reactive force fields: concepts of reaxff
TRANSCRIPT
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Adri van Duin
Material and Process Simulation Center, California Institute ofTechnology
CH-121 lecture February 4 2008
Reactive force fields: concepts of ReaxFF
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Aim: simulation of the dynamics of large, complicatedreactive systems
Simulation of the decompositionof a archaeol lipid biomarker byexposure to high-velocity (30eV)N-radicals
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Outline- Energy minimization and molecular dynamics methods- Simulations on the dynamics of chemical reactions- How to make a force field reactive: building the ReaxFF reactive force field
- Concepts of covalent non-reactive force fields- Introduction of bond orders- Non-bonded interactions in a reactive force field- Charge polarization- Current status of the ReaxFF method- ReaxFF program, in- and output files
- Force field development for Si/SiO systems- Applications of the Si/SiO reactive force field
- Hydrogen diffusion in Si/SiO2 interfaces- Thermal decomposition of PDMS polymers
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Energy minimization (EM) and molecular dynamics (MD)methods
EM
- Temperature (=velocity) is zero- Only sample 1 system configuration
MD
- Non-zero temperature- Sample configurational space; the higher the temperature the moreconfigurations become available- Energy conservation: Ekin+Epot=constant
velocity vector
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Energy minimization methods: structure
Input structure
Force calculation(QM,FF)
Output structure
Energy minimizer(Steepest descent, conjugate gradient,Newton-Raphson)
Iterative cycle
Updatedgeometry
Have I reachedconvergence ?
Yes
No
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MD-methods: structure
Input structure
Force calculation(QM,FF)
Iterative cycle
Updatevelocities
from forces
Updatepositions from
velocitiesNVE:do nothing
NVT: rescale velocities to controltemperature
NPT: rescale system volume to controlpressure
MD
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FF energy minimization of a methylphenanthrene radicalusing a steepest descent method
EM
MD
FF NVE molecular dynamics of a methylphenanthreneradical at T=700K
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Applications of EM and MD
EM- Determine static (0 Kelvin) properties of a single systemconfiguration.- Can be used to calculate IR, NMR-spectra, geometry information,relative energies.- Usually employed on a single molecule; not relevant for multi-molecular systems.
MD- Used to sample the configurational space; average over multiplesystem configurations.- Can be used to model temperature and pressure effects- Can be used to calculate diffusion constants, reaction rates.- Can be employed on multi-component systems.- Almost always FF; QM/MD is very expensive
Fluorimidazole/HTFS system
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Simulations on the dynamics of chemical reactionsTi
me
DistanceÅngstrom Kilometres
10-15
years
QM
ab initio,DFT,HF
ElectronsBond formation
FF
Empiricalforce fields
AtomsMolecular
conformations
MESO
FEA
Design
Grains
Grids
QM methods:- Fundamental- Expensive, only small systems
FF methods- Empirical; need tobe trained- Much cheaperthan QM, can beapplied to muchlarger systems
Atomistic
Super-atomistic
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QM-methods
H = !! !!!!<<
+"+#"#"ji iji i A Ai
A
BA AB
BAi
A
A
A rR
Z
R
ZZ
M
1
2
1
2
1 22
Kinetic energy
Nucleus-Nucleusrepulsion
Nucleus-Electronattraction
Electron-Electronrepulsion
(analyticallyunsolvable)
HΨ=EΨ
- Allows calculation of atomic interactions First Principles- Computationally expensive, especially for finding accurateapproximations of electron-electron repulsion term
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Force field methods
©2005 Markus Buehler, MIT
b
φ
Θ
- Empirical, we need to derive values for the force field parameters(intuition, compare to experiment, compare to QM)- MUCH faster than QM; can be applied to bigger systems
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QM and FF-based approaches to reactive MD
- Option 1: Burn CPUs with QM/MD (e.g. Raty et al., PRL 2005)
- Option 2: use empirical assumptions to make QM faster (semi-empirical methods)
- CINDO/MINDO/AM1/MOPAC (e.g. Pople and Segal, JCP 1966;Stewart, J. Comp. Chem. 1989)
- Tight-binding (e.g. McMahan and Klepeis, PRB 1997)
- Analytical Bond Order Potentials (e.g. Pettifor and Oleinik, PRB1999)
- Option 3: Add ability to simulate reactions to FF-method(empirical bond-order based force fields)
- Tersoff /Brenner /AIREBO (Tersoff, PRL 1988; Brenner, PRB 1990,Stuart et al., JCP 2000)
- LCBOP (de Los et al., PRB 2005)
- EDIP (e.g. Bazant and Kaxiras, PRL 1996)
- ReaxFF (e.g. van Duin et al. JPC-A 2001)
QM
ab initio,DFT,HF
FF
Empiricalforce fields
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from Steve Stuart, Clemson University
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How to make a force field reactive: building theReaxFF reactive force field
- Concepts of covalent non-reactive force fields - Introduction of bond orders - Non-bonded interactions in a reactive force field - Charge polarization - Current status of the ReaxFF method - ReaxFF program, in- and output files
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CoulombvdWaalstorsionanglebondsystem EEEEEE ++++=
( )2obbond rrkE !=
( )2ovangle kE ""!=
( ) ( )## 3cos12cos132
+$+!$= VVEtorsion
%&
%'(
%)
%*+
,-
./0
1223
4556
7!$$!,
-
./0
1223
4556
7!$=
vdW
ij
ij
vdW
ij
ijijvdWaalsr
r
r
rDE 1
2
1exp21exp 88
ij
ji
Coulombr
qqCE
$$=
CoulombvdWaalstorsionanglebondsystem EEEEEE ++++=
( )2obbond rrkE !=
( )2ovangle kE ""!=
( ) ( )## 3cos12cos132
+$+!$= VVEtorsion
%&
%'(
%)
%*+
,-
./0
1223
4556
7!$$!,
-
./0
1223
4556
7!$=
vdW
ij
ij
vdW
ij
ijijvdWaalsr
r
r
rDE 1
2
1exp21exp 88
ij
ji
Coulombr
qqCE
$$=
Concepts of covalent non-reactive force fields
System energy description for a simpleharmonic non-reactive force field
- Can be parameterizedto describe structuresand energies close toequilibrium- Expansion withanharmonic termsimproves reliability andapplication range- Does not dissociatebonds properly
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C-C bond length (Å)
Ene
rgy
(kca
l/mol
)
C-C bond stretching in EthaneAround the equilibrium bond length Full dissociation curve
C-C bond length (Å)
- Although the harmonic approximation can describe the bondstretching around the equilibrium it cannot describe the bonddissociation.- Harmonic force field needs to use multiple atom types to distinguishsingle, double and triple bonded carbons.
Failure of the harmonic model
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-To get a smooth transition from nonbonded to single, double andtriple bonded systems ReaxFF employs a bond length/bond orderrelationship. Bond orders are updated every iteration.
-All connectivity-dependent interactions (i.e. valence and torsionangles) are made bond-order dependent, ensuring that their energycontributions disappear upon bond dissociation.- Nonbonded interactions (van der Waals, Coulomb) are calculated betweenevery atom pair, irrespective of connectivity. Excessive close-rangenonbonded interactions are avoided by shielding.
- ReaxFF uses a geometry-dependent charge calculation schemethat accounts for polarization effects.
From non-reactive to reactive force fields: key features ofReaxFF
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Calculation of bond orders from interatomic distances
Introduction of bond orders
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/ Sigma bond
Pi bond
Double pi bond0
1
2
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1 1.5 2 2.5 3
Interatomic distance (Å)
Bo
nd
ord
er
Bond order (uncorrected)
Sigma bond
Pi bond
Double pi bond
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Pi bond
Double pi bond0
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2
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1 1.5 2 2.5 3
Interatomic distance (Å)
Bo
nd
ord
er
Bond order (uncorrected)
Sigma bond
Pi bond
Double pi bond
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Calculation of bond energy from bond orders
!!!!!!"""
ijeijeijijebond BODBODBOfBODE #$#$##$= )(
0
1
2
3
1 1.5 2 2.5 3
Interatomic distance (Å)
Bo
nd
ord
er
Bond order (uncorrected)
Sigma bond
Pi bond
Double pi bond
-500
-400
-300
-200
-100
0
100
1 1.5 2 2.5 3
Interatomic distance (Å)
Bond e
nerg
y (k
cal/m
ol)
Sigma energy
Pi energy
Double pi energy
Total bond energy
!!!!!!"""
ijeijeijijebond BODBODBOfBODE #$#$##$= )(
0
1
2
3
1 1.5 2 2.5 3
Interatomic distance (Å)
Bo
nd
ord
er
Bond order (uncorrected)
Sigma bond
Pi bond
Double pi bond
-500
-400
-300
-200
-100
0
100
1 1.5 2 2.5 3
Interatomic distance (Å)
Bond e
nerg
y (k
cal/m
ol)
Sigma energy
Pi energy
Double pi energy
Total bond energy
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MM or MD routine
Connection table
1: 2 3 42: 1 5 63: 14: 15: 26: 2
Non-reactive force field
Atom positions
1: x1 y1 z12: x2 y2 z23: x3 y3 z34: x4 y4 z45: x5 y5 z56: x6 y6 z6
Fixe
d
MM or MD routine
Determineconnections
Reactive force field
Atom positions
1: x1 y1 z12: x2 y2 z23: x3 y3 z34: x4 y4 z45: x5 y5 z56: x6 y6 z6
1 2
3
4
5
6
Connectivity: differences in program structure
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0 1 2 3 4 5
Avoid unrealistically high amounts of bond orders on atoms
Atom
ene
rgy
BOi ji
nbonds,
=∑
1
BO (C)=4i ji
nbonds,
=∑
1BO (C)=3i j
i
nbonds,
=∑
1BO (C)=5i j
i
nbonds,
=∑
1
Dealing with overcoordination
!=
"=#
#$+$#$=
neighbours
jijii
iiijover
BOValency
BOfE
1
)exp(1
1)(
%
![Page 22: Reactive force fields: concepts of ReaxFF](https://reader030.vdocuments.site/reader030/viewer/2022040802/624d32d2ba817674af4aaae3/html5/thumbnails/22.jpg)
-To get a smooth transition from nonbonded to single, double andtriple bonded systems ReaxFF employs a bond length/bond orderrelationship. Bond orders are updated every iteration.- All connectivity-dependent interactions (i.e. valence and torsion angles) aremade bond-order dependent, ensuring that their energy contributionsdisappear upon bond dissociation.
- Nonbonded interactions (van der Waals, Coulomb) are calculatedbetween every atom pair, irrespective of connectivity. Excessiveclose-range nonbonded interactions are avoided by shielding.
-ReaxFF uses a geometry-dependent charge calculation scheme thataccounts for polarization effects.
From non-reactive to reactive force fields: key features ofReaxFF
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φ1 >φο
Bond orders: 1
Valence angles
Reactive:
Non-reactive: ( )E kangle a o= ! "# #2
Bond-order dependent part
Angle
φ1
Bond orders: 0.4φο φ1
Ang
le e
nerg
y
BO
BO
a
b
= Bond order a
= Bond order b
= Angle
= Equilibrium angleo
!
!
non-reactiveforce field
ReaxFF( )E kangle a o= ! "# #2
!
Eangle = 1"exp #3 $BOa3( )[ ]$ 1"exp #3 $BOb3( )[ ]$ ka "ka exp "kb $ % "%o( )
2[ ]{ }
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Torsion and conjugation
- 4-body (torsion) conjugation term
- 3-body (angle) conjugation term
!
Econj = f12(BOij ,BOjk ,BOkl ) " pcot 1 " 1+ cos2# ijkl $1( ) " sin% ijk " sin% jkl[ ]
!
Ecoa = pcoa1 "1
1+ exp pcoa2 " # j
val( )" exp $pcoa3 " $BOij + BOin
n=1
neighbours( i)
%&
' (
)
* +
2,
-
.
.
/
0
1 1 " exp $pcoa3 " $BOjk + BOkn
n=1
neighbours(i)
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)
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.
.
/
0
1 1 " exp $pcoa4 " BOij $1.5( )
2
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[ ]
!
Etors = f10(BOij ,BOjk,BOkl ) " sin# ijk " sin# jkl "1
2V1 " 1+ cos$ ijkl( ) +
1
2V2 " exp ptor1 " 2 % BOjk
& % f11(' j ,' k )( )2
{ } " 1% cos2$ ijkl( ) +1
2V3 " 1+ cos3$ ijkl( )
(
) * +
, -
- Torsion angle energy term
- Bond order dependent- Tested against a largedatabase of PAH heats offormation
![Page 25: Reactive force fields: concepts of ReaxFF](https://reader030.vdocuments.site/reader030/viewer/2022040802/624d32d2ba817674af4aaae3/html5/thumbnails/25.jpg)
Hydrogen bonds
!
EHbond = phb1 " 1# exp phb2 "BOXH( )[ ] " exp phb3rhbo
rHZ+rHZ
rhbo# 2
$
% &
'
( )
*
+ ,
-
. / " sin8
0XHZ
2
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% &
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( )
H-transfer in [Im-Im]+: QM-data
0
5
10
15
20
25
30
35
0.9 1.3 1.7 2.1
N-H distance (Å)
En
erg
y (
kcal/m
ol)
N--N 3.2 Å
N--N 3.0 Å
N--N 2.8 Å
N--N 2.6 Å
H-transfer in [Im-Im]+: ReaxFF-data
0
5
10
15
20
25
30
35
0.9 1.3 1.7 2.1
N-H distance (Å)
En
erg
y (
kcal/m
ol)
N--N 3.2 Å
N--N 3.0 Å
N--N 2.8 Å
N--N 2.6 Å
H-transfer in [Im-Im]+: QM-data
0
5
10
15
20
25
30
35
0.9 1.3 1.7 2.1
N-H distance (Å)
En
erg
y (
kcal/m
ol)
N--N 3.2 Å
N--N 3.0 Å
N--N 2.8 Å
N--N 2.6 Å
- Bond order dependent- Tested for a wide range ofhydrogen transfer reactions- Tested for bulk water andproton diffusion in water
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-To get a smooth transition from nonbonded to single, double andtriple bonded systems ReaxFF employs a bond length/bond orderrelationship. Bond orders are updated every iteration.- All connectivity-dependent interactions (i.e. valence and torsion angles) aremade bond-order dependent, ensuring that their energy contributionsdisappear upon bond dissociation.
- Nonbonded interactions (van der Waals, Coulomb) are calculatedbetween every atom pair, irrespective of connectivity. Excessiveclose-range nonbonded interactions are avoided by shielding.
-ReaxFF uses a geometry-dependent charge calculation scheme thataccounts for polarization effects.
Key features
![Page 27: Reactive force fields: concepts of ReaxFF](https://reader030.vdocuments.site/reader030/viewer/2022040802/624d32d2ba817674af4aaae3/html5/thumbnails/27.jpg)
Nonbonded interactions
i
j
k
l
m
Non-reactive force field: ignore vdWaals and Coulomb interactionsbetween atoms sharing a bond (I-j, j-k, k-l and l-m) or a valence angle(I-k, j-l and k-m).These exception rules are very awkward when trying to describereactions.
ReaxFF: calculate nonbonded interactions between all atom pairs,regardless of connectivity.To avoid excessive repulsive/attractive nonbonded interactions atshort distances both Coulomb and van der Waals interactions areshielded in ReaxFF.
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Shielded vdWaals and Coulomb interactions
Shielded Coulombpotential
vdWaals: Shielded Morse potential
- For metals ReaxFF only uses bond energy, overcoordination,vdWaals and Coulomb-terms (no angle or dihedrals)- vdWaals and overcoordination terms serve as a density-dependent repulsive term (as used in EAM-potentials [Daw and
Baskes, PRB 1984] ), allowing ReaxFF to describe bulk metals
0
250
500
750
1000
0 0.5 1 1.5 2 2.5 3
Unshielded Coulomb
Shielded Coulomb
Unshielded vdWaals
Shielded vdWaals
+0.5 +0.5
Interatomic distance (Å)
Energ
y (k
cal/m
ol)
0
250
500
750
1000
0 0.5 1 1.5 2 2.5 3
Unshielded Coulomb
Shielded Coulomb
Unshielded vdWaals
Shielded vdWaals
+0.5 +0.5+0.5 +0.5
Interatomic distance (Å)
Energ
y (k
cal/m
ol)
!
ECoulomb =C "qi " q j
rij3 + 1 /# ij( )
3$ % &
' ( )
1/ 3
![Page 29: Reactive force fields: concepts of ReaxFF](https://reader030.vdocuments.site/reader030/viewer/2022040802/624d32d2ba817674af4aaae3/html5/thumbnails/29.jpg)
-To get a smooth transition from nonbonded to single, double andtriple bonded systems ReaxFF employs a bond length/bond orderrelationship. Bond orders are updated every iteration.
- Nonbonded interactions (van der Waals, Coulomb) are calculatedbetween every atom pair, irrespective of connectivity. Excessiveclose-range nonbonded interactions are avoided by shielding.
- All connectivity-dependent interactions (i.e. valence and torsionangles) are made bond-order dependent, ensuring that their energycontributions disappear upon bond dissociation.
- ReaxFF uses a geometry-dependent charge calculation schemethat accounts for polarization effects.
Key features
![Page 30: Reactive force fields: concepts of ReaxFF](https://reader030.vdocuments.site/reader030/viewer/2022040802/624d32d2ba817674af4aaae3/html5/thumbnails/30.jpg)
0
1
2
........
........
1
2
1
2
1
13
,
3
,
13
,2
3
,2
222
2
13
,1
3
,1
111
1
3
1
3
1
3
1
=
!!
"
#
$$
%
&
!!
"
#
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'++=(
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!!
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"
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'++=(
(
)
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)
=
=
=
=
n
i
i
n
j
jn
jn
j
nnn
n
n
j
j
j
j
n
j
j
j
j
q
r
qCq
q
E
r
qCq
q
E
r
qCq
q
E
*
+,
*
+,
*
+,
Charge polarization- Assign one electronegativity and hardness to each element; optimizethese parameters against QM-charge distributions- Use system geometry in solving electronegativity equilibrationequations in every iteration
EEM-method(Mortier et al., JACS1986); shielding:Janssens et al.J.Phys.Chem. 1995.
Similar to Qeq-method(Rappe and Goddard, J.Phys. Chem. 1991) withempirical shieldingcorrection.
χ: atom electronegativityη: atom hardnessγ: shielding parameterr: interatomic distancesq:atom charge
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ReaxFF chargesQM
Mulliken chargesDFT; 6-31G**
-0.57-0.62
-0.49
-0.31
+0.54
+0.35
+0.26
+0.14+0.15
+0.14
+0.14-0.01
+0.26 -0.64-0.49
-0.47
-0.31
+0.61
+0.34
+0.26
+0.12+0.12
+0.12
+0.12-0.05
+0.26
- Good reproduction of Mulliken charges (similar concepts)- Combined with 1-2 Coulomb-interactions, this enables ReaxFF tosimulate polarization effects on local chemistry- EEM/Qeq methods work well around equilibrium; incorrectdescription of charge flow at high compression and dissociation (Chenand Martinez, Chem.Phys.Lett. 2006)- Most expensive part of the reactive force field; needs to beupdated every MD-step and forces sub-femtosecond steps
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General rules for ReaxFF
- MD-force field; no discontinuities in energy or forces even duringreactions.
- 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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0.01
0.1
1
10
100
1000
10000
100000
1000000
0 100 200 300 400
ReaxFF
QM (DFT)
Nr. of atoms
Tim
e/ite
ratio
n (s
econ
ds)
ReaxFF Computational expense
x 1000,000-ReaxFF allows forreactive MD-simulationson systems containingmore than 1000 atoms- ReaxFF is 10-50 timesslower than non-reactiveforce fields- Better scaling than QM-methods (NlogN forReaxFF, N3 (at best) forQM
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- ReaxFF combines covalent, metallic and ionic elements allowingapplications all across the periodic table- All ReaxFF descriptions use the same potential functions, enablingapplication to interfaces between different material types- Code has been distributed to over 60 research groups- Parallel ReaxFF (GRASP/Reax and USC/Reax) available
not currentlydescribed byReaxFF
Current development status of ReaxFF
Some ReaxFF publications-C/H:van Duin et al, JPC-A 2001, 105, 9396;Org. Geochem.2003, 34, 515; Chen et al, PR-B 2005, 72, 085416, Han et al. Appl. Phys.Lett. 2005, 86, 203108.
- C/N/O/H:Strachan et al, PRL 2003,91,09301;JCP 2005,122,054502; van Duin et al, JACS2005, 127, 11053
-Metals: Zhang et al, PRB 2004,69,045423;Nielson et al., JPC-A 2005, 109, 493; Su etal., PRB 75, 2007; Ludwig et al, JPC-B 2006;Cheung et al, JPC-A 2005, 109, 851
- Si/SiO/SiC: van Duin et al., JPC-A 2003,107, 3803; Chenoweth et al., JACS 2005,127, 7192; Buehler et al., PRL 2006, 96,095505; Buehler et al, PRL 2007.
ReaxFF transferability
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- ReaxFF is incorporated in the Grasp-framework (Aidan Thompson,Sandia) allowing parallel ReaxFF-simulations.
GRASP Performance on BG/L with ReaxFFComparison with Liberty Cluster (3GHz Pentium+Myrinet)
RDX Explosive with OxygenReaxFF force field with charge equilibration
•ReaxFF enables reactive modelling•Si/SiO2, Explosives, film growth•Each process computes energy andforces for a virtual non-periodic cluster•Low communication, duplicatedcomputation ~ P(N/P)2/3
•Uses Van Duin’s Fortran subroutines forforce calculation.•Good strong scaling•Sweet spot: 5000 atoms/processor
Parallel ReaxFF: GRASP/ReaxFF
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ReaxFF program, in- and output files
- Written in Fortran-77- Library independent- Text-based interface (graphical interface isdeveloped within CMDF)- Installed on various computers and operatingsystems (Linux, Windows, Macs)- Code divided in 6 parts:
- reac.f (10640 lines): general MD routines- poten.f (3034 lines): energy equations- ffopt.f (1581 lines): force field optimization- shanno (1718 lines): energy minimization- vibra.f (1194 lines): vibrational frequencies- blas.f (613 lines): BLAS-routines- program parameters in cbka.blk
ReaxFF program structure
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mdsavmolanal
verlet1encalc
verlet2
tdamp pdamp
main
reac
tap7threadtreg ffinptreadvregreaderegreadaddmol
readbgf inivel
vlistsrtbon1
boncor
lonpar
covbon
ovcor
srtangsrttorsrthb
calvalvalangtoranghbond
charges nonbon
efieldrestraint
mdsavmolanal writegeo newbgf outresend
Temperaturecontrol Pressure
control
output molfra.out outputxmolout, fort.7
find H-bonds find torsions find angles
H-bond energy Torsion energy Angle energy Calculateangles
end
1st step Velocity Verlet
2nd step Velocity Verlet
Calculate energiesand forces
Restraint energy Electric fieldenergy
Over/under coor-dination energy
Lone pair energy
Verlet list
in ffopt.f
in reac.f
in poten.f
Update bond orders
vdWaals andCoulomb energies
Determine charges
Read addmol.bgf Read eregime.in Read vregime.in Read tregime.in
Read geometry Read restart file
Set up Taperfunction
output molfra.out outputxmolout, fort.7
output geometryin .geo-format
output geometryin .bgf-format
output force fielderror in fort.99
Readforcefield
Reax program flow chart
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Overview ReaxFF in- and output files
Mandatory input files
- geo (input geometry)- control (run control parameters)- ffield (force field parameters)- exe (UNIX-script)
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Force field development for Si/SiO systems
Adri van Duin, Alejandro Strachan, Shannon Stewman, Qingsong Zhang, Xin Xu and Bill Goddard,Journal of Physical Chemistry-A 2003
- Concept: build a QM-based database (training set) that described reactive andnon-reactive aspects of the material and optimize ReaxFF to reproduce theseQM-data.- Bigger (more extensive) training sets yield more transferable force fields (butlonger development time!)- Things to include in training sets
- Bond dissociation- Angle bending- Under/overcoordination- Key reactions, including transition states- Charges- Condensed phase data: Equations of state, heats of formation(experiment)
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Bond energy
Si-O distance (Angstrom)
Ene
rgy
(kca
l/mol
)
Other SiOH bonds:- Si-Si- Si=Si- Si=O- Si-H- O-O- O=O- O-H
HO-Si(OH)3 bond
0
100
200
300
1 2 3 4 5
DFT Singlet
DFT Triplet
ReaxFF
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Valence angle bending1. Individual valence angles
H3Si-SiH2-OH angle
Angle (degrees)
Ene
rgy
(kca
l/mol
)
Other SiOH angles:- Si-Si-Si - Si-Si-H- Si-O-Si - H-Si-H- Si-Si-H - H-O-H- Si-O-H - O-O-O- O-Si-H - Si-O-O
- O-O-H
0
5
10
15
70 80 90 100 110 120 130 140
DFT
ReaxFF
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r1 (Angstrom)
Ene
rgy
(kca
l/mol
)
Valence angle bending2. Ring deformation
r1
0
25
50
75
100
125
150
1.40 1.60 1.80 2.00 2.20
DFT
ReaxFF
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Valence angle bending3. Ring size/ring strainΔ
E/S
iO2 (
kcal
/mol
)
0
50
100
150Monomer
4-ring
6-ring
8-ring
10-ring
12-ring
14-ring
alfa-
Quartz
QC
ReaxFF
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Over/undercoordination
Si(OH)4+ HO-OH
H3Si-O-SiH3+ H3Si-SiH3
ΔE (DFT) ΔE(ReaxFF)
Si(OH)6 +60.9 kcal/mol +48.2 kcal/mol
O(SiH3)4 +102.5 kcal/mol +87.4 kcal/mol
+28.4 kcal/mol +35.1 kcal/mol
+67.8 kcal/mol +75.5 kcal/mol
SiH2
SiH2
O
SiH2
SiH2
O
H2Si
OSiH
2
•
•H2Si
OSiH
2
•
•
H2Si
SiO
••H
2Si
SiO
••
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Reactions 1. H2Si=O + H2Si=O 4-ring
Si-Si distance (Å)
Ene
rgy
(kca
l/mol
)
0
25
50
75
100
125
150
1.5 2 2.5 3 3.5 4
DFT ReaxFF
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Reactions 2. H2O- incorporation in a Si-cluster
Ene
rgy
(kca
l/mol
)
- Reactive force field can be used to simulate theentire reaction pathway
-120
-100
-80
-60
-40
-20
0
20 DFT
ReaxFF
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- Force field recognizeshigh-pressure transitionfrom 4-coordinated (α)to 6-coordinated (β)phase
ReaxFF QC
Equations of state crystals1. All-Si crystals
Volume/Si (Å3)
Ene
rgy/
Si (
eV)
0
1
2
3
4
10 12 14 16 18 20 22 24
Si(a)
Si(b)
Si(sc)
0
1
2
3
4
10 12 14 16 18 20 22 24
Si(a)
Si(sc)
Si(b)
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Compression/expansion crystals2. Silicon oxide crystals
Volume/SiO2 (Å3)
Ene
rgy/
SiO
2 (kc
al)
ReaxFF QC
- ReaxFF reproduces the QC-data for both the clusters as well as thecondensed phases.
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MD-anneal run on bulkphase Si-α with original
ReaxFF
- Original ReaxFF overstabilizes 5-coordination for silicon bulk phase5-coordinate
Si-phase
Correcting a ‘finished’ ReaxFF force field
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0
5
10
15
20
25
30
10 12 14 16 18 20 22 24
Volume/atom (Å3)E
nerg
y/at
om (
kcal
) Si(alfa)
Si(beta)
Si(cubic)
Si(5-coor)
QC
0
5
10
15
20
25
30
10 12 14 16 18 20 22 24
Volume/atom (Å3)
Ene
rgy/
atom
(kc
al) Si(alfa)
Si(beta)
Si(cubic)
Si(5-coor)
ReaxFF
Re-optimize ReaxFF with equation of state for 5-coordinate Si-phase
- Re-optimized ReaxFF gets proper stability for 5-coordinate Si-phase- 5-coordinate phase is more stable than 6-coordinate Si(β) !- 5-coordinate Si might be important in amorphous Si
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MD-anneal run on bulk phase Si-α with ReaxFF
Amorphous
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Applications of the Reax Si/SiO force field
- Hydrogen diffusion in Si/SiO2 interfaces- Stability of PDMS polymers
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ReaxFF
Hydrogen radical in72-atom α-quartzT=100K; reaction enforceby a moving restraint
Seqquest: E(quartz_H)-E(quartz+H)= +24 kcal/mol
-Good agreement between Reaxand SeqQuest reaction energies
0
10
20
30
40
0.750.951.151.351.551.751.952.15
O-H distance (Angstrom)
En
erg
y (
kcal/
mo
l)
ReaxFF simulations on H-diffusion and bonding in α-quartz
![Page 54: Reactive force fields: concepts of ReaxFF](https://reader030.vdocuments.site/reader030/viewer/2022040802/624d32d2ba817674af4aaae3/html5/thumbnails/54.jpg)
ReaxFF simulations on H-radical diffusionthrough α-quartz
T=600K
32 H-radicals in 576-atom α-quartz system
-No reaction of H-radicals withlattice oxygens; all H-radicalsdiffuse and form H2
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ReaxFF simulations on H-radical diffusionthrough α-quartz
T=1000K
32 H-radicals in 576-atom α-quartz system
-Elevated temperatures result inH-reaction with lattice oxygens.H2 formation still dominates
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- ReaxFF has proven to be transferable to a wide range of materialsand can handle both complex chemistry and chemical diversity.Specifically, ReaxFF can describe covalent, metallic and ionic materialsand interactions between these material types.
- The low computational cost of ReaxFF (compared to QM) makes themethod suitable for simulating reaction dynamics for large (>> 1000atoms) systems (single processor). ReaxFF has now been parallelized,allowing reactive simulations on >>1000,000 atoms.
: not currentlydescribed byReaxFF
Conclusions