reactive force fields: concepts of reaxff

Adri van Duin

Material and Process Simulation Center, California Institute ofTechnology

CH-121 lecture February 4 2008

Reactive force fields: concepts of ReaxFF

Aim: simulation of the dynamics of large, complicatedreactive systems

Simulation of the decompositionof a archaeol lipid biomarker byexposure to high-velocity (30eV)N-radicals

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

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

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

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

FF energy minimization of a methylphenanthrene radicalusing a steepest descent method

EM

MD

FF NVE molecular dynamics of a methylphenanthreneradical at T=700K

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

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

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

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

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

from Steve Stuart, Clemson University

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

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

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

-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

Calculation of bond orders from interatomic distances

Introduction of bond orders

!!

"

#

$$

%

&

''(

)**+

,-+

!!

"

#

$$

%

&

''(

)**+

,-+

!!

"

#

$$

%

&

''(

)**+

,-=

6,

4,

2,

5,

3,

1,

'

exp

exp

exp

bo

bo

bo

p

o

ij

bo

p

o

ij

bo

p

o

ij

boij

r

rp

r

rp

r

rpBO

..

.

/ Sigma bond

Pi bond

Double pi bond0

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

!!

"

#

$$

%

&

''(

)**+

,-+

!!

"

#

$$

%

&

''(

)**+

,-+

!!

"

#

$$

%

&

''(

)**+

,-=

6,

4,

2,

5,

3,

1,

'

exp

exp

exp

bo

bo

bo

p

o

ij

bo

p

o

ij

bo

p

o

ij

boij

r

rp

r

rp

r

rpBO

..

.

/ Sigma bond

Pi bond

Double pi bond

!!

"

#

$$

%

&

''(

)**+

,-+

!!

"

#

$$

%

&

''(

)**+

,-+

!!

"

#

$$

%

&

''(

)**+

,-=

6,

4,

2,

5,

3,

1,

'

exp

exp

exp

bo

bo

bo

p

o

ij

bo

p

o

ij

bo

p

o

ij

boij

r

rp

r

rp

r

rpBO

..

.

/ Sigma bond

Pi bond

Double pi bond0

1

2

3

1 1.5 2 2.5 3


Bo

nd

ord

er


Sigma bond

Pi bond

Double pi bond

Calculation of bond energy from bond orders

!!!!!!"""

ijeijeijijebond BODBODBOfBODE #$#$##$= )(

0

1

2

3

1 1.5 2 2.5 3


Bo

nd

ord

er


Sigma bond

Pi bond

Double pi bond

-500

-400

-300

-200

-100

0

100

1 1.5 2 2.5 3


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


Bo

nd

ord

er


Sigma bond

Pi bond

Double pi bond

-500

-400

-300

-200

-100

0

100

1 1.5 2 2.5 3


Bond e

nerg

y (k

cal/m

ol)

Sigma energy

Pi energy

Double pi energy

Total bond energy

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

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)(

%

-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

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[ ]{ }

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)

%&

' (

)

* +

2,

-

.

.

/

0

1 1 " exp $pcoa4 " BOij $1.5( )

2

[ ] " exp $pcoa4 " BOjk $1.5( )2

[ ]

!

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

Hydrogen bonds

!

EHbond = phb1 " 1# exp phb2 "BOXH( )[ ] " exp phb3rhbo

rHZ+rHZ

rhbo# 2

$

% &

'

( )

*

+ ,

-

. / " sin8

0XHZ

2

$

% &

'

( )

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

-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.


-ReaxFF uses a geometry-dependent charge calculation scheme thataccounts for polarization effects.

Key features

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.

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


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


Energ

y (k

cal/m

ol)

!

ECoulomb =C "qi " q j

rij3 + 1 /# ij( )

3$ % &

' ( )

1/ 3

-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.

- ReaxFF uses a geometry-dependent charge calculation schemethat accounts for polarization effects.

Key features

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

=

!!

"

#

$$

%

&

!!

"

#

$$

%

&+

'++=(

(

!!

"

#

$$

%

&

!!

"

#

$$

%

&+

'++=(

(

!!

"

#

$$

%

&

!!

"

#

$$

%

&+

'++=(

(

)

)

)

)

=

=

=

=

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

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

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.

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

- 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

- 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

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

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

Overview ReaxFF in- and output files

Mandatory input files

- geo (input geometry)- control (run control parameters)- ffield (force field parameters)- exe (UNIX-script)

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)

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

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

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

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

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

••

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

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

- 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)

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.

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

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

MD-anneal run on bulk phase Si-α with ReaxFF

Amorphous

Applications of the Reax Si/SiO force field

- Hydrogen diffusion in Si/SiO2 interfaces- Stability of PDMS polymers

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

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

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

- 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

reactive force fields: concepts of reaxff

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