Ch121a Atomic Level Simulations of Materials
and Molecules
BI 115
Hours: 2:30-3:30 Monday and Wednesday
Lecture or Lab: Friday 2-3pm (+3-4pm)
Lecture 11, April 25, 2011
Reactive Force Fields – 1: ReaxFF
William A. Goddard III, wag@wag.caltech.edu
Charles and Mary Ferkel Professor of Chemistry,
Materials Science, and Applied Physics,
California Institute of Technology
Teaching Assistants Wei-Guang Liu, Fan Lu, Jose Mendoza,
Andrea Kirkpatrick
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
ReaxFF: first principles force field
Bridging the Gap between QM and MD to
describe reactive processes ranging from
combustion to catalysis, fuel cells,
nanoelectronics, and shock induced chemistry
471. ReaxFF: A Reactive Force Field for Hydrocarbons
A.C.T. van Duin, S. Dasgupta, F. Lorant and W. A. Goddard III
J. Phys. Chem. A, 105: (41) 9396-9409 (2001)
514. ReaxFF sio Reactive Force Field for Silicon and Silicon Oxide Systems
Adri C. T. van Duin, Alehandro Strachan, Shannon Stewman, Qingsong Zhang,
Xin Xu, and William A. Goddard, III
J. Phys. Chem. A, 107, 3803 (2003)
533. Shock waves in high-energy materials: The initial chemical events in
nitramine RDX
Strachan A, van Duin ACT, Chakraborty D, Dasgupta S, Goddard WA
Physical Review Letters,
91 (9): art. no. 098301 (2003)
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Motivation: Design Materials, Catalysts, Pharma from 1st
Principles so can do design prior to experiment
To connect 1st Principles (QM) to Macro work use an overlapping hierarchy of
methods (paradigms)
Need accurate force fields (potentials) with parameters
derived from first-principles QM
time
ELECTRONS ATOMS
GRAINS
GRIDS
hours
Continuum
(FEM)
millisec
Micromechanical modeling
Protein clusters
MESO
nanosec
MD
picosec
Deformation and Failure
Protein Structure and Function
QM
femtosec
simulations real devices and
full cell (systems biology)
distance
Å
nm
micron
mm
Big breakthrough making FC simulations
yards practical:
Accurate calculations for bulk phases
reactive force fields based on QM
and molecules (EOS, bond dissociation)
Describes: chemistry,charge transfer, etc. For
Chemical
Reactions (P-450© oxidation)
metals,
oxides,
organics.
Ch121a-Goddard-L11
copyright 2011 William
A. Goddard
III, all
rights reserved
Ordinary Force Fields
Bonds, angles, torsions described as elastic springs
r
A
E = kA(A-A0)
E = kr(r-r0)
Fixed charges, Empirical vdw nonbond terms,
Bonds cannot be broken, making the model unsuitable for modeling
reactions.
Examples: MM3, Dreiding, Amber, Charmm, Gromos, UFF
ReaxFF:
Allow bonds to break and form and describe barriers for reactions.
All parameters from quantum mechanics, no empirical data
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
First Principles Reactive force fields: strategy
• Describe Chemistry (i.e., reactions) of molecules
-Fit QM Bond dissociation curves for breaking every type of bond
(XnA-BYm), (XnA=BYm), (XnA≡BYm)
-Fit angle bending and torsional potentials from QM
-Fit QM Surfaces for Chemical reactions (uni- and bi-molecular)
-Fit Ab initio charges and polarizabilities of molecules
•Pauli Principle: Fit to QM for all coordinations (2,4,6,8,12)
•Metals: fcc, hcp, bcc, a15, sc, diamond
•Defects (vacancies, dislocations, surfaces)
•cover high pressure (to 50% compression or 500GPa)
•Generic: use same parameters for all systems (same O in O3, SiO2,
H2CO, HbO2, BaTiO3)
Require that One FF reproduces all the ab-initio data (ReaxFF)
Most theorists (including me) thought that this would not be possible,
but Ch121a-Goddard-L11
we claim to have achieved
validated
it for
many
systems
© copyrightand
2011 William
A. Goddard
III, all
rights reserved
Many Chemical processes: bond breaking for
5000millions atoms. This is far too large for DFT
Solution: ReaxFF first principles reactive force field
EE
Val
Valence energy
E
Coul
E
VdW
Electrostatic energy
short distance Pauli Repulsion
+ long range dispersion
(pairwise Morse function)
•Based completely on First Principles QM (no empirical parameters)
•Valence Terms (EVal) based on Bond Order: dissociates smoothly
• Bond distance  Bond order  Bond energy
•Forces depend only on geometry (no assigned bond types)
•Allows angle, torsion, and inversion terms (where needed)
•Describes resonance (benzene, allyl)
•Describes forbidden (2s + 2s) and allowed (Diels-Alder) reactions
•Atomic Valence Term (sum of Bond Orders gives valency)
•Pair-wise Nonbond Terms between all atoms (no “bond” exclusions)
•Short range Pauli Repulsion plus Dispersion (EvdW)
•QEq Electrostatics allows charges to flow depending on
Ch121a-Goddard-L11
© copyright
2011 William A. Goddard III, all rights reserved
environment and external
fields
ReaxFF reactive force field for Reactive Dynamics
(RD)
Allow bonds to break and form, describe barriers for reactions.
All parameters from quantum mechanics (no empirical data)
ReaxFF describes reactive processes (from oxidation to
combustion to catalysis to shock induced chemistry) for 1000s
to millions atoms
We use ReaxFF to prepare the structures of complex
heterogeneous systems by processes similar to experimental
synthesis (DLC, SiO2/Si)
Adri van
Duin
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Bond Order Dependent Potentials
pbo, 2


 rij
 rij  
BO ij  exp  pbo,1     exp  pbo,3   


 r0  
 r0




pbo, 4



 rij
 exp  pbo,5   


 r0

Ebond   De  BOij  exp pbe,1  1  BO
pbe, 2
ij
• Sigma Bond 1.5Å - 2.3Å
• First Pi Bond 1.2Å - 1.75Å
• Second Pi Bond 1.0Å - 1.4Å
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved





pbo, 6



Bond Order Dependence on r (CC)
Bond Order
BO-sigma
3.0
Value
2.5
BO-pi1

2.0
BO-pi2

Total
1.5
s
1.0
0.5
0.0
0.50
1.00
1.50
2.00
2.50
r
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
3.00
Bond distance
Bond distance
bond order
bond energy
bond order

 ro

BO ij exp  p bo,1 
r

 ij





pbo, 2 

 exp  p  ro ,

 bo,3  rij







p bo, 4 

 exp  p  ro ,

 bo,5  rij







pbo, 6 



4
3
Bond order
C-C bond


s
2
Use general functional form.
Determine parameters from
fitting QM bond breaking for
many single, double, and triple
bonded systems. Bond distance (Å)
100
1
0
1
1.5
2
2.5
Bond distance (Å)
Bond order
bond energy
3
Bond energy (kcal/mol)
0
 1  BO 
Ebond
  De  BOij  exp p
Ch121a-Goddard-L11
1
1.5
2
2.5
-100
-200
Sigma energy
Pi energy
-300
pbe, 2
,1 William A. Goddard
ij
© copyrightbe
2011
III, -400
all rights reserved
Double pi energy
Total bond energy
Van der Waals
Include vdW for 1-2 and 1-3 interactions since bonded
atoms may dissociate and nonbonded atoms may bond
during the dynamics
We use a Morse function rather than LJ12-6 (which is too
stiff in the inner wall region
Or exponential-6 which has problems for small R
EvdW


f 7 rij  
f 7 rij  


 
  2  exp 0.5  ij  1 

 Dij  exp  ij  1 
rvdW 
rvdW 




 
Here f7 was introduced to modify interactions for small R
This was a mistake and should be eliminated
1
Ch121a-Goddard-L11
3 3


3  1 
f 7 rij   rij   
w  


 III, all rights reserved
© copyright2011 William A. Goddard
f7
vdW Energy
6.4
4.4
3.4
2.4
1.4
0.50
1.50
2.50
3.50
4.50
5.50
6.50
r_ij
E_vdW
200
150
E (kcal/mol)
f7(r_ij)
5.4
100
50
0
1.4
2.4
3.4
4.4
-50
f(r_ij)
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
5.4
Coulomb interacions
Include Coulomb for 1-2 and 1-3 interactions since bonded atoms
may dissociate and nonbonded atoms may bond during the
dynamics
1
ECoulomb  C 
qi  q j
f 7 rij 
3 3


3  1 
f 7 rij   rij   

  w  
This f7 function provides shielding so that the Coulomb potential
goes to a constant, Cqiqj w at small R, where w is related to the
size of the atoms.
ReaxFF uses the Electron






2

Equilibration Method (EEM) of Mortier
i
i qi
to determine charges rather than
rather than QEq
Electronegativity
Mortier, W. J.; Ghosh, S. K.; Shankar, S. J. Am. Chem. Soc. 1986,108,
Hardness
4315; Janssens, G. O. A.; Baekelandt, B. G.; Toufar, H.; Mortier, W.
J.;Schoonheydt,
R. A. J. Phys. Chem.
1995,
99,William
3251. A. Goddard III, all rights reserved
Ch121a-Goddard-L11
© copyright
2011

j i
qj
Rij
Discussion about charges in ReaxFF
I believe that the use of a shielding denominator in the Coulomb
energy and the use of EEM in ReaxFF are inconsistent and a
fundamental mistake.
We should use QEq. In QEq the shielding of charges on different
centers is built in both in calculating the Coulomb energy and in
calculating the charges.
Separating them leads to potential problems for small R, where
the charges may be affected by the 1/R form in the potential.
In QEq this shielding is based on the covalent radius of the atom
and hence need not be optimized.
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Charge Equilibration for Molecular
Charge Equilibration (QEq) Dynamics Simulations
A. K. Rappé and W. A. Goddard III
•Self-consistent Charge Equilibration (QEq) J. Phys. Chem. 95, 3358 (1991)
•Describe charges as distributed (Gaussian)
•Thus charges on adjacent atoms shielded
(interactions  constant as R0) and include
interactions over ALL atoms, even if bonded (no
exclusions)
•Allow charge transfer (QEq method)
atomic
interactions
I
1 2

E {qi }J ij (qi ,q j ,rij )  i qi  J i qi 
2

i j
i 


E int rij , Qik , Q lj 

Erf 

ij kl
ij kl
rij

rij 

Qik Qkl
Keeping:
q Q
i
i
Hardness (IP-EA)
Jij
1/rij
Electronegativity (IP+EA)/2
rij
r i0 + r j0
Three universal parameters for each element:  io , J io , Ric , Ris & qic
1991:
use experimental©IP,
EA,2011
Ri; William
ReaxFF
getIII, from
fitting QM
Ch121a-Goddard-L11
copyright
A. Goddard
all rights reserved
Bond Energy
CC Bond Dissociation Energy
200
E (kcal/mol)
100
Experiment
0
-100
E_vdW
-300
-400
0.50
Mol. Eb
E_bond
-200
C2H6 90.4 - 1.533
C3H8 85.8 - 1.526
C4H10 86.5 - 1.532
Total E_bond
1.00
1.50
2.00
2.50
3.00
r
In ReaxFF the BO-BE
term is monotonic and
attractive, becoming a
constant at small R
Bond Energy
0
E (kcal/mol)
This is balance by the
vdW term which is large
and repulsive at small R
re
-50
-100
-150
-200
-250
1.00
1.10 1.20
1.30 1.40
1.50 1.60
r
1.70 1.80
To finally give the normal
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
bonding
function.
1.90 2.00
Coordination
• Deviation of bond orders from saturation
i  Vali 
nbond
 BO ;Val  C  4; H  1
j 1
ij
i


1
• Over-coordination

Eover   pover   i  
 1  exp i  i  
Penalty Energy
E_penalty (kcal/mol)
120
100
80
60
40
20
0
-3
-2.5
-2
-1.5
-1
-0.5
0
Over coordination (4-BO)
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Under-coordination
Eunder


1

  BOij,  f1 i ,  j 
  punder  1  exp  2   i  
 1  exp  1  i  


f1  i ,  j   exp  3   i   j

2
f1(delta_i,delta_j)
1.0
0.6
0.4
E_under
0.2
0.0
0.0
0
0.2
0.4
0.6
delta(delta)
0.8
E_under (kcal/mol)
value
0.8
-1.0
1
-2.0
-3.0
-4.0
-5.0
-6.0
0
0.2
0.4
0.6
delta_i
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
0.8
1
Angle


Eval  f 2 BOij  f 2 BO jk  ka  ka  exp  kb  0  ijk 
2

f 2 BOij   1  exp  5  BOij 
f2(BO_ij)
1.0
0.8
f2(BO_ij)
0.6
0.4
1.0
0.2
0.8
3.0
2.5
2.0
1.5
BO_ij
1.0
0.5
f2
0.0
0.6
0.0
0.4
0.2
0.0
1.0
1.5
2.0
2.5
r_ij
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
3.0
Calculation of 0
 0     0, 0 1  exp  7  2  SBO 2

 62 j  nbon( j )
 
SBO   j  2  2  exp 
BOj
 64  


 n 1
SBO2 = 2; SBO>2
SBO2 = 2-(2-SBO)5; 1<SBO<2
SBO2 = SBO 5; 0<SBO<1
2j = j; j < 0
SBO2 = 0; SBO  0
2j = 0; j  0
Theta_0 (degrees)
Equilibrium CCC angle
180
170
160
150
140
130
120
110
100
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Sum of Pi Bond Order
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Eangle
E (kcal/mol)
E_angle CCC
7.0
E_angle
6.0
E_vdw
5.0
Sum
4.0
E_harmonic
3.0
2.0
1.0
0.0
-1.0100
105
110
115
C-C-C angle
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
120
Torsion
Etors  f 3 BOij , BO jk , BOkl  f 4  j ,  k *
Sin  ijk  Sin  jkl 


0.5  V2  exp pt ,1  BO jk  2 2  1  Cos 2  ijkl   


0.5  V3  1  Cos3  ijkl 

•V2 diminishes rapidly when central bond deviates from BO=2
•Sin terms ensure this terms goes to 0 when the angles approach 180
•f4 accounts for over-coordinated central C-C atoms
•f3 allows for proper dissociation behavior
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
f3


f 3 BOij , BO jk , BOkl   1  exp  8  BOij  
1  exp    BO  1  exp    BO 
8
jk
8
kl
f3
1.0
0.6
F3
0.8
0.4
0.2
3.00
2.50
2.00
1.50
1.00
0.50
0.0
0.00
BO
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
f4
1
f 4  j ,  k  
1  exp  9   j   k   10 
f4
1.0
1.0
f4
0.9
0.9
0.8
0.8
0.7
0
0.5
1
1.5
delta_j+delta_k
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
2
V2
V2 (kcal/mol)
V2_effective
40
35
30
25
20
15
10
5
0
V2_eff CCCC
V2_eff CCCH
V2_eff HCCH
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
BO_jk
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Etors
E_tors
E_tors CCCC
E_tors CCCH
E_tors (kcal/mol)
1.0
E_tors HCCH
0.8
0.6
0.4
0.2
0.0
0
50
100
150
w_ijkl (degrees)
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Conjugation
Econj  f 5 BOij , BO jk , BOkl  f 6 BOij , BO jk , BOkl 
f 7 i ,  j ,  k , l  11  1  Sinijk  Sin jkl * Cos2  ijkl 
E_conj
0.0
0
50
100
150
E (kcal/mol)
-0.4
-0.8
-1.2
-1.6
-2.0
w_ijkl
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Heats of Formation for 40 compounds/radicals
Heats of Formation
Experimental
80
y = 0.972x - 0.7557
R2 = 0.9892
50
20
-10
-40
-70
-70
-50
-30
-10
10
30
50
70
90
Calculated
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Bond dissociation energies
Well Depths
300
250
200
150
100
50
0
N:::N N=N
Ch121a-Goddard-L11
N-N
N=O
N-O N:::C N=C
N-C C:::O C=O
© copyright 2011 William A. Goddard III, all rights reserved
C-O
Bond lengths and r0
Bonds
R_o
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.0
N:::N N=N N-N N=O N-O N:::C N=C N-C C:::O C=O C-O
Ch121a-Goddard-L11
1.5
1.45
1.4
1.35
1.3
1.25
1.2
1.15
1.1
1.05
1
r0
ro,pi
ro,pi,pi
C-N
C-O
C-C
N-N
© copyright 2011 William A. Goddard III, all rights reserved
N-O
O-O
RDX concerted ring breaking
Concerted RDX-dissociation
Energy (kcal/mol)
75
64.6
64.37
50
DFT
25
ReaFF
0
1
2
3
4
C-N distance (Angstrom)
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
5
RDX N-N dissociation
NO2-dissociation from RDX
Energy (kcal/mol)
50
39.00
40
34.00
30
20
ReaFF
DFT
10
0
1
2
3
4
N-N distance (Angstrom)
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
5
HONO elimination
Successive HONO-dissociation from RDX
75
DFT
Energy (kcal/mol)
50
ReaFF
25
0
RDX
-25
RDXHONO+HONO
RDX-2 HONO
+ 2 HONO
TAZ+3 HONO
-50
Reaction Coordinate
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
3 HCN + 3
HONO
DFT Calculation
E (kcal/mol)
TS 14
51.7
TS10
39.2
TS13
52.2
TS11
32.0
MN(74) + 2HCN(27) +
2HONO(47)
24.8
TS12
20.1
RDX
0.0
3HCN(27) + 3HONO(47)
14.2
INT175+HONO
-8.5
INT128+2HONO
-13.0
TAZ +3HONO
-36.4
HONO-Elimination Pathway
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
EoS
Pressure (GPa)
Pressure vs. compression
55 44
ReaFF
40
rdx.ff
18.3
25
7.2
10
-5
0.5
0.6
0.7
2.4
0.6
-0.2
0.8
0.9
1
V/V_0
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
1.1
EoS
Energy vs. compression
2500
ReaFF
E (kcal/mol)
2000
rdx.ff
1500
1000
500
0
-500 0.5
0.6
0.7
0.8
0.9
1
V/V_0
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
1.1
Over-coordination energy and van der Waals
Shielded van der Waals
E vdW
  
rij*
  ij  exp  ij 1 

   rvdW
1 

rij*
  2 exp   ij 1 

 2  rvdW


1 
r   rij3  3 
w 

*
ij
Ch121a-Goddard-L11
1
3
Over-coordination energy
30
20
10
0
3
3.5
-10
4
4.5
5
Total bond order
250
 
 

 
Energy (kcal/mol)
Eover


1


 pover  i 



1

exp


1
i


40
Energy (kcal/mol)
Over-coordination penalty
200
Unshielded van der Waals
150
Unshi
Shield
100
Shielded vdW (w= 0.8)
50
0
-50
1
2
3
C-C distance (Å)
© copyright 2011 William A. Goddard III, all rights reserved
4
Key features of ReaxFF
-To get a smooth transition from nonbonded to single, double and
triple bonded systems ReaxFF employs a bond length/bond order
relationship1,2. 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
(EEM) that accounts for polarization effects.
1:Tersoff,
PRB 1988;
Ch121a-Goddard-L11
2:
Brenner
PRB
© copyright
20111990
William A. Goddard III, all rights reserved
General rules ReaxFF
MD-force field; no discontinuities in energy or forces even during
reactions.
User does not pre-define reactive sites or reaction
pathways; ReaxFF automatically handles
coordination changes associated with reactions.
Each element is represented by only 1 atom type in the force field;
force field determine equilibrium bond lengths,
valence angles etc. from chemical environment.
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
ReaxFF uses generic rules
for all parameters and functional forms
ReaxFF automatically handles coordination changes and
oxidation states associated with reactions, thus no discontinuities
in energy or forces.
User does not pre-define reactive sites or reaction pathways
(ReaxFF figures it out as the reaction proceeds)
Each element leads to only 1 atom type in the force field. (same O
in O3, SiO2, H2CO, HbO2, BaTiO3) (we do not pre-designate the
CO bond in H2CO as double and the CO bond in H3COH as single
or in CO as triple, ReaxFF figures this out)
ReaxFF determines equilibrium bond lengths, angles, and
charges solely from the chemical environment.
Require that One FF reproduces all the ab-initio data (ReaxFF)
Most theorists (including me) thought that this would be impossible,
hence it would never have been funded by NSF, DOE, or NIH since it
wasCh121a-Goddard-L11
far too risky. (DARPA
came2011
through,
then ONR,
then
ARO).
© copyright
William A. Goddard
III, all rights
reserved
Current applications of ReaxFF
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Catalysts: Pt-Co Fuel cell cathode, Pt-Ru FC anode
VOx catalyzed oxidative dehydrogenation: propane to propene
MoVNbTaTeOx ammoxidation catalysts (propaneacrylonitrile)
Ni,Co,Mo catalyzed growth of bucky tubes
Metal alloy phase transformations (crystal-amorphous)
Si-Al-Mg oxides: Zeolites, clays, mica, intercalated polymers
Gate oxides (Si-HfO2, Si-ZrO2, Si-SiOxNy interfaces)
Ferroelectric oxides (BaTiO3) domain structure,
Pz/Ez Hysteresis Loop of BaTiO3 at 300K, 25GHz by MD
Decomposition of High Energy (HE) Density Materials (HEDM)
MD simulations of shock decomposition and of cook-off
MD elucidation of the origins of sensitivity in HE materials
Reaction Kinetics from MD simulations (oxidations)
ADP-ATP hydrolysis
Enzyme Proteolysis
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Applications to energetic materials
Sergey Zybin, Peng Xu, Yi Liu, Qing Zhang,
Luzheng Zhang, Adri van Duin and William A. Goddard III
- Force field development
- Training sets for HE-materials
- Treating organic crystals
- Overview of past and ongoing applications
- Predicting chemistry : cookoff of RDX, HMX and
TATB and carbon cluster analysis
- Prediction of sensitivity for HE materials
- Energy release: ISP prediction for RDX/Al and
hydrazine materials
- New HE-materials: all-Nitrogen
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Training set for nitramine potential
Bond and angle distortion
Reaction barriers
C-N bond dissociation in
H2C=NH
Nitromethane C-N-O
angle bending
Charge distributions
QM
Mulliken charges
DFT; 6-31G**
ReaxFF charges
+0.35
QM:PETN-I
QM:PETN-II
+0.26
+0.54
+0.12
+0.15
-0.31
+0.14
-0.05
+0.61
-0.49
+0.12
+0.12
-0.31
+0.12
Energy (kcal/mol)
-0.49
+0.26
-0.01
ReaxFF: PETN_I
ReaxFF:PETN-II
200
-0.64 +0.26
+0.14
Condensed
PETN equations of statephase
+0.34
-0.62
-0.57 +0.26
+0.14
First-row elements
150
100
50
-0.47
0
150
200
250
300
3
Ch121a-Goddard-L11
Volume ( /mol)
© copyright 2011 William A. Goddard III, all rights reserved
350
ReaxFF gives accurate description of complex chemical
reactions: Decomposition Mechanism RDX (gas-phase)
NO2 dissociation
100
INT149+
HCN+NO2
80
concerted
60
INT176+
NO2
MN+MNH+
HCN+NO2
RDRo+
NO2
O2N
N
N
N
O
N
RDR+
NO2
NO2
O
H
2MN
+LM2
O
N
40
Energy (kcal/mol)
QM
ReaxFF
New mechanism
O
+N2O
N
O
N
3MN
N
O
HO
H C N
20
MN+LM2+
N2O+H2CO
2MN+N2O+
0
O
-20
RDX
RDX''+2HONO
TAZ+3HONO
-80
N
O
N
O
N
HONO elimination
H2C=O
+N2O
+2 HCN
+2 HONO
O
N
O
N
N
HO
-40
3N2O+3H2CO
O
O
O
N
2H2CO MN+2N2O+
-60
O
N
RDX'+HONO
2H2CO
O
N N
N
H2CO
LM2+2N2O+
+N2O
+HONO
O
+N2O
+HONO
8 membered
ring
N
O
N
NO2
+N2O
+HONO
N
O
N
+N2O
+2 HONO
Concerted, NO2 and HONOReaxFF MD simulation found New
dissociation pathways
unimolecular reaction, confirmed by QM,
(part of the original training set)
More important than concerted pathway
Strachan,
Ch121a-Goddard-L11
Kober, van Duin, Oxgaard ©
and
copyright
Goddard,
2011
J.Chem.Phys
William A. Goddard
2005
III, all rights reserved
RDX shock simulations: MD with ReaxFF
•Simulate High impact shock chemistry using MD simulations
•1st step: thermalize two semi-infinite slabs of RDX (1344 atoms/cell)
•Add the shock velocity on top of the thermal velocities
•Constant NVE molecular dynamics (adiabatic)
∞ Slab: 32 RDX molecules/cell on ∞ Slab: 32 RDX molecules/cell
1 vimpact
2
 1 vimpact
2
Full-physics, full-chemistry simulations of shock induced chemistry
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Hydrocarbon combustion and metaloxide catalyzed hydrocarbon oxidation
Adri, Kimberly Chenoweth, Sanja Pudar, Mu-Jeng Cheng, and wag
cat.
O
+
2 H2O
Selective oxidation of
propene using multiMixed metal oxide catalyst (BixMoyVzTeaOb)
metal oxide (MMO)
catalysts
Develop ReaxFF based
on QM-data , use
ReaxFF to perform
high-temperature
simulations on
catalyst/hydrocarbon
reactions
First, establish that
ReaxFF can describe
non-catalytic
hydrocarbon
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all combustion
rights reserved
+
O2 (air)
Force field development: hydrocarbon oxidation
ReaxFF
QM
QM
Oxidation reactions
ReaxFF
75
75
Energy (kcal/mol)
Cp+O2 singlet
Cp+O2 triplet
25
Benzene+O2 singlet
Benzene+O2 triplet
0
Energy (kcal/mol)
50
50
25
Cp+O2
Benzene+O
Butadiene+
0
Butadiene+O2 singlet
Butadiene+O2 triplet
-25
-25
-50
-50
1
1
1.5
2
2.5
3
3.5
1.5
4
2
2.5
3
3.5
4
C-O distance (
)
C-O distance (
)
QM: Jaguar/DFT/B3LYP/6-311G**
Radical rearrangements
75
Rotational barriers
QM
ReaxFF
H3C• + CO
0
1
2
15
10
5
-180
3
C-C bond distance (angstroms)
Ch121a-Goddard-L11
4
5
45
30
15
0
0
•
H3C-C=O
ReaxFF
60
Energy (kcal/mol)
50
25
QM
ReaxFF
20
Energy (kcal/mol)
Relative Energy (kcal/mol)
QM
Angle strain
-120
-60
0
60
Torsion angle
120
180
50
75
100
O-C-O angle
- total training set contains about 1700 compounds
© copyright 2011 William A. Goddard III, all rights reserved
125
Test ReaxFF CHO-description: oxidation of o-xylene
- Oxidation initiates
with OOH-formation
- Final products
dominated by CO,
CO2 and H2O
Consumed O2
CO2
H2O
CO
o-Xylene
OOH
2 o-Xylene; 70 O2 in 20x20x20 Angstrom box
ReaxFF NVT/MD at T=2500K
Ch121a-Goddard-L11
-Exothermic reaction
-Exothermic events
are related to H2O
and CO2 formation
© copyright 2011 William A. Goddard III, all rights reserved
OH
o-Xylene oxidation: Detailed reaction mechanism
O2
H 2COOH
CH 2
CH 3
HO 2
frame 128
CH 3
O2
O
OH
H 2C=O
OH
CH 3
CH 3
frame 176
CH 2
frame 179
HC=O
OH H O
2
H
OH
H
CO
H 2O
H
H
H
H
H
OH
H 2O
O2
H 2O
frame 209
H
H
CO 2 H 2O
CO
H 2O
O 2H
O
H
CH 2
CO 2 HO 2
H 2O
OH
HO 2
O2
CO
O
H
H
O
O
H
H
H
H
frame 180
frame 193
CO 2
H 2O
H
H
frame 232
OH
CH 2 H O
2
O
frame 205
CO 2
H
O
frame 182
H
H
H
O
O
CH 2
H
H
O
O
H 2C=O
OH
CH 3
O2
O
OH
Kimberly
Chenoweth
- Reaction initiation with HO2formation
- Dehydrogenation occurs at
methyl-groups, not at benzylhydrogens
- Only after H2C=O is formed and
dissociated the benzene ring gets
oxidized
- Ring opens shortly after
destruction of aromatic system
- Ring-opened structure reacts
quickly with oxygen, forming CO2,
H2O and CO
- ReaxFF gives sensible
predictions that can be directly
© copyright 2011 William A. Goddard
all rights reserved
testedIII,against
QM
H 2CO
frame 176
frame 177
OH
CH 3
frame 175
O
H 2C=O
frame 174
CH 3
H
CO 2
H 2O
CO
H 2O
H
O 2H
O
H
frame 232
O
H
H
H
H
H
H
O
Ch121a-Goddard-L11
O
H 2O
H 2O
frame 234
H
O 2H
CO 2
CO 2 CO
H
H
HC=O
O 2H
H 2O
H 2O
Determining the parameters for ReaxFF:
MoOx
Mo17O47-crystal
(kcal/mol)
Energy
Energy (kcal/mol)
Need to describe the complicated
bonding in MoxOy polymorphs
Step 1: get ReaxFF for MoQCmetal
QM
100
diamond
Simple cubic
fcc
A15
bcc
50
0
5
10
15
20
Volume/Atom
ReaxFF
Energy
(kcal/mol)
(kcal/mol)
Energy
ReaxFF
Simple cubic
50
fcc
A15
bcc
0
5
Ch121a-Goddard-L11
diamond
100
10
© copyright 2011 William A. Goddard III, all rights
reserved
Volume/Atom
15
20
Oxidation of MoO2 slab by O3
Epot (kcal/mol)
-45000
-47500
-50000
-52500
-55000
0
10
20
30
40
50
60
Time (ps)
Initial reaction is fast
Reaction slows down as MoO2
surface gets oxidized
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Analysis MoO2 + O3 simulation
g(r)
Mo-Mo
Mo-O
O -O
Start: Mo64O128 [MoO2]
1
2
3
4
5
6
7
8
r (Å)
Mo=O
g(r)
Mo-Mo
Mo-O
O -O
End: Mo64O175 [MoO2.7]
1
2
3
4
5
r (Å)
6
7
8
ReaxFF predicts correctly the formation of Mo=O surface double bonds
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
ReaxFF for reactions on Pt catalysts
Energy (eV)
4
3
2
Pt crystals
DFT
FCC
HCP
diamond
BCC
Simple cubic
1
Dia
hcp A15
fcc
0
10
SC
A15
bcc
15
20
25
Energy (eV)
4
3
2
ReaxFF
diamond
FCC
HCP
Simple cubic
BCC
SC
1
ReaxFF gives a good description
to the EOS of the stable phases
(FCC, BCC, A15)
ReaxFF properly predicts the
instability of the lowcoordination phases (SC,
Diamond)
Dia
0
10
hcp A15
fcc
A15
bcc
15
20
25
Volume/atom (Å3)
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Test of ReaxFF for Pt metal clusters
Energy (kcal/Pt)
0
QC
-60
ReaxFF
-120
9_10_9
5_10_5
12_7
8_4
6_3
12
8
6
3
1
Cluster description
ReaxFF gives a good description for undercoordinated Pt-systems
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
QC
ReaxFF
HCCH3
CCH2
Hydrocarbon interaction with
35-atom Pt-cluster
Binding energy (kcal/mol)
150
100
50
- ReaxFF can describe different C-Pt bonding modes
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
H2CCH2(II)
H2CCH2(I)
HCCH
H2CCH3
CH3
CHCH2
CH2
CCH
CCH3
C2
CH
C
0
Equation of State for Pt bulk metal oxides
(kcal/mol)
Energy
Ef/Pt (kcal/mol)
QM
PtO (P342mmc)
PtO2 (P3barm1) in ab
PtO2 (P3barm1) in c
PtO2 (Pnnm)
Pt3O4
350
300
250
200
150
100
50
0
-50
10
15
20
25
30
35
40
45
50
55
equations of state for Ptbulk oxides from ReaxFF
are in good agreement
with QM-data
V/Pt ( 3)
Ef/Pt (kcal/mol)
Energy (kcal/mol)
ReaxFF
PtO(P342mmc)
PtO2 (P3barm1) in ab
PtO2 (P3barm1) in c
PtO2 (Pnmm)
Pt3O4
350
300
250
200
150
100
50
0
-50
10
15
20
Ch121a-Goddard-L11
25
30
35
40
45
50
55
V/Pt
( 3)
© copyright
2011 William A. Goddard III, all rights reserved
Also do Equation of State for Bulk metal oxide
phases
(kcal/mol)
Energy
Energy (kcal/mol)
60
ReaxFF MD-NVT
simulation at T=300K
MoO3
40
DFT
ReaxFF
ReaxFF
20
DFT
0
30
40
50
60
70
Volume (Angstrom3)
Do similar calculations on:
MoO2 equation of state
Equilibrium structures of MoO2, Mo8O24, Mo5O8
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Bond dissociation, valence distortions
750
HO-Mo=O angle bending in
cluster (HO)2MoO250
500
DFT singlet
DFT triplet
ReaxFF
DFT S=0
250
ReaxFF DFT S=1
0
1
2
3
4
5
6
Mo-O distance (Angstrom)
Also break Mo-OH bonds,
Mo-CH3 bonds
Mo-H bonds
Ch121a-Goddard-L11
40
(kcal/mol)
Energy
Energy (kcal/mol)
(kcal/mol)
Energy
Energy
(kcal/mol)
Mo=O bond dissociation in MoO3-cluster
30
ReaxFF
20
10
DFT
0
125
Other angle50cases: 75Angle 100
(de gre e s)
Mo-O-Mo
O=Mo=O
HO-Mo-OH
Mo-O-O
Mo-O-H
Mo-O-C
© copyright 2011 William A. Goddard III, all rights reserved
150
Reactions in training set for ReaxFF
Example test:
Oxidation of
MoO2 rutile
using ozone
Energy
(kcal/mol)
(kcal/mol)
Energy
200
150
ReaxF
F
100
DF
T
QM
ReaxFF
50
Mo3O9
3 MoO3
0
1
2
3
4
5
Mo-O distances (Angstrom)
Other reactions considered:
MoO4  MoO3 +O  MoO2 + 2O
 MoO+3O
MoO3 + 0.5 O2  (O-O)MoO2
Ch121a-Goddard-L11
Periodic (a=b=20.69 Å, c=55 Å)
192-atom MoO2-slab + 50 O3
62.5 ps. NVT MD at T = 1000K.
Analyze
final
oxidation state
© copyright 2011 William A. Goddard
III, all
rightsMo
reserved
Reactions of H2 and O2
over Pt(111) surfaces
8 H2 + 4 O 2
8 H2 + 4 O2
Pt(111) perfect
Pt (111) stepped
96 atoms
84 atoms
MD simulation at 1000K
Energy release
perfect
stepped
Perfect surface generates H2O
stepped surface gets oxidized
Energy profile for perfect surface shows
H2O generation events
Have not yet done QM with stepped
surface to compare with ReaxFF
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
Vanadium oxide based catalysts
O
Selective oxidation catalyst:
• selective oxidation of o-xylene to phthalic anhydride
• ammoxidation of alkyl aromatics (i.e. toluene, picolines)
• oxidation of benzene, olefins, n-butane (poor selectivity)
• oxidation of butane or hexane to maleic anhydride
Selective catalytic reduction:
• SCR of NOx with NH3
• controlling oxidation of SO2 to SO3 during SCR
Oxidative dehydrogenation(ODH):
• convert alkane to olefin (i.e. propane to propene)
• selective oxidation of methanol to formaldehyde H C OH
3
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
O
O
O
O
O
N
H2C
O
ReaxFF – Vanadium Force Field Development
Bond Dissociations
Angle
Dihedral
Charge
Distributions
• Include bond dissociations, angle and dihedral
distortion energies, charge distributions in
training set for small clusters
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
ReaxFF Development for Bi, Te, V, Nb, Mo oxides
Double Bond Dissociation
ReaxFF
DFT - Singlet
Te(OH)n  Te(OH)n-1 + OH
DFT - Triplet
8080
180
O
7070
O
Bi
140
O
O
O
O
Bi
Bi
O Bi O
120
H
Bi
O
O
O
O
Bi
Bi
O Bi O
5050
100
40
V
O
OH
V
O
O O
O V
O
O
H
H
O
O
V
2020
V
1010
0
00
O-Nb-O Angle Bending
60
V
O
O
O V
H
O
O V
O
H
O
O V
O
V
O
O
O
O
H
H
O
H
O
H
O
H
O
V
O
V
V
O
O V
V
O
O
O
H
QM
H
ReaxFF
O
O
O
Reactioncoordinate
coordinate
Reaction
Mo-O-V Angle Bending
Charge Distributions (VO2OH)
50
40
30
20
10
0
60
80
100 120 140 160 180
O-Nb-O Angle (degrees)
Ch121a-Goddard-L11
O
O
O
O
V O
H
O
O
V
H
H
O
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Bi=O Bond Length (angstroms)
O
O
V
H
V
H
O
3030
60
H
V
O
4040
80
20
Relative energy (kcal/mol)
O
6060
O
Energy (kcal/mol)
Energy (kcal/mol)
Relative Energy (kcal/mol)
160
Hydrogen shift in V4O10H
MSC, ©Caltech
copyright 2011 William A. Goddard III, all rights reserved
H
Derive one FF for V to describe all coordinations in
the metal and oxide and all oxidation states
Metal
FCC,
BCC,HCP,
A15, SC,
Diamond
VO
V2O3
V2O5
V:bcc
VO2
Metal
oxides
Heat of formation (kcal/unit)
100
V(bcc)
0
VO
V2O3
V2O5
V:bcc
100
QM:
SeqQuest
(SNL
Gaussianbased
periodic DFT)
VO2
V(bcc)
0
VO
-100
VO2
VO2
-200
4, 6, 8
Oxygen -300
coordination -400
VO
-100
-200
V2O3
V2O3
-300
-400
V2O5
V2O5
QM
-500
ReaxFF
-500
2
3
4
5
6
7
8
9
10
2
3
4
5
6
7
8
9
10
• Energy difference for oxidation changes is in good agreement with QM data
• Indicates
that ReaxFF is©able
to capture
energetics
ofallredox
reactions
Ch121a-Goddard-L11
copyright
2011 William
A. Goddard III,
rights reserved
ReaxFF Development: Bulk oxides
Heat of formation (kcal/mol)
TeO2
ReaxFF
QM
Density (kg/dm3)
Same ReaxFF describes: Te0, TeII, TeIV, TeVI, Bi0, BiIII, BiV
V0, VIII, VIV, VV, Mo0, MoII,MoIV, MoV, MoVI,
Energy
difference for oxidation changes is in good agreement with QM-data
ReaxFF
able to capture the energetics of redox-reactions at metal oxide surfaces
ReaxFF
slight systematic tendency to overestimate stability of metal oxide phases
PBE
GGA exchange-correlation
functional
with
Gaussian
basisIII,
sets
as implemented
in SeqQuest
Ch121a-Goddard-L11
© copyright
2011
William
A. Goddard
all rights
reserved
ReaxFF Development: Propanepropene on V4O10
ReaxFF
QM
V4O10 + O2
+ 2 propane
Binding of O2 displaces
propene product
QM (B3LYP/LACVP**): Cheng, Chenoweth, Oxgaard, van Duin, Goddard JPC-C 2007, 111, 5115.
V4O10 + 2 H2O
+ 2 propene
MSC,QM
Caltech
Kimberly
Chenoweth
Ch121a-Goddard-L11
©
copyright
2011 William
Goddard
III, all rights
reserved pathway
ReaxFF
reproduces
energies
forA.the
entire
reaction
ReaxFF MD Simulation Conditions
Started from a minimized structure
30 methanol molecules
3-layer V2O5 (001) periodic slab
Total number of atoms = 684
Slab Temp = 650K
CH3OH Temp = 2000K
Time step = 0.25 fs
Temperature damping = 100 fs
Total simulation time = 250ps
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved
ReaxFF NVT-MD Simulation: Methanol
Oxidative DeHydrogenation (ODH)
30
Methanol
Formaldehyde
H2COH Radical
Water
Others
30
20
Methanol
Formaldehyde
H2COH Radical
Water
Others
25
15
Number of Molecules
Number of Molecules
25
10
5
0
0
50
20
15
10
100
5
150
200
250
Time (ps)
0
0
50
100
150
200
Time (ps)
• methanol converts to formaldehyde with production of water
• Others include the number of hydrocarbons bound to the surface
• Expt.:
Major product is©formaldehyde
(also
H2O,III,CO
x) reserved
Ch121a-Goddard-L11
copyright 2011 William
A. Goddard
all rights
250
ReaxFF Mechanistic Details
Formation
of H2C-OH
radical
3.45ps
8.80ps
H-abstraction by surface vanadyl groups
Ch121a-Goddard-L11
Formation of
formaldehyde
© copyright 2011 William A. Goddard III, all rights reserved
ReaxFF Validation: H3COH H2C=O on V2O5 (001)
H2O desorption induced by
interlayer binding to convert
VIII … O=VV pair to VIV-O-VIV
NVT-MD simulation at 650K
with 30 CH3OH (at 2000K)
Observe conversion of CH3OH
to CH2O in dynamics
Observe
CH3OH 
CH2O + H2O
Longer
simulation also
leads to COx
Agrees
with Experiment
3.425ps
3.450ps
8.800ps
Chenoweth, van Duin,
Cheng,2011
Persson,
Goddard,
in preparation.
Ch121a-Goddard-L11
© copyright
WilliamOxgaard,
A. Goddard
III, all rights
reserved
Desorption of Water from catalyst
Snapshots from simulation showing atoms within 5.5Å of V bound to H2O
1
Water bound
to VIII, bond
very strong,
will not desorb
2
3
2nd layer has
VV=O pointing
at VIII of top
layer
Ch121a-Goddard-L11
2nd layer O
bonds to top V
get VIV-O-VIV
4
5
H2O bonds
weakly to VIV
now desorbs
© copyright 2011 William A. Goddard III, all rights reserved
ReaxFF Validation:
Reaction of Propene on Bi2O3 and MoO3
Propene + Bi2O3 Slab
Propene + MoO3 Slab
1100K
Get abstraction of allylic
hydrogen by bridging oxygen on
amorphous Bi2O3 surface
No formation of oxide products
Agree with experiment
Ch121a-Goddard-L11
No abstraction of allylic hydrogen by MoO3.
No formation of oxide products
Agree
with
experiment
© copyright 2011
William
A. Goddard
III, all rights reserved
ReaxFF Validation:
Oxidation of Propene on Bi2Mo3O12 (010)
H abstracted by Mo=O bond next to Mo-O-Bi
Had expected Bi=O bond to be involved
Allyl subsequently is trapped on a different Mo=O bond
Much Longer times required to observe oxidation of allyl radical
to form acrolein
Goddard, van Duin, Chenoweth, Cheng, Pudar, Oxgaard, Merinov,
Topics
Catal.
2006,III,93.
Ch121a-Goddard-L11 Jang, Persson
© copyright
2011 in
William
A.38,
Goddard
all rights reserved
Grasselli et al. 1984
Stop lecture 11
Ch121a-Goddard-L11
© copyright 2011 William A. Goddard III, all rights reserved