounts of bond orders on atoms
nbonds
nbonds
i 1
i 1
Eover  f ( BOij )   i 
i  Valencyi 
1
1  exp(  i )
neighbours
 BOij
nbonds
 BOi , j (C)=4
 BOi , j (C)=5
i 1
Atom energy
 BOi , j (C)=3
j 1
3
3.5
4
4.5
nbonds
 BOi , j
i 1
19
Computational expense
1000000
Time/iteration (seconds)
100000
10000
x 1000,000
1000
100
QM (DFT)
ReaxFF
10
1
0.1
0.01
0
100
200
300
Nr. of atoms
400
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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
Non-reactive force field
ReaxFF
Nonbonded
Over
coordination
Nonbonded
Valence/
Torsions
Bonds
Valence/
Torsions
Bonds
Interatomic distance
(Angstroms)
Interatomic distance
(Angstroms) 21
Binding energies in all-carbon compounds relative to Graphite
Relative binding energy (kcal/atom)
120
100
80
60
Reax
QC
40
20
0
Diamond
C60-buckyball
C20-dodeca
Hexacyclic C20
Acyclic C20
Bicyclic C17
Cyclic C17
Cyclic C15
Acyclic C14
Tricyclic C13
Cyclic C13
Acyclic C13
Acyclic C12
Tricyclic C10
Cyclic C10
Acyclic C10
Cyclic C9
Acyclic C9
Cyclic C8
C8 cube
C8 3ringII
C8 3ring
Acyclic C8
Cyclic C7
Acyclic C7
Cyclic C6
2_C3
Acyclic C6
Cyclic C5
Acyclic C5
C4 pyramid
Cyclic C4
Acyclic C4
Cyclic C3
Acyclic C3
Acyclic C2
- 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
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describe both hydro- and all-carbon compounds
Energy
(kcal/mol)
Bond formation between two C20-dodecahedrons
100
DFT
ReaxFF
50
0
Energy
(kcal/mol)
1.5
2
2.5
100
DFT
ReaxFF
50
0
1.5
2
2.5
C-C distance (Å)
- ReaxFF properly describes the coalescence reactions between C20-dodecahedrons
23
Angle bending in C9
- ReaxFF properly describes angle bending, all the way towards the cyclization limit
24
C6+C5 to C11 reaction
- ReaxFF properly predicts the dissociation energy but shows a significantly reduced reaction
barrier compared to QC
25
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
26
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)
E (eV/atom)
0.2
0.15
graphite
diamond
0.1
0.05
0
10
15
20
c-axis (Å)
-ReaxFF gives a good description of the diamond-to-graphite reaction path
27
Relative stabilities of graphite, diamond, buckyball and nanotubes
a:
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
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
28
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)
29
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
30
QuickTime™ and a GIF decompressor are needed to see this picture.
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
33